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A fkZ0NA UrR
JUL ;.300
3.9 APAE-105
THERMAL ANALYS IS OF TYPE 3 ELEMENTSIN THE SM-i, SM-lA AND PM-2A CORES
ByS. L. DavidsonI. Segalman
March 30, 1962
Nuclear Power Engineering Department
Alco Products, Inc.
Schenectady, New York
:..::..::.....::::.::..: *****,*** ~ *............. m eta dc100971
UNITED STATES ATQMiC.ENERGY COMMISSION+* DIVI$10N OF TECHNICAL INFORMATtQN
LEGAL NOTICEThis report was prepared as an account of Government sponsored work. Neither the UnitedStates, nor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-racy, completeness, or usefulness of the information contained in this report, or that the useof any information, apparatus, method, or process disclosed in this report may not infringeprivately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from theuse of any information, apparatus, method, or process disclosed in this report.
As used in the above, "person acting on behalf of the Commission" includes any em-ployee or contractor of the Commission, or employee of such contractor, to the extent thatsuch employee or contractor of the Commission, or employee of such contractor prepares,disseminates, or provides access to, any information pursuant to his employment or contractwith the Commission, or his employment with such contractor.
This report has been reproduced directly from the bestavailable copy.
Printed in USA. Price $2.50. Available from the Office ofTechnical Services, Department of Commerce, Washington25, D. C.
USAEC Div;,ion of T-chn!cl W-nfl-ato Ext-n;-, Oak Ridge, Tenne-.
APAE -105
REACTOR TECHNOLOGY
THERMAL ANALYSIS OF TYPE 3 ELEMENTSIN THE SM-1, SM-1A and PM-2A CORES
ByS. L. Davidson
I. Segalman
Approved by:M. H. Dixon, Project Engineer
Issued: March 30, 1962
Contract No. AT(30-1)-2639with U. S. Atomic Energy Commission
New York Operations Office
ALCO PRODUCTS, INC.Nuclear Power Engineering Department
Post Office Box 414Schenectady 1, N.Y.
ABSTRACT
Thermal characteristics of Type 3 elements planned for installation inthe SM-1, SM-1A and PM-2A plants were analyzed for bothsteady state and loss offlow transient conditions. Results of this analysis for steady state conditionsindicate that the SM-1, SM-1A and PM-2A Type 3 cores will operate safely atdesign and scram conditions. All steady state analyses indicated minimumDNBR's for both design and scram conditions above the minimum criteria of1. 5. Local nucleate boiling was noted in the SM-1 and SM-1A Type 3 cores.Loss of flow transient results indicate that all three Type 3 cores have minimumDNBR' s above 1. 5 and are safe from burnout. Only the SM-1A Type 3 coreindicates bulk nucleate boiling during the loss of flow accident.
iii
TABLE OF CONTENTS
Page
ABSTRACT--------------------------------------- -iii
SUMMARY----------------------------------------- xiii
1.0 STEADYSTATE ANALYSIS------------------------ 1
1.1 Introduction --------- --------------------------- 1
1. 2 Steady-State Methods of Analysis - - - - - - - - - - - - - - 4
1.3 Power Distribution-- ----------------------------- 4
1. 3. 1 Maximum Power for Each Core - - - - - - - - - - 41. 3. 2 Radial and Axial Power Distributions - - - - - - 4
1.4 Hot Channel Factors------------------------ 17
1. 4. 1 Instrumentation Tolerances - - - - - - - - - - - - 181.4.2 Fuel Plate Rippling------------------- 181.4.3 Additional Factors ------ ------------------ 19
1. 4. 3. 1 Nuclear Uncertainty Factor - - - - - 191.4.3.2 Core Power Generation Factor- -- 19
1.5 Flow Distribution -------------------------------- 19
1. 5.1 Core Flow Distribution---------------- 191. 5. 2 Channel to Channel Flow Distribution - - - - - - 19
1. 6 Selection of Elements for Analysis - - - - - - - - - - - - - 26
1. 7 Steady State Performance of Type 3 Elements in theSM-1 Reactor ----------------------------------- 31
1. 8 Steady State Performance of Type 3 Elements in theSM-1A Reactor---------------------------- 36
1. 9 Steady State Performance of Type 3 Elements in thePM-2A Reactor ------- -------------------------- 36
1. 10 Conclusions and Recommendations - - - - - - - - - - - - - 45
V
TABLE OF CONTENTS (CONT'D)
Page
2.0 TRANSIENT ANALYSIS------------------------------ 47
2.1 Introduction--------------------------------- 47
2. 2 Transient Methods of Analysis ----- ------------------- 47
2.3 Power Distributions----------------------------47
2. 4 Selection of Elements ------ ------------------------- 49
2. 5 Flow Distributions ------ --------------------------- 51
2.6 Hot Channel Factors--------------------------- 51
2. 7 Operating Parameters Used in the Loss ofFlow Analysis ------------------------------------- 55
2. 8 Flow Coastdown ----------------------------------- 55
2. 9 Departure from Nucleate Boiling Ratio (DNBR)Correlations -------------------------------------- 56
2. 10 Allowable Departure from Nucleate Boiling Ratio (DNBR)in Loss of Flow Transient----------------------- 59
2. 11 Various SM-1 Type 3 Core Cases Analyzed - - - - - - - - - - - 63
2. 12 Various SM-1A Type 3 Core Cases Analyzed - - - - - - - - - - 64
2. 13 Various PM-2A Type 3 Core Cases Analyzed - - - - - - - - - - 71
2. 14 Results of the Loss of Flow Analysis of SM-1 Type 3 Core - 80
2.15 Results of the Loss of Flow Analysis of SM-1A Type 3Core-------------------------------------- 81
2.16 Results of the Loss of Flow Analysis of PM-2A Type 3Core-------------------------------------- 81
2. 17 Conclusions and Recommendations------------------82
vi
TABLE OF CONTENTS (CONT'D)
Page
REFERENCES--------------------------------------- 87
APPENDIX A - general Description of the STDY-3 IBM 704 Code- - - - - 91
A-1 Important Correlations in the STDY-3 Code - - - - - - - - 91A-2 Input Format for the STDY-3 Code--------------- 93
APPENDIX B - Hot Channel Factors--------------------------- 97
APPENDIX C - Description of the Equations in ART-02 IBM 704 Code - 101
APPENDIX D - Updated Departure from Nucleate Boiling Ratios For theHot Element of Various Cores ----- ---------------- 111
vii
LIST OF FIGURES
Figure Title Page
1. 1 Dwg. R9-13-1052, Assembly - Fuel Element (Stationary)SM Type 3 Core 5
1. 2A Dwg. R9-13-1047, Fuel Element (Control Rod) SMType 3 Core 6
1. 2B Dwg. R9-13-1049, Type 3 Fuel Element (Stationary)for PM-2A Core 7
1. 3 SM-1 Type 3 Core Control Rod Element Axial PowerDistribution 9
1. 4 SM-lA Type 3 Core Control Rod Element Axial PowerDistribution 10
1. 5 PM-2A Type 3 Core Control Rod Element Axial PowerDistribution 11
1. 6 SM-1, SM-1A Type 3 Core Stationary Element AxialPower Distribution 12
1. 7 PM-2A Type 3 Core Stationary Element Axial PowerDistribution 13
1. 8 SM-1 Core Flow Distribution and Orifice Size 20
1. 9 SM-iA Core Flow Distribution and Orifice Size 21
1. 10 PM-2A Core Flow Distribution and Orifice Size 22
1.11 Pressure Drop Results, Single Element Flow Test for Type3 Elements 23
1. 12 Plate Surface Temperature of Type 3 Elements in the SM-1Core, Position 55 34
1.13 Plate Surface Temperature of Type 3 Elements in the SM-1Core, Position 61 35
1. 14 Plate Surface Temperature of Type 3 Elements in the SM-1ACore, Position 33 39
viii
LIST OF FIGURES (CONT'D)
Figure Title Page
1. 15 Plate Surface Temperature of Type 3 Elements in the SM-iACore, Core Position 72 40
1.16 Plate Surface Temperature of Type 3 Elements in the PM-2ACore,Position 44 43
1.17 Plate Surface Temperature of Type 3 Elements in the PM-2ACore,Position 55 44
2. 1 Flow Coastdowns Investigated in the Loss of Flow Analysis 57
2. 2 DNB Correlations Used in Evaluating the SM-1 and SM-1A 60
2. 3 DNB Correlations Used in Evaluating the PM-2A 61
2.4 ART Code DNB Correction Factor 62
2. 5 SM-1 Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Control Rod in Core Position 55, under the Conditions of Case I) 65
2. 6 SM-1 Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Control Rod in Core Position 55, Under the Conditions ofCase II) 66
2. 7 SM-1 Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Control Rod in Core Position 55,Under the Conditions of Case III) 67
2. 8 SM-1 Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Control Rod in Core Position 55, Under the Conditions of Case IV) 68
2. 9 SM-1 Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Stationary Element in Core Position 61, Under Conditions ofCase V) 69
2.10 SM-1 Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Stationary Element in Core Position 61, Under Conditions ofCase VI) 70
2.11 SM-1A Type 3 Core Minimum DNBR Vs. Time for the Hot Channel(Control Rod in Core Position 55 Under Conditions of Case VII) 72
ix
LIST OF FIGURES (CONT'D)
Figure Title Page
2. 12 SM-1A Type 3 Core Minimum DNBR Vs. Time for the Hot Channel 73(Control Rod in Core Position 55, Under Conditions ofCase VIII)
2. 13 SM-1A Type 3 Core Minimum DNBR Vs. Time for the Hot 74Channel (Stationary Element in CorePosition 72, UnderConditions of Case IX)
2. 14 SM-lA Type 3 Core Minimum DNBR Vs. Time for the Hot 75Channel (Stationary Element in Core Position 72, UnderConditions of Case X)
2.15 PM-2A Type 3 Core Minimum DNBR Vs. Time for the Hot 76Channel (Control Rod in Core Position 44, Under Conditionsof Case XI)
2..16 PM-2A Type 3 Core Minimum DNBR Vs. Time for the Hot 77Channel (Control Rod in Core Position 44, Under Conditionsof Case XII)
2. 17 PM-2A Type 3 Core Minimum DNBR Vs. Time for the Hot 78Channel (Stationary Element in Core Position 55, Under Con-ditions of Case XIII)
2. 18 PM-2A Type 3 Core Minimum DNBR Vs. Time for the Hot 79Channel (Stationary Element in Core Position 55, UnderConditions of Case XIV)
x
LIST OF TABLES
Table Title Page
1. 1 Thermal, Hydraulic and Mechanical Design Data for the
SM-1, SM-1A and PM-2A Type 3 Cores 2
1.2 Core Average Heat Flux 14
1. 3 Radial Power Factors for the SM-1 Type 3 Core,440 0 F 15
1. 4 Radial Power Factors for the SM-1A Type 3 Core,440F 16
1. 5 Radial Power Factors for the PM-2A Type 3 Core510 0 F 17
1. 6 Composite Type 3 Fuel Element Hot Channel Factors 17
1. 7 Instrumentation Tolerances for the SM-1, SM-1A andPM-2A Type 3 Cores 18
1. 8 Maldistribution Results from Single Element Flow TestsFor Type 3 Elements 24
1. 9 Results of Maldistribution Survey on Element 37 - SM-1Type 3 Core - 13.45 MW 27
1. 10 IDNBR Indexes for the SM-1 Type 3 Core 28
1. 11 IDNBR Indexes for the SM-1A Type 3 Core 29
1.12 IDNBR Indexes for the PM-2A Type 3 Core 30
1. 13 Results of the Steady State Thermal Analysis of the SM-1Type 3 Core, Power 10. 77 MW 32
1.14 Results of the Steady State Thermal Analysis of the SM-1Type 3 Core, Power 13. 45 MW 33
1.15 Results of the Steady State Thermal Analysis of the SM-1AType 3 Core, Power 20. 2 MW 37
xi
LIST OF TABLES (CONT'D)
Table Title Page
1. 16 Results of the Steady State Thermal Analysis of the SM-1A 38Type 3 Core, Power 24. 2 MW
1. 17 Results of the Steady State Thermal Analysis of the PM-2A 41Type 3 Core, Power 10 MW
1. 18 Results of the Steady State Thermal Analysis of the PM-2A 42Type 3 Core, Power 12 MW
2. 1 Minimum DNBR's for Various SM-1 Cores 80
2. 2 Results of the Loss of Flow Analysis of the SM-1 84Type 3 Core
2. 3 Results of the Loss of Flow Analysis of the SM-1A 85Type 3 Core
2. 4 Results of the Loss of Flow Analysis of the PM-2A 86Type 3 Core
A.1 Sample Input for STDY-3 Code 96
D. 1 Updated Departure from Nucleate Boiling Ratio for the Hot 112Element of Various Cores
xii
SUMMARY
A steady state and transient thermal analysis has been performed onthe Type 3 replacement cores for the SM-1, SM-1A and PM-2A plants. Thefundamental criterion for acceptable thermal design is the minimum departurefrom nucleate boiling ratio (DNBR). The minimum design DNBR at designpower conditions and scram power conditions for concurrent transient andsteady state analyses is currently specified at 1. 5.
The steady state thermal analysis indicates that the SM-1 Type 3 corewill operate safety at design conditions of 10. 77 MW and scram power of 13. 45MW with minimum DNBR s above 1. 5. Stationary elements in some peripheralcore positions experience local nucleate boiling.
The steady state thermal analysis indicates that the SM-1A Type 3 corewill operate safely at design conditions of 20. 2 MW and scram power of 24. 2MW with minimum DNBR's above 1. 5. At scram power conditions a minuteamount of local nucleate boiling in the hot channel was evident at the exit endof the most critical control rod and stationary element.
Results of the thermal analysis indicate that the PM-2A Type 3 core willoperate safely at design conditions of 10.0 MW and scram power of 12. 0 MWwith minimum DNBR's greater than 1. 5.
The analysis of all Type 3 cores shows they are safe during the earlycritical period (first 3 sec) of a loss of low transient. The correspondingminimum DNBR produced is 1.96 in the SM-iA Type 3 core at the peak powerlevel (scram power level) with the scram mechanism inoperative. Since thisminimum DNBR occurs under the severest conditions and the minimum DNBRproduced is greater than the design criteria of 1. 50, all Type 3 cores are con-sidered thermally safe. Under similar conservative conditions the SM-1Type 3 core has aminimum loss of flow transient DNBR of 4. 08 and the PM-2AType 3 core has a minimum loss of flow transient DNBR of 4. 59.
At nominal power levels theSM-1 and SM-lA Type 3 cores indicate localnucleate boiling in the hot channel while the PM-2A Type 3 core indicates no localnucleate boiling. At the scram power level all Type 3 cores indicate steady statelocal nucleate boiling in the hot channels. However, only the SM-1A Type 3 coreindicates any bulk nucleate boiling in the hot channel during the first 5 sec ofthe loss of flow accident.
In the evaluation of the SM-1 Type 3 core it has been determined that in-creasing the flow coastdown time or scramming the reactor due to reduced flowdoes not appreciably affect the minimum DNBR but helps to impede the bulkfluid temperature rise during the loss of flow transient.
xiii
1. 0 STEADY STATE ANALYSIS
1.1 INTRODUCTION
Steady state and transient analyses have been performed on the SM-1,SM-1A and PM-2A full size Type 3 cores as a part of the Army ReplacementCore Development Program under item 3. 3 of AP Note 286, Addendum 1,Revision 1. * The principal effort in this program was devoted to utilizationof Type 3 (SM-2) fuel plates in the above mentioned cores. Due to an increasein fuel content, the Type 3 fuel elements offer significant improvements incore life over the initial cores.
Various elements within each core have been analyzed to insure safe coreoperation for both steady state and transient conditions. The limitations im-posed upon the preliminary thermal analysis (1) have been removed by the fol-lowing:
A. The analytical predictions and measured nuclear power distributionshave been improved. Good agreement was found between predicted values andcritical experiment (2) values using the exactSM-1, SM-1A and PM-2A core arrays.
B. Channel-to-channel flow distribution was established as a result ofsingle element flow testing. Previous to this analysis, channel-to-channel mal-distributions were estimated(4 )
C. Improved and more realistic transient results were obtained for theloss of pump accident by the use of the transient code ART-02(1 7 ). Previousanalysis treated this as a quasi-steady state problem.
This analysis has presented the important thermal and hydraulic charac-teristics associated with SM-1, SM-1A and PM-2A cores in order to verify safecore operation with Type 3 elements installed. The design data for these coresis listed in Table 1. 1. Fig. 1. 1 and 1. 2 show the Type 3 stationary fuel elementand control rod element, respectively.
* Subsequent to the completion of these analyses a decision had been madeto make the first SM-1 Type 3 core as a prototype of a PM-2A Type 3core. The analysis of this 37 element Type 3 core in the SM-1 will becovered in a supplement to this report.
1
TABLE 1.1THERMAL, HYDRAULIC AND MECHANICAL DESIGN DATA
FOR THE SM-1, SM-lA AND PM-2A TYPE 3 CORES
1. DRAWINGS
The following drawings show the final Type 3 element configurations forinstallation in the SM-1, SM-1A and PM-2A Type 3 Cores.
