ML062690107

Vermont Yankee Hearing - Entergy Exhibit 26, GE Topical Report, Qualification of the One-Dimensional Core Transient Model for Boiling Water Reactors, Report No. NEDO-24154-A, Vol. 1

ML062690107
Person / Time
Site:	Vermont Yankee
Issue date:	08/31/1986
From:	Fischer D, Jeffery Wood General Electric Co
To:	NRC/SECY
Byrdsong A T
References
50-271-OLA, 78NED290R1, Entergy-Licensee-26, RAS 12277 NEDO-24154-A
Download: ML062690107 (493)

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D DOCKETED USNRC NEDO-24154-A 78NED29OR1 CLASS I S~9P11 3: 3 ? AUGUST 1980 DOCKET NUMBER ", FCR A p PROD. &UTIL FAC. 5 ?7- 01-4 LICENSING TOPICAL REPORT QUALIFICATION OF THE ONE-DIMENSIONAL CORE TRANSIENT MODEL FOR BOILING WATER REACTORS VOLUME I a adekr Vilmo4&

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NEDO-24154-A 78NED290R1 Class I August 1986 LICENSING TOPICAL REPORT QUALIFICATION OF THE ONE-DIMENSIONAL CORE TRANSIENT MODEL FOR BOILING WATER REACTORS VOLUME 1 C Z~,,A Approved:c 'r i?1 Approved:_____________

D. L. Fischer, Manager J.JE. Wood, Manager Cdre & Fuel Technology Core Nuclear Design NUCLEAR ENERGY SUSINESS OPERATIONS

• GENERAL ELECTRIC COMPANY SAN JOSF, CALIFORNIA I5125 GENERAL f ELECTRIC

NEDO-24154-A Neither -.he Ger.S=7l A-Zectri nz ofheon'uore to this docwient mmckes an w=r 'nte or re-presetxvion (em'ess or impZiadJ wi~th r'espect to the ceamracy, com~p ltenevs, or use fuZness of -,he information contained in thi.s doac*=ent or that the use of asuch infor~mation nk~y not infringe on orivte~y oiwned rights,-nor do theyi asamwn any' responsibiZitij for Liabi'itjy or d,-aqe of =W kind which nub' revsZs60 Jrom the use of a;w. of the

&tfo't~tioncontained in this docrizent.

SUNIT= STATES NUCLEAR REGULATORY COMMISSION

p. ~WAS34gNMK i. C. 20M5

• ~FEB~ ie Dr. G. G. Sherwood, Manager Safety and Licensing General Electric Company 175 Cur-tner Avenue San Jose, California 95114

SUBJECT:

ACCEPTANCE FOR REFERENCING GENERAL ELECTRIC LICE?1SIv.G TOPICAL REPORT NEO-24 154/NEDE-24154P The Nuclear Regulatory Commission has completed its review of the General Electric Company Licensing Topical Report NEDO-24154 Volumes I and 11 and NIEDE-24154 Volume III entitled uQualification of the One-Dimensional Core Transient Model for Boiling WIater Reactors" and the supplemental Infor mation submitted by F. H. Buchholz, letter (MFN 155-80) dated September 5, 1980. This report describes the General ElectHrc transient analysis code, 0DYN. This code Is to be used for-transient. analyses of the following eight transients:

A. For Thermal Limit Evaluation Thermally Limiting or Event Near Limitlna (Typtcally)

1. Feedwater.Controller Failure - X Maximumi Demand

2. Pressure Regulator Failure - Closed

3. Generator Load Rejection X

4. Turbine Trip X

5. Steamline Isolation Valve tain Closures

6. Loss of Condenser Vacuum

7. Loss of Auxiliary Power - All X Grid Connec:lons iii

FEE 4 1W8 Dr. G. G. Sherwood B. For ASME Vessel Overpressure Protection Pressure Limitina

1. 14SIV Closure with Position Switch Scram Failure (i.e., MSSV Flux Scram) X Other transients and anticipated operational occurrences may be analyzed with the REDY Code described in NEDO-10802.

For all operating BWRs and those currently under operating license review, we propose that the following pressurization events be reanalyzed usin ODYN:

generator load rejection/turbine trip without bypass (whichever is limiting),

feedwater controller failure-maximum demand and main steam isolation valve closure-flux scram (to satisfy ASME code pressure fequirements): These are the same pressurization events presently included in reload suinittals. As discussed in the September 5, 1980 letter from R. H. Buchholz (GE) to US.RC subject: aResponse to NRC Request for Information on ODYT Computer Modal,"

the events not included are considered to be bounded by these three.

This letter also provides the information required for application of ODY0 and justification for continued plant operation during transition from transient analyses based on ODY0. The safety evaluation and a supplementary safety evaluation are enclosed.

As a result of our review, we find the Licensing Topical Report NEDO-24154 Volumes I and II/NEDE-24154P Volume III as augmented by GE/Buchholz letter No. XFN 155-80 dated September 5. 1980 acceptable for referencing In applications for operating license within the conditions specified In the topical report, the supplemental letter. and the attached safety evaluation and supplement.

We do not intend to repeat the review of the safety features described In the topical report and found acceptable In th~e attachment. Our acceptance applies only to the features described in the topical report and under the conditions discussed in the attachment.

In accordance with established procedure, it is requested that General Electric Company publish an approved version of these reports, proprietary and non-proprietary, within three months of receipt of this letter. The revisions are to appropriately incorporate the supplementary information into the body of the report and incorporate this letter and the attached safety evaluation and supplement following the title page and thus just In front of the abstract. The report identifications of the approved reports are to have a -A suffix.

iv

Dr. G. G. Sherwood FEE 4 Should Nuclear Regulatory Comission criteria or regulations change such that our conclusions as to the acceptability of the report are invalidated, General Electric and/or the applicants referencing the topical report will be expected to revise and resubmit their respective documentation or submit justification for the continued effective applicability of the topical report without revision of their respective doc=entation.

Sincerely, Robert L. Tedesco, Assistant Director for Licensing Division of Licensing

Enclosure:

As Stated v/vi

SAFETY EV.ALATZON FOR THE GENERAL ELECTRIC TOPICAL REPORT QUAI.FZCATION OF THE ONE-*IME*SICKAL CORE TRANSIENT MMEL FOR BOILING WATER REACTRM NEDO-2414 VW NME-24254-P Valie I, 11 and III iparom.ed By Reactur Systems Brancm, CS1 Reviewers F. Odar, Laud (1F.)

L Beltracchzi

0. B. Fieno

a. M. Holamn M. K. Mendonca

. Voqiew June 1980 vii./viii

TABLE OF-CONTENTS Pace I.SUWARY OF THE TOPICAL REPORT...................* .. ..... 1-1 A. ...

I..*..........................

IROFDUC1TION.. .......... 1I1 B. SCOPE.... ........................................

o 1-2 C. StPWRY OF ANALYTICAL MODELS ............... 1-2

11. STAFF EVALUATION.............. ........... 111 A. REVWM OF ANALYTICAL MODELS. o .... .......................... 11-2

. Recirculatlon and Control System.................... 11-2 a Recirculation Loop Model ........ ................ 11-2

b. Control System Model .............. , ....... 116

c. Steam Separator Model .......... ........ 11-9

d. Upper Plenum, Vessel Dome and Bullcatr Model ..................... . II-1

2. Steam Line Modell ..................................... 110-2

3. Core Thermal Hydraulics Model .......................... 11-14

a. Drift Flux del ....... ................... 11-15

b. Mechanistic Boiling Model .................. 11-19

4. Core Physics Model ................................... 11-20

a. Assumptions in the Neutronics Model . ....... 11-20

b. Derivation of Equations for the One-Group, One-Oimensional, Time-Oependent Neutronic ooo........ 11-2 Model .... ;..............................

C. Calculation of Input Parameters .......... ... . 11-23 S. Fuel Heat Transfer Model..... ..... . . ........ . .... 11*25

6. Summary of Code Uncertaintles.......................... 11-31 a.. Margin in ACPR Calculations ..... . ..... . ........ . 11-31

b. Margin in Pressure Calcu11tlon........... .- 33 B. QUALIFIuCATION OF THE ODYN CODE........................ 11-35

1. Qualification of Neutronics Model - Comarison of ODYNwith M Care Simulator.....- t................ ... 11-35

2. Qualification of Thermal Hydraulic Model .............. 11-38 ix

TABLE OF CONTENTS (Continued)

Pace

3. Qualification Using Integral Tests ....... 11-40

a. Peach Bottom Tes .......... ts .. . ........... 11-40 11-54

b. KKm Tom*. ........ -.....0............................

4. Qualification Using Another CoMputer Code Audit Calculations............................... ....- 59

a. Development of Calculational Method .............. 11-69

b. Peach Bott*m Tests and Audit Calculatons ......... 11-61 S. Summary of Coda Qualification ............. ....... 11-75 C. EVALUATION OF THE MARGIN.......... o..................... 11-76 I II. STAFF POSM ON ................................................... 111-1 IV. REFERENCES. ................ .... . ...... IV-1 ii

1.

SUMMARY

OF TOPICAL REPORT A. INTRODUCTIOn Between April 9, 1977 and Apr11 27. 1977, three turbine trip tests were performed at the Peach Bottm, Unit 2, to examine the validity of the General Electric transient analysis methods and verify the computer codes. The first scram signal which normally would have been Initiated on the position of the turbine stop valve, was bypassed In order'to provide a transient camparable in severity to the worst transients analyzed In FSARs. Using the transient analysis method and the REDY computer code used in the licensing applications at that time, General Electric made pre-tast predictions of pressure, neutron flux and ACPR on a best estimate basis. The neutron flux and ACPR predictions were signifi cantly nonconservative and the pressure predictions were somewhat nonconser vative.

After the tests General Electric performed post-test predictions of pressure, neutron flux and ACPR using the actual or measured plant parameters with best estimate modeling assumptions as well as the licensing model assumptions. The ACPR and the neutron flux predictions were again nonconservative for both sets of calculations. Mie pressure peaks were predicted conservatively. It should be noted that General Electric showed tha. the predictions of pressure and ACPR were conservative with licensing basis Inputs When the first scram signal Initiated on turbine stop valve position was not bypassed, I.e., under normal conditions.

The comparisons of the test results and the REDY code, the licensing basis model, confir ead the existence of a stua line pressure wave propagation phenom enon in a turbine trip transient and time varying nature of the aXial core 1-1

power distribution. General Electric accelerated its model development program to include steam line dynamics and representation of the core physics and thermal hydraulics in space-time domain and produced the ODYh computer code which Is the subject of this review.

8. SCOPE The scope of this review is the evaluation of the ODYN code for use in the analysis of"certain transients in ChMpter 15 of the FSAPs.

C.

SUMMARY

OF ANALYTICAL MODELS The overall system model in the WYK code consists of a one-dimensional represen tation of the reactor core, and the recirculation and control system model.

These two models are coupled to each other. A steady stato initialization is made initially, and then the parameters for the transient are calculated.

First, the recirculation and control system are solved for the steady state conditions. Some of the initial conditions are Input and they may be plant unique. Other initial hydraulic values such as core pressure drop and bypass flow fraction, which are also Input to the steady state recirculation and control model, are calculated elsewhere. These parameters are calculated in the s.t adi state multi-channel care code (Reference 1). Using all these input values, the steady state recirculation and control model calculates the remaining hydraulic parameters in the plant. The steady state initialization In the recirculation and control model provides the loop pressure drop, core exit pressure, core inlet flow and nthalpy tU the one-dimensional reactor core model. These values are used in the reactor core model to calculate the neutron kinetics, thermal hydraulics and fuel parameters for th seteady state conditions.

I-a xii

The steady state axial pover distribution is calculated by the neutronics model. The model uses cross section fits obtained frm an analysis about cross sections for different relative coolant densities and control states and that are radially averaged for each axial plans. The fits are such that the axial power in the one dimensional model is required to yield the same axial behavior as In the t*hree-dimensional BWR Core Simulator solution. The steady state thermal hydraulic solution permits the calculation of the steady state fuel temperature distribution.

During the transient, the recirculation and control system model calculates the time derivatives. At the end of the time step, the recirculation and contr*l system model supplies the new external boundary conditions to the reactor core model. The reactor core modal calculates the new neutron flux, thermal hydraulic parameters and fuel temperatures. It also provides reactor care exit quality, flow and pressure as input to the recirculation and control system model. The recirculation and control system model calculates the loop pressure drop anm the reactor core model calculates the core pressure drop. These pressure drops are compared. If they art not equal within a certain limit, the recirculation and control system model derivatives are modified and the time step calculations are repeated.

The recirculation system is modeled by solving the mass, energy and momentum conservation equations for the st*am line, reactor vessel and recirculation loop components which included j.o pumps, recirculation polps and associated piping. The control system is modeled as a series of connected gains, filters, 1-3 Xiii

Integrators, and nonlinearities (limiters and function generators). The control system output Is valve position and thus flow control. The one-dtmenslonal core model comprises equations describing the neutron kinetics, thermal-hydraulics and heat transfer behavior of the core.

Major assumptions used in the modeling of the recirculation system are as follows:

1. Pressure variations in the system are described with ten nodes. One node

-is -usad-for-the -reactorinlet; another node is used for the reactor vessel dome, and the remaining eight nodes are used to describe the behavior of the steam line.

2. Liquid and vapor mass volume balances are used to predict the reactor vessel water level changes.

3. The recirculation loop model can simulate any combination of multi-loop systems. The entire recirculation loop Is assumed to be subcooled and incompressible.

4. Stan in the steam line is treated as single phase flow. Condensation of steam in the steam line Is precluded during the transient.

Major assumptions used in the reactor core model are as follows:

L. A one-dimensional neutron kinetics model is assumed. The neutron flux varies axially with time. One energ group diffusion theory and six delayed 1-4 xiv

neutron groups are used. Decay beat is mocield using a simple exponential

.decay heat model. The one dimensional neutron diffusion parameters are obtained by collapsing the parameters obtained from the GE threue-dmensional IWR Core Simulator (Reference 2).

2. A single ictive heated channel represents the core average conditions and another single channel represents the co*e bypass. A five equation model representing mass and energy conservation for the liquid and vapor,. and the mixture momeatum conservation are used to calculate core thermal-hydraulic behavi or.... .

3. Heat transfer to the moderator and fuel temperatures are calculated using an average fuel and cladding model at each axial location of the core. The gap conductance Is an input parameter which may vary axially In time. The conduction parameers are temperature dependent. A radially uniform (flat) power distribution Is assumed in the fuel rods.

,xlxv-1

11. STAFF EVALLUATION The staff evaluation was performed in threte parts:

A. Review f Ushe analytical models in the ODYK code and detarmination of uncertainities In the code modeling.

S. Review of the qualification of the code. This part of the review is accomplished in three areas:

L. Comparison of specific bodtls in the code with separate effects test data.

2. Comparison of integral response of the coda with the integral test data.

3. Comparison of the code predictions with the predictions of an independent code; i.e., audit calculations.

C. Review of the safety margin; i.e., evaluation of the margin when the code is used with the uncertainties assigned in the licensing basis transient.

The uncertainties of the calculations were evaluated as part of the calculatlonal model review.

The measure of all code uncertainties is made In terms of ACPR/ZCPR ratio. The "CPR" is an acronym for critical power ratio. It is the ratio of.the critical power of the limiting bundle in the core to the power of the same bundle at the operating power of interest. The critical power is an artificial bundle power obtained by increasing the power analytically until the critical quality Is reached. The analysis Is performed using the M;XL correlation. Since the hydraulic and neutronic parameters change during the transient, CPR also changes during the transient. The minim= value of the CPR is called MCPR and UZ-i xvit

Sthe difference between the Initial critical power ratio, ICPR, and MCPR Is the ACPR. Hence, the ratio of ACPR/rCPR is a measure of the relative severity of

-the transient.

The uncertainties in the coade are determined by taking semsititvty studies. An independent parameter in the code is perturbed and the resulting change In ACPR/ICPR is calculated for a turbine trip without bypass transient, which is generally limiting. These Independent parameters pertain to the varlous models such as the parameter of Cc in the Zuber drift* lux model or frictional loss coefficients in the staamline. They do not pertain to system parameters which determine the actuation of the valves since licensing basis analysis require limiting settings for these systems parameters.

A. REVIEW OF ANALYTICAL. MODELS

1. Recir*ulation and Contral Svstem

a. Recirculation Loco Model The recirculation loop system consists of the upper pleno, stam separators, vessel dome, jet pump and recirculation loop. Mass, energy and moment*m conservation equations are usecr to describe thermal and hydraulic behavior of the components. These equations are solved using an explicit finite differencing method which il presented in Reference 3.

During the steady-state initialization, the time derivatives are set equal to zero. A multi-channel steady state hydraulics code provides the stady state core pressure drop and the bypass flow fraction to the recirculation system model. This code is presented in 11-2

-Reference 1 and has been reviewed and approved by NRC (Reference 4).

The other Inputs used by the recirculation system model are plant specific such as dimensions related to plant geometry, pressure loss coefficients, separator carryunder fraction and j.et pump and recir culastion pump characteristics.

In the Initial steady state conditions the jet pump drive and suction flows can be determined from the equation of continuity and the jet pump ratio. This ratio Is defined as the ratio of the suction to the drive flow. It is valid for the mted conditions which are selected to correspond to steady state initial operating conditions.

M Using the momentum equation and the m ratio, the suction flow and the suction flow loss coefficient are determined. During the transient the ratio changes. The jet pup suction and drive flows (consequently recirculation loop and core inlet flows) are calculated using the momentum equations keeping the suction flow less coef ficient c=nstant. The sum of the suction and drive flows provide the recirculation loop flow and the sum of all recirculation loop flows provide the care inlet flow.

The recirculation system models used in the OMY and REDY codes are the same. The ROY coda (Reference 5) has been reviewed for ANS analyses and the recirculation system model has been found acceptable with some limitations (Reference 6). The following discusses and evaluates the recirculation syste. model. This evaluation, exest for the uncertainties, Is the same both for OM and RODY codes. The II-3 xix.-

Ilimitations found in the REDY code are equally applicable in the ODYN code.

During the transient, momentum equations are used to calculate the jet pump suction and drive flows. Hence, the form loss coefficients in the recirculation system affect the core flow and consequently the calculated AUR. A sensitivity study performed by General Electric using the ODYN code by decreasing the diffuser fare loss coefficfent by UM showed an incriase of 0.001 in ,CPR/ICPR. General Electric estimated uncertainties in the jet pump loss coefficients about 20;.

These uncertainties are inferred from the uncertainity in the **t pump On' ratio. General Electric noted that the decrease in the jet.

pum pressure drop loss on the order of =0 changed ACPR/ICPR by 0.01. This Is the biggest uncertainty estimat*d by General Elecric In the recirculation system. According to General Electric reason able variations in other parameters such as drive flow L/A, jet pump areas or lengths (which are manufactured t close engineering tolerances) and loss coefficients at the nole, plenum and bulbvater did not change ACPR/ICPR ratios significantly. Based on these sensitivity studies.the'timpact of these uncertainties on the values of A-PR/ICPR In the generally limiting transient is small.

During the transient, the transient terms of the moment*m equation representing Inertia may become iportant in determining the core flow.

Recirculation pump trip tests were performed at 5=, 75%, and 10=

power levels in the Oyster Cr*ek plant and reported in Reference 5.

Good agreement exists between the measured and REDY calculated 11-4 xx

core flows for the transient. This shows that the momentum equations were solved correctly to predict flow transients. Recirculation pump trip tests were also performed in Dresden-2 and they were reported in Reference 5. However, in these tests measured c*re flows were higher than those calculated because the actual pum; inertia was higher than the value used in the analysis.

One of the jot pump modeling assuMptions is that the region from the nozzle to the three% is considered to have no inertia. Zn order to validate-the transient madeling of.-tha-jet- pump, -transient Jeet pum tests were condcted at the Moss Landing Generating faclilty, Referenda 5. In these tests the jet pump drive flows were oscillated at several frequencies and measuresmts wear made of the gain and phase relationship of the drive flow. Coparison of the measurements and model predictions showed good agreement up to 5 Mz. The model did not predict a resonance condition in the cold test data at 6.5 Mz; consequently, the use of the model is limited to 5 Mz. This limitation mains that the cod will have errors if recirculation loop flow variations art sudden. The harmonic cowonents of the flow variation should be less than 5 Hz.

Another assumption which has been validated by tests is the assumption of complete nixing at the core inlet. Tests wore performed In Monticello t verify this assumption. Core flow distributions for three core flow rates, at 2=, S= and = of rated flow rates, wart measured for symmetric operation of the recircu lation pumps, Reference 7. Tests results indicate that the bundle flow rate dons not vary more than 2.=; from that in the average 11-5 Xxi

bundle with 95% confidence level. This indicates that the assumption of uniform pressure dist.ribution at the inlet of the core and complete mixing is a valid assumption for the recirculation system modeling.

The review of the analytical models and the comparison of the predictions with the tests above indicateathat the recirculation loop model and the impact of associated uncertainties on ACPU/ZCPR as presented by General Electric are acceptable. The harmonic cam ponents of the flow variation should be less than 5 Mz and the model should be valid for the analysis of transients where the fluid in the recirculation loop, downcomer and cor. inlet remains subcooled (Incompressible). In the transients to be analyzed by the ODYN code, it Is expected that these limits will not be exceeded.

b. Central System Model The control system models were evaluated for structure as well as the methodology for evaluating plan specific properties. Plant specific properties consist of response functions, gains, and time constants for the control system.

The system models art composed of transfer functions, limiters and function generators. The transfer functions are based on typical filters and proportional, Integral, derivative control laws.

Limiters and function generators are used in the modeling of flo*

valves as a means of linearizing the gain within control loops. We have reviewed the model structure for the motor generator flow contral

=~d

model, the feedwater control model ad the pressure regulation with the Mechanical Hydraulic Control. We find the structure of these mocials acceptable and typical of the type of modeling conducted with classical control system theory.

With respect to the description of the control models, the following models were-evaluated:

(a) Valve Flow Control System (b) Motor-Generator Flow Control (c) Feedwater Flow (d) Pressure Regulator and Turbine Controls (e) Reactor Safety Systems For Input signals, the Valve Flow Cont.iol model receives a turbine governor signal, a sensed steemfiow signal, a filtered neutron flux signal, a recirculation drive flow signal and a manual setpont signal. The control system is modeled as a series of connected gains, filters, integrators, and nonlimnerities (lisiters and function generators). The control system output is valve position and thus flow control.

For input signals, the Motor-Generator Flow Control model receives a load demand error, a. master manual or automatic signal as well as a loop manual or automatic signal. The control system is modeled as a series of gains, intanMrors, function generators, and with actuators of a drive motor, variable speed coupler, generator, and motor pip.

The controlled variable is reeirculation drive flow.

t*-7 xxaii

For input signals, the Feetdater Control System receives feedwatar flow disturbances, vessel pressure corrections, a level setpoint signal, a mixture level signal, and a steam flaw signal. These signals are operated on by a control modeled as a series of connected gains, integrators, filters, and non-linearities (limiters and function generators). The cont olled variable is feedwater flow.

For input signals, the Pressure Regulator receives a turbine inlet pressure signal. a pressure setoint, a turbine speed setpoint and a turtine load setpoint. These signals are operated on by a contril modeled as a series of gains, filters, control laws, control valve servos and non-ltnearities. The controlled variable is turbine inlet pressure.

The staff review finds that these models are conditionally acceptable.

Techtucallly, the models are composed of transfer function, gains, filters, and synthesized nonlinarities such as Oeadbands and saturation limits. The tecmnical form of the control system models Is acceptable to the staff.

However, the model is u*ed to establish initial control syst.em settings such as gains, time constants, and control functions. Since the selection of these settings Is made on a plant specific basis, the staff raerdres that each applicant's Safety Analysis Report reference a clearly defined basis for making these selections. The design criteria us=t be provided for each control system of the plant. The initial conrol system characteristics shall be verified as conforming to the design criteria for each control system of the plant.

xxiv

C. Steam Setarater Model The separator Is modeled using a one dimensional momentu conservation equation whereas the flow in a separator is rotational end clearly multi-dluensional. However, using separator test results (Reference 8), it was possible for General Electric to develop an Mirical one dimensional momentum equation describing the flow behavior. Tests indicated that the thickness and configuration of the layer of swirling water along separator walls is independent of the inlet flow (for 200,000 lb/hr < Flow < 800,000 lb/hr) but dependent on the inlet quality. The water layer primarily affects theffective I./A in the mo=ntum equation of the separator. Due to differences between the densities of steam and waer, the primary Inertial effects are due to the liquid. The tests of Reference 8 provided a relationship between the effective L/A and the inlet quality, and an espirical separator .pressure drop coeficient.

General Electric states that the value of pressure drop coefficient has a conservative bias in It. The higher the pressure drop or the pressure drop coefficient, the higher is the value of ACPR/ICfl.

However. General Electric did not qua*tify the conservatism In this model in terms of AarR/ICPR relative to actual plant conditions.

Therefore, no credit is given to this conservatism.

General Electric performed sensitivity studies decreasing the value of I./A by 3=. This resulted in an increase of 0.002 in A*PR/ICPR:

In order to assess if the scatter of 3= in the separator L/A is sufficient, the staff reviewed the separator date in Reference S.

UZ-,

xxv

The data indicates that the scatter in the separator L/A values can be high. The thickness of water layer can be used to make a fairly good estimate for L./. Tests indicate that the thicknesses of water layer for the same conditions can vary from each other by a factor of four. Reference 6 describes the reason for these variations as an instability.

Discussions with General Electric indicate that the value of L./A used in the ODYN code included the value of L/A for the standpipe and

-- therefore, the scatter was-not- a factor of 4 but it was judged to be 3=. The staff has no information how these separate L/A effects

.(one due to the separator and the other due to the standpipe) can be assessed.

Reviewing the analytical model we find that the separator model is acceptable; however, based on available information we judge that a factor of 2 in separator L/A variation (rather than 3=) would be more appropriate In assessing the uncertainty. Hence, we estimate the co*ponent of that APVR/ICPR uncertainty for L/A will increase from t 0.002 to

• 0.O0s.

d. U.oer Plenum. Vessel Dome and Sulkwater Model These co*ponents are. modeled using mass, energy and momentu conservation equations. Peach Bottom tests indicate that 40me pressures calculated to predict the data are higher than the experimental values. In the opinion of General Electric, the reason for the overprediction Is that the energy equation for the dome U-i2

region predicts that the bulk water mass very quickly becomes subcooled, the system becomes stiff, and therefore, the pressure rises very quickly. Since the rapid pressure rise leads to a rapid void collapse the staff concludes that the model Is conservative.

However, the Peach Bottom tests also indicate that ACPR predictions are not conservative. This implies that the conservatism of the bulk water model is offset by the nonconservatism somewhere else.

General Electric did not quantify the conservatism in this particular model. In view of Peach Bottom tests where a trade off has occUrred, no credit for conservatism can be given.

We find that the analytical methods used in these models are accepta.le; however, as stated, no credit for conservatism will be given.

2. Steam Line Model The steam line is modeled assuming single phase mass and energy conservation equations which are solved using an explicit finite dif ferencing method. The steam Is assumed to behave isentropically. The steam line is nodalized into six segments while the bypass line Is modeled using two nodes. Safety and relief valve flow rates are treated as separate flow branches.

Sensitivity studies were performed by General Electric for various numbers of nodes for a sample test problem wherein the inlet pressure is kept constant and at the outlet turbine stop valve closure is simulated. These sensitivity studies were performed using nodal arrangements of 3,4,S,5,7, uI-U

-8,20, and 40 nodes and conpared with the analytical model predictions using the method of charecteristics. The analyses indicate that a minimum of 7 nodes Is required to predict frequencies to a reasonable degree. The comparison of amplitudes of pressure oscillations between the 8 node model and the analyticAl model Is also reasonable. The conservatism of a model is dependent upon the integral of the pressure oscillations over a relatively short period of time since it Is the integral of the pressure that is Imposed on the core. The void collapse and the subsequent power increase is dependent upon the rate of change of this integral pressure.

Judging from the pressure oscillations calculated from the 8 node model and the analytical model based on the method of characteristics the staff concludes that the integrated pressures art approximately the same for both models and perhaps there Is a very slight conservatism in the 8 node model. Consequently, we find that the finite differencIng scheme and the solution method employed in the steamline model are acceptable.

Other uncertainties in the model are in the form of friction loss coefficients and In the value of the average specific heat ratio. General Electric conducted sensitivity studies by varying the specific heat ratio and form loss coefficients. The Peach Bottom tests indicated an average specific heat ratio of 1.15. The change of this ratio to 1.25 caused an increase of 0.01 In the ACPR/ICPR ratio.

We reviewe the values of the average specific heat ratios for steam at 1000 psia. The value of 1.15 Is valid for saturated steam with very little amount of dropleU in it- The value of 1.25 is valid for a slightly superheated steam. Since there is a pressure drop along the 11-12 xxviiU

steam line. we do not exect steam to be superheated. Hence, the value of 1.15 is acceptable. We also find the calculation of uncertainty of 0.01 in ACVRfLCPR ratio acceptable.

General Electric also performed a sensitivity study by decreasing the loss coefficient by =. This was based on the upper limit of steamline loss coefficient uncertainty. Decreasing the loss coefficient by 2(= increases the ratio of ACPR/fIPR by 0.01. Decreasing the loss coefficient by ZI is a reasonable assuption and we find the calculation of uncertainty of 0.01 in ACR/ICR due to pressure loss coefficients acceptable.

In conclusion, our review indicates that the analytical methods used In steam line mod1ling and associated uncertainties are acceptable.

3. Core Thernal-,Ydraulics Model Two-phase mass, energy and momentum conservation equations were used to predict the behavior of the thermal-hydraulics of the core. Two mass and two energy conservation equations representing each phase separately and one momentum equation representing the mixture comprised the five equation model. In addition to these equations, correlations for 1) interfacial heat flux, 2) Zuber drift flux model (Reference 9), 3) two-phase pressure drop, and 4) heat transfer, are used.

The interfacial heat transfer correlation Is based on the "mechanistic

• odelm presented In Reference 9. The selection of the heat transfer correlations is based on the flow regimes. In .th single-phase liquid region, the Dittus-oealter correlation is used. In the subcaoled and bulk 11-13 X*x

boaling regions, the Jens-Lotuas and Chan correlations are used, respec tively. Two-phase pressure drop correlations are based on the Martinalli-Nelson correlation. The five equation madel together with the correlations are solved using a fully implicit finite differenclng method in the space-time domain. The space domain is one dimensional in the axial direction and the core Is represented using 24 axial nodes.

To improve the accuracy of predictions within a node, a boiling boundary concept is defined. This concept defines a location in the axial direction for which the mixture enthalpy Is equal to the enthalpy at which point subcooled boiling begins. This location establishes the boundary between the liquid and two-phase regions within an axial node at each time step and the program selects the appropriate correlation for the appro priato region. The variables solved for each node art volumetric flux, vapor fraction, pressure, vapor enrtalpy and liquid enthalpy.

Two models are particularly significant in the assessment of ukertainntles In the five equation modal; they are Zuber drift flux and the subcooled boiling models. These are discussed in the following sections.

a. OrIft-Flux Model The choice of two parameters, Ca and V9jis important in this model.

The first coefficient (C)Is the concentration parameter which describes the slip due tU cross sectional averaging of a nonuniform void fraction profile. The second term (V g,) is the drift velocity which describes the local slip between the phases. The value of C0 is strongly dependent on the flo*w r*emes and gomet?*y. This 11-14

dependence has been shown In many tests (Reference 9). The drift velocity is dependent on the density differences between the phases as well as on the flow regimes.

In the model 'used by General Elecric, these parameters are empirically determined in the form of correlations based on the test data. The data were obtained both from tubes and cannels, and are reported In References 20 through 14. When the vapor fractions obtained from these parameters were used to calculate power shapes observed in BWRs, some discrepancies weae observed. Consequently.

General Electric Introduced another correlation for C0,, and a concept of neutron effective void fraction, to provide a better fit with measured power shapes. Based on phtsical considerations It Is conceivable why C0 used In thermal hydraulic calculations is different frim C0 for neutron power calculations. The thermal hydraulic C. Is based on tube geometry while neutron effective C0 Is obtained from actual core geometry. The value of Cc should be different for tubes and rod bundles because of different vapor fraction profiles and flow regimes. However, in a eleczn General Electric stated that C0 valid for thermal hydraulics gave good agreement with Atlas dat and Co valid for neutron effective void fraction gave good agreement with the core data. Hence, the differences cannot be explained based on geometrical considerations alone and there is an artificial fix in the model. According to Reference 34, this fix Is necessary to compensate for deficiencies in lattice physics methods.

11-1.5 xxxi

General Electric estimatet that the uncertainty In the concentration parameter, C., Is about t 3; at a void fraction of .70 for neutron effective vapor fraction calculations. This corresponds to a !

uncertainty in void reactivity coefficient which leads to an uncertainlty of t 0.008 in the value of ACUR/ICPR. However, General Electric uses

• 1= uncertainty in the value of Ca for Uaermal hydmlic calculations. We find no reason that the uncertainty in C0 for neutron power calculations should be different because the correlation Is used to calculate voids the same way as in the thermal hydraulics. General Electric does not state any uncertainty in V for neutron power calculations but states an uncertainty of 9 Z= for thermal hydraulic calculations.

Sised on Reference 15, we assessed the uncertainties for thermal hydraulic C0 a 2t and Vg, a 30% respectively. Reference 15 has a differet, data base froa the references that the General Electric used. Extrapolating the General Electric results, we estimate that t 2C% uncertainty in C0 would result in t i= uncertainty in the void fraction or void reactivity coefficient.

We also reviewed the void fraction data taken in the FRIG loop, Reference 16. The FRIGG tests were performed using rod bundles. The review of the data Indicated that the scatter of

• 30 in void fraction was reasonable in the low quality region. This finding also substantiated the estimate of t Z= uncertainty In the value of Cc.

'I*is xxxii

Asswuing the same uncertainty for the' neutron effactive C0 and extrapolating the General Electric results, we have estimated that the uncertainty of t 2= in C0 resulting in t 3= uncertainty in the void fraction or In the void reactivity coefficient would produce an uncort*inty' i1 0.0t 3 in ACPR/ICPR. We presented these findings in the ACS hearing, Raferenca 30.

In response to the above staff assessment, General Electric subitted additional Information, Reference 31, requesting the reduction ot the

-uncrtainty -in A*PR/ICPR.-- -The-primary-argumant was that the uncertainty of a 2 IIn the value of Ca (seven times the uncertainty of t Z which had been proposed by General Electric) leading to an uncertainty of approximately +/- 3i in void fraction was applicable for a low quality " a low vapor fraction region. The uncertainty becomes smaller at higher qualities. In addition, General Electric submitted another sensitivity study using.neutron efftc'tive C 0 a 0 and noted that this would be the bounding value for ACPR calculations.

General Electric also noted that the transient results were weakly dependent on void fractions at low qualities in the subcooled region, Reference 32.

We reviewed the new information submitted in Reference 31, and agree with General Electric that uncertainties in vapor fraction can be reduced at higher qualities and that C0 . 1.0 is a bounding value for bulk boiling. General Electric stated an uncertainty of t 5% In void reactivity coefficient at a void fraction of M*. This corresponds approximately to an uncertainty o1 a 5% in void fraction. Further 11-17

,gxii4

review of the void fraction data ithe n, FRIGG loop shows a scatter of t 3A% in void fraction at qualities of 5 and 1M. These qualities are considered relatively high and they corespond to vapor fractions of 40; and ,60 respectively. It appears that the FRIGG loop data show a larger-scatter of void fraction than that assumed by General Electric. At high qualities, the uncertainty of t I= in void fraction corresponds to approximately **1 uncartainrty in Co However, the theoretical limit for Co in the bulk loading region is L.00. It can be.higher but not lower in this region. The scatter of 1 an neutron effective would brng the value of C0 below 1.00.

Some of the scatter in the FRGG data was due to measurement errors which could be as high as t 2=. Hence, we accept the limit of Ca v.00 as bounding for the uncertainty studies. Further, sensitivity studies performed in Reference 32 indicate that the transient is weakly dependent on changes of neutron effective C0 in low quality regon. Hmnce, we acc= t the calculation of uncertainty of i O.O2 in ACPR/ICPR as suggested in Reference 31. This is approximately 30 larger than that originally proposed by General Electric.

b. Subcooled Boiling Model m

The phenomenon of subcooled boiling is modeled.by the metchanilic

• subcooled boiling model developed by R. T. L in Reference 9.

"ahe The model provides a relationship for interfacial heat flux between the bubbles and surrounding liquid. It consists of two terms: one term shows the effec of the temperatmu difference between the phases and the other shows the effect of the wall heat flux.

Il-IS xxxV

The model has been verified using the data obtained by S. Z. Rouhami (References 17 and 18). These data were obtained from a vertical annular channel. In determining the uncertainty of the correlation, General Electric provided a sensitivity study using a coefficient Ong In the correlation. The nominal value of In* is -1.0. For n a 1.25, a change of 0.009 in ACPR/ICPR is obtained. If LS is assumed, the change In ACP/ICPR is 0.014. GE states that the value of 125 provides a reasonable unc rtainty for the model but does not provide any supporting evidence or data.

We reviewed the void frac-tion vs. axial heignt curves drawn for various In* values and find that the void fraction difference betmeen the two curves drawn for n = 1.0 and n a L.5 is about 3.5% in absolute or = relative to the average measured value of the void fraction In the subcooled region. Some of the rod bundle experiments performed in the Frig; loop (Reference. 16) show 100 (relative) scatter of the data. In general, the scatter is 15 - 3U relative to the average void fraction. We believe r 3= scatter Is a reasonazle estimate of uncertainty. Therefore, we Increased the uncertainty In ACPR by a factor of 1.67 (30/28) which results in t 0.023 in the uncertainty value of AIPRICPR for the subcooled boiling model. We estimate the corresponding minimu and maximum values of On* to be 0.5 and 2.0 respectively. General Elective Is required to make sensitivity studies to verify that these values correspond to = 0.023 uncertainty in ACPR/ICPR.

11-2

The review of the analytical models describing the thermial-hydraulic behavior of the Care indicates that these models are acceptable provided the uncertainties of various comonents are increased to fthe values recomended by the staff.

4. Core Physics Model

a. Assu*.tlons in the Neutronics Model The nrutrofltcs model of OCMh is based on tm.e-Cependent, one dimensional, one-group, diffusion theory. The model includes the effect of delayed neutrons and the calculation is performed In the axial dimension of a IWR. Radial effects due primarily Uo Doppler, moderator, and control state are taken into acocunt In collapsing a three-4imenseonal model to the one-dimensional axial model. Of the three effects, the control state variation due to scram during a transient is the most Important. Some care must, therefore, be taken in choosing the Initial weighting functions U. account for these effects.

We have reviewed the assumptions in this neutronic mooel with the curnt state-of-the-art for performing space-time coupled noutronic and thermal-tydraulic calculations. We conclude, based on our review, that the assumptions on which the neutronic model of CM are based are acceptable.

b. Derivation of Ecuatlons for the One-Gru=., One-Dimensional, Time-Devencent Neutronic Moode We have follow In a step-by-step manner the derivation of the oer-ggrou, space-time neutronics modal presented primarily in 11-10 mXV..

Appendix A of Volume I of the report.' This derivation proceeds from the time-depandent form of the three-dimensional neutron diffusion equation for the fast flux as used by the General Electric three dimensional reactor simulator (Reference Z) along with appropriate equations for delayed neutrons. The three-dimenslonal time-dependent neutron flux is represented as a product of radial and axial time dependent components. Weighting functions are next introduced to make this factorization unique and to minimize errors in the procedure In some sense. The weighting functiions are taken, according to the adiabatic approximation, as the solution to a steady-state eigenvalue problem to be solved at. various points in time. In practice, the weighting functions are calculatad only at time zero for as many BWR operating states as is necessary. This procedure results In the final farm used for the one-group, one dimensional, time- dependent equations along with defining equations for the nuclear parameters that are used. The derivation also includes discussion of the average axial power distributions, Initial normalization procedures, and boundary conditions.

Section S of Volume I of the report discusses the Integration of the spatial and time variables to obtain the discrete form of the one group, one-dimensional, time-dependent equations. The procedures used for this are straight forwar-d This section also discusses the radial weighting function and the treatment of the control state.

Cross section related parameters are functions of axial core heigh*,

control state, and relative water density. These parameters are fit to quadratics in the relative water density.

11-23 xxxvil

Out review of the derivation of the equations for the ore-group, one-dimensional, time-endent neutronics model has been performed by deriving and verifying each of the equations presented in Volume I of the repor We conclude, based on our step-by-step reviev of all the teutronic equations, that the derivation of nuclear parameters and equations for the one-group, one-dimensional, time-dependent model is acceptable.

C. Calculation of Neutronlc Inout Parameters

-General Electric uses Its Lattice Physics Model and its Three Dimensional S"IR Core Simulator to process nuclear data for the 0DYh code. The Lattice Physics Model is described in Reference 19. The Three-Dimensional SM Core Simulator is described In Reference 2.

Both of these codes have been reviewed and approved by the NRC for use in BWR applications.

The Lattice Physics Model, as Its name Implies, is used to generate nuclear parameters for use as input to the 8WR Core Simulator. This data is generated as a function of fuel type, control, temperature, void fraction, void histary, and exposure. Before being used by the MWRCare Simulator, the data is transformed from the Lattice Physics Model void fraction to the Neutron Effective Void (NEV) model void fraction. This apirical procedure was developed by GE to reove a discrepancy beeen BMR Core Simulator results and oerating reactor data. The BWR Core Simulator Is used to perform the three-dimen sional analyses that are required for obtaining the data for processing intopar. etars and cross sections for the ODYN code.

11-22 xxxovi:L

Our review of the calculation of neutronic input parameters Is based on the usa of NRC reviewed and approved codes and on comparisons of three-dimensional and OMYN steady-state neutronic analyses. The approved codes are (1) the Lattice Physics Model (NEDE-20913-P, OLattica Physics Methods,* C. L Martin, June 1976 and NEDO-20939, "Lattice Physics Methods Verification,8 C. L Martin, June 1976) and (2) the 3WR Core Simulator (KEDO-20953, wThree-Dimensional BWR Core Simulator, J. A. Woolley, May 1976 and NE:O-2094M, O*R Simulator Methods Verification,' G. L. Parkos, May 1976). The steady-stteS calculations compared the 9WR Core Simulator and ODY0 results for scrra reactivity and core averaged axial power distributions, among other things, for a number of different reactors and operating states.

Same of the uncertainty values used by General Electric In response to our Question 12 need to be revised In our Judgement- We believe that the Doppler reactivity coefficient uncertainty should be increased from z 6 percent to about : 10 percent. This increase is based on the uncertainties inherent in the calculation of Uranili-238 resonance absorption, the calculation of the Oancoff factor In the complax MR lattice, the calculation of spatial weighting factors, and the computation of effective fuel temeratures. This change in the Doppl'r uncertainty will have very little effect on the calcu lated ACPR/1CPR ratio. We estimate that this will increase the uncertainty in ACPR/1CPR from t 0.0015 to

• 0.002. We believe that the scram reactivity uncertainty should be increased from t 4 percent to about

• 10 percent. This increase is based on the uncertainties 11-23 zXdx

Inherent in calculating the initial scram reactivity rate and total control rod worths. We estimate that this will increase the uncertainty in ACPR/ICPR from 1 0.01 to :z 0.02. The General Electric values for the Lattice Physics Model and BWR Core Simulator uncer tainties in the void reactivity coefficient calculation are acc:epable as given in response to our Question 12.

Since the uncertainties in the neutron effective void fraction are assessed In the thermal hydraulic section, we did not consider it as part of void reactivity uncertainty. Hence, the uncertainty in ACPR/ICPR value is reduced from :t 0.020 to +/- 0.018.

We conclude, based on our review, that the procedures and calculations performte to provide the neutronic parameters for input to the ODYh code are acceptble.

S. Fuel Heat Transfer Model Heat transfer to the coolant and temperatures within the fuel are calculated assuming a single cylindrical fuel element for each axial location. The fuel heat transfer model used in the 0DYh code calculates fuel tmperatures as a function of time In the transient as input to the Doppler reactivity calculation. The cladding well temperatures are also calculated as input to the transient cladding-to-colafnt heat transfer model. The ODYK code allows for axial variation of the neutron flux, as well as of coolant flow, density, and pressure. This results in an axially varying set of input conditions for the fuel teat transfer model.

The resulting tamperature calculations are then solved for a series of discrete axial elevations in the- core.

11-24 xl

The fuel and cladding Conductivity and heat capacity are assmed t be temperature dependent. A gap. thickness is specified betmeen the fuel and the cladding and an input gap conductance is used. Axial and time variations in the gpp conductance may be given, but a constant value is used for safety analyses. The external heat transfer coefficient and coolant temperature are obtained from the thermal-hydrulic portiqn of the code. The heat generation rate in the fuel pellet is obtained from the axial pover distribution which Is determined by the neutronics segment of O0YD. The radial heat distribution in the fuel rod is assumed to be independent-of axial -position-and -independent of tim.

General Electric derived th fuel heat transfer model from the general heat flow equation. The equation Is expressed with axisymmetry and zero axial conducýion assumed. The resulting, one-dimensional, transient heat conduction equation is solved by the Crank-Nicholson finitredlfference technique. The solution is approximate, but the procedure is widely practiced and is well docened in the open literature. General Electric has limited its description of the fuel heat transfer model to the formulation of this final equstion.

The resulting heat conduction equation is applied to a single rod with a radially averaged hesat generation rate. This rod is used to represent all of the fuel rods in the reactor core. Because axial conduction Is assumed to be negligible, the equation can be solved Independently for each discrete axial position in the core. The finite-difference technique also requires a radial nodalization of the fuel rod. The nodes may be of arbitrary size. General Electric has assueed that the fuel pellet is 11-25 xli

ivided Into seven radial nodes and the cladding into two nodes. The coefficients for both the steady-state and transient forts of the resulting finite-difference equations are given in Tables 7-1 and 7-2 of the madel description.

A number of limiting assumptions have been considered in our review of the fuel heat transfer model.

L. The ODYN core transient model is designed to handle short-term events

---

vhich occur an a tie scalueof seconds. This makes It possible to Ignore the effects of long-tamr fuel behavior phenomena, such as creep and swelling. Pre-transient conditions, such as the average fuel-to-cladding gap size, are calculated with more detailed fuel performance codes, such as GGAP-III (Reference 20) and subsequently used as Input to CYN.

2. The ODYN core transient. model is designed to handle average, rather than extrae, fuel conditions. The fuel rod Input parameters represent an average of a11 fuel rods at a given axial location.

Bounding input parameters are, in general, more difficult to establish and thus are more critical In the overall analysis.

However, the ODYN code, as a whole-cor analysis, requires only the average conditions. In this respect, we note that the ODY0transient model does not have a hot channel capability, where extreme fuel conditions would be required as Input.

11-26 Xzi

Both of these limiting assumptions were considered In our review of the gap conductance values used by the aD-YN code. Ye have reviewed (Reference 21) the selection of the axial and time variation of gap conductance to determine whether the selected values are appropriate for different transien s. General Electric stated that the core average gap conductance values are calculated by GEMAP-III (Reference 20) which is approved by NRC. The calculated conducta= is input for all axial nodes and is kept constant during the transient.

A sensitivity study was al"so performed for the most limiting presurtiztion event in which the AVPR decreases when axial varying gap conductance is used. It was shown that most of the high power axial nodes have higher than core average gap conductance. During the transient, higher gap conductance will lead to faster heat transfer from the fuel to the moderator/coolant which generates more steam voids. This results in lower stored heat In the higher power nodes. In addition. the faster conversion of fuel stored energy to steam voids in the core helps to mitigate the transient due to negative void reactivity feedback.

Therefore, the transient with axial- varying gap conductance is less severe than that with constant gap conductance.

During limiting pressurization transients, it is expected that the fuel gap conductance will be higher than its initial steady-state value due to the increase in the thermal expansion of the fuel pellet. As discussed above, higher gap conductance leads Uo a less severe transient. General Electric has not taken credit for this fact, but has stated that the use of constant conductance throughout the transient compensates for uncue 22-V x1Lii

taintles In thermal conductivity and specific heat of the fuel and cladding. We have examined these properties and find that they are appropriate over the teerature range specified by GE C300-1500 OK for fuel thermal conductivity). Therefore, It is concluded that Ute use of a constant, core average gap conductance in the proposed ODYN licensing calculations is appropriate.

We have also questioned the use of a specific core average gap conductance value of 1000 Bt/hr-ftz-OF for the analysis of the Peach Bottom Unit-2 turine trip event. General Elect*ic has shown (Q-1, Voluae 1) the calculated peak neutron flux as a function of time for gap conductance values of 500, 2000, end 1500 Dtu/h-tt-OF. Small differences In neutron flux are observed for the S00 and 1000 Duhr-fts-OF values. This Is because the entire flux pulse is only a few tenths of a second wide and a fast fuel time constant is needed to produce a moderate density feedback through the rod heat flux. The peak neutron flux is ninium for the 1500 Btu/h-fta-F value, showing that large values of gap conductance will mitigate the calculated flux response. This conclusion is in agretment with that found for aiudal and time varying conductance values.

It also'shows that a core average gap conductance value of 1000 tW/

hr-fts-OF is not, in itself, an adequately qualified conductance value for care transient analyses. We conclude that conductance values should be based on an approved fuel performancs code.

We have also reviewed the use of a radially averageqd heat generation rate rather than a radially-dependent heat generation rate. We questioned the conservatism of this assusption because flux depressions, and therefore a u-2s xliv

radially-depencent heat generation rate is expected in BWR fuels. General Electric has acknowledged that the radial power distribution within the fuel rod Is not uniform. This is because the plutonium build-up and self-shielding -of the fuel results in a radial power shape peaked sharply at the outside of the fuel pellet. Heat transfer from the inside of the pellet to the cladding occurs by diffusion through the fuel material.

When the powerlis peaked at the outside of the pellet, the average distance from the area of maximum heat generation to the edge of the pellet is less. This results In a shorter time constan than In the

-uniform power prod=ion case. A reduction in the thermal time constant results in faster feedback of heat flux to the moderator/coolant and reduces the consequences -of the pressurization transient in the sam manner that higher gap conductance does. Hence, a uniform power dis tribution assumption inside the fuel pellet is conservative from the modarator/coolant standpoint.

Although the use of a uniform radial pin power distribution and small gap conductance values lead to conservative moderator/coolant conditions, these assumptions also lead to higher fuel temperatures. The higher fuel temperatures, in turn, lead to Increased Doppler broadening in the fuel pin which Is non-conservative for transient analysis. The OWYK code assumes that all fuel at the same axial location in the core has the same temperature profile. Analyses have slow, that this approach may tend to underestimate the Doppler reactivity effects because the fuel pins wftich have the greatest resonance capture rates are near the bundle periphery and operate at higher average temperature than that calculated by the coda. This assumeption is valid only for fuel assetlies with uniform x1V

enrichment. However, the Doppler reactivity contribution to WR transient analysis appears to be of lesser importance than te scram and moderator void reactivity contributions. The use of a uniform radial pin power distribution is-therefore appropriate if the analysis of events where Dopler reactivity effects are small.

We have also questioned the application of the Crank-Nicholson method to the fuel heat transfer equation. This method suffers complications when heat generation varies with position and time, when thermal.properties vary and when non-linear boundary conditions are used. General Electric has stated that the method of solution suffers complications only when the time steps are too large relative to the fuel thermal time constnt or when the fuel properties change more rapidly than the time step of the solution. It was further stated that the BWR fuel thermal time constant Is in the rw*ge of 5-8 seconds compared Uo 0.01 second time staps taken by the ODYN code. Such extensive timn stepping is required for the hydraulic analysis and will accommodate all non-linerity problems of the fuel behavior. It was also noted that the gap conductance is conservatively held constant in the transient calculation. we therefore conclude that the method of solution Is appropriate for safety analyses.

In sumary, we find that the ODYM fuel *est transfer model is appropriate for whole-core analysis of short-term events. We note that the code is used for whole-care analysis and is not proposed for hot cannel calcu lotions. We have also exmined the list of events selected (volume I*,

table 2-1) for analysis with and find that these events are of short hODY duration or are limited in expected fuel temerature Increase. We 11-30 xlvi

conclude, therefore, that the ODYN fuel beat transfer model is appropriate for the safety analysis of these events.

6. Sumary of Code Uncertainties

a. Kandnn n ACPR Calculations In smmary, the staff agrees with some of the code uncertainties calculated by General Electric. However, same of the code uncertainties are low and the staff recomends higher values. A comparison of the coda uncertainties and the corresponding bounding values as recommended

--- by-General -1lctric and-the staff-Is presented In Table L.

