ML20052G584

Nonproprietary Statistical Combination of Uncertainties: Combination of Sys Parameter Uncertainties in Thermal Margin Analyses for Sys 80.

ML20052G584
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Issue date:	05/14/1982
From:	ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY
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ENCLOSURE 1-NP a

TO LD-82-054 STATISTICAL COMBINATION OF l UNCERTAINTIES Combination of System Parameter Uncertainties In Thermal Margin Analyses for SYSTEM 80 5 Combustion Engineering, Inc.

8 Windsor, Connecticut l

l 8205180NW

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n LEGAL NOTICE  ;

THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COM8USTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF:

A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR s IMPUED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANTABIUTY, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN YHIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS;OR

8. ASSUMES ANY LIABILITIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMAT:ON, APPARATUS, METHOD OR PROCESS OlSCLOSED IN THIS REPORT.

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STATISTICAL COMBINATION OF UNCERTAINTIES

,. Combination of System Parameter Uncertainties in Thermal Margin Analysis for System 80 m

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a ABSTRACT This report describes the methods used to statistically combine system parameter uncertainties in the thermal margin analyses for the System 80 cores. A detatled description of the uncertainty probability distributions and response surface techniques used is presented. This report demonst' rates that there will be at least 95% probability with at least 95% confidence that the lim'iting fuel pin will avoid departure from nucleate boiling (DNB) so long as

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the minimum DNB ratio found with the best estimate design CETOP-D model remains

• at or above 1.22.

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TABLE OF CONTENTS Title Page Abstract i i Tahle of Contents 11

- List of Figures iv List of Tables v Nomenclature and Abbreviations vi Subscripts and Superscripts vii 1.0 Summary of Results 1 -1 2.0 Introduction 2-1 2.1 Deterministic M;:thod 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 l

3.4 Exit Pressure Distribution 3-4 3.5 Enthalpy Rise Factor 3-5 3.6 Heat Flux Factor 3-5 i 3.7 Clad 0.D. 3-5 3.8 Systematic Pitch Reduction 3-6 3.9 Fuel Rod Bow 3-6 t

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Y TABLE OF CONTENTS (con't)

Title Page

3.10 CHF Correlation 3-6 3.11 TORC Code Uncertainty 3-7 I 4.0 PONBR Response Surface 4-1 4.1 TORC Model Used 4-1 4.2 Variables Used

• 4-1 4.3 Experiment Design 4-2 4.4 Design Matrix 4-3 4.5 Response Surface 4-3 l i

5.0 Combination of Probability Distribution Functions 5-1 5.1 Method 5-1 5.2 Results 5-2 5.3 Analytical Comparison 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 Limit 6-1 6.3 Application to TORC Design Model 6-2 7.0 Conclusions 71 7.1 Conservatisms in the Methodology 7-1

. 8.0 References 8-1 Appendix l Appendix A: Detailed TORC Analyses Used to A-1 l

Generate Response Surface i

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LIST OF FIGURES Fig. No. Title Page 3-1 Inlet Flow Distribution Used to Generate 3-8 5 Response Surface .

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- 3-2 Exit Pressure Distribution Used to 3-9 '

Generate Response Surface

- 3-3 Core Wide Radial Power Distribution 10 Used to Generate Response Surface 3-4 Hot Aste.nbly Radial Power Distribution 3-11 Used to Generate Response Surface 3-5 Channel Numbering Scheme for Stage 1 TORC 3-12 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 3-14 in Generating Response Surface 5-1 Resultant MDNBR Probability Distribution 5-4 Function

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LIST OF TABLES Table No. Title  ;, Page q-1 Ranges of Operating Conditions 3-15 ,

for Which Response Surface is l Valid  !

f 3-2 Determination of the Most Sensitive 3-16

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Axial Shape Index 3-3 Determination of the Most Sensitive 3-18 Primary System Inlet Pressure f and Temperature 3-4 As-Built Gap Width Data 3-20 3-5 Inlet Mass Velocity Ratio 3- 21 j 4-1 System Parameters Included as 4-4 Variables in the Response Surface 4-2 Coefficients for MDNBR Response Surface 4-5 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-3 MDNBR for Cases Used to Generate Response Surface I

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NOMENCLATURE AND ABBREVIATIONS 9

b coefficient in response surface i c; constant in response surface

. f arbitrary functional relationship a k number of independent variables in response surface

. n number of items in a sample p.d.f. probability distribution function psd pounds per square foot psia pounds per square inch (absolute)  !

x system parameter  !

y state parameter 4

z MDNBR values predicted by response surface ASI axial shape index (defined in Table 3-2)

CE Combustion Engineering CHF Critical Heat Flux DNB Departure from Nucleate Boiling DNBR Departure from Nucleate Boiling Ratio F Fahrenheit F"q engineering heat flux factor MDNBR Minimum Departure from Nucleate Boiling Ratio T temperature T-H thermal-hydraulic i a constant used to code system parameters (Table 4-1) 8 constant used to code system parameters (Table 4-1) n coded value of system parameters (Table 4-1) l 9 mean o standard deviation a denotes difference between two parameters O

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- subscripts i

_ denotes vector quantity '

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, 1 index

. in conditions at reaactor core inlet

j index superscripts denotes estimate degrees average value

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1.0 Summary of Results j Methods were developed to combine statistically the uncertainties in reference thermal margin (detailed TORC) analyses. These methods were applied to the System 80 core. This work demonstrated that there will be at least 95% probability with at least 95% confidence that the limiting fuel pin will avoid departure from nucleate boiling (DNB) so fong as i the Minimum DNBR Ratio (MDNBR) found with the best-estimate design

. CETOP-D model remains at or above 1.22. The 1.22 MDNBR limit includes allowances for reference analysis input uncertainties but does 1 not take into account uncertainties in operating conditions

. (e.g., monitoring uncertainties).

