ML20069B012
| ML20069B012 | |
| Person / Time | |
|---|---|
| Site: | Brunswick  |
| Issue date: | 02/28/1983 |
| From: | Borrensen S, Moberg L, Rasmussen J CAROLINA POWER & LIGHT CO. |
| To: | |
| Shared Package | |
| ML19344B748 | List: |
| References | |
| NF-1583.03, NUDOCS 8303160421 | |
| Download: ML20069B012 (142) | |
Text
-. .. . _ . _ __.
NF-1583.03 NONPROPRIETARY VERSION METHODS OF PREST 0-B A THREE-DIMENSIONAL, LWR CORE SIMULATION CODE ,
TOPICAL REPORT FEBRUARY 1983 Cp&L Carolina Power & Light Company ,
1 l
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METHODS OF PRESTO-B A THREE-DIMENSIONAL,BWR CORE SIMULATION CODE' S. Borresen L. Moberg J. Rasmussen*
- Institute for Energy Technology, Kjeller, Norway i
NONPROPRIETARY. VERSION TOPICAL REPORT Prepared by SCANDPOWER INC 4853 Cordell Avenue Bethesda, Maryland 20014 20 Jandary 1983 Reviewed by : Approved byy A.L. Watlace V
T. O. ,Sauar
>~~Q Assistant Director I--
DISCLAIMER OF RESPONSIBILITY This document was prepared by SCANDPOWER Incorporated on behalf of Cerolina Power & Light Company. This document is believed to be completely trus and accurate to the best of our knowledge and information. It is cuthorized for use specifically by Carolina Power & Light Company, SCANDPOWER Incorporated, and/or the. appropriate subdivisions within the Nuclear R2gulatory Commission only.
With regard to any unauthorized use whatsoever, Carolina Power & Light Company, SCANDPOWER Incorporated, and their officers, directors, agents, and employees assume no liability nor make any warranty or representation with regard to the contents of this document or its accuracy or completeness.
Proprietary information of SCANDPOWER Incorporated is indicated by " bars" drawn in the margin of the text of this report.
l 1
AESTRACT This report describes the methods of the PRESTO-B computer code and the basis for confidence provided by comparison with measured data and higher order methods.
PRESTO-B is a three-dimensional BWR nodal core simulator, describing the coupled neutronic and thermal-hydraulic phenomena under specified operating conditions.
The code can be used for detailed core Analysis, fuel management, reload design, operations support, or generation of safety-related core parameters, i
i
i VOLUME 2 METHODS OF PRESTO-B, A THREE-DIMENSIONAL BWR CORE SIMULATION CODE
.C .O. N .T E N
- - - - -- .T.. d-Page ABSTRACT
- 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . .. 1-1
- 2.
SUMMARY
OF MODELLING AND CODE PERFORMANCE . . . . . . . . . . .. 2-1
- 3. CORE DESCRIP1 ION . . . . . . . . . . . . . . . . . . . . . .. . 3-1 3.1 Core Geometry . . . . . . . . . . . . . . . . . . . . ... 3-1 3.2 Fuel Designation . . . . . . . . . . . . . . . . . . . .. 3-1 3.3 Nuclear Data Assignment . . . . . . . . . . . . . . . . .. 3-2 3.4 Control Rod Designation . . . . . . . . . . . . . . . . .. 3-2 3.5 Hydraulics Data Assignment . . . . . . . . . . . . . . .. 3-3 3.6 Spacer Grid Locations . . . . . . . . . . . . . . . . . .. 3-3 3.7 In-Core Detector Locations . . . . . . . . . . . . .. .. 3-3 3.8 Radial Core Regions . . . . . . . . . . . . . . . . .. . 3-4
- 4. REPRESENTATION OF NUCLEAR DATA . . . . . . . . . . . . . . . .. 4-1 4.1 Polynomial Representation of 2-Group Data . . . . . .. .. 4-1 4.2 Xenon Feedback Effect . . . . . . . . . . . . . . . . . .. 4-3 4.2.1 Steady-State Xenon Model . . . . . . . . . . . . . 4-3 4.2.2 Transient Xenen Model . . . . . . . . . . . . ... 4-4 4.3 Doppler Feedback Effect . . . . . . . . . . . . . . . . .. 4-5 4.4 Samarium Effect . . . . . . . . . . . . . . . . . , . . .. 4-6 4.5 Control Rod Model . . . . . . . . . . . . . . . . . . . .. 4-7 4.5.1 Control Rod Reactiv'.Ly Effect . . . . . . . . .. . 4-7 4.5.2 Control Rod Depletion . . . . . . . . . . . . . .. 4-9 4.5.3 Control Rod Histor"I Effect . . . . . . . . . . .. 4-10
11 Page 4-10 4.5.4 control Rod Model for Cold Condition . . . . . . . .
Cross-Section Model at Reduced Moderator Temperature . . . . 4-10 4.6 4-11 4.7 Spacer Representation . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 5-1
- 5. NEUTRON DIFFUSION MCDEL 5.1 Derivation of Equations for Calculation of 2-Group Flux Distributions and Eigenvalue . . . . . . . . . . . . . . . . 5-1 5-G 5.2 Reflector Treatment . . . . . . . . . . . . . . . . . . . .
6-1
- 6. THERMAL HYDRAULICS MODEL . . . . . . . . . . . . . . . . . . . . .
6-2 6.1 System Heat Balance . . . . . . . . . . . . . . . . . . . .
Basic Models and Equations for Void Calculation . . . . . . 6-5 6.2 6-5 6.2.1 Mass Balance . . . . . . . . . . . . . . . . . . . .
Energy Balance . . . . . . . . . . . . . . . . . . . 6-6 6.2.2 6-7 6.2.3 Momentum Balance . . . . . . . . . . . . . . . . . .
6-8 6.2.4 Two-Phase Flow Friction . . . . . . . . . . . . . .
6-9 6.2.5 Slip Correlation . . . . . . . . . . . . . . . . . .
6-11 6.2.6 Boiling Model 6-12 6.2.7 Haat-Transfer from Fuel to Coolant . . . . . . . . .
6-14 6.2.8 Heat Source Distribution . . . . . . . . . . . . . .
6-15 6.2.9 Fuel Temperature Model . . . . . . . . . . . . . . .
6-16 6.3 Calculational Procedure . . . . . . . . . . . . . . . . . .
6-17 6.3.1 Calculation of Flou Distribution . . . . . . . . . .
6-20 6.3.2 Calculation of Void Distribution . . . . . . . . . .
Treatment of Void in the Bypass Channel . . . . . . 6-21 6.3.3
. . . . . . . . 7-1
- 7. POWER DISTRIBUTION AND FUEL DEPLETION CALCULATION 7-1 7.1 Nodal Power Distribution . . . . . . . . . . . . . . . . . .
7-3 7.2 Stepwise Burnup Calculation . . . . . . . . . . . . . . . .
7-4 7.3 Cycle Burnup (Haling) Calculation . . . . . . . . . . . . .
7-5 7.4 Integration of Sm-149 and Ba-140 Concentration . . . . . . .
. . . . . . . . . . . . 8-1
- 8. PREDICTION OF CORE PERFORMANCE PARAMETERS 8-1 8.1 Model for TIP and LPRM Calculation . . . . . . . . . . . . .
Calculation of Margins to Thermal Limits - BWR . . . . . . . 8-3 8.2 Critical Heat Flux Ration (CHFR) . . . . . . . . . . 8-3 8.2.1 8.2.2 Fraction of Limiting Power Density (FLPD) . . . . . 8-4 ECCS - Fuel Heat Storage Limit . . . . . . . . . . . 8-4 8.2.3 Thermal Limits Summary Table . . . . . . . . . . . . 8-5 8.2.4 L - -- . _
111 Page-9.
XENON DYNAMICS MODEL . . . . . . . . . . . . . . . . . . . . . . .
9-1 10-1
- 10. AUXILIARY FUNCTIONS INCORPORATED IN PRESTO . . . . . . . . . . . .
10.1 Critical Control Rod Pattern Search Option . . . . . . . . . 10-1 10.2 Shutdown Margin Evaluation . . . . . . . . . . . . . . . . . 10-1 10.3 Core Reload Analysis Features . . . . . . . . . . . . . . . 10-1 10.4 . Fuel Discharce Priority List . . . . . . . . . . . . . . . .
10-2 10.5 Functional Relationships Between Heat Balance Components . . 10-2 11-1
- 11. CODE QUALIFICATION . . . . . . . . . . . . . . . . . . . . . . . .
11.1 Fine Mesh Diffusion Theory Benchmarks . . . . . . . . . . . 11-1 11-3 11.2 Qualification of Hydraulics Model . . . . . . . . . . . . .
11.3 Comparison with Gamma Scan Data for EOC-1 of HATCH-1 . . . . 11-3
. . . . . . . . . . . . 11-4 11.3.1' The Gamma Scan Measurements Simulation of the Cycle-1 Operation . . . . . . . . 11-5 11.3.2 11.3.3 Comparison of Calculated and Measured La-140
. . . . . . . . . . . . . . . . . . . 11-7 Distributions 11-10 11.3.4 Discussion of Results . . . . . . . . . . . . . . .
. . . . . . . . . . . . 11-13 11.4 Comparisons with BWR Operating Data 12-1
- 12. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDICES : Equations for Integration of Special Isotopes A-1 Xenon-Dynamics Equations A-2 Equations for Integration of the Pr - Sm Chain A-3 Equations for Integration of Y-Scan Isotopes
1-1
- 1. INTRODUCTION This report describes the methods of PRESTO-B and provides documentation on its basic and general verification. It has been prepared for Carolina Power & Light Company, in support of their submittal to the US NRC to establish reload design capability for the Brunswick steam electric plants, Units 1 and 2. A detailed evaluation of the code performance for the specific plants considered is given in a supplementary report.
The code was developed by Scandpower A/S (ScP), in cooperation with the Institute for Energy Technology (I.F.E) , Kjeller, Norway. PREETO-B is intended for application by BWR Utilites in performing various core analysis tasks, including :
Multicycle Fuel Management Analysis Reload Core Design Analysis Core-Follow Calculation Current Cycle Operations Support Calculations.
PRESTO-B is part of the ScP Fuel Management System (FMS) code package, and is usually run with lattice data generated with the code RECORD.
RECORD is described in a report complimentary to this report. PRESTO-B has also been successfully run with lattice data generated by codes other than RECORD (e .g. , CASMO) . The code is written in FORTRAN IV and has been implemented on the following computers :
CDC - CYBER 74, 175, 176, 170 CDC - 7600 IBM - 370 UNIVAC - 1110 NCR - 8450 L
2-1
- 2.
SUMMARY
OF MODELING AND CODE PERFORMANCE ,
PRESTO-B is a three-dimensional BWR core simulator with integrated neutronics and thermal-hydraulics models. The neutronics model of PRESTO is based on an approximation of two-group diffusion theory, utilizing a special coarse mesh prescription originally developed for this code (Ref. 1 ). The thermal-hydraulics model is a steady-state version of the hydrodynamics model developed for the RAMONA codes (Ref. 2).
The BWR core is modeled as a three-dimensional array of near cubical nodes, each having homogenized internal properties. The nodal structure coincides with the fuel. assembly array, horizontally, and with an axial subdivision giving approximate cubical shape.
The neutronic properties of a node are described by a set of ccnventional, two-group, homogenized macroscopic cross-section data, represenned as polynomials in fuel exposure, exposure-weighted void and instantaneous void. The thermal-hydraulic properties are described by geometzic data such as in-channel flow area, hydraulic diameter, etc. Hydrauli throt-tling is described by pressure loss coefficients.
Simulation of the reactor operation may include the following reactor conditions :
- cold subcritical
- cold critical
- h0t, zero power critical hot, operating steady-state l
hot, operating - transient Xenon
- hot, operating - fuel burnup increment The following special calculational modes are also available :
- Haling burnup calculation
- Criticality search calculation on flow or power s ._ _
2-2
- One stuck-rod shutdown margin calculation
- Reflector albedo generation Each reactor state point is specified by giving the following data as input :
- total thermal power total coolant flow rate
- core inlet subcooling (or feedwater enthalpy)
- control rod insertion pattern Consistent, three-dimensional distributions of power and steam void are then determined by iteration between the neutronics and the thermal-hydraulics models. Efficient numerical solution methods are employed to ensure fast calculation. The following local effects are accounted for in calculating the nodal powti distribution :
- instantaneous void (hydraulics feedback)
- fuel exposure exposure-weighted void control rod insertion equilibrium or transient Xenon concentration Samarium concentration
- fuel temperature (Dopplerl
- control rod history control rod depletion The following simulated core performance data are derived on the basis of the calculated distributions :
- Evaluation of margins to various thermal limits (Maximum Linear Heat Generation Rate, Fraction of Limiting Power Density, Fraction of Average Planar Power with respect to Emergency Core Cooling Design Limits, Minimum Critical Heat Flux Ratios, and various power peaking factors.
.- ~ . .
2-3
- Predicted in-core detector readings (LPRM and TIP)
The cede may determine the development of the reactor power level with time in a Xe-transient period, or determine the total coolant flow rate required to keep the power level constant during the period. Local power ramp rates are also evaluated under simulated operating transients.
Cycle length estimates for a complete reactor cycle, or for remaining parts of a current cycle, may be performed.
Fuel assemblies are individually labeled, allowing easy simulation of core reloading, including options for insertion of new fuel
- fuel shuffling
- reinsertion of fuel from an earlier operating period
- discharge of spent fuel to a simulated fuel storage An extensive evaluation program has been carried out to verify the code, both against reference calculations and against special data, such as BWR gamma scan data and measured void loop data. In addition, the accumulated experience gained in application of the code since 1971 has yielded a large number of comparisons with reactor data, such as TlP traces, com-parisons with other codes, and with process computer results.
The special diffusion theory approximation of PRESTO has been independently evaluated by comparison with fine mesh diffusion theory benchmarks (Ref. 3) .
In summary, the following results were obtained :
Eigenvalue Bundle Power Case % Diff. STD Dev. (%)
2-D 0.28 0.63 3-D 0.33 0.65 The thermal-hydraulics model of PRESTO-B has been verified against the FRIGG void loop data (Ref. 4 ). The standard deviation (RMS) in per cent void between calculated and measured voids was 2.1%, which is almost
2-4 within the experimental uncertainty of 2.0%. The detailed results of the benchmark calculations are presented in Chapter 11.
Gamma scan data, measured following EOC-1 of the Edwin I. Hatch BWR (Ref. 12),
has been used to qualify the combined thermal-hydraulics and neutronics core models of PRESTO.
Comparisons between calculated and measured La-140 distributions were per-formed for :
Bundlewise axial distributions Bundlewise average (radial) distributions Pin-wise axial distributions Bundles adjacent to partially inserted cor, trol rods
- Bundles in the core boundary versus those in the interior of the ccre The total standard deviation between calculated and measured nodal La-140 distributions was 6.4 per cent.
The total standard deviation in the bundlewise comparison was 2.5 per cent.
An overview of the results, showing plots of the bundlewise axial distri-butions for all bundles in a complete core octant, is presented in Section 11.3.
In general, very good agreement was obtained between calculated and measured La-140 distributions. This demonstrates the accuracy in results of the coupled neutronics and thermal hydraulics models of PRESTO.
3-1
- 3. CORE DESCRIPTION A BWR core is made up of a number of fuel assemblies arranged in a regular lattice grid. The fuel assembly array constitutes a physical subdivision of the core, which is maintained in the simulator model. Each assembly is further subdivided axially, usually 24 or 25 axial segments. The geo-metrically identical unit cells thus obtained are called nodes. The water-gaps associated with each fuel assembly are included in the node.
The main nodal variables (such as power density, void fraction, etc.)
calculated by PRESTO, represent average values within the node.
~3.1 Core Geometry The geometric shape of the core is described in a Cartesian coordinate system with integer coordinate values (I, J, K) , as shown in Figure 3.1.
The I, J coordinates for the nodes along the core periphery are given as input, thus defining the core shape. Each fuel assembly location is identified by its coordinates or, equivalently, by a channel number.
The core model may describe the entire, physical core, or a fraction of the core, depending on core symmetry assumption. 1/8, 1/4 or 1/2-core models may be represented, in addition to the full core representation.
Various symmetry options based on either rotational or reflective symmetry are available.
The physical size of the core is determined by the nodal dimensions speci-fled in input, together with the definitien of the core periphery and number of axial nodes.
3.2 Fuel Designation Fuel assembly images are " loaded" into the core by specifying the fuel assembly identification number corresponding to each channel.
3-2 The fuel assembly identifications are 5 or 6-digit integer numbers, lijkkk, where :
ii = fuel type designation j = identifier for fuel batch number or core quadrant kkk = identifier for individual assemblies Data characterizing the state of the fuel (i.e., exposure, exposure-weighted void and other nodal arrays) are stored on a data file maintained by PRESTO. The data are labeled by the associated fuel assembly number, thus allowing complete freedom for simulation of fuel shuffling, discharge and reinsertion. Core reload sbaulation simply consists of redefining ,
the relationship between core location and fuel assembly identification.
3.3 Nuclear Data' Assignment A nuclear data library, consisting of precalculated group constants and other data characteristic for each type of fuel design is made available to PRESTO on an input data file (so-called POLGEN file) . Each unique data set on the file is identified by a nuclear parameter set number.
The correspondence between the nuclear data sets and fuel assembly types is established by input data relating fuel type identification to nuclear parameter set number. In the case of fuel designs with axially zoned burnable poison or axially varying enrichment, each axial zone is related to a specific nuclear parameter set.
3.4 Control Rod Designation Control rods are labeled by individual identification numbers and with the locations specified through the input data.
For BWR cruciform reds, each rod usually controls the four surrounding assemblies.
The model allows shuffling and replacement of control rods (since control rod depletion is monitored by PRESTO).
3-3 3.5 Hydraulics Data Assignment General data needed for the thermal-hydraulics model are given in the form of a set of library data on input cards.
Data describing the in-channel flow area, heated perimeter and hydraulic diameter are given separately for each fuel type and will thus enable the simulation of mixed (i.e., 7 x 7 and 8 x 8 fuel) cores.
Since BWR cores usually feature coolant flow restrictions for channels near the core periphery, each such hydraulic throttling zone is labeled by a unique index and characterized by specified core inlet and outlet pressure loss coefficients.
The thermo-hydraulics parameters are thus represanted as either general data characteristic for the whole core, fuel type-dependent data or as data related to the core location.
3.6 Spacer Grid Locations The axial location of the fuel spacer grids are specified in order to account for the neutronic effect of the spacers.
3.7 In-Core Detector Locations Two types of in-core detectors are included in the PRESTO model :
- Fixed (LPRM) detectors
- Travelling (TIP) detectors.
LPRMs and TIPS are assumed to be located inside detector tubes (strings),
positioned adjacent to the corner (narrow-narrow gap) of selected fuel assemblies. Thus each string will be surrcunded by four fuel assemblies.
Detector string locations are specified by defining the four channels sur-rounding each detector.
,i
3-4 The axial locations of the fixed detectors are specified by the elevation of the detector centerline for each of the four detectors in a string.
3.8 Radial Core Regions The core may be subdivided into a number of radial regions for the purpose of output editing of volume averaged quanties like void, power, etc.
9
1 3-5 K
/
/
/
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- 6. 7. 8 9 1011 12 1314 15 16 17_18 19 20 21 22 23 24 25 26
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OOCDOT]OTOO E 0T hann is "E000 000000005 Ybb Q 7 "Elbbb a 18 FOOTO O O 05 19 " EDOOiOOiG 0:0D00i000100:05 7 20 BCDOJ$O D005 21 EG0 1EIOG01 000135 22 EODOOODOdDDO T T
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CE 0D000005 T rTEE~E 2' E550 0 CO 25 E iOD 26 E'E E'E E E E E I 'f FIGURE 3.1 Basic Coordinate System for Core Description
1 4-1
- 4. REPRESENTATION OF NUCLEAR DATA 4,1 Polynomial Representation of Two-Group Data Basic, two-group, assembly averaged cross-section data and peaking factors are assumed available from RECORD or from a corresponding lattice physics code. These basic parameters must be generated under the following conditions :
The power density must correspond to the core average nodal power at rated total core power.
