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Nuclear Engineering and Design 237 (2007) 1639–1655

Fluid mixing and flow distribution in a primary circuit of a nuclearpressurized water reactor—Validation of CFD codes

U. Rohde a,∗, T. Hohne a, S. Kliem a, B. Hemstrom b, M. Scheuerer c, T. Toppila d, A. Aszodi e,I. Boros e, I. Farkas f, P. Muhlbauer g, L. Vyskocil g, J. Klepac h, J. Remis h, T. Dury i

a Forschungszentrum Rossendorf, Dresden (DE), Germanyb Vattenfall Utveckling AB, Alvkarleby (SE), Sweden

c Gesellschaft fur Anlagen-und Reaktorsicherheit, Garching (DE), Germanyd Fortum Nuclear Services, Espoo (Fin), Finland

e Budapest University of Economics and Technology (HU), Hungaryf Atomic Energy Research Institute AEKI, Budapest (HU), Hungary

g Nuclear Research Institute, Rez (CZ), Czech Republich VUJE Trnava (SK), Slovakia

i PSI Villigen (CH), Switzerland

Received 6 July 2006; received in revised form 5 March 2007; accepted 5 March 2007

bstract

The EU project FLOMIX-R was aimed at describing the mixing phenomena relevant for both safety analysis, particularly in steam line breaknd boron dilution scenarios, and mixing phenomena of interest for economical operation and the structural integrity.

This report will focus on the computational fluid dynamics (CFD) code validation. Best practice guidelines (BPG) were applied in all CFD workhen choosing computational grid, time step, turbulence models, modelling of internal geometry, boundary conditions, numerical schemes and

onvergence criteria. The strategy of code validation based on the BPG and a matrix of CFD code validation calculations have been elaborated. CFDalculations have been accomplished for selected experiments with two different CFD codes (CFX, FLUENT). The matrix of benchmark casesontains slug mixing tests simulating the start-up of the first main circulation pump which have been performed with three 1:5 scaled facilities: theossendorf coolant mixing model ROCOM, the Vattenfall test facility and a metal mock-up of a VVER-1000 type reactor. Before studying mixing

n transients, ROCOM test cases with steady-state flow conditions were considered. Considering buoyancy driven mixing, experimental results onixing of fluids with density differences obtained at ROCOM and the FORTUM PTS test facility were compared with calculations. Methods for

quantitative comparison between the calculated and measured mixing scalar distributions have been elaborated and applied. Based on the “bestractice CFD solutions”, conclusions on the applicability of CFD for turbulent mixing problems in PWR were drawn and recommendations onFD modelling were given. The results of the CFD calculations are mostly in-between the uncertainty bands of the experiments. Although no

ully grid-independent numerical solutions could be obtained, it can be concluded about the suitability of applying CFD methods in engineeringpplications for turbulent mixing in nuclear reactors.

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2007 Elsevier B.V. All rights reserved.

. Introduction

Coolant mixing inside the nuclear reactor is the most

mportant inherent safety mechanism against boron dilution orvercooling transients and in the case of pressurized thermalhock (PTS) scenarios. In pressurized water reactors (PWR),

∗ Corresponding author. Tel.: +49 351 260 3460; fax: +49 351 260 2383.E-mail address: rohde@fz-rossendorf.de (U. Rohde).

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029-5493/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2007.03.015

oron acid is added to the water coolant to compensate the excesseactivity of fresh fuel loadings. Due to different mechanisms orystem failures, slugs of low borated water can accumulate in therimary cooling system. This can happen, e.g. as a consequencef a small break loss of coolant accident (SB LOCA), whenoolant circulation is interrupted, steam produced in the reactor

ore is condensed in the steam generator, and a slug of low boronondensate will accumulate at the cold leg of the primary circuit.uring start-up of coolant circulation after refilling the primary

ircuit with emergency cooling (ECC) water or by switching on

1640 U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655

Table 1ROCOM test matrix of steady-state mixing experiments

Run ROCOM stat Flow rate (m3/h)

Loop 1 Loop 2 Loop 3 Loop 4

01 185 185 185 18504 185 185 185 Back flow08 203.5 166.5 185 18509 222 148 185 185

To

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Table 3ROCOM and Fortum PTS tests on buoyancy driven mixing selected for CFDcode validation

Nr QCL (l/s) QHPI (l/s) QA (l/s) QB (l/s) �ρHPI/ρ

Fortum PTS tests10 0 2.31 0 0 0.1620 0 2.31 1.87 1.87 0.1621 1.87 2.31 1.87 1.87 0.16

ROCOM buoyancy mixing testsD10M05 2.72 1.00 – – 0.10

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he loop with the tracer solution injection in the test matrix is the loop numberne.

he first main coolant pump (MCP), this slug will be transportednto the reactor core causing a significant reactivity insertion byecreasing the amount of neutron absorber. The mixing of theeborated condensate with borated water in the reactor pressureessel is in that case the only mitigative mechanism to preventevere accident consequences (Kliem et al., 2004a,b). The mix-ng is also relevant in overcooling transients, when the coolantemperature in one or more loops decreases, e.g. due to a leak inhe secondary side steam system (Kliem et al., 1999). A strongecrease of the coolant temperature does also cause a reactivitynsertion due to the enhanced moderation of neutrons.