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2.0 Introduction C-E's thermal margin methodology for System 80 has been modified by the application of statistical methods. This report focuses on the statistical combination of reference thermal-hydraulic (T-H) code input uncertainties. This combination was accomplished by the generation of a

_ Minimum DNBR (MDNBR) response surface and the application of Monte Carlo a methods.

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A complete description of the methods used in the statistical combination is provided in this report. The remainder of this section outlines the

. previous deterministic and the new statistical thermal margin methods.

Section 3.0 describes the sources of uncertainty that were considered in this effort. Section 4.0 describes the MDNBR response surface. The  ;

application of Monte Carlo Methods is discussed in Section 5.0, and j results are presented. Finally, Section 6.0 describes the changes in design analyses that result from this work, in particular, the resultant MDNBR limit of 1.22 which accommodates the T-H uncertainties described in this report.

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2.1 Deterministic 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 physical system, such as the reactor geometry, pin-by-pin radial power distributions, inlet and exit flow boundary condition, etc. These are not

_ monitored in detail during reactor operation. The second type of data, a 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.

C-E thermal margin methods (2-1) utilize the TORC (2-2) and CETOP-D (2-3) codes and the CE-1 CHF correlation (2-4) with two types of models. The first model, detailed TORC, is tailored to yield best estimate MDNBR

- predictions in a particular fuel assembly for a specific power distribution. Both system and state parameter input are used in a detailed TORC model. The second model, the CETOP-D design model, requires only state parameter data and may be applied to any fuel assembly for any power distribution that is expected to occur during '

a particular fuel cycle. System parameters are fixed in the design model so that the model will yield either accurate or conservative MDNBR predictions for all operating conditions within a specified range.

Design model ENBR results are verified by comparison with results from the detailed model of the limiting assembly in the deterministic method.

After the design model is shown to yield acceptable (i.e., accurate or conservative) results, additional adjustment factors are applied to account for uncertainties in system parameter input to the detailed model. For example, engineering factors are applied to the hot subchannel of the design model to account for fuel fabrication uncertainties. These adjustment factors, though arrived at statistically, are applied in a deterministic manner. That is, although each adjustment factor represents a 95/95 probability / confidence limit that the particular parameter deviation from nominal is no worse than described by that factor, all factors are applied simultaneously to the limiting subchannel. This is equivalent to assuming that all adverse deviations occur simultaneously in the limiting subchannel. ,

2.2 Statistical Method The orobability of all adverse system parameter deviations from nominal occurring simultaneously in the limiting subchannel is extremely remote. I l With a more reasonable, demonstrably conservative method, the probability U of system parameter input being more adverse than specified can be taken into account statistically, as described herein. ,

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., The improved methodology involves a statistical combination of system i parameter uncertainties with the CHF correlation uncertainties to determine a revised design ENBR limit. Since uncertainties in system

-, parameters are taken into account in the deri,vation of the new MDNBR limit, no other allowance need be made for them. A best estimate design CETOP-D model is therefore used with the revised MDNBR limit for thermal margin analysis. This best estimate design model yields conservative or l 2-2

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accurate WNBR results when compared with a best estimate detailed model.

The resultant best estimate design model and increased MNBR limit ensure -,

with at least 95% probability and at least a 95% confidence level that the  !

limiting fuel pin will avoid departure from nucleate boiling if the predicted MDNBR is not below the limit MDNBR. f k i 5 .

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I 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 parameter 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 man, momentum, and energy. Because of the  ;

approximations involved, an inherent code uncertainty exists. Thi s uncertainty is implicitly dealt with in the CE-1 CHF correlation as discussed in Section 3.11. ,

State parameters define the operational state of the reactor.

Uncertainties in these parameters are included when the CETOP-D model is incorporated into the operating algorithms.

As explained in Section 2.1, system parameters descibe the physical environment that the working fluid encount ers. This report establishes the equivalent MDNBR uncertainty that results from a statistical combination of uncertainties in system parameters.

3.1 S^. ate Parameters Used in the Study Generation of a response surface which simultaneously relates MDNBR 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 sensitivity of MDNBR to system parameter variations. That is, the response surface can be described as:

MDNBR = g (x, yo)

, where x_ is the vector of system parameters, and yo the vector of state parameters, is selected such that a(MDNBR) ---e maximum ax

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The set of state parameters,oy , that satisifies the above relation, is referred to as the rost adve ne set of state parameters. The generation i of the response surface is discused in Section 4.3.

I 3.1.1 Method for Selecting State Parameters .

S 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 l 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 single l set of operating conditions. In the first analysis, nominal system parameters are used and the core average heat flux is chosen to yield a E NBR in the neighborhood of 1.19. A second TORC analysis uses the same heat flux and operating conditions bu+ has all system parameters (i.e., pitch, clad 0.D., enthalpy rise) perturbed in an adverse direction (i.e., MNBR 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., ENBR increases). The i

MNBR from the " adversely perturbed" gg is then subtracted for the chosen set from of the " nominal" MDNBR to yield a MDNBR operating conditions and the same is done for the TORC analysis where system parameters are " perturbed advantageously". That is, AMDNBRADVERSE

= " Nominal" MDNBR " Adversely Perturbed" MDNBR (3.1)

" Nominal" MDNBR " Advantageous Perturbed" MDNBR (3.2)

AMDNBRADVANTAGEOUS =

The percent change in MDNBR is then determined according to the following relationships:

% ChangeADVERSE = (aMDNBRADVERSE " Nominal" MDNBR) x 100 (3.3)

% ChangeADVANTAGE00S = (aMDNBRADVANTAGE005 Nominal" MDNBR) x 100 f

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This process is repeated for several sets of operating conditions to establish the sensitivity of the MDNBR throughout the allowable 1 I

i operating range. Sets of operating conditions used in this sensitivity

' study are chosen to envelop the required ranges shown in Table 3-1.

