ML20008E938

Nonproprietary Version of Responses to First Round Questions on Statistical Combination of Uncertainties Program,Part 2 (CEN-124 (B)-NP).

ML20008E938
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Site:	Calvert Cliffs
Issue date:	02/28/1981
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O -

Responses to First Round Questions on the Statistical Combination of Uncerta% ties Program, Part 2 (Cell-124 (B)-f:P)

February 1981

- COM8USTION ENGINEERIfiG, IfiC.

81031086'

LEGAL NOTICE 1

This report was prepared as an acccunt of work sponsored

, by Combustion Engineer 1r.v. 'n?. Neither Combusticn Engineering nor any person acting on its behalf:

A. Makes any warranty or representation, express or irplied including the warrarties of fitness for a particular purpose or merchantability, with respect to the accu.acy, completeness, or usefullness of the infor ation contained in this report, or that the use of any infomation, apparatus, method, or process disclosed ir this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resultir.g frcm the use of, any information, apparatus, method or process disclosed in this report.

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TABLE OF C0flTEtiTS Legal flotice i Table of Contents 11 Responses to Questions 1

Question 1 Question 2 3 Question 3 4 Question 4 12 Question 5 14 luestion 9 15 Question 12 16 Question 14 21 References 22 O

11

hestion1_(p_._3-]), "!;eminal" sys te m c erci! L.ons a m w h c ted leadiM to 3 "no.ainal" !W.%, tha ' ; - tem o r. !i t u a', a t e pcrt arbed and a

" perturbed" fE Bk is c:ticulated.  : hen A!4D!.DR = "flominal !WlIR" "parturbed" l'CNCR and

% Change = (/.!!DNBR/"i:o.ninal" MD::BR)

• 100 are defined. Then ". s t adverse state parameters" are definej as those which raxillize 4 change.

Comnen t :

This definition of "most adverse" is not consistent with the

. definition in Section 3.1 where u;st adverse" was defined in terms of r.aximum gradient, flaither definition is entirely suitable since both are sr.:le dependeit. If the perturbations ..ere selectcd to repcesent " equally likely" deviations, then the " change definition is acceptable.

Response

e Only one definition of most adverse set of state parameters was presented in Reference 1. This definition appeared in Section 3.1. The most adverse set of state parameters is that set which maximizes the gradient l- Nl, where x is the vector of system parameters.~

The discussion on p. 3-2 in Section 3.1.1 describes the method that was used to obtain nun.crical estimates of this gradient. The method was applied to quantify the influence that state parameters have on the sensitivity of FDN3R to individual systen parameters.

Both the definition of most adverse state parameters and the method applied to estimate the gradient are scale dependent.

Therefore, it is incorrect to compare estimates of the gradient

--a(f4DNBR)

, which was found by perturbing the system parametcr g

xj 11 th estimates of the gradient - b- , which was found by perturbing a different system param$ter xj. liowever, estimates of the gradient were not compared for different system parameters in Section 3. Only consistent comparisons of the influence of state paran:eters on the gradients f or individual system para..leters were i.ude. The influence of state parameters on the 14Di!BR gradient for individual system parameters was discussed in the following subsections:

3.1.2 Inlet flow Distrib; tion 3.1.3 Enthalpy P.ise factar 3.1. /l Systematic pitch Reduction D

Only one type of perturbation was used in each of these sub-Sections. For example, the " perturbed" data in Table 3-3 were all obtained by using the same perturbation to the inlet flow distribution. The tJ1DflBR data in Table 3-3 were thus self-consistent and were legitimately reviewed to establish the set of state parameters which maximizes the sensitivity of MDNBR to a constant perturbation in the inlet flow distribution. Similar data appear in Tables 3-4, 3-5, and 3-6 for the sensitivity of MDNBR to perturbations in ti.e enthalpy rise factor and Table 3-7 for the sensitivity of MDNBR to systematic perturbations in the pitch. The sets of state parameters which maximize MDNBR sensitivity to each of the system parameters are shown in Table 3-8. As explained in sub-section 3.1.5, the most adverse set of state parameters was determined using the data and also taking into account the magnitude and impact of each of the system parameter uncertainties. This most adverse set of state parameters was later verified as explained in the Response to Question 12.

