ML19341A235
| ML19341A235 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 12/31/1980 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
| To: | |
| Shared Package | |
| ML19260G483 | List: |
| References | |
| CEN-143(A)-NP, NUDOCS 8101220417 | |
| Download: ML19341A235 (109) | |
Text
,. _.. _ _.
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ARKANSAS NUCLEAR ONE - UNIT 2 DOCKET 50-368 i
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CEN-143(A)-NP i
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i CPC/CEAC SOFTWARE MODIFICATIONS FOR ARKANSAS NUCLEAR ONE-UNIT 2 i
DECEMBER 1980 1
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COMBUSTION ENGINEERING, INC.
1 NUCLEAR POWER SYSTEMS POWER SYSTEMS GROUP l
WINDSOR, CONNECTICUT 06095 g/o/2204r/7
TABLE OF C0tlTENTS 1
~
SECTION TITLE PAGE
1.0 INTRODUCTION
1-1 1.1 Report Scope 1-1 l.2 Report Summary 1-2 1.3 References for Section 1.0 1-3 2.0 CPC SOFTWARE MODIFICATI0t!S 2-1 2.1 DNBR Calculation 2-1 2.2 Generic Software Changes 2-4 2.3 Addressable Constants 2-9 2.4 Other Algorithm Changes 2-18 2.5 Diagnostic Changes 2-25 2.6 Data Constant Changes 2-27 l
2.7 References for Section 2.0 2-28 LIST OF APPENDICES APPENDIX TITLE PAGE A
Design Thermal Margin Model CETOP A-1 B-1 CETOP2 Functional Description B-1
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B-2 Accuracy Assessment of CETOP2
- B-45 Algorithm C
CPC DN3R and Quality Update C-1 Program D
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TABLE OF CONTENTS CONTINUED
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LIST OF FIGURES FIGURE TITLE PAGE 2-1 Schematic of Primary System Showing 2-29 Approximate Location of Temperature Sensors 2-2 Partition for Application of Addressabl'e 2-30 Multipliers for Planar Radials and Rod Shadowing Factors 2-31 2-3 2-32 2-4 A-1 A Typical Channel Layout of CETOP Design A-7 Model A-2 Core Wide (1st Stage) of Detailed TORC A-8 Model A-3 Intermediate (2nd Stage) of TORC Model A-9 A-4 Subchannel (3rd Stage) of TORC Model A-10 A-5 Axial Power Distributions A-ll A-6 Inlet Flow Distribution for TORC Model A-12 (Four Pump Operation)
A-7 Exit Pressure Distributicn for TORC A-13 Model (Four Pump Operation)
B-1 CETOP2 Algorithm Flow B-3 e
=-m 111
TABLE OF CONTENTS CONTANUED LIST OF TABLES TABLE TITLE PAGE 1
A-1 Comparisons Between Detailed TORC A-6 and CETOP B-1 Genefic Constants B-35 B-2 Plant-Specific Constants for B-41 ANO-2 Cycle 2 1
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1.0 INTRODUCTION
1.1 Report Scope The Core Protection Calculator (CPC) System developed by Combustion i
Engineering is a digital system which calculates the minimum Departure from Nucleate Boiling Ratio (DNBR) and the peak local power density (LPD) on-line and generates a reactor trip if either the minimum DNBR gr the peak LPD approaches the Specified Acceptable Fuel Design Cimit (SAFDL).
Arkansas Nuclear One Unit 2 (ANO-2), which employs the CPC System, received its operating license in 1978 after a substantial review of the CPC System by the NRC.
After ANO-2 received its operating license and during its first fuel cycle, two sets of software changes were made to the CPC System in accordance with the NRC-approved CPC software change procedure (References 1 and 2) and implemented at ANO-2.
The CPC software for the ANO-2 second fuel cycle contains additional functional design changes.
This report presents these changes to the latest ANO-2 Cycle 1 CPC software.
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1.2 Report Summary Modifications made to the CPC/CEAC software for ANO-2 Cycle 2 fall into three general categories: (1) those due to the implementation of an improved 0.1BR calculation, (2) those resulting from operating experience gained during ANO-2 Cycle 1, and (3) those providing improved diagnostic capabilities to the operator.
Changes in the first category consist of implementation of the new DNBR algorithm CETOP2 and a revision of the DNBR update algorithm based on CETOP2.
Changes in the second category consist of increasing the number of addressable constants and of applying the pump-de-pendent uncertainty on LPD in the UPDATE program rather than the Trip Sequence program.
Changes in the third category include modification of the CEAC snapshot buffer in order to increase the flexibility to retain the cause of a trip condition.
The general format used in describing each software modification contained in this report is a statement of the change, the reason for the change, and a detailed description of the change including algorithm descriptions in symbolic algebra.
In addition to this, appendices are included to provide a discussion of the design thermal margin model,CETOP,and detailed functional descriptions of the new DNBR t
\\
algorithm (CETOP2) and the revised DNBR update calculation based l
l on CETOP2.
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i 1.3 References for Section 1.0
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1.
CEN-39(A)-P, Revision 02, The CPC Protection Algorithm Software Change Procedure, December 21, 1978.
2.
CEN-39(A)-P Supplement 1-P, Revision 01, January 5,1979.
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J 2.0 CPC SOFTWARE MODIFICATIONS 2.1 DNBR Calculation l.) Change:
The COSM0/W-3 based DNBR calculation in the STATIC program is replaced with CETOP2 based on the TORC /CE-1 DNBR calculation.
Reason:
The TORC /CE-1 DNBR calculation is based on the TORC code, which has been described in Reference 1.
Use of the TORC /CE-1 calculation is being implemented for most of the C-E operating plants, has already been used in safety analyses for the post-ANO-2 plants, and is being used for the ANO-2 Cycle 2 safety analysis.
Therefore, replacing the COSM0/W-3 based DNBRcalculation with the TORC /CE-1 based DNBR calculation (CETOP2) in the ANO-2 software will be consistent with the Cycle 2 safety analysis and will maintain commonality of software with post-ANO-2 C-E plants.
==
Description:==
Appendix A discusses the design thermal margin model CETOP,which is based on TORC /CE-1.
Appendix B-1 describes the CETOP2 DNERalgorithm, and Appendix B-2 presents the accuracy assessment of the CETOP2 algorithm.
2.) Change:
The DNBR update calculation in the UPDATE program has been replaced with a DNBR update calculation which is based on the TORC /CE-1 DNBR calculation (CETOP2) being implemented in the STATIC program.
Reason:
This change makes the DNBR update calculation consistent with the TORC /CE-l DNBR calculation (CETOP2) being implemented in the STATIC program.
==
Description:==
Appendix C describes the revised DNBR update calculation.
3.) Change:
New curve fits have been made for determining the core coolant enthalpy/ temperature ratio.
Reason:
In order to incorporate the TORC /CE-1 calculation into the CPC software, the complete STATIC DNBR program was replaced.
A portion of the ANO-2 Cycle 1 STATIC DNBR program calculates the enthalpy-temperature ratios.
In designing the new STATIC program, pressure and temperature curve fits were developed for calculating the liquid properties 1
required for the TORC /CE-1 DNBR calculation.
The methods used yielded coefficients which calculated properties more closely approximating the 1967 ASME Steam Table values.
The same methods were utilized -
to determine constants for new pressure-temperature curve fits for the enthalpy-temperature ratios that are consistent with those used for the liquid pro-perties.
2-1
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==
Description:==
The hot and cold leg enthalpy-temperature ratio computations are performed in the Static Thermal Power Calculation ( a portion of the STATIC ONBR program).
The new curve fits are based upon improved curve fit coefficient values.
In the previous design, the curve _ fits were per-formed for enthalpy rather than the enthalpy-temperature (H/T) ratio and the H/T ratio was obtained by dividing the calculated enthalpy by the temperature.
_The. implemented curve fit fot tilg H/T ratio is order in temperature and _ ] order in pressure.
The curve fit has been designed to provide accurate values of the enthalpy-temperature for the following rances of temperature and pressure:
5Temperaturef
_psiadPressureiP)6, If the hot leg temperature is within of the saturation temperature, the CPC will initiate the currently imple-mented hot leg saturation trip.
The curve fits for HfT -ratios versus temperature and pressure are given as:
INI
- IN2 l
COUT1=
COUT2" where:
l i
1
and where: PST = static value of pressurizer pressure, psia T
= hot leg temperatures in hot h1' legs 1 and 2, respectively, aF Th2 C IN1 enthalpy-temperature ratio
=
of water i Btu /lbm g cold legs IA and IB.
F C
enthalpy-temperature ratio of
=
IN2 water in cgld legs 2A and 28, BTU /lbm - F C
enthalpy-temperature ratio o water in hot leg 1. BTU /lbm f
=
OUT1 F
C enthalpy-temperature ratio o water in hot leg 2. BTU /lbm-{F
=
OUT2 pressure dependent coefficients HTR
=
gd used to determine e_nthalpy temperature ratios (See Figure 2-1 for coolan-leg designations)
The values of curve fit coefficients are given below:
HTb0 HTR 10 HTk0 HTR 30 HTR 01 HTRig. =
HT 3
HTR31 "_
Maximum absolutf error of gurve fit =
BTU /lbm - F Maximum percent error of curve fit =
These errors are applicable over the allowable range.
2.2 Generic Software Changes 1.) Change:
The pump-dependent uncertainty on local power density (LPD) is applied in the DNBR and LPD Update (UPDATE) program instead of the Trip Sequence program.
Reason:
In the previous design,the pump-dependent uncertainty on LPD was applied in the Trip Sequence program. As a result, the LPD margin provided to the CPC operator's module and to the analog LPD margin meter had not included this uncertainty.
The uncertainty was used, however, in the trip decision logic.
This change in the present design will include the uncertainty in the LPD margin to the CPC operator.'s module and the analog LPD meters with less than four pumps running.
==
Description:==
The LPD value to be used in the trip decision is multi-plied by the pump-dependent uncertainty factor in the UPDATE rather than the Trip Sequence program.
This factor is based upon the number of pumps operating above a pre-specified speed as determined in the Primary Coolant Mass Flow (FLOW) program.
