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CEN-283(S)-NP, Part 1, Revision 0, Statistical Combination of Uncertainties Part 1; Combination of System Parameter Uncertainties in Thermal Margin Analyses for San Onofre Nuclear, Units 2 and 3
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Site:	San Onofre, 05000360
Issue date:	06/30/1984
From:	; Combustion Engineering, Westinghouse
To:	; Office of Nuclear Reactor Regulation
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STATISTICAL COMBINATION OF UNCERTAINTIES PART l CEN-283(5)-NP COMBINATION OF SYSTEM PARAMETER UNCERTAINTIES IN THERMAL MARGIN ANALYSES FOR SAN ONOFRE NUCLEAR UNITS 2 AND 3 JUNE 1984 E~POWER

.t.5 SYSTEMS COMBUSTION ENGINEERING. INC

Westinghouse Non-Proprietary Class 3 LEGAL NOTICE This notice was prepared as an account of work sponsored by Combustion Engineering, Inc.

Neither Combustion Engineering nor any person 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 resped to the accuracy, completeness, or usefulness of the infonnation contained in this report, or that the use of any infonnation, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or

b.

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.

CEN-283(S)-NP, Part 1 Revision 0 June 1984

Westinghouse Non-Proprietary Class 3 ABSTRACT This report describes the methods used to statistically combine system parameter uncertainties in the thermal margin analyses for the SONGS 2 Cycle 2 core. A detailed description of the uncertainty probability distributions and response surface techniques used is presented. This report demon-strates that there will be at least 95% probability with at least 95% con-fidence that the limiting fuel pin will avoid departure from nucleate boiling (DNB) so long as the minimum DNB ratio found with the best estimate design CETOP-D model remains at or aoove 1.31.

CEN-283(S)-NP, Part 1 Revision 0 i

June 1984

Westinghouse Non-Proprietary Class 3 TABLE OF CONTENTS Title Abstract Table of Contents L1 st of Figures List of Tables Nomenclature and Abbreviations 1.0 Summary of Results 2.0 Introduction 2.1 Deterministic Method 2.2 Statistical Method 3.0 Sources of Uncertainty 3.1 State Parameters Used in the Study

3. 1.1 Method for Selecting State Parameters

3. 1.2 Axial Shape Sensitivity 3.1.3 Pressure and Temperature Sensitivity 3.1 A Primary System Flowrate Sensitivity

3. 1.5 Most Adverse State Parameters 3.2 Radial Power Distribution 3.3 Inlet Flow Distribution 3.4 Exit Pressure Distribution 3.5 Enthalpy Rise Factor 3.6 Heat Flux Factor 3.7 Clad 0. D.

3.8 Systematic Pitch Reduction 3.9 Fuel Rod Bow CEN-283(S)-NP, Part 1 Revision 0 ii i.v V

vi 1-1 2-1 2-2 2-2 3-1 3-1 3-2 3-3 3-3 3-3 3-4 3-4 3-4 3-4 3-5 3-5 3-5 3-6 3-6 June 1984

Westinghouse Non-Proprietary Class 3 TABLE OF CONTENTS (con 1 t.)

Title 3.10 CHF Correlation 3.11 TORC Code Uncertainty 4.0 MDNBR Response Surface

4. l TORC Model Used 4.2 Variables Used 4.3 Experiment Design 4.4 Design Matrix 4.5 Response Surface 5.0 Combination of Probability Distribution Functions 5.1 Method 5.2 Results 5.3 Analytical Comparison 6.0 Application to Design Analysis 3-6 3-7 4-1 4-1 4-1 4-2 4... 3 4-3 5-1 5-1 5-2 5-2 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 7.1 Conservatisms in the Methodology 8.0 References Appendix 7-1 7-1 8-l Appendix A:

Detailed TORC Analyses Used to Generate A-1 CEN-283(S)-NP, Part 1 Revision 0 Response Surface iii June 1984

Westinghouse Non-Proprietary Class 3 LIST OF FIGURES Fig. No.

Title 3-1 Inlet Flow Distribution Used to Generate Re-sponse Surface{lhree Pump Operation) 3-2 Exit Pressure Distribution Used to Generate Response Surface 3-3 Core Wide Radial Power Distribution Used to Generate Response Sur~ace 3-4 Hot Assembly Radial Power Distribution Used to Generate Response Surface 3-5 Channel Numbering Scheme for Stage 1 TORC Analysis to Generate Response Surface 3-6 Subchannel (2nd Stage) TORC Model Used in Generating Response Surface 5-1 Resultant MDNBR Probability Distribution Function iv CEN-283(S)-NP, Part 1 Revision 0 Page 3-8 3-9 3-10 3-11 3-12 3-13 5-4 June 1984

Westinghouse Non-Proprietary Class 3 LIST OF TABLES Table No.

Title 3-1 Ranges of Operating Conditions for Which Response Surface is Val id 3-2 Detennination of the Most Sensitive Axial Shape Index 3-3 Determination of the Most Sensitive Primary System Inlet Pressure and Temperature 3-4 As-Built Gap Width Data 4-1 System Parameters Included as Variables in the Response Surface 4-2 Coefficients for MDNBR Response Surface 5-1 Probability Distribution Functions Combined by SIGMA A-1 Coded Set of Detailed TORC Cases Used to Generate Response Surface A-2 Comparison of TORC and Response Surface MDNBR for Cases Used to Generate Response Surface CEN-283(S)-NP, Part 1 Revision 0 V

Page 3-14 3-15 3-17 3-18 4-5 4-6 5-5 A-2 A-13 June 1984

b C

f k

n p.d.f.

psf psi a X

y z

ASI CE CHF DNB ONBR F

Fqn MDNBR T

T-H a

s rt lJ er Westinghouse Non-Proprietary Class 3 NOMENCLATURE AND ABBREVIATIONS coefficient in response surface constant in response surface arbitrary functional relationship number of independent variables in response surface number of items in a samp1e probability distribution function pounds per square foot pounds per square inch (absolute) system parameter state parameter MONBR values predicted by response surface axial shape index (defined in Table 3-l)

Combustion Engineering Critical Heat Flux Departure from Nucleate Boiling Departure from Nucleate Boiling Ratio Fahrenheit engineering heat flux factor Minimum Departure from Nucleate Soiling Ratio temperature thermal-hydraulic constant used to code system parameters {Table 4-1) constant used to code system parameters (Table 4-1) coded value of system parameters (Table 4-1) mean standard deviation denotes difference between two parameters CEN-283(S)-NP, Part 1 Revision 0 vi June 1984

Westinghouse Non-Proprietary Class 3 s~bscripts denotes vector quantity i

index fn conditions at reactor core j

index superscripts 0

denotes estimate degrees average value CEN-283(S)-NP, Part 1 Revision 0 inlet vii June 1984

Westinghouse Non-Proprietary Class 3 1.0 Surrmary of Results Methods that had been developed previously to combine statistically the uncertainties in reference thermal margin (detailed TORC) analyses were applied to the SONGS-2 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 long as the Minimum DNB Ratio (MDNBR) found with the best-estimate design CETOP-0 model remains at or above 1.31.

The 1.31 MDNBR limit includes allowances for reference analysis input uncertainties but does not take into account uncertainties in operating conditions (e.g., monitoring uncertainties).

The SCU analyses performed for SONGS-2 utilized the same methods previously used for Calvert Cliffs (1-1)

St. Lucie - I (1-2)

AN0-2 (1-3)

System 80 (1-4)

Fort Calhoun (1-5)

The methods and their applications have been reviewed previously and approved.

In contrast to earlier SCU analyses, the SONGS-2 analysis includes penalties imposed by NRC in their review of these methods {1-6).

CEN-283(S)-NP, Part 1 Revision 0 1-1 June 1984

Westinghouse Non-Proprietary Class 3 2.0 Introduction C-E's thermal margin methodology for $0N~S-2 has been modified by the application of statistical methods.

