ML20011E253

Arrotta Validation & Verification - Std Benchmarks Set.

ML20011E253
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Issue date:	07/31/1989
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, . ARRCTTIA i%: j Valid 3 tion and Wrification - >

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Standard Benchmarks set '

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Research Project 1936-6 '

July 1989 s

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S. Levy Inc. .c 3125 S. Bascom Avenue  :

= Campbell, California 95008 t

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4 Electric Power Research Institute -

3412 Hillview Avenue Palo Alto, California 94304 P

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Reload Management Program Nuclear Power Division i

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. ARROITA Validation and Verification -

Standard Benchmarks Set Research Project 1936-6 July 1989 i

Prepared by: I S. Levy Inc.

3425 S. Bascom Avenue Campeell, California 95008

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Electric Power Research Institute 3412 Hillview Avenue ,

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LEGAL NOTICE l

.i This report was prepared by the Electric ~ Power Research Institute, Inc., j (EPRI). Neither EPRI, members of EPRI, nor any person-acting'on their behalf:

(a) makes any warranty, express or implied,-with. respect to the use of any.  ;

information apparatus, method, or process disclosed in this report or that suchLuse 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 teport.

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L r CONTDRS -

Section . Page'-

1 TNTRODUCTION 1-00 2 ' BENCHMARK CASES 2-00

, 2.1 2-D 'BIBLIS PWR Problem 2-00

.2.2 2-D L ZION-1 PWR Problem 2-00 2.3 3-D LRA BWR Static Problem 2 '

2.4 3-D IAEA PNR Problem 2 <

2.5 ' 2-D- 'IWIGL Seed-Blanket Reactor Kinetics Problem 2-00 'j

~2.6 3-D LMW LWT Transient Problem 00 l 3 XENON TRANSIDES ANALYSIS 3 3.1 Azimuthal Xenon Oscillation 3-00 3.2 . Peak Xenon Override 3 4- HEAT CONDUCTION MODELS 4-00.

y 5 REFERENCES

~

5-00 j l

Appendix- 1

.A' INPUT LISTINGS FOR BENCHMARK CASES A-00 L

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b 1

ILLUSTRATIONS Figures Page 2- 1 Radial _ Description of the Southeast Quadrant of the Reactor .

for the 2-D BIBLIS PWR Problem 2-00 -l

)

2- 2' Normalized Assembly Power Densities for the 2-D BIELIS PWR i Problem Using a 1 Node per Assembly Representation 2-0 0 --

2- 3 Normalized' Assembly Power Densities for the 2-D BIBLIS PWR-Problem Using a 4 Nodes per Assembly Representation 2-00 L

L 2- 4 Radial Description of the Southeast Quadrant of the Reactor i for the 2-D ZION-1 PWR Problem 2-00  !

2- 5 Normalized Assembly Power Densities for the 2-D ZION-1 PWR Problem 2-00 ,.

3 2- 6 Radial Description (Axial Midplane) of the Southeast Quadrant j l of the Reactor for the 3-D LRA BWR Problem 2-00 ,

L 2- 7 Axial Description of the Southeast Quadrant of the Reactor p for the 3-D LRA BWR Problem 2-00.

Normalized Assembly-Power Densities for the 3-D LRA BWR

~

!. 2- 8 Problem 2-00 l

2- 9 Radial Description (Axial Midplane) of the Southeast Quadrant  !

of the Reactor for the 3-D IAEA PWR Problem 2-00  !

l 2-10 Axial' Description (y=40 cm) of the Southeast Quadrant of the  !

Reactor for the 3-D IAEA PWR Problem 2-00 i 2-11 Normalized Assembly Power Densities for the 3-D IAEA PWR Problem 2-00 2-12 Radial Description of the Southeast Quadrant of the Reactor l for the 2-D 'IWIGL Seed-Blt.nket Reactor Kinetics Problem 2-00  ;

l 2-13 Radial Description of the Southeast Quadrant of the Reactor j for the 3-D LMW LWR Transient Problem 2 00  ;

2-14 Axial Description of the Southeast Quadrant of the Reactor for the 3-D LMW LWR Transient Problem 2-00

._ _J

s.

.e l z( 3' t

3 .1. Catawba-I. Xenon Oscillation. MQT *>alues based on the Edge Assemblies Powers compared to measured Data. 3  ;

3-'2 Catawba-I Xenon oscillation.19 Tr Values based on the Quarter- t Core Integrated Powers compared to measured Data. 3-00 3- 3, Catawba-I Xenon override. Eigenvalue Evolution. 3-00 4- 1 Axial Puel Distribut!.on of the Radial Average Puel Temperature. Comparing ARPUTIA and VIPRE-1 results. 4-00

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l TABLES Table- Page f

2- l' Material Properties Description for the 2-D BIBLIS PWR

, Problem- 2-00.

2- 2 . Material Properties Det,cription for the 2-D ZION-1 PWR Problem 2-00 2- 3 Material Properties Description for the 3-D LRA BWR  :

Problem 2-00 2- 4 Material Properties Description for the 3-D IAEA PWR Problem 2-00 2- 5 Material Properties Description for the 2-D WIGL Seed-Blanket Reactor Problem 2-00 2- 6 Power Excursion for the 2-D WIGL Seed-blanket Reactor Problem (Step Perturbation) 2-00 <

2- 7 Power Excursion for the 2-D WIGL Seed-Blanket Reactor Problem (Ramp Perturbation) 2-00 8 Material. Properties Description for the 3-D LMW LWR Problem 2-00 9 Power Excursion for the- 3-D LMW LWR Transient Problem 2-00 3- 1 Catawba-I. Xenon Override. Eigenvalue Evolution. 3-00

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3 l-p Section l' INIRODUCTION 1

Several study cases are presented here with the intention of demonstrating the applicability and accuracy of the code ARROTIA. The' idea behind the choosing of these problems wast (a) to establish a reasonable '

number of cases that could be compared against already published or experimental results', and/or (b) to cover the range of utilization of ARROTIA i L - itself; namely the. steady-state neutronics, the transient neutronics, and the  ;

b, thermal-hydraulic models. The simplicity (easier core description) of_most.of I these problems poses absolutely no detriment to the goal of this work, since it is not the complexity of a problem that governs the way in which this computational tool (ARROTIA) will be used.

1

'Ihe. ARROTIA results presented here were obtained with the version 1.02 i' of the code dated 1/17/89 on the EPRI IBM.

1 In the neutronics methodology of ARROTIA and its antecedent, QUANDRY, one-

- always gives the statements of assumptions quite quickly at the beginning of:

the treatise. However, it must be emphasized that in order for this Quadratic Analytic Nodalization nethod to be perfectly valid, the transverse leakage in -

o- a given direction, within a given node, must be representable by the proposed

-qua rd atic polynomial.-(This is a crucial theoretical-step in the derivation of the equations in order to obtain an equation form that it integrable albeit-quite complicated.) Certainly, this assumption is very rarely matched during a normal application of the codes; nevertheless, the errors caused by its violation are quite small, not influencing the very good results that are becoming characteristic of the methodology. It has been observed, in some situations, that at the core-reflector interface the assumption tends to be sufficiently violated to cause errors that are noticeable but still not important.

a

,1' . , ..  ;

a. ,

.,f Section 2 BENODERK CASES i

Six cases werc, chosen for the benchcarking of ARRCTIA, with problems.

varying from two-dimensional static calculations to a three-dimensional '

transient simulation.~All these cases are found in the literature and qualify as good references for the comparison that follows. '

ARRCTPTA's performance' can be summarized as presenting an average eigenvalue error in the order of 1.0E-3% , and an average assembly power density error in the order of 0.3% (with the maximum of these errors observed at 2.1%). These errors were obtained when making use of a normal nodal representation of the core : one node per assembly, radially. These differences can be well reduced with t1e choice of a finer mesh structure.

For.the transient simulations, the discrepancies observed in the power-density excursions were in the order of 2.0%, reaching as high as 6.0% for ,

one' specific (and more complex) ca u.

These problems can serve _as'the basis for verification of future

. programming changes to the code and for installation of the code in a-particular computing environment.

For. completeness, one appendix to this chapter contains the ARROTTA Input Listings used for all the cases addressed in this Section.

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kN 2 .1 ~ . 2-D' BIBLIS PWR Problem Wis is a two-dimensional, twr>-group, linear. (no thermal-hydraulic feedback), static problem.

.% e core contains 193 fuel assemblies, about 23cm on each side. Higher enrichment elements are placed in the outer zone of the core, whereas its interior is loaded with three other lower levels of enrichment, in a checkerboard pattern. The homogeneous reflector surrounding the core is representative of the original baffle + water. No control rods are here considered.