General Electric claims an expected conservative bias of 0.02 (Table 3-3, Volume 11) In the calculation of the value of W:PR/ICPR due to the modeling of the gap conductance. However, the sensitivity studies performed using different values of gap conductance (Q-fl. volume nI) as well as the comparison of the Peach Bottom test data with the ODYN predIctions do not Indicate that such a conservatism in ACPR calculations exists. Consequently, 'we do not believe that the predictions have a conservative bias.

Our review shows that the ODYN code is a best estimate code and there is no inherent conservatism In predictions of ACPR/ICPR when best estimate input values are used. Consequently, we do not give credit for this claimed conservatism of 0.02.

General Electric estimated the total code uncertainty (Table 3-3, Volum 111) using the method of linearization. This maetod can 11-31 xIvii

TABLE-I COMPARISON OF CODE UNCrTA1I*nES AND CORRESPONDING BOUNDING VALUES AS ESTIMATED BY GENERAL ELECTRIC AND THE STAFF GE I ii STAFF I Boundi ng ouncOl ng

.Values of 2.;CPR Values of *ACPR Parameters =CPR Parameters I. Reactor Coae Model (1) Nuclear Model (a) Void Coefficient av *Z 0.020 av 0.018 (b) Dopler Coefficient 0.002 0.002 CW) Scram Reactivity a- 4 0.010 0.020 (d) PrcWmt Ieutron Heating 0.006 0.006 ad *+/-3 C2)-Thermal Hydraulic Model Co 3 1.00 (a) Drift Flux Paramsetrs V9 t2= 0.008 0. anl (b) Suocoaled Void Modal n a L.25 0.009 n 0.5 0.023 2.0 (3) Fuel Heat Transfer Modal (a) Pallet Heat Distribution (Conservative)

Wb Pellet Heat Transfer O Parameters (Conservative)

11. Recirculation System Model (1) System Inertia CL/A)

• 200% 0.002 L/A

• 20= 0.002 K - 20%; 0.010 K i- = 0.010 (2) Jet Pump losses 0.005 (3) Core Pressure Drop A + 1.5 psi 0.005 L5 Psi 1.

(4) Separator L/A) 0.002 -200% 0.025 (5) Separator AP (Conservati ye) 111. Steam Line Model 0.010 (1) Pressure Loss Coefficients K 20% 0.010 K 2=

(2) Specific Heat Ratto T+*.10 0.010 - 0 0.010 Total: 0.032 0.044 11-32 xlviii

estimate the output distribution only approximately. The method also assumes the Independence of the parameters. The appropriateness of the linear method should be verified by response surface and Monte Carlo analyses. However, as vill be shown subsequently, the results of the statistical analyses performed in volume III are not acceptable.

few statistical analyses, If performed by General Electric, should be based on code uncertainties based on comparison of code predictions with the test data. Consequently, we use the value of total code uncertainty calculated from model sensitivity studies and method of linearization in determining the margin of ACDR/ZCPR in Option A (to be presented in Staff Position) where statistical analysis is not required. The total coda uncertainty in Table 3-3 of Volume III as per General Electric is

• 0.031. Based on our review we increase this value to a 0.044.

b. Marain in Pressure Calculations General Electric has not performed analyses to detarmine the uncertainties In the calculation of pressure. Hence, it will be necessary for General Electric to perform these calculations using staff reoended values of the parameters listed in Table I for the Main Steam Isolation Valve closure event. We believe that there Is sufficient conservatis in the ASME vessel overpressure limit to permit General Electric to use approximate linear methods Uo determine the uncertainty In the output. This uncertainty (2a) Should be added to the ODYN calculated pressure. If General Electric demonstrates that this uncertainty is very small (e.g.. by a factor of 10 or more) relative t the uncertainty In determining ASME vessel overpressure limit, no addition of uncertainty to the calculations of pressure Is needed.

IIZ*3 xlix

B. QUALIFICATION OF THE 00Th CODE L. qualification of Neutronics Model - Comoarison of ODYN with MWR Care Simulator One of the ways in which the OYh code may be qualified is by comparison of 0ODY results with those obtained by using other codes and analytical methods. These comparisons should include both steady-state and dynamic calculations. A calculation of a BWR turtine trip without bypass licensing basis transient Is compared in a later section to a calculation performed by our consultants at Brookhaven National Laboratory (8HL). This section will discuss some steady-state comparisons made by General Electric of OTYN and the BAR Core Simulator.

The BWR Core Simulator Code (NEDO-20953, Thre-Olmenstonal BWR Core Sim*ulaitor,' J. A. Woolley, May 2976 and NEDO-2094M, 88WR Simulator Methods Verification,u G. R. Parkos, May L976) Us been reviewed and approved by the NRC. This code, as used by General Electric, predicts measured power distribution peak to ave',rage ratios as follows:

(a) Axial power distribution o 5 for uncontrolled assemblies

- for controlled assemblies (b) Radial power distribution - 99 underestimate relative to the process computer (c) Nodal power distribution - 4 for gamma scan data

- 7 to I= for process computer data ri-34 1

The BWR Core Simulator calculation of the -riticality of first cycle and*

reload BWRs results in a small bias which is taken into account for reactivity determinations of cold, xenon-free and hot operating condi Mtons. The standard deviation of these criticality calculations is about 0.002 in units of reactivity.

The quantities t be compared are the core averaged axial power shape, the scOam reactivity, and tt, void reactivity coefficient. These neutronic parameters were selected for comparison because of their Importance In the turbine-trip withoutbypass licensing basis transient In addition, It is the space time evaluation of these 4uantities that. distinguishes the 00YN calculation from a point kinetics evaluation of pressurization type transients.

The comparison of the core averaged axial power'distribution, as computed by the BWR Core Simulator and ODYN, Is given by the response by GE to our Question 36. This response states that the collapsing scheme eployed in the generation of nuclear parameters ensures that the steady-state core averaged axial power distribution and criticality computed by O0MN are identical to the BWR Core Simulator results. The response also indicates that, for a number of plants and operating states, The OM core averaged axial power distribution agreed to within 0.5 percent of the results obtained with the three-dimensional BWR Core Simulator.

The scram reactivity was compared for three BWR-4 react or operating states. The Initial scram rate CISR). defined as the scram reactivity insertion rate during the first second from the time scram is initiated, ii

1, is the quantity chosen for comparison rather than the total scram worth.

The ISR has been shown to be a critical quantity for short duration power burst transients of the load rejection type.

One operating state was for the beginning of cycle 2 but with all control rods out.' ODYN results for the neutron flux and scram reactivity us a function of control rod Insertion (or time) compared well with results obtained with the BWR Care Simulator. The XSR for ODYN was about 0.93 of the value obtained with the BWR Coae $imu2ator. The second comparison was fir the same BWR-4 but with some-control rads Inserted to achieve "a critical condition. The ISR for 0DYT was about 0.86 af the value obtained with the BW Core Simulator. The third comparison was for another BWR-4 at 50 percent of full rated power and 100 percent of full rated core flow.

This reactor had a considerable control rod Inventory and, therefore, provides a severe test for the OM code. The ISR for 0CMh was about 0.94 of the value obtained with the BW Core Simulator. For all three comparisons the 0Th result for I51 was smaller than that obtained with the BWR Co*re Simulator and was therefore conservative.

The void reactivity coefficient derived from ODYT calculations was coepared to the void reactivity coefficient derived from the 3WR Core Simulator. This coefficient is obtained by knowing the core averaged void fraction and reactivity at two different reactor operating states. The different reactor operating states were obtained by changing either the reactor-pressure or flow. For the variety of cases examined, GE states that the 00Th and PM Core Simulator void reactivity coer"ficients agree to within -Z.

11-36 lii

Our review of the comparison of steady-state BWRs calculated using the one-dimensional ODY0 code with comparable calculations using the three dimnsional 8WR Core Simulator code has been performed (1) by reviewing GE results for the scram reactivity and void reactivity coefficients and (2) by reviewing the GE response to our request for additional infornation on steady-state comparisons between the two codes.

We c=nclude, based on our review, that steady-state ODYN code calculation of core averaged axial power distributions, scram reactivity, and void reactivity coefficients are either in-goodt agreement with or conserva tively calculated with respect to comparable steady-stat results obtained with the BWR Co*re Simulator code.

Qualification of the Thermal Hydraulic Model Q.

Several cooparisons of the ODYN thermal hydraulic model to standard GE design models were performed. The standard GE design model was suf.itted In Reference I and was approved by NRC in Reference 4. Both steady state and transient conditions we.% analyzed.

The stady state analysis first compared the thermal hydraulic character istics (void fraction vs. axial location) of tw typical BWR fuel channels (high and low power channel). The results of this comparison show pad agreement between the models. This was xpeced since both models are very similar. The max mm void fraction variation between these models was approximately 5 for the high power channel and about 17= for the low power channel. These variations are for the axial locations where the void reactivity change Is expected to be most significant for 11-37 liii

the transient calculations, i.e., -4 It. axial height. The steady state analysis also compared the change in void fraction vs. axial location for a 10 psi pressure change. The maximum void fraction variation between the nmodels for this comparison was approximately 0.5% for the high paver channel and about 5 for the low power channel. These variations are within the range of uncertainty for these type of thermal hydraulic calculations. See also discussions in Section ZL.A.3.a .and b.

For the transient analysis comparison, the ODY channel thermal hydraulic

-moctLressult was compared to an analytical solution for xponential flow decay. The comparison rtquired that OWYK be modified to include a constant axial heat flux distribution, and steam and drift flux proper ties. This was done because the tests were run with a uniform axial heat flux and calculational convenience required the choice of constant ste and drift flux properties. The tests were performed using a single heated tube containing Freon-114 at relatively low pressures and temperatures; about 2S psia and 60*F respectively. There is t 10% uncertainty in the measurements of the void fraction. The calclational uncertainty seems Uo be on the order of t 5%. These tests verified that the analytical modeling technique including the drift flux model is acceptable and can be used to predict the vapor fraction. Judging the comparisons between the predic tions and the test data and the special nature of these tests, the staff estimates that an uncertainty of t 3= in transient void fraction In low qualities and

• M: in high qualities for a rod bundle geometry during reactor transients is reasonable and consistent with the findings in tMe analytical model review In the previous section.

11-38 ii1-

3. 'Qualification Using Intearal Tests In the past several years General Electric has undertaken a test program to verify the analytical methods for reactor pressurization transients.

The tests of major interest for the current discussion consist of four turbine trip experiments. Three of these tests were performed at Peach Bottom Unit 2 (P9-2) in April 1S77 and the remaining test was performed at a foreign reactor (KM) in June 1977. 1hese tests provide the experi mental data base for verification.of the ODYN code. The test results will be suarized in this section. A detailed description of the P9-2 test is presented in Reference 22, General Electric stated that ODYN has been developed from first principles and Independent of these results. The staff notes that in the ODYN code the only artificial fix is the neutron effective void correlation. The comparisons with Integral plant tests provide an independent check of the OCMN code. The evaluation concentrates on the differences between test results and corresponding ODYN predictions. The parameters which are considered in these comparisons are steamlIns pressure, reactor vessel dome pressure, core exit pressure, and transient neutron flux distri bution. These parameters are of primaiy importance in simulation of the pressurization transient. An accurate, Ch simulation of these param eters would provide some verification of the assumptions for the transient models.

a. Peach Bottom Tests The inputs used for this comparison were best estimate or measured values for the current (April 1377) Peach Bottom Unit 2 EOC2 condi tions. The three Peach Bottom Unit 2 (P*-2) tests were conducted at 11-39 lv

power levels of 47.4, 61.6, and 69.. percent of full rated power.

The tests were intended to be conducted at 100 percent of the rated flow. However, the second test was conducted at 82.1 percent of rated flow due to xenon. These three tests had different control roed distributions and fractions. For these three tests the first scram signal an the position of the turbine stup valve was disabled so that the scram would occur on high neutron flux. Disabling of the primary scram signal was necessary to obtaina significant power increase as a function of time for tests. Control rod insertion was assumed to vary linearly with time and was based an measured data. A constant value of 1000 BTU/hr-ft t -F was used for the fuel rod gap conduc tance. Sensitivity studies performed by General Electric showed that the neutron flux as a function of time was insensitive to large changes in the gaP conductance for these tests (See Q-1l, Volume 11).

The GE B*R Coare Simulator was used Uo generate three-dimensional power distributions and to collapse the nuclear parametars according to the ODYN procedures. The initial core averaged axial power distribution calculated with ODYN can then be compared with Power distributions obtained with the PB-Z process computer. Comparison shows that OY1( agrtes quite well with the process computer core average axial power distributions for all three tests. This means that the GE neutronic procedures for generating .nuclear parameters are internally consistent and provides the proper initial conditions for the start of the transient calculations.

11-40 lvi

A comparison of ts total care pover as a function of time provides an integral test of the Important reactivity feedback due to scram and moderator density changes. This comparison would also be indicative of the adequacy of the care pressure and inlet flow calculations. The couparison shows that 00hY predic-ts the initial and fall-off part of the turbine trip. transients correctly but overpredicts the peak total core power response for all three tasts.

It should be noted that the calculated consequencas of the turbine trip tests are sensitive to scram delay time and the power fraction for prompt moderator beating. It should also be noted that small changes in reactor operating state conditions such as, for example, core pressure, cause relatively large changes in the flux transient becausa of the large not reactivity of the transients.

The reactivity components displayed for these OYT calculations show that wten scram occurs the power burst is quickly quenched. This is due to the control rod distribution and fraction for each test. The Doppler reactivity component plays only a secondary role. The reactivity componets again demonstrate the necessity for their accurate assessment in any calculations of' these type of transients.

A further indication of the adequacy of the ODMN calculation can be ascertained by comparing the core power as a function of' time at the Local Power Range Monitor (LPB4) detector positions. The miniature fission detectors that comprise this LPRH system are distributed both radially and axially within the reactor cars. Analysis of the PS-2 data shows that the radial variation of the neutron power with 11-41 lvii

time is similar for each detector on an axial level. This means that a one-dimensional axial calculation such as OOYN should be an adequate representation for these test. The neutron power as a function of time does vary, however, with axial position as shown by the experimental data for the A, B, C, and 0 level LPRMs which are located at 1-1/2, 4-1/2, 7-1/2. and 10-1/2 feet from the bottom of the core. Comparison of the ODYN results for the neutron power as a function of time for these four detector levels with test data shows similar trends as observed for the total core power. The ODYN result* and test data agreement for each LPR4 level is similar to that for the total core power for each of the tasts. This indicates that the ODYN caiculation correctly models the axial neutron flux variations as a function of time for these Pi-2 turbine trip tests.

Figures 1 through 3 (reproduced from NEDO-24254) present cozmprisons of axial neutron flux variations as measured (calculated by the process computer) and calculated by the ODYN code before te initiation of the tests. Figures 4 through 6 present comparisons of prompt neutron power as measured and calculated by the ODYN code during the tests.

The OMYN calculated st1amline pressure compares well with the P9-2 data for predicted wave travel time and frequency of pressure oscillations. However, the calculated pressure curves are more spread out and the amplitudes are smaller than the measured steamline pressure. General Electric has attributed this difference to the coarseness of the spatial nsh.tn the steamline modeling. As 11-42 Iviii

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evidence of this hypothesis, General Electric showed that the stom line pressure calculation for the rJM test, which had a finer spatial mesh, was quite accurate. General Electric has also pointed out that the steamline pressure response shape is not as important to the transient behavior as is the Integrated value of the steamline pressure response.

We do not. agree entirely with General Electric. In answer to Q-29 in Volume 1, General Electric performed a sensitivity study showing the effect of nodalization (different mesh sizes) and cm*paring the results with the analytical model which uses method of character istics. The difference In amplitudes In this comparison is on the order of 1= while the difference in amplitudes In Peamch Botom tests and OYN predictions Is S=. In addition, expected differences have opposite trends. The accuracy claimed by General Electric in the KI4 test can be due to the adjustment of the valve opening time. This adjustment was made by General Electric to obtain a better agreement with the measured pressure data. It appears that the steamlnenmodel does not predict the amplitudes of oscillations accurately. This is also substantia'ted by the staff audit calculations. However, we agree with General Electric that the integrated sueamline pressure response is more important in determining the transient behavior than the amplitude of individual oscillations occurring at these frequencies. The Peach Bottom tests indicate that the dome pressures do no*t oscillate and this is the pressure to which the reactor ts subjected. Comparison of the dome pressures indicate that the dome pressure calculations performed by the ODYN code are conservative 11-49 lxv

relative to data; i.e., the overall rate of pressure rise as well as the magni*ude of the calculated pressure were higher than the data indicate.

The Initial acm pressure rise for the P8-2 tests was predicted accuratbly by 00Yh. The calculation overpredicts the pressure rise near the peak of the first pressure oscillation, thus conservatively modeling void collapse for reactivity feea.ack. ODYN appears to overpredict the peak vessel pressure rise which demonstrates a conservative basis for overpressure protection analyses. General Electric states (Reference Z3) that the overprediction Is due to the assumption made in the energy equSation for the rome region. The overprediction of dome pressure is considered a desirable conser vatism. Within the period of time that the neutron flux pulse occurs, the duoe pressure overpredictlon is approximately 15 to 28Z higher than the data.

Reviewing the steamline and dome pressure transients and based on the sensitivity studies performed by General Electric, we require that the szoamline be modeled by at least 8 nodes with maximum size of 100 ft for a node.

The core exit pressure Is one of the most important parameters for the prediction of the pressurization transient neutrun flux response.

As was the case in dome pressure comparisons, the initial rise In core exit pressure was followed well by the model for all three tests. From the comarisons of OYH to the PB-2 test results, 12-SO lxvi

General Electric has concluded that the saemline dome and vessel thermal hydraulic models simulate the overall care pressure rise rather well in all three experiments. This lends confidence to the code predictions through the full range of power levels. Measure ments indicate some oscillations in core exit pressure. These oscillations have bden attributed to instrument line effects by General Electric. This is corroborated by the lack of associated oscillations in neutron flux measurments.

-The -nmeuron -flux predictions -by-the -OYN-cod -were conservative relative to data. We estimate that the peak neutron flux is higher by 54 to 89M than the data and the integral of the nuclear power (which is a measure of the amounut of energy generated) is also higher by approximately S6to 4= than the data. Hence, the neutron fluxes were predicted conservatively In all three tests.

As a final step, General Electric has presented a calculation of ACUR/ICPR for test and model. We revi the calculational procedure and consider it appropriate. The results show that the

&CPR/ZCPR for 0DYN predicted transient conditions is within 0.02 of the values which would be predicted from test conditions; I.e., the ACPR/ICPR values calculated using the measured flow from jt* pump AP measurements, the measured pressure and the measured power during the tests. The OMY transient conditions predicted two out of three ACPR/ICPR values conservatively. The differences art betwen -5.=*

and 6.1% relative U values calculated using the data (minus means nonconservative). The differences in these three test results in 11-S2 lxvii

terms of ACPR/ICPR give p a LU.14 which represents a very slight conservatism for the mean and a a t 6.39% for the standard deviation.

Since the data (three points) are very limited, the results do not have a high degree of confidence. Table 11 presents these values of 6CPR/ICPR.

TABLE 11 COMPARISON OF MAXIMUM. &CPR/ICPR VALUES FOR PEACHi BOTTOM AND KrM TESTS

&CPR/I*PR ACPR/7CPR Test Initial CPR (Data) (IOYN)

Peach oltom.*

Turbine trip 1 2.536 0.170 0.173 Turbine trip 2 2.1.5 0.136 0.129 Turbine trip 3 L.048 0.132 0.141" KKM Turbine trip Z.279 0.077 0.084 Review of the test results indicate that all model conservatisms claimed by General Electric such as conservatism in calculation of the steam dome pressures and neutron flux, conservatism in collapsing of 3-0 core neutronics and thermal hydraulics, conservatism In the gap conductance input parameters and any other conservatism claimed in the coputer =mdel are either so small that It did not make any difference in calculating &CPR for these three tests or all of these claimed conservatisms are offset by an unidentified nonconservatism somewhere else, perhaps in calculation of flow. It is evident that the calculations of CPR are not conservative for all of the tests.

rz-s2

They can only. be regarded as best estimate, or accurate predictions.

Hence, based on the Peach Bottom tests we do not give any credit for the conservatisa In the models used in the 00Yh code. The code will be regarded as best estimate for ACPR calculations and any discrepancy between the taet results and the code will be treated as an uncertainty or an error. Further tests would be needed to reduce these uncertai ties.

b. KXM Test cfmtarison A-brief-sumary--of -Ut -tst-conditions--s-contained-in -Valum 1.

KKK plant has an unusual configuration, in that, It has two turbines and two se*ts of st aulines with a reheoter line in each steamline.

It presents soum special model considerations for DDYN simulation. A special version of OWYN was developed to simulate this configuration.

Also unique Uo this test comparison as opposed to the PS-2 comparison is the modeling of turbine stop valve and bypass valve actuations.

Measured turbine stop valve and bypass valve positions between initial and end of actuation were not available for this transient.

The stop valve behavior can be reasonably estimated from the opening to closing time. However, the transient response Is quite sensitive to the bypass valve behavior. The bypass valve opening speed of the 00Yh model was adjusted until the calculated transient turbtine inlet pressure agreed with maasuroment. This adjustment was made for only the Initial bypass valve opening speed and, thereafter bypass valve position was controlled based on the plant control Var.aeters. The remainder of the test modeling is similar to that of the P9-2 test 11-53 xix4

comparison. The fuel rod gap heat transfer coefficient was selected to be 600 Btu/hr-fts-F.

The turbine trip test conducted at 104 provided a reactor and operating state that was quite different from PO-2. The test at KK0 corresponded to an end-of-cycle condition with all contral rods fully withdrawn and with the reactor at 77 percent of full rated power and 86.5 percent of full rated core flow. The reactor itself Is considerably smaller in size than P0-2 and has a somewhat different AYstMW-jnclIWadlng two turbL-Igene~rati ng uits. The turbine trip test at 1KK resulted in a milder transient than the tests at PB-2. The ODYN results compared to the test data showed the same general agreement as was observed for PB-2 for the response of the core power as a function of time. The calculated steamline pressure response for the 1304 turbine trip appears to be in good agreement with measurement. The 111 co*parisons appear to be in slightly better agreement with measurement than do the PB-2 comparisons. As previously discussed, the characteristics of the bypass valve were adjusted to give a good agreement with the measured staamline pressure.

The measurements of dome pressure showed some oscillations. Since these oscillations did not manifest themselves in the neutron flux measurements, they were attributed t instrument line disturbances and were not considered to be actual pressure oscillations. There were also oscillations in core exit pressure measurements. Similar oscillations were not observed'in the P5-2 tests. These oscillations 11-54 ILXX

were also attributed to the instrument line disturbances since no oscillations were observed in neutron flux.

The calculated pressure responses pass through the data up to 1.8 seconds of the transient time. After 1.8 seconds the calculated pressure are higher týan those measured. The calculated core exit pressure had a 40 millisecond delay behind the data. This was attributed to the modeling of staam separator inertia. We agree with General Electric that the overall shape of the core exit pressure response is duplicated well by the ODYN coda. The agreement between the calculated and measured pressures in the dome and the steamline Is also reasonably good. There Is no conservatism in calculation of pressures up to 1.8 second of transient time.

The measurment of neutron flux indicates a double peak behavior.

This double peak was attributed to an oscillation in core pressure which was thought to be enhanced by KKM bypass characteristics. The DY0,cods overpredicted the initial neutron flux peak by approximately S= and undarpredictod the second peak. We estimated that the integral of the calculated nuclear power was higher by approximately 2C% than the data. Figures 7 and 8 present the comparisons of measured and calculated axial neutron and prompt neutron fluxes respectively.

The calculated value of ACPR/ICPR was about 9.= conservative relative to the value calculated using measured quantities (see Table 1).

11-65 lxxi

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Although there is conservatism of 9.=; in ACPR/ICPR, the difference in absolute values is small; I.e., 0.007 in terms of ACP*PCPR.

Since the value of 1CPR was L279, the value of ACPR is app .rolately 0.0M According to General Electric the mnaximu practical accuracy In ACPR is 0.01 (Volume 111). In addition. KICH transient Is a relatively mild transient. Henca, we do not give any credit for conservatism In ACPR/fCPR prediction.

4. Qualification Using Ano-uer Comuter Code - Audit Calculations Another Important mans of qualifying a code Is to compare the results of calculations with the results obtained from another code. The two codes should be as Independent as possible Including the neutronic Input parameters. The BNL-TlIGL (Reference 24) and PLAP-33 (Reference 25) codes are fully capable of analyzing these BWR turbine trip tests and satisfy the requirement of Independence. The nuclear data base for deriving the Input for the INL-TWIGL/RELAP-3B codes also satisifies the requiramnt of independence.

a. Pevelooment of Calculational Method A calculational method for the analysis of the tu*ine trip transients was developed at BNL using the RELAP3B and IUL-TTIGL computer codes.

This method was developed under two NRC Technical Assistance Programs supplementing each other, and uses the codes In an iterative manner.

The details of the method are presented In Reference 26. The RELAP2B code is used to perform the system transient analysis for the audit calculations. The BNL-TWIGL code is used to calculate the reactivity feedbacks and core power transient. The BHL-TTIGL code performs a II'58 ixxiv

space-time analysis of core neutron4c' and thermal hydraulics with feedback in two dimensions (reference 21).

The BNL-lWIGL code has a number of advantages over the ODYN code.

The calculation can be performed with twe neutron energy groups in two-dimensional (r,) cylindrical geometry. It as the capability of allowing for five radial scrm zones. Any important radial effects will, therefore, be calculated by BHL-TNIGL. The DNL-lIGL code also.

has two disadvantages relative to the ODYN code. These disadvantages are: (1) the lack of a bypass flow channel, and (2) the Independence of the Doppler reactivity with void fraction. Weighing these advantages and disadvantages of BHL*-TW!L relative to the ODYN code, it Is our Judgment that they will not adversely affect the comparison of the two codes for the turbine trip transient discussed herein.

The calculae4onal method was developed using the Peach Bottom tests as a bench mark. Assuming the measured power history (power vs.

time) in the cre as Input, RELAP38 calculates the system thermal hydraulic paromters and provides the BNL-TWICL code with the time dependent core inlet boundary conditions, i.e., pressure, flow and temperature variations with time. Then, the BNL-oIGL code performs the spacr-tmenanalysis of the core neutronics and thermal-hydraulics.

The calculated power history is then compared with the measured power which was input to the RELAP38 code. If the differences are large the calculated power history Is used in the RELAP39 code and the cal culations are repeated until the power history calculated by the BNL-TIVGL code is In good agreement with the power history input t 11-59 3lxxv

the RELAP36 code. This method was used for both the Peach lottom tests and the licensing audit calculations (turbine trip without bypass transient).

b. Peach Bot*om. Tests and Audit Calculations The RELAP3S/B0L*rW7GL calculational method described above was employed by BNL to analyze the Peach Bottom transient tests. The calculated power history agreed well with the measured power history.

There is also good agreement between the other calculated and

..... -measuredparaueters.-The-core-physics results that- were -obtained by BNL are presented In Reference 26. Reference 26, also discusses the geometric moaeling, the neutron cross sections, and the initial Izatlon of the transients. These calculations confirmed the adequacy of the BIL-I4G./RELAP-3B modeling for computing 6WR turbine trip transients. Figures 9 through 14 show samles of these agreements.

• Revised BNLM curves in Figures 12 through214 refer to a mor* detailed BNL model which will be explained subsequently.

Calculations performed with the OM code also agreed very well with the experimental results although the neutron flux predictions were slightly conservative. We believe that this can be attributed to the slightly higher 0DY0 pressure predictions during the transient. The power history calculated by BhL provides better agreaeent with the experimental data on a best estimate basis than the 0DYI code predictions.

uZ-s0 lxxvi

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At a meeting on July 14, 2978 attended by GE and our consultants from 81L, a turbine trip without bypass transient CTTWOB) was defined for calculation by GE with the ODYN code and by BNL with the INL-TWIGL/

RELAP-38 codes. This TTWOB transient was for P8-2 at end-uf-cycle 2 with the reactor at an all rods out condition and with a Haling core power distribution. The reactor trip was assumed to occur from the primary trip signal for this transient, i.e., the position of the turbine stop or control valve. All of the system input parameters were discussed and values were assigned. The reactor was assumed to be operating at a 104.5 percent of full rated power and at 100 percent of rated core flow.

The Initial calculations by GE and BINL differed considerably. The total core power as a function of time calculated by 4L %.wsabout 60 percent greater in energ output although the initial rise and falloff of the power was about the same. The BNL calculation predicted a peak power of over 7 times the initial core power at about 0.9 seconds. The GE calculation resulted in a peak power of about 4 times the initial core power at about 1.0 second.

A GE evaluation of its calculation resulted In finding two significant errors that led to a new GE calculation. One of the errors was the steamline length. It had originally been Input as 460 feet whereas the value should have been 400 feet. GE also found that one of its processing codes had Improperly ac=cunted for the Doppler reactivity feedback variation with void fraction. This new GE calculation resulted In a more severe transient than the earlier 11-67 imj*i:u

calculation. The new GE prediction of peak power was about 5.3 times the Initial core pover at about 0.9 seconds. This GE calculation had an earlier rise and an earlier fall-off of the total care power than the BNL calculation. The BNL calculation still predicted a greater energy output for the transient by about 20-25 percent. A comparison of the reactivity components showed that the void. scram, Doppler, and net reactivities as a function of time differed, significantly between the BNL and now GE calculation. As an exa tle, the BNL calculationi resulted in a prompt critical calculation with a maximum eot reactivity of over one dollar. The GE calculation resulted in a mIamum net reactivity somewhat less than 0.8 dollars.

Since it was our expection that the BNL and GE calculations would be In better agreement, a maeting with General Electric at BNL was held to resolve differences between the calculations. This meeting was held from September 27 through September 29, 1978 with GE, BNL, and NRC in attendance. Reference 27. The main differences noted between the two calculations are listed below.

rrB4 REMARK L. Relief valves (a) Set Points GE values too large (b) Delay time 94L did not Include (c) Bank capacities 8NL did not use GE values (d) Time constant for full flow BSL did not include 7- Turtine Inlet pressure GE value too large

3. Steam separator modeling (a) Separator L/A BNL value low (b) Separator mass BNL water inventory too low 11-68 lxxxiv

TTM(Camt. REMARX (Cont.)

4. Doppler reactivity feedback OHL does not include variation with void fraction S. Bypass heating effects BHL does not Include

6. Fuel gap c*nductnce BNL used variable value ( 400-500) whereas GE- used a constant value of 1000 In addition, some of the OHL neutronic data were also compared to corresponding GE data. The beginning-of-cycle infinite aultlpli cation factor (K.) wu comared for a number of fuel types both witn and without a control blade and as a function of void fraction. Only small differences were noted b*eteen the various sets of data. The initial axial distribution was also cmapared and again only small differenas were noted. It was also noted that the BNL contral worth was about IS percent larger than that of GE. These neutron cross section and K. data as a function of fuel exposure and void fraction were later provided to the staff by GE for the two dominant fuel types In the PO-2 core (Raferencas 28 and 29).

Void rtactivity coefficients extracted from the BOL and GE l£ OS calculations Indicate that the BNL value at the start of the transient is larger in magnitude by about 14 percent than the GE value. This larger BlL void coefficient Is consistent with the lattice physics data that Is used. However, the neutron effective void correlation used by General Electric conpensates for a large part of this difference (Reference 34).

A reanalysis of the turbine trip without bypass transient was performed by BL. Both analyses were presented In Reference 33.

11-69 i=XXv

Some sensitivity studies were also performed. Same of the differences noted in the meeting did not change the ML results substantially.

However the difference in the separator inventories and the required renodaltzalton around the separators to accommodate proper inven tories Inside and outside of the separators and Inclusion of a separate flow path between the steam dome and outside of the separators (bulkwatar), reduced the neutron power and the total energy output in the licensing basis transient (TTWOB). The total energy output, the integral of the neutron power, predicted by SUL during the transient was less thn that In the second calculation performed by General Electric. However, the General Electric calculation still Indicated an earlier rise and an earlier fall-off of the total core power than the ENL calculation. Figure 15 presents these tw OHL calculations as well as the General Electric calculation.

The primary reason for the change In the energy outputs as well as disagreemnt In the shape of the neutron power transient was the new inlet c*re flow calculation by the BML. The core inlet flow in the second OML calculation was in closer agreement with the second GE calculation in that It exhibited similar oscillatory behavior.

However, there were still soe differences in amplitudes. It should be noted that the differences in flow variation during the transient beten the t- SNL calculations were within 1.X of each other.

Judging from the BNL studies, Reference 33, we conclude that the modeling of separators is significant in predicting the core Inlet flow. We also note that the HL modeling of the separators is still deficient in that the Inertia ta*r, L/A, does not depend on the 12-70 lmXV1

BWR LicensinEJ-bash Tran~l ent BM0 700.0 con.0 500.0

-q I

4-0

'-4 400.0 tn L

300.0 (L

200.0 100.0 0.0 0.6 TI me(si)

I

quality at the entrance of the separators. The Q00T code contains the modeling of the L/A term which derived Its basis from experimental data obtained from separators. Hence, we judge that the 0DYT model should predict the core inlet flow more accurately than does the BNL model, and-that the neutron power transient should also be more accurately predicted by the ODYh code.

Reference 33 indicates that previous and revised BNL models predict almost similar core inlet flow variations at the beginning of the Peach Bottom turbine trip taest. However, there ar large differences between predictions after 0.8 sac. Since the power peaks occur before 0.8 sec in the Peach Batto tests, these large differences'in inlet flow predictions do not alter the predictions of neutron powers as Illustrated in Figures 22 through 14. However, as shown in the analysis of licensing basis transient, the separator inertia term and its modeling Is important In predicting the transient behavior'(or amplitude of oscillations) of the core inlet flow.

Reference 33 also Indicated that the heat flux predictions In the second OHL calculation were lower for the portion of the transient where highest ACPRs were expected to occur than those calculated by General Electric. This was expected since the Integral of neutron flux in the second BIlL calculation was smaller than that calculated by General Electric. BIlL did not perform ACVR calculations. However, the predictions of heat flux would suggest, and we would expect that the second BOL calculations would produce less ACPR than that calculated by General Electric.

11-72 IzXXViil

MNL did not report heat fluxes in their first calculations. However, the integral of the neutron flux was almost the same as that calculated by General Electric. Hence, we expect similar severity for ACPR values If AMCR calculations were made using the first calculations performed by SN!L.

A third analysis -of the TTl B transient was performed by BNL using GE calculated values of the care exit pressure and cr*e inlet flow. The BNL-TIGL calculation now predicted a transient with similar initial power rise and fall-off characteristics as the GE ODYN calculation although the peak power was higher in the SNL calculation. A sensitivity calculation with a 5 percent change In the void reac tivity feedback resulted In a BNL-T1WGL power transient that compared very well with the corresponding GE results. The change of 5S in void reactivity or the coefficient is well within the calculated uncertainty of Z as presented in Section IL.A.S.

These audit calculations established the fact that core inlet flow is a very sensitive parameter. The core inlet flow measurements (i.e..

the jet. pump Ap measurements) in the Peach Bottom tests contained some errors. Zn Section I1.2.3.a, where qualification of the 0DYN coe using Peach Bottom tests was evaluated, many comparisons betwten various parameters (such as pressure and neutron flux) were made and these parameters were always found to be conservative relative to data. Howver, despite these conservative features, the calculated values of ACPR cannot be c=nsidered as conservative. This was also poined out In Section 11.8.3.a. Based on the information submitted, 11-73 2=lx~

It is our judgment that there is some nonconservatism in core inlet flow calculation In the 0DYN code overcoming all other conservatisms.

We conclude that., although a precise audit of the GE 0DYh code was not obtained by the BlL-TWIGL/RELAP-38 codes for this licensing basis 1N38 transient, the analyses performed by BNL provided us with.

valuable insi*hts concerning this transient. We conclude that the primary reason for the disagreement of the BNL-TWIGL/RELAP-3B TTW0B results with the GE results Is due to core Inlet flow differences.

Judging from the audit calculations as well as Peach Bottom test results, we also conclude that differemaes In predictions on the order of 2= In prediction of peak neutron flux can be expected using different computer codes which represent the state of the art.

S. .Summary of Code Qualification In summary, we find that the 0DYh is a best estimate code containing models developed from first principles and provides good predictions of existing experimental data. The experimental data were obtained from separate effects and integral plant tests. The separate effects tests include core power measurents from various plants and heated tube tests to verify the void fraction model. Integral plant tests were performed at Peach Botton Unit 2 and K104. Comparison of the test data and calculations indicates that the agreemaent is within the uncertainties calculated in Section A. We find that the ACPR predictions from the 0DYN and SCAT codes are neither conservative nor nonconservative. They predict the available data well.

11-74 zc

The 00h-SCAT prediction of the three Peach Bottom transient tests and one 1(0 transient test demonstrated a 2c uncertainty of approximately 3,* of ACPR/ICPR at a 95% confidence level. We have determined this using X2 distribution. No credit was given for measurement errors. This results in a 2c AUPR/ICPR" uncertainty of 0.068 for a transient which degrades the CPR from an initial value of 1.30 to the limit of 1.06. Since these tests represent a very limited data base, It is likely that the 26 uncertainty can be reduced significantly by the acquisition of additional test data for comparison to code predictions. Hence, we reeomend that additional integral plant- t*sts -be performed-to qualify the code with a higher confidence.

C. EVALUATION OF DM MARGIN The OMYN statistical analysis was performed by General Electric at our request in order to provide a quantitIve basis for determining if the ODYN licensing basis contains an acceptable level of conservatisa. Two quantities were calculated in this analysis: the probability of the expected ACPR exceeding the licensing basis ACPR; and the probability of exceeding the thermal hydraulic design basis (i.e.. probability of exceeding 0.=Z of fuel in Boiling Transition).

The ODYN Code is intended to be used to calculate the change in Critical Power Ratio (CPR) during rapid pressurization transients such as the loss of load and feedwater controller failure transients. This information is used in com bination with the General Electric Thermal Analysis Basis (GETAB) CPR safety limit* to establish the operating limit CPR. GWTAB is a statistical analysis H-75 xci

which determines the value of CPR which corresponds to 0.J of the fuel rods in Boiling Transition. The GETAS analysis considers the effects of uncertainties on input parameters such as power, coolant tamperatue and flow as well as uncertainties in the GEL correlation.

Uncertainties in the ODYh Code need to be considered since these will affect the probability of exceeing the thermal-hydraulic design basis. One method of accounting for t1h effects of ODY0 code uncera*ntes Is to include uncer tainties directly Into the GUTAS statistical analysis. A second method is to assure that the OYH licensing calculation gives a sufficiently conservative value of ACPR to assure that the thermal-hydraulic design basis Is not exceeded.

GE has chosen to use the second methd in demonstrating the acceptability of the ODYh licensing basis.

We have determined that this approach is aczeptable In principle. In addltion, we have determined that an acceptable level of conservatism for the OH licensing basis corresponds to a 6% probability of exceeding the thermal hydraulic design basis.

General Electric has provided statistical analyses of the lass of load CTuroine Trip) and feedwater controller failure transients. These analyses use Monte Carlo calculations to predict ACMR with a second order response surface which simulates ODYN calculations. The input parameters In the response surface are:

initial power; control rod drive (CRO) speed; exposure Index (a measure of axial power shape effects): OYNTcode uncertainty; and response surface fitting uncertainties.

11-76

,xcii

The response surface was generated through a regression analysis of ACPR calculations performed using Input from the ODY0Code. The accuracy of the response surface was tested by General Electric by comparing the results of 0YN calculations to the results of response surface calculations. The accuracy checks were done for 15 load rejection transients for a BWR/3 EOC-6 and for 15 load rejection transients for a BWR/4 MD-4. These comparisons showed good agreement between the to methods. In addition, a regressional fitting error was developed from these comparisons and this fitting error was added to the response surface. This error was fotmd to have a range of one standard deviation values of 0.0076 ACPR/ICPR to 0.0126 ACPR/ICPR depending on the plant type, the time in cycle, and the transient of interest. This range of errors is three to four times .smaller than General Electric's estimate of the 00T code uncertainty (0.033 ACPR/ICPR) or our estimate of (0.044 ACPR/ICPR) see Table I. This indicates that the response surface is a faithful repro duction of the ODYN calculational results and that the response surface can be used to establish the effect of ODY0code uncertainties on the probability of exceeding the thermal-hydraulic design basis.

The distribution functions of each of the Input variables (initial power, CR0 speed, exposure Index, and code uncertainty) were reviewed. The uncertainties of the 00Yh code are discussed extensively In the code review section of this report and will not be repeated here. The uncertainty on Initial power level used by GE was + Z. We requested additional information to substantiate this value and were given extensive Information on the various elements in the plant energy balance and the uncertainties associated with each of these elements.*

The elements of the energy balance were checked against the ASHE standard for determining energy output from a nuclear 'plant, 'ASM4 Performance Test Codes, 11-77 Xciii

Test Coad for Nuclear Steam Supply Systems (PTC 32.I--1969). In addition. the uncertainty values for each element were reviewed and found to be reasonable.

We have concluded that the = uncertainty (at one standard deviation) is an acceptable value for power measurement uncertainty.

In support of the assumed distribution of CR. speeds, General Electric has provided the results of tests from 13 operating BWRs. The total data base includes 3,985 individual CRD scrams. The information was presented in considerable detail, Including the mean values and standard deviations of the times toS*, 2E=, 5= and 90 _insertion for various plant types and for full core and partial core scram tests. An extnsive and convincing statistical analysis of the data was also presented. Each data set was tested to determine If it could be tasted as part of a larger data set; and only those data set which were found to be statistically alike, at a high confidence level, were treated together. Statistical tests were performed by General Electric to determine the significance of: variations among BWR designs; variations betw*en full core tests and partial core tests; variations among operating plants; variations among scram testss; and variations among individual drives within scram tests. We conclude that these CRO scram tests are Indicative of past operating experience and that th man values and standard deviations of CR0 speed can be chosen for the statistical analysis of the 00YN code. However; we cannot conclude that these CRO scram tests will be indicative of future reactor scram speed performance. In addition, It Is also necessary to demonstrate that the scram characteristics of an Individual reactor U be licensed can be represented by the distribution used in the analysis. The scram characteristics of an individual reactor should belong to the same population. General Electric should provide an assurance or appropriate 11-78 xctLV

modifications to Technical Specifications to demonstrate that the scram characteristics indeed belong to the same population or can be represented by the same distribution. General Electric should also assess the impact of the use of best estimate distributions on providing this assurance.

The transient response to rapid overpressure events is dependent on the core average axial pover distribution and axial exposure distribution since these strongly influence both the void and control rod reactivity feedback. General Electric has defined Exposure Index as a measure of the axial exposure distri bution. Exposure Index indicates the extant to which an actual axial exposure distribution differs from the ideal, design axial exposure distribution (Haling distribution). ODYN licensing calcqlations use the Haling distribution as input. General Electric proposed to show the conservatism associated with this assumption by establishing that the axial exposure distributions actually encountered during operation are more favorable than the Haling distribution.

This conservatism was quantified as part of the overall ODYK statistical analysis by Including Exposure Index as one of the input variables in the response surface.

To establish a basis for the expected distribution of Exposure Indices, General Electric presented data from 21 operating reactors at end of cycle conditions and 15 data points for 5 operating reactors at mid-cycle conditions. In response to a request for additional data on observed Exposure Index, General Electric provided 8 additional data points. Because of the limited number of data points and the large scatter in the data we were led to question the assumption that thetdata was normally distributed. The Individual data points obtained from General Electric were subjected to the V-test for normality by 11-79 Xc,

the NRC, Applied Statistics Branch. This test indicated that there was not a sufficient reason to reject the assumption that the data were normally distributed. Based on this Information, the Inclusion of Exposure Index in the stUtistical analysis as a normally distributed variable Is acceptable. As in the case with the use of measured CRD.speeds, the implications of using best estimate values of Exposure ,d*ex based on past operating experience and the associated need for assurance and modifications to Technical Specifications to demonstrate continued acceptable performance were not addressed. Since we cannot determine appropriate modifications necessary for demonstration of the conservatism due to inability to, operate at Haling power shape for each reactor to be licensed, we find that the use of the variation of power shape from that of a Halinj shape in the statistical analysis is not appropriate.

General Electric has performed the statistical analysis using several different sets of assumptions relative to the response surface input parameters. The probability of exceeding the ODYN licensing basis AUR was calculated for each case. This corresponds to the probability of exceeding the GETAB CPR safety limit. The probability of exceeding the criteria of 0.2% of fuel rods in Boiling Transition was also calculated for some of these cases. Since General Electric has proposed that the safety limit for BWRs be based on the GETAB CPR safety limit, It is appropriate to use the probability of exceeding this value as the basis for accepting the proposed licensing method. As stated previously, we have determined that a S probability of exceeding the GETAB CPR limit is acceptable. Unless the safety limit for BMRs is redefined by General Electric and reevaluated by the staff, the use of the probability of exceeding 0.= df fuel in boiling transition is not an appropriate basis for Judging the acceptability of the ODYN licensing basis.

xcvi

In conclusion, we recomend that General Electric reperforn the statistical analysis to demonstrate the app priateness of the margin to the GETAB limit.

This statistical analysis should not take credit for conservatism in the Haling power distribution. It may take credit for distribution in scram speeds If General Electric demonstrates tha t the distribution used in the analysis Is applicable to the' plant specific case. The analysis should also be performed using th*e code uncertainrties asr evised by the staff (: 0.088 ACPR/ZCPR)twhich was based on the plant test data. General Electric may wish to convolute additional variables In the stati rtical analysis if assurance for conservatism

-for each-spectfic applicationAs :rovitdad.

II-"*

xci+/-./x-cv:ti

11Z. STAFF POSITION We stated our position on the ODYN code and its application in Reference 35. The following is a statment of that position.

I. ACPR Calculations' The analysis for ACPR must be performed in accordance with either approach A or approach B.

A. ACPR Calculations with Marotn Penalty This approach Is comprised of the three step calculation which follows:

1. Perform ACPR calculations using the ODYN and the improved SCAT (Reference 36) codes for the transients in Table III and using the input parameters in the manner proposed In pags 3-1 through 3-4 of NEDE-24154-P. The sensitive Input parameters are. listd in Table IV.

2* Determine ICPR (operating Initial critical power ratio) by adding ACPR calculated In step 1 above to the GETA8 safety limit. Calculate ACP*/ICPL

3. Determine the new value of ICPR by adding 0.044 to the value of AC:PR/ICPR calculated in step 2 above. Apply this margin to Chapter 15 analysis of the FSARs submitted for OLi, and CPs and tU reloads.

111-1 xcix

The margin of 0.044 is obtained from consideration of uncertainties in components listed in Table 1.

A sample calculation is presented below:

Stan 1.

Assume that ACMR calculations using the ODYN licensing basis have been performed and the result Is ACURC w .14 where the subscript c refers to calculations.

Stan 2 Calculate ICPR based on the calculations.

ICPRc w 1.06 + .14 w 1.20 where the GETAB limit is L.06.

CPR .14 c

Stec 3 ACPRnew v .117 + 0.044 a .1M ICPRnew ACPR, a U-new AMR 21.

A -* .14 .252 noc 1CPRnow ,aL.06 + .29 a L125 C

S. ~Statistical Amroach for Reduction of Ma*in Penalty General Electric assessed the probability of the ACPR during a limiting transient exceeding the AVR calculated for the proposed licensing basis transient (NEDE-251J4-P response to question 4). The General Electric study demonstrated that this probability, based on operating data over several fuel cycles from a group of plants, Is very low. The key paramters in the study ire scram speed, power level, power distribution, and an estimate of ODYN uncertainties. The proposed approach utilizes the conservatism inherent in the statistical deviation of the actual operating conditions from the limiting conditions assumed for the first three parameters In licensing basis calculations to compensate fo*r potential non-conservatisms from the OYh uncartainties.

The staff has concluded that the use of end-of-cycle power distributions from multi-cycles for several reactors to obtain credit for margin conservatism relative to Haling power distribution is not appropriate.

There Is no assurance that the end-of-cycle power distribution conservatisms obtained from operating reactor history are representative of the eno-of cycle conditions.which will exist for the specific core. We have also concluded that scram speed data used in the GE statistical assessment must be proved applicable to specific license and reload.applications. In order to take credit for conservatism In the scram speed performance for reloads, it must be demonstrated that there Is insufficient reason to reject the plant-specific scram speed as being within the distribution assumed In the statistical analysis. For CP and OL, the scram speed 111-3 ci

distribution for the specific plant must be demonstrated consistent with those used In the statistical approach. Similar design and prototypic performance characteristics coupled with appropriate technical specifications on scram speed' performance could provide acceptable evidence of the applicability of the data base.

Statistical convolution of the power measurement uncertainties to take credit for full power operation at a power level value below that used in licensing calculations is acceptable to the staff. However, plant specific

_ -- procedures-to -oparate .withiin -the-I Icansing-1 imit-must -be-taken into account In these calculations.

The code uncertainty penalty (0.044 in A&PR/ICPR) applied to the licensing calculations described in (A) does not account for unknown contributors.

Past experience has shown that additional margin in safety calculations is often needed to compensate for unknown non-consarvatismns in licensing calculations due to code errors or other factors. The 0DYN prediction of three Peach Bottom transient tests and one KIM transient test demonstrated a 2a uncertainty of approximately 37 of ACPR/1CPR at a 9% confidence level. This was determined using X2 distribution. No credit was given for measurement errors. This results in a 2c ACPRIlCPR uncertainty of 0.068 for a transient which degrades the CPR from an initial value of L.30 to the limit of 1.06. Since these tests represent a very limited date base, it is likely that the 2a uncertainty can be reduced significantly by the acquisition of additional test data for comparison to code predic tions. Therefore, the magnitude of the code uncertainty used in the statistical convolution may be reduced to a value consistent with the 2a 111-4 cii

value of &CPR/ICPR uncertainty at a 9S5 confidence level when such a red.ction can be Justified by additional transient test data.

In sumary, the staff has concluded that the statistical approach to compensate for potential non-conversatisms from the ODYh uncertainties is acceptable with the following limitations.

1. Power distribution conservatisms should be excluded.

2. Scram speed conservatisms must be deonstrated to be applicable to plant specific cases.

3. Calculations should be performed using a code uncertainty value which is 37= of the ACPR/fCPR for a limiting transient to account for code uncertainties, including unknown contributors (e.g., code errors),

based on the approved transient test data base. This results in a value of t 0.068 in ACVR/ICPR uncertainty for a transient extending over a CPR range of 1.30 to 1.06.

4. The transient test data base maust be expanded and submitted for staff review t* justify any reduction in the value of 0YIT Coda uncertainty (2W value of ACPR/ICPR at a 95% confidence level).

S. A new statistical analysis conforming with these limitations must be provided.

111-5 ciii

An accaptable licensing basis using the Option 9 statistical approach Is a 95/95 ACPR/ICPR for the limiting event. This can be established In one of two ways:

a. Option B can be applied on a plant-specific basis - i.e., statistical analyses aerformed on a particular plant to determine Its 95/95 ACRR/ICPL The statistical analysis procedures to be used are those defined in the 00Yh Licensing Topical Report (LTR). Volume 3, except for the modifications required by the NRC in Reference 35.

b. !Dtion B can be applied on a generic basis. This Involves the establish ment of generic &PDR/CPR adjustment factors for groupings of similar-type plants (the groupings used in the 00Yh LTR are considered to be an acceptable matrix) which can then be applied to the plantospecific ACVR/ZCPR calculations from the 0YN LTR deterministic approach to derive the estimated 95/95 values. Each plant group and transient type correction factor is based on an analysis of a typical plant in that group (e.g., 6W V/3, 4/5, and 6), In which the differences between the 95/95 ACPR/ICPR calculated per the ODYN LTR deterministic approach is determined for a specific transient (e.g., load rejection vithout bypass). The difference, which may be positive or negative, is designatad the plant group adjust*ent factor for that transient.

The generic ACPR/ICPR adjustment factors established for the various plant groupings must be submitted to the NRC for review.

111-6 civ

11. PRESSURE CALCULATIONS Calculations should be performed for the Main Steam Isolation Value closure event with position switch scram failure using the values listed in Table I* as per staff evaluation to arrive at the overall code uncertainty in pressure calculation. Add this uncertainty to the ODYN calculated pressure for this event in OL, CP and reload applications. If General Electric can demonstrate that this uncertainty is very small (e.g., by a factor of 10 or sore) relative tU the bias In determining ASJE Vessel Overpressure limit, no addition of uncertainty to the calculations of pressure is needed.

we note that there is an error In Enclosure 2 of Reference 35. The bounding values of the drift flux parameters should have been in conformancz with Table I as per staff evaluation.

