ML19343B178
| ML19343B178 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 11/30/1980 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
| To: | |
| Shared Package | |
| ML19262F332 | List: |
| References | |
| CEN-139(A)-NP, NUDOCS 8012150101 | |
| Download: ML19343B178 (66) | |
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{{#Wiki_filter:CEN-139(A)-NP STATISTICAL CO MBIN ATION OF UNCERTAINTIES COMBINATION OF SYSTEM PARAMETER UNCERTAINTIES IN THERMAL MARGIN ANALYSES FOR ARKANSAS NUCLEAR ONE UNIT 2 NOVEMBER 1980 E d$?E8us COMBUSTION ENGINEERING INC 801:2 i s o lot
l LEGAL NOTICE THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED
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BY COMBUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANV FERSON ACTING ON ITS BEHALF: A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANTABILITY, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS;OR
- 3. ASSUMES ANY LIABILITIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, METHOD OR PROCESS DISCLOSED IN THIS REPORT.
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CEN-139(A)-NP STATISTICAL COMBINATION OF UNCERTAINTIES COMBINATION OF SYSTEM PARAMETER UNCERTAINTIES IN THERMAL MARGIN ANALYSES FOR ARKANSAS NUCLEAR ONE UNIT 2 i e W l l l
( ABSTRACT This report describes the methods used to statistically combine system paramt ter uncertainties in the thermal margin analyses for the ANO-2 Cycle 2 core. A detailed description of the uncertainty probability distributions and re sponse surface techniques used is presented. This repo't demon-stratos that there will be at least 95% probability with at least 95% con-fiden e that the limiting fuel pin will avoid departure from nucleate boili19 (DNB) so long as the minimum DNB ratio found with the best estimate design TORC model remains at or above 1.24. M. 4 4 l - t { l l l l l r ia
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TABLE OF CONTENTS Ti tle Paqe Abstract i Table of Contents 11 List of Figures IV List of Tables Y Nomenclature and Abbreviations VI - 1.0 Summary of Results 1-1 2.0 Introduction 2-1 2.1 Deterministic Method 2-2 2.2 Statistical Method 2-2 3.0 Sources of Uncertainty 3-1 3.1 ' State Parameters Used in the Study 3-1 3.1.1 Method for Selecting State Parameters 3-2 3.1.2 Axial Shape Sensitivity 3-3 3.1.3 Pressure and Temperature Sensitivity 3-3
' 3.1.4 Primary System Flowrate Sensitivity 3-3 3.1.5 Most Adverse State Parameters 3-4 3.2 Radial Power Distribution 3-4 3.3 Inlet Flow Distribution 3-4 -
3.4 Exit Pressure Distribution 3-4 3.5 Enthalpy Rise Factor 3-5 3.6 Heat Factor 3-5 3.7 Clad O. D. , 3-5 3.8 Systematic Pitch Reduction 3-6 3.0 Fuel Rod Bow 3-6 iT
TABLE OF CONTENTS (con't.) Title Page 3.10 CHF Correlation 3-6 3.11 TORC Code Uncertainty 3-7
. 4.0 MDNBR Response Surface 4-l 4.1 TORC Model Used. 4-I 4.2 Variables Used 4-1 4.3 Experiment Design 4-2 4.4 Design Matrix 4-3 4.5 Response Surface 4-3 5.0 Combination of Probability Distribution Functions 5-1 5.1 Method 5-1 5.2 Results 5-2
. 5.3 Analytical Cenparison 5-2 6.0 Application to Design Analysis 6-1 6.1 Statistically Derived MDNBR Limit 6-1 6.2 Adjustments to Statistically Derived MDNBR L.imit 6-1 6.3 Application to TORC Design Model 6-2 7.0 Conclusions 7-1
. 7.1 Conservatisms in the Methodology 7-1 8.0 References 8-1 Appendix Appendix A: Detailed TCRC Analyses Used to Generate A-l Response Surface
~iii
LIST OF FIGURES Fig. No. Title Page 3-1 Inlet Flow Distribution Used to Generate Re. 3-8 sponse Surface ( Three Pump Ooeration) , 3-2 Exit Pressure Distribution Used to Generate 3-9 Response Surfa.e 3-3 Core Wide Radial Power Distribution Used to 3-10 Generate Response Sur# ace 3-4 Hot Assembly Radial Power Distribution Used 2-11 to Generate Response Surface 3-5 Channel Numbering Scheme for Stage 1 TORC 12 Analysis to Generate Response Surface 3-6 Intermediate (2nd Stage) TORC Model Used 3-13 in Generating Response Surface 3-7 Subchannel (3rd Stage) TORC Model Used in 3-14
- Generating Response Surface 5-1 Resultant MDNBR Probability Distribution 5 Function S
e o IV
LIST OF TABLES Table No. Title Page 3-1 Ranges of Operating Conditions 3-15 > for Which Response Surface is Valid 3-2 Determination of the Most Sensitive 3-16 Axial Shape Index 3-3 Determination of the Most Sensitive 3-17 Primary System Inlet Pressure and Temperature . 3-4 As-Built Gap Width Data 3-18 4-1 System Parameters Included as 4-5 Variables in the Response Surface 4-2 Coefficients for MDNBR Response Surface 4-6 5-1 - Probability Distribution Functions Combined 5-5 by SIGMA A-1 Coded Set of Detailed TORC Cases Used A-2 to Generate Response Surface A-2 Comparison of TORC and Response Surface A-13 ! MDNBR for Cases Used 'to Generate
- Response Surface l -
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*V
NOMENCLATURE AND ABBREVI ATIONS b coefficient in response surface c constant in response surface f arbitrary functional relationship k number of independent variables in response surface n number of items in a sample ' p.d.f. probability distribution function psf pounds per square foot - psia pounds per square inch (absolute) x system parameter y state parameter z MDNBR values predicted by response surface ASI axial shape index (defined in Table 3-2) CE Combustien Engineering CHF Critical Heat Flux DNB Departure from Nucleate Boiling Departure from Nucleate Boiling Ratio DNBR F Fahrenheit Faq engineering heat flux factor fiDNBR Minimum Departure from Nucleate Boiling Ratio T temperature , I T-H thermal-hydraulic a constant used to code system parameters (Ta.ble 4-1) e constant used to code system parameters (Table 4-1)
'n coded value of system parameters (Table 4-1) p mean a standard deviation a denotes difference between two parameters '
l i { (
"vi 1.
subscripts denotes vector quantity j index . in c nditions at reactor core inlet
, j index superscriots 4
denotes estim. ate O degrees
' average value l
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1.0 Summary of Results
- Methods were developed to combine statistically the uncertainties in j -reference thermal margin (detailed TORC) analyses. These methods
; were applied to the ANO-2 core. This work demonstrated that there j will be at least 95% probability with at least 95% confidance that the limiting fuel pin will avoid departure from nucleate boiling (DNB) so long as the Minimum DNB Ratio (MDNBR) found with the best-estimate design TORC model remains at or above 1.24. The 1.24 MDNBR limit includes allowances for reference analysis input uncertainties but ~
does not take into account uncertainties in operating conditions (e.g., monitoring uncertainties). S d
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2.0 Introduction C-E's thermal margin methodology for ANO-2 has been modified by the application of statistical methods. This report focuses on the statistical ccmbination of reference thermal-hydraulic (T-H)
; code input uncertainties. This combination was acccmolished by tne generation of a Minimum DNBR (MSNSR) response surface and the applica-tion of Monte Carlo methods. , . A complete description of the methods used in the statistical combina-tion is'provided in this report. The remainder of this secticn cut-lines the previcus deterministic and the new statistical thermal mar-gin methods. Section 3.0 describes the sources of uncertainty that were considered in this effort. Section 4.0 describes the MONSR response surface. The applicaticn of Monte Caric Methods is discussed in Section 5.0, and results are presented. Finally, Section 6.0
, describes the changes in design analyses that result frca this work, in particular, the resultant MDNBR limit of 1.24 which acccamodates the T-H uncertainties described in this report. i j I G e
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2-1 f L
2.1 Deteministic Method Two types of problem dependent data are required before a detailed T-H code can be applied. The first type of data, system parameters, describe the radial pin-by--pin physical system, power such as theinlet distributions, reactor andgeometry,bcundary exit flow condition, etc., These are not monitored in detail during reactor operation. The second type of data, state parameters, describe the operational state of the reactor. ' State parameters are monitored while _the reactor is in operation and include the core average . inlet temperature, primary loop flow rate, primary loop pressure, etc.