The set of state parameter values which maximize ~s the quantity

(% ChangeADVER" + % ChangeAnVANTArE00s) is chosen as the most sensitive 5et 57 state parameter v3Tuds. This set is referred to as the i ,

set of "most adverse" state parameter values and is used in determining

, the response surface.

- Since NNBR is a smoothly varying function of these state parameters l (3-2), it is likely that the theoretical set of most adverse state l

parameters will be similar to the most adverse set found by the method described above. Similarly, it is also highly unlikely that MDNBR 3-2 L

sensitivities observed with the theoretical most adverse set will differ 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 model are shown in Fig. 3-1 and 3-2. Core-wide and hot assembly power distributions are shown in Fig. 3-3 and 3-4 respectively. The detailed TORC analysis a

(3-1) consists of three stages. A core-wide analysis is done on the first stage, in which each fuel assembly near the limiting assembly is

, modeled as an individual channel. Crossflow boundary conditions from the first stage are applied in the second stage to a more detailed model of the neighborhood around the limiting assembly. Each quadrant of the 6,

. limiting assembly is represented by a channel in the second stage analysis. Crossflow boundary conditions from the-second stage are applied to the subchannel model of the limiting assembly hot quadrant in the third stage, and the MDNBR is calculated. TORC models for the first, second, and third stages of the model used in the sensitivity study are shown in Figures 3-5, 3-6, and 3-7 respectively.

3.1.2 Axial Shape Sensitivity Detailed TORC analyses as described in Section 3.1.1 are performed to ,

determine the most sensitive ASI to be used in the analysis. ~ Data from these calculatio s are 1 sted in Table 3-2. The most sensitive ASI is found to be the ASI.

3.1.3 Pressure and Temperature Sensitivity Using the ASI determined in Section 3.1.2, detailed TORC analyses are performed using the method 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 Table 3-3. From these analyses ,it yas determined that the most sensitive pressure and temperature are

]respectively.

3.1.4 Primary System Flowrate Sensitivity Detailed TORC analyses as described in Section 3.1.1 are performed to determine the most sensitive flowrate to be used in this daalysis.

Data from these calculations are listed on Table 3-3. The most sensitive flowrat9 was found to be[ ]cf . design flow. (Design flow is equal to 445,600gpm.)

3.1.5 Most Adverse 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 paraueters. The most sensitive set of parameters is chosen so that the resultant MDNBR uncertainty will be maximized. This introduces

. conservatism into the'overall treatment.

, 3-3 x ' n' N, .

• * ,s y

From sections 3.1.2, 3.1.3 and 3.1.4, it is seen that the state parameters which maximize MONBR sensitivity are:

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where 100% design flow is 445,600 gpm.

3.2 Radial Pcwer Distribution

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Inherent conservatism in the thermal margin modeling methodology makes it unnecessary to account for uncertainties in the radial power distributions that are used in TORC ONB analyses.

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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. The inlet flow distribution used in the detailed TORC cases to generate the Minimum DNBR response i surface is shown in Figure 3-1.

[T ] flow model tests were run to determine the System 80 inlet flow distribution; hence,.[U -] points are available to use in characterizing the probability distribution function (p.d.f.) associated with each of the mass velocity ratios used in the inlet flow boundary condition. C

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3 deterministic ailowances were inciudee in the inlet flow distribution used in detailed TORC analyses to benchmark the System 80 CETOP-D model. The general benchmarking methods are discussed in Reference 311.

The deterministic method used to account for inlet flow distribu- l

' tion uncertainty consisted of[  !

of the inlet fiow niass velocity: ratios for the[.

.] The[ ' . 2]

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. _] based on flow model test data are shown in Table 3-5 along with the[ -

]which are used to benchmark CETOP-D.

Since inlet flowifistribution uncertainties are taken into account using deterministic methods, these uncertainties are not included in the statistical analysis described in this report.

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3.4 Exit Pressure Distribution Sensitivity studies indicate that MDNBR is extremely insensitive to variations in the exit pressure distribution (Ref. 3-4). Consequently, the exit pressure distribution need not be included in the MDNBR response surface. ,

3.5 Enthalpy Rise Factor The engineering enthalpy rise factor accounts for the effects of

- manufacturing deviations in fuel fabrication from nominal dimensions and specifications on the enthalpy rise in the subchannel adjacent to the rod with the MDNBR (3-3). Tolerance deviations in fuel pellet density, o enrichment, and diameter averaged over the length of the fuel rods are used to compute this factor.

As-built data for 16x16 fuel were used to generate an enthalpy rise factor distribution characterized by a mean of approximmately[ *]and a standard deviation at 95%+ confidence of[' .] . ,

i 3.6 Heat Flux Factor l The engineering heat flux factor is ussd to take into account the effect i 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 may be characterized conservatively by a normal mean of[ ' ] and standard deviation at 95% confidence of :][ p.d.f. . with a 3.7 C1ad O.D.

Variations in clad diameter change subchannel flow area and also change l 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 engineering factor on heat flux, discussed in Section 3.6. The effect of 6 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 [

variations in clad 0.D. on the subchannel hydraulic parameters is 6 addressed here.

Manufacturing tolerances on the fuel clad allow for the possibility that the clad diameter will be systematically above nominal throughout an j entire fuel assembly. That is to say, the mean as-built value of the clad 1

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0.D. may differ from the nominal value. The distribution of the mean clad 0.D. for fuel assemblies may be characterized by a normal p.d.f. with a mean equal to the mean clad 0.D. and a standard deviation given by the

- relationship (3-5):

., , ,, (N-n) q n(N-1) where N is the number of specimens in the parent population and n is the sample size.