111-7 CV

TABLE. III TRANSIETS TO BE ANALYZED USING THE ODYN CODE A. For Thermal Limit Evaluatio.n Thermally Limiting or Near Limiting Event (Tyoically)

1. Feecwater Control ler Fallure X aximutm Demand

2. Pressure Regulator Failure - Closed

3. Generator Load Rejection X

4. Turbine Trip X

5. Main Steamline Isolation Valve Closures

6. Loss of Condenser Vacuum

7. Loss of Auxiliary Poer x All Grid Connections B. For ASHE Vessel Over.ressure Protection Pressure Limiting

1. NSIV Closure witth Position Switch Scrm Failure (i.e.. MSZV Flux Scrmu) X 111-8 cvi

TABLE IV INPUT PARAMETERS SENSITIVE FOR THE ANALYSES Z..CRD scram speed - at tehcnical specification limit.

2. Scram setpolnts - at technical specification limits.

3. Pr -tectian-systamlogic delays - at equipment specification limits.

4. Relief valve capacities - inimu specified.

S. Relief valve satpoInts and response - all valves at specified uper limits ef setpoints and slowest specified response.

6. Pressure drop from vessel to tel ief valves - maximum value.

7. Stilneadvess geometry -p1atnqu valves.

8. Initial power and staam flow - maximum plant capability.

9. Initial pressure and core flow - design values at maximu plant capability.

20. Care exposure/power distribution - consistent with Haling mode of operation.

Ml. Feedwater conditions - maximum temperature (maximum core average void content).

111-9 cvii

111. Other Limitations

1. Listing of important input variables such as listed in Table IV and initial plant parameters Including but not limited to control system characteristics as depicted id Figures 4-13 through 4-16 of NEDO-24254, Vol. 1, but with nunerical values provided should be provided with each submittal. The initial control system characteristics, including the model used In the selection of initial settings, shall be defined and substantiated in terms of the design basis for each control system of the plant. We .understand that neutronic parameters which were originally obtained from the GE 3-0 Core Simulator and collapsed to provide input to the MYN code, are best est*mate. If there Is a significant change in this calculational method altaring the input parameters, General Electric should submit the new procedure to NRC for its evaluation. The code uncertainty value of

. 0.068 ACPR/ICPR based on the Peach Bottom and KIK test data includes uncertainties In this calculatlonal method since this method was used in comparison of test data with cdoe predictions. Hence, any significant change in this procedure will change the code uncertainty.

2. A minimum of eight nodes should be used to represent the steam line.

However, the maximum length of any node should niot be more than 100 ft.

3. The cdoe cannot predict accurately care inlet flow oscillations with frequencies above S Hz. Although we do not expect any inlet flow oscilla tion above frequency of 5 Hz for the transients listed in Table III, General Electric should verify that the harmonic components above 5 Hz arte indeed very small if very rapid variations of flow in these transients are predicted.

111-20 cviii

4. The transients listed in Table III are short term licensing transients.

If the code Is intended to be used for long term transients or different types of overpressurization transients such as AWS, appropriate modifications should be made.

niZ-n cix

References

1. NEDE-2401-P, "Generic Reload Fuel Application," Chapter 4, Hydraulic Model Description, Hay 1977.

2. NEDO-20953, "Three-Dimenslonal BWR Care Simulator," J. A. Wooley, May 1976.

3. NEDO-20566, "General Electric Cozoany Analytical Model for Loss-of-Coolant Analysis in Accordance with 10 CFR 50, Appendix K, Volume 2," January 1976.

4. NRC letter from D. C. Elsenhut to R. Gridley, dated May 12, 1978.

5. NEDO-3O02, Amendments 10802-01 and 02, "Analytical Methods of Plant Transient Evaluations of the General Electric Bolling Water React*r,'

R. B. Linford, February 1973.

6. NUREG-0460, V. 11, Anticipated Transients Without Scrum for Liot Water Reactrs, AprIl 1978.

7. NEDO-10299, "Core Flow Distribution in Modern Boiling Water Reactor as Measured in Monticello," January 1971.

8. APED-4762, "Performance Tests of Axial Flow Primary Steam Separators,"

C. H. Robbins, January 1965.

9. NEDO-13388, "2-Phase Flow in Boiling Water Nuclear Reactors,* R. T. Lahey, July 1974.

10. Isbin, H. S., Sher, N. C., Eddy, K. C., "Void Fractions in Two-Phase Steam-Water Flow," AIChE Journal, Vol. 3, No. 1, 126-142, March, 1957.

1.. Isbin, H. S., Rodriquez, H. A., Larson, H. C., and Pattie, 8. D., "Void Fractions In Two-Phasm Flow," AIChE Journal, Vol. 5, No. 4, 427-432, Dec.

1959.

22. Marchaterre, 1. F., "The Effect of Pressure on Rolling Density in Multiple Rectangular Channels,9 ANL-522, Feb., 1956.

13. Janssen, E., Kesvinen, J. A., "Two-Phase Pressure Drop in Straight Pipes and Channels; Water-Steam Mixtures at 600 to 1400 psia," GEAP-46E6, [ay 1964.

14. Cook, W. H., "*oilingDensity in Ver.Ical Rectangular Multichannel Sections with Natural Circulation," ANL-S621, Nov. 1956.

25. Ishil, N., "One-Dlmensional Drift-Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes,"

ANL-77-47, October 1977.

122-u2 cx

15. Frigg Loop Project, Frigg-2, AB Atomenergi, Stockholm, Sweden, 1968.

17. Roubani, S. Z., 'Void Measurements in the Region of Subcooled and Low

.Quality Boiling,' Symposium on Two-Phase Flow, University of Exeter, Devon, England, June 1965.

18. Rouhani, S. L, "Void Measurements in the Region of Subc$oled and Low-Quality Boiling,N Park 11, AE-RTL-788, Aktiebolaget Atomenergi, Studsvik, Swedmn, April, 1566.

19. NEDO-20913-P, "Lattice Physics Methods,* C. L Martin, June U876.

20. OGEGAP-111: A Model for the Prediction of Pellet-Claddlng Thermal Conductance in BWR Fuel Rods, General Electric Report NEDC-2012*,

Novemoer, 1973.

21. 0. F. Ross (NRC) letter to E. 0. Fuller (GM) dated June 2, 1278.

22. EPRI NP-S64, "Transient and Stability Tests at Peach Bottom Atomic Power Station Unit 2 at End of Cycle 2,4 L. A. Carmichael and R. 0. Niemi, June 1978.

23. Letter from K. V. Cook to R. L Tedesco, MHR 3137-78, 'Transmittal of Responses to Round 2 Questions on the ODYN Transient Model,'* dated

-Dec. 13, 1978.

24. ENL-NUREG-28925, *DNL-TVIGL, A Program for Calculating Rapid W Core Transients,' 0. J. Diamond, Ed., October 1976.

25. BNLNUREG220U, 'User's Manual for RELAP-3B°4V 220: A Reactor System Transient Code,* 1877.

26. BNL-WURES-24903, 'Core Analysis of Peach Bottom-2 Turbine Trip Tests,*

N. S. Chang, D. J. Diamond, September 1978.

27. Memo from F. Odar to Z. . Roszt=oczy, uMeeting with General Electric at Brookhaven National Laboratory,8 October 17, 1878.

28. Letter from K. W. Cook of GE to Frank Schroeder of NRC, October 310, 1978 on Potential Differences between GE and SNL Models.

29. Letter from K. W. Cook of GE to Frank Schroeder of NRC, October 26, 1978, on Transmittal of Exposure Dependent Data.

30. Transcript of ACMS hearings held on March .*-20, 1879, Los Angeles, California.

31. Letter from L. V. Cook of GE to R. L Tedesco, Clarification of ODYN Model Uncertainties, MFN 123-79, dated April 30, 1979.

32. Letter from KL W. Cook of GE to RL F. Denise, Additional Void Fraction Information Requested for ODYN Review, MFN-19-79, August 27, 1579.

111-23 cxiL

33. BNL-NUREG-266U, *Analysis of LIcensing Basis Transients for a BWR/4."

M. S. Lu, H. S. Cheng, W. G. Shier, D. J. Diamond, K. M. Levine, Septa.oer 1979.

34. ENL-HUREG-23501, *A Space-Time Analysis of Void React.vity Feedbacl in Boiling Water Reactors,w H. S. Cheng, M. S. Lu, 0. J. Diamond, October 2977.

35. LeUter from R. P. Denise (NRC) to G. G. Sherwood (General Electric),*dated January 23, 1980.

35. Letter from K. W. Cook (General Electric to F. Schroeder and 0. G. Eismnhut (NRC), MPH M1-79, "Implementation of a Revised Procedure for Calculating Hot Channel Transient ACPR,I July 20, 2579.

I33-14 cxii1

Supplemen.tal Safety Evaluation For The General Electric Topical Report Qualification Of The One-Dimensional Core Transient Jbdel For Boiling Water Reactors RIEDO-24154 and NEDE-24154P Volumes 1. 11 and II Prepared By Reactor Systems Branch, DSI cxiii/cxiv

The Safety Evaluation Reporft on the ODYN code (Reference 2) is primarily an evaluation of the calculational model with little discussion of Implementation requirements. Reference 3 provides the Information required to bridge the gap between evaluation and implementation. Specifically. there are eight Items covered in Reference 3; these are:

1. ODYN Option 9 statistical adjustment factors,

2. Control rod drive scram insertion time conformance procedure for plants licensed under ODYN Option B,

3. Uncertainty in ODYN pressure calculations,

4. ODYN model temperature limits,

5. Uncertainty in subcooled boiling model,

6. Description of electronic hydraulic control model,

7. Listing of ODYN input variables,

8. Comparison of minimum critical power ratio operating limits established by REDY and ODYN.

Each of these Items is discussed below.

Item 1. Statistical AdJustment Factors Page 111-6 of Reference 2 allow two statistical approaches; one Is a plant specific statistical analysis and the other is a generic analysis for plant groups (e.g. BWR/2. 3, 4, 5, 6) and transients. The second approach Involves the establishment of generic &CPR/ICFR adjustment factors for groupings of similar-type plants which can be applied to plant-specific ACPR/ZCPR calculation from the ODYN licensing topical report (LTR) deterministic approach.

Reference 3 provides the statistical adjustment factors for the three transients which are normally limiting transients (load rejection or turbine trip without cXv

bypass, feedwater controller failure to maximum demand and pressure regulator downscale failure). These generic statistical adjustment facorsare shown in Table 1; we find them to be acceptable.

item 2. CD Scram Insertion Time Conformance Procedure Page IIZ-3 of Reference 2 states OIn order to take credit for conservatism in the scram speed performance ftr reloads,.it ast be demonstrated that there is Insufficient reason to reject the plant-specific scram-speed as being within the distribution assumed in the statistical analysis. For CP and CL, the scram speed distribution for the specific plant must be demonstrated consistent with those used in the statistical apprTach."

Goneral Electric presents the follovtzg procedure a5 one wVhic "#:icse ghe Staff*'s objecties for socra couformaace. . sh0uld be Doted that sae Utgl~Ils Using O0"M Option~I may desire to establish their. W.% conform~ance procedures.

7-e Procedure consists of testing, a: the 5= *-igIficance level, the scra=

hurn'e'112snce data at the 2C: Isertio position vwhch Is generated several times each cycle as required In the leaacZUc Control Systam Technical Specification (2o: Insertimn is repreeemtaurve of that portion of the gcr&L sot affec:ing the pressurization transien:). Mhe uIs*pe rod Bo:ch position closest to 20. (and tha approl'?iateTy adjusted time of Iasertta) is hzpwcts'd to be utilized In actual plant appllcation of this generic concept. Tor osas plants, the urveelllacea requ*r* *.s ser as folloma:

(1) al contol rods an seasured at bSegt=lg of cycle OMC, Md (2) = of control Wods are wasured evaI7 UD days drin4 c.cle CZ Is plant-dependant ad ranges from IQ to 50).

cXVi

At the eompsetion of each survei~ance test perforsed In cpliance .vich the technical epecIfIcation surveilla*ce requirments. the average value of a8 surveil*ace data at the 02a imsentio: position generated iL the cycle to date Is to be tested at the SZ sIpIf*ic*ce level agaLuwt the dSstribution assmed L the V= analyase. The suryin llance Wo(.attomo wh aech plant uasng this protedui will have to retain thzoughout the fuel cycle is the wmber of active eottol rods smasured for each surveilance test Othe first Uat La at 4 3=c =ndLs denote3ýad the Ith teat La denoted I ) mad the average sc*zan rW to the 2^ Insertio posuton fto: the active rods sessured A test:I (C). the equatiom used to calculate the verall average of all the scram data generated to date in the cycle is:

(2-13 Itt I a im er of suveilane tests pe"rformed to date In the cycle; 3: tota2 mouber of active xvds meatured to data ft the cycle; and N1,ti am of the scraw times to the 200, Insertion position of ..

lo-t active r easadured to date Ln the cycle to coaply vr.th the Tachicsa: Specification survael."asc2 requireimts.

cxVii

Thse vorage scram time I " I tested agaiASZ 'the MZIySIS ma.M, 1W2 tbe faloVU4~ eq'uation:

TSTGi 13(2-2)

Ubers T3 V Ulu Is 3-3 a ThePanasmtgr V 8d 0 gt. the Daa &adsan~dard dewtation of the distriltutlan for Svtage &CraM Inserion~ t~a to the 2=: position used In~ the CC Option I ZL~che £7c.la Avrage SCrAm time satisfies the tquaclou 2.2 CrIzerran, cci-.tinaed Plant DP@?t+/-st~c unde the C=f Option 3 operating Iltid:ut==. critical powc-r ratio (OL.'IC') for pressurization events is permitted. If not, the CL'%PK far Pressurization events oust be te-establ~sbad, based on a Issur interpolation betvatz the Optcin3 and Option A MLIURa the equation to *scabUsh the mm opera ting Un-It for pressurization eTents Is gVend bolmr.:

where Is" and r are defined In tquations 2-1 and 2-3, respectivel.y; TA the Present teChnICIl specification )..Ini On core aVeragt scram time to the 20: Insrtion position; and

&CL*=K 0 he diffez~nca between the OL?1M calculated using Optiom A and tlhn ising Option 3 for Mrssurization events .

CxViii

zots that Zquatio 2-3, vhch astabUsbes the m al.l.vabe scram inswr tion time for operation udear option 5, sy also be eMprtssed In the fnlW.*iz

, p4Ac (2-5)

Wbere As 1.65 (2-6) the ralationhip Uetwe the oefficlazt, As and the *wunt of tuie*sl*a data generated during the c7cle Is illustrated In 3"igur 2-1. As .re data bocone available throulg the performance of in-c7c11 svelOCe-tCsts, tie coefficleni decreases, as does the acceptnce criterion, 1.0 Thus, the scra

&read criterion is toing tightened as the cycle progresse, Uased on the aaesliro that, as are #zra data belom available during the cycle, the acertainty In the wean value calculatiot 1hould decrease.

We find the scram Insertion time conformance procedure to be acceptable.

Item 3. Uncera.intZ In ODYN Pressure Calculations Pate 111-7 of Reference 2 states that if GE can demonstrate that the uncertainty in calculated pressure is small (e.g. by a factor of 10 or more) relative to the bias In determining ASV vessel overprtssurm limit, no addition of uncertainty to the calculation's of pressure Is needed. A sensitivity study varying ODYN Input parameters over the range of Table 1 of Reference 2 shows the RMS uncertainty in the peak vessel pressure to be 11 psi. GE estimates the bias In the AS1E code to account for the material uncertainty to be approximately 310 psi. Therefore, there is no need to account for pressure uncertainty in Cxix

a-6a

.. the ODYK calculations.

Item 4. OYN Model Temoerature Limit An early draft of the ODYN SER limited the code calculation to fuel temperatures less than lSOOK (approximately 2240 0 F). This was because Figure 8-2 of 0

Reference 1 limited the thermal conductivity of UO2 to 1500 K. The actual equation used in ODYh.

38.24 Ks 7TMIT + 6.07123 x 10"13 (T+ 273)3 where T a fuel temperature ( 0 C) and K a thermal conductivity (wattu/Cm°C) 0 is based on data which extended to the UO2 malting temperature (3080 K).

Therefore, the fuel temperature limit for ODYN analyses is the UO 2 melting temperature (3080 0 K or 5100 0 F).

Item 5. Uncertainty in Subcooled Balling ftdel Page 11-19 of Reference 2 states OHe estimate the corresponding minimum and maximum values of In'to be 0.5 and 2.0 respectively. General Electric is required to make sensitivity studies to verify that these values correspond to + 0.023 uncertainty In LCPR/ZCPR.4 GE analyzed the turbine trip without bypass transient for n a 2.0, as requested for a 251 BOV4. The peak core average beat flux (I rated) increased from 121.6% (for n . 1.0) to 124.0 (for a a 2.0). This leads to a &CPR/ICPR sensitivity of about 0.024. It is concluded that the Staff's estimate of 40.023 for n values between 0.5 and 2.0 is valid.

eXX

Item 6. .escrittion of Electronic Hydraulic Control -odel An early draft of Reference 2 stated Oheretn electronic hydraulic controls are used in the design, the model used in selection of initial control setting shall be submitted for staff review.6 This statement was made because Reference 1 provided. information only for the mechanical hydraulic control.

GE claims that there is no functional difference between the two types of control. However, they provided a description of the model In Reference 3.

We agree with the GE claim that there Is no functional difference between the two types of control.

Item 7. Listina of ODYN Inout Variables Page 111-O of Reference 2 states "Listlng of important input variables such as listed in Table IV and initial plant parameters including but not limited to control system characteristics as depicted in Figures 4-13 through 4-16 of NEDO-24164, vol. 1, but with numerical values provided should be provided with each submittal. The Initial control system characteristics. including the model used in the selection of Initial settings, shall be defined and substantiated in terms of the design basis for each control system of the plant.' Item 7 of Reference 3 lists typical values of these initial parameters which may be included by reference Into Individual plant submittals provided the values are appropriate to the Individual submittals.

Jtem-S. -Comarison of MCPR Operating Limits Established by REDY and ODYN The Staff requested GE to provide a co=parison of CPR operating limits based on REDY and ODYN prediction. The purpose of such a comparison was to Cxxi

evaluate the appropriateness of continued plant operation under the current REDY based operating limits during the transition period in which ODYH is Imple mented for rapid pressurization events.

In addition, the Staff indicated that the initial 0DYT analysis for each BWR operating plant must include all the pressurization events identified in Table 2-1, Volume 3 of Reference 1, unless justification could be provided that fewer events (such as the limiting events presently analyzed for reload sub mittals) would be sufficient.

Table 2 shows ODYN and REDY-based CPR operating limits for the limiting pressurization events (load rejection without bypass and feedwat&r controller faflure-maxim*um demand) for plants In which both ODYN and REDY calculations are available. Two sets of ODYN numbers are provided: ODYK deterministic calcu lations per the GE letter (Reference 1). labelled "ODYN-GE LTK in Table 2; and ODYN Option 3 statistical calculations, labelled "ODU Option 20 in Table

2. Also included in the table are the plant minimum operating limits, based on all the abnormal events, when using REDY. ODYN GE LTR, and 0DYH Option B to calculate the rapid prtssurization.events.

Because the overall plant operating limits are, in all cases, either uneffected or improved, GE concludes that implementation of OMTh vwil not represent a significant .change to the operating limits for SWR plants. For those plants which use 0DYN Option B, It is generally expected to either produce no change to the limit or else to improve it slightly. We agree with this conclusion.

cxxil

The. eens for which CM. has been qu&lflfd and approved are listed tn Reference 1, Volume , and Include the foflovins: (1) fo*dvaser contr*llar failuretimxlui= demand; (2) pressure regulator failure-closed ditectioz; (3) Sem orator load rejection with and without bypass eperation; (i) main Stesul.te Isolation valve closure (trip.scra and flux scran); C5) loss of coadewser vacum; (6) turbine trTip with and without Irbass; and (7) loss of u*uliry pwver - al grid connections. CZ proposes that =17 the folloing tree events be reparted for reload submittass or safet7 wnal-sLs repoar revislans:

generator load raejctiln/urbine trip without bypass (Ahichever Is limi*ing).

fiedvater controller failure-azlum demand, and vain steauliae Isolation valve closure-fluz scre s o eactisfy A= code presure reqquIrsunta). ZTbse are the oe -pressuwzat:on events presently included In reload sublutals, and reflect the onsistenc7 O.ad tabehCe R =Ttrults. The events not included In the saTttaui are such %a sa vesm, tar Oe ruas ediscussed beal.

1) Turbine/Generator Trips With Bypass These events are cousiderAb 7 eass severe than the tsTisuents to which the lyTess s.str Is assemed to fal*. Typical turbine bypass capacities ratge trot 23m04. of rated staeanlov. This bypass capaciEt7 results to a tonsid erably milder thertal and oerpressurizati.o event.

21 Pressure Regulator Failure - Closed Ofrection The standard event evaluated In SAX analysis Is one In which the coutro2li4n pressure re~gulator Us assumed to fall In. the closed directlon. Unde': these failure c.nditioS, the backup regulator takes over control of the turbine admission valves, preventing an" serious transient. the disturbance is usd and sizilar to a pressure set point change with so significant reductions of f=2l thet ther magins $ccurin. As shownin the SASS, this event Its couidtsa.y less severe than the generator and turbine trips without bypass.

cxx:ii

-10 -

3) Loss of Condenser Vacuum Tarious system malfunctions can cause a less of condense: vacuum due to scm.e single equipment failure. The reduction or loss of vacuu is the smai turbine condenser vill sequentialy trip the main and feedvater turbines and bypass sys t= and, for some pants, close the main stearline isolation valves. WiUle these are the major events occurring, other resultant actions v-hl Include scram (from stop valve closure) and bypass opening vith the win turbine trip.

Uecause the protective actions are actuatad at various levels of condenser vacuu, the severity of the resul*:*a transient Is directly dependent wpon the rate st which the vacuu pressure Is lost. lormal loss of vacuum due to lass of cooling vater pImps or steam jet air e*jctor problem producss a vary $Clo rate of loss of vacuu Cu(nutes. nst seconds). I corrective sc:ions by the reactor operators are soa successful, thet simultaneous trips of the main and feedvuaer tVrbises, and ultimately complete IsolatIO by7 closing the Vp8ss5 valves (*ene=d vith the maIn turbine trip) and the SV&s vill occur. This event Is bounded by the turbine trip witbout bypass event.

4) Less of A=xIliary Power - All Grid Connections TMOigven: Is Initiated by & generator load 1e1ec:ion. ines the turbine bypass sysetn LI assumed to operate durlag the initial portion of this eve-.:.

it Is ccr*aral:e to the loas rejection vith bypass and is couslderstly less severe than the vwthout bypass events.

51 p~IV Closurt- - Trio Scram T0is event has a SiloDWe autoff of steag flov that the turbine triv f.thou:

piass event. Thereforte the transient LU not as severs. This has been. con firmed by C= Calclations.

cxXiv

° 11 ° The staff agrees with the GE assessment of the relative severity of the transients

'listed. Therefore, the following events should be reanalyzed with ODYN for plants which have analyses of record using REDY:

1) generator load rejectilon/turbine trip without bypass

2) feedwater controller failure maximum demand

3) main steam line isolation valve closure-flux scram.

If for a particular plant another event should be tre limiting than those just listed, then the other event should also be reanalyzed with ODYN. For the new plants with transient analyses supplied by GE, all of the events listed In Table 3 of Reference I should be analyzed with ODYN.

References

1. NEDO-24154 and NEDE-24164P, Volumes 1, II and 11, "Qualification of the One-Dimensional Core Transient Model for Boiling ietar Reactors,"

October, 1978.

2. Memorandum for T. Novak and A. Tedesco from P. S. Check, "Safety Evaluation for Qualification of the One-Dimensional Core Transient Model for Boiling Water Reactors," REDO-24154 and NEDE-24154P, Volumes 1,11 and '11,9 October 22, 1980.

3. Letter to P. S. Check (NRC) from R. . Buchholz (GE), MIR-155-80, "Response to XRC Request for Information on ODYN Computer Model ,

September 5, 1980.

Czxvi

Table 1 07 C G~L~rC £TA=STICAL. A DSZ,.=7 FACTOMS ChCWIZPR)

Gro~ings _____FC 3%R 2/3 - 4*.0.006 -0.016 ma 4/5 v/o Rn - zOC -0.039 -0.009 MM 4/5 w/o R"' - MC -0.111 -,*.009 MM 4/5 v/I?? - eC -0.024 40.016 S /4 v/i?.n- -MC -0.001 +0.026 IVR 6 - bC -0.=1 .*0.003 4-0.017 eWith the ezcsepcit of F= or P?DT Oacs, this set of adjustment factors wll be applied to all pressurizatlem events analyted vwth the C= code to establish the CPR operating l*nit, since they typIcally Involve gemerator or turbine trips.

cxxvii

T.nble 2 Operating CPR UlmIte A W10 It Plant l1tnl~mm

- 13rl (Optiot (C2 (opt ion ('ZR Vt. (opt Ion Plant Stlt *tr) nl) Lt r) 3) Rtit 1.tr) 3)

nu 1I.II 9111f1_20% ROC6 1.46 1.36 1.37 1.16 1.31 1.46 1.35 2.36 IA.a 1.42 1.22l 1.2?

uMM14-191 ENS, 2.42 1.2) 1.27 1,25 1.14 1.21(2) 1.21 1.21(2) lt$ 1.20 1.11 1.12 1.200I) 112001) 112011) 9"16-231 tc 1.16 1010 I.0l tell 1.12 Noteml 11) LUIteed by 0l0 WiltMrawal rror (2) umitea 167 Lone of 100e9 feedwuter OlWtlnS (3) Plant with 1P1

bi 2?A I Cm . M w ICT=

cxxix

GENERAL'.0, . ELECTRIC NUCLEAR POWER SYSTEMS DIVISION GENERAL ELECTRIC COMPANY. 175 CURTNER AVE.. SAN JOSE. CALIFCRNIA 95125 MC 682, (408) 925-5722 MFN-013-81 January 19, 1981 U.S. Nuclear Regulatory Commission Division of Systems Integration Office of Nuclear Reactor Regulation Washington, DC 20555 Attention: Paul S. Check, Assistant Director of Plant Systems Gentlemen:

SUBJECT:

ODYN ADJUSTMENT METHODS FOR DETERMINATION OF OPERATING LIMITS

References:

1) Telecon, H. C. Pfefferlen, R. E. Engel and R. T.

Hill (GE) with M. W. Hodges (NRC), January 5, 1981

2) R. P. Denise to G. G. Sherwood, January 23, 1980 The purpose of this letter is to document the agreement reached in the Reference 1 telecon concerning the application of the Initial Critical Power Ratio (ICPR) adjustment factors in conjuction with ODYN analysis results.

Ootion A The ICPR adjustment method to be used with the non-statistical approach (Option A) for rapid pressurization events is that given in Step 3 of Reference 2. This method is to be considered a defini tion for use specifically with the NRC derived adjustment factor of 0.044.

The application of the adjustment factor in this case can be defined as:

ICPRnew = 1.044 (ICPR)c where (ICPR) = calculated value of ICPR Option B The method to be used with the statistical approach (Option 6) has been defined to be consistent with the adjustment factors derived by General Electric. This method requires the addition of the

GENERAL e ELECTRIC U.S. Nuclear Regulatory Commission Page 2 adjustment factor (AF) to the ratio of the calculated values of

&CPR and ICPR (ACPR/ICPR) c:

ACPR (CPR

• new = T ) + AF This equation can be simplified to:

ICPRn SL CPnew I - [(Tm)c fICPR)

J +9 AF3 F

Where SL = Safety Limit MCPR It should be noted that in both the Option A and Option B cases, the ICPR is defined as Safety Limit plus &CPR for the event being analyzed.

If you have any additional questions or comments, please contact me or H. C. Pfefferlen on (408) 925-3392 of my staff.

Very truly yours, R. H. Buchholz, Manager BWR Systems Licensing Safety and Licensing Operation RHB:sem/1158-59 1F cc: L. S. Gifford M. W. Hodges

==*i/ cxca:

NEDO-24154-A.

PREFACE This document represents a compilation of the information provided to the Nuclear Regulatory Commission by the General Electric Company for the staff's review of GE's One-D4ensnional Core Transient Model.

Volume I of this report contains the One-D4ensiouanl Core Transient Model description, as vell as the questions/respouses associated with the stiff review of this description document.

Volume 1I of this report contains the document for Qualification of the One-Dimensional Core Transient Model for Boiling Water Reactors, as well as the associated staff questions/respouses.

Volume =I. of this report contains two parts: Part I provides the General Electric proposal for applicatiou of the One-Dimensional Core Transient Model, as well as the staff questions/responses related to the proposal; Part II provides two questions/responses related to the model description which involve information propri etary to the General Electric Company.

The questions referenced within this report were transmitted to General Electric by letter from the NRC staff: untitled letter, D. F. Ross to E. D. Tu.ler, dated June 2, 1978.

cx~ciii /cxxiv

NEDO-24154-A TABLE OF CONTENTS Pale ABSTRACT czl-i

1. fRIN'ODUCTION AND., SUMMAUX 1-1

2. MODEL-MODEL COMPARISONS 2-1 2.1 Nuclear Model Comparisons 2-1 2.1.1 Scram Reactivity 2-1 2.1.2 Void Coefficient 2-2 2.2 Thexmal-Hydraulic-Model Comparisons 2-3

3. ANALYSIS OF TURBINE TRIP EZPEMIMENTS 3-1 3.1 Peach Bottom Turbine Trips 3-1 3.1.1 Test Sumary 3-1 3.1.2 Model Inputs 3-2 3.1.3 Data Comparisons 3-3 3.1.3.1 Transient Pressure 3-3 3.1.3.2 Neutron Flux 3-4 3.1.3.3 Critical Power Ratio 3-7 3.1.4 Conclusions 3-8 3.2 [KM Turbine Trip 3-8 3.2.1 Test Summary 3-9 3.2.2 Special Model Considerations 3-10 3.2.3 Model Inputs 3-10 3.2.4 Data Comparisons 3-11 3.2.4.1 Transient Pressure 3-11 3.2.4.2 Neutron Flux 3-13 3.2.4.3 Critical Power Ratio 3-15 3.2.5 Conclusions 3-15 REFER-NCES 3-74 APPENDICES A RESPONSE TO N.CLEAR REGULATORY COMMISSION QUESTIONS ON SZCTIONS 1 THROUGa 3 OF VOLMS- II A-I cxrxv/cxoccvi

NEDO-24154-A LIST OF ILLUSTRATIONS Figure Title page 2-1 Plant A (BWR/4) All-Rods-Out Scram 2-6 2-2 Plant A All-Rods-Out Scram Reactivity 2-7 2-3 Plant A Initial Control Rod Pattern in Nodes Withdrawn (24 is Completely Out) 2-8 2-4 Plant A Critical Rod Pattern Scram Reactivity 2-9 2-5 Plant B Rod Pattern in Number of Nodes Withdrawn (24 is Completely Out) 2-10 2-6 Plant B (mWR/4) Scram Reactivity 2-11 2-7 Plant B Transient Axial Power 2-12 2-8 Steady-State Void Fraction Profile High Power Channel 2-13 2-9 Steady-State Void Fraction Profile Low Power Channel 2-14 2-10 Change in Void Fraction from 10 Psi Pressure Change High Power Channel 2-15 2-11 Change in Void Fraction from 10 Psi Pressure Change Low Power Channel 2-16 2-12 Void Fraction Versus Time Exponential Flow Decay Problem 2-17 3-1 Axial Power Profile Turbine Trip 1 3-19 3-2 Axial Power Profile Turbine Trip 2 3-20 3-3 Axial Power Profile Turbine Trip 3 3-21 3-4 Peach Bottom-2 Rod Insertion Fraction Versus Time 3-22 3-5 Peach Bottom Eight-Node Steamline Schematic 3-23 3-6 Peach Bottom-2 Turbine Trip 1 Sceamline Pressure 3-24 3-7 Peach Bottom-2 Turbine Trip 2 Steamline Pressure 3-25 3-8 Peach Bottom-2 Turbine Trip 3 Steamline Pressure 3-26 3-9 Peach Bottom-2 Turbine Trip 1 Dome Pressure 3-27 3-10 Peach Bottom-2 Turbine Trip 2 Dome Pressure 3-28 3-11 Peach Bottom-2 Turbine Trip 3 Dome Pressure 3-29 3-12 Peach Bottom-2 Turbine Trip 1 Core Exit Pressure 3-30 3-13 Peach Bottom-2 Turbine Trip 2 Core Exit Pressure 3-31 3-14 Peach Bottom-2 Turbine Trip 3 Core Exit Pressure 3-32 3-15 Peach Bottom-2 Turbine Trip 1 Prompt Neutron Power 3-33 3-16 Peach Bottom-2 Turbine Trip 2 Prompt Neutrou Power 3-34 3-17 Peach Bottom-2 Turbine Trip 3 Prompt Neutron Power 3-35 3-18 Peach Bottom-2 Reactivity Turbine Trip 1 3-36 cxxxvii

KEDO-24154-A LIST OF ILLUSTATIONS (Continued)

Figure Title Pace 3-19 Peach Bottom-2 Reactivity Turbine Trip 2 3-37 3-20 Peach Bottom-2 Reactivity Turbine Trip 3 3-38 3-21 Peach Rottom-2 A Level LPRM's Turbine Trip 1 3-39 3-22 Peach Bottom-2 B Level LPRM's Turbine Trip 1 3-40 3-23 Peach Bottom-2 C Level LPRM's Turbine Trip 1 3-41 3-24 Peach Bottcm-2 D Level LPRH's Turbine Trip 1 3-42 3-25 Peach Bottom-2 A Level Tlux Turbine Trip 1 3-43 3-26 Peach Bottom-2 B Level Flux Turbine Trip 1 3--4 3-27. Peach BoCttm-2 C Level Slux Turbine Trip 1 3-45 3-28 Peach Bottom-2 D Level Flux Turbine Trip 1 3-46 3-29 Peach Bottom-2 A Level Flux Turbine Trip 2 3-47 3-30 Peach Bottom-2 B Level Flux Turbine Trip 2 3-48 3-31 Peach Bottom-2 C Level Flux Turbine Trip 2 3-49 3-32 Peach Bottom-2 D Level Flux Turbine Trip 2 3-50 3-33 Peach Bottom-2 A Level Flux Turbine Trip 3 3-51 3-34 Peach Bottom-2 B Level Flux Turbine Trip 3 3-52 3-35 Peach Bottom-2 C Level Flux Turbine Trip 3 3-5"3 3-36 Peach Bottom-2 D Level Flux Turbine Trip 3 3-54 3-37 Schematic of M Steamlit- Model 3-55 3-38 Average Axial Power KKZ Test Conditions 3-56 3-39 Control Rod Motion Pattern KKK Turbine Trip Test 3-57 3-40 Turbine Pressure Turbine A KK Turbine Trip 3-58 3-41. Turbine Pressure Turbine B KKH Turbine Trip 3-59 3-4Z = Turbine Trip Steamline Pressure, Turbine A 3-60 3-43 KW, Turbine Trip Steamline Pressure, Turbine B 3-61 3-4 M Turbine Trip Dome Pressure 3-62 3-45 M Turbine Trip Core Exit Pressure 3-63 3-46 KM Turbine Trip Prompt Neutron Power 3-64 3-47 Reactivity Components fMC Turbine Trip 3-65 3-48 A Level LPIM Flux KM Turbine Trip 3-66 3-49 S Level LPRM Flux M32Turbine Trip 3-67 3-50 C Level LPM1 Flux = Turbine Trip 3-68

NEDO-24154-A LIST OF ILLUSTRATIONS (Continued)

Figure Title Page 3-51 D Level LPRM Flux MX Turbine Trip 3-69 3-52 A Level Flux WM Turbine Trip 3-70 3-53 B Level Flux M( Turbine Trip 3-71 3-54 C Level Flux IJ2 Turbine Trip 3-72 3-55 D Level Flux KKK Turbine Trip 3-73 11-1 Peach Bototm-2 Turbine Trip 3 (69% Power) Neutron Flux AIl-2 15-1 Peach Bottom-2 Turbine Trip 1 Core Exit Pressure (35Z Bypass) A15-3 15-2 Peach Bottom-2 Turbine Trip 2 Core Exit Pressure (35% Bypass) A15-4 15-3 Peach Bottom-2 Turbine Trip 3 Core Exit Pressure (35% Bypass) A15-5 cxxxix/cxl

NEDO-24154-A LIST OF TABLES Table Title i 2-1 Comparison Of Void Coefficients Obtained with Three Dimensional and One-Dimensional Coare Models 2-5 2-2 Sumary of Hydraulic Channel Conditions 2-5 3-1 Peach Bottom-2 Turbine Trip Test Conditions 3-16 3-2 Peach Bottom-2 Dynamic Test Signals 3-16 3-3 Peak Vessel Pressure 3-17 3-4 maximum ACPR Values for Peach Bottom Turbine Trip Tests 3-17 3-5 1% Turbine Trip Test Conditions 3-17 3-6 M Dynamic Test Signals 3-18 3-7 Maximum ACPR Values for the UM Turbine Trip Test 3-18 5-1 Peak Flux Values as a Function of Scram Delay Time £5-2 6-1 Summary of One Dimensional Model Sensitivity Studies A6-2 15-1 Summary of ACPR/ICPR Results for Peach Bottom Turbine Trips A15--

cxli/ cxl ii

NEDO-24154-A APSTAMCT A transienr mdeZ f~or the boiZin.- water reactor' MBR) has been deve'.2ced which contains a one-dirensiona: neutronic and rhermaZ hiiraicsimulationof the reactor core, as weZZ as a nodal repr'esentation of the pressure variations in the main steomline.

Comnpaizons are made between various par'ts of the core movdel and other nusclear and thermal hydraul~ic modeU1. ModeZ results are also conrared to data acquired from turbine tric experimente carried out at the Peach Bottom and M4 Atomic Power Stations.

Cxl iii/ cxliv

NEDO-24154-A

1. I19TRODUCTION AM SEUMaRY The transient behavior of a boiling water reactor (BWR) power plant depends not only on the mechanical response, of the recirculation and control systems but also on the power behavior of the reactor core. Previous computer models for the BWR system have used a point model to describe the thermal hydraulic and neutronic response of the reactor core. The dynamic steamline response has been described by a lumped compressible steamline node. An improved BWR transient model, which includes a more detailed desciiption of the reactor core and steamline, has been constructed and is described in detail in Reference 2. This report describes qualification studies support ing the one-dimensional core transient model. These stz;dies include comparisons with other computer models, as well as comparison with data from actual MR pressurization transients.

The improved transient model consists of an integrated one-dimensional reactor core model which is coupled to recirculation and major system control models.

The recirculation and control system models are, for the most part, identical to the point reactor model described in Reference 1. The reactor core is hydraulically coupled to the recirculation loop through the core exit pressure and core inlet flow. The core exit quality and pressure drop are computed by the core model, which, in turn, interacts with the loop parameters.

The improved model also contains a more detailed description of the pressure variations in the main stemfne. The model includes a nodalized description of the mass and moment= balances in the steamline and is capable of predicting the wave phenomenon present in the steamline during transients such as turbine trips.

The reactor core model allows for spacial variation of the neutron flux, fuel temperature, coolant flow, coolant density and pressure in the axial direction.

The neutron kinetics behavior is described by one energy group diffusion theory with six delayed neutron groups. The thermal-hydraulic model contains separate conservation and energy equations for the vapor and liquid phases as well as a mixture momentum equation. Fuel rod heat conduction equations are solved for each axial elevation in the core.

1-1

NEDO-24154-A Two types of studies v*i.l be presented in this report; model-codel comparisons and mo;del comparisons with experimental data.- The model-model comparisons are designed to show that the one-dimensional nuclear and thermal-hydraulic models of the reactor core are consistent with core models currently used in B3i design. Also, the collapsed one-dimensional nuclear model is compared with transient results obtained from more detailed three-dimensional simulations.

The model comparisons with experimental data consist of calculations of four instrumented turbine trips conducted with a delayed direct scram by bypassing of the direct trip scram, such that the scram occurred following a high flux trip. The experiments were performed at the Peach Bottom-2 and MI* BWR power plants. The model data comparisons are given for a large number of transient variables, including system pressure, reactor flow, and neutron flux. The model-data comparisons form the basis for the qualification of the one dimensional transient model.

The nuclear model-model comparisons show that the one-diensional model agrees vell with three-dimensional results for scram calculations with no thermal feedback. Also, good agreement with three-dimensional simulator results are obtained for static void reactivity coefficients. The thermal-hydraulic model steady-state results agree well with results obtained with the standard BUM design models. The comparison of transient thermal-hydraulic results is carried out on a simplified flow decay problem for which an analytic solution e*s ts.

Turbine trip data were acquired at the Peach Bottom Atomic Pover Station Unit 2 (Peach Bottom-2) for three power levels: 48Z, 621 and 69% of rated power.

The comparisons show good agreement between data and calculation for all three turbine trips. The experi mental data show a steamline wave phenomenon which is duplicAted by the model calculation. The model also thows good agreement in total neutron flux. The axial shift of the flux during the transient is apparent in the data and is duplicated by the calc.ulation. Thermal margin calculations carried out using both the experimental and calculated transient heat generation-rates showed that the calculated transient change In critical power ratio (&LCPR) divided by the initial CPR (ICPR) is within 0.01 ef the change inferred from the experimental data for all three experiments.

1-2

NOOD-24154-A An additional turbine trip experiment was carried out at the M plant in

.uehleburg, Switzerland. This turbine trip was initiated from 77Z of rated power and approximated end-of-cycle conditions. The Mi reactor is a two turbine plant and contains a more complicated steamline configuration. There fore, modifications were made to the model described in Reference 2 to adequately describe this complexity. The results of this comparison again show good agreement between data and calculation. The calculated change in critical power ratio agrees with the change inferred from the data to within 0.01 ACPR/ICPR.

The four turbine trip experiments represent the most significant part of the one-dimensional transient model qualificatIou data base. The compaisouns shown in this document show that the one-dimensional model is successful in calculating all four turbine trips, which vere initiated from different power levels and core conditions.

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IWDO-24154-A

2. MODEL-MODEL COMPA*ISONS The comparison of computer model results to experimental data obtained from actual reactor plant transients is the most desirable qualification basis.

However, comparisons with other models are also useful in showing that a specific assumption yields accurate results or is consistent with other approved design methods.

2.1 NUCLEAR MODEL COMPARISONS The solution techniques employed in the one-dimensional nuclear model are described in Section 5 of Reference 2. The ona-dlenzsiWnal dLffusion param eters are derived by collapsing three-dimensional steady-state solutions 3

obtained from the General Electric three-dimensional BWR simulator . This collapsing process is described in detail in Appendix A of Reference 2. The ability of the one-dimensional core model to calculate scram reactivity and void coefficients will be examined in this section.

2.1.1 Scram Reactivity In order to test the validity of the one-dimensional collapsing procedures described in Section 5 of Reference 2, a series of scram calculations has been compared with the one-dimensioual solutions with three-dimensional solutions obtained with the three-dimensional BWR simulator. These scram calculations have no void feedback and represent a test of the collapsed one-dimensional model in properly estimating scram reactivity worth. The basic nuclear data used in the two calculations are identical and the one-dimensional parameters have been obtained from the steady-state three-dimensional solution. Three cases are considered here. The first case examined is a BWR/4 core at the beginning of Cycle 2 (Plant A). To simulate an end-of-cycle scram situation, all of the control rods were assumed to be withdrawn. Figures 2-1 and 2-2.

show a three-dimensional, one-dimensioual comparison of total neutron flux and scram reactivity versus time. The agreement is quite good over the entire scram range. The second example, shown in Figure 2-4, shows the same core in a critical rod pattern shown in Figure 2-3. In this case, the flux and scram reactivity agreement is still good, although not quite as good as the all-rods out case. This second case is more difficult to calculate because of the rapid 2-1

NEDO-24154-A radial flux changes caused by the motion of the inserted rods. The third example shows a BWB14 reactor at 50Z power, 100% flow (Plant B). tn this case, there is a considerable number of control rods in the core, as shown in Figure 2-5. Also, the radial power distribution is complicated because of the lower power level and the complicated rod pattern. Here the agreement is still good, especially in the early part of the scram, which is the important region in the analysis of turbine trip accidents. Finally, a comparison of axial power shapes for the third example is shown in Figure 2-7 for a number 97*

of times during the scram. The change in average axial shape is followed quite well by the one-dimensional model. In st-ary, the collapsing procedures used in generating the one-dimensional neutron kinetics model -yield results which compare well with three-dimensional scram calculations.

2.1.2 Void Coefficient The one-dimensional nuclear model must accurately predict the void reactiviry response of the core in order to follow the neutron flux response during .3ML transients such as turbine trips. Table 2-1 contains a comparison of void coefficient values obtained with the one-dimenstonal nuclear model and the three-dimensional BIR Simulator. In each case, the void coefficient is cal culated as the following eigenvalue difference:

I '* (:I 1 - *a2 Void Coefficient 8

where aI and (2 are core averaged void fractions at two different reactor statesr The two reactor states were generated by varying the reactor pressure and flow, which undergo the greatest change during a turbine trip transient. In all cases, the one-dimensional and t hree-dimensional coefficiente agree to within 5%. A wide variety of power levels and control rod configurations has been covered in the cores analyzed. Thus, the oue-dimensioual model is expected to favorably reproduce the three-dimensional trarsient void reactivity response.

• q7 - Replies to M*-C questions on the text are documented in Appendix A. The symbol Q7 denotes that this topic is discussed further in the reply to IRC Questiton 7.

NEDO-24154-A 2.2 TE*EDTL-HYDRAULIC MODEL COMPARISONS Steady-state comparisons between the thermal-hydraulic model described in Section 6 of Reference 2 and the standard GE BWR channel hydraulic model have been carried out. Figures 2-4 and 2-9 show axial void fraction profiles for a high power and low power channel. Some differences exist in the subcooled void region because of different n--erical treatments of the subcooled boiling process. Also, small differences exist at the top of the channel because the current model allows pressure and saturation enthalpy to vary along the channel, while the standard GE model assumes constant pressure and saturation enchalpy.

Considering the above model differences, the overall agreement is good, to wtthtn 0.003 In vo:Ld fractlon. These same two channels were also run at 10 pal higher pressure and the-change in void-ftaction calculated as a function of axial height. The results obtained by the two models are compared in Figures 2-10 and 2-11 for the low and high power channels, respectively. Note that excellent agreement is obtained for the change in void profile generated by a pressure change. Q9 These calculations show that the channel hydraulic model gives steady-state results consistent with standard GE design tools, which have been verified against void fraction measurements in test assemblies.

In the transient mode, model-model comparisons are more difficult because the five-equation model is more detailed than currently employed design models.

However, a closed form solution exists for the one-dimensional vapor continuity equation with constant steam and drift flux properties.

5 The initial conditions for the transient considered are listed in Table 2-2. During the transient, the axial heat flux distributiou is constant and uniform. The time-dependent boundary condition is:

5 Inlet volumetric flux - 0.0002 (1 + 2 9 9 8 6 . 4 9 5e- t), ft/sec The one-dimensional hydraulic model was modified to include constant steam properties and drift flux correlations and then used to obtain a solution to the above problem. Spacial nodes were placed every 0.5 ft up the channel.

2-3

NDo-24154-A Thi solution is compared with the closed form solution in Figure 2-12. The transient void fraction at 0.5 and 12 ft from the channel entrance is plotted.

The ma3imu deviation at 0.5 ft is 0.006 in void fraction. The maxiu== devis tion at 1.2 ft is 0.0003. This numerical test shows that the overall numerical procedures employed in the thermal-hydraulic model are adequate.

NEDO-24154-A Table 2-1 COMPARISON OF VOID COEFFICIENTS OBTAINED WITH TEREE-DIDESIONAL AND ONE-DIMENSIONAL CORE MODELS Percent Percent of of Rated Rated Average 3-D Void I-D Void Power Flow Void Perturbation Coefficient Coefficient Plant (z) Fraction Mechanism (lAyV) (WVv)

Plant B (EWR/4) 48 100 0.232 Pressure change -33.9 -33.2 Plant B (BWR/4) 62 80 0.289 Pressure change -29.9 -31.5 Plant B 69 100 Pressure change -28.5 -29.2 (BWR/4) 0.301 Plant C 0.413 -21.3 -22.0 104 100 Pressure change (BWl 5)

Plant C 104 100 0.413 Flow change -24.2 -24.0 (BWR/5)

Plant D 77 93 0.321 Pressure change -26.3 -27.6 Table 2-2

SUMMARY

OF KMRDEAULIC CHANNEL CONDITIONS Inlet Volumetric Bundle Sub Flow Hydraulic Channel Flux Power. cooling Area DIameter Length Pressure Label (ft/sec) (B /lb) (f.10 Cf t) (ft) (psi)

High Power Channel 6.45 6.55 23.4 0.1065 0.0433 12.5 1055 Low Power 4.305 1.64 23.4 0.1065 0.0433 12.5 1055 Channel Transient Calcula 5.997 1.00 0 0.1115 0.0484 12 1000 tion 2-5

N4EDO-24154-A 100 I.2 U 3.0 E!.gue 2-. P2.z~ AU3tZ/4 All1-Rods-Outi Scram 2-6

0.3 0.2 R

4 N

-.1 I

t~.

0.1

• 0 TIME liwcI Figure 2-2. Plant A All-Rods-Out Scram Reactivity

NEDO-24154-A INMAL CONTROL ROD ARRAY J/1 3 5 7 9 11 13 1

3 20.4-5 12.42 0.4O 14.43 18.42 O.4S M2.4 18.2 13 0.4O 0.45 0.45 Figure 2-3. Plant A Iitia+/-fl Control Rod Pattern in Nodes Withdrawn (24 is Completely out) 2-8

U N

~0 I K

I:..

TME 1"d Fi~tgre 2-4. Plant A Critical Rod Pattern Scram Reactivity

INITIAL CONTROL ROD AHHAY l 3 5 1 11 13 1t 17 19 21 23 25 2) 29 1

10.17 14.17 19.17 0.11 0.17 0.17 017 10.17 &.17 10.17 20.17 0.17 0.17 0.11 0.13 0.11 0.17 10.17 10.11 20.17 20.11 10.17 19.17 0.17 0.17 0.17 0.17 0.17 14.17 &11? 20.17 8.17 14.17 Sb 0.11 0.17 0.17 0.17 0.17 0.17 19.17 10.17 20.17 20,17 10.17 19.17 0.17 0.11 0.17 0.17 20.11 10.17 8.17 10.17 20.17 0.17 0.17 0.17 0.17 16.17 14.17 19.17 29 IJgttru 2-5. Plasit B Rod Pattern In Number of Nodes Withdrawn (24 to Completely Out)

KEDO-24154-A 4

'Li E

4 TIME Oine Figure 2-6. Plantc B (BWR/4) Scram Reactivity 2-11

I.

NMD-24154-A.

1.5 mm.wONE.OIMENSIOIAL UOLLMON

ýTHREE-DIMENMONAL SOLL~nON 1.

AXIAL HEI0IT (ft)

Figure 2-7. Plant B Transient Axial.Pow:r 2-.LA.2

NTEDO-24154-A 0.6 0.6 U.3 Ca 0.1 0

0 2 4 6 8 10 12 AXIAL HEIGHT (W.

Figure 2-8. Steady-State Void Fraction Profile *igh Power Channel 2-43

bEDO-24154-A z

'.2 Figure 2-9. Steady-Stace Void Fracr-iou ProfileaLow Power Channe.

2-14 I

• NEDO-24154-A 2J S.

AXIAL HEIGHT INt)

Figure 2-10. Change in Void Fraction from 10 Psi Pressure Change High Power Channel 2-15

NEDO-24154-A z

2 L201 z

Mom AXIAL HEIGHT Iftt Figure 2-]11. Change in Void Fraction from 10 Psi Pressure Change Low Power channel 2-16

NEDO-24154-L 0.8 0.7 z

z K

UL C0J d

I C

a-_ AN4ALYTICAL MODEL 06 - 0t1 ONSDMENSIOIAL MODEL

. ...

• f II I 2 3 TIME fud Figure 2-12. Void Fraction Versus Time Expouencial Flow Decay Problem 2-17/2-18

NZDO-24154-A

3. ANALYSIS OF TURBINE TRIP EXEWMTS Four special turbine trip experiments were carried out on BWN reactors during 1977. An excensive amount of data vas taken at each event, providing an outstanding set of benchmarks for transient model qualification. These tests were specifically designed to obtain data which would be useful in verifying assumptions for trinsient models. The first three turbine trips were carried out on the Peach Bottom-2 reactor and the fourth an the M reactor in Switzerland.

3.1 PEACE BOTTOM TURBINE TRIPS Three instrumented turbine trips were carried out at the Peach Bottom-2 reactor during April 1977. These tests were conducted with the direct scram on stopvalve position bypassed such that a trip on high flux was obtained.

This departure from the normal reactor condition was required to obtain a sufficiently large flux response to allow a model-test comparison. A detailed description of the test conditions and measurement process can be found in Reference 4.