A detailed description for this problem is provided in Figure 2-1 and Table 2-1. In Appendix A , the reader can find the corresponding input listing used for the ARRCUTA calculation.

Wis problem is a good example of the geometric representation (radiMly) of a realistic checkerboarded PWR core. ,

The reference solution adopted for this problem is a 36 nodes per -

assembly calculation presented by Lawrence Q) based on the Nodal Green's runction Method (NGrM).

Figure 2-2 shows the normalized assembly power density results. The

~

differences observed are quite acceptable (average absolute error : 0.6% ,

maximum error : 2.1% ), especially when one realizes the degree of sittplification achieved by choosing the.1 node per assembly representation, when compared to the 36 nodes per assembly mesh structure adopted for the reference calculation. We same problem was also run with a 4 nodes per assembly structure, yielding ARROITA results (see Figure 2-3) that show even htter agreement with the reference solution. Despite this improvement in '

the results, t.he core description initially adopted (1 node per assembly) is

.still the one recommended for a normal PWR calculation.

, y

m. t f,

1 1

1

, -*l )*- 23.1226 cm j x ,

2 7 1 7' 2 6 1 '3 { (cm)  !

7- 1 7 2- 7 1 1 3

)

7 1 7 2 6 1 3 2 l- l 1

I 5 2 7 2 7 1 7 3 1 7= 2 7 , 2 4 3 I 1 6 l' ,1 6 1 4 3 3 1 1 1 7 3 3 l- i l l ,

l

i. l 3 3- 3 3 l 8 1

l I

-f y (m) 3 i

core symmetry : quarter core l assembly size : 23.1226 x 23.1226 cm external boundary condition : zero flux ,

Figure 2- 1 : Radial Description of the Southeast Quadrant of the Reactor for the 2-D BIBLIS PWR Problem.

. - .. -.a

Q -

s 4

f 1: Material Properties Description for the 2-D BIBLIS PWR Problem.

Tatde Composition Group,g Dg(cm) Eq(cm*I) Z , ( em' ) v1 cm' )

1 1 1.4360 0.0095042 0.017754 0.0058708 2 0.36353 0.075058 0.096067 2 1 1.4366 0.0096785 0.017621 0.0061908 2 0.36362 0.078436 0.10358 3 1 1,.4389 0.010363 0.017101 0.0074527 2 0.36376 0.091408 0.13236 4 1 1.4381 0.010003 0.017290 0.0061908 2 0.36653 0.084828 0.10358 5 1 1.4385 0.010132 0.017192 0.0064285 2 0.36653 0.087314 0.10911 6 1 1.4389 0.010165 0.017125 0.0061908 2 0.36793 0.088024 0.10358 7 1 1.4393 0.010294 0.017027 0.0064285 2 0.36798 0.090510 0.10911 8 1 1.3200 0.0026562 0.023106 0.

2 0.27717 0.071596 0.

i

.. - .- . . . . . .. . ._.._______________________________._1________.

n

( .

F.i'#0h-of-core layout.

. 1.0916 1.0788

-1.2% ,

1.1021 1.1180 Reference ** k-eff = 1.025103 1.0901 1.1077 ARROTIA ** k-eff = 1.025268 L -1.1% -0.9% relative error ** 1.6E-2%

l -

1.2432 1.1346 1.1227 1.2326 1.1225 1.1166

-0.9% -1.1% -0.5%'

1.2209 1.2240 1.1054 1.1612 1.2116 1.2169 1.0967 1.1604 ,

-0.8% -0.6% -0.8% -0.1%'

1-1.0889 1.0678 1.1202 1.0390 1.1229 1.0828 1.0609 1.1202 1.0384 1.1296

-0.6% -0.6% -0.11- 0.6%

0.9818 1.0317 0.9236 0.9502 0.9934 1 1.2002 0.9785 1.0302 0.9211 0.9553 1.0037 1.2252

-0.3% -0.1% -0.3% 0.5% 1.0% 2.1%

1.0939 1.0710 0.9305 0.7650 0.8748 1 0.6849  :

0.7698  ;

'1.0942 1.0710 0.9330- 0.8898 l 0.6919 44666/

0.3%' O.6% 1.7%l 1.0%l //

//

1.0131 0.9673 0.8236 l 0.5451 // '

1.0148 0.9701 0.8260 l 0.5512 I ///////////n///////

O 2% 0.3% 0.3%l 1.1%l /0/

// RErLECTOR

//

/////////////////////////////////////////

Figure 2-2 : Normalized Assembly Power Densities for the 2-D BIBLIS Plw Problem Using a 1 Node per Assembly Representation.

t.

I Eighth-of-core layout.

i i m 1.0916 1.0885

-0.3%

~

1.1021 1.1180 Reference ** k-eff =.1.025103 1.0992 1.1152 ARROTIA ** k-eff = 1.025103 l

-0.3%

-0.3% relative error ** 0.0 %

l 1.2432 1.1346 ' 1.1227 1.2406 1.1322 1.1207 ,

-0.2%l -0.2% -0.2%

1.2209 1.2240 1.1054 1.1612 ,

1.2188 1.2222 1.1040 1.1606

-0.2% -0.1% -0.1% -0.1%

1.0889 1.0678 1.1202 1.0390 1.1129 1.0878 1.0669 1.1198 1.0390 1.1241 '

-0.1% -0.1% 0.1%

0.9810 1.0317 0.9236 0.9502 0.9934 1.2002 O.9816 1.0316 0.9237 0.9511 0.9947 1.2033 0.1% 0.1% 0.3%

~ ~

1.0939 1.0710 0.9305 0.7650 0.8748 0.6849 1.0945 1.0717 0.9313 0.7659 , 0.8773 0.6864 //////

0.1% 0.1% 0.1% 0.1% 0. 3% i - 0.2%  : //

//

1.0131 0.9673 0.8236 0.5451 //

1.0140 0.9702 0.8247 .0.5465 ////////////////////

0.1%I 0.3%I 0.1%l 0.3% //

// RETLECTOR

//

/////////////////////////////////////////

rigure 2-3 : Normalized Assembly Power Densities for the 2-D BIDLIS v Problem Using a 4 Nodes per Assembly Representation.

2.2 2-D ZICN-1 PWR Problem  !

Wis is a two-dimensional, two-group, linear (no thermal-hydraulic feedback), static prcblem.

'Ihe core contains 193 fuel assemblies, about 22 cm on each side. The  ;

outer zone of the core is made up of higher enrichment assemblies; whereas the inner zone is checkerboard-loaded with two lower enrichment assemblies.

We entire core is surrounded by a baffle (about 3 cm thick) and a pure water reflector.

A detailed description for. this problem is provided in rigure 2-4 and ,

Table 2-2 , In Appendix A , the reader can find the corresponding input listing used for the ARROTIA calculation.

The explicit representation of the baffle during the nodal calculations brings added challenges to the use of ARROTTA. In order for the quadratic  !

leakage treatment to be acceptable, the mesh sizes of two consecutive nodes should be of the same magnitude. This requires the core to be represented with a mesh structure of at least a 4 nodes par assembly, which is not the normal nodal treatment for a PWR core. (But also, the baffle is not normally l explicitly represented, either.) A thourough analysis about this detail of chosing the leakage approximation is presented in Smith's work (2). ,

Because of the small mesh used to describe the reflector, this problem presents, to the r.eutronic iterative solver, a very tightly coupled inner-outer numerical contamination problem. In order for each outer iteratien to ,

proceed as theoretically intended, a sufficient number of inner iterations must be performed to guarantee that no complex eigenvalues start to appear in the outer iteration process. As long as ARROTTA is given a minimu:n of 2 inner iterations per pass in the steady state, it can compute a sufficient number of inners per outer in order to insure that this imaginary component is small enough. This imagir.ary component comes from the small, albeit finite, error that is associated with the inner iteration process.

I h e reference solution adopted for this problem is a 16 nodes per assembly calculation presented by Smith Q), using the code CUANDRY.

1igure 2-5 shows the normalized assembly power density results. The  ;

degree of agreement with the reference values is truly remarkable (average ,

absolute error : 0.0% , maximum error : 0.1%). I l

l

7

-+1 }.- 21.608 cm x

21 3 2 1 3 l 2 l 3 1 2 4 I (cm)

\ _

l l

l 1 .

3' 2 3 2 3 2 4 il 4 l-1 2' 3 2 3 2 3 2 4 ,

l 1

3 2 3 2 3 2 4 4 i

'1 1

2 3 2 3 3 3 4 l 1 3 2 3 2 3 4 4 L

I ( -

2; 4 2 .