G 2

Question 2 (p. 3-21:

Explain next to last piragraph. The terms "litely" and " highly unlikely" do not have a high precision. (Does the maxin,J:1 always lie on the periprery?)

Response: The next to last paragraph on p. 3-2 e.< plains that the methods which were used to deternine the "most adverse" set of state parameters will yield a good estimate of the most adverse set of state parameters. These methods utilized reasonable engineering approxirations to deternine the influence that state parameters have on the sensitivity of MDiBR to individual system parameters. This information was used to estimate the "most adverse" set of state parameters for use in generating the t'DNBR response surface. This set of "most adverse" state parameters was later verified by TORC cases in which all system parameters were perturbed and state parameters were varied, as discussed in the response to Question 12.

The limiting asser.biy in C-E's current thernal margin methodology is always located in the peripheral regicn of the core. This results from the fact that inlet flow is l

lower for peripheral fuel assemblies, as shown in Fig. 3-1.

i l

l I

l 3 a 4

Question 3 (pp. 3-3 to 3-5): It is not clear how the most adverst state parameters in paragraphs 3.1.2 and 3.1.5 are derived f rom the information of Tables 3-3 and 3-10. Explain how Table 3-7 shows sensitivity to systematic pitch constant for all positive

. axial shape indices.

Response: Tables 3-3 and 3-7 have been subdivided into Tables 3-3(a),

3-3(b), 3-3(c) and 3-7(a), 3-7(b) to better demonstrate the conclusions that were reached. These new tables are attached.

A typographical error was found in preparing i.hese tables.

The % change quoted in the next-to-icst line of Table 3-7

~

[ ]wasincorrect.

The correct value is[ 3 This value is listed in Table 3-7(b).

The data in Table 3-3(a) demonstrate the sensitivity of flow perturbation effects on MDf4BR to axial power shape, since all other state parameters were kept constant. These data indicate that MDitBR sensitivity to flow perturbations is maximized by the

[ laxialshapeindex(ASI). The % change found with[

] Although the maximum % change was found with[ ]the

%changefoundwitha[. .)wasveryclosetothe maximum value.

The data in Table 3-3(b) demonstrate the sensitivity of flow pertur-bation effects on MDNBR to system pressure, inlet temperature ana system flow at a top-peaked axial shape [ ]. These data indicate that flow perturbation effects on MDf48R are maximized with acombinationof[

l . ] The % change found attheseconditionswas{ ] Furthermore, a comparison of % change in l liDNBR for changes in system pressure indicates that flow perturbation effect or, MDflBR are

)Thesensi-tivity to system flow can also be determined from the data in Table 3-3(b).

A comparison of the top 4 rows of data with the bottom 4 rows of data j shows that flow perturbation effects on MDt1BR are[

! ]Insunmary,thefollowingconclusionsaboutthesensitivityof flow perturbation effects on MDfiBR are reached based upon the data

! in Table 3-3(b):

4

The data in Table 3-3(c) demonstrate the sensitivity of flow

~

perturbation effects on MD:1BR to pressure / temperature /ficw for bottompeaked[ ] ASI. [

.) A comparison of the first and third rows of data in Table 3-3(c)[

] The data in Table 3-3(c) indicate that flow perturbation effectsonfiD*lBRare[

)

Table 3-3(a) showed that flow perturbation effects are[

.)Themaximum%changewasfoundwithh however the value found with 0.337 ASI was very close to the

]ThedatainTable3-3(b)indicatedthattheflow perturbation effects were[

] finally,thedatainTable3-3(c)establishthatthe combination of[

)

l I

Therefore, the data in Table 3-3 demonstrate the conclusion presented in sub-section 3.7.2 that the greatest sensitivity of f1D:iBR with respect to a given flow perturbation is expec'.ed to occur at the following conditions:

While the maximum sensitivity will occur with these state parameters, the data in Table 3-3(a) indicate that use of h

amount.

