Coupled 3D Reactor Kinetics and Thermal-Hydraulic Code Development Activitiesat the U.S. Nuclear Regulatory Commission

(for presentation at M&C’99 in Madrid, Spain, Sept. 27-30, 1999)

by

D. Barber(l), R.M. Miller, H. JOO(2),T. Downar (Purdue Unive~ty),W. Wang (SCIENT.ECH, Inc.),

V. Mousseau(3), D. Ebert (USNRC)

ABSTRACT

The USNRC version of the 3D neutron kinetics code, PurdueSimulator (PARCS), has been coupled to the USNRC thermal-hydraulic (T/H) codes RELAP5and the consolidated TRAC (merger of TRAC-BF1 and TRAC-PF1). These coupled codes maybe used to audit licensee safety analysis submittals where 3D spatial kinetics and thermal-hydrau-lic effects are important. The coupling scheme was designed and implemented with emphasisplaced on maximizing flexibility while minimizing modifications to the respective codes. In thisdesign, the T/H and neutronic codes function independently and utilize the Parallel Vh-tualMachine software to communicate with each other through code specific Data Mapping Routines,and a General Interface. RELAP5/PARCS validation results are presented for two NEACRP rodejection benchmark problems. The validation of TRAC-M7PARCS has ordy recently been initi-ated, nonetheless, the capabilities of the coupled code are presented for a typical PWR sys-terdcore model.

1. INTRODUCTION

In an effort to more easily assess various combinations of 3-D neutronic/thermal-hydrauliccodes, the USNRC has sponsored the development of a generalized interface module (Barber,1998). Using this interface, the USNRC version of PARCS, an advanced reactor core simulatordeveloped at Purdue University (Joo, 1998), has been coupled to the USNRC system analysis

codes RELAP5(4J and TRAC-M(5).

In this scheme, the thermal-hydraulics, general interface, and spatial kinetics codes func-tion independently and utilize the Parallel Vktual Machine (PVM) software (Geist, 1994) to man-age inter-process communication. In order to facilitate this design, customized routines are

(1) Present Address - SCIENTECH, Inc.(2) Present Address - Korea Atomic Energy Research Institute

. (3) Present Address - Los Alamos National Laboratory(4) NRC beta version for developmental testing purposes.(5) NRC developmental version of the merged TRAC-BF1 and TRAC-PF1 codes.

DISCLAIMER

This report was,.prepared as an account of work sponsor~dby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.

DISCLAIMER

Portions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.

utilized which handle the communication between the General Interface and the thermal-hydrau-lic/neutronic processes. These routines help to both minimize and localize the changes necessaryto the thermal-hydraulics and spatial kinetics codes. An illustration of this designshown in Fig. 1.

-concept is

LJThermal

HydraulicsInput

MemoryStructure

(A)

MemoryStructure

(AB)

INeutronicsInput

I I

I

INeut. sideI

‘“:$Y d

M\l~r

,:Neut.‘Data AMap

D(AB)=(B) ~, ~

MemoryStructure

(B)

Fig. 1 Diagram of Interface Implementation.

For the validation of RELAP5/PARCS, the results of two NEACRP rod ejection bench-mark problems, one at Hot Zero Power (HZP) and one at Hot Full Power (HIT), will be pre-sented. Currently, the validation of TRAC-M7PARCS has been less extensive. However, asimplified Westinghouse 4-Loop model coupled to a typical PWR core neutronic model, will beused to demonstrate the steady-state initialization and critical boron search capabilities ofTRAC-M/PARCS. Using this steady-state condition, a Loss of Coolant Accident scenario will berun to demonstrate the transient capability of TRAC-M7PARCS.

A discussion of the coupling and validation for both llELAP5/PARCS andTRAC-M/PARCS is presented in Section 3 and Section 4, respectively. It should be noted thatassessment results for both coupled codes have been presented by Miller (1999) for a PWR MainSteam Line Break benchmark problem, which has recently been formulated at Pennsylvania StateUniversity through the sponsorship of the USNRC, GPU, and the OECD/NEA (Ivanov, 1997).This problem involves a “plenum-to-plenum” core/vessel model where the time-dependent flowboundary conditions are specified. Accurate 3-D neutronic/thermal-hydraulic modeling isrequired in order to correctly predict the space-time effects arising from the asymmetric coolingof the core, and the resulting scram with an assumed stuck rod.