4 4 4 l

4 4 4 4 l 5 l'

y (cm) core symetry : quarter core assembly size : 21.608 x 21.608 cm baffle width : 2.8575 cm external boundary condition : zero flux rigore 2- 4 : Radial Description of the Southeact Quadrant of the Reactor for the 2-D ZION-1 PWR Problem.

o l<

I ,

r i

Table 2- 2 : Material Properties Description for the 2-D ZION-1 PWR Problem. j Composition Group,9 D g(cm) 2 ( cm' ) 1 (cm ) J7. (cm) ,

1 1 1.02130 0.00322 0. O.

2 0.33548 0.14596 0.

2 1 1.4176 0.00855 0.01742 0.00536 2 0.37335 0.06669 0.10433 3 1 1.4192 0.00882 0.01694 0.00601 2 0.37370 0.07606 0.12472 4 1 1.4265 0.00902 0.01658 0.00653 ,

2 0.37424 0.08359 0.14120 5 1 1.4554 0.00047 0.02903 0.

2 0.28994 0.00949 0.

l P = 2.43 I

o

=.

Eighth-of-core layout, i

1.631 1.6303 1.777 '

1.683 Reference ** k-eff = 1.27469 1.7770 1.5824 ARROTIA ** k-eff = 1.274896 relative error ** 4.7E-4%

1.535 1.672 1.446 1.5339 1.6725 L 1.4455

-0.1%i 1.565 1.395 1.478 1.243 1.5656 1.3948 1.4782 1.2429 1.253 1.365 1.181 1.217 1.078 1.2528 1.3653 1.1806 1.2176 1.0777 1.164 1.033 1.081 0.8944 0.8493 0.6641 1.1646 1.0331 1.0821 0.8941 0.8493 0.6640 0.1% 0.1%

0.7972 0.9181 0.7188 0.7189 0.5272 0.3206 0.7972 0.9188 0.7185 0.7192 0.5270 0.3203 //////

0.1% l -0.1% . //

//

0.5053 0.4901 0.4393 1 0.3158 //

0.5056 0.4902 0.4395 0.3155 ////////////////////

0.1% -0.1% //

// BArrLE + PITLECIOR

//

/////////////////////////////////////////

Figure 2-5 : Normalized Assembly Power Densities for the 2-D ZIO!M Pim Problem .

t f

2.3 3-D LFA IHR Static Problem j his is a three-dimensional, two-group, linear (no thermal-hydrau11e feedback), static problem.

She sinplified core contains 312 fuel bundles,15 cm on each side. Water is the reflector both radially and axially, and the active core height is  !'

300 cm. We control rods are represented as smeared absorbers within the corresponding adjacer't 4 bundles. The problem was originally introduced as a full-core kinetics problem; however, only the rodded steady-state solution is to be addressed here. .

A detailed description for this problem is provided in rigures 2-6 , and 2-7 and Table 2-3 . In Appendix A , the reader can find the corresponding input listing used for the ARROMA calculation.

1 The reference solution adopted for this problem is actually a finer mesh ,

nodal calculation presented by Smith (2) wita the use of the code OUEDRY.

Although not a true reference, because of the relatively costse mesh structure still being edopted, it well serves the purpose of demonstrating the accursey of the nodal nethod for a very coarse mesh structure (one node per assembly).

rigure 2-8 shows the normalized bundle power density results. A very good agreement with the reference values is observed (average absolute error : 0.1% , L ximum error : 0.4%).

l I

l l

l 1

l l

..___._____,m,., -

y -

', e .

.i i  ;

O. 15. 75, 105. 135. 165. -

x (cm) 2l .

l I

1 3 6

1 2 2 4l .

3 5

?

-y (cm) ,

core symmetry : quarter core assembly size : 15 x 15 cm ,

external boundary condition : zero flux '

h rigure 2- 6 : Radial Description (Axiol Midplane) of the Southeast Quadrant of the Reactor for the 3-D LRA BWR Problem. .

S 7

t

I i o i

\ .

I

!- t (cm) 360. ,

a ., 330.. ,

l 2' 1 2 3 5 1

l l

l

• 30.

4

0. x (cm) nodal axial length : 30 cm i Figure 2- 7 : Axial Description of the Southeart Quadrant of the Reactor for the 3-D LRA BWR Problem, i

i l' I

e , -

(:,.

1 Table 2- 3 : Material Properties Description for the 3-D LRA BWR Problem, i

! Ceaposition Group,9 D g(cm) ( (cm ) 1 ( an' ' ) O Z (em' ' )

1 1.255 0.008252 0.02533 0.004602 l 1 0.1091 l 2 0.211 0.1003 2 1 1.268 0.007181 0.02767 0.004609 2 0.1902 0.07047 0.08675 j.

3 1 1.259 0.008002 0.02617 0.004663 2 0.2091 0.08344 0.1021 i 4 1 1.259 0.008002 0.02617 0.004663 2 0.2091 0.073324 0.1021 5 1 1.257 0.0006034 0.04754 0, 2 0.1592 0.01911 0.

{- Y - 2.43 s

f i

)

Eighth-of-core layout.

l 0.611a ' l 0.6140. t 0.4%' ,

0.4403 0.3995 Reference ** k-eff = 0.996394

0.4408 0.4005 ARRCTfrA ** k-eff = 0.996412 O.1% 0.3% relative error ** 1.8E-3%

0.4131 0.4067 0.4240 J 0.4134 0.4071 0.4245 1 l- 0.1% 0.1%' O.1%, l l l-  ;

I 0.5119 0.4904 0.4920 0.5524 l  ;

l 0.5120 0.4907 0.4925 0.5528 l 0.1% 0.1%' O.1%  :

_ l 0-.7901 0.6703 0.6181 0.6782 0.8643 0.7898 0.6718 0.6184 0.6781 0.8649 0.2% 0.1%i t l l- >

1.3844 0.9397 0.7826 0.8434 1 1.1521 1.8515 l  ;

j' 1.3872 0.9400 0.7826 0.8427 1.1500 1.3509 l l 0.2% -0.1% -0.2%

1 l 1.6599 1.1506 0.9667 1.0224 1.3394 2.0505 2.1607 '

l 1.6642 1.1505 0.9663 1.0213 1.3369 2.0508 2.1610 O.3% -0.1%. -0.2%

l-

t. l'.4807- 1.2806 1.1726 1.2211 1.4215 1.6796 1.6216 1.3319 '

l 1.4824 1.2823 1.1716 1.2196 1.4219 1.6780 1.6205 1.3267 /////

j 0.1% 0.1% -0.1% -0.1%l -0.1tl -0.1% -0.4% //

//

0.9239 0.8669 0.8266 0.8528 0.9324 0.9719 l 0.8484 //

0.9244 'O.8674 0.8267 0.8525 0.9317 0.9721 0.8450 ///////////

0.1% 0.1% -0.1% -0.4% // '

// RETLEC"IOR

//

//////////////////////////////////////////////////////////////////// \

l

! 1 1

Figure 2-8 : Normalized Assembly Power Densities for the 3-D LRA Bh? ,

Problem . I I

l l,

L: _ .

')

1 i

f 2.4~ 3-D- IAEA PWR Problem ,

h is is a three-dimensional, two-group, linear (no thermal-hydraulic feedback), static problem. i

%e highly simplified two-zoned core contains 177 fuel asserblies, 20 cm i on each side. We core is reflected radially and axially by water, and the active core height is 340 cm. We control rods ar* riepresented as smeared absorbers in a single fuel assembly, tour partially inserted rods are modeled. ,

%e existence of inserted control rods and a water reflector gives this problem severe local flux petturbations which make the problem quite challenging.

A detailed description for this problem is provided in rigures 2-9 , and 2-10 and Table 2-4 . In Appendix A , the reader can find the cerresponding input listing used for the ARRCTTIA calculation.

he reference solution adopted for this problem is a finite difference calculation by Vondy et. al., obtained by using varNRE (3). Vondy actually performed a series of calculations with refined mesh spacings and then applied a Richardson extrapolation to obtain his reference solution, assuming tnat the errors were reduced with the square of the mesh spacing.

Figure 2-11 shows the normaliced assembly power density resuDS.

Excellent agreement with reference values is observed (average ab51ute error : 0.3% , maximum error : 1.1% ).

i l

l

t

. t O. 10. 70. 90. 130, 150.. 170.

x  :

3l l 3 l (cm) .

4 2 i

)

3 3 i

1 i

l  !

