Annals of Nuclear Energy 73 (2014) 122–130

Contents lists available at ScienceDirect

Annals of Nuclear Energy

journal homepage: www.elsevier .com/locate /anucene

Coupled 3D neutronics/thermal hydraulics modeling of the SAFARI-1MTR

http://dx.doi.org/10.1016/j.anucene.2014.06.0180306-4549/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: 206 Reber Building, University Park, StateCollege, PA 16802, United States. Tel.: +1 814 865 0040; fax: +1 814 865 8499.

E-mail addresses: amrmecheng@gmail.com (A. Rosenkrantz), mna109@psu.edu(M. Avramova), kni1@psu.edu (K. Ivanov), rian.prinsloo@necsa.co.za(R. Prinsloo), danniell.botes@necsa.co.za (D. Botes), khalid.elsakhawy@necsa.co.za(K. Elsakhawy).

Adam Rosenkrantz a, Maria Avramova a, Kostadin Ivanov a,⇑, Rian Prinsloo b, Danniëll Botes b,Khalid Elsakhawy b

a Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, United Statesb Radiation and Reactor Theory Group, South African Nuclear Energy Corporation, South Africa

a r t i c l e i n f o

Article history:Received 31 December 2013Received in revised form 7 June 2014Accepted 9 June 2014

Keywords:NeutronicsThermal hydraulicsModelingNuclear reactorCoupling

a b s t r a c t

The purpose of this study was to develop a coupled accurate multi-physics model of the SAFARI-1 Mate-rial Testing Reactor (MTR), a facility that is used for both research and the production of medical isotopes.The model was developed as part of the SAFARI-1 benchmarking project as a cooperative effort betweenthe Pennsylvania State University (PSU) and the South African Nuclear Energy Corporation (Necsa). It wascreated using a multi-physics coupling of state of the art nuclear reactor simulation tools, consisting of aneutronics code and a thermal hydraulics code.

The neutronics tool used was the PSU code NEM, and the results from this component were verifiedusing the Necsa neutronics code OSCAR-4, which is utilized for SAFARI-1 core design and fuel manage-ment. On average, the multiplication factors of the neutronics models agreed to within 5 pcm and theradial assembly-averaged powers agreed to within 0.2%.

The thermal hydraulics tool used was the PSU version of COBRA-TF (CTF) sub-channel code, and theresults of this component were verified against another thermal hydraulics code, the RELAP5-3D systemcode, used at Necsa for thermal–hydraulics analysis of SAFARI-1. Although only assembly-averaged resultsfrom RELAP5-3D were available, they fell within the range of values for the corresponding assemblies in thecomprehensive CTF solution. This comparison allows for the first time to perform a quantification of steady-state errors for a low-powered MTR with an advanced thermal–hydraulic code such as CTF on a per-channelbasis as compared to simpler and coarser-mesh RELAP5-3D modeling. Additionally, a new cross section rep-resentation was used to ensure that the thermal hydraulic feedback effects on the core neutronics were cap-tured as accurately as possible. This cross section representation was applied to SAFARI-1 core calculationsfor the first time in this work. Such implementation helps to quantify the effect of detailed modeling of ther-mal–hydraulics feedback effects on neutronics results in multi-physics simulations.

The outcome of the study is the intended coupled neutronics/thermal–hydraulics model of theSAFARI-1 reactor.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The objective of the performed nuclear reactor core neutronics,thermal hydraulics, and coupled modeling presented in this paperis to contribute to the South African Fundamental Atomic ResearchInstallation (SAFARI-1) benchmarking project (Prinsloo et al.,2008).

In order to explore the importance of multi-physics modelingfor the simulation of reactors such as SAFARI, two tools simulatingdifferent physics phenomena in the reactor core were coupled. Inthis case a neutronics simulator and a thermal hydraulics codewere coupled. To ensure that both coupling components werevalid, their models of SAFARI-1 core were developed and testedseparately, and compared to similar codes implemented by theNecsa’s Radiation and Reactor Theory Group (RRT). After the standalone tools were verified, the multi-physics coupling was com-pleted and tested.

The general approach of the project was to model the reactorusing neutronics and thermal hydraulics computational software.The Pennsylvania State University (PSU) code Nodal ExpansionMethod (NEM) code was used to develop a SAFARI-1 MTR

Fig. 1. Radial view of SAFARI-1 core and reflector. Note that the figure is not drawnto scale, and that measurements are given along the bottom and right axes (Prinslooet al., 2008).