2. PARCS CODE DEVELOPMENT

PARCS is a modularized FORTRAN code which can be used to predict the transientbehavior of light water nuclear reactors resulting from external perturbations. The code solves thetime-dependent two-group neutron diffusion equation in three-dimensional Cartesian geometry toobtain the transient neutron flux dkribution. The first step in the solution process is to discretizethe neutron balance equations in both time and space. For the temporal discretization, thetheta-method with exponential transformation is employed in PARCS along with a second-orderanalytic precursor integration technique. The temporal discretization scheme allows sufficientlylarge time step sizes even in severe transients involving super-prompt critical reactivity insertion.For the spatial discretization, the efficient nonlinear nodal method (Smith, 1983) is employed inwhich the coarse mesh finite difference (CMFD) problems and the local two-node problems arerepetitively solved during the course of the nonlinear iteration. It has been well-documented thatthe nonlinear nodal methods perform better than the conventional response matrix formulationbecause of its lower memory requirement and the efficient linear system solvers available for theCIVE?Dproblems. It is particularly advantageous in the transient calculation because thetwo-node calculation need not be performed at every time step, leading to a very efllcient tran-sient calculation.

The major features of the code include a steady-state eigenvalue calculation, a boron criti-cality search, an equilibrium and transient Xenon calculation, a transient fixed-source calculation,and a decay heat treatment. One important feature of the PARCS nodal code which has beenadded recently is a three-dimensional pin-power reconstruction method that enables the calcula-tion of individual fuel pin power levels under both steady-state and transient conditions (Joo,1999). Through the use of the General Interface, this feature could be coupled to a subchannelanalysis code to obtain local fuel rod enthalpies under transient conditions, as well as aiding in theprediction of local DNB conditions within fuel bundles.

3. RELAP5/PARCS CODE DEVELOPMENT

The first application of the General Interface briefly described in Section 1, was to theNRC codes RELAP5 MOD3.2.2Beta and PARCS v1.O (Barber, 1998). The following sectionsdescribe both the design and the functional validation of this coupling.

3.1 Coupling of RELAP5 and PARCS

The spatial coupling of RELAP5 and PARCS relies on an internal integration scheme inwhich the solution of both the system and core thermal-hydraulics is performed by RELAP5, andPARCS only performs the spatial kinetics solution. The boundary information to be communi-cated in this scheme is discussed below. The temporal coupling of RELAP5 and PARCS isexplicit in nature, and the respective field equations of the two codes are solved with the same fre-quency. In the implementation discussed here, the RELAP5 solution leads the PARCS solution.

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In the framework of the coupled thermal-hydraulic/neutronic code, RELAP5 and PARCSare designed to be self-contained processes, which communicate with the General Interface pro-cess through the use of the constructs supplied with the Parallel Vktual Machine (PVM) package.In order to accommodate the requirements of the General Interface and minimize the coding mod-ifications to both RELAP5 and PARCS, separate code-specific data map routines are needed tomanage the transfer of data between these two processes and the General Interface. TheRELAP5-specific data map routine (RDMR) manages two basic tasks: (1) the transfer of initialand time-dependent control information needed for calculational coherency between PARCS andRELAP5, and (2) the processing and the transfer of the vectors of space-dependent solution databoth to and from the General Interface at each time step. The PARCS-specific data map routine(PDMR) manages a third task, in addition to the two mentioned above, which relates to the pro-cessing and the transfer of the spatial mapping information to the General Interface.