Fuel Element Control Rod - SM Type 3 Core
Assembly - Fuel Element (Stationary) - SMType 3 Core
Type 3 Fuel Element (Stationary) for PM-2A Core
2. HYDRAULIC DESIGN DATA
D9-13-1047
R9-13-1052
R9-13-1049
A. SM-1 Type 3 Core
Primary System pressurePrimary system flow rateAverage nominal channel mass flowAverage hot channel mass flowMaximum average channel pressuredropMaximum hot channel pressure drop
psiagpmlb/hr-ft 2 x 106lb/hr-ft 2 x 105
ft. H20ft. H2 0
B. SM-lA Type 3 Core
Primary system pressurePrimary system flow rateAverage nominal channel mass flowAverage hot channel mass flowMaximum average channel pressuredropMaximum hot channel pressure drop
psiagpmlb/hr -ft2 x 106lb/hr-ft2
x 106
ft. H2 0ft. H2 0
C. PM-2A Type 3 Core
Primary system pressurePrimary system flow rateAverage nominal channel mass flowAverage hot channel mass flowMaximum average channel pressuredropMaximum hot channel pressure drop
psiagpmlb/hr -ft 2 x 106
lb/hr -ft 2 x 106
ft H2 0ft H2 0
2
120038620.7520. 573
0.990.89
120074001.521.36
1.401.30
175048901.100. 951
1.010.91
3. THERMAL DESIGN DATA
A. SM-1 Type 3 Core
Core Inlet TemperatureMaximum bulk water temp.Maximum plate surface temperatureMaximum meat temperatureAverage plate surface temperatureAverage meat temperature for hotelementEffective core heat transfer areaAverage core heat fluxMaximum Core Heat FluxMinimum, DNBR (steady State)Minimum, DNBR (transient state)
427. 7529. 7576.4603. 2529. 5
OFft2
Btu-hr ft2
Btu- hr-ft2
566. 5589.3264, 5572. 578 x 1054.064.08
B. SM-lA Type 3 Core
Core inlet temperatureMaximum bulk water temperatureMaximum plate surface temperatureMaximum meat temperatureAverage plate surface temperatureAverage meat temperature for hotelementEffective core heat transfer areaAverage core heat fluxMaximum Core heat fluxMinimum DNBR (steady state)Minimum DNBR (transient state)
423479. 5578. 5638.3534. 0
OFft2
Btu-hr-ft2
Btu -hr-ft 2
566. 0593. 1120, 3205. 149 x 105
1.981.96
C. PM-2A Type 3 Core
Core inlet temperatureMaximum bulk water temperatureMaximum plate surface temperatureMaximum meat temperatureAverage plate surface temperatureAverage meat temperature for hotelementEffective core heat transfer areaAverage core heat fluxMaximum core heat fluxMinimum DNBR (steady-state)Minimum DNBR (transient-state)
500545610. 3620. 9572
OFft2
Btu -hr -ft2
Btu -hr-ft2
586. 5513.0768, 8492. 016 x 1054,664.59
3
4. MECHANICAL DESIGN DATA - DIMENSIONS OF FUEL ASSEMBLIES
A. SM-1, SM-1A, PM-2A Type 3 Cores
Stationary Control Rod
Meat width in. 2.650 2.40Plate width in. 2. 839 2. 589Active length in. 22. 0 21. 5Total plate length in. 23. 5 23Overall thickness (max) in. 2. 865 2. 618Overall width (max) in. 2. 874 2. 624
Two outside plates are 27 in. long.
1. 2 STEADY STATE METHODS OF ANALYSIS
The final steady state analysis was performed using the STDY-3 Code (3).It is the authors' intent in this report to discuss in general the input parametersof the code and how the code uses these parameters to arrive at a solution. Adiscussion of this code and the correlations programmed in the code appear inAppendix A.
1.3 POWER DISTRIBUTION
1. 3. 1 Maximum Power for Each Core
The steady state analysis was performed at both design power and scrampower level. This places the analysis for the SM-1, SM-1A and PM-2A Type 3cores on the most conservative basis, The scram power level condition may beobtained by operator's error, such as slow rod withdrawal. Design power levelfor the SM-1 is 10. 77 MW, SM-1A - 20. 2 MW, and PM-2A, 10.0 MW. Scrampower level setting for the SM-1 is 13. 45 MW( 5 ), SM-1A - 24. 2 MW( 6 ), andPM-2A - 12 MW('. These power levels and core heat transfer areas listed inTable 1. 2 were used to calculate average core heat flux.
1. 3. 2 Radial and Axial Power Distributions
The radial peaking factors used in the thermal analysis were calculatedusing the IBM-650 Code, VALPROD. The analytical values were com-pared with experiment to obtain correction factors to apply to the calculatedmost adverse power distributions.
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SURFACE Z soUARE ITN AXISY WITHIN.002 TI.R.
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10 ----- SEMBLY, FUEL ELEMENTSTAT T I
R9-13 1052
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ODD NUMBER PLATES - START FROM HANDLE END.
EVEN NUMBER PLATES - START^Q FROM HANDLE END- OTHER SIDE OF ELEMENT--
EVEN NUMBER PLATES - START FROM HANDLE ENDODD NUMBER PLATES - START? FROM HANDLE END
Figure 1. 2A. Fuel Elements (Control Rod) SM Type 3 Core
--
0
T,I.G.WELD(NO FILLER)
Y (TYa)
SM TYF
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2 89-13-2194 PLATE EXTEN5ION
2 C9-13-2214 SIDE PLATE16 ,89-13-2213 FUEL PLATE
N in i DESCRI"t Ct
ALCO PRODUCTS, INC.
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END or PLATE 4) LONG,. Pd TEj AISY 35 PASS T1RU POINTS , E
0IA0MTERS PARKED X CO3CENTRIC WITH AXlIS Y WITHIN .002 TI.R.JUMPISCEZSOUARE WTTII AXi$ Y WITWII.002 TI1.R
Figure 1. 2B. Fuel Element (Stationary) Type 3 for PM-2A CoreI-- -JEL- R 19- L -1F C_: ., r P
~ R9 3 9
7
I
- - -- - -- -- -
.: - -
'
"
.. -
The average and local radial peaking factors listed in Tables 1.3, 1.4,and 1. 5 were used to determine hot channel factors for both the nominal andhot channel. These are applied as follows to obtain the mechanical hot channelfactors for both the nominal and local channels used in the channel descriptioninput parameters described in Appendix A.
For the nominal channel:
For the hot channel
where FA TN , FAO N ,
FN = nuclear uncerta
QAT
QAT
F ATN
F eN
F A TH
F J 6H
- FN F@Q AT
= FN F Qo
= FN F/J QAe
= FN FVIQ e FMA6
FATH FAO = the average and local hot channelH factors respectively
inty factor for average or local condition
= power generation factor for average or local condition
= average radial peaking factor in the hot channel
= average radial peaking factor in the nominal or average channel
= local radial peaking factor
FMAT, FMA9= mechanical hot channel factor excluding
plenum maldistribution factor.Average and local, respectively.
plate spacing factor and
The relative axial power distributions for each core are shown on Fig. 1. 3,1. 4, 1. 5 for control rod elements and Fig. 1. 6 and 1. 7 for stationary elements.These values are normalized to a core average of one. One value for each axialchannel increment is used in the analysis as described in Appendix A.
8
2. 0
1. 8
1. 6
1.4
1.20
P4 1.0
.8
.6
.4
.2
0
10 12 14 16 18 20 22
INCHES FROM BOTTOM OF FUEL IN CONTROL ROD FUEL PLATE
Figure 1. 3. SM-1 Type 3 Core Control Rod Axial Power Distribution (Rod inserted 9. 5 inches) 7 Rod Bank Positioi
-V -=-L .... . .:.. .:.. .
.r .
. . . 0 e . e . . m . m . g e . . . . g a a e . . . . . .... . . ... . . . . . . . , . e . . . . . . . . ... . . .. e e a e . . e . e
. . . . o a e = a e g e g ., e e e .e g g ...., .. ....,. .......,. ..... ................ ........ .. ... .. ... ... ................... .........a e e
2 4 6 8
n
2. 0
1. 8
1. 6
1.4
1. 2
1. 0
.8
.6
.4
.2
.0
... .... .... ... ... .. ..- .:... .... .... .... ... . . . .. . . . . . . . . :-.
.... .... .... .... ... .... ... . ... .... .. ., .. .... .
4... .-. e ... . .
. ~e . .. . .. . .. g a . e a %a .. .g .. a . .. e . .. .. e. H.-. . . -- I -Hm . .. n .
2 4 6 8 10 12 14 16 18 20 22
INCHES FROM BOTTOM OF FUEL IN CONTROL ROD FUEL PLATE
Figure 1. 4. SM-1A Type 3 Core Control Rod Power Distribution (Rod Inserted 10. 5 Inches) 7 Rod Bank Position.
0
_ ; - -., -- I-_r-I--'t-M--I - I L -1--t
H L TT
"I; -"r.
t{ F- 1l-- -i- -
I t r ; -[
-' 11 , r t j - i14-
+ r" }-I4 I I ' t -F tr -t , r -r( T i. r .I -T 1 r .
tr i I r rr . ! r
-Q i Fr-- --I
114
-r } - I } 1 r -I- (- - -1'+- - i -14 iH i - - - -1t - - -C'-I-
-44
ij IM t - 1
T' -i1#1.-I
1 d- -4-j
- T - - - - ~-- -
-H -- . 1.1- ...I -1
+- I } I I 1 1 ' r j I F -- i T I l r - { - - -
- , it }1aI ti .Itsr
p 1---1- -i
C -t? iI- r -t- .: -1.- T 1+ ti 0 .#............r
2 4 6 8 10 12 14 16 18
INCHES FROM BOTTOM OF FUEL IN CONTROL ROD FUEL PLATE
Figure 1. 5. PM-2A Type 3 Core Control Rod Power Distribution (Rod Inserted 17. 5 Inches)
1. 5
1.
N
0
N
0 22
F.i .. ;
... +
t 1
1 1' r l
t T " r
H - i i .--:HHt$ f -r
E
i
N
U
rr
:.. I
Nry'
r
fi r!i -4t f trTf }
'rr
t
t t tt
1 '' H't
-1.I
1 !
. r . i {- - -. ,. . , .
i
- I r - . . ,1r ,~ T .. T I:f rt 1 F
i
- -
i IT T T '
.
20
TRods Inserted 9.5 Inches for SM-1Rods Inserted 10. 5 Inches for SM-1A7Rod Bank Position
-. 'r' - - j'H -b- 7 +L -- v -
-u-t-,2 4 6 8 10 12 14 16
INCHES FROM BOTTOM OF CORE
Figure 1. 6. SM-1 and SM-lA Type 3 Cores Axial Power Distribution (Stationary Element)
18 20
2. 0
r1.
1.0O
22
1. 5
1.0
INCHES FROM BOTTOM OF CORE
Figure 1. 7. PM-2A Type 3 Core Axial Power Distribution (Stationary Element)
2 4 6 8 10 12 14 16 18 20 22
----
:: - ' - - Rods Inserted 17. 5 Inches-r _ 5 Rod Bank Position
jiI I
: - - - -L -
e~~............. .......
----------------------------
-"i 7 -I-
Wz
W-
.5
TABLE 1.2CORE AVERAGE HEAT FLUX
Rod Bank
7
7
7
7
5
5
Control RodMeat Insertion
Inches
9.5
9.5
10. 5
10. 5
17. 5
17. 5
Core HeatTransfer Area
Ft
589.32
589.32
593.05
593. 05
513. 07
513. 07
PowerMW
10.77
13.45
20.2
24.2
10.0
12.0
*Core AverageHeat Flux
Btu/hr-ft2
64, 557
77,920
120, 320
144, 143
68, 849
82, 619
* An instrumentation tolerance of 3. 5% was applied to the core power for both design and scram levelconditions.
Core
SM-1
SM-1
SM-1A
SM-1A
PM-2A
PM-2A
TABLE 1.3RADIAL POWER FACTORS FRO SM-1 TYPE 3 CORE - 4400 F
ElementNo.
12,7613,7514, 7415,7316,7221, 6722, 6623, 6524, 6425, 6326, 6227, 6131, 5732.5633, 5534, 5435, 5336, 5237, 5141,4742,46434445
Q AT)
0. 7950.8270. 8970.9190. 8720. 8540. 8150.9151.071.0430.9240.9060. 8700.9011.201.2021.2471.0860. 8700.9421.071.2001.351.214
Q *Q MWYR
1.220.930.941.051.181.281.031.201.271.231.081.221.471.311.551.591.531.381.281.611.331.591.491.62
* Subscript zero refers to Power Factor at Start of Life** Subscript B refers to Power Factor During Life
15
QQ( A e 0 MWYR
1.731.731.831.791.831.911.301.701.621.571.361.971.981.651.901.881.811.661.551.821.641.891.811.81
Q(A T)BB
1.290.980.991. 111.241.351. 091.271.341.301.141.291.551.381.641.681.611.461.351.701.401.681.571.71
Q (Ae)B
1.831.831.931.891.932.021.371.791.711.661.432.082.091.742.001.981.911.751.641.921.731.991.911.91
TABLE 1.4RADIAL POWER FACTORS FOR SM-1A TYPE 3 CORE - 4400 F
Q 'IT)0 MWYR
1.300.960.950.931.211.150.991.171.231.261.071.200.901.201.561.551.521.291.030.881.201.571.541.67
( A 6)o MWYR
1.941.811.901.881.971.901.321.681.751.691.391.901.891.531.941.921.851.641.811.841.461.931.851.82
ElementNo.
16
Q( L T)
12, 7613, 7514, 7415, 7316,7221, 6722, 6623, 6524, 6425, 6326, 6227, 6131, 5732, 5633, 5534, 5435,5336, 5237, 5141,4742,46434445
(A T)B
1.501.111.101.071.401.331.141.341.421.451.231.381.041.381.801.791.751.491.191.011.381.811.781.93
0.790,840.880.940.850.730.800.910.871.070.920.840.810.961.221.211.261.050.860.820.971.211.341.24
(A9)B
2.242.092.192.172.272.191.521.942.021.951.602.192.181.762.242.212.131.892.092.121.682.232.132.10
TABLE 1.5RADIAL POWER FACTORS FOR PM-2A TYPE 3 CORE - 5100 F
Element Q(A\T) Q Q Q QNo. kIT/ (AT)0MWYR (A)0MWYR (A T)B (QAe)B
13,15,73,75 0.760 1.31 1.39 1.52 1.6114,74 0.739 0.75 1.22 0.87 1.4122,26,62,66 1.017 1.39 1.74 1.61 2.0123,25,63,65 0.983 1.21 1.60 1.40 1.8524,64 0.508 1.26 1.67 1.46 1.9331,37,51,57 0.839 0.83 1.32 0.96 1.5332,36,52,56 0.993 1.17 1.53 1.35 1.7733,35,53,55 1.190 1.27 1.75 1.47 2.0334,54 1.180 1.27 1.70 1.47 1.9741,47 0.792 0.96 1.02 1.11 1.1842,46 0.508 1.33 1.57 1.54 1.8243,45 1.200 1.40 1.67 1.62 1.9344 0.678 1.51 1.77 1.75 2.05
1.4 HOT CHANNEL FACTORS
The mechanical hot channel factors used in this final analysis include averageand local deviations for active core length, uranium content, and clad thickness.The preceding factors were calculated by methods described in Appendix B. Theresults of these calculations are listed in Table 1. 6.
The plate spacing and flow maldistribution factors do not appear in the STDY-3code as hot channel factors. Plate spacing appears in the hot and nominal channeldescription input parameters as an average and local dimension. This is shown oncards 81 and 82 in Table A. 1. Flow maldistribution and its associated hot channelfactor are discussed in Section 1. 5.
TABLE 1.6COMPOSITE TYPE 3 FUEL ELEMENT HOT CHANNEL FACTORS
Stationary Element Control Rod Element
FMAT FMAe FMAT FMA8
Meat Length 1.0233 1.0233 1.0233 1.0233Uranium content 1.005 1.025 1.005 1.025Clad thickness 1.007 1.012 1.007 1.012Composite Mechanicalfactor as applied inSTDY-3 Analysis 1.0357 1.0615 1.0357 1.0615
17
1. 4. 1 Instrumentation Tolerances
The worst reactor conditions were considered in the thermal analysis andtolerances applied to the reactor instrumentation. These instrumentationtolerances are listed in Table 1. 7.
TABLE 1.7INSTRUMENTATION TOLERANCES
SM-1 Core
Core PowerInlet Temp.System Pressure
Instrumentation Tolerance
/ 3. 5% at scram power level7 4. 00 at core inlet 427.7 0 F7 25 psia at 1200 psia
Value UsedIn Analysis
13.45431. 70 F
1175 psia
PM-2A
Core PowerInlet Temp.System Pressure
/ 3. 5% at scram power level7 4. 00 at core inlet 500 0 F7 35 psia at 1750 psia
SM-1A
Core PowerInlet Temp.System Pressure
/ 3. 5% at scram power level7 4. 00 at core inlet 423 0 F7 25 psia at 1200 psia
1. 4. 2 Fuel Plate Rippling
Compressive stresses result from the temperature differential betweenthe meat and side plate causing ripples in the fuel plates. To account for thegrowth of these ripples, growth factors were taken from the rippling analysis ofSM-2 elements and applied to the local hot channel dimension.
Element
Stationary
Control Rod
Ripple Ratio
1. 55
1. 20
Hot Channel Spacing
0, 136
0. 133
18
125040 F1715 psia
24. 24270 F1175 psia
1. 4. 3 Additional Factors
1. 4. 3. 1 Nuclear Uncertainty Factor
To allow for uncertainties in the calculated power distribution, a nuclearuncertainty factor of 1. 05 was used for the nominal channel and 1. 10 for thehot channel.
