M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017, on USB (2017)

Simulation of a Main Steamline Break scenario using the 3D neutron kinetic core modelDY N 3D coupled with the CFD software T R I O U

Alexander Grahn, André Gommlich, Sören Kliem

Helmholtz-Zentrum Dresden-Rossendorf, Institute of Resource Ecology,Department of Reactor Safety, PB 510119, 01314 Dresden, Germany

mailto:a.grahn@hzdr.de

Abstract - The reactor dynamics code DY N 3D, developed at Helmholtz-Zentrum Dresden-Rossendorf(HZDR), was coupled with the Computational Fluid Dynamics (CFD) solver T R I O U, developed at CEAFrance, in order to replace DY N 3D’s one-dimensional hydraulic part with a full three-dimensional descriptionof the coolant flow in the reactor core at higher spatial resolution. The article describes the coupling methodand shows results of its application to the simulation of a Main Steamline Break (MSLB) accident of aPressurised Water Reactor (PWR).

I. INTRODUCTION

Reactivity and thermal power generation in the core ofLight Water Reactors (LWRs) are very sensitive to changesin the feedback parameters moderator density and fuel tem-perature [1]. The latter is tightly connected to the moderatortemperature and to the heat transfer between fuel and coolant,and thus strongly depends on the coolant flow conditions.Experimental and CFD analyses of the coolant flow in thereactor vessel have shown that coolant mixing upstream of thecore is highly incomplete [2, 3, 4, 5], which may lead to largetemporal and spatial gradients of temperature and boron in thecore entry plane, especially in the case of cooling or borondilution transients with asymmetric behaviour of the primaryloops.

CFD methods are able to predict the coolant mixingin the pressure vessel with higher accuracy than thermal-hydraulic codes and may therefore be used to provide a reac-tor core simulating programme with more realistic boundaryconditions. In the framework of the N U R E S A F E project,the three-dimensional CFD solver T R I O U [6] was cou-pled with the core simulator DY N 3D [7] in order to improvethe prediction of coolant mixing in the reactor downcomerand in the lower plenum. In DY N 3D, fuel assemblies arerepresented by one-dimensional coolant channels which arealigned with the vertical reactor axis. This prevents the codefrom reproducing lateral mixing across assembly boundaries.T R I O U was used to replace the core thermal-hydraulicsof DY N 3D for a fully three-dimensional simulation of thecoolant flow on a computational mesh of higher spatial resolu-tion as compared to the nodal mesh of DY N 3D. The couplingis used to simulate a MSLB accident of a PWR.

II. SIMULATION CODES USED AND COU-PLING METHOD

The reactor dynamics code DY N 3D is a three-dimensional best-estimate tool for simulating steady states andtransients of LWRs and has been developed at the HZDR,Germany, for more than 20 years. It is actively developed inorder to improve the implemented and to embed new physicalmodels and numerical methods.

The neutron kinetics model solves the three-dimensionalneutron diffusion equations for two or multiple energy groups,or simplified neutron transport equations. Nodal expansionmethods are applied that are specific for the geometry of fuelassemblies. Rectangular as well as hexagonal assembly shapescan be treated. The reactor is subdivided into axial layersof variable height, producing prismatic computational nodeswhich reflect the shape of the fuel assemblies. Recently, thesolver was extended to trigonal prism nodes which allow aspatially refined nodalisation of hexagonal assemblies as wellas the assignment of variable fuel compositions over the as-semblies’ cross section.

DY N 3D includes a thermal-hydraulic model for oneand two-phase coolant flow, and a fuel rod model. Thermal-hydraulic parameters like fuel and moderator temperatures arerequired for the estimation of safety criteria, such as the me-chanical integrity of the fuel rods. On the other hand, togetherwith the temperature dependent moderator density they arealso needed for the determination of the feedback to neutronics.The thermal-hydraulic model solves the balance equations formass, momentum and energy of the one or two-phase coolantflow, the heat transport equation in the fuel rod, and determinesthe heat transfer into the coolant. In an iterative procedure,DY N 3D computes the distributions of fission power, coolanttemperature and density, void fraction and boron concentra-tion over the core, as well as safety-related parameters, suchas maximum fuel and cladding temperatures, fuel enthalpy,critical heat flux and cladding oxide layer thickness.