- The fuel temperature is the core average effective Dcppler temperature for unexposed fuel at rated total core power.
- The Xenon and Samarium isotopic concentrations must correspond to the equilibrium concentrations at rated power, at any core burnup. Equilibrium concentrations are also assumed at zero burnup.
- The moderator temperature used in RECORD must correspond to the saturation temperature at rated core pressure.
- The basic cross-sections must be generated as functions of burnup and given in discrete burnup points (about 20 points) ,
covering the range from zero to the expected maximum nodal burnup. Separate burnup calculations must be performed for three void fractions (i.e., 0, .40, .70), and for each type of fuel assembly cross-section (segment) encountered in the core. (If axially zoned fuel is used, one fuel assembly type may contain several cross-section types.)
The basic cross-section data sets are input to PRESTO in the form of polynomial coefficients generated by the auxiliary program POLGEN.
4-2 POLGEN subdivides the burnup range into intervals, each consisting of five burnup points. Fourth order polynomials are laid through the given points. Polynomial coefficients are thus given for each inter-val, each void fraction (exposure-weighted) and for each fuel segment type.
A basic cross-section for an arbitrary node in PRESTO is calculated by first locating the exposure interval of the node, then evaluating the cross-section at the actual nodal exposure-weighted void, using a second order interpolation between the three void values used in the RECORD cross-section generation.
The basic cross-sections are thus functions (g) of two parameters, exposure (E) and exposure-weighted void (a ) . Instantaneous void (a) is accounted for by additional polynomial fits (f) , as follows :
(4.1)
U W
where Normally, when the difference between a and a is small, the exposure x
influence on the instantaneous void dependence may be neglected, and the functional dependence can be determined at zero burnup :
(4.2)
W (4.3)
4-3 The simplified model (Eq. 4.3) is available as an option in PRESTO-B.
4.2 Xenon Feedback Effect 4.2.1 Steady-State _ Xenon Model Deviations in local equilibrium Xenon concentrations from the average equilibrium concentration at rated power are accounted for in evaluating the nodal cross-sections. Xenon influences the group constants both by direct neutron absorption and by distorting the thermal neutron spectrum. These effects may be taken into account by modification of the basic thermal group absorption and fission cross-sections :
(4.4)
(4.5)
) (4.6)
?
(4.7) w l
e _
4-4 W
(4.8)
Q = Actual full core thermal power
= Rated full core thermal power Q
P" =
Normalized (nodal) power density (core average = 1.0) r = Conditions at rated power density
= = Conditions at infinite power density The coefficients at , a2 and a3 are evaluated on the basis of RECORD results for no Xenon condition, rated power equilibrium Xenon condi-tion, and an additional calculation at off-rated condition.
4.2.2 Transient, Xenon _Model For calculations where the local Xenon concentrations may differ from equilibrium, a cross-section correction based directly on the nodal Xenon number density is applied :
(4.9) 4 N
(4.10) 'u where X = Nodal Xenon number density a = Effective microscopic absorption cross-section for Xenon is K = Coefficient describing the influence of Xenon on the X
thermal neutron spectrum ng = Coefficient describing the influence of Xenon on the fission cross-section due to spectrum hardening
4-5 x and ex are evaluated as functions of void fraction a, and Xenon o-density :
(4.11) w (4.12)
The coefficients Ct through C5 and n,* may be evaluated on the basis 4
of RECORD calculations.
4.3 Doppler Feedback Effect The Doppler broadening of the cross-section resonance peaks with l
' increasing fuel temperature causes increased epithermal neutron absorption and reduced resonance escape probability. This effect is accounted for in PRESTO through the following correlations :
(4.13)
(4.14) u The nodal average fuel tepperature is obtained from a correlation of nodal power accotaing to Eq. 6.30 which is described in Section 6.
l
4-6 l
4.4 Samarium Effect The basic cross-section data input to PRESTO, in the form of POLGEN polynomials, are assumed to contain the effect of equilibrium Sm-149 also at zero burnup.
The following nodal correction is performed in PRESTO to account for deviations from equilibrium concentration of Sm-149 .
(4.15)
(4.16)
L.3 (4.17)
The average number density of Sm-149 fer each fuel type is tracked in PRESTO whenever a burn;p step or a time step calculation is performed.
The initial concentratica cf Sm-149 is automatically set te zero for all 4
4-7 fresh fuel. ' Pseudo time steps at zero power may be included to simulate Pm decay and Sm buildup during periods of shut down.
4.5- Control Rod Model 4.5.1 Control, Rod,Reac tivit'f,Ef fec t The 2-group constants enter PRESTO's coupling e4uation through the nodal. quantity s , defined by Equation 5.4 :
km s.1 = (4.18)
( r-4 - 1) (Eal + Er1)
E . VE f2 l
+
- 1 (4.19) k, =
g (VE g )
a1 + r1 a2 Therefore, correct representation of control rod insertion is assured 1 if the influence on k ,and (I,g + Erl) is m deled properly. The influence of control rod insertion on the fast group diffusion ccefficient (see Eqs. 5.8 and 5.14) is generally negligible. It is also observed (RECORD) that the sum E,3 +Ir1 is alm st unaffected by control rod insertions. Hence, it is sufficient to model control rod insertion by its influence on k,, This is done by adding a control rod correction term, AEa2, to the thermal group absorption cross-section. In this way, the thermal group flux (Eq. 5.24) will be modified due to control rod absorption.
The following expression is used to evaluate dIa2 ~ '
- i (4.20)
.N La3
4-6 vhere c
k =
k, -control rod inserted (RECORD calc.)
This expression is obtained by requiring the controlled k, (obtained by adding AE a2 and solving Equation 4.19 for AEa2) to agree with a to E a2 reference, controlled k , (RECORD).
The control rod correction term, AEa2, is represented as a polynomial fit where the following effects are taken into account :
Void in the adjacent channel Fuel burnup in the adjacent assembly Depletion of the boron absorber Moderator condition (cold or hot)
- ' Partial insertion of a control rod into a node.
In addition, the effect of control rod insertion on the local power peaking factor and the effect of the control rod history on the group constants (through spectrum hardening and increased Pu production) in the adjacent fuel are taken into account. This is described in detail below. The basic expression for AE is :
a2 (4.21)
(4.22) fo w
v
4-9 b = fitted constant 5
h =
multiplier accounting for 4-bundle homogenization effects.
4 Thc following term accounts for the effect of undepleted control rods (subscript o) in fully controlled nodes .
A
=b2(E) +b 3 IE) ***D4 (E) (4.23)
E = fuel burnup a = in-channel void fraction The functions b2 , b and b are second order polynomials in E.
3 4
.s.s.2 Cenergt_agd_ceeletten The term C g -
B
- f(E) of Equation 4.21 accounts for a reduction in the rod worth due to depletion of the Baron absorber (B10). Detailed analysis of Boron depletion for SWR control rods (rodded blade rods) have shown that the rod worth, Ak, decreases linearly with increasing burnup Ak(B) = Ak (0) -C RC B (4.24)
B =
burnup obtained in the adjacent fuel during the periods of control rod insertion C =
fitted constant (different fo cold and hot condition)
RC f(2) of Equation 4.21 is a function of to 2-group constants converting the reduction C n k, into a correspsnd ng reduc don in Ca2' RC The content of B in each segment of the control rod, given in per cent of the initial B content is :
!! 1
"
- u^ *
- B - 3 4
. .. . .. . . m_ _ . - . , _ .~. .-
4-10 i
i ~where: i C and C 4are fitted constants 3
i
' Constants for the control rod depletion model have been derived for BWR rodded blade. control rods by detailed calculation of the B depletion using the codes RECORD and THERMOS. These constants are assumed to be generic for GE-type rodded blades.
l
! 4.5.3 ggggggl_ggd_gisiggy_E!! egg ,
i i
o Control rod history effects on the nodal 2-group constants are accounted for by means of a model derived on the basis of a large number of' RECORD calculations . This model allows the nodal E 2 and vE f2 to increase j
j (second order polynomial) due to increased Pu production in periods when the control rod _ is inserted; whereas, a corresponding decrease (exponential decay) of the excess quantity accounts for burnup in periods
- when the control rod is withdrawn.
i
! 4.5.4 Control, Rod,Model,for, Cold,Conditiog i
For cold condition analysis, where all or nearly all control rods are j
inserted, the basic group constants as input to PRESTO (POLGEN-File) are J
assumed to contain the effect of the control rod.
J For uncontrolled nodes, a quantity AEa2, eval ated as by Equation 4.20 replacing k ,with the uncontrolled k ,, is subtracted. Control rod l depletion and control rod history effects are applied as described above.
4.6 Cross-section Model at Reduced Moderator Temperature i
The hot cperating condition, two-group data set is applicable for analysis of reactor conditions ranging from hot, near zero power to hot full power. Separate data sets are required for analyses of zero i
I power states at reduced moderator temperature. The polynomial repre-sentation described in Section 4.1 is applied at each moderator i
J a
k t
4-11' temperature (i.e . , cold condition) , thus the group constants are.
. functions of exposure (E) and exposure-weighted void (a ) . Each low temperature _ cross-section set is assumed generated by branch-off RECORD calculations based on the isotopic composition file generated in the corresponding hot condition RECORD calculation. The branch-off calculation is performed under the following assumptions :
The power density is set to zero.
- The fuel temperature is the same as the moderator temperature (i.e.,
20 C for cold cases).
The Xenon and Iodine concentrations are set to zero.
- The Sm concentrations are kept unchanged (from the hot case).
The control rod is inserted in cold condition (see 64.5.4).
4.7 Spacer Representation Neutron absorption in . spacer grids is accounted for by adding an exposure and void dependent correction term to the thermal group absorption cross-section in nodes defined as spacer nodes. The effect of the spacer on the flux and power distributions is thus smeared out over the nodal volumr.. The following form of the spacer correction term is used :
(4.26) fd w
where b through b gare fitted constants.
6 Sp The magnitude of AE may be obtained by separate RECORD calculations a2 with spacer material included, followed by a one-dimensional diffusion calculation (MD-1) to perform the axial homogenization over the nodal volume, t
m 5-1
- 5. NEUTRCN DIFFUSION MODEL 5.1 Derivation of Ecuations for Calculation of Two-Group Flux Distributions and Eige:.ealue The neutronic equations'of PRESTO are derived as an approximation to coarse mesh diffusion . theory (Reference 1) . A constant planar mesh width (h) is assumed. The axial mesh vidth (k) is usually equal to the planar mesh width for BWRs (cubical nodes) . The method is derived for non-cubical nodes as well; however, the cubical node (k=h) formulation is described first :
A central mesh point finite difference formulation is used for the fast flux (4) equation (Reference 1) :
a $ =r *T -
h3 (5.1)
- [Gja )4 g where 2D D
( '
gj =h a
D +D i j a =
[a gj (5.3) ii Gj i and j.are nodal indices. The summation is over the six nearest nodes j surrounding node 1 (4 planar and 2 axial neighbor nodes) . T is a function of the 2-group nodal macroscopic cross-sections and the eigen-value A :
' r
- 1 (5,4) s = + vf F) -: , -I 1 f(VE f2 a2 where F = nodal thermal spectrum index. ( See Eq . 5.18.)
\
5-2 (Standard 2-group _ notation is used for the 2-group constants.)
The following approximation is used to simplify Equation 5.1 :
-2D D
= (5.5)
D.+D 1 j
[i 'E j (See Reference 1 for discussion of accuracy of this approximation.)
Equation 5.1 is then reduced to :
P $p- [ $ =-q$ -(5.6) 1 Gj where
$ =$ , (5.7) 1 1 P =
- E , (5.8).
k [6j and Y
gg =- h2 (5.9) i Further, the nodal average flux T gis expressed as an interpolation between the mesh point flux $ and the six nodal interface flux values
$ (on the interfaces between the node considered and its six nearest neighbors) :
I f=b$g+ ~ 6 { U (5.10) 6j where b is a fitted constant.
).
5-3 The interface-fluxes may be expressed as :
- Nj
=
1
$ +
i (5.11) 2/D~
j 2/D-i giving
_$g = - (b + cr g) Y +
c[$)6j (5.12) with 1-b c = 12 (5.13) and r = /D71 (5.14) i jg-6j j Introducing Equation 5.12 into Equation 5.6 gives :
Q911 =[$ 3 (5.15) 6j with P +q (b + cr g)
=
Q1 1 - eq
- 1 Equation 5.15 is the fundamental nodal coupling equation, as applied in PRESTO. All nuclear constants are contained in a single vector, Q ,
thus Equation 5.15 lends itself to uncomplicated computer representation.
The eigenvalue A, entering Equatica 5,4, must be found simultaneously with Equation 5.15. This is achieved by iterative methods (starting from a guess of A=1.0) ; A is calculated as Total neutron production (5.17)
Total neutron absorption + neutron leakage from core boundary
)
5-4 The nodal average thermal flux distribution, I , is required for calculation of the ncdal pcwer density (Equation 7.1) and for the thermal spectrum index entering Equation 5.4 y _
21
'i - (5.18)
- as 21 where-a 0,s.
s1 is the averace asymptotic flux defined as E
r1 - (5.19)
- as21 E
11 a2 Two optional models are available for calculation of 6 in2 PRESTO-B :
Option 1.
The node average thermal flux is calculated by analogy with Equation 5.10 and assuming asymptotic conditions (Equation 5.19) in the node midpoint :
1-b as as 2 0 = b * ( .20) 2 2 21 6 2ij 6)
Under this option, the non-asy= ptotic thermal flux (Eq'ation 5.20) is only used in the calculation of the ncdal power, whereas the spectrum index F is assumed asymptotic -
F= 1 (5.21)
Option 2.
The node average thermal flux is found from the thermal group neutron balance equation intecrated over the ncdal volume
)
4 i 5-5 L2
-as
- 2 ,# 21 I a (5.22) 2 where L is the net leakage of thermal neutrons per unit volume. L 2 2 is calculated using the same finite difference approximation as for the fast gr:,up flux, optionally modified by a thermal group gradient correction factor, a 2
(5.23)
J 1
i .
i (5.24) vi 4
l 1
t 2
1 Under this option, the non-asymptotic thermal flux is recalculated i in eacn eigenvalue iteration and used to calculate the spectrum index i entering Equation 5.4 and to calculate the nodal power.
Option 1 usually gives sufficient accuracy in hot condition applications, I whereas calculations involving larger flux gradients, such as cold, i single rod out cases, require the method under Option 2.
J
' 2 For noncubical nodes, the constant R = h' / k is introduced as a multi-plier on all axial neighbor node terms in the nodal summations, as shown in Reference 1. k is the vertical mesh width. Equation 5.15 is then modified to :
l QV i'i
= IT 1
- +R[7 i 2j-&xial (5.25) 4j-planar t
\
ew d-**Go-e - ~~
avv- Fu-w= -<w * ' ' - 4 ---m- r-weer *e,a w etr'=-sT--rr -
5-6 The constants b and c are expressed in terms of a new constant, a (with a=b for cubical nodes) :
1 b=33 3a+ ( 1-a) (R+2 ) (5.26) 1-a 1 c= ( 5 ' 7 )
4 3a+ ( 1-a) (R+2)
Corresponding expressions are employed for the thermal group constant b f Equation 5.20.
2 Numerous comparisons with fine mesh diffusion theory results for typical BWR configurations have shown that a 0 is close to optimum for both hot, voided condition and cold condition cases. Correspond-ingly, b =0 (Option 1) or a = 0 (Option 2) is recommended for the 2 2 thermal flux model. Cold cases using thermal flux Option 2 may require a slightly negative value of a 2 (i.e. -0.5).
Examples of comparisons of PRESTO with reference diffusion theory solutions are provided in Section 11.1. These results are the primary basis for evaluation of the constants a and a 2' 5.2 Reflector Treatment Equation 5.15 is solved subject to precalculated boundary conditions on the core reflector interface. For nodes facing the reflector, Equation 5.8 is modified to 6;n p = ) - _ .
1 " VD +B (5.28)
--- j=1 vD j i i
5-7 A constant reflector diffusion coefficient is used for " reflector nodes" in Equation 5.14.
The boundery condition 3 may be expressed as :
B =
g (5.29) 1 where n = number of " missing neighbor" nodes A = effective extrapolation length into the reflector for the grour i flux, nodq 1.
Equation 5.28 accounts for fast' neutron leakage into the reflector.
Adequate reflector treatment also requires modeling of thermal neutron return from the reflector. In PRESTO, the net thermal neutrons impinging on the core from the reflector are assumed to be completely absorbed in the periphesf nodes. -The increased thermal flux in the boundary nodes is described by :
Erl+ 1 (5.30)
T2 " g
-91 a2 The " albedo" source term, S , may be written as :
0 n 1 (5.31)
S g gg *D
= g
- A,l where the albedo S is defined by :
J1 S = -- (5.32) i J2 Jt and J2 are the fast group and thermal group net currents at the core reflector interface.
1
5-8 The albedo source term is added to the removal cross-section in Equations 5.4 and 5.19 and Equations 5.20, 5.22 are replaced by 32
- 21 f r all nodes treated as boundary nodes.
The reflector parameters B and S g are determined from a reference, two-group, fine mesh diffusion theory solution for the flux distributions in a 2-D horizontal core cross-section (side reflector) and.from a 1-D solution.in the axial direction for the top and bottom reflectors.
Evaluation of (B ,S ) is performed by the subroutine ALBMO in PRESTO.
B g is determined by inserting the reference nodal fluxes into the nodal coupling equation and the solution for P ,B is then found from Equation 5.28. Equation 5.30 is solved for S , using the reference fast n
to thermal group flux ratio.
The found values of (B ,S } are applied in a 2-D (or 1-D) PRESTO calcu-lation using the same nodal cross-sections as in the fine mesh calcula-tion.
A set of nodal correction factors, PCORR g, modifying the original B -
values, is determined in an iterative way by requiring improved agree-ment in the overall power distribution (checking the power in the center of the core as well as on the periphery) .
The side reflector boundary conditions are strictly only applicable at the axial elevation where the finc mesh, 2-D calculation was performed.
Calculations performed at different axial elevations (bottom, mid and top of core) have shown that these parameters are slightly void-dependent.
The following linear correlation has been developed on the Lasis of such calculatiens to account for the variation in void content along the channel :
B =B +C- n (D - D1 (5.33)
B = bcundary condition, channel i axial node k (3-D1 B = corresponding boundary condition at reference elevation (2-D) 3
5-9 C = constant (normal value = -0.067) n = number of missing neighbor nodes, channel i 1
D fast group diffusion coefficient, channel 1, node k ik D = reference level average fast group diffusion coefficient The method for calculation of reflector boundary conditions is automated in PPESTO. Thus, the following procedure is followed (2-D calc.) :
- 1) Select option for Sigma-file generation -
run 3-D PRESTO case -
save Sigma-file for core midplane
- 2) Run fine-mesh code (MD-2 or PDQ-71 using cross-sections from Sigma-file
- 3) Select ALBMO option -
run PRESTO case to generate albedoes and perform checking and adjustment against fine mesh, 2-D power distribution a
f
6-1
- 6. THERMAL-HYDRAULICS MODEL The large variations in coolant density in a BWR have a significant effect on the calculation of reactivity and power distributions.
Also of.some importance, is the influence of the fuel temperature (Doppler effect) . Therefore, the thermal-hydraulic analysis may be considered of equal importance as the neutronics analysis in a BWR core simulator.
The average void content (or coolant density) in each volume associated with a neutronic node is needed to account for the void feedback. This void distribution is calculated, given the nodal power distribution, total core mass flow and core inlet subcooling. In PRESTO, the interior of each flow box (fuel channel) represents one flow path, and the flow leakage outside the boxes is represented by one single bypass flow path. The flow in each such channel is one-dimensional and is discretized axially into sections of the same size as the neutronic nodes; i.e. , each- fuel assembly is divided into 24 or 25 axial sections.
The flow distribution among the channels is dependent on the flow resistance in each individual channel, and is a function of geometry, channel power, axial power shape, coolant density, etc. Obviously, the coolant conditions are, in turn, dependent on the flow through the channel. The flow rate in each channel and the bypass flow are deter-mined frem the requirement of equsi pressure drop over all the parallel flow paths.