A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130 123

neutronics model (Dynamics and Management Group, 2012). Thisis a deterministic nodal diffusion code that can be used for three-dimensional (3D) nuclear reactor simulations for steady-state con-ditions and transient scenarios. The thermal hydraulics code usedfor the coupled multi-physics modeling is the Coolant Boiling inRod Arrays-Two Fluid (COBRA-TF). The original sub-channel codehas been maintained, further developed and modified by the Reac-tor Dynamics and Fuel Management Group (RDFMG) at PSU to cre-ate a new version called CTF, which has been previously used tocontribute to several other benchmarking projects (Dynamics andManagement Group, 2012). A CTF thermal hydraulics model wascreated in cooperation between PSU and Necsa staff.

The reference solution, against which the neutronics model pre-dictions were compared, was generated with the Overall Systemfor Calculation of Reactors (OSCAR-4) Stander et al. (2008). The ref-erence solution against which the predictions of thermal hydrau-lics model were compared is the Reactor Excursion and LeakAnalysis Program (RELAP5-3D) RELAP5-3D Code DevelopmentTeam, 2005. Some aspects of the SAFARI-1 RELAP5-3D model werenot available for publication, but various specific results could becompared to the obtained results from this study, and these com-parisons are presented in Section 3.2. OSCAR-4 is utilized forSAFARI-1 core design and fuel management while RELAP-3D isused for safety analysis of SAFARI-1. As such these tools have beenvalidated using measured data from SAFARI-1.

The coupled code is called NEM/CTF, and in this study wasapplied to the SAFARI-1 research reactor, but could be used forother applications. The neutronics solution found by NEM providespower distributions for the fuel and follower assemblies to CTF,which returns fuel temperatures, moderator temperatures, andmoderator densities. Homogeneous, macroscopic cross sectionsat these thermal hydraulic conditions are then reconstructed froma polynomial cross section library for every node, and used to find anew neutronic solution in NEM. This iterative process is repeateduntil convergence is reached by the coupled code, which is deter-mined by changes in keff of less than 10�6, and relative changesin the nodal powers and state thermal–hydraulics parameters,namely fuel temperatures, moderator temperatures, and modera-tor densities, of less than 10�4, for three consecutive iterationsbetween neutronics and thermal–hydraulics solutions. The resultsof the coupled code are presented here and compared to the stand-alone models.

1.1. SAFARI-1 reactor description

The SAFARI-1 nuclear reactor is a 20 MW tank-in-pool typeresearch reactor located in Pelindaba, South Africa. In an MTR likeSAFARI-1, the reactor core is not maintained for power production,but is rather used for research and for the production of medicalisotopes. The reactor has been in operation since being commis-sioned in 1965. Though the reactor had used Highly Enriched Ura-nium (HEU) fuel for most of its time in operation, it currentlyutilizes Low Enriched Uranium (LEU) fuel since converting in2009. The SAFARI-1 benchmark problem specification used in thisstudy was developed by Necsa based on a fuel cycle that closelyresembles the fuel cycle of SAFARI-1 in 2007 (Prinsloo, 2011),and therefore contains HEU fuel.

1.2. Core specification

The core of the SAFARI-1 reactor consists radially of a 9 � 8 rect-angular array comprised of a combination of various types of assem-blies and components. The types of assemblies present in the coreare fuel assemblies, control and follower assemblies (assemblieswhich are comprised of a control segment and a fuel follower seg-ment), and reflector assemblies. The assemblies designated as reflec-

tor assemblies include aluminum water boxes, solid aluminum,hollow aluminum, solid beryllium, hollow beryllium, and solid leadassemblies. Each assembly has dimensions of 7.71 cm� 8.1 cm on atwo-dimensional (2D) plane (Prinsloo et al., 2008).

According to the SAFARI-1 benchmark specification, the reactorcore is surrounded a layer of solid aluminum, known as the corebox. This layer of aluminum has a thickness of 2.5 cm on the west,east, and south sides of the core, and 3.5 cm on the north side ofthe core. It is assumed for the sake of model construction thatthe core box is surrounded by 20 cm of water on all sides, with vac-uum boundary conditions around the water. The same assump-tions are made for the axial reflector. The radial core andreflector layout is presented in Fig. 1.