3.1.1 Test Smary The initial pover and flow conditions for each test are shown In Table 3-1.

These test conditions were selected in order of increasing power aloug a line of constant reactor flow. Prior to the second turbine trip test, it was necessary to reduce core flow to hold the power to within 1Z of planned test power level due to the xenon level in the core at the time of the test. In each of the three tests, the trip scram was disabled and the flux scram setpoint adjusted. The scram setpoints are also listed in Table 3-1.

A total of 153 signals were recorded by a digital data acquisition system. A sumary of the measured quantities appears in Table 3-2. The comparisons presented here will concentrate on important aspects of both the one-dimensioual reactor core model and distributed steamline model.

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NEDO-24154-A 3.1.2 Model Inputs As pointed out in Reference 2. most of the mathematical modeling for the recirculation and control system part of the EWRis identical to the model currently used for transient design analysis.1 The vast majority of the external loop description for the Peach Bottom plant is identical to that used in design and licensing analysis, and is taken from a description of the plant conditions found in Reference 7. A few quantities have been changed to be compatible with the one-dimensional core and eight-node steamline models. These changes are all discussed in this section.

The-initial conditions for all three tests were used by the GE BWR Simulator to generate three-dimensional power distributions. These nuclear data were then collapsed into one-dimensional parameters according to the procedures outlined in Reference 2. A comparison of process computer output and the resulting cue-dimensional axial power profiles appears in Figures 3-1, 3-2, and 3-3.

The control rod motion pattern was taken from measured data. A linear rod mo=ion pattern as shown in Figure 3-4 was assumed. Figure 3-4 also shows the measured rod positions as a function of time after the trip signal. The same motion pattern was assumed for all three turbine trips.

The steamline representation is shown in Figure 3-5. The lengths and areas associated with each node are also shown. The coefficients for pressure losses were calculated by considering the geometry of the steamline and using pressure drop correlations 6 to compute the appropriate losses over each section of pipe. These coefficients are also shown in Figure 3-5. The resistance quantity K1 is defined in Reference 2. The core thermal-hydraulic geometry used a weighted average of the dimensions from the 576 7W7 bundles and the 168 W bundles.Q10 Temperature-dependent conduction parameters were used for the fuel pellet and cladding. A value of 1000 Btu/hr-ft"-*F was used for gap conductance.

For the three turbine trip test conditions, the transient flux response was found to be a very weak function of gap conductance. That is, variations of 100Z in gap conductance produced only 5% changes in peak neutron flux.

Q1 3-2

NEDO-24154-A This low sensitivity results from the fast nature of the Peach Bottom flux transients, where thermal feedback contributes only a small part to the reactivity shutdown.

Turbine stopvalve and bypass' valve positions were also recorded during each transient4 and were then used to describe valve motion in the calculation.

3.1.3 Data Comparisons 3.1.3.1 Transient Pressure Comparisons Dynamic pressure measurements were recorded at the turbine inlet, in the steamline 90 ft-downstream from the vessel-,-the vessel dome,' and near the core exit plenum. In all of the pressure comparisons listed in this section, the data shown are the unfiltered data as recorded by the pressure sensors.

The sensors are connected to the appropriate measurement locations by water filled:sensor lines. These sensor lines have their own second-order response which can often give rise to oscillations in the recorded data. Further discussion of the sensor line effects is contained in Reference 4.

Figures 3-6 through 3-8 show comparisons of calculation and data for the pressure measured in the st--aline near the safety/relief valves. Note that the model accurately predicts the wave travel tIme down the steamline and the frequency of pressure oscillations. However, the calculated waves are more spread out and the amplitudes are smaller than the measured waves. The spreading out of the calculated wave is due to the coarseness of the spatial mesh.Q 1 However, this change in shape does not appreciably affect the dome pressure profile because. the vessel dome pressure is influenced in large part by the total steamline flow, which is proportional to the integral of the steaeminepressure. Hence, the area under each oscillation is of more interest than the detailed shape.

Plots of dome pressure over the first 1.2 sec of the transient are shown in Figures 3-9 through 3-11. Note that the calculation simulates the initial pressure rise rate quite well in all three tests. Note also that the calcula tion overpredicts the pressure rise near the peak of the first pressure oscilla tion. The peak dome pressure occurs about 2.5 sec into the transient. Values for the peak dome pressure are listed in Table 3-3. The transient model 3-3

INEDO-24154-A all three cases.

overpredicts the peak pressure by approximately 30 psi in The overprediction of peak pressure is thought to be due to the bypass flow model used in the transient model. The rated bypass capacity of 26Z of total steam flow was assumed. It is felt that the real bypass capacity is somewhat larger than 26Z. Also, the model calculations assume choked flow through the bypass valve for all valve positions. It is possible that, immediately after the valve opening, the bypass flow will overshoot the steady-state value. If this is true, the peak pressure could be oercalculated by the model.

The core exit pressure is compared in Figures 3-12 through 3-14. Accurate prediction of the core exit pressure is most important in determining the core neutron flux response. Note that, again, the initial rise in pressure is followed well by the model for all three test conditions. The oscillations in the data between 0.4 and 0.7 sec are thought to be caused by the second order behavior of the Instrument line. Note that after 0.7 sec, large oscillations occur. These oscillations begin just about the time that control rod motion starts and could be connected with a disturbance caused by the initial motion of the control rods. No oscillations in neutron flux are observed during this period, so that it is most likely that these oscillations are connected with an instrument Line disturbance.

In evaluating the model against the measured data, the sten*.Une and dome model simulate the overall core pressure rise rather well in all three experiments. As the power level is changed, the model tracks the experimental behavior and that about the same differences are observed in all three experiments. There are, however, localized portions of the transient where the model overpredicts the pressure rise. In some cases, these differences can be important, such as the portion of each curve between 0.7 and 0.8 sec where the peak neutron flux is observed. In this region, small changes in pressure can have noticeable effects on neutron flux. This behavior will be discussed further in Section 3.1.3.2.

3.1.3.2 Neutron Flux Comparisons The most important and demanding test of this transient model is the neutron flux response. The severity of the flux transient determines the transien:

critical power ratio and its prediction requires not only good core pressure 3-4

NEDO-24154-A calculations, but an accurate scram and void reactivity feedback model. The total flux results are shown in Figures 3-15 through 3-17 for the three turbine trips. Note that in all three cases excellent agreement is obtained over the initial rise and falloff portions of the flux spike. The calculation always tends to overpredict the peak flux value.

This overprediction near the peak flux value is primarily due to the fact that the core exit pressure rise is overcalculated during this time period.

Figures 3-18 through 3-20 show the reactivity components as a function of time during the transient as calculated by the one-dimensional model. The defini tions of the reactivity components are given in Appendix L of this report.

Note tha near tbh*-peak-of-the total-reactivity curve, the net reactivity is about $0.80. When the overall reactivity level is this large, small changes in reactivity can cause large changes in peak flux levels because the prompt change in flux is proportional to 1/(1-00S): where p is the net reactivity and B is the delayed neutron fraction. For the Peach Bottom transients a psi change in core pressure will generate a change of about 0.02 in the ratio p/0, which, in turn, will cause about a 10Z change in peak neutron flux. Note also that this sensitivity exists over a short time span and that 0.04 sec after the scram motion begins, the calculated flux agrees again with the data.

A second contributor to the peak flux differences is the assumed scram motion model. The model assumes that all control rods start at the same time and move with the same speed,, whereas there is actually a spread of starting times and speeds. This model approximation tends to overestimate the peak flux but also will overestimate the initial fall off rate in the neutron flux. A change in scram initiation time of 0.02 sec results in a 5% change in peak neutron flux, so that this effect is not as large as the pressure effect noted 5

above.

The-reactivity curves also show that for the Peach Bottom test conditions, the scram reactivity is very Strong and almost Immediately turns the flux transient around. This is due to the fact that many control rods are inserted in the core, giving rise to a strong scram reactivity.

3-5

.EDO-24154-A The Doppler feedback is small for the Peach Bottom Transients and the final answer is not sensitive to the Doppler coefficient. Turbine trips initiated from higher power will have larger Doppler sensitivities, but even in those cases, changes in Doppler coefficients of 30 to 40% are required to materially influence peak heat flux results.

In addition to the total APRK response, LPRM signals were recorded at 80 locations in the core. The LPRMs are located at four axial levels, which are 1.5, 4.5, 7.5 and 10.5 ft above the bottom of the fuel. These locations will be referred to as the A, B, C and D levels, respectively. Figures 3-21 through 3-24 show plots of all the Turbine Trip No. 1 LPRM signals for each level plotted

.as a percent of initial signal. All the LPRM signals .for a given level have the same time behavior, which indicates that there is very Little radial flux change during the transient. The transient behavior is not the same between the four levels, indicating that there are axial flux shifts during the transient.

The magnitude of the flux shift is considerable. The A level fluxes increase to 350%, whereas the D level increases to 550%. These trends are observed i.

all three turbine trip experiments (Reference 4). Based on this information, a one-dimensional model appears to be appropriate to describe the transient nuclear behavior of the core. Figures 3-25 through 3-36 show comparisons between calculation and data for the A, B, C and D level flux response for the three turbine trips.

The largest flux rise occurs near the top of the reactor core, which has the largest void fraction and the largest void coefficient. Detector A is below the boiling boundary for these experiments and experiences the smallest flux rise. Figure 2-10 shows that the largest void changes occur near the boiling boundary in the low quality regions. In the reactor, the bil *nug boundary is different in each channel and the variation in void fraction with axial pesi tion is smaller than the one-dimensional estimate, which contains a single thermal-hydraulic channel. For this reason, the oue-dinensioual model will overest4mate flux changes near the boiling boundary. This trend can be noticed in the Peach Bottom results in comparing the B level flux respo-se with the other levels.O'17 However, the magnitude of this overestimate near the boiling boundary is relatively small, and the A, B, C and D level comparisons are almost identical to chose observed for the total flux for all three tra=sients.

3-A

NEDO-24154-A This indicates that the one-dimensional model is accurately predicting the ax4Al flux shifts vhich take place during the transient.

3.1.3.3 Critical Power Ratio The critical power ratio (CPR) is a calculated quantity which is a measure of how close conditions in a particular channel are to transition boiling. A good measure of the relative severity of a particular reactor transient is the maximum change in CPR, divided by the initial or steady-state CPR (ZCPR).

For the Peach Bottom turbine trips, the CPR comparisons have been made by driving a hot channel transient thermal-hydraulic calculation with both experimentally determined and calculated iulet flow, pressure, and fuel heat generation rate. The pressure input was taken from the core pressure signal, which was filtered with a 5Hz low pass filter. The transient fuel beat Sen eration rate was taken to be proportional to the total APEX response. Core flow was obtained from pressure drop measurements taken across four of the jet pumps throughout the three turbine trips. Changes in core flow can be detected by assuming the jet pump pressure drop to be proportional to the square of the flow. In practice, however, this is not an accurate measure of core flow because of the large amount of noise in the jet pump pressure drop signal. In this case, a 5 Ez filter was applied to the four jet pump signals to reduce the zioise component and then averaged to obtain a pressure drop. The steady-state flow was normalized to the recorded flow at the beg-n ning of each transieut.

In both cases, the initial conditions and channel properties are identical.

Only the transient pressure, flow and flux responses are different so that a good measure of bias in CPR is obtained.

For the transient CPR calculations driven by the experimental data, uncer tainties in the input quantities will contribute to an uncertainty in the ratio CPR/ICPR. Reference 4 quotes a 12 psi uncertainty in core pressure.

This pressure uncertainty, coupled with a -3Z uncertainty in flow, results in a !:0.01 uncertainty in the ratio CPR/WTP.Q.'5'Q1B This CPR uncertainty is obtained from sensitivity calculations carried out on pressurization type transients.

3-7

NEDO-24154-A The results of the transient CPR calculations are summarized in Table 3-4.

In each case, the model driven CPR/ICPB is within 0.01 of the data driven value. This excellent agreement is an indication of the overall quality of the calculated results and shows that, while differences exist in detail between model calculation and experiment, their overall impact on CPR is small.

3.1.4 Conclusions A great deal of information has been assembled for the three turbine trips carried out at Peach Bottom. The one-dinensioual BWR transient model compares well with the measured pressure responses in the vessel dome and core exit.

The steamnlne pressure comparisons show the model underpredicting the magni tube of the pressure oscillatious -but this does not affect the dome pressure response. The peak ateamlime and dome pressures are overcalculated by the model, indicating the possibility of larger bypass flow than assumed by the model.

The flux response agreement is good for all three experiments. The model overpredicts the peak neutron flux due to a slight overcalculation of pressure near the time of muxd neutron flux. The initial and final portions of the flux show excellent agreement. The axial response is also followed well, as evidenced by comparisons with A, B, C, and D level LPRM signals.

Finally, the good qualitative agreement obtained in the pressure, flow and flux responses results in excellent transient CPR comparisons. Overall confidence in the model is strengthened by the fact that about the same degree of agree ment was obtained for all three turbine trip tests* Model input assumptions were identical for all three tests except for the core power level, core flow and known changes in valve actions and scram setpo*nts. This agreement indi cates that the model can also follow changes in transient behavior due to changes in power level and flow and can be used to predict full power turbine trip transients.

3.2 ElM TURBINE TRIP An instrumented turbine trip was carried out at the MX power plant in Muehleburg, Switzerland on June 30, 1977. The M Plant is unique for .WR's,having two cur bines and a bypass capacity of 110Z of full rated steam flow. At the time of the 3-8

NE)0-24154-A test, the reactor core was near the end of a fuel cycle and all the control rods were out of the core at rated conditions. These test conditions provide an addi tional, valuable transient benchmark because they realistically simulate end-of cycle conditions. However, the two-turbine configuration and large bypass capacity provided additional challeges for the steamline and valve flow portions of the one-dimensional transeut model. As in the case of the tests conducted at the Peach Bottom-2 plant, the direct trip scram on stopvalve position was bypassed to obtain a significant flux response during the test.

3.2.1 Test Summar The initial conditions for the MX turbine trip test are sunmarized in.Table 3-5.

The* pl~int--a ~desigd iith a large bypass capacity in order to avoid a full reactor scram following a turbine trip. Therefore, only selected rods are inserted following the turbine trip signal. For this test, the select rod insertion was disabled. The flux scram setpoint was not changed and remained at 120% of rated for the test. The normal bypass capacity at MKI is 110% of rated steam flow. Each turbine has two bypass valves which are located in the same valve chest with the turbine stopvalves. One of these bypass valves was disabled on each turbine, thereby reducing the total bypass capacity to 55Z of rated steam flow for this test.

As in Peach Bottom, a digital data acquisition system was used to record a total of 118 signals. The signals (summarized in Table 3-6) are essentially the same as those recorded at Peach Bottom. Unlike Peach Bott=o, however, the signals recording the turbine stopvalve and bypass valve positions were not available. The [DI plant has a mechanical control system to regulate bypass flow and a continuous signal recording valve position was not available.

Therefore, additional position switches were installed on these valves, but their signals were lost due to equipment problems. The only signals available are the valve initial opening time and the time at which the valve is in the full open position. The comparisons presented here will concentrate on the pressure and flux measurements which form the qualification base for the dis tributed steamline and reactor core models.

3-9

NEDO-24154-A 3.2.2 Special Model Considerations The one-dimensional transient model used for the description of the Peach Bottom turbine trips is described in Reference 2. Separate models exist for valve flow control and motor generator plants, so that with one exception all BWR/3 through 6 plants can be described. This exception is KKH, which has two turbines and two sets of steamlines. Also, each steeamline has a reheater line, a feature which Is not present on any domestic EW's. Therefore, a special version of the one-dimensional transeint model has been constructed which contains two steamlines and also correctly simulatas the reheater line.

The physical dimensions of both ateslines are identical, so the same constants are used for both lines. A schematic of the steamline model appears in Figure 3-37, along with the dimensions and pressure drop constants.

The pressure control system in use at M3 was also simulated, along with a description of the other unique control features of the WE plant. These other KEM unique model approximations had little effect on the calculated turbine trip transienC response.

3.2.3 Model Inputs With the exception of those items meutioned in Section 3.2.2, the mathematica4l modeling for the [KM transient model is identical to that described in Refer ence 2. The recirculation system parameters are based on the input procedures used for other GE transient analyses.

As in the Peach Bottom tests, the GE BWR Simulator was used to generate a steady-state three-dimensional power distribution for the test configuration.

These nuclear data were then collapsed Into one-dimensional parameters. aecording to the procedures outlined in Reference 2. A comparison of the resultant one dimensional power profile and the process computer output is shown in Fig ure 3-38.. A. total of 32 control rod drift relay signals were recorded, which

.ere then used to determine the control rod bank position with time. From these data, a linear rod motion pattern was established. This pattern is shown in Figure 3-39 along with the measured position ci a few control rods. The time zero is established as that point when the flux reaches the trip setting, which in this case is 1202 of full rated power.

3-10

NEDO-24154-A A special steaMline model was constructed for this analysis and is discussed in Section 3.2.2. The model dimensions and loss coefficients are listed in Figure 3-37.

The gap conductance used in the MD analysis is 600 Btu/hr-ft 2-. F. As in the Peach Bottom analysis, the severity of the test transient is not very large, and the calculated flux response is not sensitive to gap conductance. The core thermal-hydraulic geometry was determined from a weighted average of the dimen sions from the 12 7x7 bundles and the 228 WiS bundles in the core at the time of the experiment.

As pointed out before, measured turbine stopvalve and-bypass valve positions were not available for this transient. Because of the large bypass capacity, the calculated dome pressure and core flux response is sensitive to the bypass valve opening characteristics. In order to arrive at a realistic transient value response, the bypass valve opening time was set at 0.1 see, which was the observed time, and the bypass valve opening speed was adjusted until the calculated transient turbine Inlet pressure response agreed with the measured data. This adjustment affected only the initial valve opening speed. After the initial bypass valve opening, the MX pressure controller system was allowed to change the valve position based on the plant control parameters and the calculated pressure controller inputs. It should be pointed out that the adjusted bypass valve opening speed was more rapid than the value currently used in the KMl design calculations.

3.2.4 Data Comparisons 3.2.4.1 Pressure Calculations Figures 3-40 and 3-41 show the transient pressure comparisons at the two turbine inlets. Upon the manual trip signal, the B turbine stopvalve motion was initiated first, followed by the A turbine stopvalve motion 0.024 sec later. The stopvalve motion closing time was 0.042 sec for both turbines.

All of the plots in this section place time equal to zero at the beginning of turbine B stopvalve motion. Initially, the pressure rises and then begins to decrease about 0.2 sec after the start of stopvalve motion. This decrease is due to the opening of the bypass valve, which begins its motion at 0.1 sec.

3-11

1EDO-24154-A Other oscillations are due to the wave nature of the steamline transient pressure response. The turbine pressure response from 0.2 to 0.6 sec is sensi tive to the bypass valve motion. The best calculated response was obtained with a very rapid valve opening time (ZO.08 sec), which Is more rapid than that used in normal design calculations. The openig time of 0.08 sec agrees quite well with opening imes of 0.07 to 0.09 sec observed in the M startup test results obtained from the turbine vendor. The overall agreement is about the same in the -Aand B steamlies, the only difference being that the A results are dispaced about 0.024 sec in time and the initial pressure rise is somewhat slower in the B turbine.

Figures 3-42 and 3-43 show a comparison of transient steamline pressure for

.--- stemlines A and B, respectively. -The--first pressure -peak is narrower than those observed in Peach Bottom; the magnitude of the peak is reduced by the ope"nn of the bypass valve. The model predicts a slightly slower wave travel time. The 20 to 30 msec delay in the first calculated pressure peak relative to the data still represents good agreement between experiment and model but will contribute to a slight delay in the Initial core pressure rise. After the first pressure peak, the calculations show a 3 Hz oscillation In the steam line pressure. This same frequency is also present in the data. Note that the detailed wave shape is somewhat different in the data and calculation.

The UM model does not undercalculate the magnitude of the Initial st-line pressure peak, as observed in the Peach Bottom results.. This is due to the finer node structure in the KXM sateamne simulation. The M11 used 7 nodes to simulate a 330 ft steamline, whereas the Peach Bottom model used 6 nodes to simulace a 400 ft sceamline. The impact of the sceamline pressure differ ences is reduced because the reactor vessel pressure will depend in large part on the change in total stea-mne flow, which is proportional to the integral of the transient steamline pressure.

The dome pressure comparison is shown in Figure 3-44. The data show a large number of oscillations. These oscillations are due to a disturbance In the instrument Line. This can be verified in the test data because similar oscillations are not detected in the core pressure or neutron flux response.

Because of this behavior, detailed comparison between data and calculations is difficult. The calculated response does pass through the data, but it is difficult to determine if the timing of the pressure wave is being calculated 3-12

NDO--24154-A accurately. The dome pressure compares quite well out to 1.8 seconds, when the data starts to decrease and the calculated pressure continues to increase. No relief valve opening was observed during the test and the cause of the decrease in the observed pressure is not known nor Important in the determination of the core flux response.

Figure 3-45 shows a comparison of the measured and calculated core exit pressure. Although there is some osc4lation in the data after 0.42 sec, an overall pattern can be determined. Again, it is felt that these oscillations are due to instrument line response because no oscillations are observed in the neutron flux. The calculated pressure response lags about 40 msee behlid the data, reachling an. initial peak at about 0.5 sec. Better agreement between calculation and experiment could be obtained with an improved inertia model for the steam separators. The current model assumes the steam to be mixed with the water in the separators, which tends to overestimate its inertia.

The model used here still yields reasonable agreement and also provides a conservative estimate of the neutron flux.

In evaluating the total steam-lne and vessel model, it is important to note that all of the significant aspects of the transient pressure behavior have been duplicated. The plotted data are the raw instrument data, and the instrument line effects are still present so that precise comparisons cannot be made at this time. However, it is apparent that the overall shape of the core exit pressure response is duplicated quite well by the model.

3.2.4.2 Neutron Flux Comparisons The neutron flux response from the KKK Turbine Trip is compared in Figure 3-46.

The KKi transient flux response is interesting because of its double peak behavior. This double peak behavior is caused by an oscillation in the core exit pressure. The pressure rises initially to a peak around 0.4 sec, falls off slightly, then reaches a second peak at 0.72 see. The control rod scram motion starts at 0.6 sec and reduces the magnitude of the second flux peak.

Careful examination of the calculated core exit pressure shows that the model delays the initial pressure rise somewhat, then overestimates the first pres sure rise and underestimates the second pressure peak. This results in a calculated flux which does not have the double peak behavior, but which 3-13

NEDO-24154-A overestimates the initial flux peak and underestimates the second flux peak.

Note, however, that these are shape differences and that the overall magnitude of the transient is slightly overpredicted by the model. Also note that dif ferences between calculated and. observed flux response correlate quite well with differences between calculated and observed core pressure. This indicates that the one-dimensional reactor core model responds quite accurately to ptes sure and scram changes.

The calculated reactivity components are plotted in Figure 3-47. The initial reactivity rise is due to void collapse. Rowever, the scram does not begin until the transient has turned around. Note that the scram reactivity curve has a smaller slope than observed in Peach Bottom. This is due to the all

-- rods-out-configuration. . - .. . ...

As a further test of the reactor core model, the A, 1, C and D level LPR signals were also compared. Figures 3-48 through 3-51 show the A, B, C, and D level LPRU all plotted as a percent of initial power. Note that the overall behavior Is one-dimensional, s-ilAr to the observed behavior at Peach Bottom.

A comparison between calculated A, B, C and D level response and the average observed response at each level is shaw in Figures 3-52 through 3-55. In each case, the calculated curve differs from the measured response. However, the deviation in each case is about the same as observed in the total flux. Note chat the A level flux decreases much more rapidly after the scram begins because of its close proximit to the control rods, whereas the D level flux has only decreased to 120% of initial after 1.2 sec. This same pattern is also evident in the. calculated values.

In attempting to evaluate the one-dimensional model's ability to calculate neutron flux response, it should be pointed out that the M transient is a mild one compared to the Peach Bottom transients. In Peach Bottom the neutron flux peak value was as high as 5502 of initial, whereas the maximum M increase was 220%. Beciuse of its larger bypass capacity and subsequent reduced pres sure rise, the detailed flux response was more sensitive to small oscillations in the pressure, wich, in turn, was influenced by the turbine and bypass valve behavior. Even with the differences in flu= shape, the total energy release is approximated quite well by the one-dimensioual model. The impact on the transient critical power ratio is discussed in Subsection 3.2.4.4.

3-14

NEDO-24154-A 3.2.4.3 Critical Power Ratio Critical power ratio calculations vere also carried out for the M transient using both the model transient and the data transient as inputs to the hot channel calculation. The CPR results are summarized in Table 3-7. Note that good agreement is achieved between the data driven and model driven maximu ACPR values. The uncertainty on the data driven ACPR/ZCPR values is +0.01.

3.2.5 Conclusions Analysis of the KM turbine trip presented a few unique challenges for the cne-dimenslioal trausient model. The wo-turbine, configuration and the large bypassicapacity*required careful consideration of the steamline model and the turbine stopvalve and bypass valve characteristics. The final dome pres sure and core pressure response was followed quite well by the model, although.

the exact shape of the transient pressure response was not duplicated. The overall magnitude of the flux response was duplicated quite yell, even though the double peak shape was not duplicated by the model. However, the success of the model in duplicating the transient is demonstrated by the excellent agreement obtained in the transient CPR values.

The CKH transient was in many ways quite different from those at Peach Bottom, yet the transient model was successful in duplicating its behavior as well, lending additional confidence to its ability to calculate pressurization transients.

3-15

NEO)-24154-A Table 3-1 PEACE BOTTOM-2 TURBINE TRI? TEST CONDITIONS Core Power Care Flow Fl-x Scram Setting (Z Rated) (106 lb/hr) (%Rated) (Z Rated)

Turbine Trip 1 1562 47.4 101.3 100.3 85 Turbine Trip 2 2030 61.6 82.9 82.1 95 Turbine Trip 3 2275 69.1 101.9 100.9 77 Table 3-2 PEACE BOTTOM-2 DYKNAIC TEST SIGNALS No. of Signals Recorded Test Signal. Description 80 LPRK Signaml 4 APEX Signals 2 TIP Signals 4 Jet Pump (Calib) dPs 1 CORE d 2 Steamflow Nozzle dPs 2 Steaflow Nozzle Upstream Pressures 2 Turbine Inlet Pressures 2 Reactor Vessel Pressure Core Exit Pressure Reactor Feedpump Flows 1

Reactor Feedwater Temperature 2

Recirculation Loop Flows 2

Recirculation Pump Inlet Temperatures 2

Reactor Water Level 32 Control Rod Drift Relays 1

Scram Solenoid Relay 4 Turbine Stop Valve Position Switches (2 at 10Z and 2 ac 90%)

Turbine Bypass Valve Posi:ion Switches (2 at 10% and 2 at 90%)

4 Turbine Bypass Position Turbine Stop Valve Position 3-16

KEDO-241.54-A Table 3-3 PE VESSEL PRESSURE Data* Model Calculation Turbine Trip 1 1042 1070 Turbine Trip 2 1052 1072 Turbine Trip 3 1069 1100

• Data value is biased to the same initial value as calculation.

Table 1-4 MAXn0M ACPR VALUES FOR PEACH BOTTOM TURBINE TRIP TESTS ACPR/ICPR &CPR/ICPR Initial CPR (Data) -(Model)

Turbine Trip 1 2.536 0.170 0.173 Turbine Trip 2 2.115 0.136 0.129 Turbine Trip 3 2.048 0.132 0.141 Table 3-5 K=M TURBINqE TRIP TEST CONDITIONS Core Power 769 Mwt 77% Raced Core flow 25.69 x 106 1b/hr 86.5Z Rated Flux Scram Setting 120Z Rated Vessel Pressure 1023 psi 3-17

NEDO-24154-L Table 3-6 M~ DYtAZII1C TEST SIGXALS No. of Signals Recorded Test Signal Description 52 LPRM Signals 4 APM Signals 2 TIP Signals 4 Jet Pump (Calib) dPs 2 Core dP 2 Steamflow Nozzle dPs 2 Steamflov Nozzle Upstream Pressures 2 Steai*nlne Header Pressures 2 Turbine Inlet Pressures I Reactor Vessel Pressure 1 Core Exit Pressure 32 Control Rod Drift Relays 1 Scram Solenoid Relay 2 Relief Valve Positions 2 Relief Valve Downstream Pressures 4 Turbine Stop Valve Position Switches (2 at 10Z and 2 at 90%)

4 Turbine Bypass Valve Position Switches (2 at 1C0 and 2 at 90%)

Table 3-7 MIMM &CPR VALUES FOR THE M TURBINE TRIP TEST Initia.l CPR 1.279 ACPR/ICPR (Data) 0.077

&CPR/ICPR (Model) 0.084 3-18

NEO--24154-A U

z'U C

C

'U

~oJ w

C AXIAL HE!IGHT Ilt)

Figure 3-1.. Azia2. Power ProfiLe Turbine Trip 1 3--19

NEDO-24154-A Ih z

AXIAL HEIGH! 1ft Figure 3-2. Axial Power Profile Turbine Trip 2 3-20

NEDO-24154-A 1.6 1.4 k mmmPROCESS COMPUTER AXIAL AVERAGE ONE-DIMENSIONAL MODEL I

1.2 -

B LEVEL C LEVEL 1.0 1-I U'

C I

C C-A,- 0 C

0.6 oA 1-j 0.2 I-I Ca 2 6 8 10 12 AXIAL HEIGHT Ift)

Figure 3-3. Axial Power Profile Turbine Trip 3 3-21

1.0 05% OF ALL NODS WHIMIN THIS RANGE 0.9

. 0

.8 -,

/,/,,,/

o., -_ ,";, -

0400 *.ASES R0014 ,e SOWESTfVE ROD MTO 4' I ~- -OBSERVED ROD MOTION p

• FHOP MOTION ASSUMED DELAY OF 0.17. #n IN CALCULATION 0.2 ASSUMtES IN CALC 4/ I A LT 0L 0 0.6 1.0 1.5 2.0 2.0 3.0 3.6 4.0 TIME AFTF.I FLUX REACHES TRIP SETTING dl Figure 3-4. Peach nottom-2 Rod Insertion Fraction Versus Time

!I

Ag - ag6 X 8,1 2

IIN UIEADY-1TATE A14 a KI 0 1 Ai a 2.44 ht2

• 1~~ I~~1x1--P'- GOEP GR 2T CONTAINMENT X7, - 1.37 X 104 32h

• -3 I-)

Figure 3-5. Peach Bottom Eight-Hode Steamline Schematic

I 1040

'U I, ~l020 I

A.

0 0.3 0.0 oa 1.2 1.5 1.9 2.1 2.4 21 3.0 3.3 3.6 &.9 TIME ISMI Figure 3-6. Peach nottom-2 Turbine Trip I Steamline Pressure

IL w

1. Am 13 J.

t; F

'p.

2.1 3.9 TIME hoc)

Fig.,re 3-7. Peach Rottom-2 Turbine Trip 2 Steamline Pressure

v A

.12 CK4 0.300 0.6m0 O.VA 11200 Ism0 I.e80 2 le 100 400 2.100 3.000 3.300 3.sm 3.SW Siue -. reac Boto- Tubn *Ti Stemle 5O ueS e C Figure 3-8. reacht Dottom-2 Turbine Trip 3 Stcanatine Pressure

W YA 1020 eOW C, I tI I I iII , I ... II

• a 0.3 0.6 0.9 1.2 1.5 1.6  !.1 2.4 .17 3.0 S.3 3.8 2.9 TuiE T I e s Pigure 3-9. Peach Dottom-2 Tur~bine Trip 1 Dome Pressure d

I NA Id NI TIME tuc)

Figure 3-10. Peach Bottom-2 Turbine Trip 2 Dome Pressure

I iU Im 1020 1000 0 0.3 0.6 0.3 1.2 1.$ 1.8 1.1 24 2.. 3.0 3.3 3.3 TtM-2E be 3 Pe Figure 3-11. ?each Bottotw-2 Turbine Trip 3 Dome Pressure

Ic 0

8 0.0 1.2 1.5 1. 2.1 2A 2.1 3.0 TIME heei Figure 3-12. Peach Dottom-2 Tuibine Trip I Core Exit Pressure

o1040 ¶ V I-.

98.)

040 e *5 S o S

"." 05 551"-'---o 5*

0 0.3 0.6 0.9 1.2 1.S 1. 2.1 2.4 2.7 3.0 3.3 3A3 3.0 TIME foci" Figure 3-13. Peach Bottom-2 Turbine Trip 2 Core Exit Pressure II

lowI Im 1:04 I t%2 4~.

I I,.

0 Oj 0.60 0.0 1. 1.5 1.8 i1 2.4 2.1 &0 33 3.6 3.9 TIME hodTi Figure 3-14.* Peach Rottost.-I Turbine Trip 3 Core Exit Pressure

G2s 450 I DATA

-375 2251 La5

-IS

-75 0 0.15 0.0 0.45 0.80 0.75 0.90 1.05 1.20 1U3 1.50 1.65 1.90 1.01 2.10 2.21 TIME I"lc Figure 3-15. Peach Bottom-2 Turbine Trip I Prompt Neutron Power I

dwo 626 450 - MODEL I,*o,-,*,e -- ,*DATA

'ow go 37S 300 Z10 0

_75I

-7, a 0.11 0.30 0.45 0160 0.7 0.90 1.01 1.20 1.3 1.10 1.6 1.00 1."0 2.10 2.21 2.40 TIME Inmc)

Figure 3-16. Peach Bottom-2 Turbine Trip 2 Prompt Neutron Power

MODEL

-10 a 0.16 030 0.41 IBM US1 0.00 1.05 1.20 1.35 1.50 V.61 1.50 1.96 2.10 2.26 2.40 TPM! Wue Figure 3-17. Peach Bottom-2 Turbine Trip 3 Pro~pt N~eutron Power.

NEDO-24154-A U.

I-

-0.4

-0.6 0 0.2 OA OX* .3 1.0 1.2 TIME (sed Figure 3-1.. Peach Bottom-2 Reactivity Turbine :rip 1 3-36

NEDO-24154-A 1.0 0.8 0.8

-0.2

-CA

-4A TIME fadc Figure 3-19. Peach Bottom-2 Reactrivity Turbine Trip 2 3-37

NEDO-24154-A OA w 0.2 lIME Inud Figave 3-20. Ptach Bottam-2 NLeactivity Turbine Triv*3 3-38

2 w

L.8

'0 I

3.0 TIME fwel Figure 3-21. Peach Bottom-2 A Level LPtlH'a Turbine Trip 1

3 ta 0 400 U

-I X 300 I

08 0.9 1.2 IA 1.8 2.1 2.4 2.7 3.0 TIME Ind Figure 3-22. I'ench nottan-2 B Level LPRH's Turbine Trip I

LPRM FLUX IFERCENT OF INITIAL)

C rw oq

IL u

IL. NI TIME 4wcd FIRurU 3-24. Peach bRttom-2 0 Level 1PRM'. Turbine Trip I

NZDO-24154-A MO.

ý am Gen DATA mwmý MODEL 700 x400 300

//

200 0 I

0. (.4 06081.0 TeALE Tid Figure 3-25. Peach Bo~tom-2 A Level Flux Turbine Trip I 3-43

NEDO-24154-A DATA MODEL I

x I'

VI00 0 0.2 0.4 C. 0A 1.0 1.2 TIME fma Figure 3-26. Paeb Ecttam-2 B Level Flux Turbine Trip 1 3-44

ZEDD-24 154-A DATA MODEL 700 4w 16 U. 1.0 TIME (mci Figure 3-27. Peach Borctcm-2 C Level Flux Turbine Trip 1 3-45

IUMO-24154-A 700 1o0 S400 200 100 TIME Ibed Figure 3-28. Peach Sottow-2 D Level Flux Turbine Trip 1 3-46

NEDO-242.54-A DATA MODEL 700 300 too a

0.3 0.8 GAEo Figure 3-29. Peach Bo*t=o-2 A Level Flux Turbine Trip 2 3-47

NEDO-24154-A 700

-I x

-a U.

300 200 too a

a.,

TIME UmcI Figure 3-30. Peach Bot*cm-2 B Level Flux Turbine Trip 2 3-48

?4EDO-24154-A 7w0 300 0

TIME bdJ Figure 3-31. Peac~h Boctom-2 C Level Flux Turbine Trip 2 3-49

NEDO-24154-A CATA ANOOEL 700 ow 3W0 a 0.8 1.0 0 0.2 0.4 CA TPE Ind F.gure 3-32. Peach Boctom-2 D Level Flux Turbine Trip 2 3-50

NEDO-24154-A

-a 0.6 TIME bead Figure 3-33. Peach Bottom-2 A Level flux Turbi[ne Trip 3 3-5i

MMDO-24154-A DATA MODEL I

-a K

-a

'a.

300 0

0 0.2 0.4 TIME (wec FLgure 3-34. Peach Bottom-2 B Laval Fl=~ Turbine 4.rip I 3-52

NEDO-24154-A K

U.

0 0.2 04 0.S 0,8 1.0 1.2 TME ImcJ Figure 3-35. Peach Boctom-2 C Level Flux Turbine Trip 3 3-53

M*DO-24154-A 7tO

-a E

£

~

-a ma.

300 100 0

a 0.6 TIME Imc)

Figure 3-36. Peach Bottem-2 D Levell Flux Tuxrbine Trip 3

3-54

I I STEADY STATE. at - 0 I

fll~tF VLVS All - C.111l13 CA I a PLOW NOZZLE Kg a 4"X.2 t A* 2 , OTS.

A-t'- v6P Ov A2IflAf: . .2 2.44 1.89 1.89 1.80 2.1 KIL OSS COEFFICIENT 4.29 10" 6.66u t04 6.563 2.:1.3 IO 3.3 0.! 10--6 3.31 x 10"s1.6. 0 NIBYPASS VALVE Figure 3-37. Schematic of KK1 Steamllne Model

. MPROCEIM COMPUTER AXIAL AVERAGE 1.4 1.2 IO ~c 0.8 - A 0.4 0.2 0.

0 1.3 3.0 4.6 6.0 7.5 9.0 10.5 12.0 AXIAL HtMtif 1tf)

Figuire 3-.1. Average Axial Power K)t Tent Conditions

OS ma.

0.6 t*)

NI 01h 1.0 1.6 2.0 .5 2.0 3.a 4.0 TIME AFTEFl FLUX AEACSES TRIP UTTMNG fei Figure 3-39. Control Rod Motion Pattern KKM Turbine Trip Test

EMO-24154-A 461 I

TrME lad Fig,*e 3-40. Tuirbine Pressure Turbine A ~M Turbine Ti~p 3-58

KEDO-24154-A 103 TIME 6.)

Figure 3-41. Turbine Pressure Turbine B IK Turbine Trip 3-59

4L 3I I

TIME fuel Figure 3-A2. KKM Turbine Trip Steomline Pressure, Turbine A

S U'

I a.

I-.

IU I I gD.

TIME fol Figure 3-43. IHTurbine Trip Steamline Pressure, Turbine 5

11:0 1090 4%00 1040 Iwo MODOEL

• 4

• m DATA 0

0 0.3 0 0.3 1.2 1.6 1.3 2.1 2.4 2.7 3.0 3.3 TIMI fmc)

Figure 3-44. KKH Turbine Trip Dome Pressure I

t:

I Job 0.6 0.9 1.2 I. 1.8 2.1 2A TIME fud Figure 3-45. KKH Turbine Trip Core Exit Pressure

15 T-ISO IO 0

-son hoar e* m~n 4o e 4M0 . d"Wo0 eO0 Mwoom. *g*l "". a in *N *mdlb

• in..-0

a. 0 . 0h 0.0 0~o

.46 0.50 0.15 0.90 1.06 ,.20 1.36 1.10 III 1.80 1.01 -----.

2.10 2.26 TIUE (toe Fiaiure 3-46. KlUH Turbine Trip Prompt Nleutron Power

NEDO-24154-L 0

9 S..

U w

9.20. 0.6 0.8 I TIME imci Fi&g~1e 3-47. Reactivity Compouen.ts MH Tuzbine Trip 3-65

NEDO-241.54-A I-Ma 7.n a Q3 1.2U 1.5 1.9 2.

TIME toga Figur~e 3-48. A Lzve.1 LM~ Flux M{ Turbine Trip 3-66

I NEDO-24154-A Z

Gw ou 1.2 TwIfowss Figure 3-49. B Level LFR Flc 1 TM Turbine Trip 3-67

NEDO-24154-A Ew liME inoS Figure 3-50. C Level LPUI{ 71i= KX Turbine Trip 3-68

NEDO-24154-A I~M w

AL a 0.3 06 a. 1.2 3A5 1.8 2.1 TIME fad Figure 3-51.. D Level LPRM Flum KKX Turbine Trip 3-69

MMDO-24i154-A 0 &2 CA4 La.

TIME berj Figue 3-52. A Level Flux EM Turbine TriLp 3-70

NODO-24154-A S

-5 I-x TIME (MCI Figure 3-53. B Level Flux MC Ttrbiue Trip 3-71

NE30-24154-A 320 200 I.6 100 liME !uc Figure 3-54. C Level1 Flux M~ Turbine Trip 3-72

REDO-24154--

I 6

x TIME 4usd Figure 3-55. D Level Flux MX Turbine Trip 3-73

KEDO-24154-A REFERENCES

1. R. B. Linford, AnaZytioaZ Methodse of PZant Tr'ansient Zva Zuattionz of the Genera, E-Tectric Boilin Water Reactor, NEDO-10802, February 1973.

2. One-DimeneionaZ Core 2.ransient Modet, MM-24154, Vol. 1, October 1978.

3. J. A. Woolley, 2%ree-DiiensionaZ BO Core Simuator, M=DO-20953-L.

4. L. A. Cazrichael and R. 0. Ni.em, franient =d StabiZity' Teste at Peach Bottom Atomic Power Station Unit 2 at End of 4i:ae 2, EPR* NP-564, June, 1978.

5. R..T. Lahey, B. S. Shiralkar, J. K. Gonzalez, L. E. Schnebly, The Ana Zyvi of Critical

--- z'sent Eeav Fu=, GEAP-3249, April 1972.

6. FZow of zluida -Through Valves, Fittings an'd Pipe, The Crane Co. Technical Paper No. 410, 1969.

7. N. H. Larsen, Core Design and Operating Data for Cycles Che .?d of 2n Peach Bottcm-2, EPEI-0563, June 1978.

8. eneric Roeoad .vuel Application, MEDE 24011-P-3, May 1977.

3-774

NEDO-24154-A

4. P.ECIPCUIATIOfl A21D CONTROL SYST MODEL The recirculation and control system is simulated by solving the mass, energy, and momentum balances over all of the appropriate steam line, vessel, and recirculation loop components. The control and safety system functions are simulated through digital logic in the transient model. The model block diagram is shown in Figures 4-la and 4-IL. These figures can be used to refer ence the equations in this section.

4.1 VESSEL AND STEAf LIY!E HYDP.ATLIC .CDEL The saturated regions of the reactor vessel and steam lines are simulated by lumped transient mass, energy, and volume balances. This division is repre sented schematically in Figure 4-1c.Q18 4.1.1 Uoper Plenum Model In formulating the mass, energy, and momentum balances, the following assumptions are employed:

1. A homogeneous mixture of steam and liquid phases exists in all regions.

2. Thermodynamic equilibrium exists.

3. Inertial and friction momentum losses can be ignored in the core exit plenum.

4. YMass and enery, storage variations in the separators are negligible.

5. Friction dissipation of energy is negligible in exit plenum regions.

The mass balance is written,

, M fc

-C + MfB +m +m gB +m Cs -mm21 - m 11 C4-1)

Q18 - Responses to NRC questions on the text are documented in Appendix B. The symbol QI8 denotes that this topic is discussed further in the response to NRC Question 18.

4-1

NEDO-24154-A where mfc, mfB, mgC and m are obtained from the core hydraulics model (see Section 3.2) and m2 1 and m11 are the vapor and liquid flow leaving the upper plenum. The plenum density is given by Mi 1l/Vl (4-2)

The liquid and vapor masses and plenum quality are given as Hg . VI/Vfgl - (Vfl/Vfgl) M1 , C4-3 1 M - M1 -. Mg , (4-4) x1 gl/ 1m. (4-51 The momentum balance is given by 0 - 144 ()e - "Pe gp II (4-6) le c The energy and volume balances can be used to obtain the following energy equation:

hfg 1 (m + m ) vg-+

v fg1 ac gB 11 g (mfc + MfB - m2 1 + mCS) Vfl dh+ dhf 144V,

+ race (h cs - hf l ) dP fl dP

= I(Mgl dvf)1 i (4-7)

Vfgl + MflM "P- dt V fggl 4-2

NEDO-24154-A Figure 4-1a. Model Block Diagram with Motor-Generator Flow Control 4-3/4-4 I

NlEDO-24154-A Fture 4-lb. Model Block Diagram with Valve Flow Control 4-514-6

RELIEF VALVES STEAM LINE NODES 3 - 6 MIT ISOLATION - TURBINE VALVES CONTROL VALVES Oft STOP VALVES I

-,4 Sd2.

h0 2 STEAM LINE NODES I ANDS I

a.

miIs mdI.hDI BYPASS VALVES M3, h3, RECIRCULATION DRIVE PUMP I mRL I hRLt INLET PLENUM Figure 4-1c. Thermodynamic Hodel Schematic

ICEDO-24154-A 4.1.2 Separator Model As the separator mixture leaves the core plenum pressure node, it =ust underro a slight adjustment in quality because of the change in saturated properties from the core plenum to the vessel pressure node. The quality in the vessel pressure node can be determined from the folloving assumptions:

1. The quality of the saturated mixture entering the separators is the average plenum quality.

2. The saturated mixture entering the vessel node mndergoes a free expansion in a massless region at the separator inlet.

From an energy balance, the quality of the mixture entering the vessel node is given by X l 71 + h fl - hf 2 X2 - hfg2 (4-8)

Assuming the average density of the fluid in the separator barrel to be approximately the same as that in the plenum and standpives, the mass of steam in the separators is given approximately by Ms " "IXIVs" (4-q)

The saturated liquid mass is then M - vs - ssM C4-10)

The transient steam separator flow equation can be derived based on the folloving assumptions:

1. The transient behavior of the stem separators is adequately described by the dynamic response of one averape separator.

4-8

NEDO-24154-L

2. The compressible flow effects in the separators can be neglected.

3. The steam separates near the inlet of the separator, giving a central core of vapor and a layer of liquid spiraling -up the separator vail.

4. The principal inertial effeets are due to the layer of liquid. CA-l other L/A terms are small compared to this value.1 A force balance on the liquid flow spiraling along the wall gives (L .m - 144(P p)  !(_ el ++/- 2).

I C4-11)

(9A 21le 2 9cSep sep where separator geometry is given in Figure 4".2.

Experimental steady-state measurements of the pressure drop across the separatols) are correlated by AtP sep -C m 2 2N sep m3s /01.sep (4C-12)

An estimate of the effective length-to-area ratio in the separator Barrel, and hence its calculated inertia, may vary considerably from the physical dimensions if it is assumed that an average particle of fluid must travel a spiral path from the inlet to the outlet.q'5 Studies concerning design, analysis, and testing of the separators have led to further understanding of the liquid layer thickness, velocities, and effective i/A (flow length/area) relationships. These studies showed several important relationships which led to the model simulated here.

1. The water laver along the separator was virtually independent of the total flow (200,000 < Flow < 800,000 lb/h).

2. This water layer thickness (jnd thereby the effective L/A) was dependent upon the quality at the separator inlet.

4-9

IqZ.O-24154-*.

Rr* LSO Figur~e 4-2. Steami Separator Schematic 4-10

KEDO-24154-A Typical variation of 3/A with quality is shown in Figure 4-3. The other length-to-area ratio in equation may be evaluated directly from physical dimens ions.

The steamflow entering the vessel is then obtained from:

m12 -' x2 3s (4-13) and liquid flow from m22 ' m3s - "12 (4-14) 4.1.3 Vessel Dome and Bulkwater Model 4.1.3.1 Vessel Pressure Rate The analysis of the transient thermodynamic conditions in the vessel pressure node is deri-ved on the basis of the following assumptions:

1. The rates of mass transfer at the steam/water interfaces, other than carryunder in the bulkwater, are negligible.

.2. When the vessel pressure rate is positive and the carryunder mass in the bulk water is zero, the bulk wateT is subcooled.

3. Enthalpy changes in the bulk water due to pressure changes are negligible when the bulk water is subcooled.

4. The mixing of feedwater, bulk water, and carryunder occurs in a massless region whose position Is independent of time.

S. The mass of liquid in the separators always remains saturated.

6. Heat loss from the vessel and intervals is neglected.lQ48 4-11

NEDO-24154-A 200 2.5 160 2.0 120 1.5 j Au d"

0 z

NJ

-J N.

Mi N. s0 N.

NJ 40 05 a

0 4 a 12 16 20 SPARATOR INLET CUALnY %1)

Figure 4-3. Centrifugal Stea- Separator Characteristics versus Tnlet Quality - 200,000 c toterl flow < 800,000 lb/hr 4-12

NEDO-24154-A The mass, volume, and energy balances for the vessel pressure node are:

Mass Balances Mg2 - m12 - mgfb -m - m13 (4-15)

' m2 2 + mgfb " (4-16) f2 23 Volume Balance V2 - 4g2 vS2 + Mf2 vf2 (4-17)

Energy Balance (m2 -mcu - 13 ) h.2 + (M 2 2 m 33)hf 2 ug2 u.2

+

• 144P 4f2u22 i 22 (4-18)

Noting that V2 - 0, the combination of Equations 4-15, 4-16, and 4-17 gives the expression for the vessel pressure rate, hfS2[Ivf(22 - mn2 3 ) ' v,2 ('1 22 - m13 - m)1 - 2 (429 where for Mgb > 0, D (M fb + XfS dP gd +

X gb) -dP 21 h rdYf +(4-20) dv1 2 2 vfg2 I(Mb+Mfg dP gd gb -(2 4-13

NEDO-24154-A and.,for Mgb - 0, and P 2 > 0; mcu- 0 and D2 [ fs f~

h fg2

+Md gd 144V2 J

!a2 21 "dP g F dvf 2

+

+Md dv R dvs]

+ ifb n -- J (4-21) 4.1.3.2 Mass Balance The total mass of the vessel bulk water can be obtained from the mass balance.

fb 22 mgfb 23 (4-22) and the carryunder entrained in the bulkwater is obtained from Agb - Xcu '22.-m'c - mgfb (4-23)

The mass of steam in the vessel dome is obtained from the mass balance in the dome (4-24)

~gd ' '12 -Xcu '22 - 13 The volume of bulk water and entrained carryunder above the feedwater sparger is given by Vb+cu - M"f vf 2 +÷Mb vS2 - V5 (4-25) 4.1.3.3 Downcomer Flow The carryunder flow entering the downeomers is proportional to the product of the mass ratio of entrained steam to bulk water and the liquid flow from the

vessel, m

Ecu (4-26) fb 4-14

NEDO-24154-A At the 'eedwater sparger, the application of flow continuity yields:

' 31 ' ' 23 +' fw 'cu c - (4-27)

Using (4-26) for ncu , it is possible to solve (4-27) for in2 3

.23 = (31 - fw - *ci) (+ Mfo

.M (mn3 - m -i~/( + (4-28) 4.1.3.4 Carryunder Condensation Rate Because of the carryunder from the steam separators, an entrained mass of stem bubbles will be present in the bulk water of the vessel. This mass of steam has an influence on the pressure rate in the vessel, and consideration of its dynamics is included for that reason. Mass and energy balances can be written for vessel bulk water and carryunder as follows:

Mass Balances Hgb -X cu '22 - m'cu - -gfb C4-29)

Mfb m2 2 + gh -~ '23C4-30)

Energy Balance Sh22 hf2+Xcu 22 hg2 m23 hf2 cu hz g2 144V P Mgb ug MB 2 + Mfbuf 2 (4-31)

Ccmbining the above two equations leads to an expression for carryunder condensation rate dh 2 +2 _144 (Vz + Vhfb 2 (4-32) ngfb hfg2 LXgg P ft dP Ijt 4-15

NEDO-24154-A If carryunder completely condenses, (4-33)

Mgfb = Xcu m2.2 At the feedwater sparger, the saturated liquid, carryunder, and any high pressure core injection flow is assumed to mix perfectly with the subcooled feedwater.