This report focuses on the s~atistical combination of reference thermal-hydraulic (T-H) code input uncertainties. Thi.s combination was accomplished by the generation of a Minimum DNBR (MBNBR) _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 section out-lines the previous detenninistic and the current statistical thennal mar-gin 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 results are presented.

Finally, Section 6.0 describes the changes in design analyses that result from this work, in particular, the resultant MONBR limit of 1 w31 which accommodates the T-H uncertainties described in this reportand includes penalties imposed by NRC in previous analyses.

CEN-283(S)-NP, Part 1 Revision 0 2-1 June 1984

Westinghouse Non-Proprietary Class 3 2.1 Detenninistic 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., lhese 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.

C-E thennal 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 MDr:BR predictions in a particular fuel assembly for a specific power distribution. Both system and state ~arameter input are used in a detailed TORC model.

The second model, th~ CETOP-0_ design model, requires oi:,ly st~te ~ara~ter data and may be applied to any fuel assembly for any power d1str1but1on that 1s~expected to occur*:during a particular fuel cycle. System pafameters are fixed in the design model so that the model wi11 yield either accurate or conservative MDrlBR predictions for all operating conditions within a specified range.

Design model MDrlBR 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 statisti-cally, are applied in a deterministic manner.

That is, althouch each adjustment factor represents a 95/95 probability/confidence limit that the particular parameter deviation from nominal is no worse than des-cribed 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 subchanne1.

2.2 Statistical Method The probability of all adverse system parameter deviations from nominal occurring simultaneously in the limiting subchannel is extremely re~ote.

With a more reasonable, demonstrably conservative method, the probability of system parameter input being more adverse than specified can be taken into account statistically, as described herein.

The improved methodology involves a statistical co~bination of system parameter uncertainties \\~ith the CHF correlation uncertainties to determine CEN-283(S)-NP, Part 1 Revision O 2-2 June 1984

Westinghouse Non-Proprietary Class 3 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 CETOP-D model is therefore used with the revised MDNBR limit for thennal 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 MONBR 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.

CEN-283(S)-NP, Part 1 Revision 0 2-3 June 1984

Westinghouse Non-Proprietary Class 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 mr 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 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 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 Generation of a response surface which simultaneously relates MONBR 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-sitivity of MDNBR to system parameter variations. That is, the response surface can be described as:

MDNBR = f (~~,l.0 )

where xis the vector of system parameters, and ti:, the vector of state paramet~rs, is selected such that a(MDNBR) ax

-+ maximum The set of state parameters, y_0, 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.

CEN-283(S)-NP, Part 1 Revision 0 3-1 June 1984

Westinghouse Non-Proprietary ~lass 3 3.1.1 Method for Selecting State Paramet~rs 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 perfonned for a sinale set of operating conditions.

In the first analysis, nominal system -

parameters are used 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., MONBR in-creases). The MDNBR from the 11adversely perturbed" al')alysis is then subtracted from the 11nominal 11 MDNBR to yield a ~DNBRlADVERSE) for the chosen set of operating conditions and the same is done for the TORC analysis where system parameters are "perturbed advantageously 11 That is, tiMDNBRADVERSE

= '"Nominal" MDNBR -"Adversely Perturbed" MDNBR (3.1) tiMDNBRADVANTAGE(lffl"Nomina 1 " -MDNBR - "Advantaaeously Perturbed"MDNBR (3. 2)

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

% ChangeADVERSE

=I {tiMDNBRADVERSE/Nominal" MDNBR) x 100 I (3.3)

% Change;o.DVANTAGEDUS =I (tiMDNBRADVANTAGIDUS/Nominal" MDNBR) x 100 (3. 4)

This process is repeated for several sets of operating conditions to establish the sensitivity of the MONBR throughout the allowable operating range~

Sets of operating conditions used in this sensitivity study are chosen to envelope the required ranges shown in Table 3-1.

The set of state parameter values which maximizesthe quantity(% ChangeADVERSE +

% ChangeADVANTAGEous> is chosen as the most sensitive set of state parameter values. This set is referred to as the set of 11most adverse" state parameter values and is used in detennining the response surface.

CEN-283(S)-NP, Part 1 Revision 0 3-2 June 1984

3.1.2 3.1.3 3.1.4 Westinghouse Non-Proprietary Class 3 Since MONBR is a smoothly varying function of these state parameters (3-2), it is likely that the theoretical set of most adverse state parameters will 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 b.Y 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 (3-1) consists of *two 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.

Also, each quadrant of.the limiting assembly is represented by a channel.

Crossflow boundary cond~t~o~s from the first stage are applied to the subchannel model of.the l1m1t1ng assembly hot quadrant in the second stage, and the MDNBR 1s calculated.

TORC models for the first, and second stages of the model used in the sensitivity study are shown in Fig. 3-5 and 3-6, respectively.

Axial Shape Sensitivity Detailed TORC analyses as described in Section 3.1.1 were performed to determine the most sensitive ASI to be used in the analysis.

Data from these calculations are listed in Table 3-2.

The most sensitive ASI was found to be the [

] ASI.

Pressure and Temperature Sensitivity Using the ASI determined in Section 3.1.2, detailed TORC analyses were perfonned 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 was determined that the most sensitive pressure and temperature are [

] respectively.

Primary System Flowrate Sensitivity Detailed TORC analyses as described in Section 3.1.1 were performed to determine the most sensitive flowrate to be used in this analysis. Data from these calculations are listed in Table 3-3.

The most sensitive flowrate was found to be[ ]of design flow.

(Design flow is equal to 396,000 gpm).

CEN-283(S)-NP, Part 1 Revision 0 3-3 June 1984

Westinghouse Non-Proprietary Class 3 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 5o tha~ __ the resultant MDNBR uncertainty wil 1 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 396,000 gpm.

3.2 Radial Power Distribution Inherent conservatism in the thennal margin modeling methodoloqv makes it un-necessary to account for uncertainties in the radial power distributions that are used in TORC DNB 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 flow factors 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 factors results from measurement uncertainty. This measurement uncertainty is considered random and may be characterized by a normal probability distribution function (p.d.f.).

Sensitivity studies (Ref. 3-10) have shown that MDNBR in the limiting assembly is unaffected by changes in the inlet flow of assemblies which are diagonally adjacent to the limiting 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.

Exit Pressure Distribution Sensitivity studies (Ref. 3-10) indicate that MDNBR is extremely insensitive to variations in the exit pressure distribution.

Consequently, exit pressure distribution need not be included in the MDNBR response surface.

CEN-283(S)-NP, Part 1 June 1984 Revision O 3-4

Westinghouse Non-Proprietary Class 3 3.5 Enthalpy Rise Factor 3.6 The engineering enthalpy rise factor accounts for the effects of manu-facturing deviations in fuel fabrication from nominal dimensions and specifications on the enthalpy rise in the subchannel adjacent to the rod with the MDNBR.

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-built data for 16x16 fuel v,ere used to generate an enthalpy rise factor distribution characterized by a mean of approximately[ J and a standard deviation at 95% confidence of[

J.

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 (O.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 nonna1 p!d.f. with a mean of[

]and standard deviation at 95% confidence of (

J.

3.7 Clad O.D.

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 O.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 0.0. on subchannel flow area is included in the rod bow penalty, discussed in Section 3.9. The effect of systematic varia-tions in clad 0.0. on the subchannel hydraulic parameters is addressed here.

Manufacturing tolerances on the fuel clad allow for the possibility that the clad diameter will be systematically above nominal throughout an entire fuel assembly.

That is to say, the mean as-built value of the clad 0.0. may differ from the nominal value. The distribution of the mean clad O.D. for fuel assemblies may be characterized by a nonnal p.d.f. with a mean equal to the mean clad 0.0. and a standard deviation given by the relationship (3-4):

(3.5) where N is the number of specimens in the parent population and n is the sample size.