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i As-built data for 16x16 fuel indicate that the maximum systematic clad 0.D. is[ ] inches. Since the adverse effect of clad 0.D.

variations is already taken into account by the engineering heat flux factor, and use of a less than nominal clad 0.D. would increase subchannel flow area, benefiting the ENBR, the maximum value[ ]is used in this study. The mean at the 95% confidence level isI_ ]

inches and the standard deviation of the mean at the 95% confidence

, levelis[ .] i nches. The double accounting for both the adverse effe-t 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.

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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 reduction 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 normal distribution characterized by the mean value of the pitch and the standard deviation of that mean value.

As-built gap width data for 16x16 fuel are presented in Table 3-4.

The minimum systematic gap width is seen to occur in the AKBT02 assembly

]and is

((from SeTtion 3.7]indicates inches. T'is, h combined with the maximum clad 0.D.

that the minimum pitch is[

inches. The mean at the 95% confidence level is[

]

] inches, and the deviation of the mean at the 95% confidence level is[ jinches.

3.9 Fuel Rod Bow The fuel rod bow penalty accounts for the adverse impact on MDNBR of random variations in spacing between fuel rods. The methodology for  :

determining the rod bow penalty is the subject of a C-E topical report l (3-6). Appendix G of that report (3-7) applies a formula derived by the NRC (3-7) to compute the rod bow penalty for C-E fuel. The penalty at 20,000 MWD /MTU for C-E's 16x16 fuel is 0.8% 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 (3-9) (3-10) is used in the TORC code (3-1) to determine whether a departure from nucleate

,' boiling (DN8) will occur. This correlation is based on a set of 731 data points. The mean of the ratio of observed to predicted CHF using the CE-1 correlation is 0.99983, while the standard deviation of that ratio is 0.06757. CHF correlation uncertainty may be characterized by a normal distribution with a mean 0.99983 and standard deviation of 0.06757. This yields a 1.13 NNBR limit to satisfy the criterion of "95% probability at 3-6 i

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f the 95% confidence level that the limiting fuel pin 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 I 95/95 MDNBR limit to 1.19. This penalty may be conservatively treated by displacirg the above normal distribution by +0.06 producing a displaced normal distribution with a mean of 1.06 (.99983 + 0.06) and _the same

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standard deviation as above.

3. 1 TORC Code Uncertainty The TORC computer code (3-1) represents an approximate solution to the conservation equations of mass, momentum, and energy. Simpli fying 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. Comparisons between TORC predictions and experimental data (3-1) (3-11) have shown that TORC is capable of adequate predictions of coolant conditions.

As explained in Section 5.0 of Reference (3-11), the TORC code was used 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-1 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.

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Figure 3-1 INLET FLOW DISTRIBUTION USED TO GENERATE RESPONSE SURFACE

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Figure 3-2 CORE EXIT PRESSURE DISTRIBUTION USED TO GENERATE RESPONSE SURFACE

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Figure 3-3 l CORE WIDE RADIAL POWER DISTRIBUTION USED TO q GENERATE RESPONSE SURFACE .

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. STAGE 1 TORC ANALYSIS 'l '

CHANNEL NUMBER #

0.6214 0.7988 0.8583 0.8760 ASSEMBLY AVERAGE 5 6 7 8 9 10 RADIAL PEAKING FACTOR 0.6164 0.8874 1.1028 1.0924 1.1875 1.2187 11 12 13 14 15 16 17 l SEE NOTE 1.2565 0.7041 1.0931 0.9475 1.1313 0.8671 1.1985 FIGURE 3-5 18 19 20 21 22 23 24 25 0.6200 1.0882 1.1759 1.1552 0.9717 1.1152 0.9383 1.0597 26 27 28 29 30 31 32 33 i 0.8329 0.9516 1.1610 0.8639 1.1272 0.9625 1.0173 0.6237 34 35 36 37 38 39 g a 0.6260 1.0990 1.1326 0.9695 1.1332 0.9980 1.1905 0.9509 1.h293 l

i l l@ l i l 0.7962 f 1.1004 j 0.8692 1 1.1118 1 1.1852 1.2466 1.2038 0.l9913 I l 0.9669 i  ! --__ - - . - . - ,!

I 1 i l 0.8549 ll 1.1959 1.2073 0.9373 l 1.0188 l0.9473 1.1981 1.0167 1.l1645

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0.8719 I 1.2146 1.2547 1.0675 0.9947 1.1589 0.

_..,18740 l 1.0350 -t s u [0.6231 l

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Figure 3-4 HOT ASSEMBLY RADIAL POWER DISTRIBUTION USED TO GENERATE RESPONSE SURFACE

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i i Figure 3-5 l CHANNEL NUMBERING SCHEME FOR STAGE 1 TORC ANALYSIS

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. NOTE: CIRCLED CHANNEL NUMBER DENOTES 1 2 3 4 ,

A FLOW CHANNEL IN WHICH SEVERAL ASSEMBLIES HAVE BEEN " LUMPED" INTO T.H ANALYSIS i

5 6 7 8 9 10 l i

CHANNEL NUMBER 15 16 17 11 12 13 14 IN FIRST STAGE --.

TORC 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 g i l

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- INTERMEDIATE (2ND STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE 9

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Figure 3-7 SUBCHANNEL (3RD STAGE) TORC MODEL USED IN

, GENERATING RESPONSE SURFACE 9

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. f Operating Conditions Units Range

- Axial Shape Index -0.600 1 A.S.I. 1 + 0.600 Inlet Temperature F 465 1 Tin <_ 615-System Pressure psia 17851Psys12400 System Flow  % Design

• 75 1 iW l20 NOTES *: See note (1) on Table 3-2 for definition of axial shape index

+ Thermal margin design flow = 445,600 gpm TABLE 3-1 Ranges of Operating Conditions i for which Response Surface is Valid I

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a n h a C h C -

l l

e .