The enthalpy of the fluid entering the downcomer is given by:

h33 = (hfw m' + h£2 i 23 + bg2 mcu +mct hci) m31 (4-34) 4.1.3.5 Vessel Level Referring to Figure 4-4, it is apparent that the vessel level change per unit volume, bulk water, and carryunder will vary with vessel level. Defining level in the model to be the height of carryunder and bulk water above the bottom of the separator, the vessel level may be expressed as follows:

Vb+cu- ALlVb+cu,O Lv <0 (4-35)

Vb+cu " Vb+cuO 1 - hsep

• Lv , 0 (4-36)

AL2 V- b+cu - Vb+cu,0 AL2 hsep +

L -3 h Sep' (sepl > Lv > hseo) (4-37)

Vb+cu - Vb+cu, - AL2 hsep I

- AL 3 (lsepl - hsep) + sepl Lv > sepl (4-38) bulkwater volume when Lv - 0 (volume of the bulkwater where Vb+Cu,O is the region below the separator discharge skirt) 4-16

NEDO-24154-A I

LEVEL SENSOR FUgure 4-/4. Vessel Level Schematic 4-16a

NEDO-24154-A and AL, - Av -Nsep ASp (4-38a)

AL2 - Av- sep AB (4-38b)

AU -- NSep AOB (4-38c)

The level sensor measures the differential static pressure between a tai on the side of the vessel and the bottom of a reference leg of water, maintained at constant temperature. The level signal appearing at the input to the feedwater control system, in terms of height of saturated water, is given by (Is+ Lv) 0 s 0 f2 b+cu where Pb+cu bc (Mfb + Mgb) (4-40) 4.1.4 Steam Line Model Description The pressure and flow behavior in the steam line is described by the conserva tion of mass and momentum equations:

_ .(4-41) where o is the density of the steam, P is the pressure, Q is the mass flow per units area, and x is the distance along the steamline. The flow-squared term in Equation 4-42 represents losses due to friction. The steam is assumed to behave isentropically, so that the energy balance is described as, P- a constant (4-43) wY where y is the ratio of specific heats for steam.

4-17

NEDO-241254-A Differentiating Equation 4-43 with respect to time yields o 0 dP ao P dP- (4-44)

Ot TPd7t permitting Equation 4-41 to be expressed as,

• QO YP (4-45) at "X Equations 4-42 and 4-45 are solved by nodallzing the-steam and bypass lines.

An eight node steam line is shown schematically in Figure 4-5. Note that the main steam line is divided into six segments, or nodes, and the bypass steam line is described by two nodes.Q19 The first node incorporates the steam line volume between the vessel and the safety and relief valves, while the second node includes the remaining volume up to the MSIV's. The four nodes downstream of the .'SIV's describe the remainder of the main steam line and their dimen sions can be adjusted to provide for varying cross-sectional pipe areas and to allow correct placement of the bypass line which can be attached at nodes 3, 4, 5, or 6. Associated with each node are six physical quantities. These quantities are: Ai, node cross-sectional area; li, node length; 0.i, flow through node; P., pressure at end of node; pi, density of steam within node; and KI, a frictional loss coefficient. In addition, in this model the dome is treated as a pure source of pressure, P0 . which varies according to the thermo dynamic response of the vessel dome during system transients. Equations 4-42 and 4-45 are integrated over each node segment to obtain Pi P I" R+/- iQi Nil

-~"L

( -6 (4-.46) and

= +/-i Qi+x s (4-47)

(i 4-18

top i j BYPASS VALVES L ~ BYPASS LINE ATTACHES AT ANY OF NODES 3.4. 5, o q6 4~ RlELIEF AND SAFETY VALVES DOME 01 0 P03 P3 1 04 P 0 .I 01 Po4 f405 p5 0 2 -- 0,- - +I f ---- QTSV TUHBINE 21, 014 f !4 VALVES Figure 4-5. Eight No de Steam Line Schematic

NEDO-24154-*

where Ri W- ( i + P IV) (4-48) 1i" (144)(32.2) Ai c a A' +/- (4-50)

YPi i

The quantity QB represents the flow through a branch contained in node L. This branch may be the bypass line, in which case it is Q7 , the flow through the first bypass node. It also may represent the safety and relief valve flow. At the end of the steam line, Qi+l is replaced by the turbine or bypass valve flows. These flows are based on total steam flow and valve position.

Tt is seen that each of the R, L, and C elements are dependent on readily available parameters. The lengths and areas of each node vary with the plant being simulated, values of K are obtained from initial pressure drop data, and the density, 0i, is calculated at any time using Equition 4-64. Near 1000 psia (typical operating pressure), y varies from 1.26 to 1.05 based on quality and steam temperature and is obtained from steam tables.

4.1.4.1 Safety and Relief Valve Model The relief and safety valves provide high-pressure relief for the vessel if their setpoints are exceeded. The location of the relief and safety valves is along the steam line prior to the isolation valves. Generally, the relief and safety valves do not reseat at the setpoint pressure where they open.

The typical valve lift characteristics for pop-action relief and spring-action 4-20

NEDO-24154-A safety valve operation are shown in Figure 4-6. The flow throUgh the relief valves is governed by (RC - mRU)/TRV (4-51)

PRL

- - L .if

'( PR. > or P >P after >P .

0 otherwise (4-52) where P L,0 is the initial line pressure.

The total relief valve rated capacity, OEG is obtained from the individual relief capacity at initial line pressure mRC - Nv CRv (PRo)" C4-53)

The safety valve flow is determined similar to the relief valve flow (sc O - 'su)/"sv (4-54)

MSU(ýR-) , if PgL > Pss'i or PRL > PSR,i after PRL > Pss' i (4-55) roSY " /0 otherwise.

Because of the characteristics of the relief and safety valves can be different, the rated capacity of the safety valves is

'su EKsvi CSv

• o) fsv (Pz' Ps,1) 4-56) all open groups, i where f SV (PRL Ps,t ) is the lift characteristic of the individual safety valve set to open at P ss," The function fSV can, of course, be used to simulate a wide variety of characteristics, including those of the relief valves if the 20 characteristics are the same.Q 4-21

IMEDO-24154-A RELIEF VALVE LIFT 60 1%OF FULL OPEN) 0 PRS PRL SAFETY VALVE LIFT 60 M OF FULL OPEN) 0 PSR PS PRL Figure 4-6. Typical Safety and Relief Valve Characteristics 4-22

NEDO-24154-A 4.1.5 Core Inlet Plenu- Enthalpy Balance There is a time delay before a perturbation in feedwater enthalpy affects the drive and driven flows in jet pump plants. In non-jet pump plants, the delay also exists through the recirculation loops, but due to the separation of downcomer flow into a drive and driven flow in jet pump recirculation systems the jet pump plant time delays affect the recirculation flow in a more complicated fashion. All model flow time delays are obtained in the same manner. They begin by considering an enthalpy balance on a length of line in wb.ich no back mixing occurs with negligible heat loss, i.e.,

a ml ah (4-57) with the boundary condition that h - 33 (t) at x - 0 (feedwater sparger) where h is the enthalpy and a is the density of the fluid.

4.1.5.1 Jet Pump Recirculation Systems The enthalpy balances of the core inlet plenum and jet pump regions depend on the following assumptions:

1. Perfect mixing of suction and drive flow occurs in the jet pump throat.

2. Perfect mixing occurs in the vessel inlet plenum.

3. The liquid entering the core is at the average enthalpy of the plenum.

4. The inlet plenum is incompressible so that pressure rate effects on properties and enthalpy can be neglected.

4-23

NEDO-24154-A The solution to Equation 4-57 at the jet pump-throat entrance is the familiar delay solution h ti h33(t - TDC) - t ' TDC (4-58) hti - h 33 (0) t-'TDC (4-59) where mLi/."r dt' - VD/NL. (4-60)

L-ZDC There is an additional delay through the recirculation loop so that drive flow enthalpy at the nozzle exit becomes h 3 3 (t TDC - 'Ri) - 1 1 o'Z/ (4-61) hnozi - - 0 3 1 ,t I TDC +I TR Sno zi h 3 3 (0) -lo$0 /m 3 1 , t I i* + TRi (4-62)

Again the time delay, xn, can be obtained from a volume balance similar to TDC I md dt t' -'

VN+

+ V.R (4-63)

Finally, the diffuser exit enthalpy is the mixing throat enthalpy delayed by flow transport similar to the enthalpy delay through the other parts of the recirculation system t > 'DE (4-64) hDE(t) - *i(I - TDzi) 4-24

NEDO-24154-A t

Prdtt.

"R VDiff V (4-65) f-DE hDEL(t) - hDi t < =DEi (4-66)

The quantities hDi and mdi are obtained from the following mass and energy balances:

Jet pump mass balance (loop i)

-Ri mSCTiL 'di" (4-67)

Energy balance inside jet.pump

'*Li bhD - eSCTi hi+mdi hIoi. (4-68)

Energy balance of driven flow entering inlet plenum hDE lN R + hDE2 N2 mF1 2- (4-69) m31 h 3v -

4.1.5.2 Non-Jet Pump Recirculation Systems Assumptions 2 through 4 of Subsection 4.1.5.1 also apply to non-jet pump recirculation systems.

The non-jet pump plant recirculation flow enthalpy at the lower plenum is due to a single delay through the entire dovncomer-recirculation loop:

-Lpi h33 (t TNXi) - Eloe/,3l t > rRJi (4-70) los /a , t -Nj" (4-71) h +/- . h 3 3 C0) - 31 <

4-25

KEDO,-24154-A where T.J. is obtained by solving ftV RLi/Prdt + (4-72)

The energy balance of inlet flow is expressed as 714, ma, h a 1 h3v -*" (4-73)

-i 4.1.5.3 Lower Plenum Enthalpy Balance (Applied to Jet Pump and Non-Jet Pump Plants) 31 --

• 3(h 3v - h3l) (4-74)

VLP 7r The core inlet subcooling is given by Ah - hf - h 3 1 (4-75) 4.2 RECIRCULAION FLOW MODEL 4.2.1 Vessel Inlet Flow 4.2.1.1 Jet Pump Recirculation Systems Refer to Figure 4-7 for a diagram of a jet pump and terminology used in this part of the analysis. While the model shown includes only a single-nozzle jet pump, it is possible to simulate multi-nozzle jet pumps by varying the area of throat and nozzle and adjusting the friction coefficients for flow through the recirculation loops to correspond to the multi-nozzle loop. The momentum balance equations are based on the following assumptions:

1. All recirculation flow liquid is subcooled, Incompressible, and one dimensional.

4-26

81 NEDo-24154-h.

od1 DRIVE PUMP mRL2mL Figure 4-7. Jet Pump Schematic 4-27

NED0-24154-A

2. Velocity heads in the bulk water, downcomer, and lower plenum are negligible.

3. Flow mixing in the jet pump throat occurs in an inertia and loss free region which extends from the nozzle downstream to complete momentum exchange.

4. Static pressure is uniform across the suction and drive flow area at the nozzle exit.

5. Inertia in the suction flow jet pump entrant region is negligible.

6. Mixing of suction and drive flow is not appreciable until the jet pump throat entrance is reached by both flows.

The drive flow loop momentum balances are,

1. Pdwn to vessel outlet

( -D . 1 d - Pvoi d44 g 0r D " dwn "di (4-76)

2. Vessel outlet to nozzle exit (LRL\ 'di 144 + _

-Poi + 2 14c4(P pi jeti) - (Kd + noz Mdi

)nd 3 g . 1o S unni 2 a om- di(2 gA;,) g_ WrAZ (4-77)

3. Suming 1 and 2 above

+c di 2

-(Kdwn4K+K m'di (4-78) d +oz d*i -270r c no:

4-28

NIEDO-24154-A The dovncomer pressure is calculated from.

P + T (.b + Lv) '- mRb4LJ 144 (4-79)

The total driven flow is given by

1. P dwni t Fjeti eo 2 (4-80) jeti ~dwni -CT)

2. Pthi to core Inlet daj- - 144CP P)+J &

- Kif - 2g /

2cr A2)'RLi (-1 in3 1 - K1 m1I+. " 2 mR 2 * (4-82)

Si.1ng Equations 4-79, 4-80, and 4-81 with the additional substitution for '31 from differentiation of Equation 4-82 gives the overall momentum equation for each loop:Q24 IL d LLP Lb )+ 144(P22 - e)

+ '~i 1 4 4 (Pthi -

+%LP 2dif

+ dif + T(a

&rZ + Lv) -b+di 2~ - rSCT + 2BA~ 1 4 4 AP (483 2gcýmR~i 2 - 2g.,..t -bJ S~

4-29

NEDO-24154-A The jet pump mixing region pressure difference, 4Pjeti" is calculated by per forming a momentum balance in the momentum exchange of the jet pump. Since this region is small, it can be considered inertia free. The inertia-free momentu= balance for the momentum exchange region can be written generally for one-dimensional flow in the following form:

rF (mout Vout - min Vin)/g . (4-84)

The Vin and Vout are the velocities in and out of the region, respectively, and are assumed to indicate flow direction at this point. The idealized geometry of the nozzle, suction channel and throat regions is shown in Figure 4 -8.Q21 For for*ard flow in both loops, it is possible to write the following mass and momentum balance equations:

MRLi Mdi + ms'rCi (4-85) 2 u Vouti (4-86) rAth v

mIn Vln, M$£ V* +m di Vdl. (4-87) 2 2 US5 Ti + Udi (4-88) i~n i~n Or Asct ;r Ano:

The force balance on the momentum exchange region is:

AF w (PJet (oz+ ASCT) - Pthi Athi)144 (4-89)

IF - 144 ((Pthi - Pe) Ath) - 144(-APjet Ath). (4-90) 4-30

NEDO-241.54-A

.pjgti wp'- pjkt Figure 4-8. Jet Pump Throat Diagram 4-31

HEDO- 24154-L hence 2 2 L4g Aetje Ac A) r gC Ath (4-91) n tz The result of Equation 4-91 holds in all flow cases for the geometry of Figure 4-8. The specific cases are: (1) all flows forward, (2) suction flow reversed ("d - mSCT + ORL), (3) suction and diffuser flow reversed with forward drive flow (mSCT mmd + mRL), and (4) all flows reversed (mRL a md + mSCT).Q22 4.2.1.2 Non-Jet Pump Recirculation Systems Refer to Figure 4.7a for a diagram illustrating the non-jet pump terminology.

Summing the momentum balance equations from the vessel outlet through the recirculation system and back into the vessel inlet plenum, gives L ('Rý) * - 144(AP + P0voi) + 9c & R IpiI +Pv RL r 9c ARL MRU 2 2 (4-92)

- RL ORLi - rLP RLi (-2 This equation describes the transient loop flow through either recirculation loop of the system.

The equation for the flow in the downcomer is LD 1l44(P.) - Po) +c a

-A RUi v XCcr4D+bL+ &)

, V 2 (4-93)

-KD RLI Differentiating the mass balance in the lower plenum yields dm31 duMi (4-94) dt-i dt 4-32

KEDO-24154-A Figure 4-7a. Non-Jet Pump Schematic 4-32a

NEDO-24154-A Substituting Equation 4-94 into Equation 4-92 and adding Equations 4-92 and 4-93 yielda the following equation describing the transient flow In loop i 1 [1R "D]%( ~L i " 144(P - P + p . + 'b(Lv+ l 'b)

÷ 2 Scc 2 2 -95) 23 where %PC is obtained from the core model.Q 4.2.2 Recirculation Pump Drive Systems 4.2.2.1 Pump and Pump Drive Motor The recirculation pump drive motor power comes from either a drive motor connected to a generator unit through a fluid coupler or the power plant output directly. In either case, the pump torque requirements and pressure head produced can be approximated by the following equation "fits" to the manufacturer's curves as a function of pump flow and shaft speed, T ro " K IT].n 2 +

pndi + KPT 2 mi ni

+ KPT3 (mri + "PT4 Op1 ) Ju~i KPT4 'PIl (4-96) and AP KMu n2 + R~i1 mpi + KPM(m i + 1'pHd)IzPi + KM~4 1 (4-97) 4-33

N~EDO-24154-A for forward and reversed flow operation. Typical curves are shown in Figures 4-9 and 4-10. The equation describing pump-motor shaft speed is rJ du i (4-98) 30Z-C dt (Te'i - Tmi)

Disregarding small motor time constants, the electrical drive-motor torque is found from its torque-speed characteristic. Typical curves are shown in Figure 4-11.

T eii = T eti (n pi) (4-99)

In analyses of a specific plant, it is, of course, necessary to use the pump curves appropriate for the equipment installed in the plant.

4.2.2.2 Motor-Generator Units If pump motor power comes from an M/C set, the response of the fluid coupler must be included in the transient model of the plant. Torque transmitted by the coupler is related to slip between the drive motor and generator and the coupling position of the scoop tube by fitting the following formula to the manufacturer's curves Tci a TC,rated xcifKCTl nn1( C(d,ratedl td) (4-100)

Typical curves of Tci are indicated in Figure 4-12 neglecting small time constants.

The drive motor shaft speed is obtained from the torque balance between electrical and coupler drive torques, dndi TJdi (4-101) 3 0C"*-d Tedi ci 4-34

NEDO-24125A-h 240 200 160 120 RATED OPERA?

sO 40 0%

0

-.80 -40 0 40 FLOW C%OF RATEDI Figure 4-9. Typical Recirculation Pump versus Flow and Speed 4-35

I NEDO-24154-A 160

• a 120%

S 120 RATED OPERATING POINT SPEED OF RATED so

,w \

60%

0

-. 8 -40 0 40 so 120 160 FLOW M OF RATED)

Figure 4-10. Typical Pump Torque Characteristic versus Flow and Speed 4-36

NEDO-24154-h.

2w0 IW I

Co U

C 50 0

0 WEED(M OF RATED)

Figure 4-Ul. Typical Recirculation Pump Motor Electrical Torque versus Speed (Conscant Excitation Voltage) 4-37

0

-4 0

4

.4 41 A

i cob I4

-4 (03 IVI :10 %13 fovoL

8. " .

NEDO-24154-A The electrical torque to the drive motor, T edi s obtained from the is manufacturer's torque speed characteristics which will be similar to Figure 4-11.

The generator shaft speed follows from the torque balance between the coupler output and pump motor power requirements wJdn._i=

,rfLK T -T (4-102) 30g c dt ci gi The recirc pump electrical torque, Tezi is coupled to the generator torcue through the pumping power and the effiziency of the generator and pump units T ngP T-el * (4-103)

Tgi ngi n.,n rp.mp 4.3 CONTROL SYSTEMS 4.3.1 Valve Flow Control The valve flow control block diagrams are shown in Figures 4-lb and 4-13. Gains, Q 2 time constants, and limiters must be input for the specific plant design.

.4.3.2 Motor-Generator Flow Control The motor-generator flow control block diagrams are shown in Figures 4-la and 4-14. Gains, time constants, and limiters must be input for the specific plant design. Q43 4.3.3 Feedwater Flow The three-element feedwater control system used in the transient model is presented in Figure 4-15. By proper choice of the steam flow gain, .I , the steady-state level may be programed with power, depending on the requirements of steam separator performance. The transient response of steam-driven 4-39

0EDO-24154-A SIAS FLOW CONMOL VALVE Figure 4-13. Valve Flow Control Block Diagram 4-40

TO SPEED CONTFIOL SYSTEM LOOP a fSAME AS LOOP At I

i.J

'am.

Figure 4-14. Hotor-Cenerator Flow Control Block Diagram I

IWDO-24154-A MIXTURE IIL,.31LEVIEL I fl v

FEEDWATER SYSTEM INPUT IS ISOLATION VALVE FLOW.

4SO. MIXTURE LEVEL. Ly.

AND STEAMFLOW. m13 Figure 4-15. Feedwater Control 4-42

NEDO-24154-A feedwat~er pumps is simulated through the use of the optional compensator and Q44 constants KA and T 4.3.4 Pressure Regulator and Turbine Controls A typical pressure regulator and turbine control system simulation used in the transient model is presented in block diagram form in Figure 4-16. Numerical values for gains and time constants must be input for each plant design. Q45, Q47 4.4 REACTOR SAFETY SYSTEMS That part of the reactor safety system concerned with the high flux scram, the high vessel pressure scram, and the manual scram, is simulated through digital logic in the transient model. The safety system model includes the differential equations describing a flux filter which may be switched in or out of the high flux scram circuit. With this circuit active, true neutron flux Is related to the circuit output by Ks(1 +- T2 s)Cl +- T3 s)

" K (I + T2s)(M + T3s) n (4-104) where T1 < T2 < T3 < T4 Automatic scram of the reactor occurs when neutron flux or pressure exceed the scram setpoint. In the case of neutron flux, the setpoint can be adjusted with the sensed recirculation loop flow. The sensed flow is related to the actual flow through a sensor time constant. In Laplace transform variables, this Q47 relationship is: Q46.

nM31 (4-105) a 1 +TCS a 4-43

MEDQ-24154-A VALVE FLOW CHARACTERISTICS CONTROL VALVE SERVOS VALVE FLOW MIT I.

Figure 4-16. Pressure Regulator Block Diagram 4-44

NEDO-24154-A The flux scram set point then becomes an ( m nset Sse nsec° Seto + . 31 k31, im3 rated

t )1 ' < m319 (4-106)

If the sensed flow, ms, dxceeds the rated flow, the setpoint of the flux scram is the full-power flux scram setpoint, nseto* Thus, nset nseto' ma--2 m31, rated (4-107) 4.5 NMWCLATLRE 2

Ab Bulkwater and dowrcomer flow area, ft 2

ADowncomer flow cross section, ft 2

ALP Inlet plenum flow cross section, ft 2

Ap Vessel plenum flow cross section, ft ARL Recirculation line cross section, ft 2 Asp Separator standpipe cross section, ft 2

A Separator 1nner downcomer cross section, ft 2

AOB Separator outer downcomer cross section, ft 2

A Effective separator rotational flow cross section, ft 2

Av Pressure vessel cross section, ft 2

Ath Jet pump throat area, ft 2

Aopen Full open area of isolation valves, ft 2

Isolation valve aria at time t, ft A(M) 2 Anoz Jet pump nozzle area, ft 2

ASct Jet pump suction area, ft Vessel area at standpipes, ft2 ALI.

2 barrel, ft AL 2 Vessel area at inner separator downcoier 2

barrel, ft AL3 Vessel area at outer separator downcomer 4-45

IEDO-24154-L Csep Separator friction coefficient CRV(PRLO) Capacity of individual relief valve open at PRL,O' lb/sec CSV (FX.LO) Capacity of individual safety valve open at pRL,0' lb/sec D2 Denominator of vessel pressure rate equation, Btu/psi Characteristic of bypass valve, per unit f sv(PI ,PS5,i) Safety valve capacity characteristic, per unit Characteristic of jth turbine control valve, per unit 2

g Acceleration of gravity, ft/sec sc Newton's law, conversion factor lb-ft/sec -lbt h3v Mixed enthalpy at lower plenum inlet, Btu/lb h31 HMxed enthalpy at core inlet, Btu/lb h3 3 Enthalpy in vessel downcomer, Btu/lb High pressure core spray enthalpy, Btu/lb hfi Liquid saturation enthalpy in ith pressure node, Btu/lb hg1 Steam saturation enthalpy in ith pressure node, Btu/lb hfgi Heat of vaporization, Btu/lb h ci Enthalpy of high pressure coolant injection flow, Btu/lb hsci Average enthalpy of subcooled liquid in core, Btu/lb hfw Feedwater enthalpy entering vessel, Btu/b h Vertical height above skirt where steam separator diameter changes, sep ft hLP Enthalpy of recirculation flow entering inlet plenum for non jet pump plants, Btu/lb th loop, Btu/lb bDi Recirculation enthalpy at jet pump throat - I hDEi Diffuser exit enthalpy - ith loop, Btu/lb hti Suction flow enthalpy - ith loop, Btu/lb hnozi Drive flow enthalpy at Ith jet pump nozzle, Btu/lb 4-46

NEDO--24154-A Ah Core inlet subcooling, Btu/lb Hlos Energy lost in Recirculation system, BTI/sec 2

Jdi Drive motor inertia, Lbm-ft 2

Generator inertia, bm-ft Jgi J Mechanical equivalent, of heat, lb/Btu 2

JpPPump-motor inertia, lbm-ft Ki Flow squared loss coefficient for steamline node; Psi-sec2/lb IsIV Flow squared loss coefficient for MSIV valves, Psi sec 2/lbm 2m Kb Eulkwater friction coefficient, psi/(lb/sec) 2 K i Constants in coupler torque numerical fit 2

Kdif Jet pump diffuser friction coefficient, psi/(lb/sec) 2 Exit plenum friction coefficient, psa/(Ib/sec)

K Downcomer friction coefficient - jet pump throat to vessel outlet, psi/(lb/sec) 2 2

Kd Drive loop friction coefficient, psi/(lb/sec) 2 Knoz Jet pump nozzle exit coefficient, psi/Clb/sec)

K Gain in. flux suppression filter K Flow coefficient for steam line to pressure relief valves, SLI in-ft 3 / 2 /sec

• L2 Steam line flow coefficient for flg*from relief valves to isolation valves to turbine, ins-fta" fsec KTOWt Steam ;jaw coefficient for flow through isolation valves, in-ft3/2/sec 2

F-RL Recirculation line friction coefficient, psi/(lb/sec) 2 SVessel lower plenum friction coefficient, psi/(lb/sec)

SDowncomer friction coefficient, psi/(lb/sec 2) (non jet pump plant)

KPTi Constant in numerical fit of pump torque curve IC*t Constant in numerical fit of pump head curve 4-47

NEDO-24154-A KSCT Jet pump suction coefficient, psi/(lb/sec)2' True vessel mixture level reiative to separator skirt, ft Lye Sensed vessel level relative to separator skirt, ft Lf Length of. active fuel, ft Lc Length of total core, ft effective separator length, ft

• D Length of flow path in downcomer, below jet pump throat, ft Lb Length of bulkwater and downcomer flow path to jet pump throat, ft Length of flow path in t.nlet plenum, ft Length of steamline node i I Length of flow path in upper plenum, ft Elevation difference between level sensor tap and separator discharge skirt (ft)

Length of recirculation line, ft sep Length of separator barrel, ft sepl sep2 Length of separator downcomer, ft Effective length of flow path in separator, ft Length of separator standpipe, ft sp 1

Idif/Adif Effective jet pump diffuser length to area ratio, ft i 31 Core inlet flow, lb/sec Total separator flow, lb/sec Steam flow leaving plenum, lb/sec mzs Liquid flow leaving plenum, lb/sec

'lS Ml21 Steam flow leaving separators, lb/sec

'120 Steam flow through isolation valves, lb/sec in 2 Liquid flow leaving separators, lb/sec 2

m1l3 Steam flow leaving vessel, lb/sec Liquid flow leaving vessel, lb/sec m23 4-48

NEDO-24154-A mIT Steam flow entering turbine admission valves, lb/sec m1B Steam flow entering bypass valves, lb/sec "sv Steam flow entering safety valves, lb/sec may Steam flow entering relief valves, lb/sec MIV M High pressure core spray flow, lb/sec Cs U Carryunder steam flow entering downcomer, lb/sec cu Mgfb .Carryunder condensation rate in vessel bulk water, lb/sec mfw Feedwater flow, lb/sec Recirculatlon flow in ith loop, lb/sec Recirculation suction flow in ith loop, lb/sec 2SCTi Recirculation drive flow in i+/-h loop, lb/sec

'Mdi tm Bypass valve capacity, lb/sec R

'BV lb/sec Capacity of jth turbine control valve, Recirculation pump flow - adi for jet pumps, *rLi for full mpi flow recirculation (lb/sec)

U Sensed recirculation loop flow, lb/sec High pressure coolant injection flow, lb/sec m

Uncompensated safety valve flow rate, lb/sec

~11T msc tM Relief capacity at setpoint of valves, lb/sec RC law Uncompensated relief valve flow rate, lb/sec Safety capacity at steam line pressure P RL lb/sec MSc Hfs Mass of saturated liquid in separators, lb Mgs Mass of saturated steam in separators, lb Mass of steam in vessel plenum, lb gl Hfl Mass of saturated liquid in vessel plenum, lb MS2 Mass of steam in vessel, lb Mf2 Mass of saturated liquid in vessel, lb 4-49

NEDO-21..54-A gd Mass of steam in vessel dome; lb Mfb Mass of saturated liquid in bulk water, lb Mgb Mass of steam entrained in vessel bulk water, lb Mc+p Total mass of fluid in plenum and core, lb Ml Total mass of fluid in vessel plenum, lb ng1 Generator speed in ith loop, rpm ndi Drive motor speed in Ith loop, rpm nd, raced Rated drive motor speed, rpm npe Punp dr:Lve synchronous speed, rpm Ps n Output of flux suppression network, per unit n set flux scram setpoint, per unit nsetO Full power flux scram setpoint, per unit npi Pump speed inth recirculation loop, rpm N' Number of recirculation loops represented by model loop 1 N2 Number of recirculation loops represented by model loop 2 Ni Number of loops of a given flow, mIL 1 Nf Number of fuel rods in core, dimensionless N Number of separators, dimensionless sep NB Number of open bypass valves, dimensionless KRv Number of open relief valves, dimensionless Flow adjustable flux scram set point, %

set Number of safety valves in group I, dimensionless Nv NTV Number of open turbine control valves, dimensionless P dwai Pressure in downcomer of Ith loop, psi Pressure in ith node, psi P1 P1 Upper Plenum Pressure, psi PIS Core Inlet pressure, psi Pjet Jet pump nozzle exit pressure In Ith loop, psi 4-50

NEDO-24154-A Ple Plenum exit pressure, psi FTRL Steam line pressure at pressure relief valves, psi Reset pressure of ith relief valve, psi PSR,£ Reset pressure of i£th safety valve, psi PSL Steam line pressure at turbine stop valve, psi P sst£ Setting of i h relief valve, psi Pus Pvoi Pressure at vessel outlet, for loop, psi P.S ,iq Setting of i h safety valve, psi PT Turbine inlet pressure, psi Pthi Jet pump throat pressure in i+/-h loop, psi Pressure drop across Jet pump mixing region in it loop, psi

'APJeti Pump head in ith recirculation line, psi APC Core pressure drop, psi

$ Laplace transform variable, sec-l t Time, sec Ti Flux filter constants Mechanical shaft torque of i h recirculation pump drive, ft-lb Electrical torque of i h recirculation p.mp drive, ft-lb TC, rated Coupler rated torque, ft-lb T ct Torque transmitted from drive motor to generator by fluid coupler in itl loop, ft-lb T cs Recirculation flow time constant, sec T ed£. Drive motor electrical torque in ith loop, ft-lb Ufj internal energy of saturated liquid in i pressure node, Btu/lb

-h ugi Internal energy of saturated steam in I+/-th pressure node, Btu/lb th 3 vfS Specific volume of liquid in i pressure node, ft /lb 3

Specific volume of steam in ith pressure node, ft /lb 4-51

MMO-24154-A vfi vfg gi v9 vs - vf fi 3

vs Specific volume of subcooled bulk water, ft /lb 3

VmbVolume of steam entrained in vessel bulk water, ft a3 3 skirt, ft Vb+cu,O Volume of bulk water region below separator discharge 3

sparger, ft Vb+cu Volume of steam and liquid above feedwater 3

Vfb Volume of bulk water liquid, ft 3

Volume of vessel downcomer, ft VD 3

VLpVolume of vessel inlet plenum, ft VI Volume of core exit plenum, ft 3 3

Volume of steam separators, ft V

ft3 VB Volume of bulk water and separators, 3

line, ft VR Volume of recirculation 3

ft VDiff Volume of Jet pump - throat to diffuser exit, 3

VNE Volume of downcomer from jet pump throat to vessel outlet, ft Xci Coupler position, 2 x Core exit quality, dimensionless ec X1 Plenum exit quality at separator inlet, dimensionless x2 Quality at separator outlet, dimensionless XCU Carryunder fraction, dimensionless unit XBJ Bypass valve (j th) opening, per Xr Control rod insertion location, dimensionless XTJ Position of j th turbine control valve, per unit

&Zb Flow elevation change, bottom of separators to downcomer, ft

&ZD Flow elevation change, downcomer to vessel exit, ft AZdif Flow elevation change, diffuser of jet pump to core inlet, ft A"L Flow elevation change, exit plenum, ft AZ, Flow elevation change, recirculation system, ft 4-52

tMDO-24154-A 1Recirculation sen drive generator efficiency, dimensionless Recirculation pump efficiency, dimensionless Density of saturated liquid in node i, lb/fc 3 Cfi 0gi Density of saturated vapor in node i, lb/ft3 3

1-r Recirculation loop average density, lb/ft a-b Bulk water density, lb/ft 3 DC Downcomer transport delay, sec TRi Recirculation transport delay from i loop downcomer at jet pump suction, sec TNji. Recirculation loop delay, non jet pump plant, sec TDEU Transport delay through i th loop diffuser, sec PRV Relief valve time constant, sec TSV Safety valve time constant, sec 4-53/4-54

NEDO-24154-A

5. NIEUTRON KINETICS MODEL The time-dependent neutron flux distribution is calculated assuming a single energy group, six delayed neutron groups, and time-dependent diffusion only in the axial direction. The three-dimensional neutron diffusion parameters used in the GE BEWSimulator are collapsed into equivalent one-dimensional parameters by procedures which are deicribed In Appendix A of this report. This section describes the solution of the one-dimensional kinetics equations and the techniques used to obtain diffusion parameters for use in transient calculations.

5.1 THE ONE-Dn-oNSiOuLA KINETICS EQUATION The one-dimensional equation derived in Appendix A is written,

) (5-1) a~t a: 3 re +r ac l B i 6 (5-2) at "ici where the diffusion parameters are derived and defined in Appendix A.

At time t, the boundary conditions are (5-3) 0' 3: az-b - rb~l-D(t-)

ratio at boundary b. Q31 where i the steady-state neutron current to flux isb Once the quantity #'(zt) is obtained, the axial power distribution is given by f(Z't) #'(Z't) (5-4)

The defihition of f(z,t) can be found in Appendix A.

Q31 _Responses to NRC questions on the text are documented in Appendix B. The symbol Q31 denotes that this topic in discussed further in the response to NRC Question 31.

5-1

NEDO-24154-A During a specific transient, the diffusion parameters will change due to changes in water density, fuel temperature, and control rod motion. The resultant changes in # and hence, T(z,t) are determined by solving Equations 5-1 and 5-2 numerically. This process is described in Section 5.2.

5.2 NEUTRON IMETICS EQUATION SOLUTION This section discusses the numerical solution of Equations 5-1 and 5-2. The numerical techniques are 6 quite straightforward and have been used in other GE neutron kinetics models. The model is outlined here for completeness. The time difference equations are found by integrating Equations 5-1 and 5-2 from tkto tk+l Vo*k+l(-)_ ck(z))

8 - , + (r- r f'i*,dt Cidt (5-5) tk c (Z) - cki(z) cji dt 4T FO 'dt (5-6)

- x .rr k tk where c(z) (5-7)

- ci(z, tk)

• k(z) (5-8)

- 40-(tk) 5-2

IMDO-24154-A Note that Equation 5-5 contains an integral of Ci(zt) over time. The first step in eliminating this integral is to assue that c (z,te-it varies linearly from tk to tk+ 2 . Then using Equation 5-6, we find Ci(z,t)dt = J: Tk k4 i I , C k'k t1k

+ B1 (1 - Y*)f F,'dt] (5-9) where t k4-+l t k (5-10)

At

+ 1 (5-11)

Yi k i Ar'k oL l- e"lAtk (5-12) 1 ci Substituting Equation 5-9 into Equation 5-5 yields Equation 5-13, which now only involves time integrals of the flux 4'; i.e..

_ .k(Z))

-(Ok~l(z) at r

+ (I - blO' - ,Idt (5-U)

LI i 4 (z) Atk 5-3

NEDO-24154 where Sk -iS (5-13a)

Equation 5-13 involves'integrals of the form tk+1 JA(t) *'dt which are approximated as c (1 - ¢)Akk) (5-14)

A(t) &tk (do 4k k'dtok+l .+

where a, is an interpolation parameter.3 Following a change in cross section, the flux behaves as e+Ivt Eence, (5-15) v t.--

For most time step sizes of practical interest, the parameter ai 0s essentially 1.0 and, hence, the flux integration is purely implicit. The resultant spatial equations are (including a 4 for generality):

a2 -k+L 4[F £ k+l l 4 k+1 + (1

" " . (1 L.k (:l-+  : = (5-1) 5-4

NEDO-24154-A In order to obtain the spatial solution, the core axis is divided into a number of equally spaced nodes, as shown in Figure 5-1. Integrating Equation 5-16 from zj.- to zj+ yields the following equation:

~$ji L

D tk+1 dz

~Zj.,

+ hG 1 *L+ - h 7"04 J k+l hGkfk+ h

+ - %)+ D Jdz I jJ IAtk(l

+ hazj.0

+ *YcL~jh = (5-17) where kz)d (5-18) di

~f+

k cj(z) di (5-19) a-h a Z j+- zj (5-20) and Q34

_ . . k*

. (5-21) 5-5

NEDO-24154-A NODE 1 + 1 Zi.1- - I÷j NODES

+ __

- aI'1+

NODE i - I

"-i-A Figure 5-1. Neutron Kinetics Spatial Mesh All of the nuclear parameters are assued to be constant over node J. The derivative term D? Iz_ + is evaluated using a difference expression for at the node boundary and applying the current continuity condition at the node boundaries. The result is

- g. nt (5-22)

,j dz h t--

where k k D +DDI (5-23)

Dj Dk +Dk I j 5-6

NEDO-24154-A Defining a matrix Ak with elements Ak 1 k (5-24) 2 J-1i h 'Jl~

Ak 1 k AMAk - A+k + Gk (5-25) j'j J-idj J+l,j j ij 0 the discretized form of the neutron kinetics equations can be written,

-v1 1 k+1 [= _a)Ak+ 1 k fA. -at- -vAtk

- .ckk (5-26) k kk k ¢k+1 where 0k and cki are vectors with elements i and cij. The vector can be obtained from equation 5-26 and C[UJ. is given by, c =- ck Y1k.c1i ]

"[I yk[f4l + _

1 .k~k] (5-27) 1 Thus, the flux and precursor solution (0k+ and ct ) can be determined once is normalized such that fk Ak+l and pk are known. The steady-state solution is constant (See Appendix A).

5-7

NEDO-24154-A 5.3 RADIAL FLUX APPROXIHATIONS The choice of the three-dimensional radial weighting function O(r,t) is an important factor in the success of the one-dimensional neutron model in accurately predicting the transient neutronic behavior. In the steady-state 2

reactor simulator.

condition, an "exact" solution is available from the 3-D However, during a specified transient the application of the adiabatic approx imation requires a large number of additional three-dimensional flux calculations which would make its strict application impractical. Therefore, the approach taken in the current one-dimensional model is to make use of the initial 3-D steady-state solution to estimate *(r,t) throughout the entire transient. In choosing approximate forms for *Cr,t) and the weighting function ¢Ot), it is important to know how *(F,t) varies in the radial (x,y) direction, because

• -,t) - O(r,t)/l(z,t) (5-28) where (Ft) is the three-dimensional flux distribution and *(zt) is the average axial distribution. Therefore, attention should be directed to the possible radial flux changes in a transient when choosing tGr,t).

There are three main mechanisms which cause flux changes in a transient. These are fuel temperature (Doppler) changes, moderator density changes, and control rod motion. In this model, it is assumed that radial flux shape changes due to Doppler and void effects are small, and that the steady-state (t-0) radial distribution holds if only moderator density and Doppler change. Control rod motion, however, can have a significant impact on radial flux shape. When a group of control rods enters a given axial region, the radial shape may change drastically because the flux will drop in those regions near the control rods and will change by a smaller amount in regions away from control rods.

For transient analysis, the most common control rod motion pattern is the control rod scram. Therefore, the procedures developed here for approximating *(r,t) are designed to predict flux changes during a reactor scram. Figure 5-2 is a schematic diagram showing a typical steady-state control rod pattern in a BTWR.

Note the divisions defining radial "control states*"

5-9

NEDO-24154-A CONTROL TOPOF FUEL gl STATE

___NEW ROD POSITION I 42 O P11 I 2 Z EN t

AREAS 20 WHERE CONTROL STATE -4 HAS INITIAL CHANGED ROD POSITION DURING Z.

TRANSIENT 9

BOTTOM OF FUEL FULL ROD BANK 6 Figure 5-2. Control State Schematic A control state is defined as a unique radial rod pattern. In this example there are six unique control states, including the full rod bank which in this case is fully withdrawn. Also shown is the height of each control state zci.

At some time ta in the transient, let us assume that the control rods have moved some distance ds . Note that for certain regions of the core (denoted by the shaded area), the control state has changed. For these regions, there fore, the radial flux is also changed and approximated as P(X,y,Zt s) - *(X,y,zrt,0) (5-29) where c, is the new control state at z at time t.. This procedure amounts to assming that the radial flux in the vicinity of the control rod tip remanls constant as the control rod moves up the core during a scram. It is Important to ensure that the flux near the control state interfaces are calculated accurately because in most transients involving scram, the first several inches 5-9

NEDO-24154-A of control rod motion is most important, and the greatest reactivity change occurs near the control rod tips. The weighting function is

@(xy,z,t) - f(zO) P(x,y,zzcl,0) (5-30)

The radial flux approximations employed in this section permit the generation of one-dimensional parameters, using only the steady-state 3-D distribution obtained from the BWR Simulator, while still accounting for radial flux changes during a reactor scram. Q2 5.4 NEUTRON PARAMETER FITS All of the parameters in Equation 5-1 can be calculated from the list of quantities listed in Table 5-1. Their definition can be found in Appendix A.

from Q35 The quantity F in Equation 5-1 is evaluated fi-))

+ MF(VT Y+ YZ(5-31.)

The flux-to-power conversion factor is given by k~[( (1+ ED0OP (OT - 6))-~ ]k~ (5-32) where we have assumed that CDOP - CDOP (5-33) and r - K1 *(5-34)

T 5-10

NEDO-24154-A Table 5-1 NEUTIRON PARAMETERS Symbol Definition Defining Equation 1 T/v Inverse neutron speed (A-64) 2 Diffusion coefficient (A-65) 3 3 Br Radial leakage CA-66) 4 f v-fission cross section (A-68) 5 CDOP Doppler correction coefficient (A-69) 6 T Absorption cross section (A-72) 7 Removal cross section (A-73) 8 T Flux weighted absorption (A-88)

Flux weighted removal (A-91) 10 1 Delayed neutron fraction (A-67)

Decay constant for precursor i (A-74) 12 #1 Neutron flux ratio (A-48) 13 ci Precursor concentration (A-45a)

In order to carry out the transient solution, the variation of each quantity in Table 5-1 with water density and control must be specified. The first nine quantities in Table 5-1 are functions of three variables: axial height, relative water density, U - pv/pref, and control state, defined in Section 5.3.

Specifically, a given parameter (denoted here by Z) is fit as a quadratic i.e.,Q4 9 function of U for each control state at each axial height;

=[ 1+ aC(z) (U - U ) + bc(z) (5-35)

E0 )I 0 (U - U0 ) 2 ]

5-11

NEDO-24154-A where -c is the value of J-c obtained when the relative density U is equal to the steady-state density at position (z). In practice, *0 is calculated using the base density profile. The density is then perturbed as 0'(x,y,z) - PO(x,y,z) + A (5-36) where Ap is constant Li position, and Z is recomputed. This process is repeated for a range of relative densities and the results fit to the form of Equation 5-35.

For a given axial height z, this process is repeated for all possible control.

states. Therefore, for a problem with 10 control states and 24 axial nodal positions, a total df 10 x 24 - 240 quadratic fits will be generated for each of the first nine quantities in Table 5-1.

The flux approximation used for each control state and height is in accordance with the procedures outlined in Section 5.3.

The quantities 0 and A are weak functions of density and, hence, are not fit as U. A total B is computed for each axial height and each control state. The individual precursor fractions are jiven by 1 ~(5-37) where (6i/0) is constant for the entire core. Also, X is given as a constant.

Note that the fitting process uses the parameter U0 (z) which is the steady-state density distribution obtained from the 3-D solution. When the fits are applied in the one-dimensional model, this base density is changed to the one obtained with the one-dimensional hydraulics model, as shown in Section 3.2. This procedure ensures that the steady-state one-dimensional solution will be the same as the 3-D average axial solution. Also, reactivity changes will be tied to changes In the "average channel" density, rather than changes in total core density. It is expected that this procedure will work veil for situations where the initial power of the core is high and the radial variation in density is not too large. At lover powers the sensitivity of density to quality is large and radial variations in density may be significant and the one-dimensional approach Q38 to reactivity feedback will be less accurate.Q2, 5-12

NEDO-24154-A

6. THERMAL-HYDRAULIC MODEL The reactor core pressure drop, exit qualities, and water density distribution are calculated by a model designed to predict two-phase flow (steam and water) in transient conditions.' The governing five equations in the model consist of a continuity equation of each of the vapor and liquid phases, an energy equation for each phase, and a momentum equation for the mixture. In addition, the location of the "boiling boundary" is tracked using an additional independent equation.

The basic variables consist of volumetric flux, pressure, void fraction, liquid and vapor enthalpies, and the boiling boundary location.

Numerically, an implicit scheme using "field" and "flow" variables is employed, where the flow variables are tabulated at discrete node boundaries and field vari ables are associated with node interiors. Precautions have been taken to ensure numerical stability.

The implicit equations are solved using a Modified Newton method, which takes advantage of the sparse nature of the non-linear equations.

6.1 TWO-PHASE CONSERVATION EQUATIONS The one-dimensional two-phase conservation equations of mass, momentum, and energy can be written in many different forms, ranging from the simplest three equation homogeneous model to a general six-equation two-fluid model. The most general formulation would include two continuity, two momentum, and two energy equations. It also needs empirical correlations for interfacial heat transfer and shear terms. The interfacial shear terms in particular are largely undetermined at present, being complex functions of the local flow regime.

In view of this, we have adopted a five-equation model which includes separate continuity and energy equations for each phase, but retains a total (mixture) momentum equation. With this formulation, another equation is needed to specify 7

the problem in the form of a "void fraction correlation." This correlation has a large data base for steady-state conditions and the uncertainties in using this are considerably less than in specifying interfacial forces.

6-1

IEDO-24154-A The five-equation model has as its dependent variables:

"- j + J -- Total volumetric flux a - vapor volumetric (void) fraction P - pressure h W vapor enthalpy ht - liquid enthalpy as functions of time and space.

The system of equations meets the following requirements:

1. Separated flow description

2. Capable of handling counter-current flow

3. Capable of handling flow reversals

4. Momentum coupling

5. Thermodynamic non-equilibrium

6. Pressure effects on properties within the core

7. Retain non-linear nature of the equations The equations can be readily derived using a control volume as shown in Figure 6-1. We use the concept of an infinitesimal interface, where all 6-2

NEDO-24154-A phase changes take place. With the notation shown in Figure 6-1, the following equations can be derived:

1. Vapor Continuity aE (a ) + L (P~ ig A) =r (6-1) 2

2. Liquid Continuity a i (P J - - rS (6-2) a)) [t-] +*

3. Vapor Enerny q" P a(a, * -aRP + a(P h* A) -r h *+ vRA HE at' 9 J at ATz- Egg 9 gi A (6-3)

4. Liquid Energy S[(1 - P h]- (1 -a 0 at 1 h(r (6-4) wII P q" Pi 5+ aW" eA 1 BI - L P i +

A.n

5. Moment~um Equation

+ j1 a 9 jR2 a CI J12 O a IA aP1 .

-r 0£J CL - 1 M))Al

"- -"r*ap - 2f (pil +Pg i 2_ g cos G (Pt (1- a) + 9a]

az fDoltlt (6-5) 6-3

)MDO-24154-L LIQUID VAPOR Figure 6-1. Thermal-H.ydraulic Comtro1 Volume 6-4

NEDO-24154-A where 2 <

Cg - g* ,C <1 -- CL)VD >2 (6-6) 0>1 In addition, we have the following:

6. Interface Energy Balance (qg 4" q;L, LiA rg (h i -hzi) (6-7)

7. Drift Flux Relationships Q(c0 j + Vgj (6-8)

I-J- etc )O (6-9)

V gj Equations 6-8 and 6-9 can be used to express j and Ji in terms of j and a In the conservation equations.

it is possible to expand the derivati ve terms in the conservation equations and express them in alternate forms. In particular, the continuity equations can be subtracted from the energy equations to obtain simpler expressions. Hovever, the equations are retained In this form because when differenced, they maintain their "conserving" property.

Note that pressure is assumed to be uniform in both phases. Also, in general h* - h + 1/2 V2 + 3z.

The interface velocity is specified to be (V$ - V )/2.

8. Boiling Boundary Equation 6-5

NEDO-24154-A If 09.hg' 1 , pits his JL, hid are considered functions of the axial variable z, then the boiling boundary Zbb is defined as that value of z for which the mixture enthalpy is equal to h dU the point at which subcooled boiling begins. In mathematical terms, at z - bb we must have 9 hg gj+ 0thoL I h - 0 (6-10) 6.2 THERMAL-HYDRAULIC COREELATIONS 6.2.1 interfacial Heat Fluxes In general, the interfacial heat fluxes are empirically specified in the form, qiL(g) " F.(T(g)T T "t) +F2all (6-11) pressure and ethualpy.Q16' Q28 where the quantities FI and F2 are functions of 6.2.2 Drift Flux Parameters The parameters C0 and V in Equation 6-8 are calculated through correlations based on flow and quality.

6.2.3 Friction Losses Local irreversible pressure drop losses caused by flow obstructions such as orifices and fuel rod spacers are calculated as A2 K G 1 + v-£X) (6-12)

Loc toe 2gcC Q16 - Responses to NRC questions on the text are documented In Appendix B. The symbol Q16 denotes that this topic is discussed further in the response to NRC Question 16.

6-6

NEDO-24154-A where G is the flow, given by G PPit+ i .

• (6-13)

The vall friction losses are given APf f( )2&G20 2 (6-14) where DH is the hydraulic diameter and f and .2 are given by correlations involving pressure and flow.

6.2.4 Heat Transfer Coefficients Regions of applicability for the various correlations for heat transfer coefficients are given in Table 6-1.

Table 6-1 HET TRANSFER CORRELATIONS Tý cTw 'Tm X(X Bulk Boiling Chen Tain a. Minimum wall temperature for film boiling Twi, Tti - conditions at incipience of boiling x- a transition quality 6-7

NEDO-24154-A 6.3 EQUATION SOLUTION 6.3.1 Discretization of Equations A modified donor cell technique has beem employed, similar to that used in the KACHINA code developed at the Los Alamos Laboratory. The variables are 9

classified int.o flow variables (J. j 1 J.) which are tabulated at boundaries between nodes, and field variables (a, P, hi, h which are defined at the center of the nodes (Figure 6-2). Further, the continuity and energy equations are classified as field equations and integrated from node boundary K to node boundary K+l. The momentum equation (flow equation) is integrated from node center K to node center K+l (i.e., across node boundary).

We subdivide the channel into nodes by designating the values of z at the nodal interfaces:

S1 0 z 2 < z3 < z4 .. ZJOUTLT ZJOUTLT+1 The presence of the "zero volume nodes t ' at either end is to accommodate the boundary conditions. Thus, z 2 corresponds to the inlet and ZJOUTLT corresponds to the outlet.

We have associated the index of a field quantity with the index of the nodal boundary Immediately below. Thus, z 2 would correspond to an inlet boundary condition for field quantity Q, Q2 would correspond to that field quantity in the node boundary by z2 and z 3 , etc.

The convective fluxes (JQ) at node boundaries are approximated as follows:

(J>k - Jk [(1/2 + Ek) Qk-l +(1/2 - ) Qk Ck - 'l fz IVkI + S2 Sn (6-15) 6-6

NEDO-24154.-A NODE K-1 K K+1 J*= AZK..

jZ- la*

0K* - f I *1 I I IK ftOK-1 14K-1 ftS haK + hik,, 2 K1 K K+1 K*2 SOUNOARY ZK-1 ZK zK÷l ZK 4 2 Figure 6-2. Nodalization of Channel 6-9

N)DO-24154-A where.Vk is the velocity of the particular phase for which the flux is computed, and 0 < , <- 0.5 0 ' a2 -< 0.5 so that 1 1 For Oz - 0.5 and Ba - 0, we have a pure donor cell technique, whereas for 0 02 - 0 the flux is purely space centered and the method is often unstable.

The use of this method assists in reducing truncation error without the necessity 29 of explicit artificial di'ffusion.Q The donor cell technique is especially use ful for problems involving flow reversals. The time integration scheme is fully Implicit.Q9 The entire discretization process is described in detail in Reference 9. The discretized equations are:

momentum

(.k. k k ,. k+ )L k.k k 'I i/I i+t h kj II -- ))k I i L+1/2-1 1

+ S. SA-L/I ( cij

÷ .1\k+

1l..1/

1 z£L/ II S.

CLdt\

9.$1/2./

1+

1-)-1/2 12 L-12) .1 IkeL Ik.L it.,

AZL~ ++2

+ [. (vSk - 14+k+1 1 I

, 1-1/ 'g.1-1/2 eL-1/2) 111

+ 1/2 IL+ *.+1/ ~+1 ak k+ £ Cos fat a 0 (6-16) 6-10

NEDO-24154-A (Here the k index denotes the k time step.)

Vapor Continuity (Liquid continuity is similar.)