5

The data in Table 3-7(a) demrmstrate the sensitivity of systematic pitch reduction offects on MDNBR to axial power shape, since all other state parameters were kept constant. These data indicate that systematic pitch reduction effects are naximized by a[ )

Furthermore,thesedatashowthatthesensitivity[

)

The data in Table 3-7(b) demonstrate the sensitivity of systematic pitch reduction effects on MDNBR to ASI and inlet temperature at

[ ] The naximum sensitivity occurs at }

)

The original set of state parameters that maximize systematic pittte reduction effects on MDNBR was stated in subsection 31.4 and Table 3-8 as:

. 3 This set of state paraineters was chosen because the data in the first part of Table 3-7, attached here as Table 3-7(a) indicated that[

] llowever, reexamination of the data in the present format showsthatthesensitivitytoASIchangesat[

] Data in Table 3-7(b) indicate that the following set of state parameters maximize systematic pitch reduction effects on MDNBR.

These cata match the set that was chosen in subsection 3.1.5 as the most adverse set of stat parameters for use in generating the MDNBR respense surface.

6

\xial Shape -

fiDNBR Index liomiill rTcw Terturbed F low  : change

-0.070

-0.020 0.000 0.317

~

0.337 0.444 0.527 ,

Note: The following state parameter values were used in the above analysis:

100% design flow rate 2200 psia system pressure 550 F inlet temperature Table 3-3(a): Sensitivity of flow Perturbation Effects on f1DNBR to Axial Shape e

7

P f

J

,i i System inlet System -

f4DNBR

-l Pressure Temperature flow psia f  % design Nominal Flow '~Perturbe_d_T ~ii,_~ Chanac I

2400 580 120

. 1750 580 120 2400 465 120 2 -

1750 465 120 2400 580 77 1750 580 77 4 2400 465 77 l 1750 465 77 Note: axial power shape used in above analysis l'

i Table 3-3(b): Sensitivity of Flow Perturbation Effects on 14DflBR to Pressure, I

i Temperature and Flow at flegative ASI' 4

t 6

8 L

System Inlet System Pressure Temperature l' 10w 14Di'BR psia F  % Design flominal Flow Perturbed flow % Change 1750 580 77 1750 465 77 1

1750 580 120 i

flote: { 3axialpowershapeusedinaboveanalyses Table 3_3(c): Sensitivity of Flow Perturbation Effects on fiDflBR to j Pressure, Temperatt're and Flow at Positive ASI I

e 9

Axial Shape ttp ';m Index ~~~~liominal Perturbed 7. Change

~

.317

.070

.000

.317

. .337

.527 _

flote: Above cases run with the following operating conditions:

100% design flow 2200 psia system pressure 550"F inlet temperature Table 3_-_7(al: Sensitivity of Systematic Pitch Reduction Effects on f1D?iBR to Axial Shape w

s 10

(

Axial Shape Inlet MDNBR Index _ remperature

- F Nominal Perturbed  % Change

.070 580

- .337 580

.337 465

.527 465

.527 580 Note: Above cases run with the following operating conditions:

Table 3-7(b): Sensitivity of Systematic Pitch Reduction Effects on MDNBR to Axial Shape and Inlet Temperature O

m 4

11

a

. a ;_  :.

Question 4 (p. 3-5):

It i.s not clear that the inherent con crv.itiso of PDQ is greater than uncertainties in radial pp.ter distribution. ,

a. , Does the limiting assembly always, cccur at the periphery?