CEN-283(S)-NP, Part 1 Revision 0 3-5 June 1984

Westinghouse Non-Proprietary Class 3 As-built data for SONGS-2 Cycle 1 fuel indicate that the maximum system-atic clad O.D. is [

] inches. Since the adverse effect of clad O.D. variations is already taken into account by the engineering heat flux factor, and use of a less than nominal clad 0.0. would increase subchannel flow area, benefitting the MDNBR, the maximum value [

1 is used in this study.

The mean at the 95% confidence level is

[

] inches and the standard deviations of the mean at the 95%

confidence level is [

] inches.

The double accounting for both the adverse effect of a decrease in clad 0.0. in the engineering factor on heat flux and the adverse effect of a systematic increase in clad O.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 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 16xl6 fuel are presented in Table 3-4.

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

[

J and is

[

] inches. This, combined with the maximum clad 0.0.

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 Tne 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 CE topical report (3-5). Appendix G of that report (3-5) applies a formula derived by the NRC to compute the rod bow penalty for CE fuel.

The penalty at 30,000 MWD/MTU for CE 1s 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 CE 1 Critical Heat Flux (CHF) correlation (3-7) (3-8) 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 CEN-283(S)-NP, Part 1 Revision 0 3-6 June 1984

Westinghouse Non-Proprietary Class 3 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 MDNBR limit to satisfy the criterion of 1195%

probability at the 95% confidence level that the limiting fuel pin does not experience DNB 11 However, because the _NRC staff has not yet conclud-ed its review of the CE-1 correlation, a 5% penalty has been applied as required by NRC; this raises the 95/95 MDNBR 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.

The NRC has stated in the past during their reviews of various C-E SCU program reports that the effect of so ca 11 ed II prediction uncerta i nty 11 in the CHF correlation must be included in the calculation of new MDNBR limit.

Inclusion of this uncertainty in t~e calculation has little effect on the MDNBR limit, (MDNBR increases from 1.132 to 1.137); howev-er, it has been incorporated into this analysis as discussed in Section 6.1 according to the guidelines provided by the NRC in Reference (3-6).

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.

Comparisons between TORC predictions and experimental data (3-1) (3-9) have shown that TORC is capable of adequate predictions of coolant conditions.

As explained in Section 5.0 of Reference {3-9), 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.

However1 NRC in their previous SCU reviews have consistently stated that uncertainties exist for all subchannel codes, and that consistent appli-cation of a code, such as in the case of DNB data analysis and DNB evaluation, does not nullify this uncertainty.

Based upon this argument, NRC has stated in the past that a 4% uncertainty (2cr value) must be imposed to cover code uncertainties, plus an additional 1% {2a value) for transient code uncertainties. According to the NRC guidelines (3-6), the 4% and 1% values are combined statistically with the standard deviation of the response surface to assess the effect of code uncertainties on the DNBR limit.

As indicated in Section 6.2, a TORC code uncertainty penalty factor on MDNBR calculated based upon the NRC guidelines (3-6) has been included in the present analysis.

CEN-283(S)-NP, Part 1 Revision 0 3-7 June 1984

Westinghouse Non-Proprietary Class 3 FLOW FACTOR = LOCAL INLET MASS VELOCITY CORE AVERAGE MASS VELOCITY NOTE:

CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMBLIES HAVE BEEN "LUMPED" INTO A SINGLE CHANNEL FOR T

H ANALYSIS Figure 3-1 INLET FLOW DISTRIBUTION USED TO GENEATE RESPONSE SURFACE (THREE PUMP OPERATION)

CEN-283(S)-NP, Part 1 Revision 0 3-8 June 1984

NOTE:

Westinghouse Non-Proprietary Class 3 CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMBLIES HAVE BEEN "LUMPED" INTO A SINGLE CHANNEL FORT - H ANALYSIS Figure 3-2 EXIT PRESSURE DISTRIBUTION USl;D TO GENERATE RESPONSE SURFACE CEN-283(S)-NP, Part 1 Revision O 3-9 June 1984

NOTE:

Westinghouse Non-Proprietary Class 3 CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMBLIES HAVE BEEN "LUMPED" INTO A SINGLE CHANNEL FOR T - H ANALYSIS Figure 3-3 CORE WIDE RADIAL POWER DISTRIBUTION USED TO GENERATE RESPONSE SURFACE CEN-283(S)-NP, Part 1 Revision 0 3-10 June 1984

Westinghouse Non-Proprietary Class 3 Figure 3-4 HOT ASSEMBLY RADIAL POWER DISTRIBUTION USED TO GENERATE RESPONSE SURFACE CEN-283(S)-NP, Part 1 Revision 0 3-11 June 1984

NOTE:

Westinghouse Non-Proprietary Class 3 CIRCLED CHANNEL NUMBER DENOTES A FLOW CHANNEL IN WHICH SEVERAL FUEL ASSEMBLIES HAVE BEEN "LUMPED" INTO A SINGLE CHANNEL FOR T - H ANAL VSIS Figure 3-5 CHANNEL NUMBERING SCHEME FOR STAGE 1 TORC ANALYSIS CEN-283(S)-NP, Part 1 Revision 0 3-12 June 1984

Westinghouse Non-Proprietary Class 3 Figure 3-6 SUBCHANNEL (2ND STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE CEN-283(S)-NP, Part 1 Revision 0 3-13 June 1984

Westinghouse Non-Proprietary Class 3 Operating Conditions Units Range Axial Shape Index

-0. 600 ~A. S. I. 2. 0. 600 Inlet Temperature OF System Pressure psia System Flow

% design+

NOTES

Axial shape index=

o l/2 f

Fzdz -

f F d

-L/2 o

z z L/2 f

Fzdz

-L/2 Fz = core average axial peaking factor at axial location Z 0

= core mid-plane L

= active core length

+ Thennal margin design flow= 396,000 gpm 490 ~

1785 70 TABLE 3-1:

RANGES OF OPERATING CONDITIONS FOR WHICH RESPONSE SURFACE IS VALID CEN-283(S)-NP, Part 1 Revision 0 3-14

\\n <

605 P~ys 2. 2415 w

~ 120 June 1984

Westinghouse Non-Proprietary Class 3 TABLE 3-2 Determination of Most Sensitive Axial Shape A. S. I.

Ternc. °F

+.601 553

+.601 605

+.601 520

+.601 490

+. 527 553

+.527 605

+.527 520

+.527 490

+.444 553

+.444 605

+.444 520

+.444 490

+.337 553

+.337 605

+.. 337 520

+.337 490

+.317 553

+.317 605

+.317 520

+.317 490 CEN-283(S)-NP, Part 1 Revision 0 Press ( osia)

% Flow

% L:iMDN~R

~

2250 80 1785 70 2000 70 2415 90 2250 80 1785 70 2000 70 2415 90 2250 80 1785 70 2000 70 2415 90 2250 80 1785 70 2000 70 2415 90 2250 80 1785 70 2000 70 2415 90 3-15

( 1)

June 1984

A. S. I.

Temo.

+.000 553

+.000 605

+.000 520

+.000 490

-.070 605

-.070 520

-.070 490

-.079 553

-.079 520

-.079 605

-.359 553

-.359 605

-. 359 520

-.359 490

-

527 553

-. 527 520

-. 527 490

-.604 553

-.604 605

-.604 520

-.604 490 (1)

See Section 3 CEN-283(S)-NP, Part 1 Revision O OF Westinghouse Non-Proprietary Class 3 Table 3-2 (cont.)