The void distribution in each channel is calculated frcm the mass and energy balance equations, together with correlations for steam slip, heat transfer and evaporation / condensation rate, which are valid for
, thermo-dynamic nonequilibrium conditions.
An average. fuel temperature in each node is required to account for the Doppler effect. PRESTO-B uses a linear correlation between nodal power and effective Doppler temperature.
v
6-2
}.1 System Heat Balance The reactor system, as described in PRESTO-B is illustrated in Fiqure 6.1.
The energy and mass balance equations may be written as :
-Energy flowing out Energy flowinc .
Energy added to the. ,
,into the system, _ fluid in the system, ,of the system ,
. Total mass flowing ,
Total mass flowing
_into the system ,
,out of the system _
Reactor vessel energy balance :
U w h +w h +Q th -Q +Qp -Q c1 = wS{hf (6.1) fw fw cr er rad + (1 - fcm) hfg}
Vessel mass balance :
w f,
+w =w g (6.2)
Downcomer energy balance :
+w h cr cr
+w DC f h +f wh cu T fg +Qp -Q cl =whT in (6.3)
Downcomer mass balance :
(6.4)
"fw + "cr * "DC * "T Reactor core energy balance -
wh h (6.5) 7 +QTH " Tf+ gT where -
)
6-3 SD g
\
d I j \
/ ~'/~~/ _$twoFLOW
- '# T $
G I ~~l~~
y s l~~ P $r cm rad
_; ;, g _h ^ -
__ __. i t
a CU W fy
,h f F MAIN FEED FLOW RECIRCULATION LOOP h/ 0
\/ JL a
P c
P f
m w
T JL n ad u Q
a l Cleanup Der.:ine ra li ze r System L
ll .
Al Rod Drive w er Feed Flow h r
?
FIGURE 6.1 Reactor System with Heat and Flow Components, as Modelled in PRESTO ,
}
6-4 Q = core thermal power Q ad = radiative heat loss Q = recirculation pump heat Q = cleanup demineralizer system heat removal hg,, = feedwater enthalpy h = control rod drive flow enthalpy SD h = heat of evaporation at steam dome pressure fa c heat of evaporation at core pressure h fq =
S h,D = saturated water enthalpy at steam dome pressure c = saturated water enthaley at core pressure h,
h = water enthalpy at the core inlet h = control rod drive flow enthalov ~~
cr w = total core mass flow T
w g,, = feedwater flow w = control rod drive flow cr wg = steam flow w = downcomer inlet mass flow f = steam carry-under fraction into downcomer cu f = liquid carry-over fraction into steam lines X = core exit steam quality The heat balance equations (6.1 - 6.5) are derived under the assumption of a constant pressure, PSD' ## #
comers a'nd another pressure, Pc, valid for the core recion. The S c S c thermodynamic properties (h ,D b , , h .D
. tq, h,a) are evaluated at the corres-pondinc pressures, usina a steam table function internal to PRESTO-B.
Equations 6.1 - 6.4 are combined to eliminate the variables wg,, wg, w # # ^ * *C '* * *" ^ Y DC ""
6-3 h = h +f hqD in f cu g SD SD (6.6)
(Q-Qrad) (hg -h ,,) - (Q -Q +w h c c w cr fw ~
I cm fg wT{hf + (1-f )h cm fc -h_}tw s
4 The core inlet enthalpy is used in the calculation of flow and ' old conditions in the core, as will be outlined in sections 6.2 and 6.3.
The main components coino into the heat balance equations are the core i
power (Q h), the total flow (w,r) and the.feedwater enthalpy (hg),
which all have to be provided as input data. Of second order importance are the parameters Q p , Ocl, wer ,her, f cm and f cu also l specified as input. The steam dome and core pressures may be ulven directly as input (in which case P =P # "Y * * #" ^* Y SD the code (cf. Section 17.5).
As an alternative to calculating the core inlet enthalpv from the feedwater.enthalpy, etc., the core inlet subcooline may be specified directly as input.
i a6. 2 Basic Models and Ecuations for Void Calculation The thermal-hydraulics model is specially designed to describe the coolant conditions in a BWR under power generating conditions. It was originally developed at the Institute for Energy Technology, Kjeller, Norway (Ref. 2 ) . The prime source of experimental data used for verification of the model is the FRIGG Loop Experiments (Refs. 4 and 5) on both 36-rod and 64-rod, full-scale geometries. The basic model has also been applied in the transient codes RAMONA and NORA (Refs.
6 and 7 ) .
Details on the model are given below :
4 6.2.1 Mass _ Balance i
The mass balance for section i is given by :
i
- 6-6 ,
a Steam : w -w +$ i =0 gi g1+1 (6.7)
. Water : w -w gg, -$ =0 ff with w = steam flow into section i-f l w = liquid flow into section i ff P
evaporation rate in section i (correlation for $ given below) 6.2.2 Energy Balange ,
The energy balance for section i is given by :
"gi *gi + "fi *fi ~ "gi+1 *gi+1 - "fi+1 *fi+1 *9 1 =0 (6.8) with 1
Q = heat flux rate into section i e f ,e = specific energy (index f for fluid and g for steam)
.The steam temperature is assumed constant and equal to the saturation temperature. The water temperature in section i is determined by i
fi o * 'fi vi (6.9) with T = a reference temperature C . = specific heat of water v1
. . _ . . _ , . . . , . . _ . . _ _ _ _ _ . . . . - _ _ _ ~ _ _ _ . , . . _ _ _ . _ _ . _ _ , , ._. . - . .
._ . . - , .-~ ._ - _ _ _ - . .
1 6-7 6.2.3 Momentum _ Balance The momentum equation can be written as i
~ -
- 3g
- Bu
+
BF 32 + jGi jGi +9 ( 1-G) Pr+G
- P g_
(6.10) acceleration, friction static acceleration
. restriction 4
with p = pressure 1
u = momentum flow l g = constant for gravitational acceleration a = void 4
p = water density g
0 = steam density F = friction z = elevation coordinate The momentum flow is given by u= (1-a)p v 2+ "O V g g (6.11) with-vg = water velocity v = steam velocity Integrating Equation (6.10) from z to z 2 Yi '1d3
- j j
6-8
- (p2 -P) 1
=
~
z ~
2 (u2- ul) +
(F2- F1) +
gog (z2- zt) -g(p-p)'[adz (6.12) z1 ,
re friction static head ct n The pressure drop over a restriction (i.e., spacer, channel inlet and outlet) is modelled by Ap ' = - K u (6.13) with K = loss coefficient The momentum equation is, in PRESTO-B, applied in the integrated form, Equation 6.12, combined with Equation (6.13).
6.2.4 Two-Phase, Flow Friction The pressure loss due to friction is calculated using a single-phase friction factor, based on Weisback's formula and a two-phase friction multiplier, described by the Becker correlation (Ref. 8 ) .
The friction loss is given by :
h=f R -
(6.14) with single-phase friction factor (Weisbach's formula) :
G1 2
2D Re i
6-9 and two-phase friction multiplier (Becker correlation) :
R =
K 1+A F
(E) p
- 0. 9 6 (6.16) where A = flow area o = liquid density f
w = total mass flow D = hydraulic diameter Re = Reynold's number X = steam quality p = pressure G1,G2,A = e P i rical constants given in Table 6.1 F
The calculation of Reynold's number, Re, is based on total nass flux G and liquid properties GD Vg D p g
Re = =
N N f f where pg = dynamic viscosity G = w/A 6.2.5 Eli E_Correlatign To account for differences in cross-section averaged steam and water velocities, a modified Bankoff slip correlation is applied.
The steam velocity is given by .
I
\
6-10 v =S v, + v g I o (6.17) where 1-a S=
B-a (6.18) with v =
steam velocity vg =
water velocity v =
bubble rise velocity a =
void fraction B is a flow dependent parameter given by the following empirical correlation .
(6.19) u At very high voids, the Bankoff slip correlatien is modified to better describe the flew under annular ficw conditions. Therefere above a certain cuteff void, a , Equation 5.18 is replaced by i
6-11 (6.20) u 4
(6.21) 6.2.6 Boiling,Model The boiling model describes evaporation at the heated cladding surface as well as bulk flashing / condensation. The surface term is based on a mechanistic approach, describing the formation of void bubbles and the " pumping" effect from the bubbles leaving the wall. This describes the process, when first the formation of a steam bubble pushes hot wate out from the hot boundary layer into the colder bulk fluid, and then, how the steam bubble detaches from the wall and the occupied volume is refilled with colder water. For details, see Ref. 2.
Steam Generation on the Heated Surface :
B
$sF " p p C (6.22) h fg+CP(T -T g fp )1 + (TCA-T g p) (d - 1)2 l 9 9 Flashing / Condensation in Bulk Fluid :
$B =ft (a) * (Tf -T g ) +<-lT-Tl f g f 1(a) = Ro + R a (IMt) i (6.23)
6-12 where Tg = water temperature T = steam temperature 9
Tg = cladding surface temperature hg = heat of evaporation C = spec. heat capacity of water p
p = density of water g
p = density of steam
=
QB heat flux to the coolant (under boiling conditions)
Ro Rt > = correlation coefficients given in Table 6.1
/
a = void fraction The surface evaporation term (6.22) applies only under heated surface boiling conditions. If no boiling occurs on the surface, it is set equal to zero, $
- SF The two evaporation terms are additive to give the total evaporation rate
$=$ 37
+
B (6.24) 6.2.7 Heat Transfer from Fuel to Coolant The heat transfer from the cladding surface to the coolant is des-cribed by Jens-Lotte's Correlation for boiling heat transfer and by the Colburn Correlation for nonboiling heat transfer.
Boiling Heat Transfer :
QB " ^S CA - S) (6.25)
6-13 with
-7 K
B
= 1.266 e +1. 61 10 p Non-Boiling Heat Transfer :
QNB AS'K NB CA - f) (6.26) with lp y, l0.8 C'*" A'*6 K
- NB
- D n c f and A = heated surface area g
T = cladding surface temperature T. = water temperature I
Tg = saturation temperature of coolant p = pressure v = core inlet water velocity C = specific heat capacity of water A = thermal conductivity. of water O = viscosity of water f
D = hydraulic diameter Under steady-state conditicns, the heat flux, Q, from the cladding surface to the coolant is given directly by the power producticn in the fuel. By setting Q " E "U E ' #" Y 9 B NB (6.25) and (6.26), respectively, two different values on the cladding temperature, T , can be evaluated. The minimum value,
)
6-14 T = Min T .is)
T **"'
(6.28) will be utilized.
Or, expressed dif ferently, of the two heat transfer correlations,_
Equation (6.25) and Equation (6.26), the one giving the maximum heat flux will always be selected and used for calculating the surface temperature.
6.2.8 Heat, Source, Distribution The energy produced in the fission process is mainly conducted as heat through the fuel into the . coolant. However, a small part is deposited directly in the coolant by means of neutron slowing down and gamma heati Qcond
- Efiss " ' ll (6.29)
Q E fiss
- 2) in-chn with O fiss =
power produced by fission
=
Qcond p wer conducted through the cladding into the -
coolant Q in-chn- =
total power absorbed in the in-channel coolant 61 ,62 =
constants given in Table 6.1 The total power absorbed in the bypass channel is given by bypass 9 fiss -
2 i
6-13 Optionally, the bypass heat generation rate in the interchannel volumes, may be assioned different values depending on whether or not a control rod is inserted.
6.2.9 Fuel, Temperature,Model The temperature distribution in a fuel pin is primarily a function of power density and gap conductance. The latter varies strongly with irradiation due to pellet expansion, cracking and fission gas release.
The dominating effect, especially for unpressurized BWR fuel, is the decrease in gap conductance due to the fission gas release into the gap. The buildup of crud en the clad surface may significantly affect the heat transfer properties and thus the fuel temperature.
These burnup effects of the fuel are typically very difficult to pre-dict since they cannot be correlated solely to the accumulated irradia-tion but are also very much dependent on the operating history of the fuel.
Due to resonance self-shielding effects, the volumetric average fuel temperature can not be used directly as the parameter describing the Doppler effect. Instead, an effective Doppler temperature, averaged ove r the fuel pin with a higher weight on the outer regions of the pin, has to be utilized.
Fortunately, dhe Doppler effect is of relatively small importance in static BWR analyses, and the temperature calculation can be considerably simplified. Roughly estimated, the Doppler reactivity effect is of one order of magnitude less than the void reactivity effect for a given power perturbation at operating BWR conditions. The influence en the power distribution is also cuch less from the Doppler effect tian that from the void effects.
PRESTO-3 correlates the effective Doppler temperature to the power density. Burnup-dependent terms are included to ?.ccount for, mainly, the variation of gap conductance with expcsure
6-16 T g =T +C DOP ' ~ Ref
- T =d +dE+dE 2 3 C !
DOP " ~ 5 Ref with Tg =
actual Doppler temperature o
Tg =
Doppler temperature at rated power dens. tty P = actual power density P = rated power density Ref E = fuel exposure dl,d2 ,d3 ' 5 = input Parameters The parameters d , d2 , d3 *" 5
^"*
- d* *#* "* # " *E*" *"
fuel temperature calculations, and are specified individually for each fuel type. A rule of thumb for estimating the effective Doppler temprature is to reduce the volumetric average fuel temperature by 10 - 15% at rated power conditions.
6.3 Calculational Procedure The calculation of the coolant conditions in all the parallel channels can be visualized as a two-step procedure
- 1) calculation of flow distribution
- 2) calculation of axial void distribution However, the first step, the ficw calculation, is dependent on the results of the second step, the void distributien in the channel.
Numerically, the ccmplete probles can be sclved by, e.g., iteration between the two steps.
)
6-17 The calculational method applied in PRESTO-B is based on the following observation :
The pressure drop over a channel, which will determine the flow, is not so much dependent on the detailed void distri-bution in the channel, but can be calculated with relatively good accuracy, knowing the elevation of the bulk boiling boundary and the total steam production in the channel.
To reduce the computing time, PRESTO-B uses a special procedure with a simplified void model for the calculation of the flow distribution.
Once the flow is determined, however, the void distribution in the channel is calculated with the detailed void model.
6.3.1 Calculation _gf_ Flow Distribgtiog For a specified total core flow rate, each individual channel flow is determined by equalizing the pressure drops across all flow paths.
The channel flow, or equivalently, the channel inlet velocity, v ,
is related to the pressure drop by the following relationship AP = A v 2 +Bv +C (6.31) which is solved iteratively for all channels.
The constants A, B and C can be evaluated by integrating the momentum balance equation (Eq. 6.12) over the height of the channel, and com-bining it with the expressions for friction (Eq. 6.14) , acceleration and restriction losses (Eq. 6.13).
(6.32) v
6-18 with K ,K = Restriction loss coef ficients at channel inlet and outlet, respectively u ,u = Momentum flow at channel inlet and outlet, respectively F -F = Friction forces integrated over the channel g = gravity acceleration constant pf,p =
, density for water and steam, respectively 1 = channel height a = void fraction This formulation assumes restriction losses at the inlet and the outlet of the channel only, which then should also include the effect of the spacers.
Equation (6.32) will require information on steam quality, slip and void locally throughout the channel. For these parameters, the following approximations are made :
n the slip has a constant value, S.
n the steam quality varies linearly between zero at the bulk boiling boundary and X, 1 at the core exit. The bulk boiling boundary, as well as the exit quality are calculated assuming thermo-dynamic equilibrium :
(6.33) u (6.34)
) ,
6-19 (6.35)
Ln The void distribution is now given by X(z) a(z) =
(6.3E) p - 0 X (z) + ji-X (z) .S d L _
Pg Introducing Equations (6.35) and (6.36), together with the expression for the momentum flow, Equation (6.11), and the friction correlation, Equation (6.14) into Equation (6.32) will yield
6-20 (6.37) u The exponent, , within the integral is now approxitated by 1 and the expression within the bracket (containing the logarithm) is approximated by a second order Taylor expansion around a civen point o
in*
Equation (6.37) then takes the quadratic form associated with Equation (6. 31 ) and the inlet velocity can be calculated, given the pressure drop. In the iteration process, several channels are first lu= ped together into larger groups. After a few iterations, the problem is solved for individual channels until the pressure drop over all channels is equalized.
6.3.;
Calculation of Void Distribu_
--- tion The detailed void calculation starts af ter the ficw calculation, des-cribed in $6.3.1 above, is finished. There is no return path frem the void calculation to the flow calculation.
6-21 The mass and energy balance equations (Eqs. 6.7 and 6.8), are applied to each sectin" 'n the channel, and are combined with the boiling model (Eqs. 6.22 and d.23); the slip model (Eq. 6.17) and the heat transfer models (Eqs. 6.25 and 6.26). All material.thermo-dynamic properties are assumed constant in the reactor core and corresponding to the specified system pressure.
The inlet mass flow and temperatures for both steam and water are known from the solution in the previous section. The set of equations may then be condensed to
$ = f(T ,a) g Tg = g($)
a =
h($)
or alternatively,
$ = f [h ($) , h(Q)] = F ($) (6.33)
Equation (6.29) is solved by an iteration procedure.
The results of the calculations are the flows, temperatures and void fractions on the volume interfaces. The mean void fraction in section 1, given by a = i+1 1} (6.39) where -
a = void fraction on the inlet to section i is being used as the feedback parameter to the neutronics solution.
1
6-22 6.3.3 Treatg.ent of_ Void _in,the_Bvoass_ Channel In the flow and void calculations outlined above, the bypass flow is modelled as one flow channel, represecting all flow paths not encountering any heat conduction from the-fuel pins. The nuclear cross-sections are normally generated with no void in the inter-channel flow area or in the internal water holes, se any veld appearing in the bypass flow channel will therefore have no nuclear feedback.
As an option, PRESTO-B may calculate the bypass void fraction individually for each fuel assembly, and by adding this void volume to the in-channel void for that bundle, account for the nuclear feedback from the bypass void. These calculations include the following simplifications :
- the single ( lumped ) bypass channel flow is distributed between the fuel channels, accounting for interchannel area differences and the presence of control rods
- the heat generation rate is affected by inserted control rods
- the axial void distribution is calculated in the individual bypass flow volumes assuming a homogeneous equilibrium model with constant flow
- the calculated bypass void is spread out over the corres-ponding in-channel flow area to yield an effective in-channel moderator density.
f
6-23 TABLE 6.1 Thermal Hydraulic Model Parameters
^ ' '
PARAMETER ACRONYM NO. VALUE Two-Phase Friction Coefficient A (6.16) 2400.
F
- ' O.22 Fanning Friction Factor G2 (6.15) 0.2 Slip Coefficients B1 (6.19)
B2 (6.19) vt (6.19) v2 (6.19) v (6.17)
C 6D (6.21)
Boiling Model Coefficients Re (6.23) 'u R1 (6.23)
K (6.23)
Direct Heat Fractions S1 (6.29) 02 (6.29)
I
7-1
- 7. POWER DISTRIBUTION AND FUEL DEPLETION CALCULATION 7.1 Nodal Power Distribution The relative nodal power is calculated on the basis of the nodal two-group flux distributions :
P'" = C(I It + I f2
- I2) (7.1) f where C is a normalization constant such that :
NMAX
[P" (NMAX V
" [V n=1 "
= 1.0 (7.2) n=1 where NMAX = number of nodes V = nodal volume n
The nodal average linear heat generation rate (APLHGR) is calculated in W/cm as follows :
COND ,p rel (7.3)
APLHGR = N N (I) D where Qg =- full core thermal power '(w)
Q COND = ac n p wer c n u e ough cla M ng N O N = total number of nodes in a full core N (I) = number of fuel pins - depends on fuel type (I)
D = nodal height (cm)
7-2 The nodal maximum linear heat generation (MLHGR) rate is calculated as :
MLHGR = APLHGR
- P (7.4)'
P is the relative pin-power peaking factor in the node :
P 1 =P7(E,a ,a) 1 + C(I) .
- C f
(7.5) with P7(E,c ,a) = peaking factor, Fuel Type I (obtained from RECORD) ,
represented as polynomial fit in fuel exposure (E) ,
exposure-weighted void (a 1 and void (a) in the same way as the basic cross-sections (see Eq. 4.1) .