Response

Since Ref. I was issued, physics tethods at C-E have been todified to

- improve the agrecrent between predicated and measured power distributicns.

Therefore the overprediction of radial peaking factors in the core peripher, by pDQ has been renoved. However, radial power aistributien ur. certainties r.3.e been, and continue to be, taken into account in a conservative, determinis-

', tic manner in C-E's thermal nargin . methods. These nethods are described in Reference 2 and are su=rarized belc>t. . -

e A Simplified TORC (S-TORC) todel,also referred to as the TORC design codel, is applied in C-E's thermal margin r.ethodology l for design CNS cargin calculations. Core specific data are '

included in the design rodel such that this model yields accurate or conservative MONBR predictions when compared wi+S MCUBR data frca Detailed TORC (D-TORC) analyses for the core undet sensideratien.

The corp.lete set of radial pc.ver distributicns that the core will ,

encounter thrcughout one cycle are surveyed in the preparation of a TORC desiga nadel. Candidates for limiting pc.-ter distributicns are selected for fuel assenblies with low inlet fic.< based upon ,

the following criteria:

i 4

Thefirstcriterionwaschosenbecausethereis[ ] '

associated with the radial peaking factors. Therefore, a pin which iswithia( ] peak can, in fact, be the naxirum '

after uncertsinties are taken into account. The second criterion isappliedto( i energy transportbetweensubchannelsinthelinitingassembly.] I The non-uniform inlet flow distributions used in Detailed TCRC cases always have

_ 1R

W

](Fig.3-1ofReference1isatypical example). For this reascn, limiting assemblies always occur in the peripheral region of the core.

~

Detailed TORC analyses are performed for the limiting assembly using the radial power distribution which sa+.isfies the two criteria cited previously. MDtGR results from analyses using the design TORC model are compared with Detailed TORC results to verify that the design model is appropriate. In preparing the Detailed TORC input, the power in the limiting assembly is[

4

] This deterministic adjustment accounts for uncertainties in the radial power distribution.

A sample application of this adjustment is provided in the response to question 14. Further allowances are made for uncertainty in the maximum one pin peak, as described in References 3 and 4.

4

! Sufficient margin exists in C-E thermal margin methodology as applied to Calvert Cliffs to account for radial power distribution uncertainties because of explicit detenninistic adjustments made to account for radial power distribution uncertainty. Therefore, the radial power distribution uncertainty need not be included in the statistical combination of system parameter uncertainties. Uncertainty in t:1e magnitude of the radial peak is treated in References 3 and 4 13

Question 5_ (p. 3-9): Does not the validity of paragraph 3.11 require that the experimental test section be identical to fuel elements in the reactor?

Response

TORC code uncertainty iacludes the uncertainty associated with the prediction of both core-wide and local coolant conditions. As explained in Reference 7, deterministic

. conservatisms are included in TORC models to account for the uncertainty associated with prediction of core-

. wide coolant conditions.

The uncertainty associated with the prediction of local coolant conditions is implicitly included in the MDNBR limit associated with the CE-1 CilF correlation. The test sections used in C-E CHF experiments (References 5 & 6) model sections of actual reactor fuel bundles, thereby assuring that local flow phenomena in the test section match those that would occur in the reactor core.

The TORC code was used to predict the local coolant conditions in the test sections for correlation of the CHF data. Therefore any calculational uncertainty associated with the TORC code has been implicitly included in the MDNBR limit that is associated with the CE-1 CHF correlation.

Furthermore, comparisons made in References 5 & 5 between CHF test data from other experinents and predicted values from the TORC /CE-1 method show that TORC /CE-1 ccnsistently underpredicts CHF. These comparisons demonstrat e that TORC /

CE-l yields conservative results when applied tc geometries which deviate from the test geometry used in the CE-1 CHF

. experiments.

, A typographical error was discovered in line 6 of Section 3.11 in Reference 1. The references cited should have been "(3-ll)through (3-13)" not "(3-10) (3-13)" as stated.