This mapping data is represented by permutation matrices which consist of a block struc-ture, where each block submatix corresponds to a particular solution variable (e.g. subvector) tobe permuted. The data to be mapped from RELAP5 to PARCS consist of the following thermal

hydraulic subvectors (in order): moderator temperature (T~), liquid density (P1), vapor density

(pv), void fraction (~), and boron concentration (B). These subvectors are then followed by the

heat structure subvectors (in order): average fuel temperature (~~), fuel centerline temperature

(7”), and fuel surface temperature (T’). The data to be mapped from PARCS to RELAP5 relate

to the space-dependent powers obtained from the spatial kinetics calculation, and consist of the

total power to thermal-hydraulic volumes ( Q~m ) to account for direct gamma heating to the

coolant, and total power to heat structure components ( Qy ). Fig. 2 illustrates the structure of

these permutation matrices.

5=(# of volumes) +3“(# of heat structures)

[1Tm

[P!1[1P“

[1a

[:B

Thermal-Hydraulicto NeuwonicSubmatrices

-J4

Heat Structureto Neutronic.:1[1

fSubmatrices

L’[1T?

[1T:. L

Fig. 2 Structure of the Permutation Matrices.

2“(# ofneutronicnodes)

4~+mm ,,H - Neutronic to

1[ ]

[1’i&’ P Qt Thermal-Hydraulic252922 [1HS Submatrix

r

Qtzi=lz~**

Nekronic toHeat StructureSubmatrix

The process flow for RELAP5/PARCS begins with independent input processing forRELAP5 and PARCS, which is followed by respective calls to the RDMR and PDMR to synchro-nize the calculation and setup the communication between RELAP5, the General Interface, andPARCS. Once this is complete, the second unit of the RDMR is called to transfer thermal-hydrau-lic initial condition data to the General Interface. This data is then used by PARCS to incorporateappropriate feedback into the cross sections and construct the linear system to be solved. PARCSthen performs an eigenvalue calculation to obtain the core k-effective and initial power shape, andcalls the third unit of the PDMR to send the space-dependent neutronic powers to the GeneralInterface. The third unit of the RDMR is called by RELAP5 to receive these powers and mapthem to the appropriate RELAP5 memory locations.

The time-dependent calculation is initiated by first advancing the heat conduction andhydrodynamic solutions. Following this solution, the second unit of the RDMR is called to pro-cess all necessary time- and space-dependent thermal-hydraulic data and send this data to theGeneral Interface. The second unit of the PDMR is called to obtain this data from the GeneralInterface. Once this data has been received and stored in memory, PARCS incorporates theappropriate feedback into the cross sections, constructs the linear system, and performs thetime-dependent spatial kinetics solution for the time step dictated by RELAP5. PARCS then callsthe third unit of the PDMR in order to transfer the time- and space-dependent neutronics power tothe General Interface. The third unit of the RDMR receives and stores this data in RELAP5 mem-ory, and returns control to RELAP5, which will perform the thermal-hydraulic calculation if thefinal time step has not been performed. This procedure, which is depicted in Fig. 3, is repeateduntil RELAP5 indicates that the calculation should be terminated, or a fault signal is detected. Itshould be noted that this procedure is the same for steady-state initialization cases.

.

l_E&w!J Initialiwtion~&sino I

1m::[-]-psrmutation matrbs

-1-Advance Thermal-Hydraulic Solution- 1

RELAP5-to-PARCS Mappfng

--+em’’’’””?B

Update CrossSections andLinear System

Compute NodalPowers

PARCS-to-RELAP5 Mapping

obrain time-dep. POWCJ b%sfer time-gependent

&~

from General Intsrface 4-- power to General M&ace

?-*

Fig. 3 Process Flow for RELAP5/PARCS

3.2 Validation of RELAP5/J?ARCS

Two PWR rod ejection problems from the NEACRP Benchmark Specifications (Finne-mann, 1992) have been used for the validation of the RELAP5/I?ARCS coupling. These problemsare largely kinetic events where Doppler temperature is the dominant reactivity feedback mecha-nism. The first NEACRP problem examined here involves the ejection of a control assemblyfrom the center of an initially critical core at hot zero power (problem Al). The second NEACRPproblem uses the same core geometry and data, except the control rod is ejected from an initiallycritical core at hot full power (problem A2). After the ejection of the control assembly, the cou-pled neutron flux field, and temperature/fluid field equations are solved for a period of one sec-