1.2.1. Assembly specificationsSAFARI-1 uses plate-type fuel, the detailed specifications of

which can be found in the benchmark specification (Prinslooet al., 2008). In total, there are 26 fuel assemblies within thereactor core, each of which contains 19 fuel plates. The details ofthe geometry of the fuel assembly and affixing mechanisms canbe seen in Figs. 2 and 3. The reactor also has six distincttypes of reflector assemblies. These are the aluminum water boxtype assembly, the hollow aluminum type assembly, the solidaluminum type assembly, the hollow beryllium type assembly,the solid beryllium type assembly, and the solid lead assembly.The terms ‘‘hollow’’ and ‘‘solid’’ here refer to a larger or smallercross sectional flow area of water through the assembly.

The primary control mechanism of the SAFARI-1 reactor con-sists of six control rod and fuel follower assemblies. The controlrod is a cadmium absorber, and the fuel follower is made up of15 fuel plates.

2. Code and model descriptions

2.1. The neutronics code

NEM is a deterministic, multi-group, 3D nodal diffusion neu-tronics solver which was developed at PSU. The primary solvingmethod used by the code is the nodal transverse integration

Fig. 2. Radial view of a fuel assembly (Prinsloo et al., 2008).

Fig. 3. Radial view of fuel assembly adaptor mechanism (above) and axial view ofentire fuel assembly (below) Prinsloo et al., 2008.

124 A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130

method, which makes use of either polynomial or semi-analyticaltransverse flux representation and a transverse leakage approxi-mation (Dynamics and Management Group, 2012). It currently

supports up to 70 energy groups. The modeling geometry optionsin NEM include 3D Cartesian, hexagonal-z, or cylindrical geome-tries, but only the Cartesian geometry was used in this study. Fortransient applications the neutron flux time dependence is approx-imated through the use of a first order fully implicit finite differ-ence scheme, which includes an exponential transformationtechnique. Neutron precursor distributions are modeled with asimpler linear time-integrated approximation. Iteration limits forinner, outer and up-scatter iterations are set by the user, alongwith convergence criteria for nodal fission sources and the effec-tive multiplication factor (Dynamics and Management Group,2012). NEM uses the Response Matrix (RM) technique for inneriterations with respect to each evaluated energy group and thestandard power iteration method for outer iterations is acceleratedby asymptotic extrapolation (Dynamics and Management Group,2012).

2.2. The neutronic model

The development of the NEM neutronics model for SAFARI-1was done primarily using the SAFARI-1 benchmark specification(Prinsloo et al., 2008). Six energy groups were used in the model,because the neutron spectrum in SAFARI-1 varies more dramati-cally within the core and is more strongly influenced by leakageeffects at the periphery than in the case of larger power reactors.This necessitates the use of more than the two group core calcula-tions that are often used for Light Water Reactors (LWR). It alsorequires correct modeling of neutron up-scattering in multi-groupformulation.

The NEM model was created using Cartesian geometry, due tothe unique assembly geometry types. The SAFARI-1 has a largelyrectangular build, and no convenient axes of symmetry, whichrequires modeling of the full core. The model assumed steady-statehot full power (HFP) operating conditions. At HFP, the core iscooled by forced top-to-bottom coolant flow with a flow rate of3050 m3/h. The nominal inlet temperature is 38 �C with an averagecoolant temperature of 45 �C and a fuel temperature of 60 �C. The

A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130 125

nominal coolant density is 0.99284 g/cm3 at atmospheric pressure.It was also assumed that the Xenon concentration had reached itsequilibrium concentration at 20 MW.

After evaluation of the behavior of the model, it was concludedthat optimal results with respect to accuracy and computationalresources are achieved with 100 outer iterations, and 4 inner iter-ations per outer iteration. Upscattering was considered for transferfrom all energy groups to all higher energy groups. It was deter-mined that two upscatter iterations per outer iteration are the bestcombination of accuracy and efficiency in NEM solutions.

Probably the most particular details of a reactor model are theway in which it is nodalized for use of the homogenized cross sec-tions. The nodalization was done for the entire 3D space of thereactor. The core was divided radially into assembly-sized node,while the outer reflector nodes were based on material boundaries,as presented in Fig. 4. Axially, the active core was divided into 13unevenly sized nodes, the sizes of which are available in the bench-mark (Prinsloo et al., 2008), resulting in a total of 2520 nodes(mesh cells) for analysis. Fixed cross sections at nominal core con-ditions were used in the stand-alone model, since no feedback wasused.

2.3. The thermal hydraulics code

COBRA-TF is a subchannel code used for thermal hydraulicsanalysis of nuclear reactors. In this study, a version called CTFwas used, which resulted from the improvements made by theRDFMG at PSU. The primary use of CTF is for estimation of safetymargins in LWR nuclear power plants. CTF makes use of a three-field representation of two-phase flow using semi-implicit, time-averaged conservation equations and donor cell differencing forconvective phenomena. The code was designed to support theuse of both Cartesian and subchannel geometric systems, the latterconfiguration being the more frequently used for standard powerreactors (Dynamics and Management Group, 2012).