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C-E thermal margin methods (2-1) utilize the TORC code (2-2) and the CE-1 CHF correlation (2-3) with two types of models. The first model, detailed TORC, is tailored to yield best estimate MD"CR predictions in a particular fuel assembly for a specific power distribution. Both system and state parameter incut are used in a detailed TORC model. The second model, design TORC, requires only state parameter data and may be applied to any fuel assemoly for any pcuer distributien that is expected to occur.during a particular fuel cycle. System paraneters are fixed in the design model so that the model will yield either accurate or conservative MCUSR predictions for all cperating conditions within a specified range. Design model MDtSR results are verified by comparisen with results from the detailed model of the limiting assembly in the deterministic method. After the design ecdel is shown to yield acceptacle (i.e. accurate or conservative) results, additional adjustment factors are applied to account for uncertainties in system parameter inout to the detailed model. For examole, engineering factors are apclied to the hot subchannel of the design model to account .for fuel fabrication uncertainties. These adjustment factors, though arrived at statisti-cally, are applied in a deteministic nanner. That is, although eacn adjustment factor represents a g5/05 probability /cenfidence limit that , the particular parameter ceviation from neninal is no worse than des-cribed by that factor, all factors are apolied sinultaneously to tne
- limiting subchannel. This is equivalent to assuming that all adverse i deviations occur simultanecusly in the limiting subchannel. .
l l l 2.2 Statistical Method ' The probability of all adverse system parameter deviations frca ncminal occurring simultaneously in the liniting subchannel is extremely re: ote. With a more reascnable, demcnstrably ccnservative method, the probability of system parameter input ceing more adverse tnan specified can be taken into account statistically, as described herein. The improved methodology involves a statistical combination of system parameter uncertainties with the CHF correlation uncertainties to determine . l l l I 2-? l
a revised design MDNBR limit. Since uncertainties in system para- , meters are taken into account in the derivation of the new MDNBR limit, no other allowance need be made for them. A best estimate design TORC model is therefore used with the revised MDNBR limit for thermal margin analysis. This best estimate design model yields conservative or accurate MDNBR results when compared with a best estimate detailed model. The resultant best estimate design model and increased MDNBR limit ensure with at least 95% probability and at least a 95% confidence level that the limiting fuel pin will
- avoid a departure from nucleate boiling if the predicted MDNBR is not below the limit MDNBR.
O e t t
.2-3
3.0 Sources of Uncertainty Four types of uncertainty are identified in MDNBR predictions from the TORC code:
- 1) numerical solution parameter uncertainty ii) code uncertainty
, iii) state parameter uncertainty iv) system parame ter uncertainty Numerical solution parameters are required input that would not be necessary if analytic methods could be used (e.g., radial mesh size, axial mesh size, convergence criteria, etc.). The uncertainties associated with these parameters are dealt with in a conservative manner (3-1) in C-E's present methodology.
The numerical algorithms in the TORC code represent approximations to the conservation equations of mass, momentum, and energy. Because of the approximations involved, an inherent code uncertainty exists. This uncertainty is implicitly dealt with in the CE-1 CHF correlation (3-2) (3-3). State parameters defire the operational state of the reactor. Uncertainties in these parameters are included when the TORC model is incorporated intn the operating alcorithms. As explained in Section 2.1, system parameters define the operational state of the reactor and describe the physical environment that the working fluid encounters. This report establishes the equivalent MDNBR uncertainty that results from a statistical combination of uncertainties in system parameters. 3.1 State Parameters Used in the Study i Generation of a response surface which simultaneou'ly s relates MDNBR l to both system and state parameters would require an excessive number of detailed TORC analyses. Consequently, a conservative approximation is made and a response surface relating MDNBR to system parameters only is created. To achieve conservatism, it is necessary to generate the surface for that set of state parameters which maximizes the sen-l . sitivity of MDNBR to system parameter variations. That is, the response l surface can be described as: MDNBR = g (x., y.o) , where x is the vector of system parameters, and yo the vector of state parameters, is selected such that 3(MDNBR) ; maximum a x, Eo The set of state parameters, ro, that satisfies the above relation, is referred to as the most adverse set of state parameters. The generation of the response surface is discussed in Section 4.3. 3-1
i 3.1.1 Method for Selecting State Parameters Allowable operating parameter ranges are presented in Table 3-1. These ranges are based upon reactor setpoints including measurement uncertainty. The response surface must be valid over these ranges. As indicated above, a single set of operating conditions is chosen from these ranges to maximize the sensitivity of MDNBR to system parameters. This set of state conditions is determined from detailed TORC analyses in the following manner. Three TORC analyses are performed for a sinole set of operating conditions. In the first inalysis, nominal system parameters are u;ed and the core average heat flux is chosen to yield a MDNBR in the neighborhood of 1.19. A second TORC analysis uses - the same heat flux and operating conditions but has all system para-meters (i.e., pitch, inlet flow, entholpy rise, etc.) perturbed in an adverse direction (i.e., MDNBR decreases). A third TORC analysis uses the same heat flux and operating conditions but has all system parameters perturbed in an advantageous direction (i.e., MDNBR in-creases). The MDNBR from the " adversely perturbed" analysis is then subtracted from the " nominal" MDNBR to yield a AMDNBRtADVERSE) for the chosen set of operating conditions and the same is done for the TORC analysis where system parameters are " perturbed advantageously". That is,
= "Ncminal" MDNBR " Adversely Perturbed" MDNBR (3.1)
AMONBRADVERSE 1
"Advantaaeously Perturbed"MDNBR (3.2)
AMDNBRADVANTAGEOUS:"Nor:iinal" MDNBR The percent change in MDNBR is then determined according to te following
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relationships: i
% Change " " ADVERSE m nal" MDNBR) x M (3.3)
ADVERSE
- % Change.hVANTAGEOUS= @DNBRADVANTAGEDUS-
" Nominal" MDNBR)T100 (3.4) ,
This process is repeated for several sets of operating condicions to establish the sensitivity of thr MDNBR throughout the allow 5ble operating , range. Sets of operniiig conditions used in this sensitivitj study are - chosen to envelope the r%uired_ ranges shown in Table 3-1. The set of state parameter values which maximizesthe quantity (", ChangeADVERSE + is chosen as the most sensitive set of state
% ChangeADVA"Tues.OUS)is parameter va TAGE Th set is referred to es the set or,"most adverse,'
state parameter values and is used in determining the response surface. 3-2
Since MDNBR is a smoothly varying function of these state parameters (3-2), it is likely that the theoretical set of most adverse state paramete*s . vill be similar to the most adverse set found by the method , described above. Similarly, it is also highly unlikely that MDNBR sensitivities observed with the theoretical most adverse set will dif-fer appreciably from MDNBR sensitivities which occur using the most adverse set found by the above method. Inlet flow and exit pressure boundary conditions for the codel are shown in Fig. 3-1 and 3-2. Cora-wide and hot assembly power distributions are shown in Fig. 3-3 :nd 3-4 respectively. The detailed TORC analysis (3-1) consists of three stages. A core-wide analysis is done in the first stage, in which each fuel assembly near the limiting assembly is modeled as an individual channel. Cr6ssflow boundary conditions from the first stage are applied in the second stage to a more detailed model of the neighborhooc atSund the limiting assembly. Each quadrant of the }imiting assemb'Jy is represented by a channel in the second stage analyhi;. Cross. ? flow boundary conditions from the second stage are applied to the sub-
; channel model of the limiting assembly hot quadrant is the third stage, and the MONBR is calculated. TORC models for the firstr second, and third stages of the model used ir; the sensitivity study are sann in Fig. 3-5, 3-6, and 3-7 respectively.
3.1.2 Axial Shape Sensitivity Detailed TORC analyses as des,criced in Section 3.1.1 are performed to determine the most sensitive ASI to be used in W analysis. Data from these ca hulations are listed in Table I-2. *Re o1st sensitive ASI is found to be the[ JASI. 3.1.3 Pressure and Temoerature Sensitivity Using the ASI determined in Section 3.1.2, detailed TORC analyses are performed using the rr.ethod described in Section 3.1.1 to determine the pressure and temperature to be used in defining the Response Surface. Data from this analysis are found.in Trble 3-3. From these analyses it was determined thats the most sensitive pressure and temperature are [ jrespectively. 3.1.4 Primary System Flowrate Sensitivity Sensitivity studies indicate that at low primary system flowrates MONBR has a maximum sensitivity to perturbations in other system parara
,! ( i . e . ,
[Theresponsesurfaceisvalidtoaminimumcoreflowrateof the]of322,000gpc). Therefore,[ ]was cbsen to be used in gencrctina resnonse surface. i 1-3 __ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ - - - - - - - __ _ _____.-.____.______________u
3.1. 5 Most Adverse State Parameters As explained in Section 3.1, the set of state parameters chosen for use in generating the response surface should maximize MDNBR sensitivity to variations in system parameters; this is the most adverse set of state parameters. The most sensitive set of parameters is chosen 50 that the resultant MDNBR uncertainty will be maximized. This introduces conservatism into the overall treatment. , From Sections 3.1.2,. 3.1.3 and 3.1.4, it is seen that the state parameters which maximize MDNBR sensitivity are: , where 100% design flow is 322,000 gpm. 3.2 Radial Power Distribution Inherent conservatism in the thermal margin modeling methodolocy makes it un-necessary to account for uncertainties in the radial power distributions that are used in TORC DN8 analyses. 3.3 Inlet Flow Distribution An inlet flow boundary condition is used in detailed TORC analysis. Ratios of the local to core average mass velocity are input for every flow channel in the core-wide analysis. Mean values of the inlet ficw splits for three pump operation are presented in Fig. 3-1. Three pump operation with its inherent reduced flow gives a more conservative result than four pump operation. A large part of the uncertainty in the flow splits results from measurement uncertainty. This measurement uncertainty is considered random and may be characterized by a normal probability distri-bution function (p.d.f.). , Sensitivity studies have shown that MDNBR in the limiting assembly is unaffected by changes in the inlet flow of assemblies which are diagonally
- adjacent to the limitina assembly. Because of this insensitivity, inlet flow in assemblies which are diagonally adjacent to the limiting assembly may be omitted from the response surface. Only inlet flow to the limiting assembly and those assemblies which are immediately adjacent to it are included in the response surface.