1. 4. 3. 2 Core Power Generation Factor
In order to account for the fraction of fission heat liberated in the coolantdirectly (F W/f1) a factor of 0.95 was applied to the power generated in the fuelplates for local conditions. The fraction of power generated in the core (F )is 1. 00 for average conditions.
1. 5 FLOW DISTRIBUTION
1. 5. 1 Core Flow Distribution
Element-to-element core flow distributions for Cores I are shown in Fig,1. 8, 1. 9, and 1. 10. It is expected that the flow distribution within the Type 3cores will be identical with SM-2 elements installed.(10) Core flow distributionswere obtained from full scale air flow rigs described in Ref. (11), (12), and (13).Orifice plates were developed for each core to give the required element flows.The orifice plate schedules are also shown on Fig. 1. 8, 1. 9 and 1. 10.
1. 5. 2 Channel-to-Channel Flow Distribution
In the preliminary thermal analysis (1) a maldistribution of 12 percentwas assumed. This was based on past experience of SM-2 single element flowtesting (14) excluding end box effects. MTR and ETR (15, (16) single elementflow tests have shown channel to channel maldistribution as high as 25%.
A single element flow test program was conducted at Alco's GeneralEngineering and Test Laboratory to provide channel-to-channel maldistributionfactors for the steady state and transient thermal analysis. The basic philosophyfor optimum channel distribution is that any departure from the desired uniformprofile must not cause below average flow at the outermost channels and latticeswhere flux peaks are expected to occur.
The flow test program was set up to provide factors for the three cores toinsure conservatism in the analysis. The most adverse flow distribution wasmocked up by testing each core with its stationary element of minimum orificediameter. The unorificed control rod elements for each core were also tested.
19
12* 13 1.4 15 116
46.571. 190
56. 271. 345
59. 571. 380
57. 631. 325
45. 601. 220
21* 22 3 24 25 26 27*C.R.
43.66 67.13 89.64 93.34 88.28 66.75 45.601.190 1.500 1.750 1.720 1.520 1.190
31 32 13 34 35 36 37C.R.
55.30 87.70 89.20 100.90 100.60 87.31 56.85
Inlet 1.330 1.750 2.010 1.920 1.800 1.280
41 42 43 44 45 46 47C.R. C.R. C.R.
57.63 94.69 106.13 94.34 105.16 92.16 62.891.390 1.940 1.890 1.315
51 52 53 54 55 56 57C.R.
58.60 86.34 97.40 106.13 89.00 88.48 57.431.330 1.720 1.830 2.020 1.780 1.270
61* 62 63 64 65 6 67C.R.
44.24 67.91 92.75 94.69 86. 93 67.99 45.211.190 1.500 1.740 1.750 1.500 1.190
72
47. 151. 200
73
58. 601. 340
74
58. 991. 380
75
50. 251. 325
76
45. 211. 210
Core Position
xx.xx Element Flowrate (gpm)X.XXX Orifice Size (In.)
*Positions Tested In Type 3Single Element Flow Test
Figure 1. 8. SM-1 Core Flow Distribution and Orifice Size
20
12* 13 14 11-615
12
1381. 758
72
1341. 734
13
1461. 882
73
1471. 800
14
1481. 870
74
1491. 810
Core Position
XX -Element Flowrate (gpm)
XXX Orifice Size (In. )
15
1481. 855
75
1491. 925
16
1361. 745
76
1411. 820
* Position Tested in Type 3Single Element Flow Test
Figure 1. 9. SM-lA Core Flow Distribution and Orifice Size
21
-
Inlet
22* 23 24 25 26 27C.R.
132 127 142 147 142 131 1311.705 1.680 1.764 1.808 1.734 1.673
31 32 33 34 35 36 37C.R.
146 135 147 157 149 135 1451. 767 1. 720 1. 815 1. 823 1. 730 1. 815
1 42 43 44 45 46 47C.R. C.R. C.R.
148 147 152 147 155 147 1481.773 1.823 1.864 1.833
51 52 53 54 55 56 57C.R.
146 135 153 155 147 141 1551.817 1.707 1.840 1.790 1.820 1.802
61 62 63 64 65 66 67C.R.
132 127 136 147 143 129 1291. 740 1. 735 1. 733 1. 790 1. 736 1. 750
23
1091.93
Inlet
13
1151.93
14
1131.96
15
1131. 97
22 24 25 224
C.R.110
31 32 33 34 35 36 37
115 114 115 108 115 114 1141.90 2.03 1.99 1.99 1.87 1.97 1.90
41 42 43 44 45 46 47C.R. C.R. C.R.
115 110 111 110 115 110 1171.94 2.05 2.01 1.93
51 52 53 54 55 56 57
115 115 114 116 110 113 1151.94 1.97 2.03 1.96 1.89 1.97 1.94
64
C.R.110 114
1.88
i i i
1131.90
63
73
1131.97
1091.93
74
1181.94
ore Positionxx
xxx Element Flowrate (gpm)x.xx Orifice Size (In. )
65
75
1151.87
66
1141.84
* Position Tested in Type 3Single Element Test
1132.05
Figure 1. 10. PM-2A Core Flow Distribution and Orifice Size
zz
22*
113
1. 83
25 26
115
1.94
62
Total Element Pressure Drop vs Flow
SM-1 1. 19" Orifice
II I I I I
SM-1 1. 19" OrificeWith Diffuser
SM-1 and SM-iA___No Orifice
PM-2ANo Orifice
20 30 40 50 60 7080 90 100Element Flow - GPM
1 I11
Figure 1. 11.
Results of Pressure Drop, Single ElementFlow Test, Stationary Type 3 Fuel Elements
23
100908070
60
50
40 -
30 H
20 K0
N
10987
6
5-
4
3
2
IL
f N
I l I I --- I I I - -
//
)
Velocity probes in each channel were connected by tubing to a manometerboard and the element installed in the test rig with its appropriate orifice plateat the inlet of the end box for SM-1 elements and the exit of the end box forSM-1A and PM-2A cores. Water was circulated through the elements at flowrates corresponding to those obtained in full scale flow testing. Velocity headmeasurements were obtained for each probed channel and graphed for ease ofinvestigation. A detailed test report, Ref. (4) contains these graphs along witha complete summary of the test program. Table 1. 8 lists maldistributionresults obtained from single element flow tests. The maldistribution resultsare the maximum percentage deviation from the average channel flow. Thistable lists the data which was used for calculating the maldistribution factors inthe thermal analysis.
MA LDIS TRIBUTIONTABLE 1.8
RESULTS FROM SINGLE ELEMENTFOR TYPE 3 ELEMENTS
FLOW TESTS
Type ofElement
Stationary
Stationary
Stationary
Control Rod
Control Rod
Control Rod
Stationary
Control Rod
Control Rod
Stationary
Stationary
Control Rod
Control Rod
Orifice Diam,In.
1.19
1.19
1.19
No orifice
No orifice
No orifice
1.68
No orifice
No orifice
1.83
1. 83
No orifice
No orifice
FlowGPM
87
75
52
99
76
50
125
120
100
125
100
120
100
PercentMaldistribution
/70. 5-70. 0/44.0-58.0/44.0-55.0/23. 5-27. 8/21. 6-25. 9/18. 0-21.0/6. 1-6. 7/13.2-22. 8/12.0-21.2/6. 2-11. 1/5. 8-10. 8/13. 2-22. 8/12.0-21.2
24
Core
SM-1
SM-1
SM-1
SM-1
SM -1
SM-1
SM-1A
SM-1A
SM-iA
PM-2A
PM-2A
PM-2A
PM-2A
To insure conservatism in the final analysis, maldistribution data wasobtained from the minimum orificed elements. The poor distribution in theSM-1 stationary elements is attributed to the orifice plate being on the inletside of the element. The SM-1A and PM-2A cores have orifice plates on theexit side of the elements. The maldistribution results, excluding the SM-1stationary elements, are in good agreement with previous single element flowtesting conducted on the MTR and ETR elements which had similar end boxconfigurations. (14), (15)
Overall element pressure drop was measured for the stationary elements.This data was not used in the final thermal analysis, however it served as anindication of the magnitude of overall pressure drop for the SM-1, SM-1A andPM-2A cores with no orifices and the range of pressure drops for the SM-1 fromminimum orifice 1. 19 to no orifice. These results are shown on Fig. 1. 11.
To improve the flow distribution within the SM-1 stationary element severalflow fixes were tested. The most successful, a conical diffuser located in theinlet end box improved the maldistribution and element flow profile from a -55%to a -23%. The overall element pressure drop was thus reduced as shown onFig. 1. 11. Further details of this test and other flow fixes are contained inRef. (4).
As a result of the single element flow testing of Type 3 SM-1 elements, amaldistribution study was performed to determine the effects of varying thechannel to channel flow distribution on an element's thermal performance. Variouschannel to channel maldistributions were inserted into the STDY-3 code. Sinceonly changes in frictional pressure drop are considered;
A Friction - (G)1.8
K1 = (1 -6)1.8
where G - mass flow rate - lb/hr - ft2
6 = channel-to-channel flow maldistribution -%
K1 = plenum factor used in the STDY-3 code
Results of this analysis are shown in Table 1. 9 for SM-1 element position 37.The 42% maldistribution was extrapolated from experimental data. The resultsindicate very small variations in DNBR due to increases in flow maldistribution.Plate surface temperatures and meat centerline temperatures remained essentiallythe same along the length of the channel with the largest variation of these para-meters occurring in the first few inches at the entrance of the channels. The hotchannel flow and the hot channel pressure drop decreased with increases in mal-distribution. Local nucleate boiling does not occur for maldistribution less than20%. The inception of local nucleate boiling in the hot channel is approximately6 in. at 42%, 8 in. at 60% and 9 in. with bulk nucleate boiling at 80%.
25
It is apparent that no major improvements in DNBR could be made byimproving channel flow distribution. This is likewise true for plate surfacetemperatures and meat centerline temperatures. DNBR's are well above thedesign minimum of 1. 5 for steady state operation at 13.45 MW. However, localnucleate boiling is evident for maldistributions above 20% and improvements couldbe made to reduce the extent of local nucleate boiling in the hot channel. Thiscan be accomplished with the conical diffuser mentioned above.
1. 6 SELECTION OF ELEMENTS FOR ANALYSIS
An analysis has been presented (8) in which a basis for element selectionhas been determined. A burnout index was established for each core in which
I = 1 5w K QADNBR 2 H T Q Q
and K = 0 avg AH U) o f' (Z)n=o
where
IDNBR = burnout index
Ho = reactor inlet enthalpy, Btu/lb
G volumetric flow rate, gpm
AH = effective core heat transfer area, ft2
0avg = average core heat flux Btu/hr-ft2
f'(Z) - axial power distribution for the jth position
p = fluid density, lb/ft3
For the SM-1 core this equation is
I = 1 / 16. 67 QAT) AQ (1.1)DNBR G
For the SM-1A core this equation is
IDNBR 1/ 31.01 Q AT Q L® (1.2)
For the PM-2A core this equation is
ID = 1 /15.76 GT Q (1.3)DNBR G
26
TABLE 1.9RESULTS OF MALDISTRIBUTION SURVEY ON ELEMENT 37 - SM-1 TYPE 3 CORE, 13.45 MW
Hot ChannelBulk Temp.Rise
82.0
103.0
124.22
135.70
Hot ChannelEnthalpyRiseBtu/lb
95.3
121. 28
148.23
166.76
Max. Max. TM-TS Min.TS- F TM- F (max) DNBR
575.90
575.90
575.90
575.90
600.49
600.49
600.49
600.49
24.6
24.6
24.6
24.6
6.14
5.97
5.88
5.75
HotChannelLocalBoiling
No
Jm11*
J.8*
J=7*
BulkBoiling Quality %
No
0
0
J-22*
0
0
0
0.4
* Axial increment at which nucleate boiling begins, measured in inches from bottom of core
% Mal-Distr.
20
42
60
80
NominalChannelFlowlb/hr-ft2
5. 90x105
5. 90x105
5. 90x105
5. 90x105
HotChannelFlowlb/hr-ft2
5. 17x105
4. 06x105
3. 32x105
2. 95x10 6
Avg. HotChannelPressureDrop-psi
0.736
0. 703
0. 688
0. 669
TABLE 1.10
IDNBR INDEXES FOR THE SM-1 TYPE 3 CORE
Core Position
1213141516212223242526
*27*313233
*3435
*3637
*414243
*444546
*475152
*5354
*5556
*57*61
6263646566677273
*747576
G, GPM
46.5756.2759.5957.6345.6043.6667.1389.6494.3488.2866.7545.6055.3087.7089.20
100.90100.60
87.3156.8557.6394. 69
106.1394.34
105.1692.1662.8958.6086.3497.40
106.1389.0088.4857.4344.2467.9192.7594.6986.9367.9945.2147.1558.6058.9950.2545.21
QAT
1.290.980.991.111.241.351.091.271.341.301.441.291.551.381.641.681.611.461.351.701.401.681.571.711.401.701.351.461.611.681.641.381.551.291.141.301.341.271.091.351.241.110.990.981.29
Q IDNBR - (1/ 1 6 . 6 7 QAT) QAe
1.831.831.931.891.932.021.371.791.711.661.432.082.091.742.001.981.911.751.641.921.731.991.911.911.731.921.641.751.911.982.001.742.092.081.431.661.711.791.372.021.931.891.931.831.83
2.682.362.462.502.803.061.742.212.122.071.943.073.072.192.612.532.422.242.292.862.162.582.442.432.272.792.172.242.442.502.612.193.033.091.832.052.112.231.743.032.782.492.472.422.70
28
TABLE 1.11
IDNBR INDEXES FOR THE SM-1A TYPE 3 CORE
Core Position
12131415
*16212223242526
*273132
*33*34
3536374142
*4344454647515253
*54*55
5657
*61*62
6364656667
*7273747576
G, GPM
138146148148136132127142147142131131146135147157149135145148147152147155147148146135153155147141155132127136147143129129134147149149141
QAT1.501.111.101.071.401.331.401.341.421.451.231.381.041.381.801.791.751.491.191.011.381.811.781.931.381.011.191.491.751.79
1.801.381.041.381.231.451.421.341.141.331.401.071.101.111.50
QAe2.242.092.192.172.272.191.521.942.021.951.602.192.181.762.242.212.131.892.092.121.682.232.132.101.682.122.091.892.132.212.241.762.182.191.601.952.021.941.522.192.272.172.192.092.24
IDNBR= 1/31.01 QAT1 QA
2.992.582.692.662.992.872.042.512.622.572.072.902.662.323.092.992.912.542.622.572.173.052.932.912.172.572.622.542.893.003.092.292.632.902.082.592.622.501.942.893.012.662.692.572.98
29
'DNBR INDEXES
TABLE 1.12FOR THE PM-2A TYPE 3 CORE
Core Position
*131415
*22232425
*263132
*33343536
*374142
*43*44
45464751525354
*555657
*62636465
*66737475
G, GPM
115113113113109110113115115114115108115114114115110111110115110117115115114116110113115113113110114114109118115
Q~AT
1.520.871.521.611.401.461.401,610.561.351.471.471.471.350.961.111054
1.621.771.621.541.110.961.351.471.471.471,350.961.611.401.461.401.611.520.871.52
QA 61.611.411.612.011.851.931.852.011.531.772.031.972.031.771.531.181.821.932.051.931.821.181.531.772.031.972.031.771.532.011.851.931.852.011.611.411.61
IDNBR= 115. 76QAT] Q e1.951.581.952.462.222.262.182.451.732.102.442.392.442.101.731.362.222.372.572.362.221.361.732.102.442.362.462.101.732.462.212.342.212.471.961.581.95
30
/i \ Li V
The above correlations were used to determine the relative values of theDNBR between elements. To insure the thermal safety of the cores the mostcritical elements for each core were analyzed. These elements appear with anasterisk in Tables 1. 10, 1. 11, and 1. 12. With the selection of these elements acomplete thermal history of each core was obtained.
1.7 STEADY STATE PERFORMANCE OF TYPE 3 ELEMENTS IN THE SM-1 CORE
A steady state thermal analysis was performed on 12 elements within theSM-1 core. These elements were selected based on their burnout indexes pre-sented in Table 1. 10. In some instances elements even with low burnout indexeswere selected because of their critical location, such as element number 74.adjacent to the core reflector.
The analysis included studies at both design power 10. 77 MW and at scrampower 13 MW with average core heat fluxes of 64, 557 Btu/hr-ft2 and 77, 920Btu/hr-ft2 respectively. Plate surface temperature, bulk water temperature,departure from nucleate boiling and quality were calculated for one-inch incrementsup the 22 in. channel. The results of this analysis at 10. 77 MW are shown onTable 1.13 and at 13.45 MW on Table 1.14.
Local boiling is indicated at design power and design flow conditions forelement positions 27, 31, 41947, 57 and 61. Local boiling is also indicated atscram power for the identical element positions with the inception of boiling occur-ring slightly below that indicated at design conditions. The inception of local boilingis characterized by a flat plate surface temperature profile. This profile forelement position 61 is shown on Fig. 1. 13. Element 55 shown on Fig. 1. 12 ismarginally away from local boiling as shown by the flatness of the plate surfacetemperature curve at the exit end of the element and the fact that 11. 0 degrees ofsuperheat exists between saturation temperature and maximum plate surfacetemperature.
The results of this analysis indicate that no SM-1 element is in danger ofburnout since the most critical control rod element, #55, and the most criticalstationary element, #61, exhibit minimum DNBR's of 4. 91 and 5. 21, respectively.This is based on DNBR's well above the steady state minimum DNBR of 1. 5,when a transient analysis is performed. See Section 2. 10.