Press (osia}

% Flow 2250 80 1785 70 2000 70 2415 90 1785 70 2000 70 2415 90 2250 80 2000 70 2415 70 2250 80 1785 70 2000 70 2415 90 2250 80 2000 70 2415 90 2250 80 1785 70 2000 70 2415 90 3-16

% ~MDNBR fl)

June 1984

Westinghouse Non-Proprietary Class 3 TABLE 3-3

% ~MDNBR for System Parameter Perturbations at Various State Parameters Pressure 70% of 4 Pump Flow 90% of 4 Pump Flow (psi a) 1785 I

1900 2000 2100 2250 2415 Temp (0 F) 490 520 Axial shape index= +0.337 100% Des~gn Flow= 396,000 gpm CEN-283(S)-NP, Part 1 Revision 0 553

-I I i

i I

I i

605 490 520 553 3-17 605 June 1984

Span Number

~

10 6

2 CEN-283(S)-NP, Part 1 Revision 0 AKA050 I

Westinghouse Non-Proprietary Class 3 AKA051 I

Assembly Identification AKBTOl AKBT02 AKC107 I

I Mean

~ xxxx(xxx)

+

number of measurements xxxx

+

standard deviation of mean TABLE 3 AS-BUILT GAP WIDTH DATA {inches) 3-18 AKC201 I

June 1984

Westinghouse Non-Proprietary Class 3 4.0 MDNBR Response Surface A response surface is a functional relationship which involves several independent vartab1es and one dependent variable. The surface is created by fitting the constants of an assumed functional relationship to data obtained from 11experiments".

The response surface provides a convenient means by which accurate estimates of a com~lex 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 detai.led TORC 11experi-ments11 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 HDNBR p.d.f.*

4.1 TORC Model Used The inlet flow distribution (shown in Fig. 3-1) is compared with radial power distributions to detennine the limiting location for DNB 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 comprises channels [

J of this model.

The second stage model used in this analysis is shown 1n Figure 3-6.

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 thennal margin model-1 ing methodology factnrs makes it unnecessary to account for un~ertaint.Y in the radial power distribution used in DNB analyses.

Hence, the radial power distribution was omitted from the response surface.

CEN-283(S)-NP, Part 1 Revision O 4-1 June 1984

Westinghouse Non-Proprietary Class 3 The sensitivity study discussed in Section 3.4 indicates that large pertur:-

bations in the exit pressure distribution have negligible effect on the pre-d1cted.MONBR.

Thus, the exit pressure distribution is not included in the response surface.

The heat flux factor {Fq.. ) is applied to the MDNBR calculated by TORC in the following manner:

.MDHBRroRc.

MDNBR =

(4.1)

Since the functional relationship between MONBR and Fq 11 is known, the heat flux factor is not used in generating the response 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 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 desian limit MDNBR as discussed in Section 6.2.

The calculational uncertainty associated with MOUBR predictions using the TORC/CE-1 package is implicitly included in the CHF distribution uncert-ainty, as exp 1 a i ned in S.ections 3. l O and 3. ll. Hence no exp 1 ici t a 11 o~ance for code uncertainty is included in the response surface.

However, as discussed in Section 3.11, the NRC in previous reviews has consistently imposed a penalty factor in MDNBR to account for this TORC code prediction uncertainty.

In the present analysis, a 5% TORC code uncertainty has been combined with other sys tern pa rarreter un certain ti es using the SIGMA code.

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

4.3 Experiment Oesiqn An orthogonal central composite experimental design {4-2) is used to gen-erate the response surface applied in this study.

The total number of exper-iments needed to_generate a response surface using this experiment design is 2k + 2k + 1 where k is the number of variab1es to be considered.

The desired response surface consists of seven variables, hence 143 11experiments 11 or detailed 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 1 = (n' 11r1 ln~}r (4.2)

CEN-283(S)-NP, Part 1 Revision O 4-2 June 1984

Westinghouse Non-Proprietary Class 3 where z is the vector of experimental results, to y;eld the coefficients which define the response surface 7

7 2

7 7

= b + t

b. 11. + J:

b.. ( n. -c) + t b n a, (4 3) 0 i=l 1 1 1*1 11 1

1=1 tj=l ij i j 1<j In the above e~uations, then. are coded values of the system parameters (x.)

to be treated 1n the respoo.se 1surface, as indicated in Table 4-1 The b. rep-resent the constants found from the TORC results by means of Eq:4.2. and c is a constant determined rrom 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. b.u"i"j) were neglected. However~ such interaction effects are included in tne 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 eighth columns of then matrix cited in Eq. (4.2). Both coded and uncoded versions of the desian matrix used in this study are presented in Appendix A along with resultant MDMBR values.

The design matrix was con-structed such that each independent variable inc1uded 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 Eq. (4.3) are oresented in Table 4-2.

Comparisons made bet\\1een TORC predicted MONGR and response surface predictions show excellent agreement.

The 95: confidence estimate of the response surface standard deviation is 0"001$5.

The heat flux factor is included analytically in the response surface by combining Eq. (4.l) with Eq.(4.3).

The final relationship is given by MOtlBR

_ 1

{

7 7

2 7 7

~

- tqn bo** + I:.

b,. "'1*+ t

b.,(ri* -c)+ l: r b,.J* 'l,*nJ*

(4-4) 1=1 i=l l

i=l j=l CEN-283(S)-NP, Part 1 Revision 0 4-3 f <j June 1984

Westinghouse Non-Proprietary Class 3 The coefficient of detennination, 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.9999, which 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 0.001639 The relative error is 0.14%_, indicating that this model performs well.

CEN-283(S)-NP, Part 1 Revision 0 4-4 June 1984

Westinghouse Non-Proprietary Class 3 System Parameter Variable Index Coded Values**

( i) 1 t1; hot assembly inlet fljw factor

( ch an ne 1 s [ _

}

Xl 1

channels [

]inlet flow factors X2 2

channel [

] inlet flow factor X3 3

channel [

] inlet flow factor X4 4

enthalpy rise factor XS 5

systematic pitch (inches)

X6 6

systematic clad O.D. (inches)

X7 7

Channel numbers refer to Figure 3-5

- Variables coded according to relation"l i = Xi

- cl i where theOl i 15*

are chosen such that "2 i = O at nomi na 1 conditions ~nd the /3 i are chosen such that the range of the response surface will include

"'2 0- ranges of each of the system parameters.

TABLE 4-1:

SYSTEM PARAMETERS INCLUDED AS VARIABLES IN THE RESPONSE SURFACE CEN-283(S)-NP, Part 1 Revision 0 4-5 June 1984

Westinghouse Non-Proprietary Class 3

.. *- *-- *** *---- ~*- *** -

MDNBRRs

= b 0 ""f bi 11.i +f b;; l'1.,:i.- c)., f z b ~ rpr,

- .2.

i*~

i=~ :r~

J TABLE 4-2:

COEFFICIENTS FOR MONBR RESPONSE SURFACE i,j CEN-283(S)-NP, Part 1 Revision 0 4-6 June 1984

Westinghouse Non-Proprieta.ry Class 3 5.0 Combination of Probability Distribution Functitins The MDNBR 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 uncer-tainty. 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 MGAte Carlo and stratified sampling techniques to combine arbitrary p. d. f. 's numeri ca 1 ly (S-1). This code is used with the response surface to combine system parameter p.d.f.

1s with the CE-1 CHF correlation p.d.f. into a resultant MONBR 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 AMDNBR caused by deviation of the system.parameters from nominal:

ti.MDNBR

= MONBRR.* S. _ MONBRNOM (5.1) where MDNBRg 5 is the MCNBR found by substituting the set of system parameters into the response surface and MDNBR~'OM is the MONBR value predicted by the response surface with nominal 'system parameters. A point is then randomly chosen from the CHF correlation p.d.f. and combined with the AMDNBR f~om Eq. (5.1) to yield a MONBR value:

MDNBR = MDNBRCHF + tiMONBR (5.2)

This process is repeated by the SIGMA code for 2000 randomly selected sets of system parameters and random1y selected points from the CHF correlation p.d.f.; *~nd a resultant MDNBR p.d.f. is.generated.

The system parameter p.d.f.

1s input to SIGMA are listed in Table 5-1.