3.4 Exit Pressure Distribution, Sensitivity studies indicate that MDNBR is extremely insensitive to variations in the exit pressure distribution. Consequently, the exit pressure distribution need not be included in the MONBR response surface.
~ 3-4
3.5 Enthalpy Rise Factor The engineering enthalpy rise factor accounts for the effects of manu-facturing deviations in fuel fabricetion from nominal dimensions and specifications on the enthalpy rise in the subchannel adjacent to the rod with the MONBR. Tolerance deviations in fuel pellet density, enrich-ment, and diameter averaged over the length of the fuel rods are used to compute this factor. As-buil.t data for ANO-2 Cycle 2 was used to generate an enthalov rise factor distribution characterized by a mean of approximately[ Janda standard deviation at 95%+ confidence of[ J. 3.6 Heat Flux Factor The engineering heat flux factor is used to take into account the effect on local heat flux of deviations from nominal design and specifications that occur in fabrication of the fuel. Random variation in pellet enrichment, initial pellet density, pellet diameter, and clad outside diameter (0.D.) contribute to the effects represented by the engineering heat flux factor. Tolerance limits and fuel specifications ensure that this factor ma be characterized conservatively by a nomal .d.f. with a mean of[ y ]and standard deviation at 95% confidence of 3 3.7 Clad 0.0. Variations in clad diameter change subchannel flow area and also change the local heat flux. The impact of both random and systematic variations in fuel clad 0.D. on the local heat flux is accounted for by the engineer-ing factor on heat flux, discussed in Section 3.6. The effect of random variations in clad 0.D. on subchannel flow area is included in the rod bow penalty, discussed in Section 3.9. The effect of systematic varia-tions in clad 0.D. on the subchannel hydraulic parameters is addressed here. - l Manufacturing tolerances on the fuel clad allow for the possibility
- that the clad diameter will be systematically above nominal throughout an entire fueTassembly. That is to say, the mean asetmilt value-of the clad 0.D. may differ from the nominal value. The distribution of the mean clad 0.0. for fuel assemblies may be characterized by a normal p.d.f. with a mean equal to the mean clad 0.0. and a standard deviation j
given by the relationsh1) (3-4F l (N-n) (*}
'u "* n(N-U l
where N is the number of specimens in the parent population and n is the sample size. I l ! 3-5
3 As-built data for ANO-2 Cycle 2 fuel indicate that the maximum systematic clad 0.0. is [- ) inches. Since the adverse effect of clad 0.D. Variations 'is ilready taken into account by the engineering heat flux factor, and use of a less than nominal clad 0.0. would increase sub-channel flow area, benefitting the MDNBR, the maximum value [
] is used in this study. The mean at the 95% confidence level-is[ ]inchesandthestandarddeviationofthemeanatthe95%
confidence level is [ ] inches.. The double accounting for both the adverse effect of a decrease in clad 0.D. in the engineering factor on heat flux and the adverse effect of a systematic increase in clad 0.D. on subchannel flow area adds conservatism to the analysis. . 3.8 Systematic Pitch Reduction The rod bow penalty, discussed in Section 3.9, takes into account the adverse effect on MDNBR that results from random variations in fuel rod pitch. The rod bow penalty does not take into account the adverse effect of systematic variations in fuel rod pitch. This systematic pitch reducticn effect must be discussed separately. Manufacturing tolerances on fuel assemblies allow for the possibility that the as-built fuel pitch will be less than nominal throughout an entire fuel assembly. Thus the systematic pitch refers to the mean value of the pitch in an assembly. The systematic pitch distribution is assumed to be a nomal distribution characterized by the mean value of the pitch and the standard deviation of that mean value. As-built g6p width data for ANO-2 Cycle 1 fuel are presented in Table 3-4. The minimum systematic gap width is seen to occur in the AXBT02 assembly [ ] and is [ ] inches. This, combined with the maximum clad 0.D. from Section 3.7 indicates that the minimum pitch is [
]. The mean at the 95% confidence level is [ ] inches,-and the standard' deviation of the mean at the 95% confidence level is [ ] inches.
- 3. 9 Fuel Rod Bow _
The fuel rod bow penelty accounts for the adverse impact on MDNBR of random variations in spacing between fuel rods. The methodology for determining die rod bow penalty 's the subject of a C-E topical report l* (3-5). Appendix G of that report (3-6) applies a formula deriveTby . l the NRC (3-7) to compute the rod bow penalty for C-E fuel. The penalty l at 30,000 MWD /MTU for t-E's 16x16 fuel is<2.0% in DNBR. This penalty is applied directly to -the new-MDNBR limit derived in Section 6. , 3.10 CHF Correlation The C-E 1 Critical Heat Flux (CHF) correlation (3-8) (3-9) is used in the TORC code (3-1) to determine whether a departure from nucleate boiling (DNB) will occur. This correlation is based on a set of 731 l l l l
.1-6
t i
- data points. The mean of the ratio cf observed to predicted CHF using i the CE-1 correlation is 0.99983, while the standard deviation of that .
ratio is 0.06757. CHF correlation uncertainty may be characterized i by a normal distribution with a mean 0.99983 and standard deviation of 0.06757. This yields a 1.13 MDNBR limit to satisfy the criterion of "95% probability at the 95% confidence level that the limiting fuel oin does not experience DNB". ~ However, because the NRC staff has not
. yet concluded its review of the CE-1 correlation, a 5% penalty has been applied; this raises the 95/95 MDNSR limit to 1.19. This penalty may be conservatively treated by displacing the above normal distribution by . +0.06 producing a displaced normal distribution with a mean of 1.06
(.99983 + 0.06) and the same standard deviation as above. 3.11 TORC Code Uncertainty , The TORC computer code (3-1) represents an approximate solution to the , conservation equations of mass, momentum, and energy. Simplifying assumptions were made, and experimental correlations were used to arrive at the algorithms contained in the TORC code. Hence, the code has associated with it an inherent calculational uncertainty. Com-parisons between TORC predictions and experimental data (3-1) (3-10) have shown that TORC is capable of adequate predictions cf coolant conditions. As explained in Section 5.0 of Reference (3-10), the TORC code was usad to determine local coolant conditions from data obtained during the CE-1 CHF experiments. These local coolant conditions were then used to develop the CE-l CHF correlation. Thus, any calculational uncertainty in the TORC code is implicitly included in the MDNBR limit that is used with the TORC /CE-1 package in thermal margin analyses. i f 4 1 f 3-7
-- -- - ~ . -
. . = . , . - , -_ - .-, -- - -
1 l d l
-s 7
J NOTE: ~ I CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH c' SEVERAL FUEL ASSET.1SLIES HAVE BEEN " LUMPED"INTO A SINGLE Y. CHANNEL FOR T- H ANALYSIS _ I l F*em l1 i INLET FLOW DISTRIBUTION USED TO l GENERATE RESPONSE SURFACE (THREEPUMPOPERATION) 3-8
l _ _r _J
~
NOTE: ! CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH C SEVERAL FUEL ASSEMBLIES HAVE BEEN " LUMPED"INTO A SINGLE L CHANNEL FOR T H ANALYSIS Figure 3-2 EXIT PRESSURE DISTRIBUTION USED TO GENERATE RESPONSE SURFACE 3-9
LIMITING ASSEMBLY IS BOX NUMBER 16 N l N 24 16 8 l STAGE 1 TORC ANALYSIS CHANNEL NUMBER .8736
- 1.1237 , 1.1734 37 '31 23 15 7 ASSEMBLY AVERAGE RADIAL PEAKING FACTOR 0.7252 1.0676 1.1592 1.2056 1.2470 .
41 36 30 22 g - 14 6 0.6704 0.8274 1.0757 1.0296 1.2052 1.0447 43 40 35 29 21 13 5 0.7252 0.8245 0.6465 0.8348 1.2389 0.9651 1.0816 42 39 34 28 20 12 4 1.0713 1.0757 0.8383 0.8081 0.9062 0.9278 0.9186
, 38 33 27 19 11 3 0.8680 8 1.1591 1.0270 1.2387 0.9046 1.2315 0.9492 1.2414 I
~~~~ ~
~ ~j 32 26 18 10 2 1.1216 l 1.2054 ,' 1.202G 0.9661 0.9262 0.9445 1.0006 0.8244 I .s l . 25 17- 9 1 1.1715 1 1.2455 3 1.0414 1.0803 0.9162
--{
1.2425 0.8241 0.5126 - i : , i - NOTE: I CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMBLIES HAVE BEEN " LUMPED"lNTO A SINGLE (L , CHANNEL FOR T H ANALYSIS Figure 3-3 CORE WIDE RADIAL POWER DISTRIBUTION USED TO GENERATE RESPONSE SURFACE 7-10
l l l l l l Figure 3 4 l HOT ASSEMBLY RADIAL POWER DISTRIBUTION USED TO GENERATE RESPONSE SURFACE 1 t I 3-11
CHANNEL NUMBER IN FIRST STAGE MODEL
'24 16 0 i
{ 37 31 23 15 7 41 36 30 22 14 6 43 40 35 29 21 13 5 42 39 34 28 20 12 4 I 38 33 27 19 11 3 I I I I ~1 32 26 18 10 2 i l@ I I e . . I 8
, 25 17 9 1 3
1 l k- 1 _ -k [ l 5 l . I NOTE: CIRCLED CHANNEL NUMBEirDENOTES A FLOW CHANNEL IN WHICH k' . SEVERAL FUEL ASSEMBLIES HAVE BEEN " LUMPED"INTO A SINGLE - ! CHANNEL FOR T - H ANALYSIS Figure 3-5 < CHANNEL NUMBERING SCHEME FOR STAGE 1 TORC ANALYSIS 1 3-12
.w + ,&- --* h* - _ 4 -o-. m E1 rs.k , -
- r l
i i' f e i i , ~ a i ,1 l i i n i ii + i , - Figure 34 INTERMEDIATE (2ND STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE a t 3-13
. . - . ~ . _ . . - . .-.. . . . - . . . . - . _ . _ - . . - _ . - . - - _ . _ _ . . = - . - .- . _ . ~.
a i l RADIAL PIN PEAKING FACTOR i \ i i 1 i i A
- l. .