31
TABLE 1.13RESULTS OF THE STEADY STATE THERMAL
ANALYSIS OF THE SM-1 TYPE 3 CORE, POWER 10.77 MW
Core Position
273134364144475355576174
G-NominalChannel Flow
x 106 lb/hr-ft2
0.4740.5741.0480. 9070. 5981.0760. 6531.0111.0150. 5960.4590. 613
G-Hot Channel FlowX 105, lb/hr-ft2
3.2593.9469.177.9364. 8597.3974.4898. 8466.9784.0973. 1564. 597
Hot ChannelBulk OutletTemp., F
521.2521.0474.3474. 5517. 8465. 7517. 7474.0469.1517.8524.0486.1
Hot ChannelMaximumPlate SurfaceTemp., OF
575. 6576.1551.9550.9576.4571.7576.4550.9576.3576.1575. 6575.0
MinDNBR Qlty.
5.225.245.746.515.725.175.685.964.915.225.215.85
000000000000
* Axial increment at which nucleate boiling begins, measured in inches from bottom of the element.
W-'N
*LocalBoiling
790090700770
TABLE 1.14RESULTS OF THE STEADY STATE THERMAL
ANALYSIS OF THE SM-1 TYPE 3 CORE, POWER 13.45
Core Position
273134364144475355576174
G -NominalChannel Flow
X 106 lb/hr-ft 2
0.4740. 5741. 0480.9070. 598+1.0760. 6531.0111.0150. 5960.4590. 613
G-Hot Channel FlowX 105, lb/hr-ft 2
3.2593. 9469. 1707.9364.4857.3974. 8598.8466. 9784. 0973. 1564.597
Hot ChannelBulk OutletTemp. , OF
535.3535. 0476. 0479. 6531. 3469.0531.2479.0473.2531.3538. 6493.5
Hot ChannelMaximumPlate SurfaceTemp. , F
576.1576.7565.0571.9576.9576. 7576.9571.8576.8576.7576.1575.5
MinDNBR
4.283.754.765.384.664.314.664.934.064.284.274.84
*LocalQlty. Boiling
000000000000
660050500650
* Axial increment at which mucleate boiling begins, measured in inches from bottom of the element.
580
570
560
550
540
530
520
510
500
490
480
470
460
450
440
430
4201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Length Along Element Plate - InchesFigure 1.12
Plate Surface Temperature of Type 3 Elements in the SM-1 CoreCore Position 55
0
a,
a,VA
Ci2
T Saturation /
-I
13.45 MW
I 10. 77 MW
-/
-
ifi- ---- ----- L------LL
0
580
570
560
0 1 2 3 4 5 6 7 8 9 10 11 12 12 14 15 16 17 18 19 20 21 22
Length Along Element Plate - Inches
Figure 1.13
Plate Surface Temperature of Type 3 Elements in theCore Position 61
SM-1 Core
- 13. 45 MW
-- - -T Satu:ration
1l10.77 MW0
a
a
)
CU)
4a
550
540
53 0
520
510
500
1.8 STEADY STATE PERFORMANCE OF TYPE 3 ELEMENTS IN THESM-1A REACTOR
A steady state thermal analysis was performed on 10 element positionswithin the SM-1A core. These elements were selected based on their burnoutindexes presented in Table 1. 11.
The analysis included studies at both design power 20. 2 MW and at scrampower 24. 2 MW with average core heat, fluxes of 120, 320 Btu/hr-ft2 and144, 143 Btu/hr-ft 2 , respectively. Plate surface temperature, bulk water temper-ature, departure from nucleate boiling and quality boiling were calculated forone inch increments up the 22-in. channel.
The results of this analysis at 20. 2 MW are shown on Table 1. 15 and at24. 2 MW on Table 1. 16. There is no indication of local boiling at design powerconditions. However, local boiling is indicated at the extreme exit end ofcontrol rod elements 33 and 55 at scram power conditions. The inception oflocal boiling with its characteristic flat surface temperature profile is shownon Fig. 1. 14 for element 33. Element 72 shown on Fig. 1.15 represents thestationary element with the lowest DNBR. The flat profile for plate surfacetemperature indicates that this element is marginally away from local boilingwith 13 degrees of superheat.
The results of this analysis indicate that no SM-1A element is in danger ofburnout at design conditions of 20. 2 MW, since the most critical control rodelement 33 and the most critical stationary element 72 exhibit minimum DNBR'sof 2.39 and 2. 70, respectively. These elements also meet a minimum DNBR of1. 5 at scram power conditions 24. 2 MW
1.9 STEADY STATE PERFORMANCE OF TYPE 3 ELEMENTS IN THEPM-2A REACTOR
A steady state thermal analysis was performed on 10 elements within thePM-2A core. These elements were selected based on their burnout indexes pre-sented in Table 1. 7.
The analysis included studies at both design power 10. 0 MW and at scrampower level 12 MW with average core heat fluxes of 68, 849 Btu/hr-ft2 and 82, 619Btu/hr-ft 2 , respectively. The results of this analysis at 10. 0 MW are shown onTable 1. 17 and at 12 MW on Table 1. 18. There is no local boiling indicated ateither design power or scram power levels. Fig. 1.16 and 1.17 show the platesurface temperature for the two most critical elements in the core, positions 44and 33. However, element 44 is marginally away from the inception of local boilingat the scram power level with 6. 2 degrees of superheat.
The results of this analysis indicate that no PM-2A element is in danger ofburnout since the most critical control rod element 44 and the most critical station-ary element 33 exhibit at 12 MW minimum DNBR's of 4. 66 and 5.00, respectively,both in excess of the design minimum 1. 5.
36
TABLE 1.15RESULTS OF THE STEADY STATE THERMAL ANALYSIS OF THE SM-lA
TYPE CORE, POWER 20.2 MW
Core Position
16273334435455616272
G-NominalChannel FlowX 106,lb/hr-ft 2
1.4261.3731.6921.6461.5931. 6251.6921.3841.3311.405
G-Hot Channel FlowX 106-, lb/hr-ft2
1.3371,2871,2691.5431.4931.5231.2691.2971.2481.317
Hot ChannelBulk OutletTemp., 9F
472.4473. 5473.9477.3479. 5478.0473,9473.1469.9473.0
Hot ChannelMaximumPlate SurfaceTemp., OF
577.7577. 6578. 5578. 5578. 5578. 5578.5577. 6564. 6577.7
MinDNBR
2.702.802.392.772.742.772.392.803.862.70
*LocalQlty. Boiling
0000000000
0000000000
* Axial increment at which nucleate boiling begins, measured in inches from the bottom of the element.
TABLE 1.16RESULTS OF THE STEADY STATE THERMAL ANALYSIS OF THE SM-lA
TYPE 3 CORE, POWER - 24.2 MW
Core Position
16273334435455616272
G-NominalChannel FlowX 100, lb/hr-ft 2
1.4261.3731. 6921. 6461. 5931. 6251.6921.3731.3311.405
G-HotChan el FlowX 10 , lb/hr-ft2
1.3371.2871.2691. 5431.4931. 5231.2691.2871.2481.317
Hot ChannelBulk OutletTemp., OF
479.2480. 5481. 1485.1487. 7485.9481.1480. 5476.3480. 0
Hot ChannelMax. PlateSurfaceTemp., oF
578.2578.2579.1579.1579.1579.1579.1578.2577.8578.2
MinDNBR
2.25.2.331.982.302.272.301.982.333.212.24
*LocalQlty. Boiling
0000000000
002100021000
* Axial increment at which nucleate boiling begins, measured in inches from the bottom of the element.
580
570
560
550
540
530
d 520
510
500
490
480
470
460
450
440
430
4204 5 6 7 8 9 10 11 12 13 14 15 16 17
Length Along Element Plate (Inches)
Figure 1. 14
Plate Surface Temperature of Type 3 Elements in the SM-1A CoreCore Position 33
18 19 20 21 22
T Sat uration
/
-- 24. 2 MW-
- 20. 2 MN
0 1 2 3
-- T Saturation
07
/--\-24.2 MW
/ 20.2 MW
- I
I--
0 1 A 3 , o o 6 7 109I1 f11 1nI 13h1 Gd *J :2 U V 1 4 IV 11U~L
Length Along Element Plate - Inches
Figure 1.15
Plate Surface Temperature Type 3 ElementsCore Position 72
in the SM-1A Core
0
c)
4-4
0P
580
570
560
550
540
530
520
510
500
490
48013 10 10v
I1G 1I: I'7 i8 19V2 2i 22
A
TABLE 1.17RESULTS OF THE STEADY STATE THERMAL ANALYSIS OF THE PM-2A
TYPE 3 CORE, POWER 10.0MW
Core Position
13222633374344556266
G- NominalChannel FlowX 106 , lb/hr-ft 2
1.1121.0931.1121.1121.1021.0731.1681.0641.0931.102
G-HotChannel FlowX 105, lb/hr-ft 2
9.730
9. 5649.7309.7309. 6429.3898.7609.3109.5649. 642
Hot ChannelBulk OutletTemp., OF
539.4542. 1541. 5538.4526. 8543.0545.0539.9542.1541. 8
Hot ChannelMax. PlateSurfaceTemp., OF
587.6599.1597.7596. 6572.7597. 7610.3600.0598. 8598.4
MinDNBR
7.536.036.035.998.026.285.615.996.036.03
*LocalQlty. Boiling
0000000000
0000000000
* Axial increment at which nucleate boiling begins, measured in inches from the bottom of the element.
TABLE 1.18RESULTS OF STEADY STATE THERMAL ANALYSIS OF THE PM-2A
TYPE 3 CORE, POWER 12 MW
Core Position
13222633374344556266
G-NominalChangel FlowX 10 , lb/hr-ft2
1.1121.0931.1121.1121.1021.0731.0511.0641.0931. 102
G-HotCha el FlowX 10 lb/hr-ft2
9.7309.5649. 7309.7309.6429.3897. 5899.3109. 5649.642
Hot ChannelBulk OutletTemp. , OF
542. 5545.7544.9541.2527.4546.8556.4543.0545.7545.3
Hot ChannelMax. PlateSurfaceTemp. , F
594.1614.0612.4611.1582.4612. 4620.7615.2614.0613.3
MinDNBR
6.285.025.035.006.705.234.664.995.025.03
*LocalQlty. Boiling
0000000000
0000000000
* Axial increment at which nucleate boiling begins, measured in inches from the bottom of the element.
_ _ _ _ _ _ y _R__
630
620
610
600
590
580
570
560
550
540
530
520
510
500( 1 Z 3 5 7 8 9 10 11 12 13 14 15 1 17 1E
Length Along Element Plate - Inches
Figure 1.16Plate Surface Temperature of Type 3 Elements in the PM-2A Core
Core Position 44
8 19 20
0
C,)
4-4
C,
T Saturation
12MW-
- --- 10 MW
-/
-- JL- % 0
21 22A
T Saturation
- 12 MW
- 10 mw-
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Length Along Element Plate - Inches
Figure 1. 17
Plate Surface Temperature of Type 3 Elements In the PM-2A CoreCore Position 55
0
Q)U44
Q)
620
610
600
590
5 80
570
560
550
540
530
5200 1
1.10 CONCLUSIONS AND RECOMMENDATIONS
1. The SM-1 core with Type 3 elements will operate safely at designconditions with some local boiling in the outermost elements. Thissituation is slightly worse at scram conditions. There is no evi-dence of local or bulk boiling for the average channels and minimumDNBR's are well above 1. 5.
2. The SM-1A core with Type 3 elements will operate safely at designconditions with no local boiling evident for the average channels withminimum DNBR's for the two hottest elements above 1. 5. At scramconditions a minute amount of local boiling was evident at the exitend of the most critical control rod and stationary element. Mini-mum DNBR's for these elements were within the design minimum of1. 5.
3. The PM-2A core with Type 3 elements will operate safely at both de-sign power conditions and scram power with no local boiling presentfor either case. The minimum DNBR's for the two hottest elementsare greater than 1. 5.
4. A decay heat removal study has been omitted from this report, theanalysis of which would require an extensive analytical treatment.The decay heat removal models for the SM-1, SM-1A and PM-2Ashould not change at all since the increase in maximum heat fluxwithin Type 3 cores over the original cores is in general not ap-preciable. Best judgment indicates the cores will be thermally safein the decay heat removal condition. All plants are very conservativeduring this operation.
It is recommended from the above results that:
1. For the SM-1, the amount of local boiling in the hot channels couldbe reduced with the addition of a flow fix in the inlet end box of thestationary elements to improve the channel-to-channel flow distribution.This was evident from the results of single element flow testing in whichan improvement from -55% to -23% in maldistribution was obtained bythe addition of an interchangeable conical diffuser in the inlet end box.However, a flow fix is not recommended for the SM-1 elements since thepresence of local nucleate boiling is not expected to have any adverseeffects on cladding material, the improvement of channel-to-channel flowdistribution has an insignificant effect on DNBR, and the insertion of thisdevice in the inlet end box would add complications to the present design.
2. For the SM-1A, no improvement is necessary in the stationary elements;however, a slight improvement with a flow fix could be made in the con-trol rods where maldistributions are in excess of 20%. The improved
45
flow distribution for this core is attributed to the orifice plate beingon the exit side of the elements. Flow fixes are not recommendedfor the SM-lA control rod elements.
3. For the PM-2A, since channel-to-channel stationary element flowdistribution is within 12% and control rod distribution is approxi-mately 20%, flow fixes are not recommended for these elements.
4. Prior to operation of these cores, if analytical proof of adequatethermal margin is required during decay heat removal, an analysismust be performed
46
2.0 TRANSIENT ANALYSIS
2.1 INTRODUCTION
The thermal analysis of the Type 3 cores in the SM-1, SM-1A and PM-2Aduring the critical period immedi tely following a loss of flow accident has beenanalyzed by means of the ART-02 17) IBM-704 Code. Determination of thesafety of these three cores has been achieved by analyzing the hottest elements ineach core as evaluated by the IDNBR (Section 1. 6). If these analyzed elementsprove to be safe during a loss of flow transient, as measured by the departurefrom nuclear boiling ratio criteria (DNBR), then the individual cores analyzedwill be thermally safe.
2.2 TRANSIENT METHOD OF ANALYSIS
The detailed study of the core during the loss of flow transient has been per-formed by means of the ART-02 (17) Code. This code utilizes a one-dimensionalmodel to predict the behavior of a water-cooled and moderated reactor withplate type elements during transients which are slower than a prompt excursion.The model utilized in the cases studied was a single pass core operating initiallyat steady-state conditions. The reactor is then subjected to a variation in flowrate with or without a variation in reactivity as induced by control rod motion tosimulate a loss of flow with or without a scram.
The nominal behavior of the individual elements of a core is representedby a single coolant channel in each element. Thermal calculations are also per-formed on an additional channel which represents the hot channel with itsassociated extremes in dimensions, pressure drop and heat input.
The version of the ART Code used in the present analysis is based upon fogor homogeneous flow. Though this analysis is somewhat less rigorous than theslip flow model as presented in ART-04 (18) it has been utilized in the absenceof good void fraction data. The important correlations and equations used in thecode are presented in Appendix C.
2.3 POWER DISTRIBUTIONS
As in the steady state analysis (Section 1. 3. 2) the loss of flow analysis hasbeen performed at the design power level. However to insure the convervatism ofthe analysis, an instrumentation tolerance has been applied so that all three coreshave been evaluated at the worst feasible condition of the maximum overload orscram power level. The design and scram power along with the reference steadystate heat generation per unit area, q0 * (Eq. C. 2) are tabulated below,
47
DesignPower Level
10. 77 MW
20.2 MW
10.0 MW
q0 *, Btu/hr,ft 2
64, 600
120, 300
68, 800
ScramPower Level
13. 45 MW
24. 2 MW
12.0 MW
q *Btu/hr, ft2
77, 900
144, 100
82, 600
The axial power distributions in the transient analysis are identical to thoseused in the steady state analysis (Section 1. 3. 2) and are plotted for the Type 3stationary and control rod elements of the three cores, in the following figures:
SM-1 Stationary Element
Control Rod Element
SM-1A Stationary Element
Control Rod Element
PM-2A Stationary Element
Control Rod Element
Fig. 1.6
Fig. 1.3
Fig. 1.6
Fig. 1.4
Fig. 1.7
Fig. 1. 5
Average radial power peaking factors in the nominal channel (Q A T) and hotchannel (Q AT) along with local radial peaking factors (QAQ)are tabulated in thefollowing tables:
Table of Radial Power Peaking Factors
Core
SM-1 Type 3 Core
SM-1A Type 3 Core
PM-2A Type 3 Core
PeakingFactors
Table 1. 3
Table 1.4
Table 1. 5
QAGMax.
ElementCorePosition
2.09 31,57
AxialMax,
1. 911
2.24 12, 76 1.911
2. 05 44 1. 429
Approx.Locat.fromBottomof Core
CorePeaktoAverage
7" 3.99
7"1
10"
4.28
2.93
48
Core
SM-1
SM-1A
PM-2A
The following tabulation of the peak fluxes at nominal conditions (i. e. ,SM-1 at 10. 77 MW) shows the relation of Type 3 cores to previous cores.