Cross sections and other neutronic parameters are pro-vided to the code in the form of libraries for different com-binations of burnup and feedback parameters, and interpo-lated for each individual node and time step during a transient.Boundary conditions, like pressure drop over the core, boronconcentration, coolant mass flow and coolant temperature dis-tributions over the core inlet, are provided in the form of tablesor by thermal-hydraulic codes coupled to DY N 3D. Burnupdistributions can be provided as input data or calculated bysimulating power operation histories. Transient calculationsmay account for perturbations of the core inlet temperature,mass flow, boron concentration, outlet pressure, pressure dropand for control rod movement.

The code T R I O U is an open-source CFD simulation

M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017, on USB (2017)

software, developed at CEA France. The code is designed totreat turbulent flows, fluid/solid coupling, multiphase flows (bymeans of front and particle tracking) or flows in porous media.Problem types that can be handled and which are relevant forLWR simulation comprise purely turbulent hydraulic as wellas thermal-hydraulic problems with and without dissolvedspecies transport. For these problem types, T R I O U solvesthe conservation equations of mass , momentum, internal en-ergy and dissolved species concentration. T R I O U makes useof the Boussinesq approximation, assuming constant values offluid density ρref everywhere except in the body force term ofthe momentum equation. There, temperature and concentra-tion dependency is represented by expansion coefficients βTand βC. Also, the specific heat capacity cp is assumed to beconstant.

The part of DY N 3D which solves the one-dimensionalequations of momentum, boron and heat convection in a fuelassembly-wise manner is to be replaced by the fully three-dimensional simulation capabilities of T R I O U. However, forthe sake of acceptable computation times no attempt is madeto model the coolant flow down to the fuel pin level. Instead,a porous body approach is used for modelling the reactor core.DY N 3D computes the heat conduction in the fuel and thecladding, as well as the heat transfer into the coolant based onthe coolant velocity which it receives from T R I O U. For thispurpose, DY N 3D makes use of well-established correlationsfor the heat transfer at rod bundles that are implemented inits thermal-hydraulic module and which account for differentheat transfer regimes occurring at heated surfaces. The ac-tual data interface between the codes is the volumetric heatsource q̇′′′ calculated by DY N 3D and sent to T R I O U. In theopposite direction, boron concentration, coolant velocity vz,temperature T and pressure p are sent to DY N 3D. The quan-tities received from T R I O U are needed to correctly calculatethe neutronic feedback on nuclear power as well as the heattransfer into the coolant.

On the coding level, the coupling of DY N 3Dand T R I O U makes use of the S A L O M É platform(http://www.salome-platform.org). It is an open-source software for pre and post processing numerical simu-lations as well as a programming framework for the integra-tion and coupling of third-party simulation codes based onopen standards. For the purpose of code coupling it providesprogramming classes and methods for data storage, data in-terpolation and the generation of computational meshes. Forperformance reasons, the coupling executable does not makeuse of S A L O M É’s graphical user interface, but is configuredby means of a text file in the ini format and run from the com-mand line. Nevertheless, result files are written in S A L O M É’snative MED format and can be immediately evaluated by itspost-processing tools. Instructions for building and using thecoupling application are given in [8].

In order to communicate with each other, the simulationcodes to be coupled must implement a common programminginterface. For this, S A L O M É defines IC O C O which standsfor Interface for Code Coupling. [9]. It is a purely abstract C++programming interface to be implemented in the codes. Everycode is represented by a programming object whose methodsallow a supervising programme to initialise and terminate the

code, to increment the problem time, to invoke the solutionof a time step, to extract solution fields from the code and tosend fields to the code. Fig. 1 sketches the coupling betweenDY N 3D and T R I O U and shows the exchanged quantities.

Supervisor:calculation flow,data exchange anddata interpolation

IC O C O

DY N 3DIC O C O

T R I O U

q̇′′′ q̇′′′

T, p,vz,C T, p,vz,C

Fig. 1. Coupling scheme and quantities transferred betweenDY N 3D and T R I O U

III. MSLB SIMULATION RESULTS

The transient response of a light water reactor to asecondary-side steam line break was simulated using the newlydeveloped coupling between T R I O U and DY N 3D. Thecomputational domain of the problem comprises the reactorvessel with its four inlet nozzles of the corresponding primarycoolant loops, the downcomer, the lower plenum up to thecore inlet plane, and the reactor core up to the core outletplane. The time-dependent boundary conditions at the nozzleinlet (coolant mass flow, temperature, boron concentration)are provided as tabulated input data and were generated byprior system-code calculations.