C(I) = factor accounting.for modification of peaking factor for. rodded nodes, Fuel Type I C = effective nodal control fraction f
The following fortala is used to account for 3-D effects near the tip of a control rod :
C = 1.0 if X t 1.0 f
C = X if 0<X<1 f
Cg = 0 if Xs0 with X= (T - k + 11/2 (7.6)
P where T is the control rod insertien depth (nedesi P
k is the axial node index (starting from K=1 for the bottom node)
7-3 7.2 Stepwise Burnup Calculation After calculation of the steady-state power distribution, the calcula-tion may optionally continue with a so-called burnup step calculation.
A new steady-state calculation may, again optionally, take place upon completion of the burnup step calculation. In this way, core-follow or predictive analysis may be performed through the operating cycle.
The following are involved in a burnup step calculation :
The nodal fuel exposure and exposure-weighted void distributions are integrated through the step.
The fuel type dependent average Sm-149 and Pm-149 concentrations are integrated through the step.
The nodal concentration of one (Ba-140) or two fission product isotopes (used for y-scanning) is integrated through the step.
The nodal exposure distribution E" at the end of Burnup Step n is calcu-lated as :
U~
E =E + SE *E O (7.7) where AE" = Length of Burnup Step n (MWD /TU)
O = Nodal, homogenized Uranium density (q/cm ) provided as input data for each fuel type (for fresh fuel) o = Core average nodal hemogenized Uranium density (g/cm )
E = Nodal' relative power averaged over time through Step n Normally, E is taken as the bocinning of step relative power distribution; however, optionally the following formula may be used -
E=P
- R C
+P (1-RC) (7.9) where R is an input constant (i.e., 0.5).
4 i
7-4 Since P" depends on E", an iterative solution is employed.
The exposure-weighted void distributicn is calculated as follows :
V" a =
(7.9) with V"
X
= Vx ~ + a" AE '(7.10) 7.3 Cycle Eurnup (Haling) Calculation Let F of Equation 7.7 represent the average power distribution over an operating cycle, AE the cycle length in MWD /TU, and E"' the beginning of cycle exposure distribution. The end-of-cycle power distribution, P ,
will then be a function of the end-of-cycle exposure distribution, E ,
and the end-of-cycle operating conditicn. The following relationship is assumed :
U P=F g *P (7.11) whe re Fg is a fuel type (il dependent correction factor (normally : F = 1.0 for all il Starting from a guess for P (=P 1, a first estimate of En is calculated from Equation 7.7. With this exposure distribution, a new P distribu-i tion may be calculated. The iteration is continued until certain con-vergence criteria on E" are satisfied. The resulting exposure distri-i bution, E , represents the end-of-cycle state which would be obtained with a cycle average power distribution F related to the end-of-cycle distribution P" through Equation 7.11. The correction factor F may be used to account for known power sharing characteristics among different fuel types.
7-5 The cycle length AE may either be input or calculated by the code from a given end-of-cycle k,gf-value :
0 " ~ * '
eff,j where Sk -1 3k -1 = given (input) coefficient =
BE j = iteration index Haling calculations taay be performed for one, two or three-dimensional problems.
7.4 Integration of Sm-149 and Ba-140 concentrations Certain fission product isotopes are tracked as functions of time in a simulated reactor operation. The fuel type average concentrations Pm-149 and Sm-149 are followed to account for the influence of nonequilibrium Sm-149 on the calculated k,ff (the influence on the power distribution is negligible) . Equations are given in Appendix A2.
The nodal concentrations of Ba-140 and of one additional isotope (User specified) are treated to enable direct comparisons with distributions measured by y-scanning of exposed fuel.
Each fission product concentration is integrated through one or more time steps per burnup step. Each time step is characterized by its length in days and by the reactor total power. .
The equations for integration of the Y-scan isotopes are given in Appendix A3.
8-1
- 8. PREDICTION OF CORE PERFORMANCE PARAMETERS 8.1 Model for TIP and LPRM Calculation Fixed, in-core, local power monitors (LPRMsl and travelling, in-core probes (TIPS) may be included in th'e PRESTO core simulation. The instru-ment tubes (TIP strings) are assumed to be located in the watergaps between-the fuel assemblies, each stiing being surrounded by [$ar assemb-
]' " lies. The string locations are 'spe'cified by giving the channel numbers for each of these four assemblies.' TIP strings located outside the q ;
modeled core fraction -(if not full core model) may be included by, folding into symmetric positions within the modeled fraction. Four LPRMs are assened to be 1ocated at different axial elevations (Levels . A, B, 'C and D) within each string. The axial height (cml of each detector level is specified as' input. The calculated TIP or LPRM signal, at a given axial height, is a function of the local conditions in each of the four assemb-lies surrounding the string :
4 T (8.1) k" gg "k,i
- P'x,1 -
where Ty = calculated signal, axial node k mk,i = instrument factor, axial node k, assy. no. 1 P = relative nodal power, axial node k, assy. no, i o
The instrument factor (m-factort is obtained by interpolation in data given as input for various values of fuel exposure and exposure-weighted void. The m-factors are also given for both control-rod-in and control-rod-out conditions.
The m-factor is defined as the signal generated per unit nodal power.
Such m-factors are calculated in RECORD. The normalization of the m-factors is irrelevant; however, it is recommended to use values around unity.
i
8-2 The calculated TIP signal is obtained from Equation 8.1 with k = 1, 2, .... KMAX. The calculated LPRM signal at a given axial level is obtained by interpolation between the two nearest (axially) axial nodes
< q -
of the TIP calculation.
s Measured TIP data may be provided as input for comparison between calcu-s lation and measurement. y..
- x O.
The total area under all measured curves is calculated and compared to 'i v
the total area under the corresponding calculated curves. The measured TIP values are then normalized, using the ratio of calculated-to-measured total area as a normalization factor. Thus, the ratio of calculated-to-measured area for each curve (after normalizationi serves as a comparison between the calculated and measured radial power distribution.
x.
M^
The difference between calculation and measurement in each of the KMAX points for each string is used to calculate the statistical standard i deviation (RMS). Standard deviations are also calculated for each string; <-
for each of four axial core regions (KMAX divided into four equal regionJ),
and for " rodded" and "unrodded" regions, separately. J The calculated LPRMs are normalized to an average value of 100
- CALPRM, where CALPRM is a User-specified (input) calibration constant. LPRMs are printed out in a special map format, similar to the usual BWR process computer format. The LPRM map format may be specified as a full-core map, even if only a core fractional (e.g. ,1/4-core) model is used. TIP strings located outside the modeled fraction will then be shown in their real positions. .
s Results of TIP calculations and comparisons between calculated and measured TIPS may be plotted as lineprinter plots by PRESTO, or plotted externally by the TIPPLOT Program.
Measured LPRM readings may be provided as input data. Whenever such data is input, the ratio of measured-to-calculated signal of each detector is calculated and stored for use in subsequent runs.
..y
8-3
- % f Predicted LPRM readings at time points where no measured readings are given are defined as :
ESTPRM (I,K) = COFPRM(I,K) PLPRM (I, K) (8.2)
. where ESTPRM (I, K) = predicted LPRM reading, String I, Level K
' ; 13 -
PLPRM(I,X). = calculated LPRM signal, String I, Level K
~~
COFPRM (I ,K) = ratio of measured-to-calculated signal,
.- String I, Level K, from last time point with measured data These predictions represent best-estimate predictions of expected LPRM readings and are reco::. mended for use in reactor operations support l applications.
i 54 l" . 8 0.2 '
< calculation of Marcins to Thermal Limits - BWR s ,
l-\ ; 8.2.1 C_ r_i_t_ic_a_ _l_H_ea_ _t_. F_ lu_x__R_a_ _t_io_ __(C_H_F_R__)
g- ,
f;T J L
[ .The critical heat flux. which is the value of the heat flux at the onset of nucleate. boiling, is calculated for each node by applying the Hench-
\. -
Levy Correlation (Ref. 9). The flow quality and the mass flow rate, as N-calculated in the thermal-hydraulics module, are input to the correla-t ,
g., , tien t vations.
+ 5, .
Subsequently, the critical heat flux ratio is found as the ratio between
, the critical heat flux (Q ) and the maximum actual cladding heat flux 5
p ., ,
t (Qm ) within each node :
s 1
"CHFR = Qc /Q (8.3) 1
$a .
with w -
4: ,. ._ .. i w- , ~ _ _-__
8-4
=
OTa' I
- P rel P
Qm Ag pin (8.4) where
=
Q Total core thermal power (w) 61 =
Fraction of power appearing as heat transferred through cladding A = a ea e surface area (cm )
S, TOT P =
Nodal relative power (see Eq. 7.1)
P =
Pin-power peaking factor within node (see Eq. 7.5) pin s.2.2 gragtign gf tigigigg_gewgg_ggnsigg_1ggggt
=
A linear power density, considered as limiting with respect to vital fuel performance parameters, such as clad integrity, may be given as input to PRESTO. Different values may be given for each fuel type.
The ratio between the actual maximum linear heat generation rate (MLHGR) , as calculated by Equation 7.4, and the corresponding limiting value (HGRLIM) is calculated for each node :
MLHGR FLPD = HGRLIM (8.5) s.2.3 ECCS_:_gug1_Hgg3_syg53gg_pigig Fuel type and exposure-dependent values of average linear heat gener-ation rates (EXPECC), considered as limiting with respect to the LOCA behaviour, may be given as input to PRESTO.
The ratio between the actual average linear heat rate (APLHGR) and the limiting value is calculated for each node -
8-5
. ECCSR = APLHGR EXPECC
.(8.6) 1
} APLHGR.is calculated by Equation 7.3.
4 8.2.4 Thermal, Limits Summa g ,TQle 1
The 12 most limiting positions in the core with' respect to maximum linear heat generation rate and the three limiting ratios described f
above, are compiled and edited in a special output table for User
. conveaience.
i e
t, i
j.
j t
i 1
l I
9-1
- 9. XENON DYNAMICS MODEL Reactor operations involving slow transients, such as reactor startups, power cycling and control rod pattern exchange maneuvers, may be simu-lated with PRESTO-B, using the Xenon transient, multi-time-step mode of calculation. Under conditions involving transients in local or global power, the local Xe concentration will be out of balance with its pre-decessor I-135.
Since Xe has a strong influence on the local neutronics properties as described in 4.2.2, both reactivity and power distribution will be influenced under transient Xe conditions.
The time-dependent nodal Xe concentratica ir calculated in PRESTO.
starting from a state of equilibrium or from Xa-free conditions.
Analytic solutions of the differential equation for the time-dependant I and Xe nodal concentration equations are used to find the concentrations at time t + At, starting from the concentrations at time t. The assump-tion of constant local power and neutronic properties during the time step at is assumed. The equations, as programmed in PRESTO-B, are given in Appendix A1.
The reactor o,erating period to be simulated is described by the User by specifying the reactor operating data (power, flow, subcooling and rod pattern) , characterizing the reactor state for a number of time points through the period. A 3-D converged power-void calculation is obtained at each time point. The interval between two successive time points is subdivided into a User-specified number of substeps for the purpose of Xe-integration.
The relative power distribution as calculated at time point i is used for the interval i to i + 1; however, the total reactor power and, thereby, the absolute nodal power values are adjusted at each substep, as illustrated in Figure 9.1.
9-2 Criticality search options on reactor power level or coolant flow rate may be exercised in the Xe-dynamics mode of calculation. The calcula-tion at each time point will then include an outer iteration to deter-mine the power level (or flow rate) required to maintain a given, critical k gg value. The iteration is terminated by a convergence criterion, which is a factor of 2 larger than the k gg -criterion applied within the power-void loop.
Also included under the Xe-transient option is a calculation of the maxi-mum rate of change of, nodal power density with time (maximum power ramp rate) , and recording of the core location whero the maximum ramp rate occurs. The search for the maximum ramp rate is limited to nodes where the power exceeds a User-specified limit. This feature allows User to compare simulated ramp rates with limits recommended for fuel integrity protection.
9-3
.P0hER n
g TDEPOINT i + 1 1 ACTUAL POWER l
--_--_-----J Power Assumed for Xe-Integration ISUBX(i)=1 c TDE l
i t P0hER j.
2+1
' r 7- -- - 3 ' ACTUAL FOiER n
_JN s Power Assumed for Xe-Integration i ISUBX(i)=2 l*
l 1
l; i
I I I j At/2 j at j At/2 j FIGURE 9.1 Illustration of Substeps Used for Xe-Integration Between Each Statepoint Calculation (i) 9
10-1
- 10. AUXILIARY FUNCTIONS INCORPORATED IN PRESTO-B A number of auxiliary functions are built into PRESTO-B to aid the User in performing specific analytical tasks. The underlying methods are not described in this report.
10.1 Critical control Rod Pattern Search Option A search option is available, where the insertion of certain User-defined control rods is determined in an iterative way, to obtain a feasible rod pattern with otherwise given reactor operating data. The rod pattern is considered feasible when the calculated k,gg is close to a given target value. The method normally produces acceptable power distribu-tions, however, the User may oerform a manual correction to further improve the soluticn. The critical rod search algorithm in PRESTO-B is based on and similcr to that described in Reference 10.
10.2 Shutdown Margin Evaluation Performing a cold condition analysis with all control rods fully inserted, the User may select an option that performs a " stuck rod priority selection". The control rods are sorted according to expected rod worth, using a simplified perturbation theory methed or a method based on flux-weighted, average k ,-values for the four bundles adjacent to each control rod. The code may also be set to pull single control rods according to the priority list, and perform a series of criticality calculations to determine the single stuck rod chutdown margin.
J0.3 Core Reload Analysis Features All fuel assemblies involved in the PRESTO-B Model are kept on a separate data file and updated as to the fuel history parameters in each PRESTO-B calculation. Fuel assemblies from the file may be
" loaded" in any core location, enabling easy simulation of fuel shuffling and reinsertion. Fresh fuel, which may be added, will automatically be included on the fuel file. Fuel that has been
10-2 discharged from the. core will remain on the file until it is deliberately deleted by the User. A number of User aids, in-the form of special checking and editing routines, are available in PRESTO-B to facilitate reload simulation.
j 10.4 Fuel Discharge Priority List An option is provided for guiding the User in selecting fuel assemblies 1
to be discharged at the end of an operating period. All fuel in the core is sorted according to certain criteria (a combination of reacti-I vity and burnup) and a discharge priority table is printed in the '
a output.
s 4
- ) '10.5 Functional Relationships between Heat Balance Cc=ponents The User normally provides the process data entering the heat
! balance calculations outlined in Section 6.1.
3 However, as an option, plant specific functional relationships may be specified in order to facilitate predictive calculations or perturbation studies where process data are not available.
The following system functions are defined :
Steam dome pressure vs. steam flow :
, "S "S s P SD
=P syst +Ci( rat 2 rat - 1) 2
- 1) +C( (10.1)
"S "S Core pressure vs. core exit flow conditions :
2 P =P +C *0 +C *-T (10.2) i; C SD. 3 x 4 0-X
10-3 Pump heat vs. total core flow :
2 3 Qp *w +C *w +C *w (10.3)
=C5+C6 T 7 T 8 T Bypass flow fraction vs. total core flow :
"T "T f
B
=C 9
+C 10
(
rat
- 1) +C 11
(
rat
- 1)2 (10.4)
T T Feedvater enthalpy vs. stean. lond :
w A
h =f * (10.5) fw ( rat)
S where P " * *# " E'* * '
SD P = c re pressure C
P = " system" pressure syst w = steam flow g
rat w = rated steam flow g
0 = density at core exit w = total core mass flow T
Qp = pump heat w ypass flow B
hg = feedwater enthalpy C ...C = input constants 1
TABLE f = input data ta,le c
11-1
- 11. CODE QUALIFICATION 11.1 Fine Mesh Diffusion Theory Benchmarks A benchmark problem for 3-D neutronics code evaluation, originally developed by the Danish Atomic Energy Commission, is descrfbed in Refer-ence 3. Specifications for this problem, also referred to as the IAEA 3-D Benchmark, are provided in Figure 11.1. Several fine mesh solutions have been published in Reference 3. At the moment, the most accurate solutien is considered to be tne so-called " VENTURE-extrapolated". This was produced by extrapolating to an infinite number of mesh points, baserf on solutions with increasingly finer mesh :
1 - 17 x 17 x 19 mesh 2 - 34 x 34 x 38 mesh 3 - 68 x 68 x 76 mesh 4 - 102 x 102 x 114 mesh 5 - Extrapolated The VENTURE-extrapolated solution is taken as the reference in this report.
Solutions for the corresponding 2-D problem (core midplane of the 3-D problem) have also been produced with many different codes. The current reference is an ultra-fine mesh PDQ solution, also published in Reference 3.
PRESTO results for the 2-D and the 3-D problems are given below. Option 1 for the thermal flux calculation was used. (See Section 5.1.)
An overview of the calculations performed is given in Table 11.1. Mesh widths of 20 cm and 10 cm were used and the 3-D problem was run with both cubical and strongly noncubical nodes.
Results are given in the following Figures :
- . - . . - . - - . - .~ . _
11-2 Figure 11.2 2-D Bundle Power, 20 x 20 cm nodes t
Figure 11.3 .2-D Bundle Power, 10 x 10 cm nodes Figure 11.4 .3-D-Bundle Power, 20 x 20 x 20 cm nodes Figure 11.5 .3-D Bundle Power, 10 x 10 x 20.cm nodes j
' Figure 11.6 ' Axial' Power, Partly Rodded Bundle, 20 x 20 x 20 cm nodes l
Figure 11.7. Power Along X-Axis, Core Midplane, 20 x 20 x 20 cm nodes A series of 2-D benchmark results of four-bundle power sharing and j eigenvalues were generated for six different, typical BWR configu-
) rations as shown in Figure 11-8.
f l rwo bundle enrichments and three void fractions were employed. A control blade was inserted adjacent to one of the four bundles in three cases.
The refererce data were generated by RECORD /MD-2 5-group diffusion -
theory solutions, with zero current boundary conditions, and with exactly the sace, detailed geometrical representation of fuel pin cells, watergaps and control rods as in RECORD.
PRESTO results were generated using both Option 1 and Option 2 for the thermal flux representation. (See Section 5.1.)
Results are given in Figure 11.8. The following statistical data.
were obtained :
"" *# * * " ~
Model Eigenvalue Nodal Power Option 1 1 1.6% +.000401.00114 Option 2 1 1.2% .000301.00066 i
Excellent agreement in both nodal power and eigenvalue was obtained with Option 2 (more detailed thermal flux model) ; however, the results for Option 1 are fully acceptable.
These results are the primary basis for evaluation of the gradient p- correction factors of the PRESTO neutronics model.
11-3 11.2- Qualification of Hydraulics Model The FRIGG void loop experime'ntal data (Ref. 4) were analyzed with the thermal-hydraulics model of PRESTO. The measurements were performed on a full-scale coolant loop with an electrically heated fuel assembly mockup. The operating conditions of the experiment are listed in Table 11.2. The range of the parameters characterizing
'the operating conditions are given in Table 11.3. The PRESTO-hydraulics model parameters used are listed in Table 11.4. Results showing calculated and measured axial void profiles for 31 differenf experimental conditions are shown in Figures 11.9 - 11.39. The overall standard deviation, RMS, of the difference between calculated and measured void, in per cent veid, was 2.11, This quantity was defined a.2 :
f N l '
RMS -
nr[ (x1 - i) 2 c11,1) 1"1 ..
with X =a -a (g) calc meas N = Number of points The number of points N was 243, and the total mean deviation X was 'O.58%
void.
The experimental standard deviation determined from calibration measure-ments with a plexiglass mockup was 2.0% in void.
The overall correlation between calculated and measured void is illus-trated in Figure 11.40.
11.3 Comparison with Gamma Scan Data for EOC-1 of HATCH-1 An analysis of the HA'ICH-1 EOC-1 gamma scan data was performed by Scandpower as part of a general benchmarking effort of PRESTO-B, using i
11-4 RECORD lattice physics data. The work was funded by members of the European FMS User Group, the Institute for Energy Technology, Norway, and Scandpower A/S, Norway.
The HATCH gamma scan data represents a valuable data base for evaluation of the ability of a code system like RECORD / PRESTO to predict complicated BWR power shapes. In particular, detailed measurements of the influence of partially inserted control rods on the power distribution in adjacent fuel were carried out. Thus, predictions of the important power shaping aspect of BWR control rods may be evaluated.