Core
SM-1 Core I
Spiked andRearranged
Core II
Type 3 Core
SM-iA Core I
Reference
APAE No. 85 (8)
APAE No. 17(19)
Type 3 Core
PM-2A Core I APAE No. 39 (7)
Type 3 Core
Peak Flux at NominalPower, Btu/hr ft2
1. 881 x 1053. 000 x 10 5
2. 766 x 105
2. 578 x 105
3.198 x 10 5
5.149 x 10 5
1. 772 x 105
2.016 x 105
The tabulation shows that the Type 3 SM-1 Core represents a 39% increasein the peak flux in relation to the SM-1 Core I. Similarly, Type 3 SM-1A Coreis a 61% increase over SM-1A Core I and PM-2A Type 3 Core is a 14% increaseover PM-2A Core I. However Type 3 SM-1 Core is a 14% decrease in peak fluxin relation to SM-1 Core I Spiked and Rearranged.
2.4 SELECTION OF ELEMENTS
Verification of the safety of the three cores has been achieved by analyzingboth a stationary element and a control rod element with the highest ratio ofpower generation to available flow (IDNBR). If these elements prove to be safeduring the loss of flow transient, then each of the cores analyzed will be thermallysafe.
49
By means of the IDNBR index (Section 1. 6) the most vulnerable elementsin each core are:
SM-1 Type 3 Core
Core Position Type of Element IDNBR
61* Stationary 3. 0927 Stationary 3.0731 Stationary 3.0755* Control Rod 2. 6133 Control Rod 2. 61
SM-lA Type 3 Core
Core Position Type of Element IDNBR
55* Control Rod 3.09
33 Control Rod 3.0943 Stationary 3.0572* Stationary 3.0154 Stationary 3. 0012 Stationary 2. 99
PM-2A Type 3 Core
Core Position Type of Element IDNBR
44* Control Rod 2. 5766 Stationary 2.4755* Stationary 2.4662 Stationary 2.48
* Elements investigated during the transient loss of flow analysis.
50
2. 5 FLOW DISTRIBUTIONS
As in the steady state analysis (Section 1. 5), the element flow distributionsutilized in evaluating the initial flow rates during loss of flow accident wereestablished by the full scale air flow rigs (11), Ci2), (13) and are graphicallypresented in Fig. 1. 8, 1. 9 and 1. 10. The channel-to-channel flow maldistribution
(6 ) for the various elements investigated during a loss of flow have beenevaluated by the latest single element testing . (4) These maldistributions ( 5 )along with the following maldistribution factors, Kpf for friction and Kpa foracceleration which are utilized in formulating the pressure drop balance of thehot channel in the ART code (Eq. C. 15) are tabulated below:
Channel toCore Flow Rate Channel Mal- HC HCPosition gpm dis0tribution(S),%Wt. Kpf-(1).8 Kpa
SM-1 Type 3 Core
55 89.00 -28.0 .554 .51861 44.24 -55.0 .237 .203
SM-1A Type 3 Core
55 147.0 -22.8 .628 .59672 134.0 -6.7 .883 .870
PM-2A Type 3 Core
44 110.0 -22.0 .640 .60855 110.0 -10.9 .812 .794
2.6 HOT CHANNEL FACTORS
The hot channel factors used in this analysis were formulated for averageconditions which affect heat generation rates and for local conditions which affectlocal heat fluxes in the DNB correlations. Numerically, the value of the indi-vidual factors used in the transient analysis are equal to those used in the steadystate analysis (Section 1. 4). However, the input format for the ART code issomewhat different than STDY-3 and the manner of formulating these factorsis presented in this section.
51
The heat generation rate at any particular axial section of the core is ex-pressed in (Eq. C. 2) as:
q.. = q0* f'(Z) F (P/P0).p1 0 M AT 0 1
where FM .T, the average power peaking factor, is composed of average en-gineering hot channel factors (FA T), and a radial power peak either in the hotchannel Q A T or in the nominal channel Q T. The average engineering hotchannel factor in turn is composed of averae factor for core length deviations(F core length), for clad deviation (Fclad), and for average deviations in uraniumcontent and homogeneity (FHoM). Therefore, the average power peaking factorFN AT is
FM A T = A T FNF core length Fclad F Hom for the hot channel (2. 1)
FM A T AT FN F core length F clad F Hom for the nominal channel.
However, the engineering factors in the nominal channel are consideredunity and
FM T =FQ s T2) MAT AT N(2.2)
LThe factor which affects the local heat flux ( in the DNBR correlations(Eq. C. 19) is a multiple of the average radial power peaking factor in steady state:
0.= q. (1-r) and 0 L <0_ L 0Jo JO JO Jo (2.3)
or 0.o = ( AL) q 0 (1-r)Jo 0
Using the nomenclature in Appendix B.
0 L FM A00 FM AT
where F AG, the local power peaking factor, is composed of local engineeringfactor, iocal nuclear uncertainty factor and the (local) hot plate radial power peak-ing factor.
52
FM A AeFL
NFL
core length FLclad FL Hom
Land the local heat flux correction factor ( )is
0
FLN
LAT
FL FL FLcore length clad Hor
F F F FN core length clad Hom
Using the numerical values of hot channel factors given in Table 1. 6 andEq. (2. 1), (2. 2), (2. 4), the value of power peaking factors for Type 3 controlrods and stationary elements are:
Stationary Elements
Nominal Channel
Hot Channel
F = 1. 05 QM A T dT,
F = 1. 0 8 7 AQTMT A T,
OL/ 0QG (3
= 1.112Q, T
0 L/ = 1.074
Control Rods
Nominal Channel
Hot Channel
FMAT - 1.05 Q AT,
FM A T =1.087 QAT,
L/ =1.112
Ae
QAT
QAe
eAT
OL/ - 1.074 ___A_
Q A TUnlike previous thermal analyses (9), there is no hot channel factor
formulated for plate spacing deviations as induced by tolerences or rippling.This factor is omittd because the ART Code will accept a local mass velocitycorrection factor (G /G) as direct input to evaluate variations in the local massvelocity (Ge). Therefore, the variations in plate spacing which cause varia-tions in local mass velocities are fully covered by the local correction factor(GL/G) or
GL GLG. (_G-)G
1
53
(2.6)
0 L
(2.4)
0
(2.5)
The local mass velocity correction factor is related to the plate spacing(inclusive of rippling) in the following manner:
WG = W - GA
where W = flow rate lb/hr, which is constant for a channel
A = Area, ft2
But A = Sb
b = channel width
s = channel spacing or thickness;
and in thin channels where b the width is very nearlya constant,
W = G1 bS1 =G2 bS2
or G2 S1
G1 S2
The Type 3 element with channel spacings, including rippling as shown belowand repeated from Section 1. 4. 2 has the following local mass velocity correctionfactor (GL/G) :
Nominal Min Max. Local LStationary Elements Channel Spacing Channel Spacing G /G
Nominal Channel .123 .127 .969Hot Channel .119 .136 .875
Control Rods
Nominal Channel . 123 .127 .969Hot Channel .119 .133 .895
54
2. 7 OPERATING PARAMETERS USED IN THE LOSS OF FLOW ANALYSIS
As in the steady state investigation (Section 1. 4), the conservatism ofthe analysis has been insured by the use of the most adverse operating condi-tions. The values of the operating parameters (inclusive of instrumentationtolerances) for all the cores studied during a loss of flow analysis were:
Design Power Scram PowerSM-i Type 3 Core
Core Power, MW 10. 77 13. 45Inlet Temperature, OF 431. 7 428System Pressure, psia 1175 1175
SM-1A Type 3 Core
Core Power, MW 20. 2 24. 2Inlet Temperature, F 427 425System Pressure, psia 1175 1175
PM-2A Type 3 Core
Core Power, MW 10.0 12. 0Inlet Temperature, OF 504 500System Pressure, psia 1715 1715
2.8 FLOW COASTDOWN
The flow coastdown of the reactor which is the driving force for the transientportion of the code, has been represented by decreases in flow in the nominalchannel of:
G = 1 1.25 (2.7)G0 (1 / bt)
where t = time, sec
b = constant
For conservatism, the analysis is based on the most adverse pump coastdown,that of a stuck or frozen impeller. For SM-1, the value of b is 2. 2 as evaluatedby the methods in APAE Memo No. 87, (20) which include a measured term for thepump pressure drop. This is a considerable increase in the severity of the coast-down over that measured in TP-600, (21) in which the impeller was free torotate.
55
The value of b used in evaluating the PM-2A is 4. 00 as reported in APAENo. 49 (22). In the case of the SM-1A where the pressure drop in the pumpwith a frozen impeller is not accurately known, the value of b has been conser-vatively taken as 4. 00. It would appear that the choice of the coefficient bwould be very important; but results of the analysis of the SM-1 whereb = 2. 2 and b = 4. 00 in this report indicate only very minor variations in DNBR.Similar effects have been obtained in the loss of flow analysis of the SM-2 (23)with different coastdown rates. A plot of flow as a function of time for the twopump coastdowns considered in the analysis of the Type 3 cores investigated, isgiven in Fig. 2. 1.
2.9 DEPARTURE FROM NUCLEATE BOILING RATIO (DNBR) CORRELATIONS
The latest available data on rectangular channel departure from nucleate boilingheat flux for system pressures below 1850 psia is reported in WAPD-188. (24)In general, this departure from nucleate boiling heat flux has an enthalpydependence which is less steep than the -2. 5 power associated with a systempressure of 2000 psia. However, as the fluid enthalphy increases, the correlationwhich is associated with enthalpy to the -2. 5 power is more applicable and thetwo types of correlations tend to intersect. Therefore, at all times the STDY-3Code and ART Code should make an evaluation to determine whichcorrelation produces the more conservative (applicable) results. Fortunatelythe STDY-3 code does, but the earlier ART code does not have the desired cor-relations programmed into it and its resulting DNBR's must be re-evaluated..This is presently being performed by means of the ART Reduction IBM-650code, which corrects the ART DNBR's to the proper correlations in STDY-3.
Mathematically DNB is a function of enthalphy H at the Kth temperature.
DNB = DNB (Hk)
Therefore the correction factorDNB (Hk) STDY-3 (2.8)
C = DNB (Hk) ART-02
and the corrected DNBR is:
DNBR - Cj DNBR ART-02DNB(Hk) STDY-3 (2.8A)
or DNBR = DNBR ART-02 [.]DNB(Hk) ART-02
56
1.0
.90
.80
.70
0 .25 .50 1 2 3 4 5
Time - Seconds
Figure 2. 1
Flow Coastdowns Investigated in the Loss of Flow Analysis
57
I
\
I
\ -e--G/Go =( 1 / 2.2t) 1.25
\ 1
G/GO "-(1 4.O t) 1.2 5
1
O
C,
0
W0
b)
0d
.60
*50
.40
.30
.20
.10
.05
For a system pressure of 1175 psia which is applicable to the thermalevaluation of the SM-1 and the SM-1A, the following proper correlations arein the STDY-3 code;
DNB
105
-2.5- 3. 25
e-0. 0012 L/S F(P)
where F(p) = 1.1875
[H._-12.5DNB J
= 3.482105 100.
orDNB
105
e
H. --. 72
8. 9_1000_
-0. 012 L/S
-0. 0012 L/Se
where the STDY-3 code takes the minimum value between Eq. 2. 10 and 2. 11.
However the ART code utilizes the following correlation under a systempressure of 1175 psia.
-2. 5
FH..J
1000
DNB= 3.86
105 e-0. 0012 L/S
Equation 2. 10 thru 2.12 are plotted in Fig. 2. 2 where the geometry factor
e -0. 0012 L/S is taken as unity (corresponds to channel length L = 0). It isnoted in this particular case that Eq. 2. 11 produced more conservative resultsthan Eq. 2. 10 for H = 590 u and it is the STDY-3 solution for DNB, wherethe enthalphy is less than 590 tu/lb m
For the PM-2A thermal evaluation where the system pressure is conservativelytaken as 1715 psia the STDY-3 code utilizes the following correlations:
DNB L H. 1 -2.5
5 = 32510 1000] e
-0. 0012 L/S FOP)
58
(2.10)
(2.11)
(2.12)
-
IHj
1000
where F(p) = function of pressure = 1. 042
DNB
105
or
DNB
105
H -- 2. 5
3.386 [1000
F - -0.72
8.9 IL 1000 _
-2. 5
e
e
and the ART-02 code uses;
DNB - H.= 3. 48
105 1000 . e
-0. 0012 L/S
-0.0012 L/S
-0.0012 L/S
Equations 2. 11, 2. 13, and 2. 14 are plotted in Fig. 2. 3. In this particularcase Eq. 2. 11 is valid to H- 5 8 19tu/lbm and Eq. 2. 13 is valid for H - 581 Btu/lbm.Therefore, the solution as obtained from the STDY-3 code is a composite of thesetwo correlations dependent upon the fluid enthalphy.
Since the DNB's as obtained from STDY-3 are the desirable correlations asindicated in WAPD-188, ART results are multiplied by the correction factor Eq.2. 8A. A plot of the correction factor vs. fluid enthalphy is presented in Fig. 2. 4.
2.10 ALLOWABLE DEPARTURE FROM NUCLEATE BOILING RATIO (DNBR)IN LOSS OF FLOW TRANSIENT
By utilization of the new departure from nucleate boiling correlations forrectangular channels at pre sures below 1850 psi (Eq. 2. 11, 2.12 and 2.14),as suggested in WAPD-188 24) the following qualifications, as formulated byWestinghouse are known:
a. The uncertainty associated with the lack of transient burnout orpressure drop data is 1. 10.
b. The uncertainty due to meager data on non-uniform heated channelsis 1. 10. The combined uncertainty factor is multiplative and is equalto1.10x1.10= 1.21.
59
(2. 13)
(2.11)
(2. 14)
L4
V-1
z
0
H+
35
30
25
20
15
10
5 Eq. 2. 11 DNB = 8.9
Eq. 2. 12 D = 3. 8.6105
440
H p -2. e -0. 0012 L/S
-0. 02/ STDY-3 Solution[ 0] -0. 7 -0. 0012 L/S
H -2.5 -0. 0012 L/S ART-02 Solution1000 e
460 480 500 520 540
40
Eq. 2.-10DNB-N = 3482105
400 420FLUID ENTHALPY - BTU/LB
Figure 2.2. DNB Correlations Used in Evaluating the SM-1 and SM-1A
560 580 600
I t i I I I I I I
IA A I I I I I I1-" 1 1 1 1 1 A I -L I-L-Li LA
v r r
- ----
cNHrz4
H
0
HP4l
4
400 420 440 460 480 500 520FLUID ENTHALPY - BTU/LB
Figure 2.3. DNB Correlations Used in Evaluating the PM-2A
540 560 580
35
T-
30
25
20
15
10 H -0- 72Eq. 2.11 -=8.9 e-0 .0 0 1 2 L/k
] t l l t l l 5 1 1 15 I1 0i I N
51-LL 2 D . -H 2 . 5 -0.-0012 L/
Eq.D2.14DNB =3.48 Hi 2.5.0012 Li 105 100 e
IIKIIILLL
VI A-1 p
A -1
lal
I IA-Lt I -1-h
r w
T- _
-L-1 11I t ILL11 ILLI L I I
I I I F
L ILA
600
1.00
G4
z 0.900
0.800U
S0.700
N ~ 0.60
U
zS0.50
0
S0.40
r 0.30400 420 440 460 480 500 520 540 560 580 600
FLUID ENTHALPY - BTU/LBFigure 2.4. ART Code DNB Correction Factor
In light of these facts the minimum DNBR cannot be permitted to dropbelow 1. 21 during the severest possible transient. The selection of a higherminimum DNBR for additional safety is somewhat arbitrary but a level of 1. 50is currently specified for transients (25, 26). The deviation between 1. 50 and 1. 21is the added margin of safety utilized to account for general uncertainties, suchas the fact that the experimental data which formulates the basis for the DNBcorrelations has not been specifically generated for SM type cores. Thus, eventhough the presently utilized (Westinghouse) correlations are valid for the rangeof pressure, peak flux, degree of inlet sub-cooling, and channel geometry, thisadded safety factor is included.
The 1. 50 minimum allowable DNBR currently specified for transients ismore than adequate for the less severe condition of steady state. If, however,only a steady state analysis is made, a minimum DNBR level of 2. 0 is desired toconservatively allow for some potential drop in DNBR during the transient.
This criteria differs from earlier minimum allowable DNBR criteria inthat there is no specification for the minimum steady state DNBR when transientanalyses are performed. Furthermore, it should be noted that previous analyseshave been based on the best fit "departure from nucleate boiling heat flux"equations due to some code limitations. Thermal evaluation in this report andsubsequent Alco reports is being performed on the most conservative correlations,namely, the DNB design equations. With the conversion to the use of designequations rather than the best-fit equations, the allowable minimum DNBR of 1. 50during a transient is not only acceptable but conservative. However, some earlierwork which either uses the best-fit equations or very old DNB correlations, sufferfrom updating and their results lead to considerable confusion. For this reasonreason Table D. 1 in Appendix D, which lists the various hot elements in eachcore, the report where the information was obtained, the old DNBR and the up-dated DNBR, is presented in this report.
With this procedure, it is now possible to evaluate the relative safety ofthe SM-1, SM-1A, PM-2A and SM-2 cores under the same bases since theminimum allowable DNBR in each case is 1. 50 during a transient. In particular,the safety of the Type 3 cores is determined if the most critical elements (highest
IDNBR Index) do not have a minimum DNBR of less than 1. 50 during a loss offlow transient. If the critical elements do not exceed this criteria, each core isdeemed safe for the duration of the thermal transient.