1 i d i . i t i i 1 l '.i
- i
- Figure 3-7
! SUBCHANNEL (3RD STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE i i l I
~3-14 i -
Operating Conditions Units Range , Axial Shape Index * -0.600 < A.S. I . < 0.600 Inlet Temperature oF 465 < Ti n 1 605 System Pressure psia 1750 < Psys < 2400 System Flow % design + 60 < W <120 NOTES
*See note (1) on Table 3-2 for definition of axial shape index
+ Thermal margin design flow = 322,000 gpm TABLE 3-1: RANGES OF OPERATING CONDITIONS FOR WHICH RESPONSE SURFACE IS VALID i
I e i
, 3-15 n 4
HDilBR
% Change Axial Shape llominal System System Parameters System Parameters #
Index Parameters Adversely Perturbed Advantageously Porturbed % Change
--- Advantageous (1) --- ---
(2) _ ~
-0.627 -0.359 -0.070 0.00 Cosine +0.317 +0.337 +0.444 +0.527 "
L l l l (1) Axial Shape Index = Fz dz - L/2 F7 dz
-L/ 2, o Fz = co7e average axial peaking factor at axial location z FZ dz o = core mid plane
_t/
"#' ' "9 (2) See Section 3 TABLE 3-2 -Determination of Host Sensitive Axial Shape Index 3-16 .
MDNBR Pressure / Temperature Nominal System System Parameters System Parameters % ChangeAdverse Parameters Adversely Perturbed Advantageously + Perturbed
% ChangeAdvantageous psia /*F - - -
(1)
-I .-
2400/605 1750/605 1 2400/465 1750/465 - 1 I i (1) See Section 3 (2) For these state parameter combinations, CE-1 quality limits are exceeded for MDNBR's in excess of 1.19, therefore, these state parameters were not considered to be the "most sensitive" in _. generating the Response Surface. TABLE 3-3 Determination of the Most Sensitive Primary System Inlet Pressure and Temperature 1 3-17 I ,
Assembly Identification riunwr AKA050 AKA051 AKBT01 AKBT02 AKC107 AKC201 10 6 2
-i I i 1 i i l' Mean + xxxx(xxx) + number of measurements xxxx + standard deviation of mean TABLE 3 AS-BUILT GAP WIDTil. DATA (inches)
. . 3-18 , ,
4.0 MDNBR Response Surface A response surface is a functional relationship which involves several independent variables and one deoendent variable. The surface is created by fitting the constants of an assumed functional relationship to data obtained from" experiments". The response surface provides a convenient means by which accurate estimates of a comolex or unknown function 's response may se obtained.
. Since the response surface is a relatively simple expression, it may be applied in analytic techniques where more complex functions would make an analytic solution intractable.
In the present application, a single detailed TORC analysis is treated as an " experiment". A carefully se'ccted set of detailed TORC "experi-ments" is conducted, and a functioral relationship is fitted to the MDNBR results. This response surface is then used in conjunction with Monte Carlo techniques to combine probability distribution functions (p.d.f.'s) for each of the independent variables into a resultant MDNBR p.d.f.. , 4.1 TORC Model Used The inlet flow distribution (shown in Fig. 3-1) is compared with radial power distributions to determine the limiting location for DMB analysis. For the purpose of generating the response surface, the limiting loca-tion is defined as the assembly in which the impact of system parameter uncertainties on MONBR is the greatest. The core-wide and limiting assembly radial power distributions used to generate the response sur-face are shown in Figs.3-3 and 3-4, respectively. The first stage TORC model used in this analysis is shown in Fig. 3-5. The limiting assembly occurs in channel of this model. Second and third stage models used in this analysis [ar]e shown in Figs. 3-6 and 3-7, I respectively. 4.2 Variables Used A careful examination of the sources of uncertainty discussed in Section 3 shows that several of these sources of uncertainty can be omitted from the response surface. As explained in Section 3.2, inherent conservatism in the thermal margin model-ling methodology factnrs makes it unnecessary to account for uncertainty l in the radial onwer distribution used in DNS analyses. Hence, the j radial power distribution was omitted from the response surface. 4-1
The sensitivity study discussed in Section 3.4 Indicates that large pertur-bacions in the exit pressure distribution have negligible effect on the pre-dicted. mci;3R. Thus, the exit pressure distribution is not included in the response surface. The heat flux factor (F u) is applied to the MMBR calculated by TORC in the following manner: 9
- .MDf;BR TORC -
MDNBR = (4.1) F p Since the functional relationship between MDf;BR andqF " is known, the heat Instead, this flux factor is not used in generating the response surface. factor is combined with the resultant surface, as explained in section 4.5. A method has already been developed (4-1) to ac cunt for red bow uncertainty, Instead, the No rod bow effects are included in the response surface. rod bcw penalty determined with existing methods (4-1) is aoolied to the desian limit MDilBR as discussed in Section 6.2 The calculational uncertainty associated with MDllBR predictions using the TORC /CE-1 package is icplicitly included in the CHF distribution uncert-ainty, as explained in s ecticns 3.10 and 3.11. Hence no explicit allowance for code uncertainty is included in the response surface. The systen paraceters included as variables in the response surface are listed in Table 4-1. 4.3 Experiment Design , An orthogonal central composite experimental design (4 2) is used to gen-erate the response surface appliec in tnis study. The total cumber of exper- . iments needed to generate a response surface using this experitent design is 2k + 2k + 1 The desired resconse surface where k is the number of variables to be considered. consists of seven variables, hence la3 "exceriments" or detailed TCRC The analyses results of these were needed for a full orthogonal central ccaposite design. experiments may then be canipulated by ceans of the least squares estimator (4.2 ) e [n' nr' [n-} t ,
- 4-2
i ' where z is the vector of experimental results, to yield the coefficients which define the response surface 7
= b gg(nf -c) + 7E I b Z =
l10fiBR RS b, + ys] b gng + ,] g q nt g)) (4,3) i <j
~
In the above ecuations, the n are coded values of the system parameters (x ) to be treated in the respor.se i surface, as indicated in Table 4-1. The b4 rhp-resent the constants found from the TCRC results by means of Eq. 4.2. and c is a constant determined from the number of experiments conducted. , _ The number of TORC analyses needed to generate the response surface could be reduced significantly if some of the interaction effects (i.e. bg ;ngj n) were neglected. However, such interaction effects are included in tHd present method. 4.4 Desien Mat.rix The set of experiments used to generate the response surface is referred to as the design matrix. This matrix, in coded form, c::msrises the second through eichth columns of the n matrix cited in Eq. (4.2). Both coded and uncoded versions of the design natrix used in this study are presented in Appendix A along with resultant M0f!3R values. The desien matrix was con-structed such that eacn independent variable included in the response surface extends just beyond the 2a range of its associated p.d.f. 4.5 Response Surface Equation (4.2) was solved numerically using the data in Appendix A. Coefficients for the response surface as given by Eo. (4.3) are presented in Table 4-2. Comparisons made between TORC predicted M:ti3R and respense surface predictions shcw excellent agreement. The 955 confidence estimate of the response surface standard deviation is 0,00313.
~
i The heat flux factor is included analytically in the response surface l by combining Eq. (4.1) with Eq.(4.3). The final relationship is given by
=
H0flBR ,, I b + bg ng+ I bgg (nj -c)+ b gj ngnj (4-4) q g ,
' i=1 =1 i=1 ]=1
- j<j
~
4-3
_. -. .._ _ - .- _. - . . . - .-.. _. - . .~ .- ._. . _ _ . l 1
'i '(
The coefficient of determination, r, provides an indication of how well the i response surface explains the total variation in the response variable (4-3). When r = 1, a true model has been found. The r value associated with the response surface generated in this work is 0.9988, which indicates that this
- response surface is a gcod model.