In the previous design, the local power density margin is calculated in the UPDATE program as:
LPDT " EPD0' ERR 3 PDMAR DA3(LPDSP ~ LPDT}
where L
= the maximum compensated local power density PD0 B
= an addressable local power density ERR 3 uncertainty factor LPDT the LPD used in the trip decision
=
L
= the LPD trip setpoint PDSP K
= a a DA3 r scaHng UD fy D/A conversion L
=
e ca pwr ens hy margin M PDMAR output to a D/A converter
In the Trip Sequence Program, the LPD trip contact output is set if F2*LPDT 4 PDSP and the LPD pre-trip contact output is set if F2*LPDT 4C2 where F
= A pump-dependent uncertainty factor 2
C
= LPD pre-trip setpoint 2
Thus, the value of F2 was not factored into the calculation of local power density margin.
Since F equals 1.0 with four reactor coolant pumps running.
2L ngo was correct with four pumps running. With plen Ehan four pumps running, the value of F, may not equal 1 and therefore the indicated margin to trip may be incorrect. Since part-loop operation is not allowed by the ANO-2 Cycle 1 Technical Specifica-tions, there is no impact on ANO-2 Cycle 1 opc: stion.
However, the CPC design is being modified at this time in the event Technical Specifications for future cycles
( ANO-2 or other plants) allow part-loop operation.
In the new CPC design the pump-dependent uncertainty factor F is applied in the UPDATE program.
The value 2
of L is calculated as PDT L
"EPD0. BERR 3. F2 PDT In the Trip Sequence program the LPD trip contact is set if EPDT>lPDSP and the LPD pretrip contact is set if EPDT>C2 l
b3
2.) Change:
Some fixed numbers in the POWER calculation have been changed to Data Base constants.
Several fixed numbers in the POWER calculation Reascn:
were based upon ANO-2 design and Cycle 1 conditions.
Changing these numbers to Data Base constants makes the POWER calculatien in the CPC software generic; and therefore, future chcr.gc: to these numbers due to plant specific designs will not(require changes ),
to the CPC Functional Descriptien 1.e., algorithms
==
Description:==
The fixed numbers which have been changed to data base constants are:
a) b)
Three data base constants have also been added to the calculation of the final corrected ex-core detector signals to correct for the fractional amplitude of each detector signal (Ampm, Agp), and Ampu}-
Following is a list of new Data Bas.e constants, their previous fixed values and their definitions:
Data Base previous Constant __
Fixed Value Definition PMINU PHIN1.
A,p, A,p) l
'A l
mpu
- PWR, t
0
PWRU1 PWRU2 N1 PWRL2 3.) Change The Control Element Assembly Calculator (CEAC) logic has been modified to allow for a two (2) CEA subgroup.
Reason:
The CE 3410 Nt plants have one 2-CEA subgroup.
The CEA's in the 2-CEA subgroup are not assigned to a specific core quadrant.
A CEA core quadrant deviation counter is incremented for each CEA deviation in a core quadrant, and if this number exceeds a pre-specified number of deviations, the CEAC failed sensor flag is set.
The tEAC logic is modified to bypass the core quadrant deviation counter for a CEA deviation in the 2-CEA subgroup. Since ANO-2 does not have a 2-CEA subgroup, this change will have nu impact on the ANO-2 CPCS.
However, it has been added to the ANO-2 software with the intent of establishing a common set of software with Post-ANO-2 plants.
==
Description:==
For a CEA deviation within the 2-CEA subgroup the CEA at the more withdrawn position is arbitrarily considered to be the deviating CEA.
The CEA at the lower position defines the subgroup position.
The existing logic results in a CASE =+1 type deviation in the 2-CEA subgroup. But the CEA's in the 2-CEA subgroup are not assigned to any quadrant and deviating CEA's within this subgroup should not be in the core quadrant deviation counts.
Thus, the present design is such that the CEA deviation quadrant counter is incremented when CASE =+1 only in N
/2.(whereNCEA= nunber of CEA's in subgroup).
CEA em
4.)
Change:
The update period for the CE.iC CRT display has been changed to 3.0 seconds.
Reason:
The update period of the CEAC CRT display for the '
ANO-2 Cycle 1 software is 2.0 seconds.
For post-ANO-2 plants, which have more CEAs then ANO-2, the 2.0 second update period will not provide enough time to redrite the entire CEAC display for certain CEA configuraticns.
Therefore, the display update time is being lengthened.
This change is included in the ANO-2 software with the intent of establishing a common set of software, and will not impact AN0-2 operations.
==
Description:==
This update consists of a fixed algorithm scheduling rate, which will be no greater than 3.0 seconds.
A 5.) Change:
The CPC Point ID table has been revised.
Reason:
Modifying the ANO-2 CPC design requires revision to the Point ID table.
The Point ID table is an array of significant parameters stored by the CPC programs, which include system inputs, addressable constants and selected calculated variables.
These parameters can be displayed on the CPC operators module on the plant control board. Replacing tne COSM0/W-3 based DNBR calculation with CETOP2 requires that variables associated with the former DNBR calculation be replaced by variables which are being calculated in both the modified STATIC and UPDATE CNBR programs.
Expanding' the addressable constants will also require changing the Point ID table.
The Point ID table is revised a) to include's,sw l
==
Description:==
n variables resulting from changes to the CPC b) to delete variables from the table which are no longer calculated or which provide needless infor-mation, c) to group together frequently used and recorded variables for ease in operator call-up.
- m
' 2. 3 Addressable Constants p
1.)
Change:
Addressable constants have been added for:
a)
CEA shadowing factor adjustments.
b) planar radial peaking factor adjustments, and c) boundary point power correlation coefficients (B
}I PPCC The application of these cefficients has also been simplified.
Reason:
The ANO-2 Cycle 1 CPC design included addressable constants capable of adjusting CEA shadowing factors and planar radial peaking factors, based on field measurements for different CEA configurations.
In general, each constant adjusts the CEA shadowing factors or the planar radial peaking factors for more than one CEA configuration.
However, ANO-2 Cycle 1 startup measurements showed that required adjustments (i.e., to meet acceptance criteria) were not uniform for the different CEA configurations serviced by a single addressable constant.
For these conditions,an alternative method for making adjust-t ments was applied so that a given CEA configuration would always be conservative.
Required adjustments were made to an addressable constant to make its serviced CEA configurations meet acceptance criteria.
If any of the serviced CEA configuraticns still fell or remained outside its acceptance criteria,
- the. additional required uncertainty was accommodated by increasing other addressable uncertainty terms (BERRi) applied in the ONBR and LPD calculations.
lUseofB terms is an indirect means of accommodating ER8i CEA shadowing adjustments and requires determination of equivalent BERRi changes.
Since this is more complex and less direct than individual shadowing adjustments, iadditional addressable ccnstants for CEA shadouir.g factor
' adjustment have been added.
Because planar radial peaking factor addressable constants are applied through the same program logic as the CEA shadowing factor adjustments, the number of addressable constants for the planar radial peaking factors was also increased..
The original logic used in the CPC power distributie algorithm selected one of two sets of four boundary point power correlation coefficients (BPPCC's) based on the condition of the EOL flag
-(BOL or E0L) and on the gross characteristics of the axial power distribution (cosine, flat, or saddle).
The CPC algorithms i
were " frozen" (i.e. a reference set was established) in 1975 during the NRC review.
Subsequent to the " freezing" of this -
algorithm it was determined that a single sit of four BPKC's could be used to adequately detemine power distributions.
- Thus, the CPC data base for ANO-2 Cycle 1 was provided with two identical sets 'of four B
's to minimize algorithm changes.
Verification of power di bution synthesis during startup of AN0-2 Cycle 1 confirmed that a single set of BPPCC's was suitable for CPC power synthesis.
l u
During AriO-2 startup testing, out-of-acceptance-band measurements of Bpp g's were accommodated by equivalent adjustments to the ERRi addressable constants. While this was an adequate means of compensating for differences between predicted and measured BPPCC's, adjustments to the BPPCC's themselves is more direct and avoids an additional component to the B eRRi terms.
The implementation of address-able BPPCC's in the~ existing algorithm would have required eight addressable constants even though only four distinct values were necessary.
The algorithm thus new uses a
's which are addressable.
single set of four BPPCC Addition of addressable constants in these three areas avoids applying additional components within the BERRi terms.
Adjustments to these addressable constants is more direct and applies the adjustment only where required.
==
Description:==
Three additional addressable constants have been added to both the planar radial peaking factor and the CEA shadowing factor determination at each core axial node (total of six additional constants).
Four B
's located in the Data Base have been made a$d ssable.
The appropriate sections of the POWER program have been modified to accommodate this change.
Figure 2-2 indicates the table cartition to be used for determination of the addressable multipliers to the planar radials and rod shadcwing factors.
The f.olicwing logic is used to select the correct multipliersi based on CEA conf,iguration.
If I, = 1 and if J = 1 then A
= 1.0 Sn and A Rn R1 If I = 1 and if 2 (J 41 n
col then ASn " S2 and A "N2 Rn If I = 2 and if J = 1 n
'then A,= d 3
S3 and A h
R3 If I, = 2 and if 2 4J4Icol I
then A "N4 Sn
'and A Rn R4
~
then A, = c(35 3
and A
<R5 h
If 34I 4 I and if 24J4I n
row col Sn "N6 then A and A h
R6 I f I, > 1 r if J> I row col then A Sn S7
< R7 and A h
where:
I"
= row index based on CEA Regulating Group positions (see Figure 2-2).
J
= column index based on part-length rod (PLR)and Shutdown Bank positions (see Figure 2-2).
A
= multiplier on CEA shadowing factor at sn axial node n A
= multipliar on planar radial peaking factor Rn at axial node n I
= constants that define partition of table cgj '
in Figure 2-2.
y row (N
= number of columns in the planar radial col and shadowing factor table) through B The addressable multipliers B replaced the Data Base consta $$k throughkCC4
The application of the BPPCC's has been simplified.