2.11 VARIOUS SM-1 TYPE 3 CORE CASES ANALYZED
Both the control rod in core position 55 and the stationary element in coreposition 61 have been analyzed under the expected flow coastdown of b - 2. 2 andthe severest conceivable conditions of scram power level (13.45 MW) andno scram. In order to determine the extremes of expected DNBR' s and the
63
effect of variation in flow coastdown on thermal conditions, the control rod incore position 55 has been evaluated with the same severe conditions but with anarbitrary (high) chosen value of b = 4. 00.
In order to evaluate the effectiveness of the reactor scram mechanism, thehottest element in the core, the stationary element in core position 61, has beenscrammed when at the conservative flow coastdown of b = 4. 0. The time delayof 0. 060 sec has been conservatively used to represent the time delay prior toactivating the 90 percent flow scram setting and the delay in the release mechanismitself. This is a consider larger time delay than the 0. 02 sec that wasdetermined experimentally X27) at the SM-1 site but it is based upon experimentalwork performed at Alco's Mechanical Engineering Laboratory (28).
To complete the thermal history of the SM-1 Type 3 core, the stationaryelement in core position 61, and the control rod in position 55 have been evaluatedat the nominal power level of 10. 77 MW and no scram, with b - 4. 0.
The table below is a summary of the cases run on the SM-1 Type 3 core.
Flow CoastdownCore Scram Nominal Channel-to
Case Core Power, G/Go= ( 1 / bt) 1. 25 Time, Channel Channel Mal-No. Position MW b Sec Flow, GPM distribution %
I 55 10.77 4.0 00 89.00 -28.0II 55 13.45 2.2 c' 89.00 - 28.0III 55 13.45 4. 0 a 89.00 - 28. 0IV 55 13.45 4.0 06 89.00 28.0V 61 10. 77 4. 0 co 44.24 -55. 0VI 61 13.45 2.2 a 44.24 -55.0
Plots of the minimum DNBR in the hot channel are presented in Fig. 2. 5 to2. 10.
2.12 VARIOUS SM-1A TYPE 3 CORE CASES ANALYZED
Due to the shortage of IBM-704 time the analysis of both the SM-1A Type 3Core and the PM-2A Type 3 Core has not investigated the effect of variation in thecoastdown function and the safety as induced by the scram mechanism. All effortswere directed toward evaluating the hottest stationary and control rod elements ofthe cores under the most realistic yet conservative conditions.
In the case of the SM-1A Type 3 Core the hottest elements, the control rodin core position 55 and a hot stationary element in core position 72 have beeninvestigated at the nominal power level of 20. 2 MW and the scram power level of24. 2 MW. Both elements were analyzed under the conservative conditions of noscram and a coastdown function with b = 4. 0. The table below is a summary of theSM-1A Type 3 core cases run.
64
10
z
0
9r4
a)o4
0G4
0)
4
65
Control od in Co ePosition 55, Unde theConditions of Cas I
Local Nucleate Boiling
.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0Time - Seconds
Figure 2. 5.SM-i Type 3 Core -
Minimum DNBR vs. TimeFor The Hot Channel
10
66
Control Rod in C rePosition 55 Unde theConditi ns of Caae II
Local Nucleate Boiling
.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.0 3.0 3.2Time - Seconds
Figure 2.6.SM-i Type 3 Core -
Minimum DNBR vs. TimeFor The Hot Channel
z
0
0
0G4
zs
014
A0
8
.2 .4 .6 .8 1.0 1.2 1.4Time - Seconds
1.6 1.8 2.0
Figure 2. 7
SM-1 Type 3 Core Minimum DNBR Vs. TimeFor the Hot Channel
67
Contr 1 Rod in CorePosition 55 un er theCondi ions of Case III
WLL_ L LL| -
7
6
0
b0C
0
$4
0
$4
5
4
25
20 - -
15
Control Rod in Co ePosition 55, under theConditio s of Case IV
10
5
4 _ Local Nucleate BoilingA n n4 n n 4 A '
1. 0 1. Z 1.b 1.ti
Time - Seconds
Figure 2.8SM-1 Type 3 Core Minimum DNBR Vs. Time
For The Hot Channel
68
z
0
0
4
4)$4W
V4
zU
. 2 . 4 . 6 1. 4I
14
12
2 4 6 8 10 12 14 16 18 20 22
Time - Seconds
Figure 2.9
SM-1 Type 3 Core Minimum DNBR Vs. TimeFor The Hot Channel
69
Stat onary Element inCore Position 61 underCon itions of Case V
Local Nucleate Boiling
z
0
0
a)V.
z0
a)
a)
10
8
6
5
.2 .4 .6
12
10
.8 1.0 1.2 1.4 1.6 1.8 2.U Z .2
Figure 2. 10.SM-1A Type 3 Core -
Minimum DNBR vs. TimeFor The Hot Channel
70
Stationary Element inCore Position 31, UndeCondi tions of ase VI
Local Nucleate Boiling
z0W
0 -
z0
wX
a)
8
6
4
Flow CoastdownCore 1Power, G/Go= t)1. 25MW b=4.6O'
20. 224. 220.224.2
4. 004.004.004.00
ScramTime,Sec.
0000
0000
NominalFlow, GPM
147147134134
Channel-to-ChannelMaldistribution,
wt %
-22.8-22. 8-6.7-6.7
Plots of the minimum DNBR of the hot channel in these cases are presentedin Fig. 2. 11 thru 2. 14.
2.13 VARIOUS PM-2A TYPE 3 CORE CASES ANALYZED
In the analysis of the PM-2A the hottest element in the core, the controlrod in core position 44 has been analyzed at the nominal power level of 10.0 MWand the scram power level of 12. 0 MW. Similarly the hot stationary elementin core position 55 has been analyzed at the nominal power level of 10.0 MWand the scram power level of 12. 0 MW. The table below is a summary of thevarious cases of the PM-2A analyzed.
Flow Coastdown
G/Go - (1/bt)y. 25b
4.004.004.004.00
ScramTime,Sec.
000000
00
NominalChannelFlow, GPM
110110110110
Channel-toChannelMaldistribution,
Wt %
-22.0-22.0-10.9-10.9
Plots in the minimum DNBR of the hot channel in these cases are presented
in Fig. 2. 15 thru 2.18.
71
CaseNo.
VIIVIIIIXX
CorePosition
55557272
Case.No.
XIXIIXIIIXIV
CorePosition
44445555
CorePower,MW
10.012. 010.012. 0
8
0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.23.4
Time - Seconds
Figure 2.11
SM-1A Type 3 Core Minimum DNBR Vs. TimeFor The Hot Channel
72
Control Rod in orePositi n 55 und rCondit ons of C e VII
LocalNucleate Boiling Bulk Boiling --
LLL | L ffifrL I I I I
6
4
0
bDl
z0
4
-. y
CU
2
6
5
.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
Time - Seconds
Figure 2.12
SM-1A Type 3 Core Minimum DNBR Vs. TimeFor The Hot Channel
73
C ntrol Rod in CoreP sition 55, underConditions of Case II
Local
Nucleate Boiling Bulk Boilin
z
0
0
0
4
3
2
Stationar Elemen inCore Po ition 72, UnderConditions of Case IX
2
Local Nucleate BoilingSI I I I I i .
.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2Time - Seconds
2.4 2.6 2.8 3.0 3.2 3.4
Figure 2. 13.SM-1A Type 3 Core
Minimum DNBR vs. TimeFor The Hot Channel
74
101
z
0
CU
CU
.-
0
C)
0~
a)
-- Irl - i
I II1II1II1
8
Time - Seconds
Figure 2. 14
SM-1A Type 3 Core Minimum DNBR Vs. TimeFor The Hot Channel
75
Statio ary Ele ent inCore osition 72 underCondi ions of C e X
Local Nucleate Boiling -Buk Boiling
.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
6.
4
z
0
4
W)
0)
2
20
z'150
0
a>
c
a)
z10
I.
5
76
Contr 1 Rod i CorePosition 44, UnderCondit ons of Case
Local Nucleate Boiling
.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Time - Seconds
FIgure 2. 15.PM-2A Type 3 Core
Minimum DNBR vs. TimeFor ThP Hot Channel
17. 0
16. 5
16. 0
16. 0
15. 5
15. 0
14. 5
14. 0
13. 5
13. 0
12. 5
12.0
11. 5
11.0
10. 0
9. 5
9. 0
8. 5
PM-2A Type 3 Core Minimum DNBR Vs. Time for the Hot Channel
77
Control Rod in orePos iti n 44 und rCondi ions of C se XII ____
Local Nucleate Boiling
0 0.3 0. 6 0.9 1.2 1. 5 1. 8 2. 1 2.4 2. 7 3. 0 3. 3 3. 6 3.9 4. 2 4.5Time - Seconds
Figure 2. 16
z
0
z0
U)
a)
8. 0
7. 5
7. 0
6. 5
6. 0
5. 5
5.0
4. 5
20
15
10
Station y Eleme t inCore P sition 55, UnderCondition of Cas XIm
5
I 1
.2 .4
Local Nucleate Boiling_I I I 1.I I I I I I I I I I
.6 .8 1.0 1.2 1.4 1.6 1.8 2.0Time - Seconds
2.2 2.4 2.6
Figure 2. 17.PM-2A Type 3 Core
Minimum DNBR vs. TimeFor The Hot Channel
78
0:0
0
Wu
aA)
L
,II a II
20
15
0
0
a)
a)z
Ez
2)
5)
.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0Time - SecondsFigure 2. 18.
PM-2A Type 3 CoreMinimum DNBR vs. Time
For The Hot Channel
2.2 2.4
79
Statioary Elea ent inCore osition 5 , UnderConditons of C se XIV
- Local Nucleate Boiling
2.14 RESULTS OF THE LOSS OF FLOW ANALYSIS OF THE SM-1 TYPE 3 CORE
The results of the transient analysis of the hottest control rod in coreposition 55 and the hottest stationary element in core position 61, as presented inFig. 2. 5 to 2. 10 and tabulated in Table 2. 2 indicate that:
a. There is no effect of the flow coastdown function on the minimum DNBRsince the minimum DNBR is the steady state DNBR. This can be seenin Cases II and III. However, the utilization of a fictitiously high coast-down function of 4. 0 does cause bulk boiling at 4. 2 sec and an exitquality of 0. 025 at 5. 00 sec.
b. The scram mechanism is not effective during critical early periods of aloss of flow accident since in all cases the minimum DNBR is thesteady state minimum DNBR. However, the utilization of the scrammechanism inhibits the bulk temperature rise and the creation of bulkboiling as can be seen by the difference between cases III and IV.
c. All evaluations of the hot stationary element 61 and the hot control rodin core position 55 indicate that at steady state the hot channel is inlocal nucleate boiling.
Therefore it is concluded that under the realistic conditions of a flow coast-down of 2. 2 at the scram power level of 13.45 MW, the hottest element in the core(control rod in core position 55) will have a minimum DNBR of 4. 08 when thescram mechanism is not considered to be operative. Similarly, the hotteststationary element, the element in core position 61, will exhibit a minimum DNBRof 4. 28 under the same conditions and bulk boiling will occur at 4. 43 sec. Sinceboth these elements far exceed the criteria of a minimum transient DNBR of1. 50, these elements and the entire SM-1 Type 3 core is considered safe duringa loss of flow transient.
In relation to previous cores and maximum heat flux as tabulated in Section1. 3 and the minimum DNBR's as tabulated in Table D. 1, the following is noted:
TABLE 2.1MINIMUM DNBR'S FOR VARIOUS SM-1 CORES
Peak Heat Flux Core Min.Core Btu/hr/ft2 x 105 Power, MW DNBR
I 1.881 10.77 7.60I 2.349 13.45 6.10I Spiked & Rearranged 3.000 10.77 4.13I Spiked & Rearranged 3.747 13.45 3.27II 2.766 10.77 5.02II 3.454 13.45 4.00Type 3 2. 578 10.77 4. 87Type 3 3.220 13.45 4.08
The Type 3 cores are considerably cooler than the Spiked and Rearragned CoreI and are of approximately the same magnitude as Core II.
80
2.15 RESULTS OF THE LOSS OF FLOW ANALYSIS OF THE SM-1ATYPE 3 CORE
The results of the transient analysis of the hottest control rod in coreposition 55 and the hottest stationary element in core position 72 under con-servative yet realistic conditions of no scram, with flow coastdown functionb = 4. 00, are presented in Table 2. 3 and Fig. 2. 11 to 2. 14. These indicate:
a. The hottest element in the core, namely, the control rod in coreposition 55, exhibits bulk boiling at 1. 13 sec and exit quality at5. 0 sec of 0. 1275 when the core is at the peak power of 24. 2 MW.
b. The control rod in core position 55 indicates a core minimum DNBRof 1. 96 when the core is operating at the scram power level of24. 2 MW.
c. The hot control rod in core position 55 and the hot stationary elementin core position 72 exhibit local nucleate boiling in the hot channel atsteady state when the core is at scram power level.
d. Only the hot control rod in core position 55 exhibits steady state localnucleate boiling in the hot channel when the core is operating at thenominal power level of 20. 2 MW.
From this information it is concluded that since the core minimum DNBR(1. 96) at the scram power level without a scram exceeds the minimum allowabletransient DNBR of 1. 50, this element is safe in a loss of flow transient.
In comparison to SM-1A Core I with a nominal peak flux of 3. 198 x 105Btu/hr/ft 2 , the SM-1A Type 3 Core with 5. 149 x 10 Btu/hr/ft2 has a much higherheat flux. However, the previously reported (12) minimum DNBR of 1. 80 forCore I when operating under the nominal conditions of 20. 2 MW must be in error,and the increase to 2. 40 can be attributed to improved computation techniques.Therefore even though the SM-1A Type 3 core is somewhat hotter than Core I,it exceeds the minimum transient DNBR criteria and it is considered thermallysafe during a loss of flow transient.
2.16 RESULTS OF THE LOSS OF FLOW ANALYSIS OF THE PM-2ATYPE 3 CORE
The results of the transient analysis of the hottest element in the core, thecontrol rod at core position 44 and the hottest stationary element in core position55 under the conservative yet realistic conditions of no scram, with coastdownfunction b = 4. 0, is presented in Table 2. 4 and Fig. 2. 15 to 2.18.
81
The results indicate that:
A. The hottest element in the core, namely, the control rod in coreposition 44 indicates a core minimum DNBR of 4. 59 at the scrampower level of 12. 0 MW and no scram.
B. The PM-2A core exhibits no steady state nucleate boiling when operatingat the nominal core power 10. 0 MW.
C. The PM-2A does not exhibit any bailk boiling at 5 sec after the loss offlow transient.
D. Only the hot control rod in core position 44 exhibits local nucleate boilingat steady state when operating at 12. 0 MW.
E. The hot stationary element in core position 55 exhibits a minimumDNBR of 4. 90 when operating at the scram power level of 12. 0 MWwithout the scram mechanism operative.
Furthermore, it should be noted that in the PM-2A Type 3 Core casesanalyzed, the effect of local nucleate boiling on DNBR is graphically demonstratedby the drops in the DNBR under the local boiling conditions as shown in Fig.2.15, 2.17 and 2.18.
Therefore it is concluded that since the lowest DNBR in the core is 4. 59during a transient with the scram mechanism not operative, the entire core issafe during a loss of flow transient.
In comparison to PM-2A Core I with a nominal peak flux of 1. 772 Btu/hr/ft2
the PM-2A Type 3 Core with a peak flux of 2. 016 x 105 Btu/ht/ft2 has a muchhigher maximum heat flux. The minimum DNBR in Core I during a transientwas 5. 53 and logically Type 3 Core with a higher peak heat flux has a minimumDNBR of 4. 59. This decrease in DNBR is not hazardous since the DNBR farexceeds the minimum allowable transient DNBR of 1. 50; thus the PM-2A Type 3Core is considered thermally safe.
2.17 CONCLUSIONS AND RECOMMENDATIONS OF LOSS OF FLOW TRANSIENTANALYSIS
The results of the transient analysis as presented in Tables 2. 2 to 2. 4indicate that:
1. All three cores are safe during a loss of flow transient since theminimum DNBR produced is 1. 96 in the SM-1A Type 3 Core at thescram power level of 24. 2.MW.
82
2. Only the SM-1A Type 3 Core indicates any bulk boiling during thefirst 5 sec of a loss of flow accident.
3. At the nominal power levels, SM-1 and SM-1A Type 3 Cores indicatelocal nucleate boiling while PM-2A Type 3 Core indicates no localnucleate boiling.
4. At the scram power level all three Type 3 cores indicate localnucleate boiling at steady state.
5. A comparison between the minimum steady state DNBR as obtained bymeans of the STDY-3 and ART-02 codes produces excellent agreementwhich indicates that the models used in each code are equivalent.
6. Increasing the flow coastdown function b, or scramming the reactorhas only the effect of reducing the exit bulk temperature in the caseof the SM-1 Type 3 Core.
With the prevalent steady state and transient analysis, the thermal safetyof Type 3 cores has been established. Since, the SM-1A Type 3 Core has aminimum DNBR of 1. 96, increased confidence can be obtained if a morecomprehensive analysis is performed on this core, to remove any conservatismyet insure the thermal safety of the core. Therefore, it is recommended thatthe SM-1A Type 3 core be investigated under the conditions of:
1. Rod and load perturbations to complete the thermal analysis.
2. An axial flux distribution to account for the shift in distribution cor-responding to a maximum xenon override.
3. Utilizing the improved two-dimensional transient codes such as XITE( 2 9 )or TITE (30) while incorporating reactivity effects due to boiling.