. b r

su

. rt er t e eP m

ay

- rl as Pu x o e me eg d n -

t a I st yn e Sa p v a d h A S l

i a

d x se A rb er e t u v et 2 i mr ae - t 3 i R rP s B a E n N Py L e D l B S M me es A T t t r s se o yv M Sd A f o

n o

i t

m a e n ts i sr m ye r St e e t laam e D

- nr i a mP -

N o _ _

=

) x

- . I e _

_ I d l n 5 4 0 aI 6 7 4 7 0 1 i 3 2 4 3 0 0 5 6 7

• xe 6 5 4 3 0 0 0 0 0

. Ap a 0 0 0 0 0 0 0 0 0 h + + + + - - - -

S uh i  ;

MDNBR Change Adverse Axial II)

+

Nominal System System Parameters System Parameters Shape Index Parameters Adversely Perturbed Advantageously Perturbec % Change Advantageous (2)

-0.079

-0.094

-0.317

-0.359

-0.527

-0.636 w

J. -0.094 (1) Axial Shape Index = f /2

) Fz dz - Fj dz Fz = core average axial peaking factor at axial o location z

= core mid-plane L/2 L = active core length .

Fz dz _

~ operating .

-L/2 conditions *

(2) See Section 3 . .

(3) See Section 3.1.1 TABLE 3-2 (cont'd)

Determination of Most Sensitive Axial Shape Index

)

(

2 s

u o

e e g s a r t e n ,

v a d v A d A , _

e _

g e -

n g a n h a C h C

% + %

i e

b sr ru et tr ee mP a

ry al Ps s u n mo ee i

o tg t sa yt i

d Sn n a o v C d

A g i

n t

T a .

d r se e -

rb p .

er O tu et 3 e R

mr ae 3 i

v B rP t N a E i D Py L s -

M l B n .

me es A e T S t r se t yv s .

Sd o A M .

f o .-

n m

e o

i t s t sr ye a n

St i e m ..

l m r .

aa e .

nr t -

i a e mP o

_ D -

N

)

y d

wg 0 oi 5 5 5 5 0

- l s 5 5 1

. Fe 7 7 7 7 7 7

/ / / / / /

/D /

5 5 5 0 5 p 5 5 6

6 6 1 5 m%

e/

1 6

6 4 4 5 6 5 5

/ / / / / / /

TF 5 0 5 5 0

. /0 0 0 5 s/ 0 0 8 5 8 8 7 2 7 7 2 sa 4 4 1 2 1 1 2 ei 2 2 rs P p y ;5

i i

s

)

2

(

m _

s u

o ~

e g

e a s t r n .

e a _

v v d d A A eg e

g _

n n _

a a -

h h C+C e

- b sr ru et _

tr _

ee mP a

ry al Ps s u n mo ee i o

t g t sa i yt d Sn n a o v C d

A g n

i t

d a _

se r .

rb ) e p

er d t u O et 't R n i r n e B ae o v N rP c i D a ( t i

M Py 3 s l

me - n es 3 e t r S se E yv L t Sd B s A A o T M -

f o -

n o

i m t e a t s sr n ye i -

St m -

r e e l m m p t -

aa e ia nr '

g D -

mP 0 o 0 N 6, 5 1 4

4 1 l = 3 k

wq 0 0 0 w

o o n

oi 0 0 0 0

• l s 0 2 2 2 2 2 2 l i Fe 1 1 1 1 1 1 1 F t

/D / / / / / / / c p 0 5 5 5 5 0 5 n e g S m% 5 1 6 6 1 5 6 e/ 5 6 4 5 6 5 4 i TF / / / / / / / s e

. f 5 0 0 0 5 5 5 e e s/ 8 0 0 5 8 8 8 D S sa 7 4 4 2 7 7 7 _

ei 1 2 2 2 1 1 1 ) )

rs 1 2 P p ( (

[e _

- l ,l

1 0

2 C s K

A t n n a e e

. m m e

r f

, u o s

a n

. e o m i t

7 0 f a 1 o i C v K r e A e d b

m d ~

u r .

n a .

d n

+ a n t o 2 s i 0 )

t T x )

s a B x +

c K x e i A ( h f x x c i x x n t x x i n x x (

e a d t I +

4 a y - D l n 3 b 1 a h m 0 e E t e T H L d s B B i s K A W A A T p

a G

t l

i u

1 B 5 -

0 s A A K

A 0

5 0

A K .

A r

e 0 6 2

_- b 1

. u N

IE

,I  !

I i

l i

I t .

INLET MASS VELOCITY RATIO Fuel

. Assembly Number *

. I TABLE 3-5

• Assembly numbers refer to Figure 3-5 1

e 3-21

o l

4.0 MDNBR Response Surface l l

A response surface is a functional relationship which involves several l Independent variables and one dependent variable. The surface is created I by fitting the constants of an assumed functional relationship to data l obtained from " experiments".

The response surface provides a convenient means by which accurate estimates of a complex or unknown function's response may be 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 selected set of detailed TORC " experiments" is conducted, and a functional 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 DNB analysis.

For the purpose of genersting the response surface, the limiting location is defined as the assembly in which the impact of system parameter uncertainties on MDNBR is the greatest. The core-wide and limiting assembly radial power distributions used to generate the response surface 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 are shown in Figs. 3-6 and 3-7, 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 modelling methodology factors makes it unnecessary to account for uncertainty in the radial power distribution used in DNB analyses. Hence, l the radial power distribution was omitted from the response surface. '

Since the inlet flow distribution uncertainties are taken into account using deterministic methods, as explained in Section 3.3, these uncertainties are not included in the statistical analysis.

., The sensitivity study discussed in Section 3.4 indicates that large J perturbations in the exit pressure distribution have negligible effect on the predicted MDNBR. Thus, the exit pressure distribution is not included in the response surface.

4-1

The heat flux factor (F ")q is applied to the MDNBR calculated by TORC in the following manner:

MDNBR TORC (4*1)

MDNBR = p 4 q

Since the functional relationship between MDNBR and F " is known, the heat flux factor is not used in generating the respon0e surface.