Data Base constar +.s have been added to differentiate between upper and lower core values of:
a) breakpoints for setting boundary point powers to lower limit values, and b) the lower limit values themselves, based upon both absolute and signal limit values for the upper and lower ex-core ' detector values.
The time in life and the characteristic shape dependency have been eliminated.
The entire new boundary point power correlation calculation is given below,-
The power vector needed to calculate the spline function amplitudes requires the generation of boundary point power values for both the top of the core, y(0), and the bottom of the core, f(L), based on the average power in the end regions.
The correlations are empirically based on four addressable constants. " ppg through B and the minimum pennitted bounda point powebCC4,he boundary point powers are calcu3ated P
T as follows:
If P
< SIG, y
then V (0) = Bminul If P ) SIG y
u then y (0) = (BPPCC3. P ) - B 3
PPCC4 If P < SIO 3
L then V (L) = Bmin 11 m
"M i
[
w
If P ) SIG 3
g theny(L)=(BPPCC1. P ) + B
~
3 PPCC2 In order to avoid negative boundary point power values for excessively low virtual in-core de.tector signals,P ,
j the following checks are employed:
If y (0)( B EPSU then redefine T (0) = Bminu2 If y(L) 4 BEPSL then redefine y (L) = Bmin 12 where:
P
g the final adjusted detector response
=
in the i'th segment T(0),
the upper and lower core boundary point
=
y(L) powers, respectively BPPCCl-the addressable boundary point power '
=
B correlation coefficients PPCC4 SIG,
U upper and lower signal limits
=
SIG f r setting 3r(0) and 7/r(L)
L to their lower limits 1 wer limits for boundary point B
=
B,minul, powers based on signal limits 43)3
- BEPSU, breakpoints for setting boundary
=
B point powers to lower limits EPSL B
= absolute lower limits for boundary point B
p wers n
l
- 2. ) Change:
The slope of the coolant temperature shadowing factor (Cg3)hasbeenmadeanaddressabicconstant.
Reason:
The AND-2 Cycle 1 CPC design included a temperature shadowing correction factor in the Data Base to adjust the neutron flux power and the power distributirn calculations for the moderating effects of coolant flow in the reactor vessel downcomer.
During Cycle 1 startup, the measured value fell outside the acceptance criteria for the value in the Data Base.
As a result, an additional uncertainty was included in the values of the B ERR 1 and Bqaq3 uncertainty factors.
As an addressable constant, the slope of the shadowing factor can be adjusted based on test measurements without having to implement an indirect adjustment via the B uncertainty factors.
ERRi
==
Description:==
The constant Ct1 as previously a non-addressable Data Base value in UPDATE.
It is now an addressable constant which can be updated at the operator's module based on startup test measurements.
3.) Change:
The DNBR and LPD pre-trip setpoints have been made addressable constants.
Reason:
This change adds flexibility in setting pre-trip alarm setpoints and allows for adjustment of the setpoints without a revision to the Data Base.
As an example, during normal operations with CDLSS in service, the plant personnel can set the pre-trip alarm setpoints at nominal operating condition values.
If COLSS is out of service, the plant personnel can set the pre-trip alarm setpoints to the LCO values specified in the Technical Specifications, and thus more efficiently monitor the margins to the DNBR and the K'#FT LCO's continuously using the CPC system.
Making the pre-trips addressable constants allows the plant the flexibility of adjusting the pre-trip alarm set-points based on plant operating conditions.
I seta
The DNBR pre-trip setpoint (A dimensionless) and the -
==
Description:==
7 LPD pre-trip setpoint (in W/FT) have been added to the list of addressable constants which may be changed from the operator's module.
This change does not require a change to the DNBR pre-trip logic. However, since the LPD pre-trip setpoint has units of W/FT and the LPD has units of percent of core average, the following change is made.
If local Power Density pre-trip limit is violated, issue a Local Power Density pre-trip signal:
C = LPDPTS. CLPD 2
If ZbCg then. PD pre-trip C.0. = 1 L
othenvise reset the LPD pre-trip C.0.,
LPD Pre-Trip C.O. = 0 dynamically compensated Local Power Density where Z
=
computed in DNBR and Power Density Update Program.(%)
LPDPTS = Addressable Local Power Density pre-trip Setpoint(W/FT)
Conversion Factor (%/(W/FT))
C
=
LPD L cal Power Density pre-trip setpoint (%)'
.C
=
2 Local Power Density pre-trip f
LPD Pre-Trip C.O.
=
Signal Addressable DNBR pre-trip setpoint A
=
2 The functional design grcup will provide the default values
~
of A and LPDPTS.
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w
4.)
Change:
A method for automated reentry of certain CPC addressable constants from a disk has been implemented.
Reason:
The CPC System is designed so that the CPC addressable constants do not need to be re-entered after periodic off-line testing or after CPC auto-restarts.
- Mcwever, if the CPC system software must be reloaded from disk (for example, after CPC hardware maintenance), all addressable constants will revert to their default values contained on the load disk. Therefore, any required changes to the addressable constant values must be made through a reentry process.
With the ANO-2 Cycle 1 software, this reentry must be performed manually through the CPC operator's module.
Such a procedure is time-consuming and requires careful checking to ensure proper entry.
In addition the values of many of the addressable constants are calculated and implemented during startup testing and are not recalculated during the rest of the fuel cycle.
Therefore a change has been implemented which provides a method of automated reentry of the addressable constants whose values are not expected to change or whose values are expected to change very infrequently during the fuel cycle.
This change permits a quicker reentry of these constants via a floppy disk, provides a hard copy record of the addressable constants that were entered from the disk or transferred to the disk and retains the capability of entering new values of the addressable constants through.
the.CPC operator's module.
==
Description:==
Each CPC addressable constant is placed in one of two categories. The constants in the first category, called Type I, are those constants which are expected to change more frequently than the other constants.
The Type I constants include the flow and power calibration coefficients,
theCEAC/RSPT inoperable flag, the azimuthal tilt allowance, and the pre-trip setpoints.
The Type I addressable constants also include those addressable constants related to diagnos-tics which may be changed by the CPC software, such as the sensor status words and the TRIPS Buffer flag.
All other addressable constants are called Type II addressable con-stants.
The Type II addressable constants include the addressable CPC uncertainty factors; the correction mul-tipliers for CEA shadowing, planar radial peaking factors, and CEA deviation penalty factors; the boundary point power correlation coefficien'ts; the temperature shadowing._
slope; and the end of life flag.
This CPC modification applies only to the Type II addressable constants.
2-16
Two functions to facilitate the automated reentry of the Type II addressable constants have been added to the CPC system software.
Either of these functions may be selected when the CPC is placed into test via the test initiate switch on the PPS Test Par.el.
The
~
first option writes the values of all of the Type II addressable constants and their associated checksum
~
to a floppy disk, called the Addressable Constant Disk (A separate Addressable Constant Disk is assigned to each CPC channel).
In 6ddition, a hard copy of the values of the Type II addressable constants and their checksum is output to the Teletype.
The second function enters the values of the Type II addressable constants from the Addressable Constant Disk into CPC memory and calculates a checksum of these constants.
This checksum is compared with the expected one stored on the disk.
If the checksums do not agree, the CPC rejects the values of all of the addressable constants for the entry attempt and retains the values from before the entry attempt.
If the checksums do agree, the CPC will use the loaded values in its calculations.
During the loading function, a hard copy of the Type II addressable constants and their associated checksum are output to the Teletype.
The automatic entry of the Type II addressable ccnstants is performed following the loading of the CPC system software.
CPC Periodic Testing is performed after the automatic reentry of the Type II addressable constants to verify the loading of the CPC system software.
Note that this modification provides a method only to reenter Type II addressable constants from a floppy disk after the CPC system software is reloaded.
Initial entry of Type II addressable constants is made through the CPC operator's modules.
o
- 4Wum I
2.4 Other Algorithm Changes 1.)
Change:
Planar radial peaking factors are now adjusted by a Reason:
O
==
Description:==
9 l
9 6
M l
-C
,o,L l
i i
unaman M
O 4
I e
e 6
i 1
h 4
1!
I I
N i.
e
- 6
-- - - - ~ _
n.
N euman f
N I
e o
d 9
9 m
O
-=
h
- 4&*
- 4Mm&
6 e mee
l 2.) Change:
New curve fits have been made for core coolant specific volume determination.
Reason:
The hot and cold leg specific volumes are computed as part of the flow resistance calculation in the FLOW program.
In addition, the specific volume is used as input to the calculation of the density correc-tion factor for the planar radials (see change 2.4.1 above).
In the ANO-2 Cycle 1 CPC design,.the specific volume calculation is based only on temperature.
Because specific volume and density are dependent on both temperature and pressure, and because of the additional use of the specific volume, pressure dependence has been added to the calcul6 tion of specific volume.
==
Description:==
The implemented specific _volame curve fit is order in temperature and order in pressurb. -
The ranges on temperature and pressure for which the curve fit was designed is
_$ Temperature 6 psia S Pressure (P) 5 If the hot leg temperature is within of the saturated temperature, the CPC will initiate tn'e currently implemented hot leg saturation trip.
The curves fits for specific volume versus temperature and pressure are given as:
1-D
Y
=
c 1
Y. el" V
=
Yh i
h1 "
Yh2 "
where:
and where:
V
= n rmalized average cold leg specific c
volume V
= normalized specific volume in cold leg c1 1A or IB V
= n rmalized sperific volume in cold leg d
2B or 2A
'V
= n rmalized average hot leg specific h
volume V
= n nnalized specific volume in hot leg 1 hl Y
= n rmalized specific volume in hot leg 2 h2 T
= average cold leg coolant temperature,
.F c
T
= coolgnt temperature _ in cold leg 1A or cl 18 F
T
=c lant temperature in cold leg 2B or c2 2A, OF h
" operage hot leg coolant temperature, T
l m
coolant temperature in hot leg T
=
h1 1, OF coolant temperature in hot leg T
=
h2 2, OF P
primary pressure, psia
=
See Figure 2-1 for coolant leg des nations)
The values of curve fit coefficients are given below:
=
g SV01
=
=
gg SV 21 SY
=
33 SV
=
43
'ximum absolute error of curve fit =
riaximum percent error of curve fit =
T.hese errors are applicable over the allowable range.