14

Question 9 (p. 6-1): The statement is made that "A comparison of TORC results and response surface predictions indicates that the la error associated with the respnnse surf ace is a =  ;... ."

Please clarify what is meant. Is a based on s the residual sum of squares? If so) what degrees of f reedom were used?

Response

The response surface error, as, is based upon the residual sum of squares. The value quoted in Reference 1 is based upon 142 degrees of freedom, which is incorrect. The experimental design used to generate the response surface used 143 data points, so 143-1 or 142 data points were used to determine o g. However, 36 constants for the response surface were determined from this data set, hence 143-36 or 107 degrees of freedon should have been used to calculate o s. The estimate of based on 107 degrees of s

freedom is 0.003912; at the 95% confidence level, c =

0.004412. Since the value of a isroot-sum-squarb 9

with the 95% confidence estimate bf the MDNBR standard deviation which is two orders of magnitude larger, the increased value of s has an insignificant impact on the final MDiiBR limit.95 The value of a tot changes from 0.10218 to 0.10221.

15

Question 12 (pp 3-3 and 4-1): Thr'se two sections sr'em to imply di f f erent core wide power distributions were uwd during the determination of "most adverse state parameters" and during generation of response surf ace. Please clari fy.

Response

Two dif ferent core wide power distributions were used in Reference 1 to avoid scheduling difficultics. The sensitivity study to determine the most adverse set of st-:e parameters

. was conducted using the inlet flow and radial power distri-butions shown in Fig. 3-1 and 3-3, respectively. The

. response surface was generated using the inlet flow and radial power distributions shown in Fig. 3-8 and 4-1, respectively.

To explain the manner in which the sensitivity study was conducted, let FDNBR = g (x, y),

as in Section 3.1 of Reference 1, where g = functicnal relationship between MD?iBR and system and state parameters x_ = vector of system parameters y = vector of state parameters The sensitivity study was conducted to determine the effects that state parameters had on the derivative . Single

~

effects were studied in the work documented in Section 3.1. The i

sensitivity of MDtlBR to one particular system parameter (e.g.

hot assembly inlet flow) was determined for various sets of state parameters. No interaction effects between system l parameters were taken into account in this study. Results of l

this study were used to estimate the "most adverse" set of t

' state parameters to use in generating the response surface.

l Since the system paraneter perturbations are local ef fects, it was expected that the same set of state parameters would maximize the sensitivity of MDNBR to system parameters for all inlet l flow and radial power distributions. Ilence, the following l

l 16 i

L_

two assumptions were made in using the esticate of the most adverse set of state parameters found in Section 3.1 to generate the respcose surface.

1) Interaction effects between system parameters and !CBR would not change the estimate of the most adverse state parameters. That is, the sensitivity of MD'iBR to simultaneous perturbation of several systen parameters would be maxinized bj the set of state parameters found by perturbing system para-n'eters individually.

2) The estimate of the most adverse set of state pararreters found for the inlet flow and radial power distributions shown in Figures 3-1 and 3-3 would also maximize idD'!BR sensitivity to system parameters for the dist. ibutions used to generate the response surface.

These assumptions were verified by a series of TORC cases in which the inlet flow and radial power distribution used to generate the response surface were modeled. Values of

% change in MDf!BR were calculated for various sets of state parameters using a method similar to the one described in sub-section 3.1.1. However, all system parameters were simultaneouslychangedby[ ] to compute " perturbed MD.*lBR" in these verification analyses.

This simultaneous perturbation of the system parameters by[ ] allows for the possibility of interaction between system parameters in their effect on f1DriBR.

Data from these verification cases are sunriarized in Tables 12-1 and 12-2. The data in Table 1 verify that [

.) since the % change in MDNBR found using this shape was far greater than the others. The data in Tabic 2 verify that the combination of[

] flow / pressure / inlet temperature combination.