.

end. This transient involves a large redistribution of core power and is a severeneutronics and core related thermal/hydraulics capability in a reactor simulation code.

test of the

For this problem, the PWR fuel assembly consists of an array of fuel rods and water chan-nels which are homogenized for purposes of both the neutronic and hydrodynamic calculations.Each fuel assembly of the core is modeled as one T/H channel with four radial neutronic nodes.Eighteen axial nodes are used for the neutronic model and fourteen axial nodes are used for theT/H model, with the three small axial nodes located at both the top and bottom of the core beingcollapsed into a single node. Fig. 4 illustrates this neutronic and thermal-hydraulic discretization.

nActive Fuel

l!%

Reflector

Composition

—.

,.

. ..

NodalFissionPower ~

4

ZoneTempJOens.

..---- —.—--- —..

•1 Fuel Assembly ❑ Reflector

❑✎✎✎✎✍✍✍✍✍:-:-:-:-. Rodded Fuel Assembly----

IIzlRod to be Ejected

.-. ...-.

lQlBank to be Withdrawn

Neutronic Node T/H Volume/Heat Structure

Fig. 4 NEACRP Model: Left - Axial Nodalization; Right - l/8-Core Neutronic Model.

The solution was analyzed by comparison with a published reference solution (Knight,1996) obtained by using a finer spatial and temporal resolution than in standard calculations. Thetransient core power and doppler temperature response for the NEACRP-A1 problem is shown inFig. 5, and the transient core power response for the NEACRP-A2 problem is shown in Fig. 6. Asindicated in Fig. 5 and Fig. 6, RELAP5/PARCS closely matches the reference solution of PAN-THER for both problems.

.

I

) 1.0 2.0 3.0 4.0 5.0

Time (s)

Fig. 5 NEACRP (Al) Core Transient Response

Fig. 6 NEACRP (A2)

110.0

108.0

106.0

104.0

102.0

100.0(

\\ \

-. --

-------------- ~_

1.0 2.0 3.0 4.0 5.0

Time (s)

Core Transient Response.

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c>“&.f:-ly\m:.\;~,,....,,,..; . .. —-,...,.

4. TRAC-NUPARCS CODE DEVELOPMENT

The application of the General Interface was extended to the coupling of TRAC-M andPARCS v1.O (Miller, 1998). The coupling schemes used for RELAP5/PARCS andTRAC-WI?ARCS are essentially the same with minor differences. Specifically, both use an inter-nal integration scheme for the spatial coupling, and the temporal coupling is treated explicitly.One key difference between the two coupled codes is the solution sequence for the field equa-tions, which will be discussed in the following section.

4.1 Coupling of TRAC-M and PARCS

The spatial and temporal coupling of TRAC-MYl?ARCS is the same as that used forRELAP5/PARCS, however, the order of solving the field equations within TRAC-M differsslightly from that in RELAP5, as will be dkcussed in the following paragraph. In addition, theTRAC-M-Specific data mapping routine (TDMR) supports all the functionality of theRELAP5/PARCS coupled code while also providing the user with the ability to perform a boroncriticality search during steady-state calculations.

Although the coupling scheme in the TRAC-MPARCS code is explicit in nature, theorder in which the hydrodynamics, heat conduction, and neutronics equations are solved can bemodified to increase the implicitness, and thus enhance the numerical stability. In theTRAC-NVPARCS coupled code, the hydrodynamic condition is updated prior to the solution ofthe heat conduction equations. Once the hydrodynamic and heat conduction solutions have beenobtained, the neutronic nodal powers are computed at the end of the time step. This schemeshould improve numerical stability for transients in which the neutronic time constant is thesmallest and the hydrodynamic time constant is the largest. It should be noted that for situationsin which the hydrodynamic time constant is smaller than the heat conduction time constant (i.e.pressure-driven events), this scheme will have reduced implicitness. Fig. 7 depicts the processflow for TRAC-M when coupled to PARCS.