9
=
1 w.
3.)
Change:
A pre-selected 20-node axial power distribution is used during low power operation.
Reason.
O i
==
Description:==
i l
i h
I i
A
- ~ - _
2.5.
Diagnostic Changes The CEAC snapshot buffer is changed to be similar 1.} Change:
to that for the CPC's.
In the previous CEAC design, a buffer was filled with a snapshot of CEAC input and output data if a CEACT Reason:
penalty was calculated.
every S seconds for as long as the penalty existed.
Based on ANO-2 operating experience, more useful di-agnostic infonnation may be obtained if the CEAC s is recorded for the first penalty factor calculated by the CEAC and is not ovemritten unless plant perso
. manually clear the buffer. snapshot diagnostic sim 1
diagnostic.
A snapshot of CEA positions is initiated by 1) a CEAC PF greater than 1.0, 2) the large PF flag, 3) a CEAC
==
Description:==
failure caused by either an excessive nunter of sensor failures or an excessive nunber of deviating CEA's in The CEA positions are stored in a e a core quadrant.
buffer and cannot be ovemritten until that snapshot is printed out at a teletype or the buffer is cleared by plant personnel through an addressable const nt The added to the CEAC Point ID table.
which is addressable constant shall also be a flag indicating filled or clear. As an the status of the buffer ; be zero (0) for a cleared example the constant could Changing buffer and one (1) for a filled buffer.
the constant from 1 to O could be used to clear the buffer.
The failed sensor ID nunbers used to indicate large differences in the CPC.PF's have been changed.
2.)
Change:
In the previous design, the failed sensor ID number generally the same as the Reason:'
However, the CPC
[
for a given sensor was Point ID number for that sensor.
failed sensor ID's for the maximum allowa ences between the DNBR and LPD penalty factors we ID's 038 and 039, which did not correspond to the infonnation in CPC Point ID'.s 038 and present design.
~
m -
==
Description:==
The CPC failed sensor ID numbers used to indicate large differences in the ONBR and LPD PF's have been changed from locations 038 and 039 to locations S98 and 999, respectively.
e.g., if PF -PF
>' E '
1 2
D or if PF
-F
>E L1 L2 L
then sensor ID's 998 on 999 are entered into the failed sensor stack CEA deviation penalty factor for where:
PF,PF
=
y 2
DNBR from CEAC1, CEAC2 respectively.
CEA deviation penalty factor for PFgy,PFL2 LPD from CEAC1, CEAC2, respectively.
=
maximum allcwable differences between E'L the DNBR and LPD penalty factors,
=
D respectively 3.)
Change:
Logic and an addressable constant have been added to the CEAC to rewrite the entire CEAC display.
Reason:
In the previous design, the entire CEAC display was rewritten only during CEAC initialization after a restart.
The CEA position bar graph was rewritten every 10 seconds.
Spurious electronic noise may interfere with those portions of the CEAC CRT display which are not periodically updated.
The new software provides two means to clear the entire CEAC CRT display without restarting the calculator.
==
Description:==
Logic is added to the CEAC Executive Program to auto-matically rearite the entire CEAC CRT display every 15 l
minutes.
In addition, a CEAC addressable constant is added to the CEAC Point ID table to allow the operator to rewrite l
the entire CEAC CRT display.
o i
=
2.6 Data Constant Changes In addition to the data constants associated with the above-listed modifica-a.
tions, the following data constants which could be potentially cycle-dependent are being reviewed for ANO-2 Cycle 2:
l.
Pump-dependent uncertainty factors for DNBR and LPD.
2.
Cold leg temperature dynamic compensation coefficients..
3.
CPC scaling constants related to CEAC penalty factor transmission.
4.
CEAC/RSPT inoperable mode penalty factors and preselected CEA positions.
5.
Dynamic thennal power constants.
6.
Heat flux filter coefficients.
7.
Asymetric steam generator transient data.
8.
LPD filter coefficients.
9.
CEA shadowing factors.
10.
Planar radial peaking factors.
- 11. Augmentation factors.
12.
Axial Shape dependent danstants to calculate an axial shape and pump-dependent projedtion constant representing the product of the DNBR flow projection time constant and the partial deriva-tive of DNBR with respect to core coolant mass flow rate.
13.
Axial shape dependent constants to calculate the DNBR operating limit for use in the flow projected DNBR calculation.
- 4.
Subgroup deviation penalty factor constants.
15.
Xenon, DNBR, LPD penalty factor constants in CEAC.
O j
2.7 References for Section 2.0 1.
CENPD-161-P, TORC CODE:
A Computer Code for Determining the Thermal Margin of a Reactor Core, July, 1975.
Y a
e M
M w
i IA, COLD LEG 2A COLD LEG n
~
s SGI SG2 1 HOT LEG 2 HOT LgG X
M CORE O-c X = RTO LOCATIONS a
~
~
v 1
COLD LEG l B COLDTEG FIGURE 2-1 Schematic of Primary System Showing Approximate Location of Temperature Sensors 4
m
- e l
us
OR SD'S NO SD'S ICOL ICOL+1 NCOL J=
1 2'
- I=
R1 R2,62 NO REGULATING GROUPS 1 JUST BANK NREG 2
R3, S3 R4, S4 BANKS NREG-1 AND NREG 3 RS. SS RS, S6 IR0W IR0W+1 R7, S7 BANKS 2-NREG NREG ALL REGULATING NREG+1 GROUPS FIGURE 2-2 PARTITION FOR APPLICATION OF ADDRESSABLE MULTIPLIERS FOR PLANAR RADIALS (oCRi)ANDR00SHAMWING(%g)
FACTORS m
unee e e
C l
l
\\
l 9
p FIGURE 2-3 M
i 2-31
ubS M 1
l l
i l
e 0
1 I
f v
[
I l
N I
W D
C3
.4 k.
W "M
l l
1 1
2-32
APPEtlDIX A DESIGil THEPJ1AL fMRGf tl MCDEL CETOP The C-E method for applying' TORC for detailed core DilB margin calculations was given in section 4.0 of Reference A-1.
While yielding accurate predictions of core margin to DilB, this method is cumbersome for analyzing a large number of reactor operating conditions.
Therefore, a simplified modeling method was developed for using TORC in design analyses.
Reference A-2 describes this simplified method for generating a TORC design model.
The CETOP code described in detail in Reference A-3 replaces the simplified TORC method.
The CETOP code calculates MDilBR by using the same open-core thermal-hydraulic methods and equations a' in the simplified TORC method, but in less computer time.
This is :ccomplished by reducing the number of channels needed in the model by using a simplified non-iterative scheme to calculate channel coolant ccnditions.
The CETOP code is used to derive and verify the CPC on-line thermal margin algorithm, C5 TOP 2.
This appendix presents a typical CETOP design model for use in design DNB margin calculations.
The following sections provide a summary of the design method for computing margin to OflB with CETOP, a description of the design model, a comparison of design model results with a detailed TORC analysis, and discussion of the derivation and verification of the CPC DNB algorithm, CETOP2.
A.1
SUMMARY
OF DESIGft METHOD FOR COMPUTING CORE MARGIN TO OflB WITH CETOP_
The CETOP design model for DNB margin calculations consists of a simpl*ified core model and a core-s'pecific base input data set.
The design model is chosen to produce appropriate margins to DNB for all operating conditions for a given reactor and fuel cycle loading.
The design model specification includes a normalized radial power distribution for a quadrant of the hot assembly and geometric parameters for a simplified representation of the core and hot quadrant.
The variables not fixed in the design model are the specific reactor operating conditions, namely, core inlet temperature, primary system pressure, cure ikx, core power, axial power distribution, and maximum rod radial peaking factor.
=
+e A-1
A.2 DESCRIPTION OF CETOP DESIGN MODEL The CETOP design model uses a'one stage approach to performing DNB calculations as compared to a two stage approach used in the simplified TORC method.
This one stage approach utilizes a three dimensional lumped channel model to radially 4
group flow channels in the region of the core where minimum DNBR (MDNBR) occurs.
~
The size of a lumped channel'may vary from one flow subchannel surrounded by fuel rods, to a group of flow channels, comprising several fuel assemblies.
The conservation equations for the lumped channel model are similar to the ones used in TORC except that transport coefficients are included in the equations to reduce the number of subchannels needed to define the correct lateral transport of mass, energy and momentum into the MDNBR hot channel region.
More discussion on transport coefficients is given in Reference A-3 and A-4.
A.2.1 Geometry of CETOP Desian Model The CETOP design model has a total of four thermal-hydraulic channels to model the open-core fluid phenomena.
Figure A-1 shows the typical layout of these channels.
Channel 2 is a quadrant of the hottest assembly in the core and Channel 1 is an assembly which represents the average coolant conditions for the remaining portion of the core.
The boundary between channels 1 and 2 is open for crossflow, but there is no turbulent mixing across the boundary.
Turbulent' mixing is or.iy allowed within channel 2.
The remaining boundaries of cnannel 2 are assumed to be impermeable and adiabatic.
The lumped Channel 2 includes channels 3 and 4.
Channel 3 lumps the subchannels adjacent to the MDNBR hot channel 4.
The location of the MDNBR channel is determined from 1 2 or 3 stage Detailed TORC analysis of a core quadrant.
The Simplified TORC design model uses a similar channel layout (see Reference A-2, Figure 4.1) except an octant of the hot assembly is used and more sub-channels are required to define the correct lateral transport of coolant conditions.
The u'se of a quadrant of the hot assembly instead of an octant produces more accurate DNBR calculations in CETOP.
e A-2
A.2.2 Radial Power Distributions for the CETOP Design Model The radial power factor for channel 1 in CCTOP is unity since this channel represents the average coolant conditions in the core.
The radial power distribution for the hot assembly quadrant in CETOP is similar to the one used in the corresponding Detailed TORC analysis.
This radial power distribution is part of the core-specific base input data and is chosen after examination of a representative set of physics calculations for a given core.
The quadrant radial power distribution for CETOP is normalized to unity for the quadrant.