Ck+ k+l k+l k k g,i 1+1/2 ogi+l/2 - '1+l/2 0.1+l/2 L+1/~i2 Azi 1<9 5ý+

-r at 0 (6-17) where A

F.

()l k (6-18) e node i unless node I contains the boiling boundary.

In that case, A (rk)+ 1 (Zi+*"-Zb) (b-19) wg ab d)hode i Azl the1bi with zbb denoting t.he location of the boiling boundary.

6-.1

REDO-24154-A Vapor, Energy (Liquid Energy is similar):

rk~ 2kI

+ g cos ezil/

k+l E9.,t = k+l k+l

+1/2 pg,i+1/2 h k-I- +

22 (Igi12

\~k/i k k

"+1/2 Pgi+i/2 hk g,[+l/2 + kos :/2)+ g

,k+1/2 1+1 k+l Vtk+l "1+1/2 1+1/2 -p 1+)Ji~/2 (6-20)

+ gz cos /+

+_ A At Ai+1j 2 4A~i 9 Sý 9~S (h- (AB2

\r 2 At A ig & + g: Cos ey,- 1 +.&Z. Q where A 1 k+l Azi -A 1 Q9 ( 9,S) k++ll/ 2 Az , -(r . k.1+ / Z2 ri+-/2 (Qg:)i+1/2 (6-21) with appropriate modifications in the boiling boundary node.

6.3.2 Equation Solution at each In both the steady-state and transient conditions, we wish to solve value of t - tk+1 6-12

NEDO-24154-A k+l

$,i 0 k+1 k+ - 0 1 - 2,3, ... , JOUTLT- 1 (6-22)

Ek+1 g,i"0 I

-k+l 0 Mk+l JOTJTLT-0 where the terms on the left are defined by Equations 6-16, 6-17, and 6-20.

Define the vector a:1+ 1 / 2 f: . l+1/2 (6-23)

I 6-13

NEDO-24154-A and the vector Ck+"

IFk+1. Ck+1 (6-24) i g, i E jl Then the equations we wish to solve can be written in the form, F(0, zbb) - 0 (6-25)

B(§,Zbb) " 0 where the boundary conditions have been incorporated into 9 and whee rei.bb) denotes the boiling boundary equation (6-10).

We use a modified Newton method to solve (6-25). Let FO(Ozbb) denote the Jacobian matrix of partial derivatives of F with respect to the independent variables 4. Let Fb'b(,zbb) denote the (column) vector of partial derivatives of F with respect to Zbb.

Next, let B (O.Zbb) denote (row) vector of partial derivatives of B with respect to 0 and finally B;(OZbb) the derivative of Bwith respect to z.

Newton's method for solving Equation 6-25 starting from an initial estimate

, %b can be described as follows:

[IFC Solve (D % ) FZb (gk. %b) 1,`F (6-26)

(k. kb BZ (Ok, kb)I ~bI L

b b)JL"zbbJ 6-14

NEDO-24154-A and then set k4-1 k a (6-27) k+1 k

%b bbA It is particularly important to take advantage of the structure of the matrix F'.

In particular, we find that F. has the form r.,ý a-f21 a9

- 0 F La*\

F; a

\\\ LfJOUTLT-1

\0J

.UL

[a-6Ot L

\ af a

UTLTr-1 ýLýJOUTLTJ where each of the bracketed terms, with the exception of the ones in the lower right-hand corner, represents a 5x5 block of partial derivatives of f 1 with respect to the variables in 4j. The exceptions reflect the fact that the vect fand JOUTLT OTLT really contain only one component.

6-15

NEDO-24154-A If the number of nodes is of moderate size (about 20 to 25), then there is considerable savings in the solution of Equation 6-26 if we take into account the banded structure of F' Equation 6-26 can be wr*.tcen,

[F; o r)- F] r 1 F (Be) T aB (d)T , F] 0 1 J

Boutd (6-29)

Then 40 and AZbb can be computed as, B- (B) T (F )I F (6-30)

"bb B' -()T (F'h'7 1 (6-31)

As " (F;)F- Azbb (F)* F; 6.4 IO*MCIATURE (All Units are SI Units) 2 A Channel cross sectional area, a B Residual for boiling boundary equation Cj.C9 Constants in momentum equation C0 Drift flux constant DH Hydraulic di4amter, m F Residual vector for 5 equation model G Total flow, kg/m 2 -eec 2

9 Acceleration of gravity, a/sec hA(g) Liquid (vapor) enthalpy, joules/kg h* h + V2/2 + zg, total enthalpy, Joules/kg 6-16

NEDO-24154-A h1(g) sat Liquid (vapor) saturation enthalpy, joules/kg hgsat-hasat, Joules/kg hAd Enthalpy at inception of boiling, joules/kg Mixture enthalpy, joules/kg 9g Interfacial heat transfer coefficient, watt/m2 -Ok Mechanical equivalent of heat Volumetric flux, m 3/sec J£

.1 Volumetric liquid (vapor) flux, m3 /sec Volumetric flux at time tk and mesh interface i, mi3/sec X1.c Local loss coefficient Kf Friction loss coefficient P Pressure, newtons/m 2

APf Friction pressure drop, newtons/m 2 AP toec Local pressure drop, newtons/mi Pi Interface perimeter, m PH Reated perimeter, m 1i+1/2 k Field variable at time t and mesh center node i 2

Wall beat flux to liquid (vapor), watts/m H

qlt(s) 1 Tfj(g) Interfacial heat flux to liquid (vapor), watts/m 2 Liquid (vapor) temperature, *K Tt Tsat Saturation temperature, oK Liquid (vapor) specific volume, ms "gl) vI(S) sat Liquid (vapor) saturated specific volume, ms V Liquid (vapor) velocity i/sec USg) 6-17

NEDO-24 154-A vvg 'sat . Vgsat' rn Vgj Drift flux cons tant, a/sec X Flow quality z Axial position, a LVoid fraction r Vaporization rate, kg/Mr-sec 3

Volu-etric heat generation rate, watt/u

¢2 Tvo-phase friction multiplier S(g) LiLquid (vapor) viscosity, Liquid (vapor) density, kg/m3 6-18

NEDO-24 154-h

7. FUEL HEAT TRANSFER MODEL 7.1 MODEL ASSUMPTIONS The fuel heat transfer model used in the one-dimensional reactor core model provides the time-dependent fuel temperature as input to the Doppler reactivity calculation and provides the cladding vail temperature used in the transient heat flux calculation. A single rod with a radially averaged heat generation rate is used to represent all of the fuel rods in the core. Radial conduction equations are solved for each discretized axial position in the core. Axial conduction is assumed to be negligible. The fuel pellet is divided into seven radial nodes and the cladding into two nodes (see Figure 7-1). The fuel and cladding conductivity and heat capacity are assumed to be temperature dependent.

A gap thickness Is specified between the fuel and cladding and an input gap conductance is used. Axial and time-dependent gap conductances can be specified.

The external heat transfer coefficient and liquid temperature is obtained from the thermal-hydraulic calculation. The heat generation rate in the fuel pellet is obtained from the axial fission distribution determined in the nuclear calcu lation. The radial heat distribution is assumed to be independent of axial position and independent of time.

7.2 CONDUCTION EQUATIONS In cylindrical geometry, the partial differential equation governing the temperature can be written PC p 1-3T ar( T +LS r ar Q1 (7-1) where material density Cp heat capacity K - conductivity T - temperature r - radial position Q1"1- rate of internal heat generation 7-1

NEDO-24154-L COOLANT Tcowt 0 TYPICAL NOOALIZATION~

A MINIMUU NOOAUZATION Figure 7.1. Sample Geometry and Nodaliuatian 7-2

NEDO-24154-A In cartying out the time integration, the Crank-Nicholson formalism is used.Q4 0 This formalism assumes that the temperature varies linearly between time t and t + At.

The finite-difference equations can be obtained by considering an energy balance on representative nodes. The conservation of energy equation for this case is I-rate of -rate-o F-rate of rate of change in. Jeg energy ergy stored energy: -in Lout' *eneration In general, three nodes are considered for each finite-difference equation. By definition, consider energy in to be heat transferred from the adjacent node closest to the center of the cylinder to the middle node of the three. Energy out is heat transferred from the mididle node to the next node farther from the center. The finite difference equations are of the form,

&4 T 4 _ 1 +-b 4 T4 +-c 4 T..., ý d4 (7-2) 7.2.1 First Node For Solid Cylinders

/

4 02 2

Q40 . Responses to NRC questions on the text are documented in Appendix Z.

The symbol Q40 denotes that this topic is discussed further in the response to NRC Question 40.

7-3

NEDO-24154-A

- C VT Change in stored energy P it

" CpV)

(p p IT (t + at) - Tmt) (7-3) i'A(TI - T2)

Energy out . k ,. (7-4) where k. is the average of the thermal conductivities at nodes 1 and 2, and Y - 1/2 [T (t +At) + T(t)] (7-5) 2r

(-

vI. 22rN _ -T-2 (7-6)

-, 2aS r 1 Ar_7 a2" 2 (7-7) 7.2.2 Interior Nodes For interior nodes, it is simpler to obtain the finite-difference equations from the partial differential equation than from an energy balance. From Equation 7-1, The stored energy term is approximated by

[T(t + At) - T(t)J (7-8) at 7-4

NEDO-24154-A The first conduction term, containing the thermal conductivity within the derivative, is given by (ki_2 i) _

(k1-T) 1 2t-(ki-1 + 2ki + 5+),- + -(k +12ki+,) Tf (7-9) where T is a weighted average between the temperatures at the new and old time given by Equation 7-5.

The first derivative term can be approximated by k OT 1 1 [(kc + k.+,) (T i+i -" .)

Sr-a T 2 Ar

+ (k 1 1 + ki) i - T1 1 ) (7-10) 2 Ar J The coefficients, a, b, c, and d are given in Table 7-1.

7.2.3 Last Node of Annular Regions The coefficients for the last node of an annular region depend upon whether or not the region is adjacent to the coolant. For the last node of any region, the geometry is shown in the following sketch:

1#1 REGION L+1 OR COOLANT S REGION L IA 7-5

Table 7-1 STEADY - STATE FINITE-DIFFERENCE COEFFICIENTS Node: Iu1 2- z I V ., I l1.

Region: L- I Coefi. Sotd CyflnfdM L -1 an L L LMAX L -LMAX d _W tiWAWsk s AW 1+ GAP(L-1) 14W 1.W 1.W R(L) 0.

4vi,

- a, -C, a, - C, - a. - c. - k,. We - W. h,.,

I l~~~

4k, k1 W, c, V'* k0 Ws W4 t%,, 0 LT a, _0too _ o.,, _ Q,,, _ 0o., - 0~'

0"'

-0.. ...- T,..,

.- W4- hi..

NEDO-24154-A If region L is the last region (L - L + 1), then T is the coolant temperature and if region L is an interior region, T 1+1 is the i+1 first node of the next

• region.

The volume of the last uode of any region, per radian, is

" 2 "r i - ")J2L (7-li)

S(ri- ) (7-12)

The mean heat t-ransfer area, per radian, is

- (r+/-~~)(7-13) and the surface area of the region, per radian, is Ai - r, (7-14)

The energy into the volume element consists of the energy entering the shaded area by conduction, plus the energy generated. The conduction from i 1 to 1 is kl+ki~Am (TAr- (7-15)

If the region is not the last region, the energy out is the energy transferred across the gap:

If the region is the last region, T--i is replaced by the coolant temperature, vhich Is assumed to be a known quantity.

7-7

NEDO-24154-A The stored energy term and the heat generation term are approximated as it was done for the other nodes. The coefficients, ail b1 , c,, and di are given in Table 7-2.

When a physical gap exists between two regions, the gap heat transfer is accounted for by using a gap conductance. The heat transfer is based upon the

-outside surface 'area of the inner region of the two regions being considered.

7-8

Table 7-2 TRANSIENT FINITE-DIFFERENCE COEFFICIENTS I-I I =1.

Region: L- 1 Cos"?. Sold Cy~lnder L>1 aft L L < LMAX L - LMAX dWs hA -At k At W, ,kA At W -or k, At W,

, L1 GAP(L--R(L) 1 j pC. pCo pC.

b1-. l-a.-c, 1a-s-c 1-8a,-c, 1

-d -8 N,$

p C.

-J

',0

,-4i*rl - k, At W, pC,,

-a k, at W, pC,

- ra W h1+1 PC. I S (1 - P) T, (1 V)at ht W, T,., (1- a) k. At WeT,.:, (1-) k At W2 T,-, (I -)kA At W&T,-,Ip Co PC, + GAP(L.-] * ,c. C.

+ PC. Tate + (1 - Pj,)T, + (1 - PJ T, + (1 - ,) T, + 1 - P1,) T,

"' at -, At W, (I + (1 -o o)k. At W, T,,, + (I- ,) W, h,, atT,,i + W4 hkIAtT..8/PC.

+ 7 +-pC, C. peC pC.

+ O"#Al/p C, + O- -.hlp Cd + 0o" Altp C. + O'0 A/p C, 4 + C, It - d,) Allp c,. (1 - r) At (1 -P C)

P, PC. C..t 11- p C.,

a) A.

w S+ k 1I . +G,-'

AP(L-1'I 1-

.-,, We + k, Wi *N we, f.-W,, NtoIl *N wt, +,W, 1149,1

NEDO-24154-A 7.3 NOMENCLATURE.

a 1 , bi, ci, di Coefficients in finite-difference equations C Constant C Specific heat pII (GAP (L - 1) Radial distance between regions L - 1 and L h *1Heat transfer coefficient between a surface and the fluid, or between two regions k Thermal conductivity kA jK(I-1) + K(1)] /2 k1, I:K(I) +. K(I+1)1 /2 2

m2 PC0 Cur) /k A(

N Number of nodes Pf Radial peaking factor in a region, a function of r PCi Stability (accuracy) parameter defined in Table 2-1 ql'f'i, Q'11 Heat generation, energy/(time -volume)

P.L) Outer radius of region L-1 r Radial coordinate r Radial location of the ith node Ar Distance between nodes. It can be different for each region.

t Time At Time increment Ti' Temperature at new time (t+At) at node i Ti Temperature at old time (t) at node i Y nT' + (1 - 0)T 7-10

NEDG-24154-A T cout Fluid temperature outside cylinder Vi Volume of ith node V0 Constant 2

wl [14 (2O + Ar)/(4 +Ar)/(Ar)

-i W2 1* 4 (2 r+/- - Ar)/(4 ri - Ar)J/IAr)2 2

W31 [8 ri 4r/(4 r + Ar)I/RAO)

W4 1 Ar/(4 -i 60)J/(Ar) 2 W61 [1 - Ar/(2 ri)/(Ar)2 PL Density in region L 0 explaicit r, metehod o

a 0.5, Crank-Nicolson method 1, pure implicit method 7-11/7-12

KEDO-24154-A

8. REFERENCES

1. R.B. Linford, AnaZy*iicaZ Methods of Plant Transient Evaluavions-of rhe Genera* EZectric BoiZing Water Reactor, NEDO-10&02, February 1973.

2. J.A. Wooley, Aree-Dimensional BER Core Simulator, NEDO-20953, May 1976.

3. D.A* Mandell, CA - A Program for the One-Dimensional 'ransient C'onduction Heat Transfer in a CyZindz'icaZ Geomnetry, NEDE-21234.

4. D.E. Patterson and T.H. Bredt, GEDACO3 - S*eten Overview and Sumoay, NEDE-11379, June 1976.

5. C.H. Robbins, Perforr~we Tests of A.ial FZow Prima'y Sten Separators, APED-4762, January 1965.

6. H.S. Cheng, .On the Accuracyj and Stabilityj of the Variable rmplicit Time Integrated Method of the Program ZASZ, NEDH-11038-58, July 30, 1971.

7. R.T. Lahey, Two Phase Flow in BoiZing Water NucZear Reactors, NEDO-13388, July 1974.

8. F.H. Harlov and A.A. Amsdeu, Nwnerical CaZculation of MWutiphase FZuid

-'o, J. Computational Physics, B17, 1, January 1975.

9. J.H. Avila, SoLution of Two Phase One-Dimensional Transient Flow Equations, to be published.

6-1/8-2

NEDO-24154-A APPENDIX A RESPONSE TO NUCLEAR REEGATORY COMISS ION QUESTIONS ON SECTIONS I.THROUGH 3 OF VOLME ZU A-I/A-2

.nDO-24154-A QUESTION 1 (Enclosure 2)

In the case of the stean£ine pressure predictions, "the coarseness of the spatial mesh," which models the steanline, is said co be the cause of "the spreading out of the calculated wave" as compared to measurement. In order to verify this difference, provide a sensitivity study of the effects of spatial mesh sizes. Th s study should demonstrate the eaffect of increased noding in the steamline on the steamline pressure predictions. If this sensitivity study does, not verify the postulated effect on steamline pres sure predictions for the three Peach Bottom-2 turbine trip tests, an alternate explanation and verification should be provided.

RESPONSE

The effect of the mesh size on the satam-Lne pressure prediction can be verified by comparing the results obtained with the three Peach Bottom tests and the M steamline results. The Peach Bottom analysis shows a spreading out of the Initial pressure pulse relative to the measured data, while the agreement is much better for the M steamLine pressure.

The Peach Bottom stea=lie is about 400 ft long (100 ft inside the contain ment and 300 ft outside the containment). Six spatial nodes were chosen to represent this length. The IM steamline is 327 ft long (93 ft inside and 234 ft outside) and is represented with 7 nodes. The average node length is about 30Z smaller In the M analysis and the Improvement to the steamline pressure prediction is clear by comparing Figures 13-14 and 13-15 with Figures 13-1, 13-5, and 13-9 provided in response to Question 13 of Appendix B, Volume I. Despite this noding effect in Peach Bottom, the dome pressure is simulated quite well by the calculations for all three Peach Bottom Turbine Trips.

A1-l/A1-2

NEDO-24154-L QUESTION 2 (Enclosure 2)

"The fact that heat loass terms are ignored in the transient calculation" was identified as the cause of the discrepancy between the dome pressure predic tions and measurements. Provide a calculation to justify the basis for this explanation. Provide all assumptions on surface areas, volumes, specific heat, heat transfer coefficient, reactor coolant temperature, and steam and water flow rates. If this calculation does not fully verify the extent of the discrepancy, additional explanation and verification should be supplied.

RESPONSE

Studies conducted since the time the draft qualification report was issued have shown that a large energy loss rate Is required to expla*En tha observed pressure overprediction. (See response to Question 39, Appendix 1, Volume 1).

The exact cause of this peak pressure bias is not known. The audit calcula tions carried out by BNL indicate a sim-lar bias if a 26% bypass capacity were used, as in the' ODYN calculation.

A2-1/A2-2

IMDO-24154-A QUESTION 3 (Enclosure 2)

Provide calculatioual verification chat the core exit pressure oscillations betweei 0.4 and 0.7 sec are due to "Tinging" in the instrument line. This verification should show that the magnitude and frequency of the oscillations correspond to those for the natural frequency of the instrument line.

Provide a full explanation and verification of the phenomenon.

RESPONSE

A discussion of sensor line effects on the transient pressure response measurements in the Peach Bottom tests is given in Section B.2.1.1 of the Peach Bottom turbine trip test report (Reference 4).

A,3-l/A63-2

NEDO-24154-A QUESTION 4 (Enclosure 2).

For the Larger core exit pressure oscillations at times greater than 0.7 sac, the control rod movement has been postulated as the cause. Provide the core exit pressure response to other scram signals vhich verify this hypothesis.

These other scrams should be reactor trips with minimum pressurization transients.

RESPONSE

No other experimental data exist to verify the postulate that the control rod motion was the cause of the sensed core exit pressure cacillations.

It is highly unlikely that these oscillations occurred in the reactor exit plenum, because oscillations in the neutron flux would have been observed.

&4-1/A4-2

NEDO-24154-A.

QUESTION 5 (Enclosure 2)

In the evaluation of the neutron flux differences, to major contributors Vere identified (core pressure and scram motion). The variation due to these con tributors should be quantified and the total effect on neutron flux verified.

RESPONSE

The variation in peak neutron flux due to scram initiation time for the Peach Bottom Transient Test conditions is summarized in Table 5-1. The delay time assumed in the model is 0.17 sec for all three tests. A variation of 0.02 sec about the mean was chosen for this analysis. The peak neutron flux is not very sensitive to the scram initiation tize in tests =nmbers I and 2, because the rate of void reactivity increase has decreased by the time the scram has started. More sensitivity is observed in the third turbine trip.

Overall sensitivity of flux to pressure variation is diffitcult to quantify because of the dynamic nature of the problem. L specific assumption about the transient pressure variation has to be made and the transient reevaluated.

The qualification report quoted a flux change of 10 due to a 1 psi pressure change. This relationship exists over a very short period of time, while the reactivity is high. No generalizations to other transients can be made about this sensitivity because it was only used to explain differences between the calculated and observed data.

&5-1.

NEDO-241.54-A.

Table 5-1 PEAK~ FLUX VALUES AS A FUNCTION OF SCRAM DELAY TIME Peak Neutron Flux Scram Delay Time TT1 TT2 TT3 0.15 330 420 340 0.17 338 438 420 0.19 338 440 560 A5-2

NEDO-24154-A QUESTION 6 (Enclosure 2)

In order to assure that no unexpected anomalies occur in the usage of ODYN, provide a sensitivity study on the key parameters and explain and verify any observed anomalies. The sensitivity study should be conducted for the Peach Bottom-2 tests, and for turbine trip without bypass and MSIV closure transients for typical BJR licensing conditions. Some of the key parameters which should be varied through the range of potential BWR transient conditions are scram rate, void reactivity coefficient, void distribution, flow rate and distribution, core pressure drop, stopvalve closure time, MSIV closure time (for pressurization transient), core exit pressure, axial power distribution, etc. Refar to the response for other studies requested in these questions as necessary.

RESPONSE

A considerable number of sensitivity studies have been carried out for license basis conditions. Input parameters have been varied in the response to ques tions in Enclosure 3. The peak neutron flux peak heat fluxes and ACPRs have been tabulated in these responses. Model sensitivities have been carried out in response to the questions in Append' 3, Volume 1. Table 6-1 contains a summary of the results of the ODYN model sensitivities.

A6-1

NEDO-24154-A Table 6-1

SUMMARY

OF ONE DIMENStONAL MODEL SENSITI STUDIES Peak Core Average Heat Flux Model Perturbation ClRated)

(1) Base Case 121.6 (2) Void Response Reduced 15Z 117 .8 (3) Void Response Reduced 5% 120.6 (4) Void Response Increased 4.8% 122.4 (5) Void R.esponse I areased 14Z 123.7 (6) Prompt neutron heating - 0.015% 122.6 (7) Prompt neutron heating - 0.022% 121 *4

-Bypas-flow -fraction increased 20%Z 121.2 (9) Jet pump suction loss coefficient decreased 20% 121.7 (10) Jet pump suction and diffuser losses decreased 20Z (increased M ratio 5Z) 122.5 (11) Separator L/A decreased 30% 122.0 (12) Separator L/A d-creased 901 120.4 (13) Separator pressure drop decreased by 50% 118.9 (14) Recirculation loop L/A increased by 100Z 123.4 (i5) Core Pressure drop increased by 0.81 psi 121.4 (nominal - 24 psi)

(16) Core pressure drop decreased by 0.7 psi 121.8 (17) Core pressure drop decreased by 2.4 psi 122.3 (18) Carry under fraction - 0.2% (Nominal - 0.1%) 121.4 (19) Carry under fraction - O.01l 121.7 (20) St-ealine pressure drop losses decreased 20% 122.5 (21) StesAline specific heat ratio y - 1.3 123.8 (22) Stesamlie specific heat ratio Y - 1.2 12.2.6 (23) Core thermal hydraulic drift flux parameter Co increased 10Z 121.5 (24) Co decreased 102 12.1.9 (25) Drift flux parameter Vgj increased 20% 121.6 (26) VgS decreased 20Z 121.5 (27) Subcooled void model R.. decreased 20: 121.5 (28) Rl increased 20% 121.6 (29) Subcooled void parameter *2n a - 0.5 116.2 (30) R2 n - 1.25 122.4 (5 1) R2a n - 1.50 123.1 A6-2

NEDO-24154-A QUESTION 7 (Enclosure 2)

In Section 2.1.1 the scram reactivity is compared using one-dimensional and three-dimensional procedures. In the three cases that were presented, the scram reactivity insertion calculated using the oue-dimensioual model is more conservative than that calculated using three-dimensional model except for the initial stages in the third case. At the initial stages of the scram in the third case, the power predicted by the three-d4mensional pro cedure is higher than that predicted by the one-dimensional procedure.

Explain the reason for this nonconservatism, and assess its effect on the neutrop flux in the Peach Bottom tests and in ACPR prediction. Discuss how the turbine trip without bypass transient would be affected because of these differences in three-dimensional versus one-dimensional procedures.

RESPONSE

The case analyzed in Figure 2-7 of the qualification report is quite similar to the core conditions for Peach Bottom Turbine trip test number one from 50Z power. At around 0.1 sec into the scram, the one-dimensional model under calculates the scram reactivity by about 10%. With the large number of con trol rods in the core, the radial flux distribution is quite compicated., and the approximation scheme chosen to represent the time dependence results In a nonconservative bias. This bias in scram reactivity becomes smaller as the rod insertion fractiou increases and Is -1% at 0.4 sec. In the analysis of the Peach Bottom test conditions, the one-dimensional. scram reactivity model would predict fluxes about 62 lower than the three-dimensional scram curve for that portion of the transient after the start of rod motion. If this particular scram curve were to be used in a turbine trip without bypass transient, there would be no appreciable flux transient at all because the start of rod motion would be triggered by the trip scram mechanism, causing the rods to begin moving about 0.5 sec earlier, so that at 0.4 see, when the pressure wave hits the reactor core, about $0.35 negative reactivity has been Inserted.

At 0.8 see, about $3.0 scram reactivity exists, which is much larger than the positive void reactivity contribution.

At end-of-cycle conditions, the scram reactivity increases much more slowly with time, as can be found by comparing Figures 2-2 and 2-4 of the qualifica tion report. In the end-of-cycle case, the most important portion of the scram curve occurs from 0.2 to 1.2 se= after the initiation of rod motion and during the time of the rapid pressure increase. Here the end-of-cycle compar isons show the one-dimensional model to be conservative. Also. biases occurring early in the scram motion, when the total reactivity is small, do not have a significant impact on the transient severity.

A7-1/A-7-2

lNEDO-24l54-A QUESTZON 8 (Enclosure 2)

In Section 2.1.2, the void coefficient Is defined.

a. Is the void fraction the effective neutron void fraction or is it the void fraction calculated in the thermal-hydraulic analysis?

b. It is stated that one-dimensional and three-dimensional void coefficients agree to vithin 5Z. Present the details of the wide variety of power levels and contral rod configurations to show how this 52 is determined.

c. How is this uncertainty of 5% introduced in the ODYN model? What is the sensitivity to ACPR in the licensing basis transient?

RES.ONSE

a. All void fractions quoted are void fractions calculated by the thermal hydraulic analysis.

b. Further discussion of the one-dimensional and three-dimensitoual void response comparisous is presented in the response to Question 2, Appendiz B, Volme 1.

C. The difference between oue-dimensional and three-dizensional void coefficients is a bias and not an uncertainty. It is shown In the response to Question 2 that. this bias is always in the conservative direction for license basis conditions, and, therefore, no model uncertainty is assigned to the one-dimensional collapsing process.

A8-1/AS-2

NEDO-24154-A QUESTION 9 (Enclosure 2)

In Section 2.2 thermal and hydraulic models are compared.

a. Present the details of the standard GE BEWchannel hydraulic model referred to in this section.

b. I: is stated that some differences in void fraction exist between the standard .GE BWE model and the ODYN code. These are attributed to dif ferent numerical treatments and assumption of constant pressure in the standard GE model. No difference is attributed due to the thermal nonequilibrium model and drift flux model in the ODYN coda, particularly in the subcooled region. Discuss the sensitivity of the void fractious to these models.

c. Present all verification details of the standard GE EBW channel hydraulic model with void fraction measurements.

d.- Provide -comparison of the OD- thermal-hydraulic model with experi mental data.

RESPONSE

a. The detail of the standard GE E*W are presented in Chapter 4 of Reference 8.

b. The model used in the one-d4-4sonal model is a mechanistic subcooled boiling model and is described in more detail *n the response to Question 28 in Appendix B, Volume I. This model was used becuse it is compatible with the separate liquid and vapor continuity and energy equations used in the transient model. The steady-state hydraulics model uses a dif ferent model for subcooled boiling in which the subcooled flow quality is determined from the "profile fit", which is a function of the bulk enthalpy and the quantity hid, the enthalpy at which subcooled boiling begins. The "profile fit" is an analytical expression for the interfacial heat flux up the channel. The sensitivity of the void fractions and transient results to subcooled void models is discussed in the reply to Question 28 of Appendix B, Volume 1. The drift flux correlations are identical to those used in the standard GE hydraulic model.

C. Comparisons with void fraction and pressure drop measurements using the CE correlations are presented in the response to Question 28 of Appendix B, Volume I.

hi-1

NEDO-24154-A

d. The ODYN thermal-hydraulic model has been specificaly compared to

.exprime*ital data. It has been compared to the standard GE design models waith close agreement. The standard GE design model or equiva lent equations have been used to test the appropriate void fractious and pressure drop estimates against experimental data.

A9-1

• M-O-24L54-A QUESTION 10 (Enclosure 2)

In Peach Bottom tests a certain weighted average for 7x7 and W8 bundles was used for calculations.

a. Present the details and basis for the weighting procedure.

b. Is the same procedure to be used in licensing basis transient analysis?

c. What is the uncertainty in ACPR associated vith this procedure in the licensing basis transient?

RESPONSE

a. In the initial analysis of the Peach Bottom transient, the rod geometry parameters were weighted in proportion to the number of fuel rods of each type in the core. Since that time, a design procedure for transient analysis has been formulated which uses the rod dimensions of the dominant fuel type. That is, the fuel dimensions of the rod type having the largest number in the core is uied. The Peach Bottom reactor at end-of cycle 2 has 576 7:7 bundles and 188 WiB bundles. Use of the 7x7 paramý eters rather than the weighted average yeilded the same transient results for the Peach Bottom tests.

b. The dimensions of the dominant rod type will be used in the licence basis analysis.

c. The 7x7 fuel rods are larger in diameter and therefore have a longer time constant. Therefore, their use will yield a more severe transient than the 8x8 parameters resulting in a conservative ACPR estimate. For Peach Bottom-2 this estimate is 0.002 ACPR/ICPR greater than the result obtained with average fuel rod parameters. A nonconservative result may be obtained, however, if 8x8 fuel were the dominant type but a significant amount of 7x7 fuel remained in the core. An examination of the current reload conmfigurations shows that when the 8x8 fuel is dominant, there is less than %25%7x7 fuel remaining. Based on the sensitivity study quoted above and a 20Z loading of 7x7 fuel, the uncertainty .connected with this procedure is estimated at =0.002 ACPR/ICPR.

AI0-1/A10-2

NEDO-24154-A QUESTION 11 (Enclosure 2)

A value of 1000 Btu/ft -hr-_F yas used for the gap conductance in ?each Bottom tests. It is stated that a 100Z change produced only 5Z change in peak flux.

Describe bow the gap conductance was changed. What is the estimated change in ACPD.?

RESPONSE

Figure 11-: shows the Peach Bottom Turbine Trip 3 total neutron flux calculated 2

with. gap conductances of 1000 Btu/hr-ft 2 and 500 Btu/hr-ft . Sma differences in neutron flux are observed because the entire flux pulse is only about 0.3 sec wide. Therefore, a very fast fuel time constant is needed to produce a moderate dens*t7 feedback through the rod heat flux. Much larger values of gap con ductance will produce changes in the calculated flux response, as evidenced 2

by the response with a gap conductance of 1500 Btu/hr-ft . The estimated difference in aCPR/ZCPR between these exteme values is 0.005.

All-I

NEDO-24154-A 8OO 400 w0 I

K 0

0 C.A UA U. 1.0 1.2 TIME bad)

Figure 11-1. Peach Bottcm-2 Turbine Trip 3 (69% Power) Neuzron Flux.

Al-3-2

NEDO-24154-A QUESTION 12 (Enclosure 2)

Treseut the details of Insitrument line da.ping and equations for.the second order response, including the characteristics of the transducer. Assess measurement uncertainty for both Peach Bottom and KM tests.

RESPONSE

A discussion of the instrument line model appears in Section B.2.1.1 of Reference 19. This discussion references three papers which give the details of the equations used. A physical description of the sensor lines is also provided in Appendix B of Reference 4.

A12-1/AL2-2

NEDO-24154-A QUESTION 13 (Enclosure 2)

Extend the pressure plots of Figure 3-6 through 3-14 and 3-40 through 3-45 through a period of 3.0 sec to include the peak pressure region both for Peach Bottom and Ji tests.

RESPONSE

Figures 3-6 through 3-14 and 3-40 through 3-45 have been modified to include in excess of 3.0 sec in the qualification docuencation.

A13-1/A13-2

ITOO-241.54-A QUESTION 14 (Enclosure 2)

Assess the effect of not co.sideriug system beat loss in terms of &CPR.

RESPONSE

The current practice of neglecting system heat loss has a negligible effect on ACPR. See the response to Question 39 of Appe.dix B, Volume 1.

A14-1/A14-2

NEDO-24154-A QUESTION 15 (Enclosure)

It is stated that a 1 psi change in pressure causes a change of 1OZ in peak neutron flux.

a. Assess this difference in terms of &CPR.

b. Assess the differences In &CPR for the Peach Bottom and KUM tests assuming the calculated conservative neutron flux inputs and the measured pressure inputs.

RESPONSE

a. It is quite difficult to assess the transient influence of pressure differenncts on flux calculations without some assumption about how the pressure differences vary in time. The statement about pressure differences in the qualification document was meant to show that small changes in pressure could change the flux near the peak value because the net reactivity was quite high, near $0.80.

b. In order to simulate the measured pressure inputs, the Peach Bottom transients have been calculated with a higher bypass capacity (i.e., 35%

instead of 26%). (This is not meant to infer that the actual bypass capacity is 35Z, but is assumed for pressure simulation purposes only).

The core exit pressure traces are shown in Figures 15-1 through 15-3.

Critical quality depends directly on pressure and will be influenced mainly by the pressure near the time of peak heat flux, which for the Peach Bottom tests is around 1.1 to 1.2 sec. The 352 bypass calculations show the flux to be virtually identical to the 26Z bypass results shown in Question 13. However, after 1.0 sec, the core pressure has been reduced to agree cuch better with the experimental data. In the case of

=D, the calculated pressure agrees quite well with the experiment out to about 1.8 sec. The ACPR/ICPR calculated with these pressure responses are stmarized in Table 15-1 along with the data given and previously quoted. Hence, there is negligible difference between ACPR's obtained with measured and calculated pressure responses.

A15-I

NEDO-24154-A Table 15-1 SU1M~AR oF ACPR/ICfl RESLTS F0R PEACR BOTTOM~ TUMfl-E T=S ACPR/ICPR &CPI/ICPl ACPR/ICPR (Data) (26Z bp) (35Z ba)

Test PB2TTl 0.170 0.173 0.170 0.136 0.1.29 0.135 PB2TT2 0.132 0.141 0.131 PE2'TT3 0.077 0.084* 0.084*

• M1 results obrane'"d with 50% bypass.

A15-2

1100 logo 1060 1040 Im

~1000 I

0

,"MEbft)

Figure 15-1. Peach Bottom-2 Turbine Trip I Core Exit Pressure (352 Bypass)

IU I

i I

.a o0. 1.2 1.8 Is1 1.8 2.4 2.7 3.0 3.

e -IMF 2Coe Figure J5-2. Peach Bottom-2 Turbine Trip 2 Core Pxit Pressure (35% Bypass)

1100 Im I 1020 I

I 1000o I~.

ON a

1.8 3.'

TIME 4"9)

Figure 15-3. Peach Bottom-2 Turbine Trip 3 Core Exit Pressure (35% Bypass)

NZDO-24154-A QUESTSiON 16 (Enclosure 2)

Discuss the effect of the uncertai*ty In the Doppler coefficient on dCPR calculations for the turbine trip vithout bypass transient in a typical SWR14.

RESPONSE

Uncertainty in the Doppler coefficient and its impact on the transient analysis is discussed in the responses to Questions 12 and 38 of Appendix B, Volump r.

A26-11A,16-2

NEDO-24154-A QUESTION 17 (Enclosure 2) it is stated that in the reactor the boiling boundary is different in each channel and the variation in void fraction vith axial position is smaller than the one-dimensional estimate. It vas also stated that the one-dimensional model represents the average conditions. Present the procedural details for representing the three.dimensional void fraction variation in one-dimensional.

RESPONSE

The procedural details are presented in the One-Dimensional Transient Model report. The effects on the void response and the transient are discussed in the response to Question 2 of Appendix B, Volume 1.

A17-1/A17-2

a.

NEDO-24154-A, QUESTION 18 (Enclosure 2) it is stated that measurement uncertainty in pressure is +/-2 psi and in flow

,it is t3Z. This gives an uncertainty of 0.01 in ACPR/ICPR.

a. Provide ACR/ZICPR versus time curves for all Peach Bottom and WK tests.

b. Discuss the effects of instruneutation filters on the uncertainty assessment.

C. It is noted that the model and data driven ACPI.IICPR. values are also within 0.01, although the differences between the experimental and calculated values of pressures may be an the order of 10 psi. Discuss this apparent discrepancy in view of the statement that was made on pressure measurement uncertainty of +/-2 psi and also an earlier statement that 1 psi difference in pressure may make a difference of 10% change In peak neutron flux.

RESPONSE

a. The General Electric Company does not normally generate plots of critical power ratio (CPR) versus time. Following General Electric Thermal Anal ysis Basis (GETAB) procedures, the most limiting pressure and power increase transients are evaluated to determine the largest change in the critical power ratio (ACPI).  :

The addition of the ACPR to the safety Limit Pt provides the minimzn= operating CPR required to avoid violating the safety limit should this limiting transient occur. The operating limit and the safety limit H=. are independent of the path taken by the transient.

Therefore, plots of CPR versus time serve no useful purpose and are not generated.

b. Instrumentation eaffects on the eper"inteal uncertainty are discussed in Appendix B of Reference 4.

C. The draft qualification report unfortunately gives the impression that the +/-0.01 uncertainty was entirely due to the pressure and flow uncer tainty. In reality, the change in CPU due to flow and pressure changes are significantly smaller than inferred from the report. In fact, based on ACPR sensitivities in pressurization transients, a 2 psi pressure uncertainty results in a 0.001 uncertainty in ACPRIZCPR, and a 3% flow uncertainty results in a 0.002 ACPLICPR uncertainty. The draft report should have stated that tie 10.01 &CPC/ZCPR uncertainty was based purely on a judgment of the uncertainties involved in the entire process of A18-1

NEDO-24154-A evaluating ACPR from the experinental data. Based on the pressure sensitivities, the 10 psi pressure difference observed between the calculation and experiment would result in a 0.005 ACPR/ICPR. In reality, the dependence on pressure is more complex. A more accurate evaluationco the ACPR effects due to pressure is presented in the response to Question 15.

A18-Z

NED0-24154-A QUESTION 19 (Enclosure 2)

In the meeting on May 3, 1978 to discuss the review of the ODYN computer program, it was stated by General Electric that they would provide a letter discussing the subject of scram reactivity and how it would be included In the ODYN documentation. This docunentation of the scram reac tivity calculations by General Electric is required to satisfy commitme=ts on, for example, the GESSAR-251 docket. Therefore, General Electric should provide this information describing how they intend to address the topic of scram reactivity.

RESPONSE

The ODYN Engineering Computer Program contains the analytical models for treating the interaction between neutron physics, core thermal hydraulics, and the fuel heat transfer mechanisms. These coupled sets* of differential equations are solved so as to include the effects of time dependent varia tions in the axial direction. The forzmlation of this model, coupled with the required input from the GE three-dimensional steady-s"tate simulator program, provides a technically sound way of computing scram reactivity.

The required Inputs for performing plant transient analyses for reactor scram is reactivity data as a function of control blade insertion. As. stated in our previous coz=micatiou concerning the Implementation of the ODYN code, we plan to continue to use the REDY code for analyses of specific transients, even after the NC has approved the application of ODYN for a .prescribed set of transients. In order to use our best technology available, GE plans to use the ODYN code to calculate scram reactivity as an input for those cases where the REDY code will be used to perform the plant transient analysis.

This will be implemented by a change to GE's Technical Design Procedures to use the ODYK code to calculate scram reactivity for all cases where it is required as an input for REDY plant transient analysis.

The primary ground rules for this analysis will remain identical to those used in our current Technical Design Procedures. These are:

1. Iunrital conditions are calculated using the standard steady-state three-dimensional core simulator.

A19-1

NEDO-24154-A

2. Pressure is mAintained at a constanC value.

3. Recirculation punp speed is maintained at a constant value.

4. The effects of void collapse in the core due to decreasing fuel surface heat flux are included in the calculation.

Implementation of this improved Technical Design Procedure will assure application of our best technology on a consistent basis.

A19-2

NEDO-24154-A QUESTZO 20 (Enclosure 2)

Provide References 4, S and 6 in M 014-78.

R.ESPONSE Reference 4 of M 014-78 has been published and the Staff has received copies.

This report is EPRIZ-1P-564, dated June 1978.

Reference 5 is attached.

Reference 6 is a &tanda2d reference for fluid flow and should be readily available to the Staff.

A20-1/&20-2

NEDO-24154-A Using Equation (A-4, Equation A-83 becomes

. t) ) L0 (A-84) where V . g " 1,2,3 (A-84a) noting thac v 0 Comparing Equations A-82 and A-84 and zEfcr~t) a(D 1B 2 + zr) 01 (A-85)

To obtain an expression for f(z,t), substitute Equation A-a5 Into Equation A-81

+ Er) -91(r',t) dxdy f(zt) M x fyDB2 m A (A-86) didy Following the same procedure used to obtain Equation A-55, Equation A-86 becomes

(/r-O))

f(z,t) 0 !(L>

1. dxd) (+~

-- 7 (A-86a)

- ko . fif x y

$Z'dxdy +kf f

Er dxdy}/t.f4dxdy A-21

NEDO-24154-A or f(Z't) k- I (1 a +CDO5P (VI - z)-+zr (A-87) where ff ddy /f didy (A-88) yY

- L&'C fX DOP dxtd (A-89) ffdxdy E ffX y VZOd /f.f-dxdy (A-90)

• r f. r Yl f fd dxdy (A-91)

A.6 1-D BOUNDARY CONDITIONS Let the time-dependent 3-D boundary conditions be expressed as (expanding on the steady-state formglationA-1"

.D, ( ) V. (R.t)t) (A-92) where 3 is the core boundary. To obtain the l-D boundary condition, rearrange Equation A-92, multiply by the weighting function, 0', and integration over x and y.

A-22

NMDO-24154-h

- (0', DVO) - (4',4i) (A-93)

Using Equation A-7, i.e.,

4 - 0*(A-94) in Equation A-93 yialds

- (v'. Dv (*#)) - (v,or)

Assuming, as was done in Section A-4, that 0 - *', and using Equation A-94 yields

-(s', DV(,'O')) - (s',4'r)w' (A-95) where Expanding the first term of Equation A-95 yields

-s' (0', DVO') - (V',@'D) - (o',*r) w- o' (A-96) at Reerange Equation A-96

" *' a: - (,',DV4') + (@',rt,) (-97)

Note that DVO' . 4g-*D - v (A-97&)

where use has been made of Equation A-92. Inserting this result in Equation A-97 and rearranging yields A-23

NEDO-24154-A (O'DO') 80 4.6 P. re A-8 01 az (r' D /

Note that at t-0, r-r 3 ,,.D-, r'-r. and D'-D0; thus 00 o- Do * - (A-98a) which agrees with the result obtained in Section A.4 that *o'is flat.

Normally r -_ r.o constant which reduces Equation A-98 to

-4DO) .-. . r ( .

O, 1 - (A-99)

• ' z '~D'1 Recall that D' contains no feedback effects.

A.7 DEFINITION OF TRANSIENT REACTIVITY CoMONENTS In the analysis of reactor transient behavior, it is often convenient to separate the reactivity components due to important changes in reactor parameters such as voids,, fuel temperature, and control rod motion. The point neutron kinetics equation is w.ritten, dT (OT - ) 6AlO d0 ^ T (t) + A C (t) (A-100) dt A ii ZA - -L_ T (t)- Cic(t) (A-101)

A i dt A-24

NEDO-24154-A In terms of the quantitieb defined above, the amplitude function T(t) is defined to be T(t) ja 0 (k.t) 4 ,t). dr) (A-102)

While the remaining huantities are evaluated as Ci(t) =f Wi , t) Ci (tt) dr (A-103) i(t) - 1(z,t) T 0'(z) dz / Ft'(z)dz (A-104)

Pt) =f M(z,t) 0'(zt)dz f F *'(z,t)dz (A-105)

V J f 0'(z,t)dz (A-106)

Where M(z,t) is defined as

+ F-

_(z-zb) - ID~r 2 M(z,t) - rb - Db(t=o) (A-107)

Throughout the transient, the quantity M(z,t) depends on the void fraction dis tributiou, a (t), control state distribution, C (t), and fuel temperature Tf(t).

The various reactivity components can be found by splitting the change in M (z,t) in the following manner:

aM a M (a(t), C(t), Tf(o)) - M(a(o), C(t), Trf(o)) (A-lo8)

AM = M (a(o), C(t), Tf(o) - M (a(o), C(o), Tf(o)) (A-109)

A NM (a(t), C(t), Tt(t)) - M (a(t), C(t), Tf(o)) (A-11o)

A-25

NEDO-24154-A The reactivity components are then defined as:

Control Reactivity PC (t) ffdz A MC (z,t) 0' (z,t) /1f TF0' (z,t)dz (A-1ll)

Doppler Reactivity aD (t) - f dz A MD (zIc) t ' (zt) If 7 0' (zt)dz (A-112)

Void Reactivity Pv (t) - f dz AM.v (zt) o' (zt) If T' (zt) dz (A-113)

These definitions ensure that PT (t) PC (t) + 0D (t) + ov (t) (A-114)

A.8 NMENC*AZTURE FOR APPENDIX A 3-D neutron flux for i h group; i 1,3 Di Fast group diffusion coefficient vi Neutrons produced per fission for group i; 1 - 1,3 k0 Effective ultiplication factor for steady state zfi Macroscopic fission cross section for group i; i - 1,3 Zr Removal cross section for the fast group B2 Buckling - (k./k0 - 1)/(M2 - A./ko k Infinite multiplication factor M22 Migration area - H'i M2 HM migrati*on area for group I A-26

NEDO-24154-L A 0/rr [V zi (qI .+q) + V2 r f2 (*p2/*

(3 ]

()]2 QA8 Group 2 to group 1 ratio for an infinite lattice

'2 One-dimensional flux amplitude function 3-D flux shape function 3-D concentration for +/-th precursor group ct 1-D concentration for ith precursor group th precursor coucentration K 3-D shape function for +/-

0Weighting function for the flux Wi Weighting function for the ith precursor A (1 - 6) (De2 + ) 1

-(r, t) 3-D power

f( rt) conversion factor of 3-D flux to pwer f(Ft) conversion factor of l-D-flux to power iY(zt) 1-D power A.8 REFERENCES A-I J.A. Woolley, Three-Dimensional BWR Core SimLunto, NEDO-20953, May 1976.

A-2 A.F. Henry, "iucZear Reactor AnaZysia, MIT Press, Cambridge, Mass., 1975.

A-3 J.A. Lamarsh, I.rtroduction to Vuc~ear Reactor Theory, Addison-Wesley, Reading, Mass., 1966.

A-4 A.F. Henry, and N.J. Curlee, Verifi.aticn ,*f a Method for Treating

.",,:ttron Space-Time Problems, Nuclear Science and Engineering, B4, M727-744 (1958).

A-27/A-28

NEDO-24154-A APPENDIX B RESPONSES TO NUCLEAR REGULATORY COMMISSION QUESTIONS ON SECTIONS 1 THR-UGH 7 A2D APPENDIX A

NE)O-24154-A QUESTION 1 Provide References 3, 4, 6, 8 and 9. Provide an appropriate reference for the void fraction correlation used in the model.

RESPONSE

The references requested have been supplied, as available, in Reference 9.

The void fraction correlation used in the model is described fully in the response to Question 28 of this question set.

Ql-l/Ql-2

NEDO-24154-A QUESTION 2 The core model including neutronics, thermal-hydraulic and fuel are based on a one-dimensional representation. Describe how radial variations in the core due to a different control state or a stuck rod during the trip would cause deviations from the assumed one-dimensional model. Assess these deviations between the actual three-dimensional representation and the assumed one-.

dimensional model. QuAntrify the effect of this uncertainty on &CPR.

RESPONSE

As pointed out in the model report, the three main causes of flux level change, as well as flux distribution change, in a BWI core are: (1) void changes; (2) control changes; and (3) fuel temperature changes.

A strict evaluation of the void effects on radial flux distribution during a pressurization transient requires a full three-dimensional evaluation of the turbine trip transients which is currently not available for BWR's. However, much can be learned from the results of the four turbine trip tests outlined in the qualification report.

Zn the case of the Peach Bottom tests, the entire flux rise is caused by void collapse. Due to the large number of control rods in the core during the steady state condition, the scram strength was quitet large, causing the flux to decrease Immediately after the control rods began to move. The experimentally measured flux as recorded by the LPFR signals is plotted for each of the four levels and for each turbine trip in Figures 2-1 through 2-13. Each LPRM response is plotted as a percentage of initial value. All of the curves show all of the flux responses at any one level reaching the same peak value within 5%, indicating that the radial flux distribution remains almost constant during both the void collapse and post-scram parts of the transient. This behavior is noted for all four experiments carried out on the two plants. These experi ments present evidence that void collapse effects do not appreciably perturb the radial flux distribution, supporting the use of a one-dimensional neutronics model.

- Q2-1

KEDO-24154-A Control rod motion is the most important factor in the reduction of the severity of the transient and can cause significant changes in radial power distribu tion. When a few rods are inserted into the core at midcycle conditions, for example, the flux in the vicinity of the control rod tips will decrease faster during a scram in those bundles adjacent to control rods. This results in local changes in radial flux shapes as partially inserted control rods move through the core during a scram. The gross radial flux shape also remains constant during the transient as evident in Figures 2-1 through 2-13. The current one-dimensional model contains a procedure which, when used with the three-dimensional collapsing process, accounts for radial flux shape changes by using radial flux shapes adjacent to the control rod tips. (See Chapter 5 of the model report.) Three-dimensional transient scram calculations have been carried out to determine the adequacy of this procedure and the results are des cribed in Reference B-1. The most limiting pressurization transient case occurs at end of cycle, with all of the rods out of the core. In the end-of-cycle case, the radial flux perturbation due to control rod motion is minimal, and the two dimensional and one-dimensional scram calculations show good agreement, being within 1.OZ over the important position the scram curve.

The effect of a stuck rod during a scram is negligible. Scram reactivity calcu lations carried out with a three-dimensional kinetics code show that a stuck rod has less than a 0.5% effect on scram reactivity. Sensitivity studies determining

&CPR versus scram speed show that this 0.5% reduction in scram reactivity amounts to less than 0.001 in ACPR in a typical load rejection transient. As discussed in the response to Question 1, Enclosure 3, the effect of a stuck rod is conservatively accounted for in the application of the model. Fuel temperature, or Doppler reactivity, is, in general, about 10 of the void reactivity response. Since the void collapse produces small changes in radial flux distributions, Doppler effects do not change the radial flux shape during a pressurization transient.

While the test results and collapsing procedures indicate that a one-dimensional neutronics model is adequate, a one-dimensional thermal-hydraulic model is also used, and the total integrated thermal-hydraulic and neutroni, package must be made to respond to changes in core pressure and flow. The core thermal-hydraulic model represents the behavior of a single channel with average power. In a SWI, the density change during a pressurization trans ient is not entirely uniform. To illustrate this point, refer to Figure 2-14, 2

Q2-

NEDO-24154-A which is a schematic of a typical BWR core at full power operation. The overall radial distribution of power consists of a central region of higher power bundles surrounded on the periphery by low power bundles. The low power bundles are orificed to a lower flow rate, but still have a lower power-to-flow ratio than the interior bundles.