4 l

l l 1 I

l l

y (cm) core symetry : quarter core assembly size : 20 x 20 cm external boundary condition : zero flux Figure 2- 9 : Radial Description (axial midplane) of the Southeast Cuadrant of the Reactor for the 3-D IAEA PWR Problem.

s

t 5

4 L,

i.g z (cm) i i 380.

p 5' 4 5 4 5 ' 4

. , 360. -

i 3

l l 280. l l l

I l  ;

31 2 3 2 1 4

.1 1

20. l '

l 4 I i

, O. x (cm)

• partially inserted rod : 30 < x <50 cm , 30.< y <50. em 5 nodal axial length : 20 cm Figure 2-10 : Axial Description (y=40 cm) of the Southeast Quadrant of the Reactor for the 3-D IAEA PWR Problem.

l_

i l

(;

1

I' I I Table 2 ' 4 : Material Properties Description for the 3-D IAEA PWR Problem.

Composition Group,9 Dg(cm) (cm' ) 1 (cm' 02 ( cm' ) ,

1 1 1.5 0.01 0.02 0.

2 0.4 0.08 0.135  ?

2 1 1.5 0.01 0.02- 0, 2 0.4 0.085 0.135 3 1 1.5 0.01 0.02 0. .

2 0.4 0.13 0.135 .

4 1 2.0 0. 0.04 0, 2 0.3 0.01 0.

5 1 2.0 0. 0.04 0, 1 2 0.3 0.055 0.

1 1

1 5

1 i

5

I A.

'l Eighth-of-core layout.

0.729 0.732 0.4%'

~

1.281 1.397 Reference ** k-eff = 1.02903 1.277 1.393 ARROTIA ** k-eff = 1.02899

-0.3% -0.3% relative error ** -3.9E-3%

1.422 1.432 1.368 1.418 1.429 1.366

-0.3%' ,

-0.2%. -0.1%l

-l- t -

1.193 l 1.291 l 1.311 l 1.178 1.190 1.288 1.310 1.178

-0.3% -0.2% -0.1%

0.610 1.072 1.181 0.972 0.476 0.611 1.070 1.180 l 0.972 0.476 0.2% -0.2% -0.1%

0.953 1.055 1.089 1 0.923 0.700 0.597 0.951 1.052 ' 1.087 0.925 0.706 0.601 /////

-0.2% -0.3% .

-0.2% 0.2%I 0.9%I 0.7%1 //

- - //

0.959 0.976 1.000 0.866 0.611 //

0.956 0.972 0.997 1 0.871 0.618 ////////////

-0.3% -0.4% -0.3%l 0.6% 1.1% //

l // RETLECTOR 0.777 0.757 0.711 I //

0.770 0.753 0.710 l ////////////////////

-0.9% L -0.5% -0.1%l //

//

//

////////////////////////////////

rigure 2-11 : Normalized Assembly Power Densities for the 3-D IATA t'em Problem .

j

'f .*

l 1

2.5 2-D %'IGL Seed-Blanket Reactor Kinetics Problem Wis is a two-dimensional, two-group, linear (no thermal-hydraulic feedback), transient problem.

We seed-blanket reactor is 160 cm square and unreflected. We transients

.to be addressed are a step and a ramp positive reactivity insettions in the corner seed region.

Due to the way the code ARROTIA is written, the two problems are simulated in a fictitious nonlinear manner in order to get the mean power densities printed as the transient progresses.

A detailed description for this problem is provided in rigure 2-12 and Table 2-5 . In Ap pndix A , the reader can find the corresponding input listing used for tie ARRCTTIA calculation.

The solution for this problem was first presented by Hageman and Yasinsky (4); however, succestive studies of the same problem making, use of different s thods (finite differences, finite elements and nodal schemes), have updated the reference solution. In this study, the results presented by Smith (2_),

with the use of the code QUANDRY and a fine mesh structure, are adopted as the refer 4ence solution.

In passing it must be noted that the original Hageman and Yasinsky paper was a demonsttation of a proof of principle; it was not the generation of a benchmark standard. The original work used a finite difference grid with a uniform 8 cm mesh. Consequently, it is not surprising that all recults generated with modern nodal methods get somestiat different results including the system eigenvalue.

Tables 2-6 and 2-7 show the power excursion resulting from the two '

sim.tlations. A very good agreement with the reference values is observed.

- . . . l' . - - . . . .

m-I .t D. 24. 56. 80.

x (cm) 3 2 (blanket) (seed) 1 2 1 l (seed) (pert. seed) l I

3 (blanket) y (cm) core synnetry quarter core assembly size : 12 x 12 cm (blanket), 16 x 16 cm (seed) external boundary condition : zero flux rigure 2-12 : Radial Description of the Southeast Quadrant of the Reactor for -

the 2-D TWIGL Seed-Blanket Reactor Kinetics Problem.

)

l,

• i Table 2- 5 : Material Properties Description for the 2-D 'NIGL Seed-Blanket Reactor Problem.

Composition Group,9 DS (cm) & (cnI' ) 2, ( cm' ) d(em" )

- 1 1 1.4 0.01 0.01 0.007 l

2 0.4 0.15 0.2 2 1 1.4 0.01 0.01 0.007 2 0.4 0.15 0.2 3 1 1.3 0.008 0.01 0.003 2 0.5 0.05 0.06 9 = 2.43 v, = 10 cvs k = 3.204 x 10 W.s/ fission v, - 2 x 10 cm/s Family,d pg A g (s'I )

1 0.0075 0.08 1

Perturbations In composition 1, Step : 62 = -0.0035 cm  ; t=0 i

Zy (0)(1-0.11667t} ; t ( 0.2 Ramp [ A (t) =

t > 0.2 2^A(0){0.97666) ;

i

's ,

n i

I Table 2-6 : Power Excursion for the 2-D M GL Seed-Blanket Reactor Problem :'

(Step Perturbation).

Power (Watts)

Time (s) Reference ARROTIA 0.0 1.000 1.000 t

0.1 2.061 2.062 i 0.2 2.078 2.077

! 0.3 2.095 2.094 ,

0.4 2.113 2.122 ,

0.5 2.131  ?.130 l h

Table 2-7 : Power Excursion for the 2-D M GL Seed-Blanket Reactor Problem (Ramp Perturbation).

Power (Watts)

Time ,

(s) Reference ARROTIA ,

0.0 1.000 1.000 ,

0.1 1.307 1.306 (-0.1%)

0.2 1.957 1.954 (-0.2%)

O.3 2.074 2.074 0.4 2.096 2.092 (-0.2%)

0.5 2.109 2.109 Reference ** k-eff = 0.91321 ARROTIA ** k-eff = 0.91323 2.2E-3%

I 2.6 3-D UW IMR Transient Problem  ;

Wis is a three-dimensional, two-group, linear (no thermal-hydraulic feedback), six-precursor, transient problem. '

%e simplified core contains 77 fuel elements, 20 cm on each side. Water is the reflector both radially and axially, and the active core height is  !

160 cm. Five control rods are parked in the upper reflector, and four control  !

rods are inserted from the upper reflector to the axial midplane of the core.

We transient is initiated by withdrawing the bank of four partially inserted ,

control rods at a rate of 3 cm/sec. rubsequently, the bank of five control i rods (initially parked in the upper reflector) is inserted at a rate of 3 cnVsec. We resulting transient is followed for 60 seconds. ,

Due to the way the code ARROTIA is written, a fictitious nonlinear problem is being simulated in order to get the mean power densities printed as the transient progresses.

A detailed description for this problem is provided in Figures 2-13 ,  ;

and 2-14 and Table 2-8 . In Appendix A , the reader can find the ,

corresponding input listing used for the ARROTIA calcuhtion. '

. l The reference solution adopted for this problem was presented by Langenbuch et. al. (5). In that work, two possible forms of approximation ,

were presented in orBer to solve a space-time reactor physics problem :

QUABox and CUbBOX.

Table 2-9 shows the power excursion resulting from the simulation. The ,

data obtained from an equivalent QUANDRY simulation are also presented. A  !

good agreement with the reference values is observed.

The choice of Langenbuch's results as reference for this study brings with it a slight drawback : there is a disagreement in the way the control-rod is represented. While the CUBBOX (or QUABOX) method attempts to model the ,

partially inserted rod explicitly, the methodology within ARROTIA requires that the cross sections be spatiklly constant within a node. (This problem had already been acknowledged by Smith (2) in his discussion of the "cusping" effect.) In the study presented here, the choice of a 10 cm axial mesh had the intention of minimizing such problem however, its total elimination would only be accomplished with even smaller dimensions, also requiring the adoption of new reference values (not available, never published) from th..

calculational method CUBBOX chosen here. The fact is that any well accepted calculational method carries with it some approximation to the real solution, unless it is stretched to an infinitesimal limit. The advantage of a nodal methodology lies mostly on its ability to generate acceptable results well before a minutely detailed geometric description of the problem is required.

w=

1\ \

l

0. 10. 50. 70. 90. 110.-

• x (cm)

. 21 rod i 2 I i ,

V group 2 l 1 I

1 ,

t s

rod 2/

group 1 /

I 2 3 l I

\

4 i l

y (cm) core symetry : quarter core assembly size : 20 x 20 cm external boundary condition : zero flux rigure 2-1) : Radial Description of the Southeast Cuadrant of the Reactor for the 3-D LMW IRR Transient Problem.