Both "best estimate 11 and 95~ confidence estimates of the standard deviation are included. Standard deviations at the 95% confidence level are input to SI~1A to ensure that the standard deviation of the resultant MDNBR p.d.f. is at least at the 95% confidence limit.

CEN-283(S)-NP, Part 1 Revision O 5-1 June 1984

Westinghouse Non-Proprietary Class 3 5.2 Results The resultant MDNBR p.d. f. is shown in Fig. 5-1.

The mean and standard deviation of this p.d. f. are 1.00572 and.123559,. respectively.

As Fig.

5-1 indicates, the resultant MDNBR p.d.f. approximates a normal distri-bution.

5.3 Analytical Comparison An approximate value of the standard deviation of the resultant MONBR p.d.f.

may be found by analytic methods.

These methods are based upon the assumption that the uncertainties are small deviations from the mean (5-2). Given a functional relationship (5.3) the effects of small perturbations in x on y may be found from 4.Y-dy... a.! ~x1 + 3 f Ax2 + * * * + !! ~x (5.4)

~x1 ax2 axn n

Hence. ff several normal distributions are combined by the relationship expressed in Eq.(5.3), th~ variance of the resultant p.d.f. is 012 2 ( a f ) 2 a 2 +( !.f ) 2 a 2 +. * * + ( !f ) 2 a 2

(

5 5

)

ax1 x1 a-x2 x2 axn xn where the partial derivatives are evaluated at *the mean values of the ~1*s.

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

MDNBRRS where ft =-

i (5.7)

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

. 2 1l' R S CEN-283(S)-NP, Part 1 Revision 0

( a ( MONS R ) a ri; ) 2 a 2 xi ofl i ax1 (5.8) 5-2 June 1984

Westinghouse Non-Proprietary Class 3 Differentiating Eq. (5.6) and (5.7) with respect to ~1and x1:

(5.9)

(5.10)

,<3. '

Substituting Eq.{5.9) and (5.10) into Eq.(5.8) results in a relation be-tween the resultant MONBR variance and the system parameter variances:

This equation is a~ -

R.S.

(5. 11) simplified when evaluated at the mean values of the n1:

7 2

ax2 (5.12)

= t bf i

i=l

~i 2

( i. e

11 ; =o )

The CHF correlation p.d.f. and system parameter p.d.f.'s are related to the resultant MDNBR 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

a. MDNBR 2

1,1MDNBR where ut s.: O 2

2

= ~~.S. + ~CHF +

2 (iiR.S.. + iicHF)

(5.13)

Substitutinq values from Tables 4-1. 4-2, 5-1, and Section 4.5 into Eq. (5.11)

.and Eq (5.13) yields c, MDNBR = 0.12181 which is in exce 11 ent agreement with the va 1 ue predicted by the SIGMA code simulation using the response surface.

CEN-283(S)-NP, Part 1 Revision 0 5-3 June 1984

0.10 0.08 Westinghouse Non-Proprietary Class 3 FREQUENCY = - - ~....

n = NUMBER OF POINTS IN INTERVAL

( DNBR - \\~DNBR, DNBR + ~~DNBR)

TRUE GAUSSIAN Q

ACTUAL DISTRIBUTION OBTAIN.ED FROM MONTE CARLO CODE 'AND RESPONSE SURFACE 0

0 0

/60 ',

t;

0. 06

/

0' 0 0

\\

z Lu CY w

0:::

LL..

0.04 0.02 I

90 Q/

Q,,7 I

\\

I

\\()

910

\\

I I

QI(!)

I I

\\

\\ o,

\\ a

\\

\\ oQ

'Q

_a" ooo

0. 00 I Q C)-OOQ::O !3

,--o.o-~.Q) 0.8 0.9 1.0 1.1 1.2 1.3 CEN-283(S)-NP, Part 1 Revision 0 DNBR Figure 5-1 RESULTANT MDNBR PROBABILITY DISTRIBUTION FUNCTION 5-4 June 1984

Westinghouse Non-Proprietary Class 3 DISTRIBUTION hot assembly inlet flow factor (channels

[

])

channel [

] inlet flow factor channel [

J inlet flow factor enthalpy rise factor systematic pitch {inches) system clad 0.0. (inches) heat flux factor CE-1 CHF Correlation TORC Code Uncertainty

channel numbers refer to Figure 3-5 MEAN

.99983 1.00 STANDARD DEVIATION AT 95% CONFIDENCE

.07065(l)

.03275( 2)

TABLE 5-1:

PROBABILITY DISTRIBUTION FUNCTIONS COMBINED BY SIGMA (1) An additional 5% penalty has been applied to the CHF standard deviation to account for 11prediction uncertainty" cited in NRC reviews of' previous analyses.

(2) TORC code uncertainty is applied in response to penalties imposed in NRC reviews of previous analyses.

CEN-283(S)-NP, Part 1 Revision 0 5-5 June 1984

Westinghouse Non-Proprietary Class 3 6.0 Application to Design Analysis This section discusses the application of the statistically derived MDNBR p.d.f to design analyses. Deterministic methodology (6-1) involves use of a design model for TORC analysis which includes deterministic allow-ances for system parameter uncertainties. These deterministic penalties are replaced with a higher MDNBR limit in the statistical methodology.

This higher MDNBR limit is used with a "best estimate 11 design model in thermal margin analyses.

6.1 Statistically Derived MDNBR Limit The MONBR p.d.f. described in Section 5.0 is a normal distribution having a mean of 1.00572 and a standard deviation of 0.123559.

This standard deviation is at least at the 95% confidence level. A comparison of TORC results and response surface predictions indicates that the la error associated with the response surface is cr5=0.001639; at the 95% confi-dence level, this value is cr595 =(.OOl639 x l07/84.125) =.001848.

The MONBR standard deviation was found to be 0.123559 by means of Monte 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 MONBR standard deviation, adjusted for the finite sample size used is (0.123559 x ~1999/1896.131) = 0.126866.

The root sum square of the adjusted MDNBR standard deviation and the response surface standard deviation at the 95% confidence level is cr tot = J ( 0.126866 )z + 0. 001848 f = 0. 126880 confidence estimate of the mean is The corresponding 95%

(l.00572 + (1.645 X.123559)/ J2000) = 1.010265.

Since the resultant MDNBR p.d.f. is a normal distribution, as shown in Figure 5-1, the one-sided 95% probability limit is 1.645cr.

Hence there is a 95% probability with at least 95% confidence that the limiting fuel pin will experience DNB if the best estimate design model TORC calcu-lation yields a MDNBR value greater than or equal to (1.010265 + 1.645 x 0.126880) = 1.219.

6.2 Adjustments to Statistically Derived MDNBR Limit The statistical MDNBR 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 16xl6 fuel, this penalty is 1.75% 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 (1.0175 x 1.219) or

1. 240.

CEN-283(S)-NP, Part 1 Revision 0 6-1 June 1984

Westinghouse Non-Proprietary Class 3 The NRC has not yet completed review of the application of the CE-1 CHF correlation (6-3) to non-uniform axial heat flux shape data (6-4).

Consequently, 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 1 s non-unifonn 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 1.300. After including a 0.01 ONBR penalty due to the HID-I grid design the MDNBR limit was determined to be 1.310 (6-5).

Thus, the new MDNBR limit which contains allowance for uncertainty in the CHF correlation and system parameters as well as a rod bow penalty and the interim 5% penalty on the CE-1 correlation imposed by the NRC is 1.31.

' 6.3 Application to TORC Design Model 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 CETOP-D model used with the new MDNBR limit of 1.31 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 CETOP-0 model will yield accurate or conservative MDNBR predictions when compared with MONBR values from detailed TORC analysis (6-1).