83
TABLE 2.2RESULTS OF THE LOSS OF FLOW ANALYSIS OF THE SM-1 TYPE 3 CORE
CoreCase Core Power,No. Position MW
Coastdown ScramFunction Time
b - sec
Time ofInitiation ofNucleateBoilingin the HotChannel, sec
MinimumDNBR atSteadyState(=0)By Meansof STDY-3Code
MinimumDNBR atSteadyState (7=0)By Means Minimumof ART-02 Trans.Code DNBR
OD 0.00
CD 0.00
OD 0.00
0.06 0.06
a, 0.00
CO 0.00
I0
UIII
Em
IV
V
VI
55
55
55
55
61
61
10.77
13.45
13.45
13.45
10. 77
13.45
4.0
2.2
4.0
4.0
4. 0
2.2
Hot SpotQualityor BulkTemperature
TimeIntervalofCaseSec.
Initiationof BulkBoiling,Sec.
4.91
4.06
4.06
4.06
5.21
4.27
4.87
4.08
4.08
4.08
5.25
4.28
4.87
4.08
4.08
4.08
5.16
4.28
562. 650F
545.91F
.0252
476. 740F
523.100F
.0343
5.00
5.00
5.00
2.90
3.36
5.00
4.26
4.43
TABLE 2.3RESULTS OF THE LOSS OF FLOW ANALYSIS OF THE SM-1A TYPE 3 CORES
CoreCase Core Power,No. Position MW
55
55
72
72
20.0
24. 2
20.2
24.2
CoastdownFunction
b =
ScramTimesec
4.00
4.00
4.00
4.00
Time ofInitiation ofNucleateBoilingin the HotChannel, sec
0.00
0.00
0.15
0.00
MinimumDNBR atSteadyState( r= 0)By Meansof STDY-3Code
2.39
1.98
2.70
2.24
vnu
vm
Ix
x
MinimumDNBR atSteadyState ( 7&0)By Meansof ART-02Code
2.40
2.02
2.73
2.23
MinimumTrans.DNBR
2.40
1.96
2.73
2.23
Hot SpotQualityor BulkTemperature
.0435
.1275
562. 680F
590.04 0F
Initiationof BulkBoiling,Sec.
1.62
1.13
TimeIntervalofCaseSec.
4.4
5.0
5.0
5.0
TABLE 2.4RESULTS OF THE LOSS OF FLOW ANALYSIS OF THE PM-2A TYPE 3 CORE
CoreCase Core Power,
00 No. Position MW
XI
XII
XIII
XIV
44 10.0
44 12.0
55
55
10. 0
12.0
CoastdownFunction
b-
4.00
4.00
4.00
4.00
ScramTime,Sec.
OD
CD
OD
GO
Time ofInitiation ofNucleateBoilingin the HotChannel, sec.
0.10
0.00
0.40
0.30
MinimumDNBR atSteadyState( 'r =0)By Meansof STDY-3Code
5.61
4.66
5.99
4.99
MinimumDNBR atSteadyState ( T=0)By Meansof ART-02Code
5.53
4.59
5.88
4.90
MinimumTrans.DNBR
5.53
4.59
5.88
4.90
Hot SpotBulkTemperatures,
of
590.04
595.96
607.30
613.76
TimeIntervalofCase,Sec.
Initiationof BulkBoiling,Sec.
5.00
5.00
5.00
4.70
REFERENCES
1. Davidson, S. L., Oggerino, J. P., "Interim Report on the Use of SM-2Elements in SM-1, SM-1A and PM-2A Cores," APAE Memo No. 291,June 20, 1961.
2. Oggerino, J. P., "Nuclear Analysis of Type 3 Elements in SM-1, SM-1Aand PM-2A Cores, " APAE-104 to be issued.
3. Pyle, R. S. , "STDY-3 , A Program for the Thermal Analysis of a Pres-surized Water Nuclear Reactor During Steady State Operation, " WAPD-TM-213, June 1960.
4. Krause, P. S., "Single Element Flow Tests For Type 3 (SM-2) FuelElements in SM-1, SM-1A and PM-2A Cores," APAE Memo No. 297,November 27, 1961.
5. Rosen, S. S., "Hazards Summary Report for the Army Package PowerReactor SM-1, " APAE 2, Revision 1, May 1960.
6. Gallagher, J. G., "Hazards Summary Report for theSM-1A," APAENo. 13, Supplement 2, Rev. 1, October 7, 1960.
7. "Design Analysis of a Prepackaged Nuclear Power Plant for an Ice CapLocation (PM-2A)," APAE No. 39, Alco Products, Inc., January 15, 1959.
8. Lee, D. H., Robinson, R. A., Segalman, I. "Experiments and Analysisfor SM-1 Core II with Special Components, " APAE No. 85, April 26, 1961.
9. "SM-2 Core and Vessel Design Analysis," APAE No. 69, Volume I, AlcoProducts, Inc., March 8, 1961.
10. Birken, S. H. , Matthews, F. T. , Lee, D. H. , "Analysis of Rearrangedand Spiked SM-1 Core I," AP Note 243, Alco Products, Inc. April 8, 1960.
11. Ingeneri, S. M. , 'Coolant Flow Tailoring Program of the APPR-1 CoreEmploying a Full Scale Model of the Reactor Vessel, " APAE Memo No.108, November 15, 1957.
12. Matthews, F. T., "Revised Thermal Analysis of the SM-1A Core,"AP Note 307, Alco Products, Inc., December 8, 1960.
87
13. Matthews, F. T., "Results of the Experimental Flow Distribution Programfor the PM-2A Reactor - Summary Report," AP Note 266, Alco Products,Inc. , May 31, 1960.
14. Krause, P. S., "SM-2 Single Element Final Test Report," APAE MemoNo. 267, October 28, 1960.
15. Conner, W. P. , "MTR Technical Branch Quarterly Report, " Firt Quarter,June 8, 1956.
16. Beck, R. G., "Hydraulics of Modified Fuel Elements for ETR",November 7, 1958.
17. Meyer, J. E., Smith, R. B., Gelbard, H. G., George, D. E., andPeterson, W. D., "ART-02 - A Program for the Treatment of ReactorThermal Transients on the IBM-704, WAPD-TM-156," November 1959.
18. Meyer, J. E., Peterson, W. D., "ART-04 - A Modification of the ARTProgram for the Treatment of Reactor Thermal Transients on the IBM-704," WAPD-TM-202, July 1960.
19. Alco Products, Inc., "APPR Field Unit No. 1 APPR-1A," APAE 17,Supp. 1, July 1957.
20. ASTRA, "Pump Failure and the APPR-1." APAE Memo No. 87, May 1956.
21. Morrison, J. H., Lee, D. H., "Final Report Test 600 - Evaluation of Lossof Flow Accident in SM-1," Alco Products, Inc., Test Report, April 1960.
22. Rosen, S. S., 'Hazards Summary Report for a Pre-packaged NuclearPower Plant for an Ice Cap Location (PM-2A)," APAE No. 49, July 1, 1959.
23. Segalman, I., Bradley, P. L., "Steady State and Transient Thermal andHydraulic Analysis of SM-2 - Termination Report, APAE No. 91,September 8, 1961.
24. De Bortoli, R. A., Green, S. J. , LeTourneau, B. W. , Troy, M. ,Weiss, A., "Forced Convection Heat Transfer Burnout Studies for Water inRectangular Channels and Round Tubes at Pressures above 500 PSIA,"WAPD-188, October 1958.
25. Scoles, J. F., "Criteria for Evaluating Hazards Involved in Proposed Testson and/or Modifications to the SM-1, " APAE No. 106, October 18, 1961.
88
26. Personal Communication by J. G. Gallagher to M. H. Dixon, AlcoProducts, Inc., on "Thermal Design Criteria and Corresponding EndBox Configurations," February 22, 1962.
27. Personal Communication by F. G. Moote, Alco Products, Inc., toW. M.S. Richards, Alco Products, on July 20, 1961 on "Test 600 -Loss of Flow".
28. Krause, P. S., "SM-1A Control Rod Drive Production Test Report,"AP Note No. 293, Alco Products, Inc., October 22, 1960.
29. Pyle, R. S., Rose, R. P., "XITE-1 Program, WAPD-R(J)-73, to beissued.
30. Miller, R. I. , "A Digital Program for the Prediction of Two-Dimensional,Two-Phase Hydrodynamics," WAPD-TM-240, to be issued.
89
APPENDIX AGENERAL DESCRIPTION OF STDY-3 IBM 704 CODE
A. 1 IMPORTANT CORRELATIONS USED IN THE STDY-3 CODE
The burnout correlations used in the code are controlled by the local enthalpy,the channel mass flow rate and system pressure. The general form of the equa-tion selected for system pressures <1850 psia is given as:
-N0.72_DNB_ 0. 890 [H_ I -7 -0. 0012 L/S (A. 1)
106 1000
ODNB = departure from nuclear boiling heat flux
H. = local enthalpy at a specific axial increment
L = channel length
S = channel spacing
The burnout ratio or DNBR is found by dividing the heat flux found inEq.(A.1) by q* F P9f' (Z)
DNBR = DNB
%o* FADOtf' (Z) (A. 2)
where go* = average core heat flux
F = local hot channel factor
f (Z) = axial power at j th elevation
The criteria of local boiling in a channel is based upon a comparison be-tween the average film drop (of) and the film drop as calculated from the Jens-Lottes correlation (9 & L) with bulk parameters. If the average film drop ex-ceeds or equals the film drop as calculated from the Jens-Lottes correlation,the channel is considered to be in local boiling and the proper pressure dropcorrelations for local boiling are utilized.
91
Local boiling exists if of
h* FA T f,
h
60
Tsat +
E 0 J &L
(Z)
q F A T ff (Z)
106
e P/900
Kand h = .023 (De)
where of
8 4(N) 8 (NPR)
= Avg. film temperature drop, OFJ & L = Avg. film temperature drop as calculated
Lottes, correlation, OFh = Avg. film coefficient, Btu/hr-ft 2 OFTsat
by the Jens-
= Saturation temperature of the fluid, F
P = System pressure, psia
T.J
K
= Bulk temperature of fluid at specific axial position, OF= Fluid thermal conductivity, Btu/hr-ft OF
De = Average equivalent diameter of channel, ft
NR = Reynolds Number
NPR = Prandtl Number
Since the purpose of this criteria is not to establish the plate surfacetemperature but to determine whether the increased pressure drop and de-creased flow associated with nucleate boiling occurs, the analysis is kasedupon bulk or average parameters upon which pressure drop is dependent. How-ever, when calculating plate surface temperature, the film drops are comparedas in the previous situation, but local parameters are inserted in Eq. (A. 6) to(A. 8) below.
-- T.+ 8L
92
and OJ & L
(A.3)
1/4
(A. 4)
(A. 5)
T
where L = 9 fL 1 f L o &L L 0 J&L
or L =-g 9 L f 9 &or9 9J & L if 8f L= J & L
L = q0 * FAG f (Z) (A. 6)f h*
60( q FA f? (Z))1/4
10
L = T__ + -_____ T. (A. 7)9 J&L =Tsat+ P900
e
L K L 84and h = .023 4 L (N ) (N )'4 (A. 8)
(De*) RE PR
where the nomenclature is the same as previously used but the superscriptLrefers to the local conditions.
With these correlations utilized by the STDY-3 code for defining whennucleate boiling occurs, it is conceivable to have a condition in a channel wheresome portion of the channel is essentially at a uniform surface temperature witha reasonably high superheat and yet it is not in nucleate boiling. This has beenobserved in some of the elements investigated which are reported in sections1. 7, 1. 8 and 1.9.
A. 2 !NPUT FORMAT FOR THE STDY-3 CODE
This section discusses the input parameters of the STDY-3 code and howthe code uses these parameters to arrive at a solution. For illustrative purposes,control rod element position 44 in the SM-1 core has been selected. Refer toTable A. 1.
The STDY-3 code consists of a title card, a control card, a pressure card,a flow card, an inlet temperature card, a core average heat flux card, nominaland hot channel description cards, a plenum card, and axial flux weighting cards.
a. The title card, card number 1, contains up to an eight digit code numberand space for an alpha-numeric title. This card is required for thecompatability of input with the logic deck.
b. The control card, card number 2, reading from left to right containsthe number of system pressures, the number of channel mass flow rates,
93
the number of first pass temperatures, the number of channel flux varia-tions, the number of passes, the number of first pass channels, the num-ber of 2nd pass channels, clad thermal conductivity, meat thermal con-ductivity, channel length, fraction of flow heated, degree of mixing be-tween first and second pass in order to calculate 2nd pass inlet tempera-tures, multiplier applied to the average channel flow to obtain a hotchannel flow, equation choice (number refers to burnout equations inreference (3), choice of solution, (number refers to solution choicein reference (3).
c. The pressure card, card number 3, contains the numerical value ofsystem pressure. The instrumentation tolerance for the SM-1 primarysystem pressure is + 25 psia.
d. The 1st pass flow card, card number 4, contains the numerical valueof channel mass flow rates. Note that the code accepts five differentmass flow rates.
e. The first pass inlet temperature card, card number 6, contains thenumerical value of first pass inlet temperature. The instrumentationtolerance for the SM-1 primary system inlet temperature is + 40.
f. The average core heat flux card, card number 71, contains the averagecore heat flux based on the thermal output of the core and the core heattransfer area. A 3. 5% instrument tolerance was accounted for in calcu-lating the SM-1 average core heat flux.
g. The nominal channel description card, card number 81, contains thefollowing items reading from left to right: channel average thickness,channel local thickness, contraction coefficient, expansion coefficient,constant (K1 ) to describe the nominal channel friction factor and con-stant (K2 ) to describe the nominal channel friction factorboth to ac-count for variation in friction factor with Reynolds number, clad thick-ness, meat thickness, fuel plate bundle entrance area ratio, fuel platebundle exit area ratio, the combined product of the specified hot channelfactors affecting average flux, the combined product of the specified hotchannel factors affecting local flux.
h. The hot channel description card, card number 82, has the same itemsas described above in (g).
i. The plenum maldistribution factor card, card number 91, contains theplenum factors which are used to modify the nominal channel pressuredrop to account for the following changes in the hot channel:
1. Changes in channel length affecting elevation and friction losses.2. Changes in acceleration losses.3. Changes in channel flow rate affecting friction losses.
94
Of these three losses ,only differences in flow rate between the hotand nominal channels have been considered in the presently designedAlco reactors. The channel-to- channel flow maldistribution is causedby the element inlet e box. This factor was obtained from singleelement flow testing. )
j. The axial flux weighting cards, card 01 through 06, appear as the lastset of input data. The values given are the average heat flux axiallyfor both the nominal and hot channel. These are obtained from an axialpower distribution curve as calculated by digital techniques(2). The axialpower is plotted versus core length and an average obtained by weighingeach increment of core length.
In order to evaluate the thermal performance of a core, the STDY-3code first determines the hot channel flow. The code obtains this hotchannel flow from the core average heat flux, card number 71, andenthalpy conditions at a particular axial increment. Enthalpy condi-tions are obtained from the pressure and temperature input cards, 3and 6. Within the element there is a channel with adverse mechanicaldimensions, a theoretical hot channel. The local and average dimen-sions for this channel are located on card 82. The fuel plates adjacentto this channel have,in addition to adverse mechanical dimensions, in-creased fuel concentrations and other factors that tend to increase theheat generation. These factors and dimensions also appear in card 82as a combined mechanical hot channel factor. Flow maldistribution dueto plenum effects is taken into account by card number 91. Channelpressure drop is calculated by the code from the channel length givenin control card 2, and channel inlet and exit coefficients, channel width,and variation of Reynolds number with friction factor given in card 82.The flow maldistribution factor listed on card 91 reduces the channelpressure drop, resulting in the available pressure drop for the hot chan-nel. The STDY-3 code iterates until the hot channel flow equivalent toavailable flow given, in flow card number 4 satisfies the hot channel pres-sure drop. The code gives for each axial point in the hot channel, bulkenthalpy, bulk temperature, plate surface temperature, steam quality,meat centerline temperature and minimum burnout ratios. If local orbulk nucleate boiling exists, the axial. position at which the phenomenonexists is designated.
95
TABLE A. 1SAMPLE INPUT - STDY-3 CODE
Card
Title -
Control -
Pressure -
Flow -
Temp. In -
Flux -
ChannelDescription -
ChannelDescription -
Plenum Factor-
Flux Weighting -
Flux Weighting -
Flux Weighting -
Flux Weighting -
Flux Weighting -
Flux Weighting -
CardNo.