CTF is a deterministic code governed by convergence criteriaand iterative limits, similarly to NEM. It applies mass, momentumand energy conservation, along with the standard theories of heattransfer. The phases and material conditions simulated by CTFinclude continuous vapor, continuous liquid, entrained liquid

9 6 2.5 7.71 7.71 7.71 7.71 7.71 7.71 7.71 7.

9

6

2.5

8.1

8.1

8.1

8.1

8.1

8.1

8.1

8.1

3.5

4.6

15

South

Eas

t

North

Fig. 4. Radial nodalization scheme of SAFARI-1 used within NEM models. Note that the fiaxes.

drops, non-condensable gas mixture, and additional fields to repre-sent the small drops field as a result of large drops breaking upupon impact with spacer grids or other blockages (Dynamics andManagement Group, 2012).

Specific phenomena modeled by CTF include: gravitation, diver-sion cross flow, head losses, interfacial drag forces, turbulent mix-ing, void drift, as well as entrainment and deposition of droplets inannular flow (Dynamics and Management Group, 2012).

CTF requires as input the full discrete description of the prob-lem geometry, as well as the main problem control data and infor-mation on power distributions. The user must therefore specify thephysical models that will be used together with boundary and ini-tial conditions and material properties tables.

2.4. The thermal hydraulic model

The CTF model of the SAFARI-1 MTR was for the purpose ofeventually creating coupled neutronics/thermal hydraulics models.Some of the assumptions that were made while constructing themodel include ignoring insignificant, thin films of water as wellas modeling hollow aluminum and beryllium assemblies as theirsolid counterparts. Care was taken to ensure that the total bypassflow was accounted for.

As was mentioned before, the model used steady-state hot fullpower operating conditions for the SAFARI-1 MTR. The nodaliza-tion scheme is the same as for the neutronics case described above.There are 72 subchannels modeled, consisting of all reactor assem-blies, and neglecting the aluminum core box and water surround-ing the core. The duration simulated is 3.0 s, for which the codeeffectively achieves equilibrium under steady-state, constantpower conditions.

An important set of input values used in the CTF model of theSAFARI-1 reactor is the radial power distribution. While the radialdistribution will be received as an output of the neutronics calcu-lation in the coupled code, with the initial distribution read intoCTF only acting as a first guess, some initial distribution must besupplied in the stand-alone model. The input therefore contains adistribution similar to the results from the stand-alone neutronicscalculations. For the axial power distributions, a different distribu-tion is given for each fuel, control and follower assembly. Like the

Fuel Assembly

Control Assembly

Water

Aluminum Core Box

Solid Beryllium

Hollow Beryllium

Solid Aluminum

Hollow Aluminum

Aluminum Water Box

Solid Lead

71 7.71 2.5 6 9

Wes

t

gure is not drawn to scale, and that measurements are given along the left and top

126 A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130

radial power distribution, the axial power distributions used in thestand-alone CTF test were close to those produced by the neutron-ics codes, and will not be of great significance in the final coupledmodel, since they will be produced anew by NEM for eachiteration.

Table 1Multiplication factors comparison of OSCAR and NEM stand-alone models.

Code keff Difference [pcm]

OSCAR 1.02288NEM 1.02294 5

2.5. The coupled code

NEM/CTF is the general name for a coupled multi-physics code,which combines the neutronics of NEM with the thermal hydrau-lics of CTF. This work was aimed at creating a coupled code thatis specifically applicable to MTR reactors with plate-type fuel,which distinguishes it from previous works that have traditionallybeen tailored for larger power reactors. The reactor nodalizationscheme for the coupling was not modified from its previousdescription. Thus, the coupling created here will be a fixed cou-pling, one which maintains a one to one relationship between sim-ulated nodal volumes. Each assembly gets one radial node in bothNEM and CTF, and axial nodes are equivalent between codes andbased on the axial material distribution.

In the steady-state coupling procedure, which is the mode usedfor this study, various feedback mechanisms serve as the primarycommunication relays between NEM and CTF. At the beginningof one iteration, the neutronics solution found by NEM providespower distributions for all nodes in the reactor core to CTF. CTFprovides nodal fuel temperatures, moderator temperatures, andmoderator densities to a polynomial interpreter. The interpreteruses a parameterized cross-section library to obtain multi-grouphomogenized cross-sections for each node based on local nodalconditions at given iteration. These cross-sections are used byNEM to create the next neutronics solution. The cross sectionlibrary used was created for beginning of cycle conditions, andtherefore contains cross sections that correspond to a core withoutany Xenon.