CEN-283(S)-NP, Part 1 Revision 0 6-2 June 1984

Westinghouse Non-Proprietary Class 3 7.0 Conclusions Use of a 1.31 MDNBR limit with a best-estimate design CETOP-0 model for the SONGS-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 1.31 MDNBR limit includes explicit allowances for system parameter uncertainties, CHF correlation uncertainty, rod bow, the NRC penalties for the TORC code uncertainty, CE-1 CHF correlation 11 prediction uncerta i nty 11

, and the 5% interim pena 1 ty imposed by the NRC on the CE-1 CHF correlation, as well as a 0.1 penalty for the HID grids.

7.1 Conservatisms in the Methodology Several conservatisms are included in the present application.

The significant conservatisms include:

i) combination of system parameter p.d.f.'s at the 95% confidence level to yield a resultant MDNBR at a 95% + confidence level ii) use of pessimistic system parameter p.d.f.'s iii) derivation of the new MDNBR limit such that it applies to both 4-pump and 3-pump operation iv) use of the single most adverse set of state parameters to generate the response surface v) application of the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation vi) application of additional NRC CHF correlation uncertainty penalty ("prediction uncertainty")

vii) application of NCR imposed code uncertainty penalty viii) application of the 0.01 HID grid penalty imposed by NRC on the CE-1 CHF correlation CEN-283(S)-NP, Part 1 Revision 0 7-1 June 1984

Westinghouse Non-Proprietary Class 3 8.0 References 8.1 Section 1.0 References (1-1) 11Statistical Combination of Uncertainties 11, CEN-124(8)-P, Part 1, December 1979, Part 2, January 1980, Part 3, March 1980.

(1-2) 11Statistical Combination of Uncertainties", CEN-123(F)-P, Part 1, December 1979, Part 2, January 1980, Part 3, February 1980.

( 1-3) 11Stati stica l Combination of Uncertainties '1, CEN-139(A)-P, November 1980.

(1-4)

"Statistical Combination of Uncertainties 11

, enclosure 1-P to LD-82-054.

(1-5)

"Statistical Combination of Uncertainties", CEN-257(0)-P, Part 2, November 1983.

(1-6) Safety Evaluation by the Office of Nuclear Reactor Regulation Supporting Amendment No. 24 to Facility Operating License No. NPF-6, Arkansas Power and Light Company, Arkansas Nuclear One, Unit No. 2, Docket No. 50-368.

8.2 Section 2.0 References (2-1) "TORC Code:

Verification and Simplified Modeling Models,"

CENPD-206-P, January 1977.

(2-2)

"TORC Code:

A Computer Code for Determining the Thermal Margin of a Reactor Core, 11 CENP0-161-P, July 1975.

( 2-3) 11C-E Crit ica 1 Heat Flux:

Critical Heat Flux Corre 1 at ion for C-E Fuel Assemblies with Standard Grids, Part 1:

Uniform Axial Power Dis-tribution," CENPD-162-P, September 1976.

8.3 Section 3.0 References (3-1) "TORC Code:

A Computer Code for Determining the Thermal Margin of a Reactor Core 11

, 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.

CEN-283(S)-NP, Part 1 Revision 0 8-1 June 1984

Westinghouse Non-Proprietary Class 3 (3-5) 11 Fuel and Poison Rod Bowing 11

, CENPD-225-P-A, June 1983.

(3-6) Telecon from Galen Hesson (Battelle); NRC Reviewer of Statistical Combination of Uncertainties Methodology for System 80 Reactors to Tom Bracke (Combustion Engr.), August 3, 1983.

(3-7) 11C-E Critical Heat Flux:

Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 1:

Uniform Axial Power Di stri but ion-," CENPD-162-P, September 1976.

(3-8) 11C-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.

(3-9) 11TORC Code:

Verification and Simplified Modeling Methods 11,

CENPD-206-P, January 1977.

(3-10) CEN-124(B)-P Part 2, "Statistical Combination of Uncertainties*i, January, 1980.

8.4 References for Section 4 (4-1) 11 Fuel and Poison Rod Bowing, CENPD-P-A, June, 1983.

( 4-2) R. H. Myers, Response Surf ace Methodo 1 ogy, 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.

8.5 References for Section 5 (5-1) F. J. Berte, 11The Application of Monte Carlo and Bayesian Probability Techniques to Flow Prediction and Determination, 11 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.

8.6 References for Section 6 (6-1) 11TORC Code: Verification and Simplified Modeling Methods, 11 CENPD-206-P, January 1977.

(6-2) 11Fuel and Poison Rod Bowing, CENP0-225-P-A, June, 1983.

(6-3) 11C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution, 11 CENPD-162-P, September 1976.

CEN-283(S)-NP, Part 1 Revision 0 8-2 June 1984

Westinghouse Non-Proprietary Class 3 (6-4) 11C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 2: Nonuniform Axial Power Distribution, 11 CENPD-207-P, June 1976.

(6-5) Safety Evaluation by the Office of Nuclear Reactor Reuulation Re*, ated to the Operation of San Onofre Unit 2 and 3, supplement 4, OOcket No. L0-361 and 50-362.

CEN-283(S)-NP, Part 1 Revision 0 8-3 June 1984

Westinghouse Non-Proprietary Class 3 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 (RS) used in this study. All first order f nteraction effects ( f.e. XiXj *terms) were retained in the R S.

The R S used 1n this study included seven variables. The coded set of detailed TORC analyses performed to generate the RS is presented in Table A-1; variables were coded as shown in Table 4-1.

The actual valu*es of the input parameters are presented in Table A-2 along with the resultant MONBR values.

References (A-1) R.H. Myers, Response Surface Methodology, Allyn & Bacon, Inc., Boston, 1971, p. 133.

CEN-283(S)-NP, Part 1 Revision 0 A-1 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Entha l PY Systematic Systematic Number Chs [

].

Chs [

J Channel [ J Channel [

]

Rise Factor Pitch Clad 0.0.

1

-1

.. 1

-1

-1 2

-l

-1

-1 1

3

-1

-1 1

-1 4

-1

-1 1

1 5

-1

-1 1

-1

-1 6

-1

-1 l

-1 1

7

-1

-1 1

1

-1 8

-1

-1 1

1 1

9

-1

-1 1

-1

.:.1

-1 10

-1

-1 1

-1

-1 1

11

-1

-1 1

-1 12

-1

-1 l

-1 1

l 13

-1

-1 1

l

-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 CEN-283(S)-NP, Part 1 Revision 0 A-2 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

l Chs[ J Channel [ J Channel [ J Rise Factor Pitch Clad 0.0

14

... 1

-1

l l

l

-1 l

15

-1

-1 1

l l

-1 16

-1

,..1

-1 1

l 1

1 17

-1

-1 1

-1

-1 18

-1

-1 l

-1

-1 1

19

-1

-1 l

-1

-1 1

-1 20

-1

-1 1

-1

-1 l

l 21

-1

-1 1

-1

-1 22

-1

-1 1

... 1 1

23

-1

-1 1

1

-1 24

-1

-1 1

1 l

25

-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)

CEN-283(S)-NP, Part 1 Revision 0 A-3 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

_J~

Chs[ J Channel

[ J Channel [

J Rise Factor Pitch Clad 0.D.

27

-1

.-1 1

l

-1 1

-1 28

-1

-1 1

1

-1 l

1 29

,..1

-1 1

l 1

-1

-1 30

-1

-1 1

l 1

-1 l

31

-1

-1 1

1 1

l

-1 32

-1

-1 1

l l

l 1

33

-1 1

-1

-1 34

,..1 1

-1

-1 l

35

-1 l

-1

-1 1

-1 36

-1 1

-1

-1 1

l 37

-1 1

.. 1

-1 l

-1

-1 38

-1 l

-1

-1 l

39

... 1 1

-1

-1 l

1

-1

channel numbers refer to Fig. 3-5 See Table4-l 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)

CEN-283(S)-NP, Part 1 Revision 0 A-4 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

1* Chs [

]

Channel [] Channel l J Rise Factor Pitch Clad 0.0.