I e ,

C '

F Initial rod positirc5 rinal rod positions

' ,s (cm) z (cm) .

200, 2' 4 l 2h 2 ll 4 l e- 4 2 2l h

4 180.

( -gr up 1 -

l (_ Nr p 2 2 2 2 I I 100. ' l group # >

1d t k- k 1 1

4, 9"P) 20.

4 l 4 g 0. .. x l

(fa) (cm) i nodal axial length : 20 cm ,

l l Figure 2-14 : Axial Description of the Southeast Quadrant of the Reactor for the 3-D LPH LWR Transient Problem.

l

• 9

.?, 3 -

i Table 2- 8 : Material Properties Description for the 3-D IJM LMR Problem.  :

Composition Group,9 Dg(cm) 7 ( ci' ) 7 (cm' ) 0 7. ( e m' )

1 1 1.423913 0.01040206 0.01755550 0.006477691 -

2 0.3563060 0.08766217 0.1127328  ;

2 1 1.423913 0.01095206 0.01755550 0.006477691 2 0.3563060 0.09146217 0.1127328 3

3 1 1.425611 0.01099263 0.01717768 0.007503284 4

2 0.3505740 0.09925634 0.1378004 4 1 1.634227 0.002660573 0. 0*.

• E 9693 0.

2 0.2640020 0.04936351 0. l 0 = 2.5 v3 - 1.25 x 10 cvs

-k = 3.204 x 10 W.s/ fission v, - 2.5 x 10 cvs ramily,d [Lg Xj (s ~ )

1 0.000247 0.0127 2 0.0013845 0.0317 3 0.001222 0.115 4 0.0026455 0.311 5 0.000832 1.40 6 0.000169 3.87 l

Perturbations :

Rod group 1 remmed at 3.0 cv s , O < t < 26,666 s Rod group 2 inserted at 3.0 cm/s , 7.5 < t < 47.5 s

l Table 2-9 : Power Excursion for the 3-D LMht LWR Transient Problem.

Comparison of four different solutions.

Mean Power Density (W/cc)

Time (s) QUABCX CUBBOX ARR WIA QUANDRY 0.0 150.00 150.00 150.00 150.00 1.0 152.47 152.09 152.01 (-0.1%) 151.91 (-0.1%)

2.0 155.27 154.96 155.30 ( 0.2%) 155.11 ( 0.1%)

5.0 167.09 167.18 167.69 ( 0.3%) 167.86 ( 0.4%)

10.0 196.56 198.18 197.78 (-0.2%) 200,14 ( 1.0%)

15.0 232.48 235.24 230.84 (-1.9%) 236.08 ( 0.4%)

l 20.0 255.61 257.81 249.78 (-3.1%) 256.24 (-0.6%)

25.0 250.38 250.12 239.11 (-4.4%) 244.54 (-2.2%)

30.0 217.88 214.23 203.37 (-5.1%) 205.58 (-4.0%)

40.0 133.32 129.30 122.16 (-5.9%) 122.01 (-6.0%)

50.0 80.26 78.84 76.22 (-3.3%) 75.45 (-4.3%)

60.0 61.04 59.77 58.44 (-2.2%) 57.87 (-3.2%)

l l

CUBBOX results are taken as reference for the calculation of the relative error.

f

i i

Section 3

• XDCH T!WNSIDirS ANM.,YSIS i

'the availability of experimental data to be used for comparisons ,

always represents an important asset in the evaluation of a simulation code.

In this section, ARRCSTA is used to represent two events observed at the Duke Power Co. Catawba Unit I related to xenon poisoning of the core.

In doing so, not only is the overall capability of the code under analysis l but, more specifically, its xenon modeling is being tested.

The two sune events are also simulated making use of ICDE P2 (6) ,

which is of wides read use among the utilities. The disadvantages of-chosing a more si lified approach when trying to simulate these transients is enforced when e results predicted by ARRCnTA show a much closer ,

agreement with the experimental data.

5 9

t

t I

3.1 Arymuthal Xenon oscillation he ARROTTA advanced nodal code was applied to simulate an actual xenon oscillation that occurred during the startup testing of the Duke Power Co. Catawba Unit I.

he ARRWTA input generation for the Catawba model, its static verification, and its relationship to the standard core follow procedure are discussed in another document (7). Each assembly was represented with only one node in the radial plane and twelve axial nodes.

Catawba Unit I is a modern Westinghouse 4 loop 3411 PWTh reactor with 193 assemblies of 17 x 17 ora fuel in three enrichments of 1.6, 2.4, and 3.1 w/o enriched U-235. During its Bob testing (8), as part of the "below bank rod test," Catawba-1 had a single asymetrili control rod (D-12) inserted into the core long enough to excite, upon removal, a full core xenon oscillation. Wree hours elapsed in movino this rod from the top of the core to full insertion, where it remained in place for eight hours. It was then removed completely in two hours. The experimental oscillation was followed analytically for two complete periods or another two days. The utility format for reporting the data is to compare the average of the measured results to each individual measured result; thus obtaining a maximum quadrant tilt (MQT).

Due to the placement of the external detectors on the diagonals in the Catawba plant, it is most accurate to use the two assemblies straddling the diagonal which are closest to the detector location as a measure of the- 1 normalized detector response. Although the quarter-core integrated powers '

do show the proper behavior qualitatively, they cannot be as representative of the power response at the edge of the core as the actual diagonal edge assemblies. he ARROTIA generated MW based on the edged assemblies or on the quarter-core integrated powers are shown in rigures 3-1 and 3-2 ,

respectively. In both cases the period of the data is quite well reproduced; however, only rigure 3-1 shows results that agree in amplitude with the measured data. Not only do these calculations demonstrate the ARRCfrTA spatial xenon transient capability, but dramatically show the consistent correlation between edge assembly powers and excore detector response.  ;

i 1

, r o, .

it i '-

y/

A standard PWR nodal code, NODE-P2-(6), was also used to calculate this event with an MQT. NODE-P2 reproduced the time scale of this oscillation well, but did a poor-job at matching the MQT actual severity

'of the tilt versus the experimental information as also shown in both-Figures 3-1 and 3-2 .. W e NODE-P2 prediction of MQT were consistently _ low.

NODE-P2 does an accurate core follow analysis including equilibrium xenon-upon proper normalization to higher order calculations. However,'this type of extreme asymetric oscillation is beyond its basic core follow capability.

We superiority of the advanced nodal methodology of ARROFIA versus

-the standard nodal methodology of NODE-P2 is based on the difference of the-neutronic modeling inherent in the two programs. ARROFIA has a true-two group flux solution and an explicit spatial representation of the baffle / reflector regions while NODE-P2 simply uses leakage factors (albedo like quantities) that are constant throughout the event m is approximation for the reflector tends to damp out the amplitude of such radial oscillationr.. that is, the reflector bour.dary conditions tend to enforce the full core symetry even when it is not appropriate. Also, in the case specifically of ARROITA versus NODE-P2, the ARROFIA two group input cross sections as a function of the feedback parameters provides a more precise representation than the k-infinities and M-square formulation of NODE-P2.

Thus, ARROTIA has been validated against-actual reactor data for spatial xenon oscillations of substantial amplitude.

l l

j,,y

'y ,

1 l >;

t l

i l 'l ll I

).f QaARROTTA i NODEP2: l 3 ,

. ......,..g,....... .i.........i.........

, j 1,

l o - .

l1 l J 1

1 I, - -

j r . . .

1 . . J

< tn. 8,

• _ .I i: yo w

.1 i

)y s

?

l l~ .

H- . .

Q . . s

.E .

f .

e

., o . s .

1

. f .

l .

.{

1 .

l

.s, * -

l. .

s -

........i i., ..i.

f .d .. .. , . .,.

m -

I

0. - 20 40 60 80 TIME (HRS) .l l

l l

• measured data (using average ex-core powers) ,

l 1

. Figure 3- 1 : Catawba-I Xenon Oscillation. MQT values based on the

'l l Edge Assemblies Powers compared to measured Data. l l

1

. .. t r

a 1

4 5

A MEEP2 QDARROTTA

., ii ii. .-P . i ; 4 .., 3 i i . j .: 6 i i i i , . .. '

3

-o :  :

. 1

- a _ ,

g ,

ig .

{-

a .

y .