900 Run 1 Task 3. 3 SM-1 Core With SM-2 Elements Pos. 44 10. 77 MW STDY-3
2 1 5 1 1 1 2 0 22 11.2 9.68 22.0 0 0 1.25 2 3
3 1175
4 1. 076E 06 9. 680E 05 8. 610E 05 7. 530E 05 6. 460E 05
6 431.7
71 6.4557E 04 6.4557E 04
81 0. 123 0. 123 0.0 65 0. 058 0. 192 0. 210 0. 005 0. 030 0. 760
82
91
01
02
03
04
05
06
0. 119
0. 5540
0. 0030
0. 2080
1. 8570
0, 0030
0. 2080
1. 8570
0. 133
1. 000
0. 0060
0.314
1. 7640
0. 0060
0.314
1. 7640
0. 065
1. 000
0. 0090
0. 5150
-0. 0
0. 0090
0. 5150
-0. 0
0. 058
1. 000
0. 0140
0. 9450
-0. 0
0. 0140
0. 9450
-0. 0
0. 192
0. 0200
1. 2300
-0. 0
0. 0200
1. 2300
-0. 0
0.210 0.005 0.030
0. 0300
1.470
-0. 0
0. 03 00
1.470
-0. 0
0. 0440
1. 6640
-0. 0
0. 0440
1. 6640
-0. 0
0. 0650
1. 8010
-0. 0
0. 0650
1. 8010
-0. 0
0.760 1.42 2.00
0.760 0. 760 1.71 2. 12
0. 0950
1. 8900
-0. 0
0. 0950
1. 8900
-0. 0
0. 1400
1. 9110
-0. 0
0. 1400
1. 9110
-0. 0
APPENDIX BHOT CHANNEL FACTORS
B. 1 URANIUM CONTENT DEVIATION
B. 1. 1 Average Hot Channel Factor
Both fuel elements forming the hot channel are assumed to contain the maxi-mum allowable uranium density per plate. If, on the average, the uranium con-tent is higher by a certain percentage than the nominal, this will increase thewater temperature, since more heat will be sent into the coolant moving betweenthe two plates.
W w (1+5 =i+)F = ha = n(=1+6AT Wn Wn
where 5 is the fractional deviation in the positive direction on uranium density.
B. 1. 2 Local Hot Channel Factor
In addition to the fraction of uranium content deviation per plate, whichaffects the total sensible heat in the channel, there exists some possibility ofhaving a non-homogeneous mixture which might have deviations also. Designa-ting the deviation in the positive direction as being +9, (the fractional deviation),and assuming that a maximum positive homogeneity can occur simultaneouslywith, the-will then essentially designate the criteria for affecting the localheat flux at the hot spot.
Therefore, the effect of +?"is on the film temperature rise, which is
FAG = 1+
B. 2 ACTIVE CORE LENGTH DEVIATION
For a given volume of meat per plate, a negative deviation in active lengthincreases the amount of meat per unit length and therefore per unit heat transferarea. This affects both the bulk coolant temperature rise and the film gradient,based on the conservative approach that the decreased length increases only meatthickness and not active width.
LFT = n = F
ST Lmin A
97
B. 3 CLAD THICKNESS DEVIATION FACTORS
If the two clad thicknesses of a fuel plate are unequal, a greater portion ofthe total heat generated in the meat will pass out through the thinner clad becauseof lower thermal resistance. A hot channel, therefore, is defined as being com-posed of two fuel plates whose inner and outer clad thicknesses are at the mini-mum and maximum observed values, respectively. Both the average and localhot channel factors are then equal to the proportional increase in the heat trans-mitted through the inner sides. The water temperature and film coefficients areassumed equal on both sides of the fuel plate shown below.
Nominal channel
Tw, h
Ts
Clad Meat
TP
Tci
Clad,
Tc2
c66
Nominal channel
Tw, h
x
The differential equations describing the mode of conduction heat transferfor the plate are:
d2 T1
dx2=0
d2 Tm _
cx 2
d2 T 2
2 = 0dx2
ch
-Q t fxt + tk ch- ch m
tch + tm:'X ' tch + tm + tco
98
(B.1)
(B.2)
t 4B.3)
NTs2
lp
I
I
In the meat region (i. e., tch X tm + tch)
at X=th, Tm= Tc; atX=tch+t , Tm = Tc
Solving (B. 2) and the appropriate boundary conditions, the heat flux intothe hot channel is
Qtmh ~ 2 +(Ykm
k
1 + t J3
twhere = o+k
c
2 + tch + tcoP h kc
But nominally the heat flow to either surface would just be m if theclad thickness were the same 2
_ tm + 2Qkmtm + km
if =2 (where tco = tch) then F = 1 as expected.
The hot channel factor for this eccentricity of heat flow can therefore be definedas
qhFA
, = q
tm + 2Qkm
tm + km
The local factor, FA 0, is computed similarly except that different values ofand 9 corresponding to the local point conditions are used.
99
eF = h
qn
APPENDIX CDESCRIPTION OF THE EQUATIONS IN ART-02 IBM-704 CODE
C.1 ENERGY BALANCE
The sketch below shows a typical axial increment (A Z) of a reactorchannel.
An energy balance can be written as heat stored equals heat generatedminus heat out, where the heat generated in the plate and water in the jth axialsection and at time i is q ji A Z 15, but a fraction (r) of this total is generateddirectly in the water and the heat generated in the plate is (1-r) qji A Z 15.The total heat flow out of the plate to the water is Oj A Z 15.
1 1 =Channel -
Half Thickness
WaterFlow
Channel
AZ
Cla MeatHalf
Thick-ness
= Channel Width
(j Fuel Plate
12 = Clad Thickness
13 = Meat Half Thick-ness
The heat capacity of the plate is A Z 15 (pC)c 12 + (9 C)m 13'
where (PC)m = heat capacity of the meat per unit volume
(PC)c = heat capacity of the clad per unit volume
101
15
Therefore, the energy balance for the plate result in the following differen-tial equation for the mean plate temperature (Tmj)
AZ15[(pC)c'2 + (pC)m13 dTmj = (1-r)gjZ 15-j AZ1 5L cm J dt
or in finite difference form,
(Tm) j, i + 1 = (Tm) ji Pc 2 i 13) i - qi (1-r) (C. 1)
where
qji= Total heat generation rate per unit area, Btu/hr-ft2
r = fraction of heat generated in water
0ji = heat flux, Btu/hr-ft2
and
qji= q0* f' (Z)1 FM AT (P/P) (C. 2)
whereq0 * = Steady state reference heat generation per unit area=
total core power/core heat transfer area, Btu/hr-ft2
f '(Z) = local to average axial power ratio at the jth position
FMA T=Average power peaking factor inclusive of average engineeringHot channel factors nuclear uncertainty factors, and averagehot channel radial power peaking.
(P/Po)i = Power coastdown function at the ith time increment.
The correlation for the heat flux from the plate to the water at steadystate is equal to the heat generated in the plate:
Ojo = q. (1-r)
During the transient, this equality is not valid, since the heat flux is a functionof the average meat temperature.bulk fluid temperature, etc., and it is evaluatedin the ART code as the larger of the following expressions.
= Ui [(Tm)ji - (Tw)ji (C. 3)
K F1Si =__4. (Tm)j - (T) ji(C.'4)
14102
where Ui the over-all heat transfer coefficient
U =. . Btu/hr-ft 2 -OF_14 _ (C. 5)
Kc = Thermal conductivity of the clad Btu/hr-ft0 F
14 = Equivalent plate conduction length where the mean platetemperature exists, 0 F
hi = the average water film coefficient evaluate at the ith timeincrement when the average channel mass velocity is Gi,Btu/hr-ft 2 OF
(Tw)ji = bulk fluid temperature corresponding to the enthalpy Hi, F
(Tc)ji = local boiling surface temperature predicted from the Jens-Lottes correlation as is used in STDY-3 code.
60 j, i-1(Tc)ji = Tt+ e P/600 L 06 ](C. 6)
where Tsat = fluid saturation temperature, 0F
P = System pressure, psia
and as long as nucleate boiling does not occur the actual surface temperature
(Ts)g is evaluated as
1 $.(Ts).. = (Tm).. - 4 Ji (C. 7)
Kc
In a similar manner, an energy balance is performed for the water con-tained in the jth axial section to obtain the enthalpy (and temperature) of the fluid.
Heat generated directly in the water - rqg A Z 15
Heat flux added to the water = i A Z 15
Heat convected away by the water = Gi 15 11 (H 1 - ,H_)
and in a constant pressure process the stored energy = P AZ. 1 15 dt
103
Writing the energy balance in finite difference terms,
v..At. Gi1
Hj = i + 1 H+ 1 [( + r )Z(H -Hj _ ) (C.8)
ft3where v.. = the specific volume, lb
J1 lb
C. 2 PRESSURE DROP
The pressure drop for any given channel is broken into the following terms:
1. Losses resulting from entrance and exit terms and frictional pressuredrop (APf)i
2. Losses resulting from change in elevation (APe1 ) i
3. Pressure drop from spatial acceleration (A Pa2 ) i
4. Transient acceleration drop resulting from mass velocity changes withtime ( Pal) i
or APi = (APf)i+ (APel)i+( Palii+( Pa2)i (C.9)
where (APf)i =Ke (voi G 2 + Ke (vniG1 2
f - -e 2
(f. vN)-i (f .v ) (. Z)
+[(o o + f- v-- + nivn1 L (C. 10)2 = 1312 2 Dh
where Kc and Ke = Unrecoverable loss coefficient for the channelentrance and exit.
voi, vni = Specific volume of the fluid at the ith time incrementjust inside the channel inlet and exit, respectively,ft3 /lb
Dh = Channel hydraulic diameter, ft.
f o fni = friction factor used to predict frictional resistanceto fluid flow at the ith time increment just inside thechannel inlet and exit respectively.
104
As in the STDY-3 code the friction factor f i is given by
f = (f)iso .i (f s) for a subcooled liquid, H..<-Hf
and f = (f iso (vf/vji) ( 2 ) for a steam-water mixture, Hsi Hf
where f
Hf
(f. ).iso 1
(f/fso)
f/f.1s0
where FH
FH
*and 9..
SJi
where b
= specific volume of a saturated liquid, ft3 /lb
= enthalpy of a saturated liquid, Btu/lb
= Isothermal friction factor at the ith time increment
= Function to fit saturation region pressure drop
j1 = Function to fit subcooled nonisothermal,pressure drop
= FH 1 + .93( j/1)3l )](C.- (G 1 /106) 2/3
= Heat contribution to subcooled pressure drop which equals thesmaller of the two
{1. or
1. 5 (1-. 0025 e* .. )
= Actual film drop as used in pressure drop calculations whichis defined as the smaller,
~ Oji = 0 ji/(hf)i or
(Tc).. - (T ) ..Ji3 wji1
i = Film drop used in pressure drop calculations based on the
film coefficient (hf) , But/hr-ft 2
(hf)i = 1.58 hi
The development of the 1. 58 coefficient is given in WAPD- TH- 300
105
11)
The pressure drop resulting from change in elevation isn-1
(Pei)i = gAz [(1/2 (1/v oi) + 1/v + 1/2 ni
where g is the component of the acceleration of gravity acting in the axialdirection, = 32. 174 ft/sec 2
Pressure drop resulting from mass velocity changes with time
(C. 12)
(C. 13)(APal i=h O Z (G+ 1 - Gl) / Lt
and the final pressure drop term for spatial acceleration
(r G2ri i
S2(AP a2 )i = - (1 + d2) (tv0 2Gil+ (1 +&n2 (C.14)
where do and Cn= area ratio at entrance and exit respectively
2 area inside channel 2-area in plenum region)
C. 3 HOT CHANNEL FLOW
For each hot channel in parallel with the nominal channel, it is assumedin ART that the total hot-channel pressure drop (AP). HC is related to the nominalchannel pressure drop (AP)NC by
1
HC HC(A P)i =K f (APf) NC KHC
pa
NCAai) +(APa2) NC + (Cei)
i +A i
where KHC and Ka are the plenum
and acceleration terms respectively.
HCKpf
maldistribution factors for pressure loss
They are evaluated:
= (1 6)18
KHC = (1_6)2Opa
where is the percent hot channel flow maldistribution.
106
(C. 15)
The mass velocity in the hot channel is established by:
+ At1
1AZ(AP ) HCali
C. 4 DEPARTURE FROM NUCLEATE BOILING CORRELATIONS
The departure from nucleate boiling correlations used in the ART code aresimilar to those used in the STDY-3 code (refer Eq. (A. 1). However the correla-tionp used in STDY-3 are the latest available information as discussed in WAPD-188 24) and the ART results.have been corrected to account for the discrepanciesin the DNB and as is discussed in Section 2.9. The equations programmed in the
ART-02 for GL 2 1. 6 x 106 lb/hr-ft 2 and system pressures below 1850 psia are:1
For SM-1 and SM-1A, where P = 1200 psia design (acutal P = 1175 psia)
(.FC)2 (C. 17)
For PM-2A, where P = 1750 psia design (actual P = 1715 psia)
( H[ -1 -2.5-DNB ji = 3. 48 H]1
15 [1000.
where0 DNBR =
LG.
1
LGL
i
where GLG
evaluated by
Departure from nucleat boiling, heat flux, Btu/hr-ft 2
= Local mass velocity, lb/hr-ft 2
GL= (- )G.
G
= local mass velocity correction factor
1.
(Dh avg. min
Dh localmax-
Since in narrow rectangular channels,the area is directly proportional to thechannel spacing.
The DNB ratio is calculated by
0DNBR = DNB
0LJi
HCi+1
HC= G (C.16)
(FC)2 (C. 18)
107
(C.19)
- H j - -2. 50DNB - - = 3. 86 1 00
10 ~J
Lwhere #J.
Ji
0 L
Ji
is the local heat flux evaluated as
_ $L
0 $ji, Btu/hr-ft2
where $ L/ local heat flux correction factor evaluated as
$L FMAOFMAT
F =MAO
(C. 20)
Local power peaking factor inclusive of engineeringhot channel factors, nuclear uncertainty factor and localhot plate radial power peaking factor.
C. 5 REACTOR KINETICS
The ART code assumes the heat generation at any point within the core isproportional to a single power coastdown function(P/P0 ). That is, the heatgeneration rate (qji) is given by:
q. j = f'(Z) F Tq(P)ij P(C. 21)
where ( p ) + (1 -(X) N. (C. 22)
cx0 = Steady state fraction of power produced by decay heating.
/x = Decay power coastdown function
Ni = Neutron power coastdown function
Therefore, it is seen that the power coastdown function is divided into a decayheat contribution and a neutron power contribution. The neutron power coast-down, Ni, is itself divided into two parts, the prompt neutron contribution andthe delayed neutron contribution. The standard reactor kinetics equation forneutron level as a function of time is:
dN 6k N d3 dXd(C. 23)
108
+
[1
a0
where
Xd
dXdand d
= prompt neutron lifetime
= effective delay neutron fraction which is the sum of thefractions of each delayed neutron group
= Normalized concentration of precursors
= A d (N - Xd)
d=1
where Ad
)Bd
= decay constant
The solution to these equations is:
=N.K 1 + (tr) F6KK=. L 1* .
K6Ki
1
K=(Kr)i
(Atr)i
2,Q,
(Atr ).
2 1*2 ded=1L
K+1 K](Xd)1 +(Xd)i
(C. 25)
K( 6K -9
+ ( Kt)i
where (Atr) = Time increment
(6Kr)i = Excess reactivity resulting from rod motion
(6Kt)i = Excess reactivity resulting from temperature change
The neutron power coastdown as given in (C.25) results from two negativereactivity eff cts. The immediate effect is the negative temperature coefficientof reactivity K when the nominal channel temperature rises. The second effect,6 Kr, which occurs at a preset (delay) time, t3 , is caused by a scram and itsassociated control rod insertion.
109
(C. 24)
K+1N.
The temperature dependent portion of the reactivity is given by
NC
('y~= i aS(6K){Z C& 'f(T,) 9 - (Tw,) jo(0.26)
where 0 T K is the temperature coefficient of reactivity, and the
na. s are the temperature weighting factors, chosen so that 2] (aj) = 1
J=1
110
APPENDIX DUPDATED DEPARTURE FROM NUCLEATE BOILING
RATIO FOR THE HOT ELEMENT OFVARIOUS CORES
111
TABLE D. 1UPDATED DEPARTURE FROM NUCLEATE BOILING RATIO FOR THE HOT ELEMENT OF VARIOUS CORES
Old DNB Correlations Updated DNBR Correlations
CoreCore
SM-1Core I
SM-1 Core I
SM-1 Core IRearranged &
SM-1 Core IRearranged &
SM-1 Core II
SM-1 Core II
SM-1 Type 3
SM-1 Type 3
SM-1A Core I
SM-1A Type 3
SM-lA Type 3
PM-2A Core I
PM-2A Type
PM-2A Type
SM-2 Core I
SM-2 Core I
3
3
Report Position
APAE No. 85(8) 44
APAE No. 85(8) 44
APAE No. 85(8) 65Spiked
APAE No. 85(8) 65Spiked
APAE No. 85(8) 65
APAE No. 85(8) 65
APAE Memo No.. 291(1)44
APAE Memo No. 291(1)44
AP Note 307(12) 44
APAE Memo No. 291(1)67
APAE Memo No. 291(1)67
APAE No. 39(7) Hot Sta-tionaryElement
APAE Memo No. 291(1)23
APAE Memo No. 291(1)23
APAE No. 91(23) 44
APAE No. 91(23) 44*Indicates pseudo-transient analysis
CorePower,
MW
10. 77
13. 45
10. 77
13.45
10. 77
13.45
10. 77
20.20
20. 20
24. 20
10. 00
10. 00
12. 00
28. 00
35. 00
7.
6.
2.
1.
9
6
18
60
SteadyState Min.
DNBR
11.7
9.4
6.4
5. 1
7. 8
6.2
8. 2
6. 5
2.9
3. 9
3.2
7. 1
TransientMin.
DNBR
11. 73*
9.42*
6.36*
5. 03*
7. 73*
6. 15*
2. 8*
1.82
SteadyState Min.
DNBR
7. 6
6. 1
4. 2
3. 3
5. 1
4. 0
5. 3
4. 2
1. 9
2. 5
2. 1
7. 7
5. 1
4. 3
2.18
1.60
TransientMin.
DNBR
7. 63*
6. 12*
4. 13*
3. 27*
5. 02*
4. 00*
1. 8*
1.82
V
1
N
%
%
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