, Instead, this factor is combined with the resultant surface, as explained in Section 4.5.

A method has already been developed (4-1) to account for rod bow I uncertainty, No rod bow effects are included in the response surface.

Instead, the rod bow penalty determined with existing methods (4-1) is applied to the design limit MDNBR as discussed in Section 6.2.

The calculational uncertainty associated with MDNBR predictions using the TORC /CE-1 package is implicitly included in the CHF distribution uncertainty, as explained in Sections 3.10 and 3.11. Hence no explicit allowance for code uncertainty is included in the response surface.

The system parameters included as variables in the response surface are listed in Table 4-1.

4.3 Experimental Design An orthogonal central composite experimental design (4-2) is used to generate the response surface applied in this study. The total number of experiments needed to generate a response surface using this experiment design is 2k + 2k + 1 where k is the number of variables to be considered. The desired response  !

surface consists of three variables, hence 15 " experiments" or detailed l TORC analyses were needed for a full orthogonal central composite design.  !

The results of these experiments may then be manipulated by means of the least squares estimator ,

i b= (n' n)~ {n'} z (4.2) where z is the vector of experimental results, to yield the coefficients which Fefine the response surface. '

3 3 3 3 2

z,= MONBRRS " ob I bg4 (n$ - c) + I b y n$ n3 (4.3) 1=1 i"i +i=1 i=1 j=1 i<j in the above equations, the nj are coded values of the system parameters (xj) to be treated in the response surface, as indicated in Table 4-1.

4-2

i ,

l The bj represent the constants found from the TORC 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 l be reduced significantly if some of the interaction effects (i.e.,bj 4ning) were neglected. However, such interaction effects-are included in the present method.

4.4 Design Matrix The set of experiments used to generate the response surface is referred to as the design matrix. This matrix, in coded form, comprises the second through fourth columns of the matrix cited in Eq. (4.2). Both coded and uncoded versions of the design matrix used in this study are presented in Appendix A along with resultant MDNBR values. The design matrix was constructed such that each independent variable included in the response surface extends just beyond the 2 o 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 Eq. (4.3) are presented i in Table 4-2. Comparisons made between TORC predicted MDNBR and response surface predictions show excellent agreement. The 95% confidence estimate of the response surface standard deviation is 0.00357 .

The heat flux fact 9r is included analytically in the response surface by combining Eq. (4.1) with Eq. (4.3). The final relationship is given by 3 3 3 3 1 2 MDNBR = g,, {b, + bj nj + bjj (nj - c) + I b jj nj nj } (4.4) 1 <j The coefficient of determination, r, provides an indication of how well the 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 0.99912 which j indicates that this response surface is a good model.

Another indication of model performance is provided by the standard error of estimate (4-4). The standard error for the response surface is 0.001711 . The relative error is 0.17% indicating that this model performs well, f 4-3

Coded Values

• Index System Parameter Variable (i) aj 8 9

Enthalpy Rise X 3

1 Factor Systematic X 2 j 2

Pitch (Inches) l l

Systematic X 3

3 l Clad 0.D. (Inches) L -

I

• variables coded according to relation nj= g where the aj are chosen such that nj = 0 at nominal conditions and the 8 are chosen such that the interval of the response 9

surface will include s 2o intervals of each of the system parameters.

TABLE 4-1 [

I System Parameters Included as Variables in the Response Surface r

m 4 -4

\

Response Surface Coefficient Coefficients Values b

c

. b)

. bg b

3 b jj b

22 b

33 b

12 [

b l3 b

23 c

i 3 3 2

3 3 [

MONBR R*S*

"D o +r bj n, + I bjj(nj -c) +i=1 r j=1 I

bj )nj n) i=1 i=1 TABLE 4-2  ;

l Coefficients for MDNBR Response Surface 4-5

5.0 Combination of Probability Distribution Functions The WNBR response surface discussed .in Section 4 is applied in Monte

, Carlo methods to combine numerically the system parameter probability

. distribution functions (p.d.f. 's) discussed in Section 3 with the CHF correlation uncertainty. A new 95/95 MDNBR 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 MDNBR 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 AMONBR caused by deviation of the system parameters from nominal:

A MDNBR = MDNBR R .S. - MDNBRNOM (5.1) where MONBR g3 is the MONRR found by substituting the set of system parameters into the response surface and MDNBRNOM is the MDNBR valu'e predicted by the response surface with nominal system parameters. A point j is then randomly chosen from the CHF correlation p.d.f. and combined with I-the WNBR from Eq. (5.1) to yield a MDNBR value:

1 MDNBR = MDNBRCHF + AMDNBR (5.2) {

t (

! This process is repeated by the SIGMA code for 2000 randomly selected sets of system parameters and randomly selected points from the CHF correlation 2

p.d.f. , and a resultant MDNBR p.d.f. is generated.

The system parameter p d.f's input to SIGMA are listed in Table 5-1. Both "best estimate" and 95% conf 1dence estimates of the standard deviation are i included. Standard deviations at the 95% confidence level are input to l SIGMA to ensure that the standard deviation of the resultant MDNBR p.d.f 3 ,

is at least at the 95% confidence limit.

5.2 Results The resultant MDNBR p.d.f is shown in Fig. 5-1. The mean and standard i

deviation of this p.d.f. .are 1.00568 and 0.0739714 respectively. As Fig. 5-1 indicates, the resultant MDNBR p.d.f. approximates a normal distribution.

5.3 Analytical Combination An approximate value of the standard deviation of the resultant MDNBR p.d.f may be -found by analytic methods. These methods are based upon the 5-1

assumption that the uncertainties are small deviations from the mean (5-2). Given a functional relationship y = f(xy,x2' *** *n) (5.3) the effects of small perturbations in x on y may be found from ayidy1(h)Axy+( 1 2

)Ax2 +'**** (axn) ^*n (5.4)

Hence, if several independent normal distributions are combined by the relationship expressed in Eq. (5.3), the variance of the resultant p.d.f. is ,

2 2

"y 2 1(af o

,x ) + (ax )

• n

+

l (aax 2

) *2 (5 5) where the partial derivatives are evaluated at the mean value of the xj's.