The homogenized six group cross sections that were used tocapture the thermal–hydraulic feedback in the coupled modelwere represented by the method described in Zivanovic andBokov (2010) and Prinsloo et al. (2009). This method allows oneto build a global polynomial approximation in a systematic waywithout assuming any pre-existing knowledge about the way thecross sections depend on the state parameters. The approximationis composed of orthogonal polynomial basis functions that are con-structed as a tensor product of one-dimensional Legendre polyno-mials. Quasi-regression (An and Owen, 2001) is used to obtain theapproximation and the regression coefficients were estimated byperforming Clenshaw–Curtis quadrature on sparse grid samples.A sparse grid is a union of low-order tensor product grids and Clen-shaw–Curtis quadrature on sparse grids is described in Gerstnerand Griebel (1998). The method has built-in error estimates, bothof the total error of representation and of the error in the coeffi-cient calculation for each polynomial term. The second estimatecan be used to exclude terms that contribute significantly to therepresentation error from the final library, which makes the libraryfaster to reconstruct from and less memory-intensive to store andread from. The contribution that each term makes to the accuracyis proportional to the square of that term’s coefficient, thereforethe library can be further reduced by excluding terms with smallcoefficients. Valuable information about the relative importanceof various state parameters can be extracted from the library byusing sensitivity analysis, which is also based on the magnitudeof the coefficients (Zivanovic and Bokov, 2010).

It should be noted that the cross-section representation meth-odology described above was applied for the first time in this studyfor whole core multi-physics calculations. The point-wise accuracyof the method has been demonstrated in Botes (2013).

The coupled code NEM/CTF has been previously verified for usefor LWR core analyses against the Purdue Advanced Reactor CoreSimulator (PARCS), a kinetic core simulator module produced byPurdue University (Gouja et al., 2010). In this verification studythe linear interpolation in 4D cross-section tables was utilized.

3. Results

3.1. NEM solutions and comparison to OSCAR solutions

The reactor multiplication factor, keff, as well as the radialpower distribution for all of the 210 radial nodes in the reactor corewas calculated using NEM. Two sets of results to the SAFARI-1benchmark problem for steady-state conditions were directly com-pared – OSCAR predictions (as reference) and NEM solutions. TheOSCAR code is a multi-group analytic nodal code, which is rou-tinely used for operational support to SAFARI-1.

The first part of the solutions to be compared is the core reactormultiplication factor. Whereas a few pcm is a fairly negligible errorin a multiplication factor, one percent (1000 pcm) error is usuallyconsidered to be an unacceptable level or error. The comparisonof keff-values as calculated by NEM and OSCAR is given in Table1. The NEM model predicts this value to be slightly higher (by5 pcm) than that one found in the OSCAR solution. This discrep-ancy in the multiplication factor is reasonable, and is in fact ofthe same order of magnitude as the convergence criterion thatwas used. In this paper, all errors are presented in absolute percentdifference, i.e. the absolute value of the difference was used.

The second part of the solution to be compared was the radialpower distribution. The differences in assembly averaged powerdistributions between NEM and OSCAR are shown in Fig. 5. Thesummary of this comparison is given in Table 2. The agreementcan be considered acceptable if the trends stay within a few%, veryclose if they are within 0.5% and ideal if they are within 0.1%(Rosenkrantz, 2012). The NEM nodal power distribution agreedwell according to the above-described guidance with the OSCARresults – the level of agreement was within 0.1% in average pernode and 0.2% as maximum in a node. These differences may beattributed to the different solution methods used in NEM andOSCAR-4.

3.2. CTF solutions and comparison to RELAP solutions

The primary role of thermal hydraulics analysis in this study isto serve as a coupled multi-physics code component along with theneutronics. As explained before, even though CTF outputs a largequantity of information, which may be very useful in some appli-cations, the predictions of interest in this study are the nodal fueltemperatures, moderator/coolant temperatures, and moderator/coolant densities.

First, we will present representative sample of the 3D detailedstand-alone CTF results, which consists of the core axially averagedradial coolant temperature distribution (see Fig. 6 – please notethat temperature values are in degrees Fahrenheit [�F]) as well asaxial coolant temperature distributions for selected assemblies.