N E o 1

t

. .j l .

t L- . 1 .

g '

I' -

., s ,

e' j , , , , , , E, i , , . ,

i, , , , i , , , ,

O. 20 40 60 .80 TIME CHRS)

• measured data (using average ex-core powers) l' l'

' Figure 3- 2 : Catawba-I Xenon oscillation. MCrr values based on the '

Quarter-Core Integrated Powers compared to measured l

Dath.

l: 4 I'

t l'. .

p -

13.2 Peak Xenon Override  ;

.. During a load rejection operational transient at the Duke Power Co.

• Catawba !! nit I cycle 1, operating conditions were such that just lowering the power level was not sufficient to keep the plant operational..

Consequently, about two hours into this operational sequence, the rods were

' fully inserted and the reactor shutdown until the secondary situation could r

, M be rectified. Once this was accomplished, calculations by the utility's online system, based on an approximate NODE-P model, inferred that there was sufficient margin to safely approach criticality eventhough the core- ,

xenon conditions were now well above the equilibrium values. In fact, they  !

were quite close to the peak xenon poisoning and when the control rods were pulled to their expected critical positions, no criticality ensued. The- -

transient xenon model available to the operations staff had underpredicted the xenon worth. Later, when the xenon had decayed further, the road to criticality was easy both operationally and calculatior. ally.

Post-incident analysis by the utility with the NODE-P model used inhouse indicated that-criticality was barely achievable, while the H experimental count rates seem to infer that the reactor had only gone about 8% of the way from the safe shutdown state to criticality.

This core condition was here analysed with ARROTIA, making use of the

' ARMP-02, ENDF-B/V based xenon and iodine yields. In order to reproduce the utility's procedures when studying the case, the code NODE-P2-(6) was used to perform an exactly equivalent analysis; therefore allowing a fair

' comparison of the results obtained. These problems were run at a single fixed soluble boron poison of 618 ppm.

The ARROTTA results show a calculational model that follows the observed reactor behavior'better than the analysis performed with the use of NODE-P2 . Figure 3-3, for example, shows that the eigenvalue difference, which starts at .001 for the steady-state, grows up to a value of .005 by the end of the xenon event, with ARROTIA showing the smallest value, which agrees with the fact that the core was further away from achieving criticality than initially thought. This same data is also presented in Table'3-1.

Some f  ; ors contribute to the discrepancy between the two codes. In ARRtyrIA, the anon / iodine information is allowed to be composition and burnup dependent, which represents a greater degree of detail when compared to NODE-P2. Also, as already mentioned in subsection 3-1, the nodal methodology adopted for ARROFIA, together with the more detailed description of the core, results in a more realistic flux distribution.

E .AW4a Fa'.-- * .(- . - . . .,h.-.# .aa_,,awa; &,,a m, , , , , , . . , , ,, ,_ _ _,

& f

,;0 h.?l', , . . -

fi 4

k y

D.

g >

0. o 6'ARROTTA a NE)EP2 i 6 e i i i g6 e i e 4 e i i i, g . 4 & 1 4 6 4 4 6 gi4 e e i a t i e gie e

• 8

- 9 m a

.O . . i C. =

emi 8

4 6 -

1 m- .

1. m e l%

= .

G M

W W 5e

=

> 0 Z -

W .  !.

g .

= _ .

U . - -

Q :

e f:. e O 9 N

m o e e W

W C : ,

A G.$ g W W m

a S

M 9

4

- , , , , , I l , , , , I , .

4 8 12 16

.f 0 l L TIME CHRS)

I, i

l; l l

i i., .,

I I

Figure 3- 3 : Catawba-I Xenon override. Eigenvalue Evolution.

1 l

l ' - '

p , , .

.* j

,1, l

t Table 3-1: Catawba-I Xenon override. Eigenvalue Evolution.

Time Power Level Eigenvalue Eigenvalue Hours Qtr. Core ARRCTFIA NODEP-2 s

0.00 835.70 1.00350 1.00452 0.25: 349.60 1.01100 1.01093 0.50 349.60 1.00940 1.00964 0.75 272.90 1.00920 1.00953 '

1.00~ 230.20 1.00830 1.00883 1.25 187.60 1.00750 1.00812 i

1.50 145.00 1.00660 1.00738 -!

1.75 93.80- 1.00580 1.00673 2.00 42.60 1.00500- 1.00601 2.25 21.40 0.98190 0.98451 1 2.50 0.10 0.98010 0.98341 2.75 0.10 0.97870 0.98144-3.00 0.10 0.97670 0.97986 3.25 0.10- 0.97500 0.97840 3.50 0.10 0.97340 0.97704 3.75 0.10 0.97190 0.97578 4.00 0.10 0.97040 0.97461  ;

4.25 'O.10 0.96910 0.97353 ,

4.50 0.10 0.96780 0.97253 4.75 0.10 0.96670 0.97161 5.00 0.10 0.96560 0.97077 5.25 0.10 0.96470. 0.96999 5.50 0.10 0.96380 0.96928 5.75 0.10 0.96300 0.96863 '

6.00 0.10 0.96230 0.96804 6.25 0.10 0.96160 0.96750.

6.50 0.10 0.96090 0.96701

6. 7 5 -. 0.10 0.96030 0.96658 '

7.00 0.10 0.95980 0.96619 7.25 0.10 0.95940 0.96584 7.50 0.10 0.95900 0.96554

.7.75 0.10 0.95870 0.96527 8.00 0.10 0.95840 0.96504 8.25 0.10 0.95890 0.96485 8.50 0.10 0.95860 0.96469 8.75 0.10 0.95840 0.96456

/.

,. ^1 f

b Table 3-1: Catawba-I-Xenon Override. Eigenvalue Evolution. (Cont'd)  ;

Tine. Power Level Eigenvalue Eigenvalue Hours Qtr. Core ARRCTIA !ODEP-2 9.00 0.10 0.95830 0.96447 9.25 0.10 0.95820 0.96440 9.50 0.10 0.95820 0.96436 9.75 0.10 0.95820 0.96434 .

. 10.00 0.10 0.95820 .0.96435 '

10.25 0.10 0.95820 0.96438 10.50 0.10 0.95820 0.96444 10.75 0.10 0.95830 0.96452  :

11.00 0.10 0.95840 0.96461 11.25 0.10 0.95850 0.96473 11.50 0.10 0.95870 0.96487 11.75 0.10 0.95680 0.96502 12.00 0.10 0.95900 0.96519 12.25 0.10- 0.95920 0.96538 12.50 0.10 0.95940 0.96558 '

1:2.75 0.10 0.95970 0.96579 13.00 0.10 0.95990 0.96602 13.25 0.10 0.96020 0.96626 13.50 0.10 0.96050 0.96652 -

13.75 0.10 0.96080 0.96678 14.00' O 10 0.96110- 0.96705 14.25 0.10 0.96140 0.96735 14.50 0.10 0.96170 0.96765 14.75 0.10 0.96210 0.96796 15.00 0.10 0.96240 0.96827 15.25 0.10 0.96280 0.96860 15.50 0.10 0.98630 0.99151 J

l l:

% e n-. '

e _

n f

Section 4 HEAT CONDUCTION MODELS he heat cenduction model adopted.for ARRC7 PIA is based on the one developed for the code BEAGL (9), where an analytical approach is used in order to find the average fuel (pellet) temperature, average gap-temperature, clad-inner surface temperature, and clad outer surface temperature for each node within the core. Wis method represents a significant change from a more commonly used finite difference technique; L yet allowing a simpler solution programming, with still accurate results.

In this section, ARRCfrIA is compared against well accepted codes on the basis of the tenperature predictions. l l

VIPRE-1 (10) is a complex thermal-hydraulic code devoted to a I thourough description of the coolant as it passes through the core in a steady-state or a transient condition. A great deal of detail is allowed for this representation, including the solution of the heat conduction in i

' the fuel rod by means of a user chosen mesh space grid within the pellet l and clad.

In order to fairly compare the results coming from ARROTIA and s VIPRE-1, two exactly equivalent calculational models for a reactor core in -!

- a steady-state condition were developed. Figure 4-1 shows the' axial power distribution of radial-average fuel temperature for several VIPRE cases and for'the ARRCTTIA case. It is clear from this comparison that there is no significant difference between VIPRE with 4 or more Indial fuel pin nodes and ARICITA.

s 4

4

~

_-'. _ _ _ _ _ _ _ _.___ . ______ _ _ _ _ _ _ _ .- .. , ~ . - - - - -

~* y.a-. .

y, y

. a. . - . --- . .. .;

L

. . _ _ . . _ _ . . . . - . . r r .  :

?' -. ..

n - - - . . . . . . . . . . . . - ..

o .