Since the measurement covered a complete core octant, relative bundle power comparisons may also be carried out. Comparisons of rodded versus unrodded bundles and core periphery versus core interior bundiss are also of special interest.
Design and operating data for Cycle 1 of EA?"_H-1 are given in EPRI Report NP-562 (Ref. 11).
The results of the measurements, as well as the gamma scan technique and the data acquisitien system, are described in EPRI Report NP-511 (Ref. 12).
11.3.1 The_ Gamma _ Scan, Measurements Gamma scan measurements of 106 bundles of the initial HATCH-1 BWR core were performed by General Electric at EOC-1, in a program jointly sponsored by EPRI and G.E.
The 106 gamma scanned bundles are shown in Figure 11.41. Seventy-five of these comprise a complete octant of the core. The additional 31 bundles are located in four-bundle cells, around real or psuedo instru-ment locations symmetric to those in the octant. These cells were chosen to evaluate any real asymmetry in the core.
All 106 bundles were measured at a minimum of 12 axial positions, as shown in Table 11.5, which correspond to the midpoints of the odd
11-5 numbered PRESTO-B nodes. Partially controlled bundles were measured at additional positions in the vicinity of the control blade tip.
Six bundles were measured at 24 or 27 axial elevations to obtain a detailed profile of the axial La-140 shape. Four of these, located at positions 14-08/14-09/15-08/15-09, Figure 11.41, were disassembled for single-rod scanning, to obtain local power distribution measurements.
The uncertainty in the measurements was determined from repeated measure-ments of the standard bundle. The total uncertainty in nodal La-140 concentration, quoted in Reference 12, is 1.7%. This value includes the uncertainty associated with representing the activity of a node by the average of the fcut corner count rates, as well as single measurement reprcducibility.
11.3.2 Simulation of the Cycie-1_Operatien Reactor operation through the first cycle was simulated eith PRESTO-2, with the objective of predicting the EOC La-140 distribution for co= pari-son with the corresponding measured distribution.
The calculation was carried out using 33 burnup steps, as shown in Table 11.6. Operating data, characterizing each step, were obtained from EPRI Report NP-562 (Ref. 11).
All core dimensiona'l data and core-specific thermal hydraulic parameters required for the PRESTO-B core model were obtained from the mentioned EPRI report.
A complete nuclear cross-secticn data bank was generated with RECORD, based on the published fuel design data.
The data bank consisted of the following :
Two-group macroscopic cross-secticns, diffusion coefficients pin-power peaking factors as functions of burnup, exposure-weighted void and instantaneous void (see Section 4.1) .
11-6 A perturbed cross-section set, assuming 15% void in the water
~
gaps at 70% in-channel void.- (No water gap voidage at 0% and '
40% in-channel void.)
Coefficients _ for the influence of: control rods, Xenon, Doppler, and Samarium models in PRESTO-B account for~ differential effects relative to the corresponding equilibrium values. The control rod and spacer grid effects are included as additive terms to ,
the thermal group-absorption cross-section The perturbed data set was used to account for a slight water gap voidage caused by plugging of the bypass flow holes in the core support plate.
This data set was used af ter the cere-average burnup had reached 4000 MWD /TU, approximately correspending to the time when the hipars plugging was performed. The reactivity effect of the assumed water gap void fraction (15%) was 0.8% in Ak at 70% in-channei veid.
i A 1/4-core symmetric core model was set up te generate the reflector boundary conditions at EOC-1. First, an approximate EOC ccndition was i
obtained by running through the 33 burnup steps with a 1/4-core model, Then, the ALBMO pro-using typical BWR reflector boundary conditions.
cedure (an option with PRESTO-B) was used to generate a specific set of boundary conditions for the EOC condition. The latter data was not significantly different from the data used in the 33 burnup steps.
These 33 burnup steps were then recalculated, using a 1/2-core model, with the specific reflector data derived as explained above.
The 1/2-core model was used to enable exact representation of.all control rod patterns associated with each of the burnup steps.
The nodal distribution of Ba-140 was automatically tracked through the 33 burnup steps and the EOC distribution was saved on a file for compari-son with the corresponding experimental La-140 distribution.
Detailed simulation, using an option in PRESTO-B where each burnup step is further subdivided into time steps, was performed for the last three months of cperation to ensure proper integration of the Ba-140 nodal concentration distribution. The reactor total power was given for each
I 11-, !
time t-tep, cicscly resembling the actual power history; thus accounting for, e.g., Ba-140 decay during periods of shutdown within the time period of a burnup step. The following staps were applied :
STEP BURNUP LENGTH NUMBER STEP NO. (!GD/TU) NO. DAYS TIME STEPS 28 377 24 13 29 427 23 8 30 54 4 3 31 236 29 9 I 32 191 12 5 33 89 , 5 3 i
Comparisons with plant data, such as the process computer core-average Axial power distribution, were performed at some points during the simulation of the operating history, to rake sure the power distribution was reasonably accurately represented. Some examples of such comparisons are shown in Figures 11.42 and 11.43.
Plots of calculated k gg and core-average void fraction versus core-
- average exposure through Cycle 1 are shown in Figure 11.44. The reactor l
power level and control density are also shown.
The cycle-average k was 0.99715, with a standard deviation of eff 0.00246. The EOC value was 0.99621.
11.3.3 Comparison _of_ Calculated __and_ Measured _La-140 Distributions The time between reactor shutdown and the actual measurement was suffi-cient to justify the assumption that the measured La-140 intensities were in equilibrium with the corresponding Ba-140 concentrations. Thus, the two distributions would be proportionate.
In order to compare calculated and measured data, normalization was performed as follows :
11-8 h* [
oc tant P
=1 ( 11. 2)
A normalization factor, c, was defined for the measured data :
P =1 (11.3) f*[t octan eas The nodal standard deviation (c) was found from the following expres-sion :
It I (I,J,K) ) 2 c = jg [ (P;,yc (I,J,K) -c P (11,4) y octant where I,J.K a coordinates of nodes with measured data N = total number of data points c = normalization factor The standard deviation thus calculated was 6.4%. Separating centrolled and uncontrolled nodes, the following result was obtained :
NO. STANDARD TYPE NODE DATA POINTS DEVIATION l
(%)
Controlled 182 6.4 Uncontrolled 828 6.5 TOTAL 1010 6.4 An overview of the plots, comparing measured and calculated data, is shown in Figure 11.45. Individual bundle plots are shown in Figures 11.46 through 11.54. These plots are shown for all six bundles measured with at least 24 axial points (Figures 11.46 - 11.50) and for typical distributions of the following categories :
11-9
- Unrodded, core-interior bundle (Fig. 11.51)
Bundle with deep control rod insertion (Fig. 11.52)
Bundle with shallow control rod insertion (Fig. 11.53)
- Unrodded, core-periphery bundle (Fig. 11.54)
Bundlewise ratios between calculated and measured, axially integrated curves are shown in Figure 11.55. This representation illustrates the average radial, or bundle power, comparison. The total standard devia-tion in the bundlewise comparison was 2.5% (75 bundles) . Three bundles (Nos. 251, 514, 487) shewed uncorrelated deviations of about 10%. Ex-cluding these three bandles, the standTrd deviation in the bundlewise cotrparison was 1.8% (72 bendlns) . We average bundle pewer rat-lo and the bundlewise standard deviatica was calc alaced ror each of,the follewing groups of bundles :
STMDA'1D AVERAGE DEVIATICN ;
NO. BUNDLES RATIO (%)
Rodded Bundles 22 1.012 1.8 Unrodded Bundles 53 0.995 2.7 Core Periphery Bundles 10 1.026 3.3 Core Interior Bundles 65 0.996 2.3 TOTAL 75 1.000 2.5 t
Excluding the three " bad" bundles, the following results were obtained :
11-10 STANDARD AVERAGE DEVIATION NO BUNDLES RATIO ( %'s Rodded Bundles 22 1.012 1.8 Unrodded Bundles 50 0.992 1.8 Core Periphery Bundles 8 1.005 1.0 Core Interior Bundles 64 0.997 1.9 TOTAL 72 0.998 1.8
)
Ccmparisons of calculated and measured axial pin-wice La-140 distri-butien were performed for four different fuel pins (the narrow-narrow and wide-wide corner pins of Assembly Nos. 373 and 393) .
2 The calculated pin-wise axial distrioutiens were obtained by multiply-ing the nodal distributions calculated by PRESTO with phrto-nede power-peaking factors cbtained frcm the RECORD Data Bank. Peaking factors for each axial node were calculated by interpolating to the nodal exposure and exposure-weighted void among the values tabulated in the data bank. Different sets of peaking factors were used for the rodded and the unrodded condition. Results are shown in Figures 11.56 and 11.57.
Calculated and measured curves were normalized separately for each pin.
In general, the pin-wise axial shapes are well reproduced. Especially the ratio between the power levels in the " rodded" and "unrodded" por-tions of the pins are in excellent agreement.
11.3.4 Discussion of Results NODAL COMPARISONS :.
An everview of the nodal gamma scan comparison is presented in Figure 11.45. 'Ihe total standard deviation was 6.4%, including 1010 data points of the measured core octant.
11-11 In general, very good agreement was obtained in comparing calculated and measured axial La-140 shapes. Although not shown in the Figure, it was found that the calculated La-140 distribution agreed well with the calculated EOC power distribution. Thus, the conclusions drawn are valid for the power distribution as well.
The discrepancies seen may be grouped into two categories, as follows :
n In the center region of the core, where the power distribution is relatively flat, the calculation shows a tendency to double hump, while the measurement shows a depression of the " bottom hump". This is probably due to inaccuracies in the calculated ,
EOC exposure distribution resulting from approximations in power distribution modelling throughout the cycle.
l n A slight cverprediction of the power-yeak is obcerved for some of the sharply top-peaked distributions in the outer reglen of tne core. This phenomenon does not correlate with control rod inser-tien, and is probably also related to exposure dintributien l inaccuracies.
The following obserJations and conclusions are made :
n The influence of partially inserted control rods (both deep and shallow insertion) on the axial power distribution in i
surrounding fuel assemblies is very well predicted by PRESTO.
This is true for the four assemblies immediately adjacent to the control blade, as well as for those located in the next
" ring" away from the blade. Both power , shape and the rodded-to-unrodded power step are in good agreement with measurements.
l ,
n The axial power shape in the throttled periphery bundles (Fig. 11.45) is as good as in the unthrottled assemblies.
BUNDLEWISE COMPARISCNS :
A comparisen of axially integrated distributions (ratios of calculation-
11-12 to-measurement) is shown in Figure 11.55. These results are directly applicable'for evaluation of PRESTO's bundle power prediction.
The following observations and conclusions are made :
a The general agreement between calculated and measured " bundle power" is quite good. The standard deviation was 2.5%, with all bundles included, and 1.8% with 3 of the is bundles excluded from the comparison.
n There are no systematic radial tilts.
f n Periphery bundle power is calculated with the same precision ;
as core-jhterior bundles.
a Rodded bundle powerc are in good agreement with measurements (average ratio 1.012) .
n Errors of about 10% in the ratio of calculation-to-measure-ment occur in three different, uncorrelated positions :
Bundle Nos. 487, 251 and 514. The reason for this is unexplained.
PIN-WISE, AXIAL DISTRIBUTION COMPARISONS :
Comparisons of calculated and measured distributions along the W-W corner pin and the N-N corner pin of two partially rodded (deep and shallow rod insertions) assemblies are shown in Figures 11.56 and 11.57.
The following observations are c:ade :
2 The axial power shape along the W-W corner rod is very well predicted. Especially the power increase from the " rodded" to the "unrodded" positions of the pin is in almost exact agreement with measurements, n The calculated axial power shape alcng the N-N corner rod is also in reasonably good agreement with measurements.
11-13 n Figure 11.57 shows that the "long distance" effect (power depression ending at 90 inches elevation) of the control
- blade inserted to Notch 14 in a diagonally neighboring assembly, is underpredicted in the N-N corner and over-predicted in the W-W corner. This is as should be expected, since the N-N corner is closer to the next control blade.
n The results shown in Figures 11.56 and 11.57 are of interest both for evaluaticn of the model used in PRESTO for calcula-tion of local maximum pin-power (max. LHGR), and for evalua-tion of models used for calculation of power shocks associated with control rod movements.
n Control rod withdrawal power shocks are n:ost important for pins adjacent to the rod blade. As seen in the Figures, power shocks seen by the W-W corner pin are very well pre-dicted by the RECORD / PRESIC " overlay" method.
4 11.4 Comparisons wirn EWR Cperating Data A list of BWR operating cycles analyzed with PRESTO since its initial ;
development in 1971 is given in Table 11.7.
Lattice data calculated by RECORD were used in all cases, except as indicated in the Table.
Although the basic assumptions of the FMS - RECORD / PRESTO Model remain valid, a number of detailed developments and improvements have been continuously implemented. Thus, a statistical treatment of the accumu- .
lated data would not reflect the current status of obtainable accuracy.
However, an overview of the experience during the ten year period is given in Reference 13. Applications of PRESTO are reported in Refer-ences 14 through 19.
Comparisons with BWR operating data have included :
- calculated and measured TIP traces
- calculated and measured LPRM readings
11-14
, l 1
detector-inferred (process computer) power distributions j process computer fuel exposure distributions predicted and actual critical control rod patterns and analysis of cold, critical cores reactivity - core lifetime predictions with actual data special gamma scan data for power distribution and exposure distribution evaluation An extensive analysis of the past operating cycles of CP&L's Brunswick BWRs is presented in a separate report. Examples of results obtained from other reactors are given in the following :
D0LEWAARD, G.E. BWR-1, 163 MWth (Nt:therlands)
The first two operating cycles cf this natural circulation, small BWR were analyted wi2 early versions of RECORD / PRES'IC during 1971.
Satisfactory results were obtained. Examples of TIP-com;nrisons are shown in Figure 11.58 (Ref. 14).
M 6 H_ L E B_ E_ R_ G_, G.E. BWR, 950 MWth (Switzerland) he first three cycles were analyzed by Scandpower (Ref. 15). We remaining cycles have been analyzed for core-follow and operations support by the Utility (Cycles 4, 5, 6 and 7) . Gamma scan comparisons have been performed as part of the qualification of the code (Refs. 16 and 17). Examples of TIP-comparisons and gamma scan results are shown in Figures 11.59 and 11.60.
BARSEBKCK, ASEA-ATOM BWR, 1700 MWth (Sweden)
Cycle 1 core-follow calculations and Cycle 4 startup analysis performed with PRES'IC. Results unpublished.
B_ R_ U N S_ B_ 0 T T E L_, KWU BWR, 2300 MWth (Germany)
Cycle 1 core-follow calculations, including detailed Xe-dynamics simu-lation of a number of operational transients, were performed. Examples
11-15 of TIP-comparisons are shown in Figure 11.61. Results unpublished.
P_ H I L,I P_ P_ S B U R G,, KWU BWR, 2300 MWth (Germany)
Cycle 1 core-follow calculations performed by the Utility. Gamma scan comparisons performed at about 4000 MWD /TU. Results unpublished.
SANTA MARIA de GAROEA, G.E. BWR, 1380 MWth (Spain)
Cycles 7, 8 and 9 core-follow and operations support performed by Utility in extensive applications. Example of TIP-comparisons are shown in Figure 11.62.
F 0 R,S M,A R K_ _ 1, ASEA-ATOM EWR, 2700 MWth (Sweden)
Cycle 1 core mode] ling and core-follow analysis performed by Scandpower.
Results unpublished.
_Q U A_ D _,,C,I_ T,I_ E S _,_,2, G.E. BWR, 2400 MWth (U.S.A.)
Cycles 1 and 2 analyzed with RECORD / PRESTO by Scandpower, as part of a fuel performance evaluation study for EPRI (Ref. 18). Examples of TIP-comparisons are shown in Figures 11.63 and 11.64.
HATCH-1, G.E. BWR, 2400 MWth (U.S.A.)
Cycle 1 core-follow and gamma scan comparison performed by Scandpower.
See 611.3.
F_ I_ T_ Z,P_ A T,R I C_ K, _ 1, G.E. BWR, 2400 MWth (U.S.A.)
Cycle 1 and part of Cycle 2 core-follow performed by the Utility.
Results unpublished.
TABLE 11.1 PRESTO 2-D and 3-D Bcnchmark Runs - Overview E
. . . DE W (sec) (k,7g h CASE NO* DIMENSIONS (Core Fract.) CDC CYBER-74 1 -1 1100 STD.DEV. %\X.DEV.
DIMENSIONS "
(cm) at a2 (k,ff ) W W 20x20 0.0 0.4 52 (1/4-Core) '4.64 0.40 0.93 2.3 4
02-01 2 t
02-02 2 10x10 0.0 0.0 94 (1/8-Core) 7.90 0.28- 0.63 1.9 03-01 3 20x20x20 0.0 0.4 884 (1/4-Core) 18.02 0.40 1.16 2.6 03-02 3 10x10x20 0.0 0.2 1598 (1/8-Core) 57.90 0.33 0.65 1.3 l
i QSee $5.1 for def. of ay and a,. (Reconanended values of an and a2 for BWR applicationa (mech vidth ~15 x 15 x 15 cm) are a1 = 0.0, a2 = 0.0 - 0.2).
i C
i i
i i
I j
11-17 TABLE 11.2 Frigg Loop Operating Data CASE NO. POWER FLOW SUBC00 LING 001 Low intermediate low 2 tow 3
4 intermediate " "
5 6
7 intermediate "
, g .. .. ..
n 9 .. ..
10 high "
11 12 high "
13 14 intermediate "
15 16 Low low intermediate 17 18 intermediate " "
$9 ..
20 high "
21 intermediate intermediate "
22 23 high "
24 i 25 intermediate high "
26 high 27 intermediate intermediate high 28 high 29 tow low 39 intermediate intermediate low 40 high low
. 11-18
'l l
TABLE 11.3 FRIGG Loop Operating Data w
TABLE 11.4 PRESTO Hydraulics Model Parameters s~
i b.
4
, , - . - - - - , - - - -e --w , - -. a e , -- ,-- - , - - -- - - , -
11-19 x
l l
TAM E 11.5 Gamma Scan Measurement Positions MEASUREMENT LOCATIONS 1
MEASUREMENT CORRESPOND. 24-NODE 12-NODE 14-NODE 3 ELEVATION PRESTO NODE SCANS SCANS SCANS 141 24 X ,.
135 23 X X X 129 22 X 123 21 X X X 117 20 X 111 19 X X X
~
2 106 18 X 97 2 17 X X X 93 16 X X ,
87 15 X X X 82 2 14 X X 75 13 X X X 69 12 X 63 11 X X X 57 10 X 51 9 X X X 45 8 X 37 2 7 x x x 33 6 X 27 5 X X X 21 4 X 15 3 X X X 9 2 X 3 1 X X X
' Distance in inches above bottom of active fuel. ,
Measurement position moved from center of c ial node to avoid spacer.
'E: ample for a bundle uith blade inserted to Notch 20. Extm measurements are added in the vicinity of control blade tips.
s m
l
%-%) '
\ '
M 11-20 k
o.
.cs TABLE 11.6 Operation Data Used in PRESTO Analysis of HA'It!!-1, Cycle 1 BUR 4.7 BUMJP DATA CORE IN1ET 7t7tAL CONTR01.
E' s .qEP EOS DATE SET SURCDOL CORE FIDI DENSITY IE* NO. (WD/TU)
U NO.