, Another indication of model performance is provided by the standard error of ;
estimate (4-4). The standard error for the response surface is 0.002826. The relative error is 0.28%, indicating that this model performs well. l e l 4 i a e I l i I . l I l i 1 - l t l "4-4
Coded Values ** System Parameter Variable Index (i) ai sj hot assembly iqlet flow factor (channel [ )) X1 1 s channel [ ] inlet flow factor X2 2 I
. channel [ ] inlet flow factor X3 3 channel [ ] inlet flow factor X4 4 enthalpy rise factor X5 5 systematic pitch (inches) X6 6 I
systematic clad 0.0 (inches) X7 7 , j l
- Channel numbers refer to Figure 3-5
** Variables coded according to relation ni = *i ~ "i- where tne og Bi are chosen such that nj = 0 at nominal conditions and the 8 t' are chosen such that the range of the response surface will include s 2e ranges of each of the system parameters.
l Table 4-1: SYSTEM PARAMETERS INCLUDED AS VARIABLES IN THE RESPONSE SURFACE 9 I i l l
. 4-5
~
r l l l 7 7 7 7 MD iBRRS
=
b, t ;f, bi rti + b;;[rt,A c) + e ij q;p-) TABLE L2: COEFFICIEiTS FOR MDriSR RESP 0iSE SURFACE I9
~
4-6
5.0 Combination of Probability DistrRution Functions The MDflBR response surface discussed in Section 4 is applied in Monte Carlo methods to combine numerically the system parameter probability distribution func. ans (p.d.f.'s) discussed in Section 3 with the CHF correlation uncer-tainty. A new 95/95 ftDriBR limit is then selected from the resultant p.d.f. This new limit includes the effect of system parameter uncertainties and thus may be used in conjunction with a best estimate design TORC model. 5.1 Method The SIGMA code applies Monte Carlo and stratified sampling techniques to combine arbitrary p.d.f.'s numerically (5-1). This code is used with the response surface to combine system parameter p.d.f.'s with the CE-1 CHF correlation p.d.f. into a resultant MDiiBR p.d.f. The methods used to achieve this combination are discussed below. The effect of system parameter uncertainties on MDNBR is combined with the effect of uncertainty in the CHF correlation by computing a tJ!DtlBR caused y deviation of the system parameters from nominal: AMONBR = MDNBRg,,3, , MDNBRNOM (5.1) where MDNBRo 3 is the MDtlBR found by substituting the set of system para.7eters 'i'nto the response surface and MDNBR., predicted by the response surface with nominal"cvsystemparameters. is the MDNBR value A poirt is then randomly chosen frcm the CHF ccrrelation p.d.f. and combined with the AMDNBR from Eq. (5.i) to yield a MDNBR value: MDNBR = MDNBRCHF + $DNBR (5.2) This process is repeated by the SIGMA code for 2000 randomly selected sets of system parameters and randonly selected points from the CHF correlation p.d.f., and a resultant MDiiBR p.d.f. is generated. k The system parambr p.d.f.'s input to SIG."A are listed in Table 5-1. Both "best estimate" and 955 confidence estimates of the standard deviation are included. Standard deviations at the 955 confidence level are input to SIG tA to ensure that the standard 4eviation of the resultant !!DfiBP. p.d.f. is at least at the 95". confidence limit. . g ,, e 5-1 ,
5.2 Results The resultant MC:lGR p.d.f. is shown in Fig. 5-1. Tha mean and standard deviation of this p.d.f. are 1.00096 and 0.088502, respectively. As Fig. 5-1 indicates, the resultant Mot ER p.d.f. approximates a normal distri-bution. 5.3 Analytical Comoarison An approximate value of the standard deviation of the resultant MDti3R p.d.f. , may be found by analytic metnods. These metheds are based u;;cn the assumption that the uncertainttes are small deviations frca the mean (5-2). Given a functional relaticnship y = f(xj ,x 2' * * * *n) .3) the effects of small perturbations in x on y may be found frca ay=dy=a a 1
*1 +
2
#*2++ n d*n . (5.4)
Hence, if several normal distributions are combined by the relationship expressed in Eq.(5.3), the variance of the resultant p.d.f. is
'y2 =( E )2 a 2 ,(M )2 a2 , , , , , (M ) 2 ,2 ax) xj 3x 2 x ax" " ' ('}
' 2 wherethepartialderivativesareevaluatedatthemeanvaluesofthexj's.
The response surface relates MDri3R to system parameters by the relationship found on Table 4-2: 7 7 7- 7 2 MDNBRg3 =b o +{,)bnj+{,)bjj(nj j -c)+[,) I,) bjj ng nj (5.6) i<j xj -ej . where (5.7) ! n$ = # 1 . t Applying Eq. 5.5 to the response surface yields the following expression < for the variance: l - 2 g2 7 (a(MDilBR)h)2,x (5.8) RS ,f=1 an j ax j l l . 5-2
0 l-L Diffsrentiating Eq. (5.6) and (5.7) with respect to ngand xg : . (5.9)
=by +2bjg ng + ghj b jj nj ang j (5.10) 351 di .
Substituting Eq.(5.9) and (5.10) into Eq.(5.8) results in a relation be-tween the resultant MDtiBR variance and the system parameter variances:
.S = =1 (b +2g bgg ng+ .g ) bgj nj ) (**1 )2 ,
(5.11) 81 This equation is simplified when evaluated at the mean values of the ng: (i.e.ni=o) a 2
=f b I
x (5.12) ' R .S . i=1 2 The CHF correlation p.d.f. and system parameter p.d.f.'s are related to the resultant MDi;BR in Eq.( 5.1) and Eq.( 5.2), and the heat flux factor is related by Eq. ( 4.1) . The resultant MDriBR variance is given by _ g 2 2 #2 _ c HDt BR , 'R.S. + 'CHF ~ , Fo" (5.13)
- i. 2 "2 Fq" l* "MDNBR (uR.S. + "CHF)2
. where pR.S.-0 __.
Substituting values from Tables 4-t 4-2,5-1, and Section 4.5 into Eq. (5.11)
.and Eq (5.13) yields _
l 8 = 0.08765 MDriBR . i which is in excellent agreement with the value predicted by the SIG"A code simulation using the res;:anse surface. l - __.5-3 l 1 1
a i i i i 2U
- - - TRUE GAUSSIAN 0.10 -
n = NUf.13ER OF POINTS IN INTERVAL ACTUAL DISTRl30 TION OGTAINED - O FROh1 MONTE CARLO CODE AND (DNBR - 1/2 A DN3R, DN3R + 1/2 A DNDR) RESPONSE SURFACE 0.08 - OO N / 6
$ 0.06 - / O _
o 9O \ O \
/ \
0.04 -
/
/
8 \ O 0.02 - 06 bg - o. Os
# Oh 0.0 0.5 0.6 0.7
'OOO[O 0.8 i i 0.9 i
1.0 i 1.1 iO 1.2 d l4 1.3 DNBR Figure 5-1 IIESULTANT MDN3R PROGADILITY DISTRIBUTION FUNCTION
. . r, _ .) . .
4 STANDARD DEVIATION DISTRIBUTION MEAa AT 95% CONFIDENCE hot assembly inlet flow factor (channel [ ]) channel [ ] inlet flow factor channel [ ] inlet flow factor channel [ ] inlet flow factor enthalpy rise facter systematic pitch (inches) systematic clad 0.0. (inches) heat flux factor CE-1 CHF Correlation - .
- channel numbers refer to Figure 3-5 TABLE 5-1: PROBABILITY DISTRIBUTIOR FUNCTIONS COMBINED BY SIGMA I
+ . 9 5-5
1 I i 6.0 Application to Desien Analyses This section discusses the application of the statistically derived MDriBR p.d.f. to design analyses. Deterministic methodology (6-1) involves use of a design model for. TORC analysis which includes deteministic allcwances for system para-meter uncertainties. These deteministic penalties are replaced with a higher
. MDNBR limit in the statistical methodology. This higher MDNBR limit is used with a "best estimate" design model in thermal margin analyses.
6.1 Stattstically Derived MDNBR Limit
+ The MDtiBR p.d.f. described in Section 5.0 is a nomal distribution having a mean of 1.00096 and a standard deviation of 0.0885022. This standard deviation is at least at the 95': confidence level. A ccmparison of TORC results and response surface predictions indicates that tne le error associated with the response surface is e 3= 0.002826 ; at the 95% confidence level, this value is
's95 * (.002826 x /142/115.461 ) = .003134 . .