Having presented a representative sample of the detailed CTFresults calculated for this study a comparison of the RELAP andCTF thermal–hydraulics solutions is shown in Table 3. The compar-

0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 -0.17 -0.2 -0.1 0 -0.13 0 0 0 0 00 0 0 0 0 0 -0.06 0.02 0.063 -0.12 -0.12 0 0 0 00 0 0 0 0 -0.05 0.01 0.2 0 0.07 0 0 0 0 00 0 0 0 0 0 0.122 0.139 0.186 0.075 -0.07 0 0 0 00 0 0 0 0 0.009 0.075 0.203 0 0.13 0 0 0 0 00 0 0 0 0 0 -0.04 0.11 0.112 -0.06 -0.07 0 0 0 00 0 0 0 0 -0.1 -0.11 -0.01 -0.08 -0.04 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Fig. 5. Numerical array comparison of the OSCAR and NEM stand-alone power distributions (differences in percent).

Table 2Radial power distribution comparison of OSCAR and NEM stand-alone models.

Statistic Difference [%]

Average per cell 0.10Maximum in a cell 0.20

A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130 127

ison can only be made in the form of a direct analysis of the RELAPsolutions temperatures averaged by assembly type with respect tothe range of CTF solution temperatures by node. One can, however,clearly see that there is good correspondence between the resultsand none of the assembly-averaged results from RELAP fall outsidethe range of node-wise temperatures predicted by CTF.

Fig. 7. Iterative convergence of the multiplication factor.

Table 4Multiplication factors for neutronics models.

Model or other source keff

NEM 6-group stand-alone 1.00207Coupled code iteration 10 1.00103

3.3. NEM/CTF coupled code solutions

The iterative convergence of the multiplication factor is pre-sented in Fig. 7. It is clear that convergence is reached at iterationthree. The nodal state parameters and power distributions wereused as convergence criteria as well, but only the multiplicationfactor plot is shown to illustrate that coupled convergence hasbeen achieved.

The primary purpose of this study was to ascertain the impactof thermal hydraulic feedback on the neutronics solution, in partic-ular the multiplication factor and the radial power distribution.

104.135 104.546 105.421 105.714 105.87104.134 104.839 113.498 113.021 115.67104.131 104.894 104.164 115.228 113.49104.9 105.274 112.004 112.511 113.22

105.816 105.749 105.366 111.494 113.49106.071 105.888 109.67 110.539 109.84105.714 106.104 105.67 111.464 113.49105.957 106.02 109.566 109.161 107.87

Fig. 6. Liquid coolant temperature array fr

Table 3Comparison and analysis of RELAP and CTF solutions.

Assembly type Material

Fuel assembly Liquid coolantFuel assembly Vaporized coolantControl and follower assembly Liquid coolantControl and follower assembly Vaporized coolant

These parameters are analyzed with their values obtained at thecoupled iteration 10. Though convergence was reached at iteration5, the only negative facet of carrying out further iterations is the

9 106.04 105.676 105.348 104.1319 104.22 114.422 104.195 104.4338 112.928 113.498 113.697 105.0493 104.202 113.574 105.931 105.2838 112.55 113.498 111.053 105.2541 105.694 110.938 105.976 105.4388 110.089 113.498 109.428 105.2525 109.028 108.4 105.574 105.315

om stand-alone CTF calculation in �F.

RELAP temperature CTF temperature range

111.335 107.875–115.679246.472 244.27–246.943105.850 104.195–105.976247.388 233.512–247.520

0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1.164 1.148 1.264 0 1.174 0 0 0 0 00 0 0 0 0 0 1.148 0.846 1.187 0.938 1.106 0 0 0 00 0 0 0 0 1.234 1.087 1.006 0 1.216 0 0 0 0 00 0 0 0 0 0 0.993 0.703 1.022 0.819 1.058 0 0 0 00 0 0 0 0 1.024 0.938 0.941 0 1.066 0 0 0 0 00 0 0 0 0 0 1.052 0.601 0.925 0.881 0.929 0 0 0 00 0 0 0 0 0.897 0.891 0.933 0.935 0.874 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Fig. 8. Numerical array of the updated NEM stand-alone code radial power distribution.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1.163 1.147 1.262 0 1.172 0 0 0 0 00 0 0 0 0 0 1.147 0.855 1.185 0.942 1.104 0 0 0 00 0 0 0 0 1.234 1.086 1.003 0 1.213 0 0 0 0 00 0 0 0 0 0 0.991 0.707 1.019 0.823 1.057 0 0 0 00 0 0 0 0 1.025 0.938 0.94 0 1.065 0 0 0 0 00 0 0 0 0 0 1.051 0.605 0.923 0.886 0.928 0 0 0 00 0 0 0 0 0.897 0.891 0.934 0.935 0.873 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Fig. 9. Numerical array of the coupled code radial power distribution.