For a given pressure increase, the change in void fraction is larger for low quality conditions than high quality conditions. This is illustrated in Fig ure 2-15, where the change in void fraction for a given pressure change is plotted vs. axial height for a typical low power and high power channel. Above the low power boiling boundary, the change is larger in the low power channel than in the high power channel. Therefore, for pressure increases, the void frac tion change will tend to be larger near the outside of the core. The extent of this void change difference is a complicated function of initial quality, per turbation type and axial power distribution. In constructing a one-dimensional collapsed model, a simplified fitting procedure has been adopted which assumes that the change in density is independent of radial position, i.e.,

Ap (x. y, Z) - Ap. (z)

This procedure has the effect of weighting the reactivity changes in the interior channels more than they would be if the correct radial density change distribution were used. The interior bundles have a larger initial void frac tion. Since Ak/AV increases with void fraction, the use of a radially constant Ap tends to overestimate the void reactivity response. This general rule is not strictly true between the high and low power boiling boundaries, but the majority of the reactivity change occurs in the upper half of the core. Some ratios of three-dimensional and one-dimensional reactivity changes due to a 10-psi pressure change are listed in Table 2-1. The first five values in the table have been reproduced from the qualification document. In general, the one-dimensional model overpredicts the reactivity response due to a pressure clange. The amount of overprediction is larger for a small reactor core than for a larger reactor such as a generic BWER/6 core design because there are proportionately more peripheral cells in the smaller core. The exception to this general trend is noted in the three Peach Bottom test conditions. In these cases, a considerable number of control rods were inserted, which created additional low power channels in the core interior. It is important to note Q2-3

NEDO-24154-A that for the full power conditions, the collapsing procedure always tends to overcalculate the void coefficient by margins from as small aa 3Z to as large as 1S5. Therefore, the one-dimensional to three-dimensional collapsing pro cedure does introduce a bias into the calculations. However, this bias is always in the conservative, direction for the license basis initial conditions. Since the collapsing process biases the results in the conservative direction, this procedure does not contribute to an "uncertainty" in ACPR.

The quantity Uo (z) will be discussed here rather than question 6, because it is connected with the one-dimensional core model. The quantity Uo is the base relative water density used in the density fitting process. When the cross-section fits are generated, a series of collapsed croem sections are calculated at a number of fixed water densities, {p:),Li.e.,

The quantity Ui is defined as U,

where OB is the saturated liquid density at 1000 paL. The set of cross sections Zi Is used to generate a fit of the form Z (p) - aZ(I + a (U-Uo) + b (U-U0)z) where Uo Is the ratio pO/,, where PO Is the average steady-state water density at axial height z. This determines the coefficients Zo a, and b for each height. Note that, when the fits are generated, Uo is the three dimensional relative density. However, when they are used in the one dimensional model, the one-dimensional estimate of Uo is used. In the steady-state, this ensures that E - Ea and that the one-dimensional axial flux shape is the same as the three-dimensional average axial flux shape.

This procedure was 9iso instituted to relate core reactivity changes to den sity changes occurring in the average channel rather than the full core. Iz Q2-4

NEDO-24154-A general, the one-dimensional estimate for Uo will be slightly smaller than the three-dimensional estimate, because of the higher density of the peripheral bundles. This also is in a direction to overestimate the void reactivity response and is also partially responsible for the differences given in Table 2-1. .

Q2-5

Table 2-1

SUMMARY

01 THREE-DIMENSIONAL - ONE-DIMENSIONAL VOID COEFFICIENT COMPARISONS Ratio BWR Ak(3D)

Product Number of Power Level Flow Exposure for 10 psi Plant Line Fuel Bundles (Z Rated) (Z Rated) Cycle Pressure Change Plant A BWR/4 764 48 100 EOC2 0.980 Plant A BWR/4 764 62 80 EOC2 1.053 Plant A BWR/4 764 69 100 EOC2 1.075 Plant B BWR/4 228 77 93 EOC4 1.080 o Plant C BWR/5 560 104 100 EOCI 1.03 Plant D DWR/4 368 104 100 EOC3 1.103 Plant D BWR/4 368 104 100 Midcycle 4 1.130 Plant D BWR/4 368 104 100 EOC4 1.120 Plant E BWR/4 560 104 100 Mideycle 2 1.145 Plant F BWR/5 764 104 100 EOCI 1.037 Ceneric BWR/6 864 104 100 EOEC 1.058

N!DO-24154-A LPRM LIVELD TMbameIdTIME Owl TIME tIed PLOTSCALE 1UITflI M~

): OF WAmALPlAOINGIDgV Figure 2-1. ftach Bottom-2 EOC2 Test Turbine fTrp Teat TT1 Care Local pcvr Mionitor Beepaust Q2-7

NEDO-24154-A LPANSTRING 1MRM I~mM LPRM R COORDINATES LEVELA LEVEL9 EE LEVEL 21-A?

27t3%

32449 ZIS 20040f IJ I 3SA%

3241 4.3%31Ln24.2%

32257 AIEDLPRm AV~.4 3A ALDLR 25.0%23..2 104%

0 0.3 0.6 0.9 1.2 1.5 0 0.3 *A 0.9 1.2 1.5 0 .

• 0. 1.2 1.5 0 0.U . .

TIME Iml TIME isee TIMEbd -TIME bud PLOTSCALE1t)NITNAHVII; 200%OF INITIAL READINGIOIY Figure 2-2. ?each lottou-2 20C2 Teat Turbine Trip Teat TTI Care Lomal Powrn Monitor Response Q24

NMZ0-2414-A LpnM STRING LtPRM LPu COORDINATES LEVEL A LPR. URM LEVEL@ LEVEL C LEVEL0 0.3 0.U 0.9 1.2 i 0 0. 91 0. 1.2 1.I 0 0.3 04 &.9 1.2 1.I 0.3 OS OS 1.2 1A TIME (id TIME Wl4 TIME bod TIME Ind PLOT MALEILIMITEJDDV) iDlY 2Mf OF INITIAL READING 7gw.e 2-3. Peach lattom-2 MOC2 Teut Turbine Trip Test TT2 Core Loal Poway

)l*e tor Reepous.

Q2-9

tMDO--24134-A LPRM STRING COORDHIATES LPRM LEVEL A

- 1 ......

LRm LEVEL S LPRM LEVEL C LPRU LEVEL 0 51.0 31.3%

32JM 16-23 17.3%

ngs a 0.3 0 a6si 1.2 1.5 02 OiA as . Ii 0.3 0.2 1.2 1 1I 0.2 0. ( 1.2 1.6 TIMEWle T Ifned TolmsIMM TomslIed PLOT SCALE lW6rO3.UIVI: 200% OF INITIAL READINGDIV y1gure 2-4. Pastch zottm-"2 0C2 Test Turbine Trip Teot TI2 Core Local Power moultor Reepouse 02-10 I

NEDO-24154-A LPRMtINATh LPN* ,MM LPEM COORMgATIS UIVULA LIVEL LVM LEVEL a LEVILS 24-25 24-4, 3240 32-41 3247 4041 03 OCA CA TimeInd TilE Irni Tim bed TimE becd l~kIT$/DM: 2M OF INMAL READIPaJOIW PLOT WCALE 71gw& 2-S. Peach Bottom-2 ZOC2 Tuet TurTbie Trip Teat TT2 Core Local Pover VAoitov Response Q2-11

N.DO-241.4-A LPRMsTRIma LPRM URNM JAM LFRV COORDINATES LEVEL A LEVEL 0 LEVELC LEVELD 4W25 62.1%

33.7% 32.9%

0 0.2 CA0. 1.2 1A 0 0 0 as 1.2 Is 0 0.3 CA 0 ,9 1.2 1I. 0.2 0* CA 1.2 1.5 TIME tm) TIMEtud ThIS loci TONE WWd F=0 SCAL.E 2M OF ITIA). RAEAINMt~V 1UIMtflAiIVI:

TipfO -6.Peacb Uettow-2 E0C2 Test Tumbime Trip Test TT2 Core Local Poweg

""fIto? Respol"O Q2-22

PMDO-24154-A LFI4 IMTPIWO 00ORINATES I.Mt LEELA Uq"M LpWM LPIM LEVELa LIVELC LEVILD 29.7% 1 37.11 1649 36.8% 3&11 24-17 0

OA 0.9 1. t.1 0 0.3 TIME1w) TIMElod~ TIME ld*"

PLOTSCALE1LM4WSIDMIV)00OFINIlTIAL READING)OIV Filure 2-7. Pseneb aotto-2 20C2 Toot ?urbineq Trip test T?3 Core local Power Nbuitor Response.

Q2-13

nDEf0-24154-A LFqu sMIGw WO*RDIkATUS$

LPWUA LEVEL^A tPJM LEVEL 8 LPRM LEVEL C LFqM LEVEL 0 24.25 29.0%

27.7%~

31.4 40-41 I 0 0.3 05  ! 0* 2 a 0.3 05 0 .2 1. 0 0.3 0.0 x.

TIMElw) TIMEtIo TIME f-,

SI~MAL READMEOIDIV

?tiVre 2-S. peach soettom-2 E0C2 Test Tutbist Trip Test TtS Core LOcal POwer 4

Q2-1

NEDO-24154-A LPPUMSTRING LPRM LPEVL LPRM COORDINATES LI VEL A LEVELSI LEVEL C LEVEL D TIME Ind PLOT SCALE IUP'MI;OIVI: 2O00 OF INITIAL READINiODIV 71gutm 2-9. Peach Bottou-2 zoc2 ?eat Turblue Trip Test TTS CUTS Local ?"or Nmuugtr fl.posu.

Q2-15

NEDO-24154-A (0

x 3

U.

IU 0 1.2 TIME Iseci Figure 2-10. A Level LPKM Flux KI= Turbine Trip Q2-16

NEDO-24154-A z

z 2

Im 0 0.3 0.8 0.9 1.2 Is 1. 2.1 TIME (sea Figure 2-11. B Level LPRM Fiux KM Turbine Trip Q2-17

NEDO-24154-A w

L-000ý IE w

'U t

'U o 0.3 0.6 0.9 1.2 1.5 18 2.1 TIME usdc Figure 2-12. C Level LPRH Flux M1OTurbine Trip Q2-18

141DO-24154-A.

==oo

• C z

t x

0 0.3 0.10 0.9 1.2 1.5 i.s TIME Ised Figure 2-13. D Level LPRM Flux 1= Turbine Trip Q2-19

NEDO-24154-A TOP OF N______________

FUEL 010 o olj 0 00 o0 o0 o 0

• oI 0 o:01 o 1I

.0 ci C 0o 0.

I 0 00 0000a I cc0 0I 0°1 00 I oj°*I.

oI 0o I I DEPARTURE POINT so OF FUEL IF.

Figure 2-14. BWRL Core Schematic Q2-20

NEDO-24154-A 0.024 0.020 0.016 us 0.1 o 0.012 w

z 0.0 0.008 0.004 0

-41004 6

AXIAL HEIGHT Figure 2-15. Change in Void Fraction for Static Pressure Change Q2-21/Q2-22

NEDO-24154-A QUESTION 3 Present your methodology for calculation of peaking factors for use in GETAB analysis if the average power level is given by the ODYN code. Discuss the conservatism of your methodology in calculating peaking factors. Provide a sample calculation for peaking factors for a typical BWR/4 such as Peach Bottom.

RESPONSE

There are three peaking factors reported with the GETAB operatihg limits:

(1) a local peaking factor; (2) an axial peaking factor; and (3) a radial peaking factor. The local peaking factor is the design maximum for a parti cular fuel design, but it is not used directly in thi GETAB analysis. Instead, the GETAB analysis uses an R-factor term which considers the distribution of local peaking factors within a fuel assembly. A detailed explanation of R-factor can be found in Appendix III of Reference B-2.

A generic axial power distribution with a peak/average value of 1.4 is used in all GETAB analyses. This axial power distribution is described in Table 5-7 of Reference B-3 and its justification is presented in Appendix V of. Reference B-4.

The conservatism in this assumed power shape is discussed in the responses to Questions 3, 5 and 6 of Enclosure 3.

The radial peaking factor (or bundle relative power) determined in the process of deriving the GETAB minimum critical power ratio (MCPR) operating limits is determined by an interative process. To start the iteration, a bundle power is assumed. The GETAB transient is initiated from this bundle power and resulting critical power ratio. The MCPR during this transient is compared with the safety limit MCPR (SLMCPR). The bundle initial power is then adjusted (upward or downward) and the transient is repeated. This adjustment and reanalysis of the transient is performed until the MCPR during the transient is equal to the SLMCPR. The initial bundle power and resulting critical power ratio (MCPE operating limit) are then reported. The bundle radial peaking factor is then derived from:

PF - BP x NB CTP x PF Q3-1

N4EDO-24154-A where RPF bundle radial pover factor; BP total energy. deposited in bundle coolant (MWt);

NB number fuel assemblies in the core; CTP core thermal power (MWt); and PF fraction of core thermal power deposited in active (in-channel).

coolant.

For a typical case (Plant A, EOC 2):

B - 6.770 MWt NB - 764 CIT - 3293 Mt PF - 0.978 and the resulting RPF - 1.606.

Q3-2

NEDO-24154-A QUESTION 4 Provide and discuss the quality of the fit of your decay heat model. Discuss its conservatism, if any.

RESPONSE

The decay heat model implemented in ODYN is identical to the model discussed in Section 2.3 of NEDO-10802, "Analytical Methods of Plant Transient Evaluations for the GE BWR". Generally, the short time response of the decay heat curves is on the order of a 100-sec time constant. This very sluggish behavior is not important in transients where only the short time behavior is significant (less than 5 sec). This can be seen from evaluating e-t/T for T - 100 sec aua t is chosen on the order of the turbine trip 1 5 0 - 0.98.

transient maximum heat flux response time, t - 2.0 sec, e / A change equal to about 2Z in the power generation occurs for full power initial power production. Since this variation (i.e., the 2Z) in power .generation is further restricted by the heat transfer from fuel to moderator, which has a 5-8 sec time constant, the influence on heat flux and moderator density is, for all practical purposes, negligible during pressurization transients.

Q4-11q4-2

NEDO-24154-A QUESTION 5 A recent paper, "The Siguificance of :'ast Moderator Feedback Effects in a Boiling Water Reactor During Severe Pressure Transients", by W. Frisch, S. Longenbuck and P. Peternell, published in Nuclear Science and Engineering:

64, 843-848, 1977, indicates that direct heating is a very important parameter in overpressurization transients. Explain hov the direct heating effects are considered in the ODYN code. Provide a sensitivity study and discuss the conservatism of the values selected. Quantify the conservatism or the effect of uncertainty on &CPR.

RESPONSE

Prompt heating effects are accounted for in the one-dimensional model according to the procedures outlined in Chapter 3 of the model report. The prompt heating fraction is a function-of the bundle and channel geometry, as well as the void fraction and control fraction of a particular bundle. Tables 5-1 and 5-2 give a summary of the bundle heating distributions for 7x7 and 8x8 fuel typical of the kind contained in the Peach Bottom-2 reactor. These data were obtained from calculations carried out with the GE lattice physics com puter code. The lattice physics heating distributions have been compared to Monte Carlo calculations employing up-to-date nuclear data. These compari sons have been documented in NEDO-23729B- 6 (See Tables 4-2 and 4-3. The column labeled "Scatena and Upham" corresponds to the lattice calculations.)

The agreement between the lattice calculations and the Monte Carlo results is very good.

The one-dimensional model assumes for lattices of the Peach Bottom type that 2% of the heat is deposited in the channel coolant, 2Z% in the out-of-channel coolant, and 96Z is deposited in the fuel. Tables 5-1 and 5-2 show that, depending on the rod configuration and void fraction, the prompt heat fraction, in the coolant can vary from 0.017 to 0.023 with 0.02 a good average value.

Q5-1

NEDO-24154-A Based on the excellent Monte Carlo agreement, the average in-channel heating fraction is assumed to be larger than 0.016 with 95Z certainty. In order to test the sensitivity to these parameters, a series of full power turbine trip calculations have been carried out with varying amounts of prompt heating.

The most severe transient was obtained with the 0.016 heating fraction and yielded a ACPR/ICPR 0.006 larger than the case with 0.02 prompt heating fraction. The uncertainty in &CPR due to prompt heating is +/-0.006 ACPR/ICPR.

Table 5-1 SUMHAY OF BUNDLE HEATING DISTRIBUTION FOR A 707 D LATTICE Uncontrolled Controlled VF-O VF-0.4 VF=0.6 VF.0 VF-0.4 VF-0.6 Fuel 0.953 0.953 0.953 0.944 0.943 0.943 Clad 0.009 0.009 0.009 0.009 0.009 0.009 In-Channel 0.023 0.020 0.018 0.024 0.021 0.019 Moderator Leakage 0.015 0.018 0.020 0.023 0.027 0.029 Moderator*

• Includes channel wall gama heating Q5-2

NEDO-24154-A Table 5-2 SUMNA LY OF BUNDLE HEATLNG DISTRIBUTION FOR AN 8X8 LATTICE Uncontrolled Controlled VF-0 VF-O.4 VF-0.6 VF-O VFO.4 VF-O. 6 Fuel 0.951 0.952 0.950 0.943 0.942 0.941 Clad 0.011 0.011 0.011 0.011 0.011 0.011 In-Channel 0.021 0.019 0.017 0.021 0.020 0.018 Moderator Leakage 0.017 0.018 0.022 0.025 0.027 0.030 Moderator*

• Includes channel wall gamma heating Q5-3/A5-4

NEDO-24154-A QUESTION 6 Provide a good description of the steady-state recirculation system model and initialization process. Justify the selection of plant parameters such as APa 0 p for the analysis. Discuss the conservatism of this value for various transients. Evaluate each component of APloop along the loop and justify with experimental data if possible. Provide sensitivity studies.

List in general terms the input parameters and output parameters.

RESPONSE

The steady-state initialization process consists of solving the equations outlined in Chapter 4 with the time derivative terms set equal to zero.

For a particular plant initial condition, the following quantities are input:

RLi£ - total flow for loop i m3 1 - total core flow miT - total turbine steam flow p - total reactor thermal power

.aPc a steady-state core pressure drop P2 a reactor dome pressure Lv - steady-state water level These input quantities are used in conjunction with other plant inputs to establish the steady-state initial conditions. The remaining quantities (e.g., plant geometry, pressure loss coefficients, separator carryunder fraction, and pump characteristics) are plant-unique but are not changed with operating conditions.

Q6-1

a.

NEDO-24154-A Flow conditions In the steady state, flow continuity is preserved and can be used to establish the initial conditions (the nomenclature is the same as Chapter 4):

m3 ' 'lT (Otal vessel steam flow)

'fw ' 'mT (total feedwater flow)

'3s , m31 (total separator flow)

In the bulk water, the carryuuder condensation rate is zero and the mass balance at the feedwater sparger yields (Equation 4-27):

=2 3 " '31"mf-'ou This can be combined with Equations 4-22 and 4-23 to yield:

Cu Mcu ýcu 1+X cu (m3 l M-W and 131"MfW

'23 "022 l+ "

The total steam flow through the separators is obtained from Equation 4-24:

'1 " '13 + 'cu '22 " '13 + 'cu (M31 " mv)./ (1+ Xcu).

In the recire line, the calculation of the drive and suction flows for the jet pump requires a pressure balance, and will be covered below.

Q6-2

NEDO-24154-A Pressures The plenum exit pressure is obtained from Equation 4-11:

Pe P + (tsepS +s'S + sep 31 le 2 144g N2 The core pressure is:

F -P t i api Le 144 The core inlet pressure is given by:

P1 a Pe + APc The jet pump throat pressure for loop +/- is ob'tained from equation (4-80) 2 ti 1 144 gc dfrr + df2 2r 1" Ac the downcomer pressure for loop i is obtained from Equation 4-79:

PnIM a P2 + [i--& r (AZb+Lv) - I E- ] / 144 the jet pump pressure is jeti'-1dwni - I4 SCT 2 g A Sn)

Q6-3

WEDO-24154-A Note we have proceeded around two sides of the loop to the jet pump throat pressure on one side and the jet pump suction pressure on the other side.

In the steady state, the drive flow is adjusted to obtain a pressure balance around the loop. Specifically, Equations 4-83, 4-91 and 4-85 can be com bined to obtain:

2 2 2 3

(MR i 1 m"SCTi) 2 SCTi ... +/- 1 A oz ASCT h TrSc A th

-144 (2 P6 - AP cP)Zif+ (AZb + L,)

Ieif "E

- I-+ - 1 M2 s

" (b+ 2 Ath r)2 c Ascrb All of the quantities in the above equation are known, with the exception of The drive flow is obtained from:

MSCTi, which can now be determined.

'di ' mRU - 'SCTi" The pressure drop loss terms in the above equation will influence the drive flow obtained for a given core pressure drop. In general, Kb and Kdiff 2

are considerably smaller than the l/2g Ath a terms and therefore do not con tribute very much to the total pressure drop balance. The suction flow loss coefficient is chosen to yield a given jet pump m ratio at rated flow conditions. The jet pump a ratio is defined as:

mSCT md and is obtained from test: data obtained for a generic jet pump design.

Q6-4

KEDO-24154-A For the drive flow loop, the pump pressure drop is obtained by combining Equations 4-78 and 4-80:

2 APi - Kd + + o L1d )J (KAST _T 2 14-'4 TSCF g ab cbS2 ASCT For non-jet pump plants the pump pressure drop is computed as A?., a Pe- P + &PC - (Lv +

p 4 vg 1"4

+ (RL + + ,14mD and PVOi in given by

~Voi 14 4 g Vrb+0 L AJ Enthalpy The feedwater enthalpy is adjusted such that the core thermal power yields the appropriate total turbine steam flow. In the steady state, Equations 4-8, 4-13, 4-14 and 4-23 can be combined to obtain:

rT 1hfs + hf1 -hf2 (1

'T [Ih f 22 .I+XChfU XC 3 Q6-5

NEDO-24154-A yielding the required core exit quality:

h -h h m- x u+

u f2 fl + hf m31 Xl hfgl hfg 1 + XCu The core exit quality can be computed from a heat balance:

h 3 1 + 948.8 p/m 31 - hfl X1 hfgI h

Equating the above two expressions yields the required core inlet enthalpy:

M-..!. + x h h- 98.8p/m + h '3 cu h3 1 - hf 2 - 948.8 P/r 31 + fg2 i 1 + Xcu where P - reactor thermal power (MW).

The feedwater enthalpy can be computed from Equation 4-34, where in the steady state, h 3 3 -. h31 hfw .(h31 '31 - hf 2 r 23 - hg2 mcu) / mfw If we substitute derived expressions for mfi, mi2 3 , and mcu into the above expressions, the result is:

h -h 948.8 p hfW 2 mlT which is the gross energy balance for the plant, assuming no external heat losses.

The discussion above shows that the loop pressure drop is required to equal the core pressure drop in the steady-state condition. The core pressure Q6-6

NEDO-24154-A drop for rated conditions is obtained from the multichannel steady-state hydraulic analysis carried out for each core. The pressure drop correlations used in this case are obtained from experimental data. The multichannel hydraulic analysis technology is described in Reference 8.

At rated conditions, the total loop pressure drop for most plants is about 25 psi. Of this, ,the majority is comprised of the elevation head in the recirc loop (14 psi).

It is important to point out that in this analysis the total core flow is an inut quantity and that the loss parameters are adjusted to yield experimentally determined jet pump m ratios. In this regard, the most important variable is the input core pressure drop, which possibly can influence the dynamic flow behavior.

Sensitivity studies of the recirculation system parameters are included in Question 24. The basis for including these results with Question 24 is that all recirculation system parametrics have been included in one package.

Q6-7/Q6-8

NEDO-24154-A QUESTION. 7 Provide and improve the graphical presentation of the recirculation system model and core model both in steady-state and transient conditions. Show all input and output (data flow) between components of each set of calculations indicating the time sequence and iterative procedures, if any.

RESPONSE

The figures in Revision 1 of the letter report, Reference B-7, describing the one-dimensional transient model have been altered to provide the informa tion requested.

Q7-1/Q7-2

NEDO-24154-A QUESTION 8 Justify the selection of the axial and time variation of the gap conductance as input. Discuss the conservatism of the selected values for different transients. Present the values of the temperature-dependent conduction param eters. Discuss the quality of the fit and conservatism of the selected values.

Quantify the conservatism or effect of uncertainty on ACPR.

RESPONSE

Core average gap conductance as calculated by the GEGAP Code ("GEGAP-1II, A Model for the Prediction of Pellet-cladding Thermal Conductance in BWE Fuel Rods," NEDC-20181, Rev. I, November 1973), which is approved by NIC, is used in the ODYN licensing calculation for transient safety performance. The calculated core average gap conductance is input for all axial modes and is kept constant during transients.

A sensitivity study performed on a BWPR/5 shows that the ACPR for the most limiting pressurization event (i.e., load rejection without bypass) decreases by A-12Z (%0.02 ACPR/ICPR) when axial varying gap conductance is used, as cal culated by a new model currently under review by the NRC. The normalized axial-dependent gap conductance is shown in Figure 8-1. in Figure 8-1 the initial axial power shape is also shown. It can be seen from Figure 8-1 that most of the high power nodes have higher than core average gap conductance.

During the transient, higher gap conductance will lead to faster heat transfer from the fuel to the moderator/coolant, which generates more steam voids. This results in lower stored heat in the higher power nodes. In addition, the faster conversion of fuel energy to steam void in the core helps to mitigate the transient due to negative void reactivity feedback. Therefore, the transient with axial varying gap conductance is less severe than that with constant gap conductance.

During limiting pressurization transients, it is expected that the fuel gap conductance will be higher than its Initial steady-state value due to increase in fuel pellet expansion, fission gas inventory and fuel temperature. As Q8-l

NEDO-24 154-A discussed above, higher gap conductance leads to less severe transient.

Therefore, it is concluded that the use of constant (core average) gap con ductance in the proposed ODYN licensing calculations is conservative

(^4.02 4CPR/ICPR) .

The thermal parameters are utilized as table values in the ODYN calculation.

Linear interpolation is utilized in the table lookup procedure. This is done for calculation efficiency. Values of the thermal parameters are given in the following equations or figures (U02 specific heat and thermal conductivity and zircaloy specific heat and thermal conductivity). Figures 8-2 through 8-4 are the U02 thermal conductivity and zircaloy parameters. The following equation form is used for specifid heat of U02 :

Equation Form (Cal/gm-mole - OC) Range ("X) 1- Cp - 19.2 + (1.62 x 10-3) T - 3.96 x 105 T-2 298 to 1175 2- Cp - 20.58 + (3.13Z x 10-4) T + (42659)2 x 75 tmel 2 (x)2 115tT R - 1.987 (Cal/gm-mole - *,)

- exp (6.25 - 42659/RT) 3- Cp - 15.63 + (4.668 x 10-3) T >Tmelt The U02 thermal conductivity is based on a value of 2805 *C Im far

• dT - 93.0 W/C{

Q8-2

NEDO-24154-A Uncertainty in these parameters is in the range of < +/-1%O. By varying thermal conductivity and specific heat of U02 10% in opposing directions, an impact of 20% on the pellet time constant due to thermal variations is obtained. This results in a ACPR/ICPR effect of 0.001. Cladding effects are much smaller in the ODYN impact. Use of the constant gap thermal conductance throughout the transient more than compensates for this effect. The conclusions is that the combination of all thermal parameters in the ODYN program result in a con servative bias in the transient calculations.

QS-3

1.4 1.4 1.2 1.2 0.1.0 10 8 0A 0.6 I- -

cc 0

Z 0.6 I

M 0.4 I- 0.4 0.2 0.4 0 K 0 0 2 4 6 a 10 12 14 I is 20 22 24 VE BOTTOM OFAXIAL CORlE Figure 8-1. Normalized Axial-Dependent Cap Conductance

NEDO-24154-A 0.07

-. 0.07 0.046 DESIGN 0.04 EQUATION 0.03 0.02 , I I I I I1 a 200 40 600 0oo 1000 120O 1400 1600 1800 2000 TEMPERATURE (OKI Figure 8-2. U02 Thermal Conductivity Q8-5

50 B-40 LVEVEL

~00 8 UPPER Oi CiONFIDENC E00 6000 LEVEL 10 10 600 .000

,0 50 20 OQ 3:0 40 0 0 I 0 we0 1000 Ism0 2000 2500 3000 3500 4000 TEMPERATURE I"PI 400 600 No0 100 1200 1400 16co 1600 2000 2200 TEMPERATURE I1K)

Figure 8-3. Thermal Conductivity of Zircaloy

0.22 r lowQ 1

800 EQUATION 131 OR 441 01 016 E - 0 600 0.12 U IL U.U up i3 400

.0l us. EQUATION III OR 121 00 0.08 200 0.04 - 0 0* p 0o. I I AI 300 500 700 900 1100 1300 Y 1900 2100 TEMPERATURE i°K1 i _I .. I I A- I_ i 80 600 S00 1I00 3000 3320 TEMPERATURE ('F1 Figure 8-4. Specific Heat of Zircaloy

NEDO-24 154-A.

QUESTION 9 Discuss the stability of the system and thermal-hydraulics model when the ODYN code is used with different power distributions and boiling boundary level.

RESPONSE

The one-dimensional transient model has proven to be stable in all of the transients analyzed so far. The vast majority of these transients have been pressurization transients initiated from high power and flow. The initial boiling boundary position ranges from 8 in. to 45 in. above the bottom of the fuel. The model has not been used to analyze low flow/high power condi tions, where physical instabilities are more likely to occur.

Q9-1/Q9-2

NEDO-24154-A QUESTION 10 Perform the analysis of the transient presented in NFN 058-78 dated February 7, 1978, with and vithout control system operation to demonstrate that with the safety system operation alone the results are conservative.

RESPONSE

Abnormal operational transients are defined as events which are results of single equipment failures or single operator errors that can be reasonably expected during any normal or planned mode of plant operations. Control system failures are among the causes. Following the assumed single failure, which is assumed to fail in the worst direction, the-resulting transient is simulated in a conservative fashion to show the response of primary system variables and how the various plant systems would interact and function. In the analysis, the plant instrumentation and controls, plant protection and reactor protection systems, except the assumed failure, are assumed to main tain normal operation unless specifically designated to the contrary in order to provide a realistic transient signature. The effects of single failures and operator errors on the transients are also discussed and presented in Chapter 15 of FSA. or PSAE and reload licensing transmittals. In these transients, the consideration of any additional failure (e.g., without control system opera tion as suggested in the question) is not considered appropriate within the realm of abnormal transient definition.

The probability of the total failure of control systems is considered to be low enough that the event could be classified as an accident should it occur.

Nevertheless, the worst plant control mode is assumed in the transient simu lation to provide a conservative safety evaluation to cover all possible plant operation modes. For example, manual flow control mode is assumed in the transient analysis. Furthermore, some control systems are saturated during the transient (e.g., pressure control is saturated during pressurization events) and, consequently, there is no effect on thermal or pressure margin during transients. In addition, most of transients analyzed are mitigated by reactor scram. Thus, the effect of control system operation on the thermal and Q10-1

NEDO-24154-A pressure margin is insignificant and z*aimal. Therefore, it is concluded that although control systems operation is assumed in transient simulations to provide realistic transient signatures, additional failures asasued in these systems vould generally not make the transient significantly more severe than the events already presented in the FSAR.

QlO-2

NEDO-24154-A QUESTION 11 in the description of the control system there seems to be a page missing.

RESPONSE

A review of the document indicates all pages and information are in the order planned for publication in the copies within GE. Possibly a printing error has occurred in the copies sent to the staff. The revised document has been reviewed to assure that all information is included and that all normal con trol functions can be simulated with the information provided when plant data are supplied.

Qll-l/QUI-2

NEDO-24154-A QUESTION 12 Provide a detailed description of the void-quality correlation to obtain aC,B(z) which is used for neutron-effective void correlations. Describe and justify any differences between this correlation and the one used in the thermal-hydraulic calculations. If the correlation contains any empirical factors, discuss their conservatism and experimental data base. Describe how the void fractions in Equation 3-12 are obtained. Justify the form of Equation 3-12. Quantify the conservatism in the empirical factors or effects of uncertainties on ACPR.

RESPONSE

The reply to Question 12 contains General Electric Company proprietary informa tion and has been documented separately in Volume III of this report.

Q12-1/Q12-2

NEDO-24154-A QUESTION 13 Derive Equation 3-23. Discuss its basis. Discuss the stability between parallel channels.

RESPONSE

Equation 3-23 is a means of updating the bypass flow fraction during a transient to reflect changes in the pressure drop balance between the active channel and bypass. The bypass flow fraction is defined as:

fr MEs*, (13-1) where

- total bypass flow, and mc total active channel flow.

We wish to find an fBp at t + At such that the bypass pressure drop equals the channel pressure drop; i.e.,

AB (t + at) - APc (t + At) ( 13-2)

Let us assume that each pressure drop is proportional to the flow squared:

2 4PB1 t + At) - KB mB (t +-At) 13-3)

AP(t+ at) -K m 2 (t +At) C13-4)

Q13-1

NEDO-241.54-A Substituting these expressions into equation (i) yields the requirement that:

ml U (13-5) or fee (t + At) 1 (13-6)

KC The ratio is estimated from the flow and pressure drop at time t; i.e.,

'4 tM C (t FZ M (t)

BAPs A*Pc (t) ml (t)

(13-7) 11,P C((t)

VFZ U (f 1 ~ Ct)

(13-8)

Substitution of Equation 13-8 into 13-6 yields Equation 3-23 in the reference; i.e.,

f 3 e (tY)" AP_

P (t)

(t) f (t + at) (13-9) q13-2

NEDO-24154-A Since the time that Equation 13-9 has been derived, studies have shown that it over-corrects the bypass flow fraction, resulting in numerical oscillations in f B" Therefore, a relaxation parameter U has been added to Equation 13-9, yielding:

f BP (t + at) + (1-u) fBP (t) 1 + (t)

(13-10)

A value of u - 1/2 removes the oscillations, still maintaining a bypass channel pressure drop balance throughout the transient.

Q13-3/Ql3-4

NEDO-24154-A QUESTION 14 Discuss the basis for the selection of initial fBp and fc. Discuss the conservatism of this selection, if any.

RESPONSE

The core bypass flow fraction is an input quantity to the transient model. Its value is obtained from a steady-state analysis of the core hydraulics with a multichannel hydraulics analysis. The basis of this analysis is outlined in Reference B-5. The bypass flow fraction is obtained by requiring a pressure drop balance between the active flow channels and the bypass or leakage flow path.

For the vast majority of full power conditions, there is no boiling in the bypass region and a negligible amount of density change occurs there during a pressurization transient. For this reason, the transient response is almost independent of initial bypass flow fraction. The quantity fc is not defined in the model report.

Q14-1/Q14-2

NEDO-24154-A QUESTION 15 The momentum equation (4-11) does not include forces exerted on the fluid from the walls and assumes one-dimensional flow. In reality, the flow is rotational.

Discrepancies from reality are taken care of by using experimental data and a correlation (Equation 4-12) for steady-state. Justify the momentum equation in its present form for its use in transients. Provide the experimental data, if needed more than that in Reference 5, and basis for the correlation and selection of the effective L/A. The correlation (Equation 4-12) should be sensitive to some parameters such as quality, slip and flow rate. Provide information as to sensitivity of this correlation to different parameters.

Present experimental techniques, describe experiments and accuracy of measure ments. Discuss the variations during the transient and provide sensitivity studies using different Ceep and L/A values for a licensing basis transient for a typical BWR/4 such as Peach Bottom.

RESPONSE

The initial application of equations of the form of Equation 4-1l occurred in the earliest history of BWR system simulation. This form was applied in an attempt to find the simplest form applicable to system simulation because of the severely limited computational capabilities of both analog and digital com puters available in the early 1960's. At that time, all of the inertial CL/A) and friction loss (W) terms were required to be constant because of compu tations (either analog or digital) limitations. The question then became one of finding a conservative representation for the transients calculated with reasonable computation cost. Early attempts at simulation fitted the profile of the liquid in the separators based on parabolic axial profiles and estimated the frictional losses in the separators as though they were due to abrupt changes in flow area. These attempts were compared to early data and, by use of constants in the fitting process, were found to yield reasonable although not entirely consistent results. The accumulation of higher quality steam water data occurred in 1965 and was reported in Reference 5 of the ODYN trans mittal letterB- 8 . These data showed that a good representation of the separator friction pressure drop could be obtained using equations of the form of Q15-1

NEDO-24154-A Equation 4-12. Reference B-8 indicates that friction head is proportional to

,wlumetric flow rate. Hence, variations of Equation 4-12 are incorporated by transferring to pressure drop. In addition, data from the GE Advanced Technology Laboratories taken during 1965 were reported in References B-9 and B-10. From these data, it was possible to obtain an effective inertial form based on the average flow trajectory of the liquid as it moved along the swirling path prior to discharge from the separators. The flow path and inertial parameter (L/A) was found to be a function of separator inlet quality.

The results of such a .determination were indicated in Figure 4-3 for an individual separator. Variation of L/A due to the flow rate was found to be negligible (less than 1%) over the range of expected operation and, therefore, was not included in the correlation. The real justification of Equations 4-11 and 4-12 actually exists in the ODYN Qualification Report. A comparison between model and data for the core exit plenum and reactor steam dome shows that gbod agreement exists in the initial pressure rise. Since only the separator region separates and couples these two regions, this comparison of pressure, particularly for Peach Bottom-2 test data, shows the separator rep resentation is adequate without change for evaluation of large pressurization transients such as turbine trip, load rejection and main steam isolation valve closure.

Sensitivity studies were performed on the inertial terms (L/A). A decrease of 30% in the effective L/A resulted in +0.002 change in 4CPR/ICPR, This is consistent with the uncertainties in the effective L/A and for practical pur poses it is negligible. The value of C sep is expected to be conservative as it stands in the model. This is based on the dome to core pressure drop observed at Peach Bottom-2 during the April 1977 testing program. Table 15-1 compares plant data and calculated pressure drops. In all cases, the calcu lated pressure drop is higher. This is due, principally, to CSep. Sensi tivity calculations show that higher values of Csep result in higher ACPR/ICPR calculations. Since this is a bias built into the model, uncertainty in this parameter is conservatively accommodated in ODYN.

Q15-2

NEDO-24154-L Table 15-1 PEACH BOTTOM-2 CORE TO DOME PRESSURE DROP Calculation Plant Data Case (psi) (psi)

• rri 8.3 7.4 TT2 7.3 4.5 TT3 9.7 6.4 Q1S-3/Q15-4

NEDO-24154-A QUESTION Discuss the effects of thermal nonequilibrium vs. equilibrium on the results of a typical licensing basis turbine trip without bypass transient using the ODYN code.

RESPONSE

Thermodynamic nonequilibrium effects are included in the core hydraulic channel model through the use of a subcooled boiling model. Subcooled boiling has a significant effect on the channel void fraction distribution and also on the axial power distribution. The effects of subcooled boiling assumptions on the pressuri:zation transient response is discussed in the reply to Question 28.

Q16-1/Q16- 2

NEDO-24154-A QUESTION 17 Figure 4-1 is insufficient to derive Equations 4-35 through 4-40. Draw the proper figures in detail, indicating the meaning of all symbols on the figures.

RESPONSE

A figure has been added to the revised model report which defines the approp riate quantities in Equations 4-35 through 4-40.

Q17-1/Q17-2

NEDO-24154-A QUESTION Provide a nodalization diagram for the whole recirculation model showing different pressures in each of the 10 nodes. Justify the selection of only 10 nodes, particularly selections of one node for the vessel, and another node for the downcomer, inlet pleni and the core. Discuss the pressure drops through dryers, downcomer, orifices and the core and justify the selec tion of one node-single pressure model for these regions. How do these pressure drops change during transients? What type of error is introduced when an iteration is made between the recirculation model and thermal-hydraulic model?

RESPONSE

The attached nodalization diagram (Figure 18-1) indicates the pressure nodes in the ODYN model. Note that the core is nodalized axially as is the steasline.

The justification for this choice of nodes is based on several factors, the most important of which are: (1) the variation of fluid or material properties is negligible over the region; (2) the fluid flowing in the recirculation system is liquid, subcooled and quite incompressible so that acceleration of the flow occurs as a single inertial unit (integral momentum); (3) wave type phenoena demonstrate wave lengths much longer than the nodes; (4) adequate approximation to the phenomena based on the modal representation of a region is made; and (5) the transient pressure drops do not result in significant changes in the approximations (2) through (4) above.

The basis for choosing a single node in the vessel dome is that the pressure drop from the downcomer inlet to the top of the dome is nearly all due to density effects. This amounts to 5 to 6 psi difference from bottom of the dome region to the top. Compared with operating pressures of typically 1000 psia or greater, the difference above results in less than 0.5Z change in fluid properties in the dome region. In addition, the dome region is a very large area compared to the height (very little inertial effect). Hence, there is no observable wave response in the dome region. Finally, since the acoustical velocity in steat is ý-1500 ft/aec, the change of pressure within the dome is effectively instan taneous whenever a flow disturbance is introduced into the reactor vessel.

Q18-1

NEDO-24154-A In 'the dowucomer region during the pressurization transients, the recirculation flow is subcooled by about 20 Btu/lbm. With this degree of subcooling, the change in liquid properties is very small due to pressure. The pressure change from the dome to the bottom of the reactor vessel is about 35 psi, most of which is due to density head and the jet pump diffuser pressure increase. Since the pressure in the downcomer and core inlet is about 1000 psia or greater, the fluid properties vary by less than 0.1%, which is negligible as in the dome region.

In addition, sonic speed is in the range of a few thousand feet per second in the downcomer and lower plenum region, which means that similar to the dome region the downcomer and inlet plenum respond to pressure disturbances in the reactor vessel almost instantaneously. This does not mean, however, that flow rate responds instantly to equilibrate pressure disturbance effects, because the recirculation system will require an additional amount of time for fluid acceleration around the loop.

The core is not represented as a single node for pressure calculations in ODYN.

The equations in Section 6 require nodal calculation in the core for pressure, density, enthalpy and flowrate. If reference is made to 'igure 4-7 (Jet Pump Schematic), please note that the APcore is indicated without the nodal structure and Pe, the core exit pressure, is indicated, which may leave the impression that a single pressure is used to represent the core. However, this is not the case as seen by implication from Section 6. The core inlet orifice pressure drop is about 10 psi and is taken into account in the ODYN core. The total core pressure drop is typically 20-25 psi, including the inlet orifice.

The pressure drop through the dryers is >12 inches of liquid water at operating pressure or 0.4 psi.

The pressure drops around the recirculation loop will increase slightly during large pressurization transients. This is due to flow acceleration due to void collapse effects in the core as the vessel is pressurized. These increases in pressure drop are about 15 to 25% or approximately 10 psi from the dome to the core inlet plenum. Such changes do not invalidate any of the arguments above regarding properties in the lumped regions. This is again due to the small pressure drop relative to the absolute vessel pressure at operating conditions of about 1000 psia or higher.

Q18-2

MO-24154-A The error introduced in the recirculation-thermal hydraulic model iteration is quantified by two criteria: model stability and accuracy. The iteration procedure is very stable and converges to a relative error criteria on core pressure drop. By choice of the error criteria, this accuracy between models can be as good as desired. Overall accuracy of this method is judged to be excellent for this particular application.

Q18-3

1"V SAFETY AND R*ELIEF VALVES MIT ISOLATION TURBINE VALVES CONTROL VALVES OR STOP VALVES

-d 2 . h02 40

-,is I

N a.

mOWh DVALVES BYPASS m31 h31 fSECIRCULATION DRIVE PUMP I mRL 2

.INLET PLENUM Figure 18-1. ODYN Pressure Nodal Diagram

NEDO-24154-A QUESTION" 19 Provide a noding sensitivity study for thM uteamline to show the convergence of the results with 8 nodes for a licensing basis transient for a typical BWR/4.

Provide a sensitivity study for different values of y (the raio of specific heats for steam) and the values of K (form loss coefficient). Discuss the sensitivity of the results for deviations from the assumption of isentropy and the presence of moisture. Quantify the conservatism in terms of ACPR.

RESPONSE

The noding studies performed to date are included in the attached Figures 19-1 and 19-2. These studies show a strong continual improvement out to about 7 nodes where a reasonable approximation is obtained. Further comparison of the 8-node model to the Moody analytical model employing the method of charac teis tics has also been performed. The comparison of the ODYN sceamline model with the method of characteristics model is shown in Figures 19-3 and 19-4.

These comparisons were made at various locations along the .steamline. The model labeled 8-node model is the ODYN model and the method of characteristics model is identified as the Moody model. The so-called Moody model also includes the convective circulation terms which have been neglected in the ODYN formula tion. The comparison case is a turbine stop valve closure simulation along a steamline with constant pressure supply at the inlet to the steamline. Hence, no dome pressure comparisons could be made. Note that the general tendency of the ODYN 8-node model is to overpredict the method of characteristics solution even though all other factors are held constant. The nodel studies were con cluded at this point on the basis that the 8-node model is satisfactory in representation of the steamline response nodes.

Parameter studies of changes in the average specific heat ratio, y, are shown in Figure 19-5 for changes between 1.10 and 1.30. These values were chosen simply to establish a range of sensitivity. Figure 19-5 shows little sensi tivity to specific heat ratio In the dome pressure. The neutron flux peak varies by 10%. The heat flux variation over this arbitrary range is 2.2Z.

Q19-1

NEDO-24154-A Uncertainties in specific heat ratio are based on the average specific heat ratio which best matches turbine trip* pressure rate (1.15) compared to the super heated steam maximum from the steam tables (1.25). This uncertainty is ACPR/ICPR is +/-0.01. Actual uncertainties in y are expected to be significantly less in specific plant analyses. The loss coefficient, K, of the steamline was decreased by 20%. This was based on the upper limit of steamline loss coefficient uncertainty. The results are presented in Figure 19-6. The change in peak neutron flux was -2% and heat flux varied by 1.0%. The ACPR/ICPR uncer tainty is 0.01 for the steamline loss coefficient. Again, the actual uncertainty is expected to be less in this parameter in specific plant analyses. The pres ence of moisture in the steamline is extremely low. The amount of liquid entrained in the steam flowing along the steamline is <0.12. The increase in steamline pressure results in a removal of the mixture from saturated conditions to a mixture consisting of superheated steam and subcooled liquid. By assuming such to- be the case, the pressurization is most conservatively represented because of the decreased steam compressibility. The presence of liquid in such small quantities has limited heat absorption capabilities so that little, if any, effect of heat transfer could occur during the pressurization phase.

Finally, all of these assumptions are borne out in the comparison of ODYK to the Peach Bottom-2 and KDM data, where a value of specific heat ratio can be ade quately determined as 1.15.

The uncertainty in this model for transient initial pressure rate is negligible because it was matched directly to pressure rate data taken at Peach Bottom-2 and other turbine trip tests. Peak dome pressures are conservatively over pre dicted by the model which are due to nonsteamline effects.

• Peach Bottom-2 data principally.

Q19-2

NEDO-24154-A 2.0 1.9 z

U zw 1.8 0

w IA.

0 40* ~l~

z

-a I 1.7 zw I

a 1.6 "

J I  ! 1'I'loll 1.5 3

1.4 5 10 Is 20 25 30 35 40 45 so 0

NUM8ER OF SECTIONS Figure 19-1. Fundamental Frequemrcy Q19-3

NEDO-24154-A 125 100 -- 6 W.*MOODY 0 *1 Np

-25 0 1.0 TIME Inc)

Figure 19-2a. Pressure Ri.se at: 0.7L 7c'

" ji 125 "*-20

_., # 4

• MOODY

-25 A w

0 L *LENGTH OF STEAMUNE 1.0 TIME (lo) 1.5 Figure 19-2b. Pressure Rise at 1.OL Q19-4

NEDO.-2 4154-A U-NODE MODEL 125 I. \

• .100 I I oo F. I ~MOODY I MODEL U I II 25 I

2, 1 0

TIME 1.2 Figure 19-3. Pressure Rise at 2/3 L During Turbine Trip with Constant Dome Pressure Q19-5

NEDO-241.54-&

1 10 71 75 0.T TIME lI.)

Figure 19-4. Pressure Rise at Turbine During Turbine Trip with Constant Dome Pressure Q19-6

NEDO-24154-A E 11a0 a 0.U 1.0 1.5 TIME (lld Figure 19-5. Dome Pressure Vs Time - Sensitiv*ty to Specific Heat Ratio, y Q19-7

NEDO-24154-A 1200 1150 -DECREASED 20%

NOMINAL i 11003 1050 1000 A 0 . 1.1.5 TIME lInd Figure 19-6. Dome Pressure Vs Time-Sen.sitivity to Steamline Loss Coefficients Q19-8

NEDO-24154-A QUESTI:ON 20 Define all notations in the Safety/Relief Valve Model. Describe how the variations of CiV, Csv and fsy are determined and present the nature of the function. Describe how transport delay times are obtained.

RESPONSE

All notation has been defined in Revision 1 of the One-Diensional Core Transient Model document. The capacity of the relief and safety valves, CV and CSV respectively, are determined by the nameplate capacities of the safety and relief valves or the minimum specified capacity for plants in the design phases prior to hardware procurement. These valve capacities are, therefore, conservative inputs which are part of the design process. Note that these capacities are both functions of nameplate actuation pressures and not func tions of the valve pressure throughout the valve operation. The safety valve characteristic, fSVP is actually applied as indicated in Figure 4-6. This is a linear opening characteristic from 501 of capacity upon initial operation to 1002 of capacity when pressure is 103Z of the safety valve setpoint. This flow characteristic is an input to the model and, therefore, part of the model application basis. The choice is made such that the input characteristic results in less flow than the actual valve characteristic. The choice will therefore be conservative. Again, the so-called transport delay times are based on equipment design limits or actual valve measurements of the time from start of the valve stroke to full flow through the valves. The choice of transport delay times is also a matter of model input which is a part of the model application basis. One final coment on the modeling of the safety/

relief valves is appropriate at this time. In the One-DIensional Core Transient Model document, there has been no mention of the valve opening delay.

In reality, the valves may not open instantaneously when pressure exceeds the setpoint of the valve. Due to the mechanical functions of the valve, there can be a time delay. This delay has been incorporated into the model, although it was not documented. The delay is, in fact, a pure time delay due to mechanical response times which occur prior to valve opening. It is simu lated as a time delay effect, not a time constant delay effect. The time line below gives an indication of simulated valve function.

Q20-l

NEDO-24154-A Also note that the safety/relief valve characteristics were indicated on the same figure strictly for convenience. The real safety and relief valves operate with different delay times, flow delay time constants and reseating pressures.

/

PAT VALVE ' 1.03 X PSETPOINT FOR SAFETY VALVES ONLY RELIEF VALVES ONLY 1.0 VALVE PATVALVE" OPENING PRSTFRI IFRACTION OR RELIEF VA OF FULLY VALVE DEL4AY SAFETY VALVES OPPENEDI,,.*.. TIME o Ill t2 23 2s TRANSIENT TIME OF TIME TIME OF TIME OF FULL STARTS PRESSURE VALVE FULL.FLOW VALVE START VALVE B*

EXCEEDING STARTS ISAME AS tZ t2 OF FECGLURt RLOUPI'Ln SETlPOINT OPENING FOR RELIEF (SAFETY VALVES)

VALVE FOR SAFETY VALVES Q20-2

NEDO-24 154-A QUESTION 21 Justify the assumption that perfect mixing of suction and drive flows occurs in the jet pump throat.

RESPONSE

The criterion of major concern for designing high efficiency jet pumps is complete mixing of the drive and suction flows. The concern is that a non uniform velocity profile will flow from the mixer region to the diffuser. If this profile is peaked to the center of the flow channel, the diffuser effi ciency can be impaired. In short, the jet pumps are designed to effect com plete mixing for effective diffuser utilization.

The measured distribution of flow entering the diffusers of typical jet pumps indicates distributions somewhat like the fully developed turbulent flow for*

multiple nozzle jet pumps and practically parabolic distributions for single nozzle jet pumps. Such distributions provide good performance of jet pump systems.

The typical BWR/4 jet pump designs yield a nozzle-to-suction velocity ratio of about 3 to 1 at rated conditions. The time to traverse the mixing section of such a pump is about 0.1 sec with velocity of the jet at about 180 ft/sec and velocity of the suction of 60 ft/sec. Mixed velocity is about 80 ft/sec. The inertial frictional time constant of the jet pump system is about I sec, which is much longer than the flow transit time. Hence, the mixing effects are practically instantaneous compared to inertial effects on the transient flow.

The approximation of instantaneous mixing is well justified in this instance.

Q21-1/Q21-2

NEDO-24154-A QUESTION 22 Present experimental verification for the representation of the jet pump recirculation system and justify the use of the steady-state equations such as Equations 4-67 through 4-69 or Equations 4-84 through 4-91 during transients.

RESPONSE

Experimental verification of the jet pump recirculation system models has been presented in NEDO-10802 in that comparisons to startup pump trip data from Dresden-2 was compared to calculations made by REDY which incorporates the same recirculation system model. These data, presented in Figures 4-10 and 4-11 priacipally, show that the model predicts somewhat faster coastdovn than observed -in the plant data. -The reasons for this diicrepancy is that plant pump inertia was somewhat higher than used in the model and also that plant flow sensors incorporate a filter to smooth the noise in the recirculation flow determination. This filter has a time constant in the range of 0.25 to 0.5 sec.