The normalized radial power distribution shown in Figure A-1 is used to determine the average radial power factors for channels 2, 3 and 4 in a typical design model.
When the maximum rod radial power factor is changed in the quadrant of the hot assembly the normalized' radial power factors for channels 2, 3, and 4 are appropriately adjusted by the code.
A.2.3 Inlet Flow Split for CETOP Design Model Core inlet flow distributions are determined from reactor flow model experiments for CE-type cores.
These inlet flow distributions are used in Detailed TORC analyses and the CETOP model.
Channel 1 of the CETOP model uses a ' flow split of unity since this channel represents the average coolant conditions in the core.
The hot assembly quadrant in the CETOP model (Channels 2, 3, and 4) initially
~
uses the flow split corresponding to the hot assembly in the inlet flow distribution.
If necessary, the inlet flow split for the hot assembly quadrant is later adjusted in the CETOP model to yield conservative or accurate MDNBR predictions as compared to a Detailed TC 1C analysis for a given range of operating conditions.
~
A.3 COMPARISON OF DESIGN MODEL RESULTS WITH DETAILED ANALYSIS This section'suppo.rts the CETOP model by comparing its predictions for a 16x16 assembly type, C-E reactor (ANO-2) with those obtained from a detailed TORC analysis.
Several operating conditions were selected for this demonstration; they are representative of, but not the complete set of conditions which would be considered for a normal DNB analysis.
A-3
A.3.1 Detailed TORC Analysis of Sample Core The detailed thermal margin analyses were performed for the sample core using the radial power distribution and detailed TORC model shown in figures A-2, A-3 and A-4 The axial power distributions are given in Figures A-5 The core exit pressure and inlet flow distribution used in the analyses were based on flow model test results, given in Figures A-6 and A-7.
'The resul ts of the detailed TORC analyses are given in Table A-1.
A.3.2 Application of CETOP Design Model to Sample Core The CETOP model described in Section A.2 was applied to the same cases as the detailed analyses in the previous section.
The results from the CETOP model analyses are compared with those from the detailed analyses in Table A-1.
It was found that a constant inlet flow split providing a hot assembly inlet mass velocity of.80 of the core average value is appropriate so that MONBR results predicted by the CETOP model are either conservative or accurate.
A.4 APPLICATION OF UNCERTAINTIES TO SIMPLIFIED METHODS Uncertainties in DNB analyses arise due to manufacturing deviations from nominal dimensions and due to uncertainties in flow model test results.
Engineering factors are used to account for the effects of manufacturing, deviations from nominal dimensions.
The engineering factors consist of the engineering enthalpy rise factor, the engineering factor on heat flux, and the pitch and bow factor.
The mechanics of applying the engineering factors and other uncertainties for AN0-2 are discussed in Reference A-5.
A5 VERIFICATION OF THE ON-LINE THERMAL-HYDRAULIC (T-H) ALG0RITHM (CETOP2)
The CETOP design model is used to verify the accuracy and conservatism of the CETOP2 on-line T-H model.
The CETOP2 algorithm is a simplified, faster running version of the CETOP code.
The simplifications implemented in CETOP2 to reduce the execution time of the algorithm result in deviations of the calculated DNBR and quality when compared to the CETOP results.
An uncertainty assessment similar to that for CPCTH in Reference A-6 is performed by comparing CETOP2 with the design CETOP model over a wide range-of conditions. --
From this uncertainty assessment a penalty factor is determined which is applied as a multiplier on the power level used by CETOP2.
The accuracy assessment and penalty factor are described in Appendix 8-2.
This penalty factor conservatively compensates for the uncertainties in the calculated DNBR and quality of the A-4
CLIOP2 algorithm to a 95/95 probability / confidence leval.
It is shown to produce conservative CETOP2 results for at least 95% of the cases in which the design CETOP model reaches a Specified Acceptable Fuel Design Limit (SAFDL).
In summary, the on-line CPC T-H algorithm, CETOP2, is shown to be con.crvative
~
with respect to the design CETOP model.
The design CETOP codel is in turn shown to be conservative with respect to the TORC /CEl model, which itself is a conservative but more realistic calculation of Dn3R and coolant conditions.
The conservatism inherent in this methodology insures that the CETOP2 algorithe provides sufficient protection of the fuel integrity by not exceeding the DNB SAFDL under all CPC Design Rasp Fvents.
A.6 REFERENCES A-1
" TORC Code, A Computer Code for Determining the Thermal Margin of A Reactor Core", CENPD-161-P (Proprietary), July,1975.
A-2 " TORC Code, Verification and Simplified Modeling Methods", CENPD-206-P (Proprietary), January,1977.
A-3 Chiu, C., Church, J., "Three-Dimensional Lumped Subchannel Model and Prediction-Correction Numerical Method for Thermal Margin Analysis of PWR Cores", C-E Paper TIS-6191, June,1979.
A-4 Chiu, C., Moreno, P., Todreas, N., and Bowring, R., "Enthalpy Transfer Between PWR Fuel Assemblies in Analysis by the lumped Subchannel Model",
Nuclear Engineering Design 53, July 1979, pgs.165-186.
A-5 " Statistical Combination of Uncertainties, Combination of System Parameter Uncertainties in Thermal Margin Analyses for Arkansas Nuclear One Unit 2",
CEN-139( A)-P, November 1980.
A-6 "CPC Assessment of the Accuracy of PWP. Safety System Actuation as Perforced by the Core Protection Calculators", CENPD-170, Supplement 1, Combustion Engineering, Inc., November,1975.
A-5
Axial Elev.
Operating Paraneters MDNBR Quality at MONBR of MDNBR(in)
Pressure Inlet Temp. Core Avg. Mass Core Avg.
Axial Shape (psia)
(*F)
Velocigy Heat Flux Index TORC CETOP TORC CETOP TORC CETOP C
2 (lbm/hr-ft x10 )(8tu/hr-ft )
ASI 2250 553.5 2.598 267437
+.527 1.172 1.144
.134
.112 52.4 56.1 2250 553.5 2.598 312561
+.337 1.169 1.066
.153
.169 142.2 142.2 2250 553.5 2.598 278307
+0.00 1.186 1.137
.q,17
.020 108.5 116.0 2250 553.5 2.598 264238
.070 1.169 1.135
.028
.039 138.4 138.5 2250 553.5 2.598 225343
.527 1.195 1.163
.076
.066 131.0 131.0 1750 605 1.407 122096
+.527 1.172 1.155
.181
.194 71.1 74.8 1750 553.5 1.547 168322
+.527 1.181 1.178
.073
.089 63.6 67.4 2400 605 2.868 227330
+.527 1.209 1.181
.069
.051 52.4 56.1 j[
1750 465 2.868 392894
+.337 1.166 1.068
.108
.123 142.2 142.2 2400 465 1.724 314014
+.337 1.140 1.048
.164
.143 142.2 142.2 2400 605 2.390 238744
+.337 1.162 1.067
.203
.213 142.2 142.2 2400 605 1.434 120256
.527 1.180 1.178
.064
.069 134.7 134.7 2400 553.5 1.562 162529
.527 1.203 1.183
.065
.055 131.0 1 31. 0 NOTE:
CETOP Model uses a.80 inlet flow split in the hot quadrant of the hot assembly (Channel 2)
TABLE A-1 COMPARISONS BETWEEN DETAILED TORC AND CETOP l
(_
OUAt)ii AN T Of I!OT A'JSTMitLY CllANNEL 2 2
q l
I I
1 N
- ~'
I I
N CORE ASSEMBLY I_
l Cil/>NNEL 1 BOX R ADI AL = 1.0 BOX INLET FLOW FACTOR = 1.0 CORE LOCATIONS OF CHANNELS 1 AND 2 1
CHANNEL 2 LUMPED CHANNEL MODEL IMPERVIOUS cot 1NDARY
.8913
.8810
.8832
.8905
.9015
.9221
.9GG1
.9235
.9169
.9250
.9353
.9448
.9573 1.013
.9932 f
2
.9558
.95GG 1.02G 1.013 1.018 1.0 ".3
.9822
.9771
.0844
.9CSC 1.039 1.039
.9932
.9771 IMPERVIOUS LINE'OF BOUNDARY SYMMETRY
\\
1.00G 1.012 1.1 54 1.053 1.004
.9344 3
4 3
1.035 1.023 1.004 1.072 1.070 1.0C8 1.010
.9947 3
'O ' l 8"
.9000 1.035 1.042 1.013 1.01G 1.031 1.013 1.010 R.'
NORMAllzE TO QUADRANT 1.029 1.002 1.067 1.064 1.CG1 1.053 1.014 1.039 RADIAL PERMEABLE BOUNDARY Figure A.1 A TYPICAL CHANNEL LAYOUT OF CETOP DESIGN MODEL A-7
HOT ASSEMBLY IS BOX NUMBER 8 g
N
'N i
STAGE 1 TORC ANALYSIS 24 1E
~ 8 I
CHANNEL NUMBER
.8736 1.1237 1.1734 ASSEMBLY AVERAGE RADIAL PEAKING FACTOR 0.7252 1.0676 1.1592 1.2056 1.2470 41 36 30 22 14 6
0.6704 0.8274 1.0757 1.0296 1.2052 1.0447 43 40 35 29 21 13 5
0.7252 0.8245 0.G4G5 0.8348 1.2389 0.9651 1.0816 42 39 34 28 20 12 4
1.0713 1.0757 0.8383 0.8081 0.0002 0.0278 0.9186 i
38 33 27 19 11 3
1 0.8680
- 1.1591 1.0270 1.2387 0.9046 1.2315 0.9492
'1.2414
- - - '"- h 7
32
~26 18 10 2
I i
I 1.1215 1.2054 l 1.2026 0.96G1 0.0262 0.9445 1.0006 0.8244 I
I l
_ _ _ 4
_ _ q. _ _ _ _ _ _ _ _ _
,25 17 9
1 1.1715
, 1.2455
, 1.0414 1.0803 0.9162 1.2425 0.8241 0.512G
~
l l
l
^^
l i
I l
l l
NOTE:
l CIRCLED CilANNEL NUr.1CER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMRLIES HAVE BEEN " LUMPED"INTO A SINGLE
(
CHANNEL FOR T. H ANALYSIS Figure A.2 CORE WIDE (1st STAGE) OF DETAILED TORC MODEL
~
A-8
= _ _ -
... = - _ = -. -.
t i
i r
I t
i.