In Fig. 2a and b, the computational geometries of the pres-sure vessel and of the reactor core are shown as surface meshes,while Fig. 2c is a sectional view of the entire computationalmesh in the vertical plane of the loop 1 and 3 inlet nozzles.Two separate, unstructured meshes composed of tetrahedralcells are used to model the reactor in the CFD calculationdone by T R I O U. DY N 3D calculates on a low-resolutionnodal mesh which is shown in Fig. 2d. It divides the reac-tor core into 32 layers between inlet and outlet, while everyfuel assembly is represented by one node horizontally, giv-ing a total of 32×193 = 6176 nodes. The refined core meshfor the CFD calculation, Fig. 2b, is obtained by subdividingthe DY N 3D nodes into a total of 1778688 tetrahedral cells.The reactor pressure vessel mesh, Fig 2a, contains 1906272tetrahedral cells.

The reference reactor is a 4-loop PWR of Westinghousedesign whose core configuration and materials compositionis given in [10]. At the beginning of the transient, the coreis at end-of-cycle and hot-zero power, with zero boron con-centration in the primary coolant and zero decay heat power.The transient is initiated by a double-ended main steam linebreak at the outlet nozzle of the steam generator in loop 1.This leads to a sudden evaporation of secondary coolant andthus to a strong temperature drop of the secondary coolant.As the temperature difference between the primary and thesecondary sides of the steam generator increases, more heat isremoved from the primary coolant which causes the primary

M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017, on USB (2017)

a)

Loop 1

Loop 3

b)

c) d)Fig. 2. Mesh geometries for the coupled DY N 3D-T R I O Usimulation; a) pressure vessel model in T R I O U (partial sur-face mesh), b) reactor core model in T R I O U, c) verticalsection of the T R I O U mesh in the plane of loop 1 and loop3 inlet nozzles, d) reactor core nodal mesh for DY N 3D

loop temperature to also drop. As a consequence, the reactorcore suffers an overcooling, which causes it to become criticaland to produce a power excursion. To increase the powergeneration during the transient and to achieve an additionalasymmetry in the core a fuel assembly with a stuck controlrod was assumed. The assembly position was chosen to be inthe same sector of the core which is also expected to be mostaffected by the overcooling originating from loop 1. Duringthe transient, all primary loop pumps continue to work at thesame constant volumetric flow rate. Fig. 3 shows the primarycoolant temperatures at the pressure vessel inlet nozzles duringthe transient.

The response of the thermal power to the overcoolingtransient is shown in Fig. 4. The power reaches the peak after92 s with a delay of 16 s as compared to the minimum coolanttemperature of loop 1, cf. Fig. 3. It starts to drop as thecoolant temperatures grow in all primary loops. Temperaturedistributions over two cross sections of the core, namely atthe inlet and the outlet positions, are shown in Fig. 5. Up tothe first 6 seconds of the simulated transient, the overcoolingis the same for all loops, cf. Fig. 3. The inlet temperaturedistribution reveals that the outer zone of the core is moreaffected by overcooling than its centre and that there is adiagonal band extending across the core with little overcooling.As time advances, temperature differences between hotter and

b)

0 100 200 300 400220

240

260

280

t/s

T/◦

C

Loop 1Loop 2Loop 3Loop 4

Fig. 3. Coolant temperature at the cold legs of the primaryloops during MSLB transient

overcooled zones grow and a sector of overcooling formsaround the loop 1 inlet position in the core inlet plane. Lateron, as it can be seen for t = 160s, this overcooling sectorvanishes again because the inlet temperatures of all loopsstart to approach each other after the passage of the minimumtemperature. In the outlet plane, beginning at t = 14s, a spotof elevated coolant temperature forms around the position ofthe assembly with the stuck control rod.

0 50 100 150 200

0

0.5

1

t/s

P/G

W

coupled RPV/core sim.given T (x,y, t) at core inlet

Fig. 4. Reactor power during MSLB transient, comparisonof coupled Reactor Pressure Vessel (RPV)/core simulationand core-only simulation with given core inlet temperaturedistribution

Based on coolant mixing tests at the RO C O M facil-ity [3, 11], an MSLB simulation was carried out which uses atime-dependent coolant temperature distribution over the coreinlet plane as the upstream boundary condition. The RO C O Mfacility is a downscaled RPV model of a KO N VO I reactor,instrumented with conductivity measurement technique, thatwas mainly used to investigate the coolant mixing behaviourupstream of the core zone. The tests cover a number of tran-sient scenarios with single and multiple loop flow rate andconcentration variations. The measured mixing scalar distri-bution of a test with single-loop disturbance was scaled onto