- M UI (ws/kt) (ks/s) 0)
PR-HAug 1 308.6 75/02/13 1 A 60 53721. 6400.0 11.0 5 45117. 10370. 8.1
' 90
- 2 493.8 75/03/05 2 75
-91 70 2.*. 75/03/28 3 A 50 79536. 4347. 9.4 1040.5 75/05/06 3 A 50 79536. 4347. 9.*4
-92 4
-93 5 1281.9 75/05/24 4 A 90 55542. 8568. 7.1
-94 6 1631.3 75/06/13 4 A 90 55582. 3568. 7.1
-95 7 2013.8 75/07/10 5 A to 61163. 7157. 9.2 2583.7 75/08/26 6 3 96 49070. 9929. 9.0
-96 8 7 8 86 55814. 8404, 10.2
-97 9 3116.1 75/09/25 3646.3 75/10/24 8 8 86 60000. 7673. 10.9
-98 10
-99 11 3948.3 75/12/30 8 8 86 60000. 7673. 10.9
-106 12 4157.7 76/01/13 9 5 80 54187. 8102. 13.7
-10'7 13 4204.0 76/01/18 9 3 80 54187. 8102. 13.7
-108 14 4319.7 76/01/25 10 A 76 42093. 9891. 16.5
-109 15 - 4685.7 76/02/18 10 A 76 42093. 9891. 16.5
-110 16 5024.1 76/03/11 11 A 79 45582. 9337. 17.0 5300.8 76/04/25 12 A 80 48373. 8996. 17.0
-111 17
- 18 5793.5 76/05/25 13 3 86 48605. 9261. 16.9
-112 6176.3 13 3 36 48605. 9261. 16.9
-113 19 76/07/05 6592.7 ,76/07/22 14 A 83 56977. 7862. 17.5
-114 20 6979.6 76/08/13 15 A 93 50698. 9488. 17.5
-115 21 7161.5 76/08/23 15 A 93 50698. 9488. 17.5
-116 22 7618.9 76/09/16 16 3 92 48605. 9878. 19.2
-117 23 8059.8 76/10/12 16 3 92 48605. 9878. 19.2
-118 24 8432.4 76/11/03 17 3 87 48838. 9551. 19.2
-119 25 8938.4 76/11/24 18 3 04 45117. 9891. 19.2
-120 20 9025.5 76/12/05 18 8 84 45117. 9891. 19.2
-121 27 9402.5 76/12/29 19 A 92 47907. 9853. 15.6
-122 28 9829.1 77/01/21 20 A 87 46512. 9916. 15.6
-123 29 .
9883.1 77/01/25 21 A 88 51861. 8984. 15.2
-124 30 10119.0 77/02/23 21 A 88 51861. 8984. 13.2
-125 31 77/03/07 22 A 91 47907. 9904. 15.2
.-126 32 10310.8 A 87 47442. 9727. 15.2
-127 33- 10399.0 77/03/12 23
- Corresponde to notation in Reference 11.
TABLE 11.7 Operating BWR's Analyzed with PRES'fO ANALYSIS TIP GAMMA COLD OPERATING CYCLE PERFORMED COMPARISONS SCAN CONDITION BY MADE ANALYZED ANALYZED REACTOR ANALYZED DODEWAARD 1,2 ScP Yes 1,2,3,4,5 ScP/ Utility Yes Yes Yes M0llLEBERG ScP Yes Yes BARSEBACK 1 ScP Yes Yes BRUNSBO'ITEL 1 Utility Yes Yes Pl!ILIPPSBURG 1 7,8,9 ScP/ Utility Yes Yes SANTA MARIA de GAROSA ScP* Yes Yes FORSMARK-1 1 QUAD CITIES-2 1,2 ScP Yes f 1,2,3 Utility Yes Yes BRUNSWICK-1 1,2,3,4 Utility Yes Yes BRUNSWICK-2 1 ScP Yes Yes llA'Irll-1 FITZPATRICK 1,2 Utility *
- Lattico data provided by Utility (CitSMO)
l l
1 11-22 l
i Peo'estion of partici'y insested rod cm cm lossemb?y 16) 17c 3sc_-
[
1 Js0 in M4 {f4,4 $5 ? 4 15 0
/
" 3'Oh p3j *G s
' 13 0 %
A; A*
s; 8
'O /5s ir 37 280 s \s
\
sr 6 3 :, A N
\
70 -
I' "
,s s.;
_ _ A's 2s 2, se 30 g?W_j s u;detone
_te __ toa rr L 7i > is0 s - -
g-- -
l'//b it ir o it is it 17 S
'o.Ed L.L l. I ' k3H 6 7 LJ_.l \
0 13 30 SG 70 90 11 0 U0 lia 170 cm \)s \
\
sN 8
s' \\
A \N Upper Octtnt: Region Assigneents N \
to.er Octant: Feel Assently Identification (
\
So6ndary Conditicas:
9 20
( h ,
[xternal Soundaries J -O ' '
c 10 70 90 130 ISO 170 cm
$yesetry Soundaries J' -0 _
Vertical Cross Section, y - 0 Group Constar.ts for 30 IAEA Benchcark Prol,les Region D, D Eg Eg E,7 v,Eg7 7
1 1.5 0.4 0.02 0.01 0.ca 0.135 fuel 1 2 1.5 0.4 0.02 0. 01 0.085 0.135 fuel 2 3 1.5 0.4 0.02 0.01 0.13 0.135 fuel 2. Red 4 2.0 0.3 , 0.04 0 0.01 0 Reflector 5 2.0 0.3 0.04 0 0.055 0 Rcil. . Rod x3 - 1.0 ,
x2 - 0.0 , vl E,j - O all upon llote: 201AEA Benchmark Problee represents sidplane z - 190 ce viih constant 2
axial buckling 5 - 0.8 x 10' for all regions and ener9y greurs
.1 FIGURE 11.1 Benchmark Problem Specifications for 3-D and 2-D Core Neutronics
> Neutrenics Model Verification.
11-23 752 1311 1431 1211 e12 923 909 753 745 1304 1449 1207 610 933 933 752 1.0 0.5 -1.2 0.3 0.3 -1.1 -2.6 0.1 1457 1482 1331 1064 1040 938 729 1430 1476 1311 1007 1035 950 734 1.9 0.4 1.5 -0.3 0.5 -1.3 -0."
1472 1344 1157 1065 990 702 1466 1343 1178 1971 977 e90 0.4 0.1 -1.5 -0.0 1.3 0.8 (k,gg) 1203 902 909 856 -* PESTO 1.033S 1191 900 909 553 = REFIRLNCE 1.0290 1.0 -0.J 0.0 0.4
- REL.DIFF. (1) 0.41 472 tSS 602 473 039 007 SFD.DLY.REL.DIFF. 1. 00'.
-0.2 -0.5 -0.8 M U.REL.DIFF. 2.6 i 595 594 0.2 FIGURE 11.2 PRESTO 2-D IAEA Benchmark Comparison. Node Size: 20 x 20 cm Relative Bundle Power 745 1316 1446 1216 610 939 931 760 745 1304 1449 1207 610 933 933 752 0.0 0.9 -0.2 0.7 0.0 0.6 -0.2 1.1 1439 1475 1318 1074 1038 945 731 1430 1476 1311 1067 1033 950 7 34 0.6 -0.1 0.5 0.6 0.3 -0.5 -0.4 1464 1340 1172 1003 967 707 1400 1343 1178 1071 977 696
-0.5 -0.8 -1.0 1.6 (Leff)
-0.1 -0.2 902 S48 l'RESTO 1.0329 1194 969 -
909 853 = REFERE.NCE 1.029b 1191 966
-0.8 -0.b REL.DIFF (1) 0.32 0.3 0.3 --
470 687 610 STD.DEV.REL.DIFF. 0.621 473 e89 607
-n.6 -0.3 0.5 % U.REL.DIFF. 1.6%
593 594
-0.2 FIGURE 11.3 PRESTO 2-D IAEA Benchmark Comparison. Node Size: 10 x 10 cm i Relative Bundle Power
11-24 733 1282 13 % 1193 609 940 933 777 729 1231 1422 1193 610 953 9
,59 777 n.5 n.1 -1.e n.n .n.+ -1.4 .e p,n 1420 1432 1307 1065 1057 962 731 1397 1432 1291 1072 1055 976 1.6 757 0.0 1.2 -0.6 0.2 -1.5 -0.8 1367 1309 1155 10S1 1014 722 1368 1311 1131 1039 2000 711
-0.1 -0.2 -2.2 -0.; 1.4 1.5 beff) 1189 905 924 877 =
ITJSTO 1.03321 1178 972 923 560 =
0.9 RL}UBCE 1.02903
-0.7 0.1 1.3
- REL.DirF. (%) 0.40 475 700 c17 470 700 011 S E.DLY.REL.DIFF. . 1.171
. .0 1.0 Mu.DLT.REL.DIFF. : 2.8 %
009 597
--.l. 0___,
FIGURE 11.4 PRESTO 3-D IAEA Benchmark comparison, Node Size: 20 x 20 x 20 cm Relative Bundle Power 727 1275 1404 1191 612 959 962 782 729 1281 1422 1193 610 953 959 777
-0.3 -0.5 -1.3 -0.2 0.3 0.6 0.3 0.6 1390 1418 1287 1072 1059 979 753 1397 1432 1291 1072 1055 976 757
-0.5 -1.0 -0.3 0 0.4 0.3 -0.5 1356 1302 1173 1088 1001 715 1368 1311 1181 1089 1000 711
-0.9 -0.7 -0.7 -0.1 0.1 0.6 k eff 117e 975 92J boo FRE51D 1.03:38 1178 972 923 S66 REFERD CE 1.02903 0.0 0.3 0.4 0.0 -
REL.DIFF (1) 1.33 482 709 017 476 700 611 1.3 1.2 1.0 593 STD.DLY.REL.DIFF. : 0.65%
597
-0.7 M W.REL.DIFF. 1.3 %
FIGURE 11.5 PRESTO 3-D IAEA Benchmark Comparison. Node Size: 10 x 20 x 20 cm Ralative Bundle Power
11-25
- a i
l l
i i n. l i
i i i i I
PflATIVE NIAL NM -
2.0 -
N, PREST 0 STD.DEV.0F REL.DIFF. : 4.86 :
~ ~
1.0 -
STD.DEV.0F ABS.DIFF. : 2.65 :
/
/
' CONTR. R0D BOTTOM TOP
' ' , i , i . t , i , I . I ,
1 3 5 7 9 11 13 15 17 AX1AL NODE INDEX FIGURE 11.6 PREST 0 3-D 1AEA BENCHMARK CCMPARISON. NODE SIZE : 20 x 20 x 20 cM AXIAL power DisTRinuTION - THIRD BUNDLE ON DIAGONAL (X,Y)=(3.3) i I I I I 1 i i RELATIVE m STD.DEV.0F REL.DIFF. : 1.35%
FUER - 's STD.DEV.0F ABS.DIFF. : 2.17%
2.0 - \ -
REFERENCE PREST 0
^
1.'O CORE CENTER CORE EDGE I I I I I I I i 1 2 3 4 5 6 7 8 NODE INOEX ALONG X - AXIS FIGURE 11.7 PRESTO 3-D I AEA BENCHMARK COMPARISON. N00E $1ZE : 20 x 20 x 20 cx RADI AL POWER ALONG X-AxtS AT CORE MIDPLANE (K- 9 )
11-26 1.1 2.6 Bundle enrichment (%)
2.6 2.6
.818 1.060 .839 1.058 REF
.815 1.061 .854 1.056 CPT1
.819 1.051 .848 1.049 OPT 2 1.063 1.045 1.060 1.032 1.078 1.053 0% VOID 40% VOID
.844 1.061 .547 1.124
.881 1.052 .555 1.107
.850 1.056 .567 1.105 1.034 1.205 1.014 1.228 1.035 1.221 80% VOID 40% VOID
.975 1.147 .696 1.074 1.006 1.123 .721 1.054
.991 1.131 .700 1.067 732 1.156 747 1.169
.745 1.164 uur 40% VOID 40% VOID, ALL 2.6% enrichment REF = RECORD /MD-2, 3-orcup, explicit OPT 1 = PRESTO, Model Option 1, a =a 0 2
OPT 2 = PRESTO, Model Option 2, a =a =0 3
FIGURE 11.8 Comparison of PRESTO 4-bundle power sharinc calculations with 5-qroup explicit (RECORD MD/2) benchmark results.
11-27
- ! e i i i , a i i a i i ,
- '. { : 3, ne.7,3.cg3 A Sperme:d cctc
, 70 - - Ccicutc:ec -
60p I Mecn Cev (*/.): 2 49 50 Std Dev. (*/.): 090 ,.
A FIGURE 11.9 40- A -
30 - -
A 20 -
10 - a -
0 2 4 6 8 10 12 14 16 la 20 22 24 Axial node no.
- i i i i i 6 6 , 6 6 i i
- c '- l Ccse no 713-002 A Greremtd ccta 70 - - Cc!cu!cted -
A 6C- -
Mean Dev. (*!.): -0.10 50 Std. Dev. (*/.): 1 26 _
FIGURE 11.10 43_ _
30- -
20- -
10- -
0 2 4 6 8 10 12 14 16 18 20 22 24 Axial node no.
8C 6 i i i i 6 i e i i 6 i
% : Ccse no.:713-003 A Lpermentc1 octo ,
70 -
- Cctcu!cted -
^
60- -
Mecn Dev (*/.):164 50 Std. Cev. (*/.):136 A _
A FIGURE 11.11 (c_ _
A 30- -
20- _
10 -
i ? ?
- I f I f f f g ? ?
2 4 6 8 10 12 14 16 18 20 22 24 Ax'cl node no.
Comparison of Calculated and Measured Axial Void Distributions
11-28
, . . . . . . . i . . . .
bd%
70 - -
60- A I
50 - -
FIGURE 11.12 40- -
30- Case no.: 713-004 ' U P'r'n'ntCl dCtc -
- Cc!culated 20- -
10- % v. ('!.): -t57 Std. Cev. ('/.): 2.46 1 t
' ' ' ' ' ' ' ' ' ' ' I 0 4
. 2 6 8 10 12 14 6 :S 20 22 24 Aict node no.
- ^
--' i i i i i e i 6 . 6 a i bd % l Ces,no:73.;;5 A Upercentc! dcto 70 - - Cc!cuteted -
A 60- -
Mean Dev. (*!.):-1.14 50 Std Dev. (*/.): 1 44 _.
A FIGURE 11.13 40- -
30- -
l 20- -
10- -
I ' ' ' ' ' ' ' ' ' ' '
O 2 4 6 8 10 12 14 16 18 20 22 24 Aict node no.
0; i i i -
a 6 e i e i 6 O ** Ccse no.. 713-006 A 6perrnente! dcta l
l 70 - - Ccteuteted -
60- 4 Mean Dev. (*!.): -t64 50 Std. Dev. (*/.): 178 _
FIGURE 11.14 40- _
l 30- -
20-10- -
l i
l c 4 2 6 8 10 12 14 16 18 20 22 24 Aict node no.
Comparison of Calculated and Measured Axial Void Distributions
11-29 6 . . i i . i e i i
. i 6 M3 'A Ccse ro : 713-037 a 6pertre .tcl ec c 7C - - Ccicuteted 60 -
Mean Dev. ('!.): 0.18 50 Std. Dev. (*/.): 2 02 A
40 -
FIGURE 11.15 ,
30 20-10-0 14 16 18 20 22 24 2 4 6 8 10 12 Axict rede no.
- ' i i i i i i i i i i i a Operreentet cctc
' W.
- Ccse no : 713 008
^-
7C'- - Ccicu:cted a a -
60-Mecn Dev. ('/.): -0 09 ^ -
50 Std. Dev. ('/.): 2.06 FIGURE 11.16 co-30-20
! 10-0 14 16 18 20 22 24 2 4 6 8 10 12 Amici node no.
i i i i i 50 i i 6 i i 6 e W d ** a Operrnentet detc C:se no.: 713-009 -
70 - - Cc!cuteted ,
60- -
Mecn Dev. ('/.): 0 94 A -
50 Std. Dev. ('/.):169 FIGURE 11.17 40-30 20-10-4 1 ' 1
- g
- t t i 1 1 1 0 12 14 16 18 20 22 24 2 4 5 S 10 Ax'c! node no.
Cociparison of Calculated and Measured Axial Void Distributions
11-30 20 , i ; i i i i i i i a i Wd 'f. Ccse no: 713-010 ^ U?"#"d #C 70 - - Cc!cuicted -
60- A-i Mecn Dev. ('!.):1.81 f
So _ Std. Dev. (*!.): 2.14 -
A FIGURE 11.18 40-A 30- -
A 20- ,
A 10-A t e t i t t 1 I f f I f 0 4 % 20 22 24 2 6 8 10 12 16 18 Axict node no.
i'i i i i i i e i i 6 i e i A LpnemtcI dcta dd i Ccse no.: 713-011 70L - Cc:culated -
i l 60- -
Mean Dev. (*/.): 310 50 Std. Dev. (*!.):4 37 ,
l FIGURE 11.19 40 - -
A 30- -
g_ A I -
A 10- -
l A ,
! A l t t t t f f f f f f f 0
2 4 6 8 10 12 % 16 18 20 22 24 Axict node rc.
50 ! i i i i i i i 6 a a i k O '* Ccse no.: 713-012 ^ UP'""'"lCI03tC
( 70 - - Cc! cute'ed -
l A 60- -
Mecn Dev. ('!.):1.91 ,
50 Std Dev. (*/.): 2.47 -
^
FIGURE 11.20 43_ -
A 30- A A
20'-
i l 10- A -
. , , , , , , , i e i t 0 4 14 16 Id 20 22 24 2 6 8 10 12 Axici node no.
Comparison of Calculated and Measured Axial Void Distributions i
11-31 80 , , , , , , , , , , , ,
W c **
- e n -7
- 3.c.9 A Ecermentcl ec'c ,
70-- - Ccicutcted -
60 -
Mecn Dev. (%):-0.36 50 Std. Dev. ('/.): 164 -
FIGURE 11.27 40-30-20-10-0 4 8 % 16 18 20 22 24 2 6 10 12 Axio! node no.
V' ; '*
A Lweentd cctc
. , , . X.
Ccse no.: 713-020 -
70 - - Cc!cu!cted 60- a Mean Dev. (%):-1.43 50 Std. Dev. ('t.): 3.56 FIGURE 11.28 43-30-20-10-
- t t t t I i t I t I i 0 4 6 8 10 12 % 16 18 20 22 24 2
Axiol node no.
. . i i e i i i i 60[ . 6 a Lpermentet ccto VC'C '* l Cese no.: 713-021 - Cciculated 70 -
60- ,-
Mecn Dev. ('!.): 0 53 50 Std. Dev. (%): 1.60 FIGURE 11.29 co _
30 20-10- A t t t ' t t i e 0 e 12 14 16 18 20 22 24 2 4 6 10 Axict node no.
4 -
Comparison of Calculated and Measured Axial Void Distributions
11-32 FC I i e i . i e i 4 i i i i
- ^ UWNtd dClO
':d % l Ccse no 73-C13 A-70 - -- Cc'cateted.
A 60- -
Mecn Dev. (*/.): 0.71 Sc Stc. Dev. (*/.): 2.79 _
FIGURE 11.21 to _
30 -
20- -
A 10- -
0 20 22 24 2 4 6 8 10 12 14 16 18 Axk:l node no.
^
50, i i i i i i i i i i a i 4 Eic *!* Ccse no.. 713-014 A Lwetd octo a 70'- - Cc!cuteted -
~
60 -
Mecn Dev. (*/.):-1.58 50 Std. Dev. (*!.): 3.01 -
FIGURE 11.22 to_
A
~
30 -
20-10-
, , , . , , , e i e 'i 0 14 18 20 22 24 2 4 6 8 10 12 16 Axici node no.
i 60 i i e i i e i i e i a i n V c ** Ccse no.: 713-015 A Dmmte! detc
- Cc!cu!cted 70-EO- ,
Mecn Cev. (*!.):-1.07 A a 50 Std. Cev. (*/.): 2.83 FIGURE 11.23 40 -
30-20-10-f f I t f f 1 i t t i 0 4 8 12 14 16 18 20 22 24 2 6 10 Ax'c 1 node no, i
Cociparison of Calculated and Measured Axial Void Distributuns
11-33 EO, , , , , , , , , , , , ,
V; 0 ** l C Se no :7:3.;;g A Leerrnentc! ccto 70 - - Cc!cuteted -
60 - -
Mecn Dev (*/.):1.31
^
50 Std. Dev. (%): 2.12 _
i FIGURE 11.24 40- A -
30- -
20- -
10- A .-
C 2 4 6 8 10 12 14 16 18 20 22 24 Ax'c! node no.