The response surface relates MDNBR to system parameters by the relationship found on Table 4-2:

3 3 3 3 MDNBRRS

• Do +I b I bjj j nj +i=1 (nj - c) + i=1 I j=1I b ij nj nj (5.6) i=1 i<j where x j - aj (5.7)

"i " sj Applying Eq. 5.5 to the response surface yields the following expression for the variance:

2 2 2"3 (a(MDNBR)

O'i

)

• i (5.8)

RS j[g anj 3x 3

Differentiating Eq. (5.6) and (5.7) with respect to and xj:

at4DNBR =

bj + 2bjj nj + b jj nj (5.9)

. an4 , 1 (5.10) 8*i 8 9

Substituting Eq. (5.9) and (5.10) into Eq. (5.8) results in a relation l between the resultant MDNBR variance and the system parameter variances:

0x 3 3 2 j 2 ORS

=I i=1 (bj + 2bjj nj +j=i+1 I b jj nj) (g) 1 (5.11) 5-2

i

{

This equation is simplified when evaluated at the mean values of the nj: (i .e. , n = 0 )

2=3 2 *i

~

'RS,$k'b i 2 (5.12)

The CHF correlation p.d.f and system parameter p.d.f.'s are related to the resultant ENBR in Eq. (5.1) and Eq. (5.2), and the heat flux factor is related by Eq. (4.1). The resultant MDNBR variance is given by 2 2 2 2 'Fq" c MDNBR " R.S. + CHF +

2 2 2 (5.13)

" HDN3R " Fq" (pR.S. + "CHF) where O

"R.S.

Substituting values from Tables 4-1, 4-2, 5-1, and Section 4.5 into Eq.

(5.11) and Eq. (5.13) yields:

o mNBR = .07694 which is in excellent agreement with the value predicted by the SIGMA code simulation using the response surface.

1 l

=

i . 5-3 l

l

--- True Gaussian O Actual distribution obtained n

from Monte Carlo code and 0.10 - Frequency = 2000 response surface n = number of points in interval (DNBR-1/2 ADNBR, DilBR + 1/2 ADNBR)

\

0'08 -

o' O

/ \

/

os 6

\

0.06- / \

/ D IE 6 \

\

i 0.04_ /

\

0.02- O

,'O \p c

'O O sDQ i i i i %GGEp i 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 -

DNBR Fiqure 5-1 Resultant MDilBR Probability Distribution function

3s s / , ,g j

. - s .

, v o .,- < g

' - ,s

, g s

P ,

1 4

.. j g s c N' Y ,

b,a

~

Standard Deviation s , , , .

s at _.

/ g%

Distribution Mean 95% Confidence m

_ s

- - 4

. , s y

Enthalpy Rise Factor i u ,. , .

Systemat' h(in) -

. s Systema. ....dOD(in) -3 Heat Flux Factor ,

CE-1 CHF Co.rrelation s

s ., .

5 m 94 4

l

.,N

, ,* c

.- s ,_

., m. ~

g, i

.._%', e s.

TABLE 5-1 ,

, .s

- s .

' ~'

Probability Distribution Functions '

, l Combined by SIGMA .

i' N, b s

,~.. ,c

. #- +

'\.

i k%,

• • 5 s

,. ? l

• % i i

e*

• b

< s

• P # e N

i

• w gs i

, . ,' g >u

^~

y w oc  % '

l - 2 , -% L g .

(* .,

a6 ,-

i g

• s

% e

• A y+

, \

g \  % 4 V 3

,8 k i

\ g ,g , go

~

8, .. % A ,

., .. r

• Ar

• s 't N , - ,

- (

! 1 5-5 * '

s , .

x n .,

I .

.. wcw o 'm

-/

s_ .

i i

l 6.0 Application to Design Analysis  :

This sr.ction discusses the application of the statistically derived MDNBR l p.d.f to design analyses. Deterministic methodology (6-1) involves use of i e design model for TORC analysis which includes deterministic. allowances  !

for system parameter uncertainties. These deterministic penalties are 5 replaced with a higher MDNBR limit in the statistical methodology. Thi s

, higher MDNBR limit is used with a "best estimate" design model in thermal margin analyses.

6.1 Statistically Derived MONBR Limit The MONBR p.d.f described in Section 5.0 is a normal distribution having a mean of 1.00568 and a standard deviation of 0.073971. This standard deviation is at least at the 95% confidence level. A comparison of TORC results and response surface predictions indicates that the 1 error associated with the response surface is as =0.00ll711; at the 95",

confidence level, this value is c S95= 0.001939 x ./5/1.15 = .00404 The MDNBR standard deviation was found to be 0.073971 by means of Monte Carlo methods. Since a finite number of points (200n) were used in these methods, a correction must be applied to the calculated value. The resultant MDNBR standard deviation, adjusted for the finite sample size used is 0.073971 x 1999/1896.131 = 0.075952. The root sum square of the adjusted MDNBR standard deviation and the response surface standard deviation at the 95% confidence level is:

tot =/(0.075952)2+(0.00404)2=0.076059. The corresponding 95% confidence estimate of the mean is (1.00568 + (1.645 x .073971) / 42000) = 1.00840 Since the resultant MDNBR p.d.f. is a normal distribution, as shown in Figure 5-1, the one-sided 95% probability limit is 1.645 c . Hence there ,

is a 95% probability with at least 95% confidence that the limiting fuel '

pin will not experience DNB if the best estimate design model TORC calculation yields a MONBR value greater than or equal to (1.00840 + 1.645 (.076059)) = 1.1335 6.2 Adjustments to Statistically Derived MDNBR Limit The statistical MONBR limit derived in Section 6.1 contains no allowance for the adverse impact on DNBR of fuel rod bowing. C-E has applied an 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 0.80% in MONBR at a burnup of 20 GWD/MTU.