E
/
1 I
i 4
1 4
t i
F
[
I a
i U
e t
Firure A-3 i
i j
INTERMEDI ATE (2nd STAGE) OF TORC MODEL l
F l
f A-9
RADIAL PIN PEAKING FACTOR e
9 P
l luGW 9
Figuro A 4 SUBCHANNEL (3rd STAGE) OF TORC MODEL A-10
14 i
i i
a i
12
+ 0.527 ASI --- ----
-0.527 ASI ---
2.0
+ 0.337 0.00G
~
- ~~
-0.070 1 1.8
/
s 7
s 1.6 N
o f
N N
d
/
\\
f % - --
\\
1.4
/
p g
/
t.u
/
\\
8 3
'2
/
/
's
/
\\
1 i
/
'/
/'
h1.0 f
f~
~
s"
,o 0.0 - /
/
/
N
/
/
/
N s
N s
0.6
-/s N
1 s
0.4 - [
/
s
\\
/i y
~~~,~
N.a.,
0.2
~,~~
0 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 1.0 FRACTION OF ACTIVE CORE HEIGHT FROr.1 tNLET t
Figure A-5 AXIAL POWER DISTRIBUTIONS
l l
l 14 i
i i
i i
i 12
+ 0.527 ASI --- ----
-0.527 ASI 2.0
+0.337 ASI 0.000 ASI ---
~
',,---s
-0.070 ASI 1.8
/
s
/
N
'd
/
\\
r 1.6
\\
O o
j N
s I
/
\\
7 % - ~~
\\
1.4 f
p g
N w
f s
52
/
/
's
/
E5
~
\\A-G 1
/
/
f x_
'/'f
\\
l'o I
~
\\
~
0.8
/
/
/
's N
s s
0.6
-/s N
\\
N
\\
0.4
/
\\
%s
/y
'~~,,%
N 0.2
~s 0
I O
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 1.0 FRACTION OF ACTIVE CORE HEIGHT FROf.1 INLET I
- Figure A-5 AXIAL POWER DISTRIBUTIONS
~
NOTE:
CIRCLED CHANNELNUMBERDENOTES A FLOW CHANNEC IN WillCH SEVERAL FUEL ASSEr.1BLIES HAVE BEEN " LUMPED"INTO A SINGLE CHANNEL FOR T H ANALYSIS Figure A 6 INLET FLOW DISTRIDUTION FOR TORC MODEL-(FOUR PUMP OPERATION)
A-12 i
F NOTE:
CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMBLIES HAVE BEEN "I, UMPED"INTO A SINGLE CHANNEL FOR T-H ANALYSIS Figure A 7 EXIT PRESSURE DISTRIBUTION FOR TORC MODEL (FOUR PUMP OPERATION) l l
A-13 i
APPENDIX B PART 1: CETOP2 FUNCTIONAL DESCRIPTION
1.0 INTRODUCTION
This document provides a functional description of the CETOP2 algorithm, which is intended to be used to perform the DN8R computations in the Core Protection Calculators (CPC's).
The methodology of this algorithm applies to a general C-E PWR, core and is to be incorporated into the generic CPC design.
The prediction-corre~ction numerical scheme and the lumped channel technique (Ref. 1) in CETOP2 are used to solve the conservation equations for a three dimensional representation of the cpen-lattice The hot channel critical heat flux is calculated using the core.
CE-1 correlation.
Several simplified correlations for calculating the fluid properties are employed to shorten the running time.
This results in more accurate DNSR prediction than the previous CPCTH approach, yet the required execution time constraints are met.
CETOP2 divides the core into fcur n.adeling channels:
Core Region Channel, Hot Assembly Channel, Buffer Channel and Hot Channel (Seebelow).
Based on the mass, momentum and energy interactions between these modeling cnannels, the local coolant conditions are determined at several axial locations (nodes) for each of the four channels.
Ultimately, the hot channel conditions are used for the ONBR calculation.
Channel 1 Channel 2 Chc.inei 3 Channel a Core Region,
Hot Assembly
' Buffer Channel Hot Channel e
_THf. FOUR MODELING CHANNELS USED BY CETOP2 La B-1
The local coolant conditions are computed at
~
Iaxial nodes, for each of the four channels.
When the hot-channel conditionsareknown,}
The ONBR is then calculated at each node and the minimum selected for output.
The major steps are:
1.
Calculation of the general operating conditions (inlet enthalpy, saturation properties, etc.);
2.
Calculation of the core and hot assembly local coolant conditions using nodes each; 3.
Calculation of the buffer and hot channel local coolant conditions using
_ axial nodes; 4.
5.
Calculation of DNBR.
A flow diagram for the CETOP2 algorithm is given in Figure B-1.
The notation used herein is employed to allow for maximum flexibility in implementation, and clarity of specification.
Many quantities are expressed as two-dimensional arrays, in the interest of clarity, but it is not a functional requirement to implement them
'in this way.
Additionally, it may be possible in some cases to combine constants into composite terms.
I Unless indicated otherwise the following convention will be employed, (using enthalpy as an example).
\\
I
.h (j) = Specific enthalpy at node j, channel i.
g The generic constants and the plant specific constants for ANO-2 are included herein.
The associated accuracy of the algorithm when compared to the design code is alsa addressed.
B-2
FIGURE 3-1 CETOP2 ALGORTTHM FLO'J F-INLET INTEGRATED 20 ELEMENT PRESSURE FLO'vl 7[C TEMPERATURE RADIAL 3
n l
I l
s 1
Of1BR 4
CALCULATION MINIf401 yVALITY.AT DNBR N00E OF MIN.
DNBR BnS
- 2. 0 ALGORITHM SPECIFICATION This section defines the specific techniques for calculating the DNBR from the known process variables.
The inputs and outputs are defined in Section 2.1.
Sections 2.2 through 2.11 comprise the body of the algorithm.
Sections 2.12 and 2.13 define two required mathematical functions.
2.1 INTERFACE REQUIREMENTS 2.1.1 Inputs The algorithm requires the following procese paraseters:
P Primary coolant system pressure (psia).
T Maximum compensated cold leg temperature (*F).
emax M
Calibrated, normalized core coolant mass flow rate.
c
$CALC Core average heat flux (% of nominal heat flux)
TR Azimuthal tilt allowance (addressable constant)
PF CEA deviation penalty factor for DNBR PD 9
Pseudo hot pin power distribution calculated in the PowerDistributionprogram,i=1([]
PIST Integrated one pin radial peak.
ASI Hot channel axial shape index.
2.1.2 Outouts The primary outputs of this algorithm are listed below.
Additional information is available if required, for example the saturation enthalpy or the hot-channel exit quality.
DNBR Minimum hot-channel DNBR.
ST X
ST Hot channel quality at node of minimum DNBR. -
8-4 I
The following outputs are required by the 2.1.3 Constants Defined in Section 3.
2.2 SATURATION PROPERTIES The saturated fluid properties are obtained from the following polynomials.
TATF
- P(I~I)
T
=
f g
i=1 II~I) h
=
TAHF9P f
i=1 I
TAHFG.
P(I~I) h
=
f9 1
t=1
.u.
I~I) f
'I'AVF$P u
=
i=1 CI~I)
'TAVGyP u
=
9 i=1 pf T AVIFj P(I~I)
=
i i=1 Where P
=
Primary coolant system pressure (psia)
T
=
f Saturation temperature (*F) h
=
Saturated liquid specific enthalpy (Stu/lb,)
f hfg '=
Latent heat of vaporization (Stu/lb, Saturated liquid specific volume (ft /lb,)
u
=
f 3
Saturated vapor specific volume (ft /lb,)
o
=
g pf Saturated liquid viscosity (lb,/ft/sec)
=
ATF,AHF,AHFG,AVF, AVG,AVIF =
polynomial coefficients, constant.
~
2.3 CALCULATI0tl 0F PRESSURE DEPENDENT TERMS The VOLUME and FRICFAC functions, defined in Sections 2.11 and 2.12, involve a number of terms which depend only on pressure.
Since the functions will be evaluated repeatedly, each time using the same value of pressure, the pressure dependent terms are defined separately.
I The following are used by the VOLUME function:
~
~~
i =) TALL.
P(3~I)
BALPL
~
~
,j ia BALPH'. = T ALH.
P(I~I)
~
~
IJ l
j=1 P
B-($
Where BALPL Coefficients for void fraction vs. quality polynomial
=
(low quality)
BALPH Coefficients for void fraction vs. quality p.olynomial
=
(high quality) e ALL
= L_ _ array of void fraction vs. quality and pressure S'
coefficients (Reference 2) - Quality <
same as above except for quality >
constant.
ALH
=
constant.
The following terms are used in the friction factor calculation.
]a
~
=
~
g where FF
=
Intermediate results used by the FRICFAC function.
=
Variousconstants(arrayof).