.. . ..J. . .. . . .. _ - - . ... .

g ,

v, a .

.v v es==.

}

(.-'

( p.us i

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REFERENCES c L1. R.'D. Lawrence, "A Nodal Green's runction Method for Multidimensional Neutron Diffusion Calculations", Ph.D. Thesis, Nuclear Engineering Program, University of Illinois at Urbana-Champaign (1979).

2. ' K. S. Smith, "An Analytical Nodal Method for Solving the 'Ivo-Group,  !

Multidimensional, Static and Transient Neutron Diffusion Equations",

Nuc. Eng. Thesis,. Department of Nuclear Engineering, Massachusetts Institute of Technology (March, 1979).

s i

3. D. R. Vondy, T. B. Fowler, and G. W. Cunningham, "VENRJRE : A Code Block for Solving Multigroup Neutronics Problems Applying the-Finite-Difference Diffusion-Theory Approximation to Neutron Transport",

ORNL-5062, Oak Ridge National Laboratory (1975).

4. L. A. Hageman and J. B. Yasinsky, " Comparison of Alternating-Direction Time-Differencing Methods with other Implicit Methods for the Solution of the Neutron Group-Diffusion Equations", Nucl. Sci. Eng., 3 , 431 (1970).

5. S.-Langenbuch, W. Maurer, and W. Werner, " Coarse-Mesh Flux-Expansion Method for the Analysis of Space-Time Effects in Large Light Water Reactor-Cores", Nucl. Sci.. Engr., 63, 437 (1977).

t

6. R. D. Mosteller and M. J. Anderson, " NODE-P2 Computer Code Manual,"

Part II, Chapter 9, ARMP-02 Documentation, EPRI'NP-4574, (1988).

7. L. D. Eisenhart, W. J.'Eich, D. M. Rowan, L. H. Flores, K. P. Waldrop,.

" Advanced Nodal Code, ARROTTA,. Normalization Experience,"Trans. Am.

Nucl. Soc., 55, 596 (1988).

8. Catawba Nuclear Station Unit 1 - Startup Report, Duke Power Co., Docket 50-413, (Sept. 27, 1985).

9. D. J. Diamond, "BEAGL-01: A computer Code for Clculating Rapid LWR Core Transients", EPRI NP-3243, (1984). 2 i

10. C. W. Stewart, "VIPRE-01: A Thermal-Hydraulic Analysis Code for Reactor  ?

Cores", EPRI NP-2511, (1983).

I 1

1 1

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APPD4 DIX A ARROTIA Input Listings for Benchmark Cases .

• ~

A.1 - 2-D BIBLIS PWR Problem ,

9 9 1 0 8 8 1 1- 0 0 1- 0 1 0 1 1 1 1 0 010000 2-D BIBLIS PWR PROBLEM

• 020100 S2 3 3 S3 2 2 S20 -1 020200 1. 1.E-6 S8 1.E-6 S1 1.E-4 1.E-4 030100 1 7 2 5~ 1 6 1 3 8 030200717271138 ,

-030300 2 7 1 7 2 6 1 3 8 030400 5 2 7 2 7 1 7 3 8 030500172724388 030600 6 1 6 1 4 3 3 8 8 030700 1 111 7 3 3 8 8 8 030800 3 3 3 3 8 8 8 8 8 030900 8 8 8 8 8 8 8 8 8 040100 1-040200 2

-040300 3 040400 4 040500'5 040600 6 040700 7 040800 8 050100 11.5613 23.1226 R7 050300 100, 051300 25. R3 060101'1.4360 .0095042 .017754 .0058708 R1 060106 .36353 .075058 .096067 R1  ;

060201 1.4366 .0096785 .017621 .0061908 El 060206 .36362 .078436 .10358 R1

.060301 1.4389 .010363 .017101. 0074527 R1 060306 .36376 .091408 .13236 R1 060401 1.4381 .010003 .017290 .0061908 R1 i 060406 .36653 .084828 .10358 R1 060501 1.4385 .010132 .017192 .0064285 R1 060506 .36653 .087314 .10911 R1 060601 1.4389 .010165 .017125 .0061908 R1 060606 .36793 .088024 .10358 R1 060701 1.4393 .010294 .017027 .0064285 R1 060706 .36798 .090510 .10911 R1 060801 1.32 .0026562 .023106 .0 .0 .27717 .071596 .0 .0 990000

l

,jj A.2_ D' z!CN-1 PWR Problem

13. 13 1- 0 6 6 1 1 0 'O' 1 0 1 0 1 1 0 0 0-010000' 2-D ZION-1 PWR PROBLEM 020100 S2 3 3 S3 2 2 S20 -1

020200 1. 1.L%6 S8 1.E-6 S1 1.E-4 1.E-4 030100 2 3 2 3 2 2 3 2 2 4 4 1 5 030200 3 2 3 2 3 3 2 4 4 4 4 1 5 030300 2 3 2 3 2 2 3 2 2 4 4 1 5 030400 3 2 3 2 3 3 2 4 4 4 4 1 5 '

030500 2 3 2 3 3:3 3 4 4 1 1 1 5 030600 2 3 2.3 3'3 3 4 4 1 5 5 5 030700 3 2 3 2 3 3 4 4 4 1~5 5 5 030800 2 4 2 4 4 4 4 1 1 1 5 5 5- -

030900 2 4 2 4 4 4 4 1 5 5 5 5 5 031000 4 4 4 4 1 1 1 1 5 5 5 5 5 031100 4'4 4 4 1 5 5 5 5 5 5 5 6

~031200 1 1 1 l'1 5 5 5 5 5 5 6 6 031300 5 5 5 5 5 5 5 5 5 5 6 6 6 040100 1 040200 2 040300 3 040400 4 040500 5-040600 6 050101 10.804 21.608 R2 2.857518.7505 21.608 2.857518.7505 050110 2.8575 18.7505 2.8575 18.7505 050300-100.

051100 10.804 R6 2.8575 7.9465 10.804 R2 2.8575 7.9465 10.804 051100 2.8575 7.9465 10.804 2.8575 7.9465 10.804-051300-25. R3 060101 1.02130'.00322 .0 .0 .0 .33548 .14596 .0 .0 060201 1.4176 .00855 .01742 .00536 R1 060206 .37335 .06669 .10433 R1

-060301.1.4192: .00882 .01694 .00601 R1 060306 .37370 .07606 .12472 R1 060401 1.4265 .00902 .01658 .00653 R1 060406 .37424 .08359 .14120 R1 060601 1.4554 .00047 .02903 .0 .0 .28994 .00949 .0 .0 990000 l-i-

l L

= _ _ _ _

ii. ,

j ll a:

k mis i 1 A.3' - '3-D 'LRA BWR Static ProblemL 11 11 3 0- 6- 6 4 1 0 2 l' O 1 0 0 0 1 1 0 010000 3-D LRA BWR STATIC PROBLEM 020100-S2-3 3 S3 2 2 S20 '

020200 1. 1.E-6 S8 1~.E-6 S1 1.E-4 1.E-4~ 7 030100 2 1 1 1 1 2 2 3 3 5 5 030200 1 1 1 1 1 1 1 3 3 5 5 030300 1-1 1 1 1 1 1 3 3 5 5 030400 1 1 1 1 1 1 1 3 3 5 5 030500 1 1 1 1 1 1 1 3 3 5 5 030600 2 1 1 1 1 2.2 3.3 5 5 030700 2 1 1 1 1 2 2 3 3 5 5 -

030800 3 3 3 3 3 3 3 4 5 5 6 030900 3 3 3 3 3 3 3 5 5 6 6 031100 5 5 5 5 5 5 5 5 6 6 6 040100 5 1 5-040200 5 2 5 040300 5'3 5 040400 5 4 5 040500 5 5 5 040600 6 6 6 050100 15. R10 050300 30. 300. 30, 051300.15. El 25. R11 15. R1 '

060101 1.255 .008252 .02533 .004602 R1 .211 .1003 .1091 R1 060110 1.255 .008252 .02533 .004602 R1 .211 .1003 .1091 R1 060198 .33333E-7 .333333E-5 .0054 .0654 .001087 1.35

'060201 1.268 .007181 .02767 .004609 R1 .1902 .07047-.08675 R1 060210 1.268 .007181 02767 .004609 R1 .1902 .070471.08675 RI.