40

-1 l

-1

-1 l

l l

41

-1 l

... 1 1

-1

-1 42

-1 1

-1 l

-1

-1 1

43

-1 1

-1 l

-1 1

-1 44

-1 1

-1 l

-1 1

1 45

-1 1

1

-1

-1 46

-1 1

1

-1 1

47

-1 1

1 1

-1 48

-1 l

-1 1

1 1

l 49

-1 l

1

-1

-1 50

-1 1

1

-1

-1 1

51

-1 1

l

-1

-1 l

-1 52

-1 1

1

-1

-1 l

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)

CEN-283(S)-NP, Part 1 Revision 0 A-5 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

.. ] _

Chs [

J. Channel [ J Channel [ J Rise Factor Pitch Clad O.D.

53

--1 l

l

-1 l

-1

... 1 54

-1 1

1

... 1 l

-1 1

55

-1 1

1

... 1 1

l

-1 56

-1 1

1 1

57

""l 1

1 1

-1

-1 58

-1 l

1 1

-1

~1 1

59

-1 l

1 1

-1 1

-1 60

-1 1

l 1

-1 1

1 61

-1 l

l 1

l

-1 62

-1 1

l 1

1

-1 1

63

-1 1

l 1

1 l

--1 64

-1 l

1 1

l 65 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)

CEN-283(S)-NP, Part 1 Revision 0 A-6 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

'] ~

Chs [

J Channel [ J Channel [ J Rise Factor Pitch Clad O.D.

66 l

-1

-1 1

67 l

-1

.... 1

-1 1

.. 1 68 1

-1

-1 1

1 69 1

-1

-1 l

.. 1 70 1

-1

-1 1

-1 l

71 l

-1

-1 1

l

-1 72 1

-1

-1 1

1 l

73 1

-1

-1 l

.. 1

-1 74 1

-1

-1 1

-1

-1 1

75 l

-1 1

-1 76 l

-1

-1 1

-1 l

1 77 1

-1

-1 1

l

-1

-1 78 1

-1

-1 l

l l

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 Id)

CEN-283(S)-NP, Part 1 Revision 0 A-7 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

l Chs [

1 Channel

( J Channel [ J Rise Factor Pitch Clad O.D.

79 1

-1

-1 1

1 l

-1 80 l

-1

-1 l

l 1

l 81 1

-1 1

. -1

-1

-1 82 l

-1 1

-1

-1 1

83 1

-1 1

-1

-1 l

-1 84 1

-1 1

-1

-1 1

1 85 l

-1 1

-1

-1 86 l

-1 l

-1 1

-1 l

87 1

-1 1

-1 l

l

-1 88 l

-1 1

l l

89 l

-1 1

1

-1

-1 90 1

-1 l

1

-1

-1 l

91 1

-1 l

l

-1 l

-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).

Tab l__g__~-J_:

Coded Set of Detailed TORC Cases Used to Generate Response Surface

( cont I d)

CEN-283(S)-NP, Part 1 Revision 0 A-8 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs-[

]

Chs [ 1 - Channel [ J Channel L ] Rise Factor Pitch Clad 0.0.

92 1

-1 1

1

-1 1

l 93 1

-1 1

l l

-1

-1 94 l

-1 l

1 1

-1 l

95 1

.. 1 l

l.

l 1

-1 96 1

-1 1

l l

1 1

97 1

1

-1

-1 98 l

l

-1

-1 l

99 l

1

-1

-1 1

-1 100 1

l

-1

-1 1

l 101 1

1

-1

-1 1

-1

-1 102 1

l

-1

1 l

-1 l

103 1

l

-1

-1 l

1

-1 104 1

l

-1

-l 1

l 1

channel number~ 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 1 d)

CEN-283(S)-NP, Part 1 Revision 0 A-9 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Entha l PY Systematic Systematic Number Chs [

.. ]-

Chs[ J _ Channel [ ] Channel c_* J Rise Factor Pitch Clad 0.0.

105 1

1

-1 l

-1

-1 106 1

1

-1 1

-1

.. 1 1

107 1

l

-1 1

-1 108 1

1 1

-1 l

1 109 1

l

-1 1

1

-1

-1 110 1

1

-1 1

l

-1 1

111 1

l

-1 1

1 l

-1 112 1

l

-1 l

1 l

l 113 1

1 1

-1

-1 114 l

1 1

-1

-1 l.

115 l

1 1

-1

-1 1

-1 116 1

1 l

-1

-1 1

1 117 1

1 1

-1 l

-1

channel numbers refer to Fig. 3-5 See Table 4-1 for coded relationships NOTE:

Coded va 1 ues determined by methods described in Reference (A-1).

Table A-1:

Coded Set of Detailed TORC Cases Used to Generate Response Surface (cont1d)

CEN-283(S)-NP, Part 1 Revision 0 A-10 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic ~ystematic Number Chs [

Jr Chs[

]

Channe 1 [* ] Channe 1 [ J Rise Factor Pitch Clad O.D.

~

118 1

1 1

... 1 1

-1 1

119 l

1 1

-1 1

1 120 1

1 1

... 1 1

l 1

121 l

l 1

1

... 1

.. 1 122 1

l l

1

-1

-1 1

123 l

1 l

1

~l 1

-1

-124 1

1 1

1 10'1 1

1 125 1

l 1

-1

-1 126 l

l 1

1 1

1 127 l

1 1

l

-1 128 l

1 1

129 0

0 0

130

l. 91 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).

Jab l ~A:1:

Coded Set of Oeta il ed TORC Cases Used to Generate Response Surface (cont'd)

CEN-283(S)-NP, Part 1 Revision 0 A-11 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factors Enthalpy Systematic Systematic Number Chs [

J1 Chs (

J Channe 1 [ J Channel [ J Rise Factor Pitch Clad 0.0.

131

-1. 91 0

0 0

0 l 32 0

1. 91 0

0 0

\\

133 0

~ 1. 91 0

0 0

134 0

0

1. 91 0

0 0

0 135 0

0

.. 1, 91 0

0 0

0 136 0

O 0

1. 91 0

0 0

137 0

0 0

... 1.91 0

0 0

138 0

0 0

0 1.91 0

0 139 0

0 0

0

-1. 91 0

0 140 0

0 0

l. 91 0

141 0

0 0

-1.91 0

142 0

0 0

0 1.91 143 0

0 0

0

-1.91

channel numbers refer to Fig. 3-5 See Table 4-1 for coded rel at ions hips 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 CEN-283(S)-NP, Part 1 Revision 0 A-12 June 1984

Case Number JCh[

I~

l 2

3 4

5 6

7 8

9 10 11 l2 13 14 15 Westinghouse Non-Proprietary Class 3 Inlet Flow Factor

______ __ i I

Enthalpy Systematic Systematic

] I Channels [

JTct,annel [

]rhanne1_c __ tise Factor Pitch**

Clad 0.0.**

Detailed TORC MDNBR

Response

TORC MONBR Residual

.ODO

-.001

.000

-.002

.000

-.001

.001

.000

.001

~I I

_J_. ____,_}, ______ j J_~_T

___ L_ I

--4---~ ____.

Chann~l Numoers Refer to fig. 3-5

- ,..\\

system parameters d1mens10n,ess except syste~

and clad 0.0.

{inches)

TABLE A-2 Comparison of TORC and Response Surface MONBR for Cases Used to Generate Response Surface CEN-283(S)-NP, Part 1 Revision 0 A-13 June 1984

Case Number Ch [

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

~

Channe CEN-283(S)-NP, Part 1 Revision 0 Westinghouse Non-Proprietary Class 3 Inlet Flow Factor Enthalpy Systematic Systematic

] Channels f

Tchanne1 c ) I Channel [

]

Rise Factor Pitch**

Clad O.D.**

I L _________ J ____ ___ - --.-.... 1 l _ _ -----.-r-L.