M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017, on USB (2017)

the MSLB conditions of the present study. The followingcomparison case with core-only simulation uses the same totalcoolant flow rate, but unlike the full-RPV simulation pre-sented before, it assumes a uniform flow rate over the coreinlet during the transient. The comparison case allows for in-vestigating the effect of a non-uniform coolant flow at the coreinlet on the overall reactor power and the resulting coolanttemperature. The thermal reactor powers of the two cases areplotted against each other in Fig. 4. The power maximum,occurring around the same time as in the full-RPV case, is byabout 0.3GW lower (dashed curve). On the local level, powerdensity and coolant temperature are higher in the core-onlysimulation, as can be seen in Fig. 7 showing the vertical pro-files in the assembly with a stuck rod around the time of thepower maximum. The differences of the simulation resultsdemonstrate that the reactor power sensitively responds tovariations of the feedback parameters at the inlet boundary.

out 283.16283.19283.23283.27283.31283.35283.39283.43283.46283.50283.54283.58283.62

t = 6 s T/◦C

in 280.43280.67280.91281.15281.39281.64281.88282.12282.36282.60282.84283.08283.33

t = 6 s T/◦C

out 273.84274.03274.22274.41274.60274.79274.98275.17275.36275.55275.74275.93276.12

t = 14 s T/◦C

in 271.95272.36272.76273.17273.58273.98274.39274.79275.20275.60276.01276.41276.82

t = 14 s T/◦C

out 253.67255.94258.20260.47262.74265.01267.28269.54271.81274.08276.35278.61280.88

t = 40 s T/◦C

in 237.77240.59243.41246.24249.06251.88254.70257.53260.35263.17265.99268.81271.64

t = 40 s T/◦C

out 243.47246.54249.61252.68255.76258.83261.90264.97268.04271.12274.19277.26280.33

t = 80 s T/◦C

in 225.25228.05230.85233.64236.44239.24242.04244.84247.64250.44253.24256.04258.84

t = 80 s T/◦C

out 253.39255.79258.20260.61263.01265.42267.83270.23272.64275.05277.45279.86282.27

t = 120 s T/◦C

in 242.92244.49246.05247.62249.18250.75252.31253.88255.44257.01258.57260.14261.70

t = 120 s T/◦C

out 259.53261.51263.49265.47267.45269.43271.41273.40275.38277.36279.34281.32283.30

t = 160 s T/◦C

in 255.92256.67257.42258.17258.93259.68260.43261.18261.94262.69263.44264.19264.94

t = 160 s T/◦C

Fig. 5. Core inlet (in) and outlet (out) temperature distributionsat different times

Fig. 6 shows the power density distribution in a planecutting the core vertically along the core axis and the centreline of the affected assembly. During the transient, starting atzero, the power density reaches values beyond 200 MWm−3.Despite the high energy release in the affected assembly duringthe power peak at t = 92.5s, the coolant passing through itonly reaches temperatures around 285 ◦C, as shown in Fig. 7,which is similar to the stationary state value. The temperaturejump with respect to the minimum inlet temperature of loop 1is about 60 K. Fig. 7 also shows the power density profile inthe affected assembly during the core power peak. Its step-likeprofile is due to the fact, that the power density distribution is

calculated by DY N 3D on the coarse nodal mesh.

0.1300.1710.2130.2540.2960.3370.3790.4200.4620.5040.5450.5870.6280.6700.7110.7530.794

t = 6 s q̇′′′/(MWm−3)

1.018.034.951.968.985.8102.8119.8136.7153.7170.7187.7204.6221.6238.6255.5272.5

t = 80 s q̇′′′/(MWm−3)

0.711.622.633.544.555.466.477.388.399.2110.2121.1132.1143.0154.0164.9175.9

t = 160 s q̇′′′/(MWm−3)

Fig. 6. Power density distribution in the vertical plane x+y= 0at different times

0 1 2 3 4

240

260

280

0 1 2 3 40

100

200

300

z/m

T/◦

C

q̇′′′ /(M

Wm−

3 )

coupled RPV and core sim.given T (x,y, t) at core inlet

Fig. 7. Profiles of coolant temperature and power densityalong the fuel assembly with stuck control rod at t = 92.5s,comparison of coupled RPV/core simulation and core-onlysimulation with given core inlet temperature distribution

One interesting feature of the temperature profile in Fig. 7is the slight decrease in the upper section of the assemblyabove z = 3m. This can be explained only by lateral mixingwith colder water from the neighbourhood of the affected as-sembly. The presence of horizontal mixing is an indication forthe existence of three-dimensional coolant flow in the reactorcore which cannot be modelled by standalone DY N 3D.