5 0 i i i i i 6 6 i i i i i A Spermentc! dcte bc ** j Ccse no : 713-017 70 -
- Cc!cuteted -
A A 60- ,
Mean Dev. (%):168 50 Std. Dev. (%): 2.74 -
A FIGURE 11.25 40 - -
A 30- -
M- ,
10- -
0 2 4 6 8- 0 12 14 16 18 20 22 24 Axiot node no.
en
-e . . i i i , 6 6 i i i i V:,c % A Lperrnentet octe Ccse no : 713-018 70 - - Cc!cuteted A 60- -
Mecn Dev. (%):0.05 50 Std. Dev. (%): 2.73 -
FIGURE 11.26 40- -
30- A -
20 - -
10 -
0 2 4 6 8 0 12 14 16 18 20 22 24 Axict node no, i
Comparisen of Calculated and Measured Axial Void Distributions
1 11-34 C- i i i i i i i i i i .
vsd Ccse no : 713-022 ^ U ?*'**Cl dC!t 72- - Cc:cdc:ed -
60- -
Mem Dev. (%): 0.85 50 Std. Dev. ('/.): t59 ,
FIGURE 11.30 (0-30 -
20- -
to-A 0 20 22 24 2 4 6 8 10 12 14 16 18 Aict riode no.
30 i , i i i i i i i i , i ed 1. C: sere: 713-023
- UP*""*"!01 dO!
70 -- - Cc:cdcted -
I ^
EC Wan Dev. ('!.):-0.14 50 Std. Dev. (%): t60 -
FIGURE 11.31 40-
- t 30-A 20 10-C % 20 22 24 2 4 6 8 10 12 16 18 Aici node no.
6C 4 i i i i i , e i e i i V0'd % A Lperrnentet dctc Ccse no.:713-024
- 70 -
- Cc'cdcted -
60-Mean Cev. (%):-0.46 50 Std. Cev. (%): 2.01 -
FIGURE 11.32 40 -
30-A 20-10- A e t . i e i e e t t t t 0 4 6 8 12 14 16 18 20 22 24 2 10 Axict node no.
t Comparison of Calculated and Measured Axial Void Distributions
' 11-35 i
- -; a i i i a 4 i i i 6 6 6
- ** l Ccse r.::713-C:5
- U P'r #'*:C! CCtc j 7C- - Cc!cuctec -
iC - -
Mean Cev (%):0.17 Sc Std. Cev. (*!.); 2.69 -
FIGURE 11.33 4 _
ac- 4-20- -
10- ' -
A
, ' t I A fi A* t t
' g 9 t t t 2 4 6 8 0 12 14 16 18 20 22 24 Ax'c! rode no.
-- i i . . . i i i i i , i
- U;e'***t:1 CC'3 Ccse n: 713-C25 70,- - Cchciec -
l 60l- -
1
- Mean Cev. (*/.): 2.84 Sob Std. Cev. (*/.): 3.59 -
FIGURE 11.34 c0- 4 -
30 - -
Y 23r- -
10,- A -
' ' ' ' ^ ' ' ' ' ' '
0 2 4 6 8 - 0' 12 14 16 18 20 22 24 Axict node no.
SC i i i . i i
. 4 a a a a i E : ** f Ces, no.: 713 027 A L;ermentcl actc 70 - - Cc:cdcted -
60- -
Mecn Cev. (*/.):-0 02 50 Stc Cev. (%): 192 -
A FIGURE 11.35 40- -
a 30 -
20:- -
t 10 i
A e t ,
t = t A t. '
9 ! t i e C -
2 4 6 3 0 12 14 '6 18 20 22 24 Ax'ct node no.
Comparison of Calculated and Measured Axial Void Distributions
11-36
. . o ,
s s e s i i s
- : *. c:3, c 7 3.;;g e. Ee:eree-te:ccts 7's - ~ - Cc::dctec -
4 i >l -
Meen Cev ('t.): 013 50 St1 Cev. (*/.): 2 87 A -
FIGURE 11.36 cc _ _
20 - -
A 36 _
10- -
A A 0
2 4 6 8 10 12 14 16 18 20 22 24 Amic! node no.
- "j e i i i 6 6 s 6 6 6 8 6 u ! C:se no : 713-C29 ^ UP"'N4 00:C 70 - - Cc'cuteted -
60 Mecn Dev, ('/.):-0.67 50 Std. Dev. (*/.): 0.93 _
FIGURE 11.37 co_ _
30 _ _
20- -
10- -
0
' ' ' '- ' '- * ^' ' ' ' '
2 4 6 8 10 ' 12 14 If, 18 20 22 24 Amict node no.
Comparison of Calculated and Measured Axial Void Distributions I,
--,-----,,sm- y n , m - , , . - - w- m - mm y e,
11-37 C. 4 i i a a i 6 i , i i .
A L;evnentc! cc*c 4: *-7G-l c: 5, re: 793.c39
- Cc:cu!c:ed -
A e
60 - -
Mecn Dev (*/.): 144 50 Std Dev. (*/.): t34 _
FIGURE 11.38 40- A -
20- -
2C- -
10 -
g I f f f f f f f f I f f 2 4 6 8 10 12 14 16 18 20 22 24 Axiol node no.
-- a i i i 6 i i . . i i i 70lL 60L -
50- -
FIGURE 11.39 40r -
30 - .Cese no.: 713. 040 A LWantal'dcto _
- Cc:culated 20- --
10 - Mean Dev. (*/.):-1.97 .
Std. Dev. (*/.): 179 0
=2 4 6 8 10 12 14 16 18 20 22 24 Axial node no.
Comparison of Calculated and Measured Axial Void Distributions 1
11-38 90 g g
g g ; ; g ,
m .
80 -
s
- 70 -
60 - **' -
g+: .
50 -
lr' p.
40 -
.+.
30 -
.. > 2 20 . -
.g . .
10 -
- p. .
__. I I I I I I I i 10 20 30 40 50 60 70 80 g 90 FIGURE 11.40 Correlation Between Calculated and Measured Void 1
11-39 1 OCTANT aos 447 es2 S12 i476 DOUNDARY 2 178 306 176 453 459 487 2 251 222 292 74 3 75 545 477 440 446 4 27 413 49 278 181 376 172 314 180 S43 491 S14 5 37s all 321 139 277 149 274 s9 29s las 243 507 5 23 257 138 279 179 361 194 339 7 233 213 359 21a 330 66 332 30
~ n s 5 169 373 220 420 211 333 197 7 310
( E )
9 393 141, 3os 165 43s 53 256 190 10 e6 391 IS6 422 11 405 137 402 145 l
12 170 404 76 143 323 126 425 13 397 104 387 29 304 3S 14 15 15 de 243 17 352 591 18 121 235 19 242 216 20 21 22 23 24 25 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 m
u EUNDLES DISASSEMSLED FOR ROD SCANNING 9 TIP LOCATIONS MXanet SUNDLE IDENTIFICATION g FIGURE 11.41 Gamma Scanned Bundles
11-40 L
1.5 --
Process computer
/e\ -----
PRESTO (March 1982)
/
- /
f N
\
1.0 -
/ 3 1 %
/
~_ -
s
\
/
\
/ \
-f \
0.5 -
4
\
. . . . l . . . . l . . . . l . . . . l . . . . l NODE 5 10 15 20 25' Core Average Axial Power Distribution on 4 July 1975 at 1984 MWD /TU n
1.5 -
= Process computer
~ N
PRESTO (Ma rch 1982)
\
% 'r\
1.0 -
N .- -
. N - "__ \
)
~
~ \
0.5 -
\
~
\
\
. . . 1 . . i i NODE
. . . 1 . . . . . . . . . ..I 5 10 15 20 25 4 FIGURE 11.42 Core Average Axial Power Distribution on 26 August 1975 at 2584 MWD /TU
11-41 1.5 -
= Process computer
. l -----
/ PRESTO (March 1982)
N
_ \
\
1.0 -
NN I,
N - w N
\
I,
. \
~
\
\
0.5 -
~
\
e i i i I i . . i I , . . , t , , , , t , , ,, ; NODE 5 10 15 20 25 Core Average Axial Power Distribution on 24 October 1975 at 3646 MWD /TU
= Process computer 1.5 -
PRESTO (Ma rch 1982)
. \
. \
/
1.0 -
g
\i
/
. /
/
/
f 0.5 - /
/ \
N0DE
= . - . l . . . i I . . . . I . , , , l , ,,,l 5 10 15 20 25 FIGURE 11.43 Core Average Axial Power Distribution on 7 March 1977 at 10 311 MWD /TU
11-42 (
g i i I e i i I 6 i 1.01 -
PLUGGING OF CCPE SUPPORT PLATE -
/ cr= 0.00246 ,
1 1.00 -. .
l . . ,
s l . .
.99 - -
CCRE << ,s AVERAGEIII
VOID 46 -
y 44 - -
42 a
40 ,
38 _ p m - -
36 -
34 - -
32 - -
30 - -
e' e s
<< ,. s POWER (%)
100 90
% y-80 1 70 - -
60 - -
50 - -
e* ,s CONTROL (%) e s c' DENSITY 20 - -
IS -
16 - -
14 -
12 - -
10 l J
8 _
1 I I I I I I I I 1000 2CCO 3C00 'C00 5000 6000 7000 8C00 9000 10000 11000 ACCU. M ULATED CORE EXPOSURE (PaDAU)
FIGURE 11.44 Calculated k pff and Core Average Void Fraction vs. Core Average Exposure through Cycle 1. Power Level and Control Density also shown
..m...__
. .ma. .m. . . . ... ......m.._.......... ..
.........m_...............
l l
y ,. .
-.~. .
/ '
N(, /,.~.'Q/ ],/. . . . _ __
/7
~
.b N
/
h x
. i
,A I
[ ,> :, , / \.
j .._.. _ w.__
,. 3 .% .__
,m 7 1
s(/ /
J.
.f. x. .,
E
/ (14) .*/ .
.- ( ,/ \
g ..__ _ _ <;
..__- - f, ._.'. . __ , __ _ .___
y
- 1 (/ *
\.
c, . - .\ f . N,-
t _._
\
I i
(8),
1
.e <
- 4. c
/ <, ,
(10).
i
- \
__ .._ .__ ~ _._
j r
, \.
\*
s y'
\
l
.f. <
f
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.p,<"
... ~
s a . _. e, ,, , . - . , . . _ x' .~ .
.x ..._ ._ ,n _
-i .
. .f .x. i g x.
\ / -
r.
g3 i
./y- .7 4
\
..s .
(17)v
][ -
~ . .,, .j . .- x 1. . J
.#' 'sj ..- 's, -
,/
1.,6. / p ...
1 4..
'\, k
- m. -
\a) y
/, ,,,
l .l p e .
j . . _ . . r . . _ _
, . . ~. ' s..
. 1 .
'\
_ y'~%
s ... . a .
, , . ~ y .7
. < g. - %. .. ! b.,.'a
/. \; /-
(7) -
t
,_. ;.__ ..__ ._. .__ . ,,1
...._./ ' N. *:
,7 . >-. N. .
N,.g . G , , ". i' e ' iae g .
,.,-. e -
3
?!
's
\.. 4 I
\j s4 _ .
l CALCUL
-2_ . -
s j s .
4* \ ._ u - g'
-/ . .
, \ . g. > ' .
x HEASUR
~p
/ (17)
_ . - - l
. ~ .. _ _
- . ,c . ,..; s, . . .
- e. .. . . .
l Q ~ _./' ;
',./ y
/* . g"' *' '
. y.
- n
, i
. . a. . . n. ,,~.. ....
. ce .
- s. . .
N *M' h
- ,/ . - - \
' \
'l -
FIGURE 11.4 5 Comparison of Calcul n W u-1. For' ' ne C
-s 11-13
.. ..e O . g a.va. , eu., ases t e e l.4e. me .C i n s.- . e..e ase s, m; e. . saa o se e.. ..e o..eesee.
.-- l ;-- ..
. _ _ 1-.-. - . . ,
. .f
.........e. - . . . . . .
jr. .-- .
6 \ a y' Nr,[ \,f' 4
Nr' . . . . . .
\
. i o s.i ..*ui
, y .7" i
. , .t t
.-- m..i ie xu, g/,~.\ ep N, v . ./ .
v s ..- N
\
l e . .. .. .. , i , , . m i.
fx '
j.. .--
\;
/ .J /
\
,/ \
\ w T .,
(15) e[
, o. .. ..
Nodes inserted g
al AL o(Icat t.00 E 51
\,
s.
43CT Aatt i ... ... ... ... ...i _ ,,,
-~ ,_ .n .. ,l
... - i,. ...
... u, .., ,. . . . m ... . .
,, ... .. ,,. ... ... m u. ... ..n n.
,,. ,,, .., ... ,,, ... ... .. ... .n . . . ...
,, .., n. ,,, n. n. . ...
... .n ... n. ... .. m ..
'. ..in g u. ... .n n. .., , ...
'...i..'... ... . . . ' .. ... ...
TED PRESTO .., . . . .., ...
.... .. ... n. n. .n 0 ... . ..,j , .. n i
STANDARD DEVIATICN
- Controlled Nodes . 6.4% ( 182 Points)
- Uncontrolled Nodes : 6.5% ( B2B Points)
- TOTAL : 6.4% (1010 Points)
~,
,ted and Measured Ax ai l La-140 Distributiens for all Bundles in Benchmark Octant, 1~el eed by FMP - PD P P'"o . _ _ _
11-44
[ AXIAL LA-140 INTENSITY HATCH-1 E00-1 g - .a - ,. ,. ..... ,
m . _ ,.
W
- z. 8-2 o -
w gM io
< 9~ '
lo '
Ltl -
~o ..
1- o
<C
- I I I I I I I
_i 0.00 6.00 12 00 18.00 24 00
$ AXIAL HEIGHT (NODES)
- AXIAL LA-140 INTENSITY HATCH-1 E00-1 m - anemursopasare g
g'M LLI i_ o z.
a maines sacaro
.. - K o - ,
- 4 .
i o .!
< 9- 3
_i o ,
y _ -
1 s.
~o wo .
I I I I I i i I 1 0.00 6.00 12 00 18 00 24 00 to cc AXIAL HEIGHT (NODES) l FIGURE 11.46 Comparisons for Bundles 278 and 279, both with 27 Measured Points m
j
11-45 I-
- AXIAL LA-140 INTENSITY HATCH-1 EOC-1 m -
- ^'**^'E8 8'8 Z
LL) . nEAsunED arise -
I- @ _ ,-
- z. ,M
~~
gM M o _
w i o
<w-
_J o ,
w _
o t- o
<d J i I I I I i l w
0.00 6.00 12.00 18.00 24.00 m AXIAL HEIGHT (NODES)
FIGURE 11.47 Comparison for Bendle 169, 24 Measured Points
_. AXIAL LA-140 INTENSITY HATCH-1 EOC-1 m
--; - CALCULATED PRESTO llI a f1EASURED tX373 t- O z 9-O -
a y
<w- x
' M w"M w -
M
> M o
o I
F--
-J i i l i I i 1 0.00 6.00 12.00 18.00 24 00 w
m AXIAL HEIGHT (NODES)
[ FIGURE 11.48 Comparison for Bundle 373, 27 Measured Points
11-46 F-
~ AXIAL LA-140 INTENSITY HATCH-1 EOC-1 U) 7 caca4rto ratsro bJ . ntasunto nxiii ME H
2 S- . M M
m-
%y%%M o -
v g a
<m- x*M Jo LU -
Ho wa
<d J
i i i i i i 0.00 6.00 12.00 18.00 24.00 tu e AXIAL HElGHT (NODES)
FIGURE 11.49 Comparison for Bundle 141, 24 Measured Points I--
AX1AL LA-140 INTENSITY HATCH-1 EOC-1 Cn Z - ****^rto entsro L1J , ec sunto nxses g 1--
z .
~-
o -
v
~
i o
< co -
-J # '
Lu -
- x*g
~o i- o
-.J i l i l i i 1 0.00 6.00 12.00 18.00 24 00 Lo e AXIAL HEIGHT (NODES)
FIGURE 11.50 Comparison for Bundle 393, 27 Measured Points
11-47 h-
- AXIAL LA-140 INTENSITY HATCH-1 EOC-1 Cn 7 - CALCULATED PnESTO ld g MAsunED HX233
+@_
z.
~-
y C - '
4 i o ,
< ~
,/
_J o -
LU -
Mi
~o F-- o
<C f I I I I I I I
-> 0.00 6.00 12 00 18 00 24.00 to cr AXIAL HEIGHT (NODES)
FIGURE 11.51 Example of Comparison for Unrodded Bundle F--
- AXIAL LA-140 INTENSITY HATCH-1 EOC-1 (n - cALcutArto Pngsro 7 ,
LU , m Asunto ax3se F- @ _
z.
M O -
9.
i o -
<m-
_-) o '
LU -
o F-- o
-J I I i l i i 1 0.00 6.00 12.00 18.00 24.00 to cr AXIAL HEIGHT (NODES)
FIGURE 11.52 Example of Comparison for Bundle with Deep Control Rod (Notch 14)
11-48 i-
~ AXIAL LA-140 IHTENSITY llATCH-1 E00-1 w
-, CALCt&ATED PAESTO g MAsumED 1084 1 3
'N t-O g- -
s.
~-
o _
1 o . . ,
< 9- .../*
._a o y _
mo -
i- o '
<C l i I I I I I I
.J[0.00 w
6.00 12 00 18.00 24 00 ,
cc AX1AL HEIGHT (NODES)
FIGURE 11.53 Example of Comparison for Bundle with Shallow Control Rod (Notch 32)
F--
- AX 1 AL_LAr4_4 0 INTENSITY HATCH-1 EOC-1 C.n 7 - CALCULATED PRESTO
[.1 ! g ftASURED HX467 1- O z 9-O -
w - ..
i o ,
<9^ ,
_J o s,
u3
-o -
I-- o
<C I I I i i i 1 J 0.00 6.00 12.00 18.00 24 00 us cr AXIAL HEIGHT (NODES)
FIGURE 11.54 Example of Comparison for Core Periphery Bundle
11-49
.988 .996 .995 1.015 1.032 1.003 1.001 1.022 1.011 1.020 1.099
.893 1.007. 1.019 1.000 .987 .997 1.011 .988 1.014 a <. )
1.005 1.039' 1.023 .979 1.004 1.005 1.014 .997 1.035 1.126 1.015 .996 .984 1.016 1.021 .992 .994 .997 .994 (10) 1.004 .994 .968 .993 1.014 .977 .985 .985
.981 1.030 .996 .960 .980 1.013 1.004 (17)
N NODES INSERTED
.980 1.032 1.022 .970 1.005 .989 1.015 .975 .990 1.013 1.017 (7) 1.008 .979 .970 .998 RODDED BUNDLES . 1.8% (22 BUNDLES)
UNRODDED BUNDLES : 2.7% (53 BUNDLES)
TOTAL : 2.5% (75 BUNDLES) 0.973 1.017 .987 (17) 1.005 1.003 Calculated / Measured 1.015 FIGURE 11.55 Bundlewise Ratios of Calculated and Measured, Axially Integrated, La-140 Distributions
11-50 l I i l l I Control Blade
( notch 14) j \
le -
l I
e 1500 -
O k
\
/' 9
/ '
\
- o I \
h1000 -
,,l s' l E I \
/
- o
- g\
t
/ I \ \
5 / o I
\\
- \\
- \\
f / '; \1 3 / \
I J 500 -
,/ j
/
j ,/
7
/ /-
/ - -- FMS-CALC y o NARROW-NARROW ROD
[ e WIDE-WIDE ROD l l 1 1 I I O
O 20 40 60 80 100 120 140 ELEVATION ABOVE BOTTOM OF ACTIVE FUEL (inches)
FIGURE 11.56 Calculated and Measured Axial La-140 Distributions in N-N and W-W Pins in HX-373
i 11-51 l l l l l l
/ \
Control Blade
/ \
( notch 34)
/ \
' \
/
/
' \
' \
^
h s' '-m \ \
- /
- f
\ \
!e _/
\ \
h1000 _.
/ __- \ g-
\
B I
/
/- \ \
g \ \
W 5 / \ \
/
/ \
\
\
\
A
/ ,, \ \
/
' \
/ l
\
500 /
' \
/
T
[
I I
/
/ ')I f
/ /,, ' / _
-- FMS-CALC o NARROW-NARROW ROD e WIDE-Wl0E ROD
/
I I I I I I 0
O 20 40 60 80 100 120 140 ELEVATION ABOVE BOTTOM OF ACTIVE FUEL (inches)
FIGURE 11.57 Calculated and Measured Axial La-140 Distributions in N-N ano W-W P1ns in HX-393.