. ~

9 p

and clad 0.D.

(inches)

Detailed Res pons e TORC TORC MDNBR MONBR

_L__ - --L--,.-----,---.... -

pt sy p

Residual

.000

-.002

.000

-.001

.000

.002

.000

.001

.003

.001 TABLE A-2 Comparison of TORC and Response Surface MONBR for Cases Used to Generate Response Surface

( continued)

A-14 June 1984

Westinghouse Non-Proprietary Class 3 I

~ -----,-

Case Number !Ch(

31 Inlet Flow Factor JI Channel_s_r--11 Chiinne1 [

l t*-ch~-nne1*j * ] R~nthaFlpy Sy~tematicj Systematic Deta1lel Response 1se actor P1tch**

Clad O.D.**

TORC TORC

~~

MDNBR MDNBR

- ~----*--*

32 I

33 I

34 35 36 37 38 I

39 I

40 41 42 43 44 45 I

~ -*

[ __ _

to Fig.""3:S--

L

**A~l system pa1rameters dinfensTcinless ex"tefrt systemftic pitch TABLE A-2 (continued) and clad 0.0.

(inches)

Comparison of TORC and Response Surface MDNBR for Cases Used to Generate Response Surface Residual

.001

.002

.000

.001

.002

.000

-.001

.001

.000

.001

.000

-.001 CEN-283(S)-NP, Part 1 Revision 0 A-15 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factor Enthalpy Systematic Systematic Deta1 led

Response

Number -- *ch [

J Channels r

--* ]- Channel [

] ~Channel [

]

Rise Factor Pitch**

Clad 0.0.**

TORC TORC Residual MDNBR MDNBR p

- - ~~----

46 i

-.001 47

.000 48 I

-.002 49 I

.001 50

.001 51

.002 52

.001 53

.002

)

54 I

.002 I

55

.001 56

.001 57

.000 58

.000 59

.000 60 i

-.001 I

~ ~ I. --.--...----J

--- _L ____ -* _ J ________ l 1,_r *~~Ln ~.l.. _______ L-.---,-*

T"""..:_ >--'

I g

p and clad 0. D.

( 1nches)

TABLE A-2 Comparison of TORC and Response Surface MONBR for Cases Used to Generate Response Surface (continued}

CEN-283(S)-NP, Part 1 Revision 0 IH6 June 1984

Westinghouse Non-Proprietary Class 3 Case I Inlet fl ow facto~--- -*--*--**-*-*

. *i En tha 1 py I Systemat k I Systematic Number

~h [

] I Channe 1 s f

] rhanne 1 [

] I Chan~e 1 [

]

Rise Factor Pitch**

Clad O. O. o 61 62 63 64 65 66 67 68 69 70 ti 72 73 74 75 Deta1 led TORC MONBR

Response

TORC MDNBR Residual

--~f 1 *-** -

-.001

-.002

.002

.001

.000

-.001

.000

-.001

.000

-.001

~

I J..

J I

_J_ ___ ~

I_

J_ ____ _ j _. :1..--=-~

A

~ F

- -- -.-.i,Tsysfem paramete~ns ionl ess except systemat1c p1tcn and clad 0.D.

(inches)

TABLE A-2 Comparison of TORC and Response Surface MDNBR for Cases Used to Generate Response Surface

{continued)

CEN-283(S)-NP, Part 1 Revision 0 A-17 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow Factor Enthalpy Systematic Systematic Detailed Number Ch[

J Channels f

] Channel [

]

Rise Factor Pitch**

Clad 0. D. **

TORC MDNBR 76 77 I

78 79 I

80 Bl I

82 83 i'

84 85 86 87 88 89 90

_L ____ J 1 ____ 1 LJ l

9 p

and clad 0.0.

(inches)

TABLE A-2 (continued)

Comparison of TORC and Response Surface MDNBR for Cases Used to Generate Response S~rface CEN-283(S)-NP, Part 1 Revision 0 A-18 Respon se TORC MDNB R tcil-Residual

-.001

-.000

-.002

-.001

.000

.002

.000

.002

.001

.000

-.001

.001

.000

.001

-.001 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet Flow factor Detailed Enthalpy Systematic Systematic Number Ch[

] Channels f ] I Chdl1ne 1 [ ]J Channel [

]

Rise Factor Pitch**

Clad 0.D.**

TORC 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

.._ i I

Channel Numbers Refer t<

TABLE A-2

{continued)

CEN-283(S)-NP, Part 1 Revision 0 MDNBR L----- --*- -.. I

...J. -- _ ___

4------------

9 pt sy ystem p and clad 0. D.

( inches)

Comparison of TORC and Response Surface MONBR for Cases Used to Generate Response Surface A-19 Respon se TORC MDNB R P1t~

Residual

-.UU2

.000

-.001

-.002

-.001

.000

-.001

.002

-.002

.000 June 1984

Case Number Ch[

106

\\

107 i

108 I

109 110 I

111 I

112 I

i 113 I

114 115 116 117 118 119 120

-~- ---

Westinghouse Non-Proprietary Class 3 Inlet Flow Factor Enthalpy

]

Channe 1 s r__

] I Channe 1-+"*

1 [

) Rise Factor I

Systematic Systematic Pitch**

Clad 0.0.**

Deta1 ted TORC MDNBR

Response

TORC MONBR

-~---

Channe*1 Number*s -Refer* to Flg. l-5

- A~l system parameters dimens ionTess except systemafic pitcn and clad 0.D.

(inches)

TABLE A-2 Comparison of TORC and Response Surface MONBR for Cases Used to Generate Response Surface (cont)

Residual

.000

.001

.000

.001

.000

.001

-.001

-.002

.000

.001

-.001 CEN-283(S)-NP, Part 1 Revision 0 A-20 June 1984

Westinghouse Non-Proprietary Class 3 Case Inlet flow Factor Enthalpy Systematic Systematic Deta1 led

Response

Number Ch [

J Channels [ ] ! Channel~ ChaR1le1 [

] Rise Factor Pitch""*

Clad 0.D.**

TORC TORC Residual MDNBR MDNBR

- ~ - -* ---

~

- I 121

.000 122

.001 123

.001 124

-.001 125

.001 126

.001 127

.002 128

.000 129

.001 130 I

.004 131

-.004 I

132

.001 133

-.001 134

-.004 135 I

.004 I

I I

L ______

___ L_~--- --~ _

I 1-.-.,,-~l _ _L ______ ___ -

I

Channe l Nuiii>ers Refer to Fi<J. 1--5

- l

<;V<;tPm nilrilmPtPrC:.,hmi:,n<;1nn PC:.<: Pvr,:,nt-c:uc:t-o.n;aotir n-it-rh and clad 0. D.

( inches)

TABLE A-2 Comparison of TORC and Response Surface MDNBR for Cases Used to Generate Response Surface (cont)

CEN-283(S)-NP, Part 1 Revision 0 A-21 June 1984

Westi~ghouse Non-Proprietary Class 3 case I lnletf1owfactor E

1st

-r r~r

. *.] I Channels c.-ir:*nel rTrhaiiRelI... ] !

Ri~!h~!~{or~ ~:t~~lC 136 137 138 139 140 141 142 143 Systematic Clad 0.D. 0 Oeta1 led TORC MONBR

Response

TORC MDNBR

ChanneTNuri>ers Refer to Fig.

j-=.~---

-- *----- -*--- * *A)r *sys tern parameters d 1 mens fon less except sys-temaf 1 c-p 1 tc h -

and clad 0.0.

{inches)

TABLE.4\\-2 Comparison of TORC and Response Surface MDNBR for Cases Used to Gene rd te Response Surf ace l'.-22 Residual

.000

-. 001

.001

-. 001

.009

-.010 CEN-283(S)-NP, Part 1 June 1984 Revision O

ML19214A144

Text

Response

Response

Response

Response

Response

Response

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