- 2. 4 CALCULATION OF INLET CONDITIONS The core and hot assembly inlet conditions are calculated as follows.
in I8[ 1(I~I) h = 9 II~I) f,=1 whereB;=[IAENgj P j=1 j" "l~BSVOL; [ ](I'I) u = i=1 O in IH *NERR)'OAVG c If P1 1 P1 I 82 ST B3 and ASI 1 ASI < ASI B2 B3 and T 1T B2 CMAX B3 and PP 1 P < PP B2 B3 Then FSPLIT = FSPLIT1 Tk2
and E = E1 and JTRP = 0 Otherwise FSPLIT = FSPLIT2 and E = E2 and J is determined as follows TRP if Pl 1 PI B1 ST B4 and ASI 5 ASI < ASI B1 g4 and T 5TCMAX < TB4 B1 and PP 1 P < PP B1 B4 then JTRP = 0 otherwise J7pp = 1 M =M eg c Where: h = Inlet core coolant specific enthalpy (8tu/lb,) in ugg Inlet core coolant specific volume (fthlb,) = i G = Coolant mass flux at core inlet (lb,/ft', sec) in ASI Hot channel axial shape index. = FSPLIT = Hot assembly flow starvation factor. T,,x Maximum cold leg temperature ( F) = c M Nomalized core average mass flow rate. c AEN = array of coefficients for enthalpy vs. pressure and temperature correlation. BSVOL Array of coefficients for specific volume vs. enthalpy = ' correlation. (Same as array ASVOL). FSPLIT1,FSPLIT2 = Region-dependent flow splits, constants. MERR Flow measurement uncertainty adjustment term. ~ = G Design core average mass flux (1b,/ft /sec). 2 = AVG . P1Bf = Integrated one pin radial break points for selection of regions ~ ~ PI = Integrated one pin model ST Tgg = Maximum cold leg temperature break points for selection of regions P = Primary pressure (psia) 8-8
PP81 = System pressure break points for selection of regions El,2 = Region-dependent algorithm uncertainty allowances E = Multiplicative power uncertainty factor for DN8R calculation (region-dependent) ASIBi Constant, ASI break points for selection of region = J = DNBR region trip flag TRP 2.5 CALCULATION OF LINEAR HEAT DISTRIBUTIONS The hot channel axial heat flux distributions are calculated as follows: $c(i) =
- CALC TR-PF PD
^ ] 4 Four ^ ]1inear heat distributions are computed for the four modeling channels. The lhot channel axial heat flux distribution is combined with the integrated one pin radial peak, and collapsed to[r- ] distributions, as follows: kyg Q yg BERR1 E = g 4 9 HOT = _ HOT BERR1 E For j= 'q (j) = -Q' na 1 AVG H1 - (b) - Q q (j) = n0 2 P AVG H2 4 ([P 9 (j) = 3 )-Qgyg n og3 4 q4(j) = Q yo n 0 3 34 where qj = 10 element core-region linear heat distribution (Btu /ft/sec) q = 10 element hot assembly linear heat distribution (Btu /ft/sec) } u
D q3 element buffer channel linear heat distribution = (Btu /ft/sec) q4 element hot channel linear heat distribution = (Btu /ft/sec) (g ~= element hot channel relative axial power distribution ($g(i) = relative power in axial segment i of the hot channel). PI = Integrated one pin radial peak. ST Q yg = core average heat flux at full power (Stu/ft /sec), 4 2 constant. O HOT = hot pin heat flux at full power (Stu/ft /sec), 2 constant n = 3.14159... constant. P 2 P 3 P = 4 D -D Hl g4 = Heated diameter of respective channel (ft), constant. BERR1 = Addressable DNSR uncertainty factor E, = Region dependent Algorithm uncertainty factor Qgyg = Adjusted core average heat flux at full power Q = Adjusted hot pin heat flux at full power HOT
- 2. 6 COMPUTATION OF CORE / HOT-ASSEMBLY FLUID PROPERTIES I
The calculations described in this section result in the enthalpy, I mass flux, cross-flow and pressure drop axial distributions, for both the core region and hot assembly channels. The hot-assembly distributions will be used in subsequent calculations. (Section 2.7) 1 I B-10
The properties at each node depend on the properties of the upstream and downstream nodes. The method of solution is a prediction / correction scheme. The technique is summarized belcw: At each of the the folicwing calculations are performed: Prediction of mass fluxes at node J. Prediction of enthalpies at node j+1. Pred,1ction of specific volumes and friction factors at node j+1. Prediction of cross-flow at node J+1. Calculation of corrected mass-fluxes at nede j[ Calculation of cross-flow resistance at node j+1. The calculations involved in each of the above steps are defined in the following sub sections. ~ 2.6.1 Initialization of State Variables em e M 6 g <m W m 8-11 d" "" ~ ca
l ) 1 M 4 4 4 i 1 j 4 i 4 l l i i 2.6.2 Nodal Loco M F f e e eg sum. B-12
_+.J -E s a _a w -A_ 2-e J a J l J 0 e 4 4 e l in n e e e 1 ) e 1 l 1 N l I 4 0 0 I 'N i i B-13
..._+-s- ~ *-._ _____s__. _s___^L _<_a.,. E ,A 1 1 I I m 1 l 4 1 i i f I 4 1 d I k T 1 .I t b d '{ J l I f i t A 4 1 L i 4 e i I. 1 i i h J l 3 I \\ i. I 1 J r I i 4 l l .i I 4' I .I ,l
- e t
] l i B-14
e 1 i 4 2 ~ 2.6.3 Calculations at ] Node F l i I ~ 1 B-15 ~ ~.
m 4 / e I e
- M M
B-16
2.7 CALCULATION OF SUFFER / HOT-CHANNEL FLUID PROFILES The calculations described in this section result in the enthalpy and mass flux distributions for the buffer and the hot :hannels. The hot channel distributions will be used subsequently in the critical heat flux calculations. _ - - ~. l l i i 2.7.1 Initialization of State Variables 58 e i ~' I M B-17
~"-- u-- y,_ e 9 e E'I 2 Modal Loco = 8 e i 1 5 i i f i i } I a l m l B-1s
m
O M m 0 0 / e 9 e l m wmm, e-- m w e '6 B-19 g,
( \\ l l I I i e 9 2.8 COMPUTE HOT CHANNEL QUALITY AND FLOW PROFILES i f-e l --...e
O
- 2. 9 HOT CHANNEL HEAT FLUX DISTRIBUTIONS The calculations described in this section result in the hot-channel critical heat flux and actual local heat flux distributions.
2.9.1 Local Heat Flux Distribution p.m 9
- e "M
B-21
.A a m. 4 puis 1 enumm e 8 i e i s h t t 4 l 9 M b
2.9.2 Hot Channel Critical Heat Flux 2.10 CORRECTION FOR NON-UNIFORM HEATING F-f e 'M u
2.11 CALCULATION OF STATIC DNBR The DNS ratio at each hot-channel node is given by For F(K) 1 0.0 orq[0 CAL (K)$0.0 DNBRg = 0.0 .0therwise, N NB DN8R g qLOCALIN) K=2,3..[] = K F The minimum is selected and adjustment terms applied. DNBRMIN = MIN [ DNBR, ONBR3... ON84 ] 2 DNBR =EONBl - [0NBRMIN + EONB2 ST 3
and i i P DNBRg = Array of DNS ratios in hot-channel DNBR = Minimum STATIC ONBR. ST EDN81 EDN82 = DNBR adjustment terms, constant 2.12 DEFINITION OF VOLUME FUNCTIONS ~~ The preceeding calculations make use of the VOLUME functions
- defined in this section.
The independent variables in these j CVP, VFRIC and V will be collectively referred to as " VOLUME" i t. w
I functions are pressure (P) and local specific enthalpy (h). The three specific volumes resulting frem these calculations are: V(P,h) Specific volume at pressure P and enthalpy b = VP(P,h) = Specific volume to be used in momentum pressure drop. VFRIC(P,h) = Specific volume to be used in friction pressure drop. First the local quality, X, is calculateo X = (h-h )/h f fg X- = MIN (X,XLIM)
- Then, V=VP=VFRIC=b)I ASVOL. - [ ] i-1)
If X < 0 I i=1 otherwise the void fraction is calculated: b] I BALPL; X(1-1) if PSP and X 1X<X BRK1 BRK1 BRK3 i=1 j X(I ) a=4 BALPH if P1P and X > X BRK1 SRK3 Xu I Xu + (1-X)u BRK1 BRKl- ~ g f e
~
- Then, u
u l g Y auf + (I a)-u \\ g (~ VP ' =u +u I (1 a) 9 a VFRIC =u f Where: BALPL,BALPH = Void fraction vs. quality coefficients defined in Sec. 2.2. u,u,h,hfg = Saturation conditions calculated in Section 2.2 f g f ASVOL = Subcooled specific volume vs. enthalpy polyncmial coefficients, constant. Xgg = Quality limit XBRKl' BRK3 = Qual hy heak points. P8RKl = Pressure break point. 2.13 DEFINITION OF FRICFAC FUNCTION The preceeding calculations make use of the FRICFAC function defined in this section. This is a function of[ ] variables and is defined as c ' FRICFAC local channel friction factor _ = where the dummy arguments are defined as B-27
A_. W e e a O 9 1 l 1 I i e b i 4 4 .I 1 I i } f J a 'I 4 I i j l O ee e N -c---
6 S M enum a O 9 O O me m 'M B-29
a -me.. s-. a e,a ug A 4 a a g g G N I e k / 1 J ? l f t i I. e I t I e e S* 1 i 6 -o M
u - -,- - e d N m 9 e O e r i t t J e O e I B-31
m M ? I I t Se 1 1 I ---._.______.m. Mi 1 l I B-32
e N M 9 e -= Snammu / e o P e e 0+ w O** 1 l -e i B-33
3.0 CONSTANTS 3.1 GENERIC CONSTANTS The generic constants, i.e. those not expected to change frem plant to plant, are summarized in Table 8-1. The numerical values of the constants are included. 3.2 PLANT SPECIFIC CONSTANTS Constants in this category may be different frca plant to plant. Additionally some constants may even differ frem fuel cycle to fuel cycle for a given plant. These constants are summarized in Table B-2. m O O 6 l I Me 9
- m i
B-34 C' LJ
TABLE 8-1 GENERIC CONSTANTS NAME VALUE(S)(a) DESCRIPTION ATF AHF AHFG AVF AVG AVIF AEN i \\ Wa e
- mumm %
B-35
TABLE B-1 (Continued) GENERIC CollSTAttTS NE VALUE(S) DESCRIPTION ~ ALL ALH 4 4 --m M B-36
I TABLE 8-1 (Continued) GENERIC C0tiSTANTS NAME VALUE(S) DESCRIPTION ASVOL ^ i i BVISC I t BTEMP BKPRD i BMPT2 BFRTH I FSPCON 08 CON i I KPRDF n Qc ~ X8RK) E BRK2 ~- BRK3 BRK4 i a B-37