The MDNBR standard deviation was founo to be 0.088502 by means of t'onte Carlo methods. Since a finite number of points (2000) were used in these methods, a correction must be applied to the calculated value. The resultant MONB:t standard deviation, adjusted for the finite samole size used is (0.088502 x
/1999/1896.131) = 0.090871 The root sum scuare of the adjusted MDriBR stardard deviation and the response surface standard deviation at the 95% confidence level a
bt " )(0.090871)2 + (0.003134)2 = 0.090925. The corresponding 95% confidence estimate of the mean is (lbO'J96 + (l.645 x .0885022)/ 720001 = 1.004216. . Since the resultant MDriBR o.d.f. is a nomal distribution, as shown in Figure 5-1, the one-sided 955 crobability limit is 1.5455. Hence there is a 95% probability with at least 955 confidence that the limiting fuel pin will not experience DNB if the best escimate design model TORC calculation yields a MDNBR value greater than or equal to (1.004216 + 1.645 x 0.090925) = 1.154. 6.2 Adjustments to Statistically Derived MDNBR Limit l -The statistical MDNBR limit derived in Section 6.1 contains no allowance for the
; adverse impact on OffBR of fuel rod bowing. C-E has appliedT6 NRC method for . taking rod bow into account in DNBR calculations (6-2). This application shows that the penalty depends on batch average burnup. For 16x16 fuel, this penalty is 2.0% in MDNBR at a burnup of 30 GWD/MTU. Batch average burnups for Cycle 2 will not exceed 30 GWD/MTU. Thus, the new limit, including an allowance for rod bow is (1.020x1.154) or 1.177. _
The NRC has not yet completed review of the application of the CE-1 CHF cor-relation *6-3) to non-uniform axial heat flux shape data (6-4). Consequently, s a 5% penalty was applied to the 1.13 MDNBR limit by the NRC. The interim MDNBR limit for use with the CE-1 CHF correlation, pending NRC approval of C-E's non-uniform axial heat flux shape data, is 1.19. For the purposes of this study, a conservative application of this penalty is to shift the mean of the MDNBR p.d. f. by 0.06. This shift results in a MDNBR limit of 1.237, rounded off to 1.24. Thus, the new MDNBR limit which contains allowance for uncertainty in the CHF correlation and system parameers as well as a rod bow penalty and the interim 5% penalty ca the CE-l correlation imposed by the NRC is 1.24. 6-1
6,3 Application to TORC Design Model Statistical ccebination of system ;;rameter uncertainties into the MD iBR limit precludes the need for deterministic application of penalty facters to the design TORC model. The design TORC codel used witn the new t'0!iSR limit of 1.24 consists of best esticate system paraceters with no engineering factors or other adjustcents to accccccate system paraceter uncertainties. The inlet flow split will, however, continue to be chosen such that the best estimate design TORC ' model will yield accurate or conservative MCilBR predictions wnen compared with j MDNBR values frem detailes TORC analyses ( 6-11 4 o 4 6-2
_ . , _ . _a fa._ .__ - * , . 7.0 Conclusions I Use of a 1.24 MDNBR limit with a best-estimate design TORC model for the ANO-2 Cycle 2 core will ensure with at least 95% probability and 95% confidence, that the hot pin will not experience a departure from nucleate boiling. The 1.24 MDNBR limit includes explicit allowances for system parameter uncertainties, CHF correlation uncertainty, rod bcw, and the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation. 7.1 Conservatisms in the fiethodolocy Several conservatisms are included in the present application. The significant conservatisms include:
- 1) combination of system parameter p.d.f.'s at the 95%
confidence level to yield a resultant MDNBR at a 95% + confidence level
- 11) use of pess'imistic s;ystem parameter p.d.f.'s iii) derivation of the new MONBR limit such that it applies to both 4-pump and 3'p' ump operation iv) use of the single most adverss set of state parameters to generate the response surface --
v) application cf the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation o I e e d
.. 7-1
8.0 References 8.1 Section 2.0 References (2-1) " TORC Code: Verification and Simplified Modeling Models," CEilPD-206-P, January 1977. (2-2) " TORC Code: A Computer Code for Determining the Thermal Margin of a Reactor Core," CENPD-161-P, July 1975. (2-3) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Grids, Part 1: Uniform Axial Power Distribution," CENPD-162-P, September 1976. 8.2 Section 3.0 References (3-1) " TORC Code: A Ccmputer Code for Determining the Thermal Margin of a Reactor Core, CENPD-161-P, July 1975, pp. 5-1 to 5-8. (3-2) Combustion Engineering Standard Safety Analysis Report, (System 80), Docket #STN-50-470F, October 26, 1979, Fig. 4.4-7. (3-3) ibid, Subsection 4.4.2.2.2.2.C. (3-4) Green & Bourne, " Reliability Technology," Wiley-Interscience, A Division of John Wiley & Sons Ltd., p. 326. (3-5) " Fuel and Poison Rod Bowing," CENPD-225-P, October 1976. (3-6) " Fuel and Poison Rod Bowing - Supplement 3'," CENPD-225-P, Supplement 3, June 1979. (3-7) Letter from D. B. Vassallo (NRC) to A. E. Scherer (C-E), June 12, 1978. (3-8) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 1; Uniform Axial Power i Distribution," CEilPD-162-P, September 1976. (3-9) "C-E Critical Heat Flux: Critical Heat Flux Correlation.for C-E
- Fuel Assemolies with Standard Spacer Grids, Part 2: Nonuniform Axial Power Distribution," CEtiPD-207-P, June 1976.
l . (3-10) " TORC Code: Verification and Simplified Modeling Methods," CENPD-206-P, January 1977. 8.3 References for Section 4 (4-1) " Fuel and Poison Rod Bewing, Supplement 3," CENPD-225-P, Supple-ment 3-P, June 1979. l l j e 8-1 l
(4-2) R. H. Myers, Response Surface Methodology, Allyn and Bacon, Inc., Boston, 1971. (4-3) N. R. Draper, H. Smith, Applied Regression Analysis, John Wiley & Sons, New York, 1966, p. 62. (4-4) ibid., p. 118. 8.4 References for Section 5 (5-1) F. J. Berte, "The Application of Monte Carlo and Bayesian
~
Probability Techniques to Flow Prediction and Determination," Combustion Engineering Technical Paper TIS-5122, presented at the Flow Measurement Symposium, sponsored by the National Bureau of Standards, Gaithersburg, , Maryland, February 23-25, 1977. (5-2) E. L. Crow, F. A. Davis, M. W. Maxfield, Statistical Manual, Dover Publications, Inc., New York, 1960. 8.5 References for Section 6 (6-1) " TORC Code: Verification and Simplified Modeling Methods," CENPD-206-P, January 1977. (6-2) " Fuel and Poison Rod Bowing, Supplement 3," CENPD-225-P, Supple-mer t 3-P, June -1979. (6-3) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution," CENPD-162-P, September 1976. (6-4) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 2: Nonuniform Axial Power Distribut.icn," CENPD-207-P, June 1976. e 1 6 9 O *:
Appendix A: Detailed TORC Analyses Used To Generate Response Surface An orthogonal central composite experiment design (A-1) was used to generate the response surface (R S) used in this study. All first order interaction effects (i.e. xixj terms) were retained in the R S. The R S used in this study included seven variables. The coded set of detailed TORC analyses performed to generate the R S is presented in Table A-1; variables were ceded as shown in Table 4-1. The actual values of the input parameters are presented in Table A-2 along with the resultant MDNDR valu-- References (A-1) R. H. Myers, Response Surface Methodology, Allyn & Bacon, Inc., Boston, . 1971, p. 133. e
~
A-1
Case Inlet Flow Factors Enthalpy Systematic Systematic flumber Channel [] Channel [] ' Channel [.] Channel [] Rise Factor Pitch Clad 0.D. 1 -1 -1 -1 -1 -1 -1 -1 2 -1 ' -1 -1 -1 -1 -1 1 3 -1 -1 -1 -1 -1 1 -1 4 -1 -1 -1 -1 -1 1 1 5 -
-1 -1 -1 -1 1 -1 -1 6 -1 -1 -1 -1 1 -1 1 7 -1 -1 -1 -1 1 1 -1 8 -1 -1 -1 -1 1 1 1 9 -1 -1 -1 1 -1 -1 -1 10 -1 -1 -1 1 -1 -1 1 11 -1 -1 -1 1 -1 1 -1 12 -1 -1 -1 1 -1 1 1 13 -1 -1 -1 1 1 -1 -1
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relat. ,iships (10TE: Coded values determined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface A-2 ,
Case Inlet Flow Factors Enthalpy Systematic Systematic Number Channel [] Channel [ ] ' Channel [] Channel [] Rise Factor Pitch Clad 0.0. 14 -1 -1 -1 1 1 -1 1 15 -1 -1 -1 1 1 1 -1 16 -1 -1 -1 1 1 1 1 17 -1 -1 1 -1 -1 -1 -1 . 18 -
-1 -1 1 -1 -1 -1 1 19 -1 -1 1 -1 -1 1 -1 20 -1 -1 1 -1 -1 1 1 21 -1 -1 1 -1 1 -1 -1 22 -1 -1 1 -1 1 -1 1 23 -1 -1 1 -1 1 1 -1 24 -1 -1 1 -1 1 1 1 25 -1 -1 1 1 -1 -1 -1 26 -1 -1 1. 1 -1 -1 1
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships NOTE: Coded values determined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface (Cont'd) A-3
Case Inlet Flow Factors Enthalpy Systematic Systematic Number Channel [] Channel [] ' Channel [] Channel [] Rise Factor Pitch Clad 0.D. 27 -1 -1 1 1 -1 1 -1 28 -1 -1 1 1 -1 1 1 29 -1 -1 1 1 1 -1 -1 30 -1 -1 1 1 1 -1 1 31 -
-1 -1 1 1 1 1 -1 32 -1 -l 'l 1 1 1 1 33 -1 1 -1 -1 -1 -1 -l 34 -1 1 -1 -1 -1 -1 1 35 -1 1 -1 -1 -1 1 -1 36 -1 1 -1 -1 -1 1 1 37 -1 1 -1 -1 1 -1 -1 38 -1 1 -1 -1 1 -1 1 39 -1 1 -1 -1 1 1 -l
- channel numbers refer to fig. 3-5 See Table 4-1 for coded relationships
- NOTE: Coded values detennined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont'd) A-4 t
Case Inlet Flow Factors Enthalpy Systematic Systematic Number Channel [] Channel [ ] Channel [] Channel [_ ] Rise Factor Pitch Clad 0.0. 40 -1 1 -1 -l l 1 1 47 -1 1 -1 1 -1 -1 -1 42 -1 1 -1 1 -1 -1 1 43 -1 1 -1 1 -1 1 -1 44 -
-1 1 -1 1 -1 1 1 45 -1 1 -1 1 1 -1 -1 46 -1 1 -1 1 1 -1 1 47 -1 1 -1 1 1 1 -1 48 -1 1 -1 1 1 1 1 49 -1 1 1 -1 -1 -1 -1 50 -1 1 1 -1 -1 -1 1 51 -1 1 1 -1 -1 1 -l 52 -1 1 1 -1 -1 1 1
- channel numbers refer to fi9 . 3-5 See Table 4-1 for coded relationships I;0TE: Coded values determined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont'd) A-5
Case Inlet flow Factors Cnthalpy Systematic Systematic Number Channel [] Channel [ ] ' Channel [] Channel [] Rise Factor Pitch Clad 0.0. 53 -1 1 1 -1 1 -1 -1 54 -1 1 1 -1 1 -1 1 55 -1 1 1 -1 1 1 -1 56 -1 1 1 -1 1 1 1 57 -1 1 1 1 -1 -1 -1 58 -1 1 1 1 -1 -1 1 59 -1 1 1 1 -1 1 -1 o 60 -1 1 1 1 -1 1 1 61 -1 1 1 1 1 -1 -1 62 -1 1 1 1 1 -1 1 63 -1 1 1 1 1 1 -1 64 -1 1 1 1 1 1 1 65 1 -1 -1 -1 -1 -1 -1
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships NOIC: Coded values determined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont'd)
. A-6 . .