Fig. 10. Three-dimensional visualization of the coupled code radial power distribution.

128 A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130

A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130 129

time required to carry out the necessary computational calcula-tions, while a positive outcome is that the solution can only eitherremain the same or become more accurate. For iteration 10, a mul-tiplication factor of 1.00103 was obtained.

The converged neutronics results of coupled code calculationswill be analyzed by comparing them to the NEM stand-alone calcu-lations. In order to perform consistent comparison the originalNEM stand-alone results presented above (in comparison withthe OSCAR results) cannot be used here because of the differentcross-section representation utilized. The original NEM stand-alone results (as well as the OSCAR stand-alone results) wereobtained using a cross-section set fixed at a steady state Xenonconcentration and other effects modeling from the nominal steadystate defined by the cross-section library based on polynomial rep-resentation used for coupled calculations. Since we want to quan-tify the effect of correct thermal–hydraulic feedback modeling theNEM stand-alone calculations were re-run using the coupled cross-section library and only fixing the moderator (coolant) and fueltemperatures and moderator density at core average values. InTable 4 the multiplication factors for the updated NEM stand-alonecalculation and for coupled NEM/CTF calculations are compared(both NEM models utilize 6 energy groups and explicit modelingof the up-scattering) showing that the coupled prediction, utilizinga more realistic representation of the thermal–hydraulic feedback,differs in about 100 pcm.

Next, the radial power distribution of the coupled calculation isexamined by comparing it with the updated NEM stand-alone cal-culations. Fig. 8 presents the normalized radial power distributionsfrom the updated NEM stand-alone calculations while Fig. 9depicts normalized radial power distributions from the coupledNEM/CTF calculations. Fig. 10 presents the same distribution inan intuitively easy to grasp 3D format. Visual inspection of Fig. 8and 9 indicates that the radial power distribution also changesbetween consistent stand-alone and coupled simulations due theeffect of better thermal–hydraulic feedback representation in thecoupled calculations. The maximum difference is 0.9%.

The effect of using the more sophisticated model is relativelysmall at the steady state operating conditions of SAFARI-1. Apply-ing multi-physics analysis as developed in this work to transientsimulations is, however, expected to have a greater impact onthe accuracy of the simulation as compared to stand-aloneneutronic or thermal hydraulic calculations.

4. Conclusions

The purpose of this study was to create a consistent model ofthe SAFARI-1 materials testing reactor. Coupled neutronics andthermal hydraulics calculations were done at steady state hot fullpower conditions as a contribution to the ongoing SAFARI-1 bench-marking project.

The study proceeded in three steps. These were the creation of astand-alone neutronics model, a stand-alone thermal hydraulicsmodel, and a coupled model which combined the two stand-alonemodels iteratively using feedback and convergence criteria.

A stand-alone computational neutronics model was developedwith NEM. The fixed cross-section set for SAFARI-1 was providedby Necsa. This cross-section set is useful only for standalone neu-tronics comparisons with different nodal (or other spatial discret-ization) methods. The results obtained with NEM were verifiedusing the Necsa’s neutronics code OSCAR. On the average, the mul-tiplication factors of the neutronics models agreed to 5 pcm, andthe power distributions per radial node agreed to within 0.2%.

Second, a stand-alone computational thermal–hydraulicsmodel was created with CTF. The CTF model of the SAFARI-1MTR was originally developed in collaboration between the

RDFMG at PSU and the RRT team at Necsa, and the model was ver-ified against the SAFARI-1 Benchmark Specification as a part of thisstudy. The model was run and its solutions were analyzed and ver-ified against another thermal hydraulics code RELAP5-3D, which isvalidated and used at Necsa for SAFARI-1 calculations. RELAP5-3Dresults were only released to a limited extent and were averagedby assembly type, but fell within the range of values for the sameassemblies in the more detailed CTF solution.