l TABLE B-1 (Continued) \\ GENERIC C0ilSTAtlTS NAME VALUE(S) DEscRIPTIOK P BRK1 'BRK2 PBRK3 CF l e e W% 9 ~. 3 B-38
_ TABLE B-1 (Continued) GENERIC C0tlSTAtlTS ~ NAME VALUE(S) DESCRIPTION C i l O 4 c'3 '45
- 6
- 7 08 B-39
TABLE B-1 (Continued) 1 GENERI; CONSTA!iTS NAME VALUE(S) DESCRIPTION ~ EX1,EX2 ~ 1 m e m M m M 9 4 e e 9 e-G w B-40
~ l \\ TABLE B-2 i _ PLANT-SPECIFIC CONSTANTS FOR ANO-2 NAME VALUE(S) DESCRIPTION 0 AVG OHOT OFUEL SKECDK P E P P4 Aj A2 A 3 A4 O H1 H2 H3 DH4 hEl E2 DE4 HPERIMI HPERIM2 HPERIM4 AX FSPLITl FSPLIT 2 ASI ASI ) g B2 ASI B3 ASIB4 fB1 82 3 Tg3 4 B-41
~ e TABLE 8-2 (Continued) PLANT-SPECIFIC CG;tSTAtlTS FOR ANO-2 NAME VALUE(S) DESCRIPTI0tl PP B1 PPB2 PPg3 PPB4 P1 81 P1 B2 P1 83 P1 84 CH CN 'o t WP1 CON E E'2 GAVG LIM O e. =m B-42
f TABLE B-2 (Continued) _ PLANT-SPECIFIC C0tiSTAtlTS FOR ANO-2 Spacer loss Coefficients Value Kg(l) Kg(2) Kg(3) Kg(4) Kg(5) Kg(6) Kg(7) Kg(8) Kg(9) Kg(10) Kg(ll) Kg(12) Kg(13) Kg(14) Kg(15) Kg(16) Kg(17) Kg(18) Kg(19) Kg(20) e B-43
d TABLE B-2 (Continued) PLANT-SPECIFIC CONSTANTS FOR ANO-2 NAME DESCRIPTION WP2 CON i CIJCON E ONB1 DNB2 MERR (a) Channel 1 - Core Region, 2 - Hot Assembly, 3 - Buffer Channel, 4 - Hot Channel. 6
- mum 1
5 B-44 s I
APPENDIX B PART 2: ACCURACY ASSESSMENT OF CETOP2 ALGORITHM 1.0 pet!ALTY FACTOR METHODOLOGY l.1 Introduction The following section provides a description of the analysis performed to determine the accuracy with which the CETOP2 static thermal margin algor-ithm infers the DNBR. The analysis is performed by ccmparing the DNB overpower margin calculated by the CPC (i.e., CETOP2) to the overpower margin calculcted by the CETOP code described in Appendix A. This method of comparison is similar to that used in Reference 3. 1.2 Obiective of An lysis The accuracy with which the CPC infers, the DNBR dcpends upon a number of factors. The objective of this analysis is to determine the errors attri-butable to the CPC synthesis of the DNBR overpower due to thermal hydraulic modeling differences. The CPC employs the CETOP2 code for determining the DNBR from an axial heat flux profile synthesized using the " pseudo-hot-pin" method (Reference 4). For the analysis, it is assumed that the CPC thermal hydraulic data is exact for the core being simulated and that the planar radial peaking factors and other burnup dependent variables are exact for each time in life investigated. That is, no uncertainty is assigned to these algorithm constants. These constants will be verified in the field during startup, and the uncertainties will be factored into the final CPC settings along with the sensor measurement and Calibration uncertainties. As a result, this analysis is an investigation of the CPC chiculation of the DNCR and has the specific goal of determining the 95/95 probability / confidence level uncertainty factor that is to be applied to the CPC calcul'ation of the DNBR.
1.3 Arnivtical L:chnique 1.3.1 General Strateav The accuracy assessment of the CETOP2 algoritt.m is performad by comparing its calculated overpcuer nrgin to that calculated by CETOP for the sa: e reactor core and coolant conditions. The reactor core simulated is typical of these plants that will use the CPC. A large data base is used in the CETOF2 cccuracy assessment to provide a sufficient statistical data base from which a comparison can be made. It is not essential to the validity of the analysis that the simulators generate exact distributions for any given CEA configuration or time in life, t'ut only to generate a large number of diverse distributions. The final rcsult of the analysis describcd above is an uncertainty f ctor vehich, when applied as a multiplicative ad,iustment to the core power level inuut to the CETOP2 algorithm, results in a calculated DNGR that is con-9 servative with respect to a CETOP evaluation of the equivalent set of operating conditions to at least the 95/95 probability / confidence level. 1.3.2 CPC Constants Calculations are performed using CETOP2 and the design code CETOP Each code is initialized with input derived from the same source.. For the I geometric constants (core active length, hydraulic diameter, etc.) the data source is constructed from print specifications of the core. For design variables such as engineering factors, the input values are taken from l data typically reported in Section 4.0 of Safety Analysis Reports. The l re..sining input itens are the process variables of core inlet temperature, ( reactor cocR4 system pressure, core ficw rate, radial peaking factor, the normalized nial power distribution, and the spcci j of D i\\ -,-C,-,
MQ gggg; Calculations are performed with identical process variable input. In this manner, the errors in the CETOP2 results are isolated to those modeling features that generate errors in predicting the Di;BR and quality at the node of minimum DfiER. 1.4 Thermal f4arcin tiethod 1.4.1 Overoower Ccmoarison The 95/95 uncertainty factors for CETOP2 are quantified in terms of overpower margin (OPit) by comparir.g OPi4 results with those from CETOP over a range of process variables wide enough to include conditions possible during some abnormal event, such as an Anticipated Operational Occurrence (A00). Therefore, CETOP2/CETOP comparisons described result in a conservative estimate of the error for, both normal and abnormal operating conditions. The uncertainty of CETOP2 will be quantified in terms of overpower margin. In order for this technique to be justified, the resultant overpower margin penalty must lead to Df!BR comparisons that achieve 95/95 statis-tical levels, at conditions resulting in a violation of the Specified Ac-ceptable Fuel Design Limit. (SAFDL). 1.4.2 Effect of the Overocwer Uncertainty Factor en DriBR The CETOP2 uncertainty is quantified in terms of overpower margin. Since the CPC computes D::BR, the uncertainty assessment is valid only if the uncertainty factor when applied to the core power input to CETOP2 pro-duces DitSR errors that meet the 95% probability level at the SAFDL. ( so demonstrate that the method cmployed in the analysis satisfies this condition, CETOP2 and CETOP are rerun at powers which are near a SAFDL i l in CETOP with the uncertainty factor applied to CETOP2. At least, 95': ( o of the CETOP2 computed D.*?DRs must be conservative with respect i
,_) -l1, i to the CETOP calculated values. This will ensure that the use of an overpower margin uncertainty is a sufficient and conservative measure l for acccem6 dating the DitBR uncertainty in the CPC. i 1 j e l i i 4 I e. 9 e e J. i I i 0 l %A6
REFERENCES 1. C. Chiu, J. F. Church, Three-Dimensional Lumoed Subchannel Model and Prediction - Correction Numerical 4'g_thod for Thermal Margin Analysis of PWR Cores, TCI-6191, June, 1J79. 2. Combustion Engineering, Inc., TORC CODE: A Comouter Code for Determinino the Thermal Margin of a Reactor Core, CENPD-1$'l-P, July, 1975. 3. "CPC: Assessment of the Accuracy of PWR Safety System Act uation as i Performed by the Core Protection Calculators," CENPD-170, Supplement 1, Combustion Engineering, Inc., November,1975. 4. "CPC: Assessment of the Accuracy of P!!R Safety System Actuation as Performed by the Core Protection Calculators," CENPD-170, Combustion Engineering, Inc., November, 1975.
- e l
l I B-49
F ~: 1 2 Outputs: '" ~ 2.1 DNDR is the current updated minimum DMG ratio. 2.2 X is the current updated quality. 3. Calculations: e 3.1 The following fluid properties are octermined with the same functions specified in STATIC. [ (I-1) h B. T 1 cmax where 8 '['] AEN P(j-1) in = g,I I 4 = J=1 3 5 [] = I AHF P(i_1) h f i=1 [] = I AHFG. P(i-1) h f9 1 j=1
- where,
.hin: Core inlet enthalpy (BTU /LBM) hf: Liquid enthalpy at saturation (BTU /LBM) fg: Latent hea't of vaporization (BTU /LBM) h [ ] array of coefficients for enthalpy vs. pressure AEN: and temperature correlation AHF: polynomial coefficients, constant AHFG: polynomial coefficients, constant t 3.2 The current quality at the node of minimum DNBR is calculated as follows: e m J d c Ju c.J u 84) Ull _s
. APPENDIX C CPC* OflBR and Quality Update Program ~. s ~ M I Inputs: % *. -. ~ t a o e O o 9 4 I ~
- .m e
0 g "1 ),
wm-e ti$;>, sj<*'4 s'#++ im.eEEv <e 1,. TEST TARGET (MT-3) ' En EM d 1.0 g a gg ifa u 1.8 1.25 1.4 l1.6 4 6" v%# '%u\\$ 9 t
M++%+ xxxx[4 %'s4 ,- T,. TEST TARGET (MT-3) 1.0 SEEBaa g a pg m m
- bb l,l e
I.8 '~ 1.25 j l.4 g = 6~ 4% 4+'/b '?fb/;/ h+:Q h, / //
3.3 The current F-correcticn factor is calculated as: ~ 3.4 The current hot channel critical heat flux is calculated as follows: o s. / l i 5 3.5 The current mini =m 0;!BR is calculated as follows: e l l C-3
4. _ Data Base Constant 5 For AND-2 : e l l s = l r e G M m e 9 M O m e e e a l 3 e g i \\ 9 .I. e i ~ o e e S 6 eO e e 9 9-e e o e e g e o e q e e e e g a e ei 0 e 4 e 9 O e e 1 l e e O e e 9 f 9 e - - -}}