Case inlet Flow Factors Enthalpy Systematic Systematic flumber Channel [] Channel [ ] ' Channel [] Channel [ ] Rise factor Pitch Clad 0.0. 66 1 -1 -1 -1 -1 -1 1 67 1 -1 -1 -1 -1 1 -1 68 1 -1 -1 -1 -1 1 1 69 1 -1 -1 -1 1 -1 -1 70 1 -1 -1 -1 1 -1 1 1 71 1 -1 -1 -1 1 1 -1 72 1 -1 -1 -1 1 1 1 i 73 1 -1 -1 1 -1 -1 -1 74 1 -1 -1 1 -1 -1 1 75 1 -1 -1 1 -1 1 -l 76 1 -1 -1 1 -1 1 1 77 1 -1 -1 1 1 -1 -1 78 1 -1 1 1 -1 1
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships fl0TE: Coded values determined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont'd) A7
i i Case Inlet Flow Factors Enthalpy Systematic Systematic Number Channel [- ] Channel [ ] ' Channel [ [] Channel [] Rise Factor Pitch Clad 0.D. 79 1 -1 -1 1 1 1 -1 80 1 -1 -1 1 1 1 1 - 81 1 -1 1 -1 -1 -1 -l
+
'i 82 1 -1 1 -1 -1 -1 1 83 1 -1 1 -1 -1 1 -1 1
84 1 -1 1 -1 -1 1 1 85 1 -1 1 -1 1 -1 -1 86 1 -1 1 -1 1 -1 1 87 1 . -1 1 -1 1 1 -1 88 1 -1 1 -1 1 1 1 89 1 -1 1 1 -1 -1 -1 90 1 -1 1 1 -1 -1 1 . 91 1 -1 1 1 -1 1 -1
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships NOTE: Coded values determined by methods described in Reference (A-1).
Table A _l: Coded Set of Detailed TORC Cases used to Generate Response Surface (cont'd) , A-8
Case Inlet Flow Factors Enthalpy Systematic Sys tema tic Number Channel [] Channel [] Channel [] Channel [] Rise Factor Pitch Clad 0.D. 92 1 -1 1 1 -1 1 1 93 1 -1 1 1 1 -1 -1 94 1 -1 1 1 1 -1 1 95 1 -1 1 1 1 1 -1 96 - 1 -1 1 1 1 1 1 97 1 1 -1 -1 -1 -1 -1 98 1 1 -1 -1 -1 -1 1 99 1 1 -1 -1 -1 1 -1 100 1 1 -1 -1 -1 1 1 101 1 1 -1 -1 -1 1 -1 102 1 1 -1 -1 1 -1 1 103 1 1 -1 -1 1 1 -1 104 1 1 -1 -1 1 1 1 9
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships fiOTE: Coded values determined by methods described in Reference (A-1).
Ta bl e A-l_: Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont'd) A-9
Case inlet Flow Factors Enthalpy Systema tic Systematic Number Channel () Channel [ ] ' Channel [] Channel [ ] Rise Factor Pitch Clad 0.0. 105 1 1 -1 1 -1 -1 -1 106 1 1 -1 1 -1 -1 1 107 1 1 -1 1 -1 1 -1 108 1 1 -1 1 -1 1 1 109 1 1 -1 1 1 -1 -1 110 1 1 -1 1 1 -1 1 111 1 1 -1 1 1 1 -1 112 1 1 -1 1 1 1 1 113 1 1 1 -1 -1 -1 -1 114 1 1 1 -1 -1 -1 1 115 1 1 1 -1 -1 1 -1 116 1 .1 1 -1 -1 1 1
~
117 1 1 1 -1 1 -1 -1
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships NOTE: Coded values detennir.ed by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont'd) A-10
Case inlet Flow Factors Enthalpy Systematic Systematic Number Channel [] Channel [] ' Channel [] Channel [i ] Rise Factor Pitch Clad 0.0. 118 1 1 1 -1 1 -1 1 119 1 1 1 -1 1 1 -1 - 120 1 1 1 -1 1 1 1 121 1 1 1 1 -1 -1 -1 122 - 1 1 1 1 -1 -1 1 123 1 1 1 1 -1 1 -1 124 1 1 1 1 -1 1 1 125 1 1 1 1 1 -1 -1 126 1 1 1 1 1 -1 1 127 1 1 1 1 1 1 -1 128 1 1 1 1 1 1 1 129 0 0 0 0 0 0 0 130 1.91 0 0 0 0 0 0
- channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships NOTE: Coded values determined by methods described in Reference (A-1).
Table A-1: Coded Set of Detailed TORC Cases used to Generate Response Surface (cont'd) A-11
s c . p it D. 1 9 1 9 i h a0 0 s m 0 0 0 0 0 0 0 0 0 0 n ed 1 1 o t a - i sl t yC a S l e , c r i t 1 1 d ah 9 9 e mc et 0 0 0 0 0 0 0 0 0 1 1 0 0 d o . ti - c sP r y o S f e 1 c r - f a 4 o r yt u pc 1 1 e S l a aF 0 0 0 0 0 0 0 9, 9 0 0 0 0 l b h 1 1 a
) e t e - T 1 s n: - n E' e A o F e ( p S s e e
'j c R n
e e [ 1 9 1 9 r e t a l 0 0 0 0 0 0 0 0 0 0 0 f r 2 e e n 1 1
- % n e
1 n n G A a i h o C d t e
] b i
d e r s s [ , 1 1 c U s r o l 0 0 0 9 9, 0 0 0 0 0 0 0 0 e s t e 1 1 d e c n - s a n s a F a d C h o h C w 'C t R o e O l
] m T F 5 t [ - y d e 1 1 3 b e l
n e l 0 9, 9 0 0 0- 0 0 0 0 0 0 0 . d l i . I n 1 1 g e a n - i n t a F i e h m r D C o t e f . r t o
] e e d t f e
[ 1 e s S 9 r e l 0 0 0 0 0 0 0 0 0 0 0 0 u d e 1 s l e n - r a d n e v o a b C h m d C u e n d - o 1 l C - ) r e A d ee n sb n : e 't am 1 2 3 4 5 6 7 8 9 0 1 2 3 a E l n Cu 3 3 3 3 3 3 3 3 3 4 4 4 4 h c O T b a o l f 1 1 1 1 1 1 1 1 1 1 1 1 1 f T ( c
s I Case Inlet flow Factor Enthalpy Systematic Systematic Detailed TORC Response TORC Nunter ** , Channel () Channel () Channel ( ) Channel ( ) 1 .93921 .50495 .004 2 .93921 .50495 .002 3 .93921 .50590 .005 4 .93921 .50590 .004 5 1.06080 .50495 .004 6 1.06080 .50495 .003 7 1.06080 .50590 .003 8 1.06080 .50590 .002 9 .93921 .50495 .001 10 .93921 .50495 .004 11 .93921 .50590 .001 12 .93921 ; .50590 .000 13 1.06080 .50495 .003 14 1.06080 .50495 .003 . 15 1.06000 .50590 .004
'Charisiel niinhers refer to flg. 3-5 **All system parameters dimensionless except systematic pitch and clad 0.D. (inches)
Table A-2 C "'partson of TonC and Response Surface MDNDR for Cases Used to Generate Response Surface A-13 --
Case inlet flow Factor Enthalpy Systematic Systematic Detailed TORC Response 10RC humber Channel () Channel () Channel [ Channel ( ] 16 1.06080 .50590 .007 17 .93921 .50495 .001 18 .93921 .50495 .004
'19 .93921 .50590 .000 20 93921 .50590 .001 21 1.06080 .50495 .006 22 1.06080 .50495 .005 23 1.06080 .50590 .007 24 1.06080 .50590 .007 25 .93921 .50495 .004 26 .93921 .50495 .003 27 ! .93921 .50590 .005 I
28 .93921 .50590 .005 29 1.06080 .50495 .000 30 1.06080 .50495 .001 t
- Char.nci siund>ers refer to fig. 3-5 **All system parameters dimensionless except systematic pitch and clad 0.D. (inches)
! Table A-2 Comparison of Torc and Response surface riota5R for Cases Used to Generate Response Surface (cont'd) , A-14 , ,
Case Inlet flow factor Enthalpy Systematic Systematic Detailed TORC Response TORC
*inMr
- Rise Factor Pitch" Clad 0.D." H0itBR NDilBR Residual Channel (-) Channel () Channel ( ) Channelh']
31 1.06080 .50590 .000 1 32 1.06080 .50590 .002 ' .003 33 .93921 .50495 34 .93921 .50495 .005 35 .93921 .50590 .004 36 .93921 .50590 .002 37 1.06080 .50495' .001 38 1.06080 .50495 .001 39 1.06080 .50590 .002 40 1.06080 .50590. .000 41 .93921 .50495 .000 42 .93921 .50495 .001 43 .93921! .50590 .001 44 .93921 .50590 .001 45 1.06080 .50495 .001