The coupled multi-physics code NEM/CTF was successfullyapplied to SAFARI-1 steady state calculations. The idea was toquantify the effect of correct and detail thermal–hydraulic feed-back modeling on neutronics results such as keff and radial powerdistribution. In order to perform consistent comparative analysisan updated NEM stand-alone steady-state calculations were per-formed using the cross-section library generated for the coupledNEM/CTF calculations. The updated NEM stand-alone results showthe following deviations as compared to the coupled NEM/CTFsteady state predictions – 104 pcm in keff and 0.9% maximum dif-ference in radial power distribution with slight change in the over-all power distribution shape. These deviations quantify the effectof correct and detailed core thermal–hydraulic feedback modelingof CTF in more realistic coupled NEM/CTF calculations. It is clearthat the impact of thermal hydraulic feedback is small at steadystate conditions, as one would expect for a low power reactor suchas SAFARI-1. The value of this work is, however, that a tool has nowbeen established with which one could, in future, analyze transientconditions and accident scenarios with full feedback modeling.

The long-term objective of the study is the intended coupledneutronics/thermal hydraulics model of the SAFARI-1 reactor, withall components having been verified through previously acceptedcodes. The next step is verification and validation of the coupledNEM/CTF simulations for the SAFARI-1 steady-state analysis alongwith the developed cross-section library based on polynomial rep-resentation. After completion of steady-state verification and vali-dation of the coupled NEM/CTF model then it can be verified/validated further to simulate transient scenarios in addition tosteady-state calculations. This tool can be used at Necsa for safetyanalysis and fuel management optimization and to support theenvisioned OSCAR developments towards extension to transientapplications and multi-physics coupling with CTF.

Acknowledgements

We would like to acknowledge the efforts of the PSU studentsDavid Colameco and Matt Kravec. We would also like toacknowledge the contribution of the Necsa representative PavelBokov.

References

An, Jian, Owen, Art, 2001. Quasi-regression. J. Complexity 17 (4), 588–607.Botes, Danniëll, 2013. Few Group Cross-section Representation Based on Sparse

Grid Methods (MS Thesis). North–West University, South Africa.Reactor Dynamics and Fuel Management Group, 2012. NEM Theory Manual.

University Park, PA: Department of Mechanical and Nuclear Engineering, ThePennsylvania State University.

Reactor Dynamics and Fuel Management Group, 2012. CTF – A Thermal–HydraulicCode for LWRs Transient Analysis, Users’ Manual, University Park, PA:Department of Mechanical and Nuclear Engineering, The Pennsylvania StateUniversity.

Reactor Dynamics and Fuel Management Group, 2012. NEM Standalone InputManual. University Park, PA: Department of Mechanical and NuclearEngineering, The Pennsylvania State University.

Gerstner, Thomas, Griebel, Michael, 1998. Numerical integration using sparse grids.Numer. Algorithms 18 (3), 209–232.

Gouja, Ilyes, Maria Avramova, Adam Rubin, 2010. Development and Optimization ofCoupling Interfaces between Reactor Core Neutronics and Thermal HydraulicsCodes, PHYSOR 2010 – Advances in Reactor Physics to Power the NuclearRenaissance, Pittsburgh, Pennsylvania, USA, 9–14 May.

Prinsloo, Rian, 2011. Personal Correspondence, 3 November.

130 A. Rosenkrantz et al. / Annals of Nuclear Energy 73 (2014) 122–130

Prinsloo, Rian, Moloko, Lesego, Bokov, Pavel, Stander, Gerhardt, Elsakhawy, Khalid,Theron, Suzanne, 2008. SAFARI-1 Benchmark Specification. South AfricanNuclear Energy Corporation, South Africa.

Rian H. Prinsloo, Pavel M. Bokov, Gerhardt Stander, Danniëll Botes, Wessel Joubert,2009. An automated cross section parametrization method for MTR application.In: International Conference on Mathematics, Computational Methods &Reactor Physics (M&C 2009), Saratoga Springs, New York, 3–7 May.

The RELAP5-3D Code Development Team, 2005. RELAP5-3D Code Manual Volume I:Code Structure, System Models and Solution Methods, Idaho Falls, Idaho: IdahoNational Laboratory.

Rosenkrantz, Adam, 2012. Coupled 3D Neutronics/Thermal–Hydraulics Modeling ofthe SAFARI-1 MTR (MS Thesis). The Pennsylvania State University.

Stander, Gerhardt, Rian Prinsloo, Erwin Müller, Djordjé Tomaševic, 2008. OSCAR-4code system application to the SAFARI-1 reactor. In: International Conferenceon Reactor Physics, Nuclear Power: A Sustainable Resource, Casino-KursaalConference Center, Interlaken, Switzerland, 14–19 September.

Zivanovic, Rastko, Bokov, Pavel M., 2010. Cross-section parameterization of thepebble bed modular reactor using the dimension-wise expansion model. Ann.Nucl. Energy 37 (12), 1763–1773.