060298 .33333E-7 .333333E-5 .0054 .0654 .001087 1.35 060301 1.259 .008002 .02617 .004663 R1 .2091 .073324 .1021 R1 060310 1.259 .008002 ~.02617 .004663 R1 .2091 .08344 .1021 R1 060398 .33333E-7 .333333E-5 .0054 .0654 .001087 1.35 060401 1.259 .008002 .02617. 004663 R1 .2091 .073324 .1021 R1 060410 1.259 .008002 .02617~.004663 R1 .2091 .073324 .1021 R1  ;

060498 .33333E-7 .333333E-5 .0054 .0654 .001087 1.35 060601 1.257. 0006034 .04754 .0 .0 .1592 .01911 .0 .0 060610 1.257 .0006034 .04754 .0 .0 .1592 .01911 .0 .0 060698 .33333E-7 .333333E-5 .0054 .0654 .001087 1.35 090100 8 6 8 7 9 6 9 7 090200 6 8 7 8 6 9 7 9 1 8 1 9 2.8 2 9 3 8 3 9 4 8 4 9 5 8 5 9 l

'090200 8 1 9 1 8 2 9 2 8.3 9 3 8 4 9 4 8 5 9 5 l 100001 330. 330. j 990000 l

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- A.4 -

3-D IAEA PWR Problem 9 9 3 0. 3 3 1 1 0 2 1 0 1 0 0 0 1 1 0 010000.3-D IAEA PWR PROBLEM 020100 S2 3 3 S3 2 2 S20 -1 02020011. 1.E-6 S8 1.E-6 51 1.E-4 1.E-4 030100 2 2 2 2 2 2 2 1 3 7 030200 2 2 2 2 2 2 2 1 3 030300 2 2 2 2 2 2 1 1 3

'030400 2 2 2 2 2 2 1 3 3 030500 2 2 2 2 2 1 1 3 3 030600 2 2 2 2 1 1 3 3 3 030700 2 2 1 1 1 3 3 3 3 '

030800 1 1 1 3 3 3 3 3 3 ,

030900 3 3 3 3 3 3 3 3 3 040100 3 1 3 040200 3 2 3 040300 3 3 3 050100 10. 20. R7 050300-20, 340. 20.

051300 20. R18-060101 1.5 .01 .02 .0 .0 .4 .08 .135 .135 060110 1.5 .01 .02 .0 .0 .4 .08 .135 .135 4 060201 1.5 .01 .02 .0 .0'.4 .085 .135 .135 060210 1.5 .01 .02 .0 .0 .4 .130 .135 .135 060301.2.0 .0 .04 .0 .0 .3 .010 ;0 .0 060310 2.0 .0 .04 .0 .0 .3 .055 .0 .0 090100 1 1 1 5 5 1 5 5

-090200 3 3 ,

100001 20. 280.

990000 i

J.;

i.

1-Ai5a - 2-D TWIGL Seed-Blanket Reactor Step Perturbation Problem

• 3 3 1- 0 2 2 1 .3 1 2 1 0 1- 0- 1 1. 1 1 0 010000 2-D 'IWIGL SEED-BLANK REACIOR KINETICS PROBLEM (STEP PERT.)- -l 020100 S2 3 3 S3 2 2 S6 0-S13 -1 .

020200 1. 1.E-6~.0 .5 .01 5 .01 .01 S2 1.E-6 S1 1.E-5 1.E-4  !

020225 0.

030100 2 1 2 r 030200 1 1 2  :

030300 2 2 2' 040100 1 040200 2 050100 24. 32. 24.

050300 100.

051100 12. 12. 16, 16. 12, 12.

051300 25. R3 052100 -1.

• 052300 -1.

060101'1.4 .01. 01 .007 9.230E-14 .4 .1465 .2 2.637E-12 ~

060110 1.4 .01.01.00*i 9.230E-14 .4 .15 -.2 2.637E-12 060169 500, 1000. 50.

060198-1.E-7 .5E-5 .0075 .08 06020111.3 .008 .01 .003 3.956E-14'.5 .05 .06 7.911E-13 060210 1.3 .008 .01 .603 3.956E-14 5 .05 .06'7.911E-13

'060269 500. 1000. 50.

060298 1.E-7 .5E-5 .0075 .08 090100 2 1 1 2 090200-2 2 100000-0.0 0;0- 1 110200 0.0 1.E+5 1.E-3 0.0 200001 2000. 500. 500. 5. 0.05 0. 0. 0.01 0. 0.0101 1. 0.0001 200013 0.005 500. O. O. 0.-

~990000

'l

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A.5b -

2-D TWIGL Seed-Blanket Reactor-Rang Perturbation Problem l

'3 3 1 0 3 3 1 3 1. 0 l' O 1 0 1 ~1 1 1 0 I'.

-010000 2-D '!WIGL SEED-BLANK REAC70R KINETICS PROBLEM (RAMP PERT.)

020100 S2 3 3 S3 2 2 S6 0 S13 -1 E

020200 1.1.E-6 .0 .505 .005 .505 .005 .005' S2 1.E-6 SI- 1.E-5 1.E-4

-020225 0. -1 030100 3 2 3 i 1 030200 2 1 3 E 030300 3 3 3 L 040100.1 l l

040200 2 l 040300 3 050100 24. 32. 24.

050300 100.

051100 12. 12.-16. 16. 12. 12.

051300 25. R3 052100 -1, 052300 -1.

060101 1.4 .01 .01 .007 9.230E-14 .4 .15 .2 2.637E-12 060110 1.4 .01 .01 .007 9.230E-14 .4 .15 .2 2.637E-12 l L 060161 -0.0035 l 060169 500, 1000. 50.

060198 1.E-7 .5E-5 .0075 .08 060201 1.4 .01 .01 .007 9.230E-14 .4 .15 .2 2.637E-12

-060210 1.4 .01 .01 .007 9.230E-14 .4 .15 .2 2.637E-12 l 1

060269 500. 1000, 50.

060298 1.E-7 .5E-5 .0075 .08 060301 l'.3 .008 .01 .003 3.956E-14 .5 .05 .06 7.911E-13 060310 1.3 .008 .01 .003 3.956E-14 .5 .05 .06 7.911E-13 '

060369 500. 1000. 50. '

060398 1.E-7 .5E-5 .0075 .08-l 120300.500. 501. 501.

120400 0.0 0.2 1.0 200001 2000. 5000000.-500. 5. 0.05 0. O. 0.01 0, 0.0101 1. 0.0001 200013 0.005 500. O. O. O. '

990000 L

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A.6 - 3-D. LMW UWR Transient Problem 3 0 '4- 4 1 '3 6- 2 1 0 -1 0 0- 0 1 1 6 6-010000 3-D IMf IMR TRANSIEh7 PROBLEM '

020100 52 3 3 S3 2 2 S6 0 513 -1 .

020200 1. 184.8 0. 60. 0.5 60. 0.5 0.5 S2 1.E-6 S1 1.E-4 1.E-4 l 030100 2 1 1 2 3'4 030200 1 1 1 1 3 4-030300 1 1 2 1 3 4 030400 2~1 1 3 3 4 I 030500 3 3 3-3 4 4 030600 4 4 4 4'4 4 -l 040100 4 1 4 040200 4 2 2 040300 4'3 4 040400 4 4 4 050100 10, 20. R4 050300 20. 160. 20.

051300 10. R19~

052300 -1, 060201 1.423913 .01040206 .0175555 .006477691 8.301809E-14 060206 .356306 .08766217 .1127328 1.444784E-12 060210 1.423913 .01095206 .0175555 .006477691 8.301809E-14 060215 .356306 .09146217 .1127328 1.444784E-12 060269 500, 1000, 50.

060298 .8E-7 .4E-5 .000247 .0127 .0013845 .0317 .001222 .115

060200 .0026455 .311 .000832 1.4 .000169 3.87 >

060301 1.425611 .01099263 .01717768 .007503284 9.616209E-14 060306 .350574-.09925634 .1378004 1.766050E-12 060310 1.425611 .01099263 .01717768 .007503284 9.616209E-14 060315 .350574 .09925634 .1378004- 1.766050E-12 060369 500. 1000. 50.

060398 .8E-7 .4E-5 .000247 .0127 .0013845 .0317 .001222 .115 060300 .0026455 .311 .000832 1.4 .000169-3.87 060401 1.634227 .002660573 .02759693 .0 .0 060406 .264002 .04936351 060410.1.634227 .002660573~.02759693 .0 .0 060415 .264002 .04936351

'060469 500. 1000. 50.

060498 .8E-7 .4E-5 .000247 .0127 .0013845 .0317 .001222 .115 060400 .0026455 .311 .000832 1.4 .000169 3.87

- 090100 1 4~4 1 ,

0 -090200 1 1 3'3 100001 100. 180.

-110101 0. 3. 26.666 0, 110201 0. O. 7.5 -3. 47.5 0.

200001 2000, 500. 500. 5. 0.05 0. O. 0.01 0. 0.0101 1. 0.0001 200013 0.005 500. O. O. O.

- 990000 r

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