11-52 2
~ - s.
a
=
_a -.
gE o
. _ - _ . ./
h
~ -
. o
\.
,L --. _
R
~
- ./" .S -
dE 1 ,#, iua
- u. A o
e 53 '[. ? E
= US o<-
3 o
o a --a. ; /./
- o
-ma- //
-./ -
3 1; ~ E :.
O
. -,/ x= .
! .. _ g -
1 -.. . _ . _
._.R
~
G ! -
E /
=
.; =.
=
g -
i i _--. _
'gl 8 = 88
- f -sI a .
8 'I. {, o / ?
o
.o ,
l 8 s
{ .o i
a
- 1 I =- >
=
. - < w ,- -
a - 4 Il g !/
n e I s ee i , o,_ 5
- ./ f e
-..-( f > c >,
a p _@ m. a ,
-.s ,
- i, -.g E
e E IAA -3 E 3 m _ . .
-I
\___ o
- e E._ -
I N .g' 5 [i .g I- (~-- Q } .
\, Ii 'y N- R R
.Ny_ _ _ _ _ _ .
,s.s. s,
- s. ' %,N' o . . o
? E 5 R 5 8 = ? 8 S R 8 =
-. s - - . * ~ ~ - - $. ..
.rusc mq amus aususo mq aaiime C
c; y 2
- . . E k
- o 3 m ) S e /.3 CM
_c2 // N _c2 // o A
/ gE b EE
.s
/ -@
.. f' -@
_u- f-
_um
. ~
-=
== l o
.. c "t o
=
oE
=g -
./ .?-
o -=g E #'j .?
m
=
E=
'/ { :. -
W
.s._ /
.i ,,,
s r n.
o a i R _
-l R s o a j
/ -
< L o
E a g U
' f */
E
=
_ $ ei d
o / .E 8
-- a 'd. . 8E_
H g
E
.] '
f
,Y I -} y O
a _ _ .
4 -
82< .? -I 81< 0 m - g a J I
g H o I } $2 *
- j 52 '
i f
5 - % .-
3 .
! 3E22
- n 1 $ 3 3 ;& -
bls '
bSb5
_-.s
\
$ N x--5f E
E
... .,... _ . s, N
' ' ~~ _ :* A --
a
-N,s g
.o
- - {
N
_o* c3
_ e.. --~ < g in
- s _
II =
4,+, e
-N s -R R
s s,-N. r.a g
- s. s. c a . . .
o m
? 8 3 $ 8 o 8 8 8 8 re.
- e. ~ - R_ = ?.
c ~ _ . E. *.
Atems0 *aao saanseiau AaM M mieloW
AXIAL PO'f:ER DE NSITY IN MUHLEBE RG AT SIS MWO/TU AXI AL POWL R (11 NSIIY IN MilHLI f!! HG AI 915 MWOITU 2 50 2 50
- CALCULATED POS 9 e CALCULATED P05.II a MEASURED a MEASURED 2 00-- 2 fx1- -
t '
1.50- - -
150- -
2 y **AV"% j I I 00-I a
J
/
N II00-
.5
,%,% w*
, y
.s,%*
0.50- *N - -
0 50-
\w g %'m --
,w 0 00: , , ,
,' ; , , 0 00 ; ! ! l l l l 0 00 3 00 6 00 9 00 12 00 15 00 18 00 2l00 24 00 0 00 3 00 6 00 9 00 17 0u 15 00 18 00 2l 00 14 00 Asial Height (Nodes) An.it flesqhe 41ed e-*
2 50- 2 50
- CALCULATED POS. 6
- CALCULATED POS 12 x MEASURED i MEASURE 0 2 00 - - -
2 00- -
N t
[ 1.50-- / 9,g - -
j 1.50 E
i / v. ~ ~ s ,
f
_-- 1.00 --
j 100-
/
[ - -
1 I
. j-0 50- .' -
0 50-
'*=g, --
.~*% ,N Om , , , , , , , ON l , l l l l ,
0 00 3 00 6 00 9 00 12 00 15 00 I 18 00 2l 00 24 00 0 00 3 00 6 00 9 00 12 00 15 00 18 00 21 00 24 03 Asial Height (Nodes) A o.it t te.qt. J,w i-u FIGURE 11.59 Examples of Comparisons of Measured and PRESTO Calculated TIP Traces (Control Rod Insertions in Adjacent Channels are Indicated.)
i
11-54 (Staa
% PRf 3fD Oo % PC-KIM 37
= 'XI IX
= l l 33 -
a 31 30 't!P 'e!i2 lEi!P l 28 l '
f l l
= l lfl l
^
!!!I:hNh'91X
=
M_ NP'91 l
,, 22_ 0 [ [' ((O [
=o
'OT6i"fi"H'81'# Tfl?? 'sfi!dhWI!# I ',
7 16 oN:tTlW
.% o I VI'!!Qtill'tifSiiW$l VI l {f f l
T X
,2 -
12 io i
W. f i
lh' e
IM,j:lP V1
,{:S I.l l IX 4
g= +
y o.
~
n oJ 0" X. '9"M -.
= X X os os os or os in I is I is I 17 I is I at 1 23 'l 2s 27 29 si sa ss 00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36 rX LEGENDE
. in-c .t... (LPWM) e m.........n..
A a.r.ne.. .
m z. .o ....... n . ... a O :-............ sa c, . . . e . . ...
FIGURE 11.60 Relative, Assemblywise Burnup Distribution at EOC-1 of KKM, as Measured by Y-scanning and Per cent Deviation of PRESTO Calculation and Process Computer Results i
11-55 as AXI AL AC ER CEP 5!TY. "S 2M3?7 AXI AL P04:4 CECSIM. KKE 29C377 3 .,
a t
- t . *'I r;t 6 23.21 *
. aau n ese.e -
3
- a. ga tasse;t a ate 3 .FC'.in E 3s. 7si 8 s
- 8-ed . .A. ,s 1.-
4% l
/ !
t,,.
e
/*
/#
d
,,N .D -*gi s
- x, s' .g
. 1
's-Nm._ %y% 'v b :
t ..
..if s, -
ii *s/ 'e :l L,' \,,.i .
ss- a,t' s; g , -
2
'p i
Et , , , , ee .
e a . e .: .. .: 3, 3 . . . e ,, ,s ,, ,, 3 SxA Ki>r acc, ngpt ,,c;y 1.,;x;,
AXIAL PCaER CENS!TY. MS 290377 . AXIAL PCWER CENSITY. KKS 290377 .
3s as a catCanta g *01 t**. 21 a setta ATE S '95 t e'.*F B
. casus: sie as
. acessoas 3., u
>e- 2. e -
> W ,
h*I -
a m
\ b e~-* N ' _ ,
h*5-m E X
. . . .l
, +
h
~
,- 'N e as-
- e,-g e
es , , , . , , t, , , , , , , ,
e a e e 3 .s .e 3, w a , e e ,, .s .. 3 >
9xi% Klet! (MS) px1% K!M l e s)
AXIAL' PC4ER CENSITY. kkS 290377 . AXIAL PCWER CEtiSITY. KK8 290377 .
I1 , 11 a Cattnett l F0% t
- 2.*Fs g a CattutATat POS (fe.IFf
. ut ASL*IC rir 27 . "CD5tagg t re 13 W_
I8- 7. 8 -
a s 11- t .1 -
~ a 33 E
os - ! 5 a.s -
,l 88 1
. . . . B8 , . . i . . ,
e a e e es is ..e 3, p. e a e o es as se 3 3.
Ax:at KI%f tes AxIA Wi>T tes AXIAL PCWER CENSITY. KKB 290377 . AXIAL PCWER CENSITY. KKS 290377
- 2. 5 21 .
a tas tumisc *0s s 2s.,r a cntcantag set i3%.,rs g
. =s a.J r3 f t p 25
. =tasacc fl* 2= g as- to-w w
'Q j .
- t. s -
y'8-18
(
s5- s.1 -
ae , . .
48 .
. i 6 e e e es 4 ee 3, w e a a e es is to as >
nx:q .Erc r( c s nx!A Kt v ( m s:
FIGURE 11.61 Example of TIP Comparison, BRUNSB TTEL (KKB) 3
11-56
, utric ac ca et%::v. vtto ex 1 rip str se.io-n ura exe On; ire. etc ex-7 f ra str is. o-ir
- <.;.<;;;is =>e'= - . cou ...e s si.s .
. . su.o E =
m 3 3 I 2 a
3 1 T -c. : -. . ~
= , s, '
. i e . n Axist 4t>f <=Ccits
.s .e 3 . e. .
e , ,,
414 t<!@t<=Ccits
., .e ,e ,,
AX:A #0.E4 Ot%tiv. NUCLIC 80C-7 f tp CET 19-10-17 MIAL PCWE2 Ot%It'. Ctc 500-7 T!p Ctr ig-eg-77 1 S
. s aumerce
. as eswege stes.s a .co.c eece sees.s .
. eses.ese 4 4 E E 5 3 3 I
, 1' I 2-i i E , E , g N
8 0 -
a a e t et 4 es
- P e 3 s t ~et n .e si -?=
ourcL sEtoer act cr:st i<to.f acts M!nt. FC42 Ot%tiv. PLCLiais B;c-7 f tp (Er og-te-17 MIAL FCwC2 Ci%!!*. noCLtc E;C-1 T!p SET 19-et 77
$ 1 sesi s s .resc. esce tres.s e
.. c.ssca ses ete sece .=w se g e-E E 3 3^
E - " ' k
,2- ,2 E- E-s , w, I t \
5 , ,
e . . . .
. e e e es es .e , w e s e e is es .e > >
anist itto.f tacctsa stata 6Ctst <=c:tt E!AL PCMR CE% TTY. MILEC BCC-7 f tp 5(T 19-to-17 414L PCwER OCNS!fv. MikC2 800-? f tp CET 19-90-17 1 5
. cesca erce steins a asee% e
. = =sveio .. css.em w s me e rc e g g .
E E
- 3 I 3 e a k ' ^
2 2 C T 5 E \
I , . . '. I, I
i 8!
s ,
s a e e se es *e ze m e a e s et *
- M sutre (t%: ts. g's;s a
.utrt i(gtw tcts:
FIGURE 11.62 Example of TIP Compariscns, Santa Maria de GaroEa (NUCLENOR) i
11-57 i
l l t
. l
= = - - = -. . = - . . = - .
, l i
L
/
t
- = . -
i i i n 8 '
' a A hl .&
@ ,c/M 3 0.98 @ 1.00 @ 1.03 @ 1.00
- = -. := - . = . - .
\
~
~
I i a 3 g g 1 g g a g 9 I e lE I A E 1
,s 1%
- st s= 1 s,
@ 1.00 @ 1.01 @ !0.98
- = -I :=.:;- - -
i
(%
= __
m f I g a 1 A i E I i i I 1
- = . .. . s u o e ::
@ 0.96 @ 1.04 h1.03 ^
/ QURO cif!C UNIT 2. TIP SET 01-03-73
\
. p.g= m...
s.-
E
}..-
g I
g .. . .
C/M = Arec under cciculated curve j ,,
Arec under mecsured curve -
- tt% 4tDat escorse FIGURE 11.63 Evaluation of Calculated Power Distributions. Comparisons with TIP-Traces, BOC-1, Quad Cities-2
i 11-58 I
l t I l I
.; = .
.= .
~~~--"4=. l
.- ! l c-% .m
,y . .
/
.., .. N
~
4: -
t
@.CM= 1.05 @ ,0.98 @ 0.98 @
i I
...= .- -
p% &# ,[ %s
'\. -
._ \
> i , . . . , , , , ,
e n ..e e a n .~ . s . . a e a u n . , , , a e e n n
@ 1.05 @ 1.00 @ iO.98 I
- F=- - W' ::= --
'm t./
g .
^ ~ . -f%
..- - - -. _2 * %.s i i , , , .
. s .
- a e e a a . i . , e e a n a
@ 0.96- @ 0.99 @[ 1.00
/ \
Qu810 CITIES UNIT 2. I1P SET 07-17-75.
Es
. ;; .g . . . .
s..
E 3 ... .
I i
!s ...... ./
C/M = Area under cciculated curve Area under mecsured curve
\
Mlet 41Det 8810K51 FIGURE 11.64 Evaluation of Calculated Power Distributions. Comparisons with TIP-Traces, BOC-2, Quad Cities-2 1
12-1
- 12. REFERENCES
- 1. S. Berresen, "A Simplified, Coarse-Mesh, Three-Dimensional Diffusica Scheme for Calculating the Gross Power Distribution in a Boiling Water Reactor", NSE 44, 37-43 (1971).
- 2. P. Backstad, K.O. Solberg, "A Model for the Dynamics of Nuclear
' Reactors with Boiling Coolant with a New Approach to the Vapour Generating Process". KR-121, Kjeller, Norway, August 1967.
- 3. Argonne Code Center, " Benchmark Problem Book", ANL-7416, Suppl. 2, ANL (1977).
- 4. O. Nylund, et al, Confidential FRIGG reports on experiments and results (1969, 1970).
- 5. O. Nylund, K.M. Becker, et al, "FRIGG Loop Project. Hydrodynamic and Heat Transfer Measurements on a Full Scale, 36 Rod BHWR Fuel Element". Sweden 1970.
- 6. R. Holt, J. Rasmussen, "RAMONA-II, A FORTRAN Code for Transient Analysis of Boiling Water Reactors". KR-147, Kjeller, Norway, 1
August 1972.
- 7. L. Moberg, et al, "RAMONA Analysis of the Peach Bottom-2 Turbine i Trip Transients". EPRI NP-1869, June 1981.
- 8. K. Becker, G. Hernborg and M. Bode, "An Experimental Study of Pressure Gradients for Flcw of Boiling Water in a Vertical Round Duct". Parts 1, 2 and 3, AE-69, 70 and 85, Aktiebolaget Atomenergi, Sweden, 1962.
- 9. R.T. Lahey, F.J. Moody, "The Thermal-Hydraulics of a Boiling Water l
Nuclear Reactor". Published by American Nuclear Society, 1977.
l
12-2
- 10. K.E. Karcher, " MERLIN - A Two-Group Three-Dimensional BWR Nodal Simulator with Thermal Hydraulic Feedback", Carolina Power & Light Company, Internal Report, December 1979.
- 11. N.H. Larsen, J.G. Goudey, " Core Design and Operating Data for Cycle 1 of HATCH-1", EPRI NP-562, 1979.
- 12. L.M. Shiraishi, G.R. Parkos, " Gamma Scan Measurements at Edwin I.
Hatch Nuclear Plant, Unit 1, Following Cycle 1", EPRI NP-511, Research Project 130-3, Final Report, August 1978.
- 13. S. Borresen, T. Skardhamar, S. Wennemo-Hanssen, " Applications of FMS RECORD / PRESTO for Analysis and Simulation of Operating LWR Cores", NEA Specialists Meeting Proceedings, Paris, November 1979.
- 14. J. Nitteberg, J. Haugen, J. Rasmussen, T.O. Sauar, "A Core-Follow Study of the Dodewaard Reactor with the Three-Dimensional BWR Simulator PRESTO", Kjeller Report, KR-145, 1971.
- 15. S. Borresen, H.K. Nass, T.O. Sauar, T. Skardhamar, F. Grandchamp, J. Rognon, R. Wehrli, C. Weigel, " Core-Follow Study of the MGhleberg BWR with the Fuel Management System - FMS", ENC, Paris, April 1975.
- 16. W. Wiest, H. Hofner, N. Naula, C. Weigel, R. Wehrli, " Gamma-Scanning in KKM und dessen Anwendung bei der Reaktorsimulation", presented at Reaktortagung 1978, Deutsches Atomforum e.V. , Hannover, 1978.
- 17. H. Guyer, H. von Fellenberg, W. Wiest, " Core Simulation and Its Experimental Verification of the Mdhleberg BWR", ENC, 1979, Hamburg, TANSAI 31, 1979.
- 18. S. Bcrresen, D.L. Pomeroy, E. Rolstad, T.O. Sauar, " Nuclear Fuel Performance Evaluation", EPRI NP-409, Final Report, June 1977.
- 19. S. Bcrresen, " Experience, Status and Advanced Applications of PRESTO", ANS/ ENS Topical Meeting Proceedings, Munich, April 1981.
APPENDIX A EQUATIONS FOR INTEGRATION OF SPECIAL ISOTOPES
)
A-1.1 A1. Xe-DYNAMICS EQUATIONS The equations used in PRESTO to calculate the nodal concentrations of I and Xe at the end of a time step t, starting from the kr.own concentra-tiens at the beginning of the time step, are given below :
The differential equation for the I concentration is :
=-A 7 I+Y 7 F (A.1) and Y
r I
eq
=
A F (A.2) where I = local I- concentration (cm-3)
A = decay constant for I (sec-1)
Y = fission yield fraction for I 7
F = local fission rate (sec cm-3)
I = local,. equilibrium I- concentration (cm-3)
The differential equation for the Xe concentration is :
=-A X-0 -
$2
- X+A I+y F (A.3) and X =
(Yx +YI )F (A.4) eq A +c C2
)
A-1.2 where X = local Xe concentrations (cm-3)
A = decay constant for Xe (sec-1) 0 = effective, local microscopic absorption cross-section 2
for Xe (cm )
$2 = local average thermal flux (cm 2 - sec -1)
X = local, equilibrium Xe concentration (cm 3)
The fission rate is obtained from the local power density 1
l F= - - - P (A.5) f where P = local power density (wacm-3)
E = energy release per fission (wsec)
Equations A.1 and A.3 are integrated analytically through a time step At, assuming constant fission rate (F) , thermal flux ($2) and Xe cross-section (c ) through the time step :
l Y
-A at 77 r r I(t+At) =
I(t) - )--I F e F (A 6)
+yI
- ~
-(A +c $2)Lt l
X ( t+At) =
X (t) - R1 - R2 e i (A.7) l -A at
- + R1 e +R2 1
A-1.3 where A *I(t) F I I
=
R1 (A,8)
A -A +0 &2 YY x 7 R2 - .p (A,g)
_ A +0 @2
A-2.1 A2. EQUATIONS FOR INTEGRATION OF THE Pr - Sm CHAIN The Pr-149 + Sm-149 chain is integrated through each time step under the assumption of constant power and thermal flux through the step :
_A .At" Pr" = Pr -
- e + *
(A-10)
Pr f_ Pr f n+1 n
~
2 -A Sm Pr Sm = Sm -R1-R2 e +R1e +R2 a (A-II)
Pr
- r -Y Pr R1
=
c (A-12)
Sm' 2-A Pr R2
' b (A-13) 03,*@2 E g
where Pr = Average concentration per fuel type of Pr-149 at the beginning of time step n Sm" = Corresponding for Sm-149 yp = Fission yield of Pr-149 Ap = Decay constant of Pr-149 og = Effective thermal group microscopic absorption cross-section for Sm-149 1
A-2.2 E = Energy release per fission f
P = Average power density for fuel type
= Average thermal flux per fuel type
$2 The equilibrium concentration of Sm-149 (at- ) is :
Sm" =R2 (A-14)
If power is zero through the time step at", the following relations are used :
Sm"+ = Sm" + Pr" 1 - e (A-15)
Su"W = Sm + Pr (A-16)
The influence of the Sm-149 concentration on the nodal cross-sections is described in 54.4. .
A-301 A3. EQUATIONS FOR INTEGRATION OF Y-SCAN ISOTOPES The y-scan isotopes are integrated as follows :
~ '
-Aat N+ = P" + "
A .
N-A P e (A-17) where p" = S_n ..p rel ,g) r Q
N+ =
Isotope concentration (arbitrary units)'at end of time step n ,
N =
Isotope concentration at beginning of time step n Q" =
Reactor thermal power (w) through time step n Q = Reactor thermal power - rated condition P = Nodal relative power Y (E) =
Effective fission yield at the nodal burnup E, calculated from polynomial expansions of tabular data A =
Decay constant of isotope considered (day-1)
At = Length of time step n, (days) r
-