IV. CONCLUSIONS

The CFD code T R I O U has been coupled with the re-actor dynamics code DY N 3D in order to replace its one-dimensional description of the core thermal-hydraulics witha fully three-dimensional simulation of the coolant flow andtemperature fields on a refined grid. Coolant velocity, pres-sure, temperature and boron concentration fields are calculatedby T R I O U and sent to DY N 3D which calculates the corepower density distribution. The latter is sent back to the CFDcode and used there as a source term in the solution of theenergy transport equation. Data storage and interpolationmake use of the facilities provided by S A L O M É, an open-source platform for simulation code integration. The objectoriented libraries of the platform are closely integrated with

M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017, on USB (2017)

the Open MPI parallelization library and are fully compatiblewith the parallelism of T R I O U.

The coupling of T R I O U and DY N 3D was used to sim-ulate the coolant mixing in the pressure vessel upstream ofthe core inlet plane as well as in the core itself. This couplingwas applied to an MSLB case which involves an overcoolingtransient in a single loop of the primary circuit. The simulationconfirmed the incomplete mixing in the downcomer and thelower plenum leading to a sector-shaped distribution of thecoolant temperature in the core inlet plane. Moreover, the sim-ulation produced a three-dimensional flow field in the reactorcore, which leads to lateral mixing of coolant on its passagethrough the core. It was shown that slight variations of feed-back parameters at the inlet boundary produce a measurableeffect on the reactor power. Coupled, whole pressure vesselsimulations can help to provide the neutronic simulation partwith more accurate boundary conditions.

V. ACKNOWLEDGMENTS

The presented work was financed by the European Unionwithin the FP7 N U R E S A F E project.

REFERENCES

1. S. KLIEM, S. MITTAG, U. ROHDE, and F.-P. WEISS,“ATWS analysis for PWR using the coupled code systemDY N 3D/AT H L E T,” Annals of Nuclear Energy, 36, 1230–1234(2009).

2. F. MORETTI, D. MELIDEO, F. D’AURIA, T. HÖHNE,and S. KLIEM, “CFX Simulations of RO C O M Slug MixingExperiments,” Journal of Power and Energy Systems, 2, 2, 720–733 (2008).

3. T. HÖHNE, S. KLIEM, U. ROHDE, and F.-P. WEISS,“Boron dilution transients during natural circulation flow inPWR—Experiments and CFD simulations,” Nucl. Eng. De-sign, 238, 1987–1995 (2008).

4. T. HÖHNE, “CFD-simulation of the VVER thermal hy-draulic benchmark V1000CT-2 using A N S Y S-CFX,” Scienceand Technology of Nuclear Installations, 2009 (2009).

5. S. KLIEM, T. SÜHNEL, U. ROHDE, T. HÖHNE, H.-M.PRASSER, and F.-P. WEISS, “Experiments at the mixing testfacility RO C O M for benchmarking of CFD-codes,” Nucl. Eng.Design, 238, 566–576 (2008).

6. P.-E. ANGELI, U. BIEDER, and G. FAUCHET, “Overviewof the T R I O CFD code: main features, v&v procedures andtypical applications to nuclear engineering,” in “N U R E T H-16,”(2015).

7. U. ROHDE ET AL., “The reactor dynamics code DY N 3D—models, validation and applications,” Progress in Nuclear En-ergy, 89, 170–190 (2016).

8. A. GRAHN, A. GOMMLICH, and S. KLIEM, “Applicationof the T R I O U-DY N 3D coupling,” Tech. Rep. N U R E S A F ED11.112, European Commission (2015).

9. E. DEVILLE and F. PERDU, Documentation of the Interfacefor Code Coupling: IC O C O, CEA, Paris (2012).

10. T. KOZLOWSKI and T. J. DOWNAR, “OECD/NEA andUS NRC PWR MOX/UO2 core transient benchmark, finalspecifications, Rev. 2,” Tech. Rep. NEA/NSC/DOC(2003)20,

NEA (2003).11. S. KLIEM, T. HÖHNE, U. ROHDE, and F.-P. WEISS,

“Experiments on slug mixing under natural circulation conditionsat the RO C O M test facility using high resolution measurementtechnique and numerical modeling,” Nucl. Eng. Design, 240,2271–2280 (2010).