f=?TRAGM

5=TRAGMInitialization

=

TDMR(l): CommunicationInitialization

TDMR(2): TRAC-M to PARCSMapping

TDMR(3): PARIX to TRAC-MMapping

I TOMR(3) J I“v”

Fig. 7 Process Flow for TRAC-NVTDMR

As mentioned, the data map routine

,

IT IFinishi

End\

within TRAC-M supports all the functionality of theRELAP5/PARCS coupled code and provides the user with the ability to perform boron criticalitysearches within the framework of the TRAC-NUPARCS coupled code. TRAC-M performs allboron transport calculations, while PARCS uses this spatial boron concentration to incorporatefeedback into the nodal cross sections. In some steady-state calculations, it is desirable to deter-mine the global boron concentration that gives a core k-effective of unity. Because of the inherentfeedback of the boron concentration on k-effective, the determination of the critical boron con-centration is performed by PARCS. However, the results of the critical boron concentrationshould be reflected in the TRAC-M model in order to provide PARCS with thermal-hydraulicconditions consistent with those required for criticality. In order to provide this consistency,PARCS computes a ratio by which the spatial boron concentration within the TRAC-M modelshould by multiplied in order to match the boron concentration calculated by the criticality search.The data mapping routine within TRAC-M then detects whether a criticality search is being per-formed and adjusts the boron concentrations accordingly.

4.2 Validation of TRAC-NVPARCS

For the functional validation of the TRAC-NVPARCS coupled code, a simplified Westing-house 4-Loop (W4Loop) PWR model (Mahaffey, 1998) is used for TRAC-M and a typical PWR

(lo)

(TypPWR) core model is used for PARCS, where the cross sections are taken from the NEACRPBenchmark Specifications (Finnemann, 1992). The TRAC-M model consists of 33 ther-mal-hydraulic components broken into a total of 124 cells and 15 heat structures. The vesselcomponent in this model is divided into 7 axial layers, 2 radial regions, and 4 azimuthal regions,making up 56 total vessel cells. The remaining cells make up the steam generators, pressurizer,and necessary piping. The nominal power for the Westinghouse model is 3250 MW, and a singleheat structure is used to model 4 average rods, each representing 9,843 fuel rods.

As discussed in the previous section, TRAC-M7PARCS has the capability to perform acritical boron concentration (CBC) search during the steady-state initialization. To demonstratethis capability, the W4Loop/TypPWR model was initialized by allowing PARCS to perform aCBC search, and subsequently updating the boron concentration levels in the TRAC-M database.Fig. 8 displays the k-effective and boron concentration results obtained from this steady-state ini-tialization. As can be seen, convergence is not achieved until the core k-effective stabilizesaround unity. The boron concentration corresponding to this k-effective of unity is 1459.32 ppm.

1.0002, , , , 1

.$ 1.0000 -zals=~ 0.9998Yal

~ 0.9996 -

~ 1650.0cl.

s.% 1600.0A~“ 1550.0c

/3g 1500.0

8

m 1450.0 , !

0.0 50.0 100.0 150.0 200.0

Time (s)

Fig. 8 Steady-State Critical Boron Search with TRAC-NUPARCS

The event used to demonstrate the transient functionality of TRAC-M7PARCS is a Iargebreak Loss of Coolant Accident (LOCA) through a simulated hot leg break. For this event, thethree intact hot legs are lumped together, while the broken leg is modeled explicitly. The brokenloop is modeled through the opening of a valve in the broken leg over the course of 0.1 seconds.This break causes a depressurization of the primary system, with significant voiding occurring inthe vessel. The depressurization and subsequent decrease in moderator density introduces a nega-tive reactivity feedback, causing a sharp drop in reactor power. Control rod scram is set at 1.4 secand represents the trip due to low pressurizer pressure. The time step size for this problem was

dictated by TRAC-M with an allowable range between 1 ms and 100 ms, and the average timestep size was approximately 30 ms.