- ' Channel unit >ers refer to Fig. 3-5 **All system parameters dimensionless except systematic pitch and clad 0.D. (inches)
Table A-2 Coaparison of TORC and Response Surface HUtlBR for Cases Used to Generate Response Surface (Cont'd) i j A-15
e I Case Inlet flow Factor Enthalpy Systematic Systematic Detailed 10RC Response TORC
*auxb" Rise Factor Pitch" Clad 0.0." N0ftBR HC'tBR Residual Channel () Channel (} Channel [ )_ Charinel( )
46 1.06080 .50495 .001 47 1.06080 .50590 .002 48 1.06080 .50590 .002
'49 .93921 .50495 .000 50 .93921 .50495 .000 51 .93921 .50590 .001 52 .93921 .50590 .001 53 1.06080 .50495 .004 54 1.06080 .50495 .003 55 1.06080 .50590. .004 56 1.06080 .50590 .004 57 .93921 .50195 .003 58 .93921 1 .50495 .002 59 .93921 .50590 .002 60 .93921 .50590 .003
- Channel numbers refer to fig.3-5
~
**All system parameters dimensionless except. systematic pitch and clad 0.D. (inches)
Table A-2 comparison of TORC and Response Surface HDf4BR for Cases used to Generate Response Surface (cont'd) A-16 .
- t. .
Case Inlet Flow Factor Enthalpy Systematic Systematt: Detailed TORC Response TORC tau.nbe' Rise factor Pi tch ** Clad 0.0." HDilBR HDilBR Residual Channel (] Chantiel() Channel (.) Channel (.) 61 1.06080 .50495 .000 62 1.06080 .50495 .001 63 1.06080 .50590 .002
'64 1.06080 .50590 .002 65 .93921 .50495 .001 66 .93921 .50495 .002 67 .93921 .50590 .002 68 .93921 .50590 .003 69 1.06080 .50495 .002 70 1.06080 .50495 .002 71 1.06080 .50590 .001 72 1.06080 .50590 .001 73 .93921' .50495 .001 74 .93921 .50495 .001 75 .93921 .50590 .004 -
' Channel santibers refer to Fig. 3-5 ,
**All system parameters dimensionless except systematic Pi tch and clad O.D. (inches)
Table A-2 Comparison of TORC and Response Surface HDilBR for Cases Used to Generate Response Surface (cont'd) A-17 -
t Case Inlet flow factor Enthalpy Systematic Systematic Detailed TORC Response TORC U "'*** F Rise factor pi tch *
- Clad 0.0.** HONBR HDhDR Residual Channel (- Ch'annelf) Channel ( ) Channel [ ]
76 .93921 .50590 .002 77 1.06080 .50495 ) .003 78 1.06080 .50495 .003 79 1.06080 50590 .003 80 1.06080 .50590 .002 81 .93921 .50495 .001 82 .93921 50495 .001 83 .93921 .50590 .001 84 .93921 .50590 .002 85 1.06080 .50495 .003 86 1.06080 .50495 .002 87 1.06080 ; .50590 .004 88 1.06080 .50590 .003 89 .93921 .50495 .001 90 .93921 .50495 .002 .annel nunters refer to rig.3-5 . **All system parameters dimensionless except systematic pitch and clad 0.D. (inches) Table A-2 Comparison of 10RC and Response Surface MDNBR for Cases (Ised to Generate Response Surface (cont'd) . . A-18 . . . ,
. . o i
1 Case tolet flow fartor Enthalpy Systematic Systematic Detailed 10RC Response TORC
""d##' #
Channelf) Channel () Channel ( ) Channel b ) 91 .93921 .50590 .003 92 .93921 .50590 .002 93 1.06030 50495 .002 94 1.06080 .50495 .001 95 1.06080 .50590 .003 96 1.06080 50590 .002 97 .93921 .50495 .001 98 .93921 .50495 .001 99 .93921 .50590 .003 100 .93921 50590 .003 101 1.06080 50495 .002 102 .50495 .002 1.06080 l 103 1.06080 .50590 .001 104 1.06080 50590 .002 105 .93921 .50495 . .003 1dADe\ blah.beri ref er 10 flg, 3-5 **All system parameters dimensionless except systematic pitch and clad 0.D. (inches) Table A-2 Conparison of 10RC and Response Surface MDflBR for Cases used to Generate Response Surface (cont'd). A-I9 ,
2 3 3 1 0 1 0 2 2 2 2 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C c R 0 _ i 1 t e a s m n e o p t s s e y R s t C p R 0 e 1 c d x e e . l e i a s c t s f a e e r D l u n S . o e i s i c s) ns o n t ee p a s m mh e e i c R t s d n y i et S ._ s( a r r e . en t e D. Ge m0 c a o i t 5 0 0 5 5 0 0 5 5 '0 0 5 5 0 0 rd t a 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 aa d m 4 5 5 4 4 5 5 4 4 5 5 4 4 5 5 pl e e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c sU t 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 n s i y ed s S t n e 0 sa y s a 2 C - sh A c r y l t o p 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 l i f l 2 2 2 8 8 8 8 2 2 2 2 8 8 8 8 A- R a 9 9 9 0 0 0 0 9 9 9 9 0 0 0 0
- l l
h 3 3 3 6 6 6 6 3 3 3 3 6 6 6 6
- i r
t D n 9 9 9 0 0 0 0 9 9 9 9 0 0 0 0 H [ 1 1 1 1 1 1 1 1 e c a f
) r
_ S u ( , i e l s e n n o f . n p a s h e C R d n
) a C
( R O l T e . n f a n o r h n o C o t s c i a r - f w ) m o ( 5 e l
- C f l e 3 t n e n .
l a lg n h I C f o 2 t
-)
r Ad e h l f e r l e 'tn e b o n s a c n r T( a e h _ b C ue i n
' l
' e e 6 7 8 9 1 2 3 4 5 6 7 8 9 0 n s #' 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 n a 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 C N" ea.
t C*
l . . . . I 4 Casa Inlet flow factor Enthalpy Systematic Systematic Detailed 10RC Response 10RC
"""'N ' Rise Factor Pi tch *
- Clad 0.D." MDNBR liDriBR Residual Channelf] Channel () Channel ( ) Channel ( ]
121 .93921 .50495 , .002 122 .93921 .50495 .001 123 .93921 .50590 .001 124 .9392) .50590 .000 125 1.06080 .50495 .005 126 1.06080 .50495 .004 127 1.06080 .50590 .002 128 1.06080 .50590 .003 129 1.00001 .50543 .002 130 1.00001 .50543 .002 131 1.00001 .50543 .002 132 1.00001 , .50543 .004 133 1.00001 .50543 .003 134 1.00001 .50543 .001 135 1.00001 .50543 . _ . .001 Channel nunters refer io Fig. 3-5 **All system parameters dimensionless except systeinatic pitch and clad O.D. (luches) Table A-2 Con 4>arison of 10RC and Response Surface HDilBR for Cases Used to Generate Response Surface (Cont'(l) A-71 _l
Case Inlet flow factor Enthalpy Systematic Systematic Detailed TORC Response' TORC Number Channelf) Channel ()____. Channel ( ) Channel ( ) 136 1 1.00001 .50543 .002 137 1.00001 .50543 .002 138 1.11612 .50543 .002 139 .88389 .50543 .001 140 1.00001 .50633 .004 141 1.00001 .50452 .005 142 1.00001 .50543 .007 143 1.00001 .50543 .007 l l i Channel munbers refer to flg. 3-5 **All system parameters dimensionless except system.2 tic pitch and clad 0.D. (inches) Table A-2 l Coraparison of TORC and Response Surface HDNDR for Cases used to Generate Response Surface j (cont'd) b22
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