Additional model verification of the jet pump model is given in NEDO-10802 Amendment 2 where the jet pump model is compared to drive flow oscillations in Figure 1 and a drive flow trip similar to the plant observed pump trips in Figures 2 and 3. These characteristics show the jet pump modeling represents the behavior of the system in both the large transients and the transfer function form.

Equations 4-67 through 4-69 are based on the fact that, during transient and normal operation, the flow in the recirculation system is substantially sub cooled. Under normal full power operation, the recirculation system is 10 to 20 Btu/lbm subcooled. An increase in system pressure increases the liquid saturation enthalpy even further. An examination of fluid properties from the 1967 ASME Steam Tables shows that liquids subcooled by this amount are only compressible to 0.3% for a 200 psi pressure change. Such compressibility has been ignored in both the mass and energy balance equations.

Further, as the flows mix upon entering the downcomer, the enthalpy change is also due to pressure effects. The change in enthalpy due to 200 psi pressure q 22-1 4

NEDO-24154-A change is less than 0.1%. This has also bedn neglected in the energy balance equations. Note, however, that flow effects for transport along flow channels has been incorporated in Equations 4-56 through 4-64.

The above compressib~ility arguments also hold in the jet pump mixing region.

Since this is the case, the influence on the momentum inertia in the jet pump throat and mixing section due to compressibility is negligible. Further, the recirculation flow is incompressible in the downcomer, drive loop, lower plenum and jet pump diffuser. For this reason, the entire fluid in the recirculation loop must be accelerated enmass due to system transient effects.

This paves the way for the integral momentum recirculation system models of ODYN. In this regard, the inertial effects of the jet pump mixing region are taken into account in term identified as -Idif/Adif. Further accounting for the momentum effects in the jet pump throat would duplicate these inertial terms in the ODYN model and, therefore, be inconsistent with the current formulation. For this reason, the inertial terms (i.e., the transient effects) have been left out of Equations 4-84 through 4-91.

Q22-2

NEDO-24154-A QUESTION 23 Present a figure showing the non-jet pump recirculation system. Present experimental verification for representation of the system.

RESPONSE

The non-jet pump recirculation system description has been expanded and a figure included in Section 4. Experimental verification of the non-jet pump model system is provided in NEDO-10802, Figures 4-13 through 4-15. The data and model comparison is for Oyster Creek Plant startup pump trip transients involving single and multiple pump trips. Generally, very good agreement is demonstrated in the core flow comparisons between data and calculation.

Q23-1/Q23-2

NEDO-24154-A QUESTION 24 The momentum balance equations such as Equation 4-83 describing the recirculation flow model contain terms for mechanical energy on the right side and a term for momentum balance on the left side. In addition, the change of direction of the velocity vector and the forces from the walls are not considered. Justify the use of the equation both in steady-state and transient analyses. Describe how the X values are determined. Provide a sensitivity study using different X values in a turbine trip without bypass transient in a typical BWR/4. Justify the selection of K values ana provide a comparison with. available experiment data.

RESPONSE

Generally, the geometry of the downcomer region is as shown in Figure 4-7 of the One-Dimensional Core Transient Model. The regions from the bulkwater section into the bulkwater, the jet-pump suction and finally down into the recirculation loop intake can be represented as a series of different flow area channels, where flow la essentially parallel to the axis with local effects due to area changes and pressure forces past internal structural bodies and channel walls within the recirculation flow. Local and wall forces in these types of sections can be represented by viscous loss effects. Because of the turbulent flow in these regions, the viscous loss effects are normally given by flow squared terms in the equations. This form of the equations for varying area flow channels can be obtained from R. B. Bird, W. E. Stewart and E. N. Lightfoot, "Transport Phenomena," Chapters 6 and 7, John Wiley & Sons, 1960. This form of the momentum equations has been applied consistently throughout the recir culation system. By insuring the system pressure losses and flows are con sistent with steady-state calculations, it is possible to determine the loss coefficients consistent with steady-state operation. The K values are determined by the initialization process described in Question 6.

Sensitivities of the recirculation parameters actually extend beyond the loss coefficients. It is possible to recognize these parameters as part of the Q24-1

NEDO-24154-A recirculation system: inertial parameters (L/A), areas of jet pump components, diffuser loss coefficient, suction loss coefficient, nozzle loss coefficient, m-ratio, core loss coefficient, lower plenum loss coefficient and bulkwater loss coefficient. The impact of varying these parameters is shown in Table 24-1.

There has been no known measurement of operating plant loss coefficients for the downcomer. The jet pump efficiencies have been determined experimentally so that flow and pressure ratios are well-known quantities. Uncertainty in the plant and suction to drive flow ratio is <5.62. Uncertainties in system loss coefficients, based on engineering evaluation and measurements of jet pumps for flow calibration, are <20Z. The flow areas and jet pump lengths are manufactured to close engineering tolerances so that these parameters vary in a negligibly small manner. The impact of this uncertainty is for all practical purposes zero.

The following have negligible impact on ACPR/ICPR for expected order of magnitude variations: (1) drive flow L/A; (2) jet pump areas; (3) nozzle loss coefficients; and (4) lower plenum and bulkwater loss coefficient. Reasonable variations of these parameters did not result in calculated ACPR/ICPR impact.

Table 24-1 RECIRCULATION SYSTEM PARAMETER SENSITIVITY Uncertainty Effect Parameter Increment on ACPR/ICPR 1- Recirculation System L/A 1- Increase by 1- +/-0.002 Factor of 2 2- Kdiff 2- Reduced 10% 2- +/-0.001 3- Total jet pump pressure 3- Decreased 20% 3- +/-0.01 loss 4- Core Loss Coefficients 4- Increase AP 4- +/-0.0045 1.5 psi Q24-2

NEDO-24154-A QUESTION 25 Indicate all quantities described in Equations 4-85 through 4-91 in a figure.

RESPONSE

The appropriate quantities have been defined in the revised version of Section 4.

Q25-1/Q25-2

NED3O-24154-A QUESTION 26 On a uon-jet pump recirculation system, provide a figure and define all terms in Equations 4-92 through 4-95 in the figure.

RESPONSE

A non-jet pump recirculation system figure has been provided in the revised version of Section 4.

Q26-1Q2 6 -2

NEDO-24154-A QUESTION 27 Correct Figure 6-1.

RESPONSE

This figure has been corrected in the revised version of Section 6.

Q27-1/Q27-2

NEDO-24154-A QUESTION 28 Provide the values of VgJS Co, F1 , F 2 , Kloc, f, 0, Twi, and xc. Provide the analytical expressions, experimental data and discuss the conservatism of the selected values.

These parameters are im/portant in determining the void fraction and the void collapse during a pressure pulse transient. Provide sensitivity studies for turbine trip without bypass transient for a typical BEW/4 using the values based on either experimental data or analytical considerations. The values chosen should be: (1) nominal; (2) upper bound; and (3) lower bound. The sensitivity studies should include &CPR calculations and uncertainties assoc iated with the above parameters should be assessed in terms of ACPR.

RESPOPSE The response to Question 28 contains GE Company proprietary information and is documented separately in Volume III of this report.

Q28-l/Q28-2

REDO-24154-A QUESTION 29 Provide the basis for selection of al and 62 and discuss the stability and accuracy of the solution.

RESPONSE

The values of 81 and 02 currently used in the model are 0.0 and 0.1, res pectively. These values were chosen by trial and error. The most accurate result is obtained when both 01 and 02 are equal to zero. Hence, the smallest value of 51 and 02 needed to achieve numerical stability were selected. The practice of using 02 - 0.1 has yielded numerically stable results with-a negligible impact on numerical accuracy.

Q29-1/Q29-2

NEDO-24154-k QUESTION 30 The report contains numerous typographical errors. Some of the symbols are not defined. Correct the errors, define the symbols and present figures showing these symbols where appropriate.

RESPONSE

A review of the model document has been conducted and a revised version has been constructed which will eliminate the majority of the typographical errors.

Q30-1/Q30-2

NEDO-24154-A QUESTION 31 In Equation 5-3, the quantity rb is taken as a constant at the top and bottom of the active core length. The equation accounts for the time variation of the diffusion coefficient. Describe the effect of varying moderator condi tions during a transient on the constant rb.

RESPONSE

The boundary condition coefficient r will change during a pressurization transient, but this change has a negligible effect on the outcome of the trans ient. In a full power turbine trip without bypass transient, the average water density at the top of the core changes by about 12% over the first 1.2 sac of the transient. Under conditions where r is held constant, the effective value r given by:

r - rb changes from 0 to about 0.1 rb over this 122 range of densities. The parameter rb is generally less than 0.5, so that the total numerical change in r is quite small. To verify the magnitude of this effect, a Peach Bottom transient was run where rb was forced to change by a factor of 2 for a 12% density change.

This variation is about an order of magnitude more than the variation assumed in the three-dimensional BWR core simulator. The results of this calculation showed a negligibly small effect on tfie total neutron flux (less than 0.01%).

Therefore, the assumption of a constant ro is adequate for transient applications.

Q31-1/Q31-2

NEDO-24154-A QUESTION 32 Provide the steps leading from Equation 5-6 to Equation 5-9 using the assumption that Ci (Z,t) varies as exp (-Xit).

RESPONSE

Equation 5-9 cannot be derived using the assumption stated in the text. The statement should read: "Ci (Z,t)e- +/- varies linearly from tt to t,,l". This error has been corrected in the revised text (Reference 2).

Q32-l/Q32-2

N.EDO-24154-A QUESTION 33 Provide the steps leading from the left-hand side of Equation 5-14 to the right-hand side of the equation for the asms-ed behavior of the flux after a cross section change.

RESPONSE

The flux is assumed to behave as ewt after a cross-section change. We also know that 0(t) " *k at tk and 0k+l at tk+1 . Therefore, for tk < t < tk+1 V - (t)

Vk )

( t:) - (

+ 4 -+l -_VZ*-v:tk))

( 1 eE t k (33-1)

The integral t._ 1 ftk~ 0(t) dt tk is evaluated by substituting'iquatiou 33-1 into the integral expression giving:

atk f .- VEt Z t k-1 J

(Z~k-1

( 1(e-e

_Zt t

Q33-1/Q33-2

NEDO-24154-A QUESTION 34 In deriving the spatial equations (e.g. , Equation 5-22), has b. been assumed to be a constant in spite of the definition for h given by Equation 5-20o?

RESPONSE

The mesh spacing ii assumed to be constant in the derivation and the model.

Q34-1/Q34-2

NEDO-2415k-A QUESTION 35 The definition for the flux-to-power conversion factor given by Equation 5-32 is not the same as that given by Equation A-87. Explain the difference in the two equations, and state which equation for T is actually used for the model.

RESPONSE

Equation 5-32 is used in the model and can be derived from Equation A-87 by making the assumptions expressed in Equations 5-33 and 5-34. These assumptions are made to simplify the numerical calculations and the size of the data file.

The approximation was checked against the more exact definition and the resulting power distributions were within 0.5% of each other.

Q35-1/Q35-2

NEDO-24154-A QUESTION 36 Describe and provide results of comparisons, obtained from steady-state calculations, using the one-dimensional core transient model described in the report and the three-dimensional BWR Core Simulator. A wide range of core conditions (flow, pressure, temperature, power level, control rod distributions) and times in cycles including different fuel cycles should be considered.

RESPONSE

The collapsing scheme employed in the generation of nuclear parameters ensures that the steady-state axial power shape and core eigenvalue are identical to the-three-dimensional results. The model one-dimensional equation is given by Equation A-2. The steady-state version of this equation is:

stte In*h'-2 -stead In the steady state:

CDOP (1- fo - I) 1 2- A ,/k° 1 0 X y However, we have defined -Br2 such that r

DBr 2DB f y dxdy s *1 - /f )

CDOP (VT° - 1 )

Therefore, D -*- - Oat t-0.

Q36-1

NEDO-24154-A Also, from Equation A-99, d4 IdZ - 0 at the problem boundaries at t - 0.

Therefore, * - constant in space at t - 0.

The flux to power conversion factor, f(zt) is computed from Equation A-87:

kr k

f(z,t) - k 0 1 + CDOP (/T"- VT r

which, when used with the appropriate definitions, reduces to:

S1 1-1 [~

S k*.. CDOP (VT- T'3 -dxdy*

y[] Y 0 - r + Er I .Z,b -.

f f ddy y

The expression inside the brackets is equal to the fission rate from Equations A-4 and A-5:

12 f(z,t) i ii' (1 ffl +

72rf2 "r1 + Y3Zf3 Ir13 , xd

I" f Y

dxdy Table 36-1 contains a list of some of the plants and conditions analyzed with the one-dimensional kinetics model. All of these analyses showed the one dimensional axial power to be within 0.5% of the three-dimensional average axial pouer.

q36-2

NEDO-24154-A Table 36-1 LIST OF PLANTS AND REACTOR CONDITIONS ANALYZED WITH 1-D TRANSIENT MODEL Number of Exposure Plant Product Line Power Level Fuel Bundles Condition Plant A BWR/4 48% 764 EOC2 62 764 BWR/4 69 764 BWR/4 104 764 BWR/4 Plant B 77 228 EOC4 Plant D BWR/4 104 368 EOC3 BWR/4 104 368 MidCycle 3 BWR/4 104 EOC4 Plant E EWR/4 104 560 EOC2 BWR/4 104 560 MidCycle 2 Plant F BWR/ 5 104 764 EOCI Plant C BWK/5 104 560 EOC1 Plant G BWR/3 104 484 EOCI BWR,' 104 560 Q36-3/Q36-4

NEDO-24154-L QUESTION 37 Discuss and provide results, demonstrating the adequacy of a one-group cored model for performing spatial transient calculations.

RESPONSE

The one-group kinetics model employed in the one-dimensional transient model employs collapsed one-dimen*sonaul cross sections obtained from three-dimensional flux solutions and infinite medium lattice cross sections. These cross sections will change throughout the transient, depending on the void fraction, fuel temperature, and control at any one time. Use of the one group method implies an instantaneous change in neutron spectrum as the void and control systems change. In order to illustrate the time constants for these spectral changes, ye write the three group kinetics equations as:

1 1 1 1 R 1 k 1fl 1 +v 2 f2 2 3 f3 (37-1) 1 42 M V'D 2 VO2 " ER2 02 + .S' 41 (37-2) 1 -03 a V*D3 V03 " 1R3 03 + Z.,= 2 (37-3)

Cl f "XtCi +- (Vl 1f 0 + V2 r2 @2 + E3££ 03 (37-4) 1 )~

1 1 +~ k 1 fl1 l~ 2 f2 2 V3 If3 *3 (7 where the above equations are a generalization for the time-dependent case of the three-dimensional BWR simulator equations. The notation is the same as used in the BEL simulator report B-11 with Ci representing the concentration of pre cursor group L, S13 the delayed neutron fraction for precursor group i, and Vi the average neutron speed for energy group i. We express the leakage in groups 2 and 3 in terms of a Buckling expression:

-V.D & vg g D g Bg 2 (37-5)

Q37-1

N~EDO-24154-A where g - 2,3.

Also, we define two new variables R 2 (37

-6) 2 1 33 43-

• ' (37. -7)

The three neutron flux equations can be expressed as equations in Oi.R2 and R3:

v1 7-V. 1 z11 4 1

+ (1-B) + V E Rf3 T Ifl* 2 f2 12 + '3 'f 3) 3

+ EL i ci (37- -8) 1 i 1 R2 " -D2 22St 2 "- ' R + (37-9) 1 33 1 (jr/ R3 a -D 3 B3z2R3 - E e' + 'sL2R (37-10)

Q37-2

NEDO-24154-A In the .steady state, It 2 and R13 are given by:

(37-11)

P2 PR22 - ( + M2 B2 ')

r E:sz (Zls.2 (37-12)

H3 - U3 - ER r R3 (l1+M2 2B22)

(1 + M32 B32)

Equations 37-9 and 37-10 can be expressed as:

(37-13) 2v 2 r 2 Fv2 1 EgSl1 SRv3" "- R" 3 (37-14) where R - rrS 12 2 (37-15)

R2 3 " £ 3 (1 + M3 832)

Note here that the time constants for changes in R2 and R" 3 are 1/V 2 rSt 2 and 1/V 3 ES 3 , respectively. Substituting values typical for a BWH:

1 a a x 10-6 sec (37-16) v2 ES12 1 - 8.3 x 10-5 sec (37-17) v3 rS.2 The time constants are several orders of magnitude less than a typical time step of 0.01 sec in the transient solution. Since an Implicit flux integration is used, Q37-3

NEDO-243154-A a "prompt jump" approximation for the flux ratio can be used with good accuracy and the spectral derivative terms can be neglected. Also, examination of a large number of pressurization transient results for typical BWR's shows that a maximum value for i1/01 is usually around 10 sec- 1 and never goes above 20 sec-1. The quantities R2 and R2 3 w are about 1.0 or 2.0; hence, R2 and R3 can be approxim4ted as:

R2 - 2 R22 ( 2R2--

~v Z"* l 01)1 (37-18)

"3 " 3 R3. 1

\\ 1-2 & f + .L v 3 .3--- I1/ (37-19)

In the current model, the terms proportional to i1/01 are also neglected, giving rise to Equation A-5 in the appendix to the model report. For

/1 A = 15, the error in R3 is still less than 0.3%. Further, it is conserva tive to neglect these terms. However, the A1/1 terms can be retained and substituted into Equation 37-8 to obtain

1 1 Rl

+(1-1) (1 fl + V2 2R + V3 f 3 R 3 )I + X C (37-20) resulting in a one-group equation with an effective neutron speed given by:

+VI V3 ZV R3" 2 I1 +~ (V2 Ef 2 P-2 + V3 E f 3 R,)

V v1 2 ZR2 (1 + M2 ' B22) 3 ZR3 (i + M32 '32 (37-21)

In summary, BEWturbine trip transients can be adequately represented by a one group, prompt Jump approximation and the time constants for spectral change are much smaller than the time scale of pressurization transient calculations.

Q37-4

NEDO-24154-A QUESTION 38 Discuss sensitivities in the cross sections as a function of the reference moderator density fuel temperature and control fraction. How are uncertainties such as these treated in the ODYN code?

RESPONSE

Cross-section uncertainties manifest themselves in transient calculations as biases and uncertainties in void reactivity coefficient, Doppler reactivity coefficient and scram strength. One should evaluate these uncertainties by comparing GE lattice and Monte Carlo calculations. The cross-section data used in the Monte Carlo studies come from the standard ENDFB-4 libraries.

The Monte Carlo reactivity calculations have, in turn, been compared to critical experiments representative of BWR configurations.

(1) Moderator Density or Void Reactivity Effects The uncertainty and bias In moderator density reactivity effects have been estimated by comparing d k./d values calculated by the GE lattice code with a simulated experimental d k./da. Monte Carlo vs critical experiment compari sons have been used to simulate the experimental values.

The GE Monte Carlo model has been used to simulate a group of five critical experiments. The comparisons are summarized in Table 38-1. These comparisons yield a weighted mean difference bet-ween the Monte Carlo criticality and experiment of:

"t'C-k 2. kExP - k] - 0.004o +/- 0.0013 (38-1) void This bias and uncertainty is applied to the Monte Carlo estimates at all fractions and is assumed to be independent.

Q38-1

NEDO-24L54-h The derivative.of the lattice k with respect to void fraction a (d k*/da) was evaluated by first calculating the lattice at three void fractions, a - 0, a - 0.4 and a - 0.7. These three values were then used to generate a quadratic fit in void fraction; i.e.,

- k=(0) (a - 0.4) (a - 0.7) - k (0.4) a(a-0.127) k (a)

-0.28 01

+ k Go (0.7) a(a -0.21 0.4) (38-2)

This expressLon can be differentiated to obtain:

d km (0 - 0.55) (0 - 0.35) + * (0.7) - 0.2) k (0) 0.14 (0.4) 0.06 k 0.105 (38-3)

The variance of d kj/da can be evaluated by assuming k (0), km (0.4) and

k. (0.7) are independent. This yields:

Vart k -- ___-/ 0.064Vart(km (0.4))0"5 (a 0. ar (ka (0.4))

+a a0. )2 2 0.105) Var (k (0.7)) (38-4)

The variances of the individual k, values can be determined from the Monte Carlo variances. The d ki/d values are compared for a - 0.4 in Table 38-2 for three lattice types typically used in existing BWER's and requisition cores. The weighted mean approach is used to determine the average bias and variance between the Monte Carlo estimates and the lattice code estimates:

Q38-2

NEDO-24154-A mean (dkC- -_ 0.081 x 10-2 Var d= "a/

d1.18 x 10 5 The final bias and uncertainty in the void reactivity coefficient can be determined by suning the lattice - Monte Carlo bias and the Monte Carlo experiment bias:

d k~P d kc (dk' dkLC +( k dkc d I . dk (38-5)

The second term on the right-hand side involves both a bias and uncertainty and the third term is assumed to have only an uncerteinty. The variance in the lattice code to experimental bias is given by:

Var dkC dk~

-am Var Ida d kMC dkCj

-daJ

+ Var a- - _n- (38-6) 1 d .

d ]

The variance in the Monte Carlo-experiment bias in d k/da can be evaluated by substituting the variance obtained from the critical experiments

[A (kMC - kEJxp) into Equation 38-4 for a - 0.4. This yields:

va da K d ) 9.6 8 x 10-6 Q38-3

NEDO-24154-A Therefore:

Mean Fd k!C dk E

1 - +0.081 x 10-2 dkLC dkExp 1 Var - J - 2.15 x 10-5 da d a 0.464 x 10-2 From Table 38-2, the values for d k fda range from 6.6 x 10-2 to 9.xl10-2.

Hence, the lattice code bias is about 1% of the average value and the la uncertainty in this bias about t6Z.

The ODYN code uses the infinite lattice data to calculate changes in cross sections with moderator density. As the bias in the infinite latt4ce data with regard to void coefficient is considered negligible, the ODYN treatment of moderator density effects is considered nominal. There is no treatment of uncertainty in the cross sections due to moderator density in ODYN.

(2) Fuel Temperature The infinite lattice cross section dependence on fuel temperature is handled by computing a Doppler reactivity decrement,B-Z2 represented by the following expression:

(Ak)k Doppler a CDoP (YT - VTo) where CDOP - constant of proportionality; T - aboolute fuel temperature; and T - reference fuel temperature.

0 Q38-4

NEDO-24154-L (3) Control Strength Calculated results based on the Doppler model have been normalized to Keflstrand's experimental dataB-14 and this normalized model, when compared to experimental

- 1 6 transients performed on the SPERT I and SPElT ItII reactors, has demon strated very good agreements. Therefore, the infinite lattice Doppler treat ment is nominal., There is insufficient data available to calculate the uncer tainty in this treatment of cross-section dependence on fuel temperature; how ever, based on the two experimental comparisons, a 4% (lo) uncertainty is considered a conservative estimate.

The one-dimensional model code employs the nominal CDOP values calculated by the infinite lattice code. Both moderator density and exposure dependence of CDOP are considered. There is no treatment of Doppler reactivity uncertainty in ODYN.

We have again chosen to evaluate possible lattice model uncertainties by comparing lattice control strengths with Monte Carlo results. Here there is a limited amount of data, so a statistical analysis is not-possible. Two lattice configura tions have been examined at two different void fractions. The results are sum marized in Table 38-3. In assigning an uncertainty, we have chosen the largest nonconservative control strength bias, which occurs in lattice A at a 0.40 void fraction. This results in a +/-4Z uncertainty in control strength.

The ODYN code uses the rod strength predicted by the infinite lattice code.

There is no treatment of uncertainty in the cross-dependence on control fraction in the ODYN code.

CDOP is treated as a function of both moderator density and exposure. Design B-13 calculations are performed using the standard lattice design code to determine CDOP values at various moderator density and exposure conditions.

The functional dependence of CDOP is based on these calculations.

Q38-5

NEDO-24154-A The uncertainty in the infinite lattice cross sections as a function of control fraction is evaluated by considering the control strength Akrod in terms of the change in k.; i.e.,

Ak kuncontrolled kcontrolled krod cc Table 38-1

SUMMARY

OF MONTE CARLO CALCULATIONS FOR CRITICAL EXPERIMENTS Critical Experiment* .Monte Carlo Eigenvalue B&W UO2 0.9950 +/- 0.0021 BWR Critical (Boron Curtains) 0.9974 +/- 0.0024 BtR Critical (Gd rods Core I) 0.9952 +/- 0.00096 BWR Critical (Gd rods Core II) 0.9968 +/- 0.00106 BWR Critical (Gd rods Core III) 0.9948 i 0.00099 2

k 1I£ i

Weighted Mean 2

-0.9956 AkMý-Exp x* 1 /ai Variance of Weighted Mean -

1 - 2.944'x 10"7 1l/0 2

" 1 - Ak) 2 - 1.461 z 10-6 Sample variance N- I Total variance - (0.2944 + 1.461)'x 106 - 1.756 x 10

- 0.00133

,k'OExp - 0.0044 t 0.00133

• The critical experiment analysis is documented further in "ENDF/B-IV Benchmark Analyses vith Full Spectrum Three-Dimensional Monte Carlo Models," C. M. Kang and E. C. Hansen, Trans Am. Nuc1. Soc. 27, page 801S, November 1977.

Q38-6

NEDO-24LU-A Table 38-2 COMPARISON OF LATTICE PHYSICS CODE AND MONTE CARLO VOID COEFFICIENT VALUES Lattice Type Lattice Code Monte Carlo Var A -7.284 x 10-2 -7.021'x 10-2 2.034 x 10"5

-9.221 x 10-2 2.487 x 10"5 B -9.187 x i0-2 2 0.8051 x 10-5 C -6.631 x 10-2 -6.865 x 10-km. .

a - 0.0813 z 10-2 AdkLC4C da Weighted Mean / i2 Variance of Weighted Mean

• 1 + 4.682 x 10-6 Sample variance m -1 ( d (k.40 -A~)

i

- 7.182 x106 1.186 x 10-5 - Var AkLC4MC Total variance -

Q38-7

NEDO-24154-A Table 38-3 COMPARISON OF LATTICE CODE AND M4ONTE CARLO CON~TROL STRENGTH CALCULATIONS ALC mHc kc red rod (Akkd -

Lattice A 0 0.2621 0.2607 z 0.0032 +0.0014 Lattice B 0 0.2377 0.2411 t 0.0038 -0.0033 Lattice A 0.4 0.3148 0.3060 t 0.0031 +0.0088 Lattice B 0.4 0.2655 0.2763 t 0.0031 -0.01086 Q38-8

NEDO-24154-A QUESTION 39 Discuss the implications of using a radially averaged hear generation rare rather than a radially dependent heat generation rate. Discuss the conser vatism of this assumption in the code. Is it conservative for calculation of the clad temperature? Quantify the effect of this assumption on ACPR.

RESPONSE

The radial power, distribution within the fuel rod is not uniform (flat) in actual operation. The plutonium buildup and self-shielding of the fuel rods result in a radial power shape peaked quite sharply to the outside of the fuel pellet. Heat transfer from the inside of the pellet to the cladding occurs by diffusion through the fuel material, which is a time-dependent pro-ess where the longer the paths of diffusion result in longer traverse times. When power is peaked higher to the outside of the pellet where the average distance from the generation to edge of the pellet is less, the thermal time constant will be lower than in the uniform power production case because a larger portion of the power travels a shorter distance. A reduction in thermal time constant results in faster feedback of heat flux to the moderator-coolant which increases the void fraction, mitigating the pressurization transient to a degree dependent upon the outer radius peaking of the power in the rods. Hence, a uniform (flat) power distribution assump tion inside the fuel pellet is conservative for pressurization transients from the power increase conditions. Since this effect is small and the pres surization transients are far from clad temperature limits in the ODYN calcu lations, the clad temperature impact is not important. Since this effect is conservatively incorporated in ODYN, no evaluation of &CPR is warranted.

Q39-1/Q39-2

NEDO-24154-L QUESTION 40 Application of the Crank-Nicholson Method suffers complications when heat generation varies with position and time, when thermal properties vary (as ODYN assumes) and when nonlinear boundary conditions are used. Discuss any restriction on the gap conductances that can be input such that the solu tions still remain valid. Radiative heat transfer becomes important in transient gap conductance. This would make hla, highly nonlinear with time.

Hence, discuss any restrictions in the calculltional method or in input selection.

RESPONSE

The Crank-Nicholson Method suffers complications when time steps are too large relative to thermal time constants and changes of fuel properties occur faster than the time stepping. The BWR thermal time constant is in the range of 5-8 sac compared to 0.01 sec time steps taken in the calculation.*

Such extensive time stepping will accommodate all the nonlinearity problems of the fuel behavior. On this basis, there have been no required restrictions on fuel gap conductance during transient calculations. It is also important to note that fuel gap conductance is discussed in Question 8. Since the fuel gap conductance is conservatively held constant in the transient calculations, heat transfer calculations proceed with no difficulties.

Radiation at operating conditions contributes less than 1% to the gap con ductance. During power increase transients, the radiant heat transfer component increases because of the fuel temperature increases. This con tributes more power to the moderator than assuming the gap conductance remains constant during the transient. Radiation, therefore, results in more modera tor voiding, mitigating the pressurization transients somewhat. Since the ODYN heat transfer model ignores the radiant component of heat transfer transient changes, the ODYN calculations will be conservative during the pressurization transients and proceed more smoothly than if the radiant heat transfer effects were included.

This is the same as the hydraulics time steps. Since the time is synchronized, this eliminates potential gap difficulties.

Q40--IQ40-2

NEDO-24154-A QUESTION 41 In the description on the control system, it is stated that the systems are simulated through digital logic. Also, the numerical values for response functions, as well as gains and time constants, must be defined for each plant design. Provide a discussion on how response functions, gains and time constants are established and verified for each design.

Furthermore, define what control system failures are evaluated with the code and define those control systems wherein operational credit is taken in the accident inalysis. For these defined control systems, provide experimental data that justifies your control system models.

RESPONSE

The response functions, gains and time constants fQr control systems are determined based on detailed computer simulations of the BWR to achieve stable system control and design objectives. The numerical values are fine tuned during, on-site startup tests.

In the transient safety analysis, the control systems, except the assumed failures, are assumed to maintain normal operation unless specifically designated to the contrary in order to provide a realistic transient signature. Nominal inputs are used in ODYN calculations. The effects of these inputs on thermal and pressure margins, which are insignificant, are discussed in the response to Question 10- Enclosure 1.

Control system failures are evaluated and presented in Chapter 15 of PSAR, or FSAR, or reload licensing submittals. They are:

(1) feedwater controller failure - maximum demand; (2) feedwater controller failure - minimum demand; (3) pressure regulator failure - open; (4) pressure regulator failure - closed; and (5) recirculation flow control failure - increasing flow.

Q41-1

NEDO-24154-A above transients The effects of single failures and operator errors on the or reload are also discussed and ptesented in Chapter 15 of PSAR or FSAR licensing submittals. The worst plant control mode is assumed in the above transient simulations.

Q41-2

NEDO-24154-A QUESTION 42 Figure 4-13 provides a block diagram of the valve flow control. Additional description of the control system is required to complete our review of the block diagram. In this regard, provide the following information:

a. The basis of the gain and lead-lag ratio for the grid compen sation function in processing of turbine governor signal.

b. A description of all function generators used in the control model.

c. The basis for the selection of the gains and time constants used in the master controller. Also, provide the basis for variations in the gains, if any, in the use of the model. Also provide this information for the flow controller and the flux controller.

RESPONSE

The block entitled, "Grid Compensation Function" in the block diagram (Figure 4-13) is a lead/lag function, the time constants of which are approximately the inverse of the lag/lead function in the pressure regula tor. Its purpose is to give the load following loop lead effect to compen sate for the lag effect inherent in the pressure regulator. Gain KG is determined by calculation and verified excperimentally both in the field and on the computer.

The control characteristics of valves including flow/position curves as furnished for each plant by the specific equipment reactor are simulated as accurately as reasonably possible. Then, mathematical function generators are devised/adjusted to linearize the steady-state gain curve for each con trol loop.

The numeric values are adjusted during on-site startup tests to ensure the achievement of stable control and design objectives.

In the transient safety analysis, nominal values are input to ODYN calcula tions. The effects of these inputs on transient thermal and pressure mar gins are insignificant and are discussed in the response to Question 10, .

Q42-1.Q42-2

NFJ0-24154-A QUESTION 43 Figure 4-14 provides a block diagram of the motor-generator flow control system. Additional description of the control system is required in order for the staff to complete its review of the block diagram. In this regard, provide the following information:

a. The basis for the selection of the gains used in the master controller and the speed controller.

b. A description of the.speed demand limits and of the function generator used in the control.

RESPONSE

The speed demand limiter at the output of the Master Control Loop M/A station is set as a function of what speed is necessary to cover the load following range of the automatic load following loop. The function genera tor in each speed loop is for the purpose of linearizing the steady-state gain characteristic of the fluid coupler.

The selection of the gains used in the master controller and the speed controller is based on detailed computer simulation in order to achieve stable flow control and meet design objectives for load following. The setting is adjusted and fine-tuned during on-site startup test program.

In transient safety analysis, manual flow control is assumed. Therefore, the numerical values of gains have little effect on the transient thermal and pressure margin. A more detailed discussion is presented in the response to Question 10, Enclosure 1.

Q43-11Q43-2

NED0-24154-A QUESTION 44 Figure 4-15 provides a block diagram of the feedwater control. Additional description of the control system is required to complete review of the block diagram. In this regard, provide the following information:

a. Further descriptions of the steam flow gain, the basis of its selection, and its relationship to the steady-state level, power, and steam separator performance.

b. A description of how the transient response of the steam-driven feedwater pumps is simulated through the rise of the optional compensator.

c. A basis for the selection of gains and the modeling used to repre sent the flow controller and the level controller.

d. A description of the function generators and limits used in modeling the system.

RESPONSE

The gain K.S can be adjusted such that steady-state water level can be auto matically changed as a function of steam flow. The theory being that, in order to have a minimum carryunder at low power and minimum carryover at high power, the level should be varied several inches as a function of power level.

The steam-driven feedwater pump and turbine is represented by a third-order differential equation, consisting of a slightly underdamped quadratic repre sented by the two integrators and the gains V, .and KV2 plus single time constant TA. The title (optional compensator) for the function determined by KA and TA was ill chosen. All three terms of the turbine description generally fall between 0.5 and 1.0 sec and are obtained from the turbine vendor.

The other two "optional compensations" need mention. The K1 , Ti, T2 function was a lead/lag unit added to inject phase lead to the turbine loops, when the turbine system was first synthesized. It is not used. Function K2, T 3 , T4 is the lag/lead network which is used in the flow loop when the model represents a single/three-element feedvater control system. When a single/three-element system is used, level controller gains are set to zero and its input feeds directly to the summer showing "optional level setpoint."

When two-loop system is represented, X2 is turned to zero.

Q44-1

.NEDO-243154-A As with the recirculation system, the attempt is made to represent the flow characteristics of each individual turbine pump or flow control/valve as per vendor specifications. Function generators are used to linearize the steady-state gain curves or at least to make the steady-state gain curves nearly identical for all flow actuators of a given system.

The selection of gains is based on detailed computer simulator in order to achieve stable feedwater control and meet design objectives of the feedwater control system. The gains are adjusted and fine-tuned during onsite startup program.

In transient safety analysis, the nominal specified inputs are used. The effects of these input values on the transient thermal and pressure margin are negligible as discussed in the response to Question 10, Enclosure 1.

Q44-2

NEDO-24154-A QUESTION 45 Figure 4-16 provides a block diagram of the pressure regulator system.

Additional description of the control system is required to complete review of the block diagram. In this regard, provide the following:

a. A description of the modeling of the setpoint adjuster and of the controller that acts upon the pressure error signal. The description is to contain the basis for the gains and time constants used in the model and the selection of numerical values for them.

b. A description of all nonlinearities presented in the model. The description is to contain the basis and verification of the numerical values selected for the model.

RESPONSE

Figure 4-16 represents a model of a typical EWR pressure regulation system for main steam turbine equipped with Mechanical Hydraulic Control (MEC).

Turbine inlet pressure is regulated by a closed-loop feedback control system, through manipulation of the turbine admission valves or steam bypass valves, utilizing the sensed inlet pressure as the feedback signal. For normal opera tion, the turbine admission valves are designed to regulate steam pressure; however, whenever the steamflow demand exceeds that which can be passed by the turbine admission values, the pressure control system demands the excess steamflow to be sent to the main condenser through the steam bypass values.

In addition, when the reactor is operating in the automatic load following mode, provisions are made within the pressure control system to allow tempor ary adjustments to the desired pressure setpoint by means of the setpoint adjuster to permit a faster steam flow response to changes in load demand, thereby utilizing a part of the stored energy capacity in the vessel. The pressure control system is designed to achieve the following design objectives:

1. Steady-State Performance. At steady-state plant operation, the pressure control system maintains primary steam pressure at a nearly constant value, to ensure optimum plant performance.

Any limit cycles, or noise, in the system must be of sufficiently small magnitude to avoid premature wear of plant equipment, or compromise of plant operation.

Q45-1

NEDO-24154-.

2. Response to Operational Transients. A broad range of routine operational transients must be accommodated without reactor trip, by maintaining pressure within operational bounds or by minimizing pressure induced effects on other reactor systems.

The pressure control system must provide responsive, stable performance to minimize vessel water level and neutron flux transients caused by plant normal-operation maneuvers (pressure setpoint changes, level setpoint changes, recirculation flow changes). The pressure control system shall also be designed for operation with other reactor control systems to avoid reactor trip after significant plant disturbances, such as:

partial- or full-generator load rejections, loss of one feed water pump, loss of one recirculation pump, inadvertent opening and closing of relief valves, and steam bypass and main turbine stop-control valve testing.

3. Response to Kajor Plant-Shutdown Transients. Events which induce reactor trip present significant transients during which the pres sure control system must maintain pressure. These transients are characterized by large variations in vessel, steamflow, core thermal-power output, and sometimes recirculation flow, all of which affect vessel water level; hence, the pressure control must respond quickly to stabilize the system pressure and thus aid the feedwater/level control in maintaining water level. The pressure control must also be capable of controlling pressure during normal (main steam isolation valves open) reactor shut down to control the reactor cooling rate.

4. Plant Startup/Reatup Operation. The pressure control system must provide for automatic control of the reactor system pressure within the bypass steamflow capacity during the plant startup and heatup. This shall permit independent control of reactor pressure and power, during reactor vessel heatup, by varying of steam bypass flow as the main turbine is brought up to speed and synchronized.

Q45-2

NEDO-24154-A The pressure regulator shown in Figure 4-16 is a proportional plus lag lead compensation. The proportional gain and lag-lead time constants are determined based upon transient simulations of the BWR to achieve stable pressure control and to achieve the design objectives stated above.

The nonlinearities shown on Figure 4-16 are representations of inherent hardware characteristics (such as control value flow vs. value position),

electronic functions generators to linearize control value flow to control value demand, hardware limiters and deadband.

The setpoint adjuster consists of a proportional gain plus a lag filter.

It is switched into service only during automatic load-following operation.

The proportional gain and the time constant are chosen for stable pressure operation such that a certain power change rate is achieved by manipulation of the reactor recirculation flow. On-site startup test participation by control system design engineers ensures that the gains and time constants are optimally tuned to achieve the stated design objectives.

The numerical values for the gain and time constants used in transient safety analysis are nominal specified values. The effect of these numeric values on thermal and pressure margins is insignificant as discussed in the response to Question 10, Enclosure 1.

Q45-3/Q45-4

NEDO-24154-A QUESTION 46 In a discussion of the reactor safety system, the operation of a flux filter is presented. It is stated that the flux filter may be switched in or out of the high flux scram circuit. Provide the basis for the use of the flux filter in the system. Also, quantitatively, describe the time impact upon the trip of the safety system in the use of the filter in the most limiting flux event, and for the bypass of the filter. The flux filter is presented as a double lead-lag filter with the lead lag ratio less that one. Provide the basis for the selection of the lead-lag ratios.

RESPONSE

The use of a double lead/lag filter In the model is for flexibility of simulation. In the actual simulation of the high flux scram circuit only the natural system response delay is considered. That is, in the licensing application of the model for transient analysis, the flux filter simulation:

Ks (1+ T 2 s)

K (1+ T3 ) N()

a ~(1 + T1 ) (l + TOT) is converted to N6 l+T 1 4s (2) by inputting the following:

K -1.0 s

T3 0.0 Q4 6-1.

NEDO-24L54-A and the input value for T4 is the equipment specified maximum allowabli APL'( flux sensor time constant. This is to simulate the sensed neutron flux by relating the actual neutron flux through a sensor time constant. The use of this sensor time constant delays the scram initiation time by about a time interval equal to one time constant. This makes the simulation more realistic, and at the same time, more conservative.

Q46-2

NEDO-24154-A QUESTION 47 Discuss the uncertainties in gains and time constants in control and protection systems.

RESPONSE

The uncertainties in the reactor protection system parameters are accounted for by using conservative maximum specification inputs to the ODYN licensing basis calculations. Specifically, the "safety limits" of the reactor pro tection system instrument setpoints and instrument characteristics are used.

If there are no safety limits specified, the maximum allowable uncertainties specified for instrument setpoints or instrument characteristics are added to the nominal values specified. The uncertainties are added in such a way that it makes the simulated transients more severe from peak power and pres sure consideration.

Uncertainties in control system have little effects on the transient thermal and pressure margins as discussed in the response to Question 10, Enclosure 1.

Q47-1/Q47-2

NEDO-24154-A QUESTION 48 Discuss the uncertainties in the overall calculations due to heat loss.

RESPONSE 48 Heat losses during a transient are assumed to be negligibly small in the one-dimensional model. This assumption is conservative for peak pressure and flux calculations.

In order to estimate the magnitude of possible heat loss, a simple heat loss model was added to the BWR plant model. In this model, the vessel dome and intervals are assumed to be equal to the steam temperature in the steady state. During the pressurization transient, the saturation temperature of the steam will increase. The heat loss is assumed to be:

Qloss 'Ai h (TsAT - TV,)

where AV, - area of vessel and intervals exposed to steam; TSAT - saturation temperature of steam; TV, M temperature of vessel and intervals; and h - heat transfer coefficient This model was tested for the Peach Bottom turbine trip number 1 test conditions. The value of the heat transfer coefficient was varied to determine the effect on peak dome pressure. It was found that, for the Peach Bottom -1 turbine trip, a peak energy loss of 77 MW, or 5% of the initial thermal power, was required to reduce the peak pressure by 8 psi.

Based on this large energy loss rate needed to sustain a small pressure loss, it has been concluded that heat loss effects have a negligibly small effect on peak pressure estimates.

Q48-Z/Q48-2

NEDO-24154-A QUESTION 49 The manner in which General Electric treats Doppler and void reactivity effects in preparing ODYN input is discussed in the report. However, the manner in which moderator temperature effects in the nonboiling portions of the moderator are included in the cross sections is not discussed.

Results obtained by our consultants indicate that the moderator temperature effect is important and should be included in the calculations. State whether or not the moderator temperature effect is included in the ODYN calculations. Discuss the effect and provide quantitative results for the Peach Bottom Unit 2 turbine trip tests.

RESPONSE

In the one-dimensional model, cross sections are assumed to be only func tions of the fuel temperature and moderator density. Moderator temperature effects on the neutron scattering law and thermal neutron spectrum are neglected. The reactivity effects of moderator temperature changes are illustrated in Table 49-1 where lattice calculations of reactivity changes due to changes in moderator temperature are tabulated for 0% void fraction and 40Z void fraction.

During a typical pressurization transient, the change in moderator tempera ture is small. At the peak of the flux transient, the temperature change is less than VC in the subcooled region and less than 40C in the saturated

-4 region. This amounts to a reactivity change of 2.2 x 10 Ak, a small per centage (2.7%) of the total void reactivity change. Since it is a negative reactivity component, it is conservative to neglect it. Further, its effect on the flux transient and ACPR is negligible.

Table 49-1 REACTIVITY EFFECTS OF MODERATOR TEMPERATURE CHANGE (BOL LATTICE CONDITIONS)

Temperature Change Reactivity Change Ak /&T- (C)'

Void Fraction

+660C -0.0033 -0.5007 x 10-4 0%

+140C -0.0007 -0.5000 x 10-4 40%

Q49-11Q49-2

A.

NEDO-24154-REPLIES TO NRC QUESTIONS ON APPLNDIX A QUESTION 1 On page A-3 of the report, it is stated that Henry suggests that 0 (z,.t) be normalized according to Equation A-l1. However, a perusal of Henry's book indicates that he normalized the quantity $ (z,t)/V - a number density.

Therefore, discuss the consequences of the two different normalization procedures with respect to the derivations presented in Appendix A of the report.

RESPONSE

There are no consequences resulting from defining the one-dimensional neutron flux as done in Equation A-11. Henry notes (p. 300) that he uses the number density rather than the flux to conform to convention. And it is the con vention to write point kinetics equations in terms of the neutron density.

However, in Appendix A of Reference 1 a one-dimensional kinetics equation is being derived rather than point kinetics, and normally space-dependent kinetics equations are in terms of flux rather than number densities.

Since V is constant and only one energy group is being considered, Equation 7.3.1 of Henry's book can be cast in the same form as Equation A-11 of Appendix A.

Considering the above statement and collapsing only in the x and y direction, Equation 7.3.1 becomes:

T (z,t) - f xy I (i,t)dxdy.

4(*)VI-*

Since V is assumed constant, it can be pulled out of the integral.

Thus:

T (z,t) -= ffw(;) 0 (,t)dxdy.

x y Al-I

NEDO-24154-A Multiplying by v*

v T (z, t) - 4 (Z. t) - !Jf x y

( C)

• ~dxdy.

A-i1. The only above equation is very similar to Equation Note that the is assumed to be in Appendix A the weighting function difference is that time.

a function of space and A1-2

N NEDO-24154-L QUESTION 2 In Equation A-15 the first term is assumed to be negligible since 1/V is very small and V varies slowly with time. However, as control rods move during a scram, the shape function V surely must change. Therefore, discuss the effect of scram on this term with respect to its being negli gible as compared to other terms in the equation.

RESPONSE

Appendix A has been amended so that the above assumption is not made.

Instead, it is shown that for 1v constant, and w a 0, the left-hand side of Equation A-15 becomes:

(k<) I -(0;V)i a vL(,)tvt This means that Equation A-64 should be:

T fft-2 L dxdy.

This change has been incorporated into the revised version of Appendix A.

Transient studies have been run which incorporate the revised definition of I/V. These studies show that the 1/V term contributes a negligible amount to the calculated neutron flux in a typical turbine trip transient.

A2-l/A2-2

NEDO-24154-A QuAestion 3 In Equation A-25, the precursor decay constant is assumed to vary both with time and with space. Since six precursor groups are being used with experimentally determined O's and X's, explain the assumed variation of X with space and time. In Equation A-26, for example, it is not varied as per Equation A-25.

RESPONSE

The text of Appendix A has been changed (Reference 2) so that the a are constants. (Equation A-25 has been eliminated.)

A3-1/A3-2

NEDO-24154-A QUESTION 4 In Equation A-1, the leakage term is represented as D, 72 1. However, since a perturbation theory analysis is used to deriv* effective cross sections, explain why the leakage term is not represented as V.D70 in the analysis.

RESPONSE

The spatial gradient of the fast diffusion is neglected because the fast diffusion coefficient, D1 , is fairly constant for 3WR's. This is consis tent with the assumption made in the three-dimensional BWR Core Simulator Topical Report (Reference 3).

A4-lIA4-2

NEDO-24154--L QUESTION 5 The shape function for the delayed neutron precursors L1 should be related to Ki and 6 Kj by an equation similar to the one for 0', '"and Sip' given by Equation A-21. Please provide this equation in the text vitb. appropriate definitions.

RESPONSE

The requested information has been added to the text of the revised ODYN technical document.

A5-1/A5-2

NEDO-24154-A QUESTION 6 Equation A-54 was the definining equation for B and was used in definininL.F in Equation A-57. In Equation A- 6 7 another defining equation is used for B.

Although the two equations for 7 have similar forms, justify the use of Equation A-67 rather than A-54 for B.

RESPONSE

Equation A-54 can be written as:

(1) i*- (0' . OF V')

4'e, e')

where:

D2 (2 F 0 H- - A / A/,,+

A.

0 rl Rearranging

( 2-A/k )

(3) F - r -ak + k*. -11 2rI Recall that:

D1 (4) 1 rl M, Substituting (4) into (3) yields:

M2 -A/k (5) F "- 0 1 D1 M2 - A/./k ic + k* -" (4 - R M, 2 I

A6-1

NEDO-24L54-A Carrying but an order of magnitude analysis one finds that:

ko+k *:ON (,T - R The magnitude of the remaining term within the brackets,

/

-A s

is not as readily evident.* The term can be rearranged as follows:

2 A./k M22 - + A/k (6) 1 2 2

However:

(7) H2 -u 2+ 2+M32.

Thus, substituting (7) into (6) yields:

- 2 A/k . HM2 . 3 +A/k0 (8)

(l M2 The fast group migration area, 1 2, is approximately an order of magnitude greater than the numerator and thus (8) can be neglected with respect to K . Thus, (5) can be written as (9) F (- + Mp. (/R* 'T("

a0 ko K -A ftk 0

A6-2

NE)0-24154-A Substitutin*g (9) into (1) yields:

0' k..

DI 1_-ko

\ 2 -A/k This is equivalent to Equation A-67. The revised text of Appendix A includes the above approximation.

A6-3/A6-4

NEDO-24154-A QUESTION 7 Equation A-57 was the defining equation for in the equation after I.

Equation A-67 another definition is presented for 7. Although the cno equations are somewhat similar, justify the use of the second equation rather than Equation A-57 for 7.

RESPONSE

The equation after A-67 has been corrected so that it is the same as A-57.

A7-1/A7-2

NEDO-24154-A QUESTION 8 The equation for A= given on page A-24 differs from that given in the report on the three-dimensional BWR Core Simulator by a leakage factor which comes from the flux ration (02,01)', and Equations 3-4b and 3-11 from the report on the three-dimensional BWR Core Simulator. Please explain the difference in the definitions of Am used in the two reports.

RESPONSE

The two equations are the same if the definition of (02/01) is used in the equation for Am on page A-24; i.e.

(1) (2) " :St 4 r2 The above relationship comes from Equation 3-lb of the report on the three dimensional BEWCore Simulator for the zero leakage case.

Substituting (1) into the equation for A. from page 24 yields:

A. Y Z l M22 2) EstlY2 Ef2 2 ZRI M RI Z£2 M (Note typo in equation for Aa in p. 24. The E inside brackets should be Efl.)

This equation is the same as that in the report on the three-dimensional BEW Core Simulator,B-1 1 Equation 3-11.

Equation 3-11 of the Simulator report also contains a typographical error.

The coefficients of Zfl and Xf2 should be v1 and v2 , respectively.)

A8-1/AS-2

NEDO-24154-A Appendix B REFERENCES B-1. Letter, MFN 014-78, E.D. Fuller to D.F. Ross, "Transmittal of Draft of ODYN Qualification Report," dated January 13, 1978.

B-2. NEDE-10358-PA, "'General Electrical Thermal Analysis Basis Data, Correlation and Design Application," January 1977.

B-3. NEDE-24011-P-3, "Generic Reload Fuel Application," May 1977.

E-4. NEDO-10958-A, "General Electric Thermal Analysis Basis Data, Correlation and Design Application," January 1977.

B-5. NEDE-24811-P, "Generic Reload Fuel Application," Chapter 4, Hydraulic Model Description, May 1977.

B-6. C. L. Martin, "Nuclear Basis for ECCS (Appendix K) Calculations,"

NEDO-23729, November 1977.

B-7. Letter, MFN 462-78, E. D. Fuller to D. F. Ross, "Transmittal of ODYN Computer Code Model Description," dated December 2, 1977.

3-8. C. H. Robbins, "Performance Tests of Axial Flow Primary Steam Separators,"

APED-4762, January 1965 (1978 Summary).

B-9. 1. H. Edelfelt, "APED Axial Steam Separator Computer Program," 65GL10, January 1965.

B-10. E. L. Lusterader, "Axial-Flow Steam Separator and Dryer Development,"

65GL11, January 1965.

B-II. J. A. Wooley, "Three-Dimensional BWR Core Simulator, NEDO-20953, May 1976.

B-12. R. C. Stirn et. al. Generation of Void and Doppler Reactivity Feedback for Application to BWR Design, December .1975 (NEDO-20964) 1-13. C. L. Martin, Lattice Methods Physics Verification, July 1976 (NEDO-20939).

B-14. E. Hellstrand, et. al., "The Temperature Coefficient of the Reasonance Integral for Uranium Metal and Oxide" Nuclear Science and Engineering, 8, 497-506 (1960).

B-15. R. C. Stiri et al. Rod Drop Accident Analysis for Large Boiling Water Reactors, March 1972 (NEDO-10527).

B-16. C. F. Stuart, SPERT Reactivity Tests, February 1974 (NEDO-20315).

1-1/1-2