The transient summary for this event, which was analyzed for a period of 25 seconds, isshown in Fig. 9. The depressurization due to the break is evident in the power response shown inthe figure. The scram signal which was received at 1.4 seconds caused the control rods to scramin over a period of 2.4 seconds. The oscillation seen in the control rod component of reactivity,and thus the total reactivity, is non-physical and arises from the nodal update scheme used in thePARCS model.

15.0 , a ,~ — Totalg 10.0 - —– Dopplerc(u 5.0 -

--- Densityso --- Control RIM ------------ .----- ----

-z-—-———-—————— ————

e -5.0 ->.= -10.0 -.=oa -15.0 - .~-

L%-20.0 , t , ,

Tb 80.0 -

%3 60.0 -

20> 40.0 -.-5

2 20.0 -

0.0 ,

0.0 5.0 10.0 15.0 20.0 25.0

Time (s)

Fig. 9 Transient Summary for Westinghouse 4-Loop/Typical PWR Model

5. SUMMARYz=

The successful coupling of PARCS to the USNRC system thermal-hydraulics codes,RELAP5 and TRAC-M, has been presented. The validation of the RELAP5/PARCS couplingwas performed using two rod ejection problems from the NEACRP LWR benchmark suite. Theresults for these problems obtained with RELAP5/PARCS compared very well against the pub-lished reference solutions. Although the validation of TRAC-NVPARCS is only in the prelimi-nary stages, the capability of this coupled code to perform both a steady-state initializationinvolving a critical boron concentration search, and a transient calculation was demonstrated for atypical PWR model.

6. ACKNOWLEDGEMENTS

This work was funded by the U.S. Nuclear Regulatory Commission, and the authors wishto acknowledge the support of Dr. Farouk Eltawila and members of the NRC staff.

7. REFERENCES

Barber, D., Downar, T. Completion Report for the General Interface in the Coupled Code,PU/NE-98-16, Purdue University, June 1998.

Barber, D., Downar, T., Wang, W. Final Completion Report for the Coupled RELAP5/PARCSCode, PWNE-98-31, Purdue University, November 1998.

Finnemann, H. NEACRP-3: LWR Core Transient Benchmark, NEACRP-L-335 (Revision 1),Nuclear Energy Agency, January 1992.

Geist, A., Beguelin, A., Dongama, J., Jiang, W., Manchek, R., Sunderam, V., 1994. PVM: Paral-lel W-tual Machine, MIT Press, Massachusetts.

Ivanov, K., Beam, T., Baratta, A., Irani, A., Trikouros, N. PWR MSLB Benchmark - Final Speci-fications, NEA/NSC/DOC(97)15, Nuclear Energy Agency, October 1997.

Joo, H., Barber, D., Jiang, G., Downar, T. PARCS: A Multi-Dimensional Two-Group ReactorKinetics Code Based on the Nonlinear Analytic Nodal Method, PU/NE-98-26, PurdueUniversity, September 1998.

Joo, H., Zee, Q., Downar, T., Ebert, D. Consistent Analytic Pin Power Reconstruction Method forStatic and Transient Reactor Safety Analysis, Proc. ML Con. Math. Comp., Madrid,Spain, Sept. 27-30, 1999, submitted.

Knight, M.P., Bryce, P., 1997. Derivation of a Refined Panther Solution to the NEACRP PWRRod Ejection Transients. Proc. IntL Cor$ Math. Comp., pp. 302-313, Saratoga NY, Oct.5-9.

Miller, R., Downar, T. Completion Report for the TRAC-M-Specific Data Map Routine in theCoupled TRAC-IWPARCS Code, PUINE-98-34, Purdue University, November 1998.

Miller, R., Joo, H., Barber, D., Downar, T., Ebert, D. Analysis of the OECD MSLB Benchmarkwith RELAP51PARCS and TRAC-MIPARCS, Proc. Intl. Con. Math. Comp., Madrid,Spain, Sept. 27-30, 1999, submitted.

Smith, K., 1983. Nodal Method Storage Reduction by Nonlinear Iteration, Trans. Am. NUCL Sot.,44,265.

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