Therefore the most adverse set of operating conditions estimated in Section 3.1 has been verified for the inlet 17

t 4

i . .

i .

I i

i 1

• 1 f kw and radial power distribution used to generate the i response surface.

i The verification was carried out in a nanner I

! Which would take into account interaction effects between the ,

l system parameters in their ef fect on t'DNSR. The two assumptions i

stated earlier in the response to this question have thus been l<

shown to be valid.  !

I i

1 i . I

!

• I i i J

t

! l l

l l 1

l i

i i

l 1 ,

I l

$ l 1

l t

i i

i i

\ -

e i

\

18 l

)

Axial Shape ~

lE!!R

~

index flomina l Perturbed ~ f Change _

-0.070 1 0.000 0.317 0.337 0.444 '

O.527 flow rate = 100':, design system pressure = 2200 psia inlet temperature = 550"F Table 12-1: Verification of the Most Adverse Axial Shape Irdex O

e 19

~

t System inlet Flow Rate Pressure Tenyera tu re _ _

MDNBR

% Design psia F Nonli nal Perturbed "

Change

~

77 1750 465 -

77 2400 465 77 1750 580 77 2400 580 120 1750 465 120 2400 465 120 1750 580 120 2400 580 .  ;

NOTE: All cases run with . -

ASI.

i l

Table 12-2: Verification 6f Most Adverse Combination of Pressure, Temperature and Flcw Rate ,

I I

l i 20

-< v t y7- w e - g '

W

_uestion Q 14 (pp. 3-12 and 3-13): Why doesn't the average of the 4 quadrant peaks in Fig. 3-4 compare with the value shown in Fig. 3-3?

Response: The maximum one pin radial peck for the power distribution shown inFigures3-3and3-4islocatedin[ jof Figure 3-3; thevalueofthemaximumonepinpeakis[ ] Although['

)containsthemaximumonepinpeak,itisnotthelimiting

~

channelbecausethe[

]Whenthe

]isfoundtobelimiting.

Themaximumonepinradialpeakin[

]CurrentC-Ethermalmargin methodology adds conservatism to MDNBR predictions by artificially increasing the radial peaking factors in the limiting assembly suchthat[ -

)forthe power distribution under consideration. Therefore, the radial peaking factors for each pin in{ )weremultipliedbythe ratio of to obtain the peaking factors shown in Fig. 3-4. This had the effect of increasing the[

]showninFig.3-3to( ,linFig.3-4.

21

4 4

REFEREflCES

1. " Statistical Combination of Uncertainties itethodology, Part 2: Combination of System Parareter Uncertainties in Themal Margin Analyses for Calvert Clif fs Units 1 & 2", CEff-124(B)-P, January,1980.

i 2. " TORC Code: Veri fication and Simpli fied liodeling Methods", CENPD-206-P ,

January, 1977.

3. " Statistical Combination of Uncertainties f!ethodology, Part 1: C-E Calculated Local Power Density and Thermal Margin / Low Pressure LSSS for Calvert Clif fs

. Units I and 11", Ceil-124(B)-P, December, 1979.

4. " Statistical Combination of Uncertainties Methodology, Part 3: C-E Calculated Departure from flucleate Boiling and Linear Heat Rate Liniting Conditions for Operation for Calvert Clif fs Units 1 & 2", CEN-124(B)-P, March,1980.

5. "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblic with Standard Spacer Grids, Part 1 - Uniform Axial Power Distribution". CENPD . -F 1 Sep tember, 1976.

6. "C-E Critical Heat Flux: Critical Heat flux Correlation for C-E Fuel Assemblies with Standard Spacer Girds, Part 2 - fionuniform Axial Power Distribution", CEtiPD-207-P, June, 1976.

7. " TORC Code: A Computer Code for Detemining the Thermal Margin of a Reactor Code", CENPD-161-P, July 1975.

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