Batch average burnups for Cycle 1 wil1 not exceed 20 GWD/MTV. Thus, the new limit, including an allowance for rod bow is (1.008x1.1335)or 1.1425.

This new MDNBR limit does not include the .01 NRC imposed DNBR penalty for the use of HID grids. With this penalty the new limit, including allowance for the HID grid loss is 1.1525.

. The NRC has not yet completed review o he application of the CE-1 CHF

1 correlation (6-3) to non-uniform axial heat flux shape data (6-4).

Consequently, a 5% penalty wes 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 FTNBR p.d.f. by 0.06. This shift

. results in a MDNBR limit of 1.213, rounded up to 1.22.

~* Thus, the new MDNBR limit which contains allowances fnr uncertainty in the

. CHF correlation and system parameters es well as a 0.8% rod bow penalty, the NRC imposed DNBR HID grid loss penalty, and the NRC imposed 5% CE-1 correlation penalty is 1.22.

I 6.3 Application to TORC Design Model f

Statistical combination of system parameter uncertainties into the MDNBR '

limit precludes the need for deterministic application of penalty factors to the design TORC model. The design TORC modal used with the new MDNBR ,

limit of 1.22 consists of best estimate system parameters with no engineering factors or other adjustments to accommodate system parameter uncertainties. The inlet flow split will, however, continue to be chosen such that the best estimate design TORC model will yield accurate or conservative MDNBR predictions when compared with MDNBR values from detailed TORC analyses (6-1) which include deterministic allowances for l inlet flow distribution uncertainties.

i t

i 6-2

3 7.0 Conclusions Use of a 1.22 MDNBR limit with a best-estimate design CETOP-D model for System 80 will ensure with at least 95% probability and 95% confidence, that the hot pin will not experience a departure from nucleate boiling.

The 1.22 MNBR limit includes explicit allowances for system parameter uncertainties, CHF correlation uncertainty, rod bow, the NRC penalty, for the HID spacer grids and the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation.

7.1 Conservatisms in the Methodology

- 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 j ii) use of pessimistic system parameter p.d.f.'s iii) use of the single most adverse set of state parameters to generate the response surface iv) application of the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation v) application of the 0.01 HID grid penalty imposed by the NRC on the CE-1 CHF correlation.

t 7-1

9 k

8.0 References f 8.1 Section 2.0 References {

( 2-1 ) " TORC Code: Verification and Simplified Modeling Models", CENPD-206-P, -

f 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) "CETOP-D Code Structure and Modeling Methods for San Onofre Nuclear

., Generating Station Units 2 and 3", CEN-160(S)-P, Rev.1-P Docket No. 50-361, 50-362, Sept.1981.

l (2-4) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Grids, Part 1: Uni form Axial Power Distribution", CENPD-162-P, September 1976.

8.2 Section 3.0 References (3-1) " TORC Code: A Computer 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) " Statistical Combination of Uncertainties, Part 2", CEN-124(B)-P, January 1980.

(3-5) Green & Bourne, " Reliability Technology", Wiley-Interscience, A Division of John Wiley & Sons Ltd., p. 326.

(3-6) " Fuel and Poison Rod Bowing", CENPD-225-P, October 1976.

(3-7) " Fuel and Poison Rod Bowing - Supplement 3", CENPD-225-P, Supplement 3, June 1979.

(3-8) Letter from D. B. Vassallo (NRC) to A. E. Scherer (C-E), June 12, 1978.

(3-9) "CE Critical Heat Flux: Critical Heat Flux Correlation for CE Fuel Assemblies with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution", CENPD-162-P, September 1976. l (3-10) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 2: Nonuniform Axial

, Power Distribution", CENPD-207-P, June 1976.

2 (3-11) " TORC Code: Verification and Simplified Modeling Methods". CENPD-206-P,

- January 1977.

I l

8-1

t 8.3 References for Section 4 j (4-1) " Fuel and Poison Rod Bowing, Supplement 3", CENPD-225-P, June 1979. 3 (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, Supplement 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 Girds, Part 2: Nonuniform Axial Power Distribution", CENPD-207-P, June 1976.

9' l

1 8-2

i Appendix A: Detailed TORC Analyses Used To Generate Response Surface 1

An orthogonal central composite experimental design (A-1) was used to generate the response surface (R S) used in this study. All first order ints. action

' affects (i.e. xt, terms) were retained in the R S. The R S used in this

~

study included tnree variables. The coded set of detailed TORC analyses

- performed to generate the R S is presented in Table A-1; variables were coded

, as shown in Table 4-1. The actual values of the input parameters are presented in Table A-2 along with the resultant MDNBR values.

References (A-1) R. H. Myers, Response Surface Methodology, Allyn & Bacon, Inc.,

Boston,1971, p.133.

.I I

l j

P A-1

l l

Case Enthalpy Systematic Systematic Number Rise Factor Pitch Clad 0.D.

1 -1.00 -1.00 -1.00 2 -1.00 -1.00 -1.00 L j

. 3 -1.00 1.00 -1.00 -

I* 4 -1.00 1.00 1.00 5 1.00 -1.00 -1.00 6 1.00 -1.00 1.00 7 1.00 1.00 -1.00 8 1.00 1.00 1.00 9 0.00 0.00 0.00 f 10 -1.22 0.00 0.00 11 1.22 0.00 0.00 12 0.00 -1.22 0.00 13 0.00 1.22 0.00 14 0.00 0.00 -1.22 15 0.00 0.00 1.22 See Table 4-1 for Coded Relationships TABLE A-1 Coded Set of Detailed TORC Cases

, Used to Generate Response Surface A-2 l

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