Mixing is relevant not only for nuclear safety, but also fortructural integrity. In the case of LOCAs, cold ECC water wille injected into the hot primary circuit. When plumes of coldater get in contact with the reactor pressure vessel (RPV) wall,

hermal stresses occur, which can be dangerous for the RPVntegrity. Mixing is even of relevance for normal reactor opera-ion, e.g. for determination of the coolant temperature distribu-ion at the core inlet in the case of partially switched off MCPs.

In the EC project FLOMIX-R, slug mixing and flow dis-ribution in the RPV has been comprehensively investigatedxperimentally and simulated by using computational fluidynamics (CFD) tools. Within this project, a comprehensive dataase on coolant mixing inside the RPV was created (Rohde etl., 2005). Slug mixing experiments have been performed witheveral 1:5 scaled facilities representing different European reac-or types: the Rossendorf coolant mixing model ROCOM andhe Vattenfall test facility, modelling a German Konvoi type andWestinghouse type three-loop PWR, respectively (Alavyoon

t al., 1995; Prasser et al., 2003; Kliem et al., 2004a,b). Addi-

ional data on slug mixing in a VVER-1000 type reactor gainedt a 1:5 scaled metal mock-up at EDO Gidropress are providedBezrukov et al., 2002). Experimental results on mixing of fluids

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able 2atrix of slug mixing tests at the ROCOM and Vattenfall mixing test facilities used f

un Ramp length (s) Final volume flow rate (m3/h) Sl

OCOM 01 14 185.0 40OCOM 02 14 185.0 20OCOM 03 14 185.0 4OCOM 08 28 92.5 4ATT-02 16 429 8P-1 2 175 8P-2 8 470 8

a Related to the original reactor.

D05M00 0 1.00 – – 0.05

ith density differences obtained at ROCOM and the FORTUMTS test facility are made available (Tuomisto, 1987; Kliem etl., 2004a,b; Rohde et al., 2005). Data from steady-state mixingxperiments at ROCOM (Kliem et al., 2004a,b) and plant com-issioning test data from the NPP Paks and Loviisa (Elter, 2002;simbalov et al., 1982) were gained and used to contribute to

he validation of CFD codes for the analysis of turbulent mix-ng problems. The commercial CFD codes CFX4, CFX5 andLUENT6 have been used (CFX, 2001, 2003; FLUENT, 2003).ables 1–3 show the test matrices for code validation.

In the steady-state mixing tests at ROCOM (Table 1), besideshe symmetrical case ROCOM stat01, there were consideredxperiments with one non-working loop (ROCOM stat04) andith asymmetrical mass flow rate distribution among the loops

ROCOM stat08, stat09). In the ROCOM slug mixing tests (seeable 2), the tests ROCOM 01, 02 and 03 correspond to theump start-up curve in the real plant, while the slug size wasaried. In the test ROCOM 08, the mass flow ramp was variedccording to Froude scaling. One slug mixing test from the Vat-enfall facility and two from the Gidropress test rig were selectedor calculations, too. Concerning buoyancy driven mixing cases,hree tests from the Fortum PTS facility were calculated withifferent combinations of mass flow rates QHPI in the ECCnjection loop and QA and QB in the loops neighbouring to thenjection loop (see Table 3). Two ROCOM tests with differentnjection loop flow rate and density differences were selectedor the calculations.

The main objective was to investigate how well mixing dur-ng boron dilution transients in PWRs can be modelled by CFD

odes. The competiveness of CFD is continuously growing duehe rapid developments in computer technology. However, com-uter capacity is still, and will be for a foreseeable future, a

or CFD code benchmarking

ug volume (m3)a Initial slug position (m)a Reactor type

.0 10.0 PWR Konvoi 4-loop

.0 10.0 PWR Konvoi

.0 10.0 PWR Konvoi

.0 10.0 PWR Konvoi

.0 10.0 Westinghouse 3-loop

.5 14.5 VVER-1000

.5 14.5 VVER-1000

ing and Design 237 (2007) 1639–1655 1641

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U. Rohde et al. / Nuclear Engineer

imiting factor for the capacity for CFD calculations to produceompletely accurate results. Simplified models for describingurbulence therefore have to be used and the computer capacityut restrictions on the resolution in space and time that one canse in a CFD calculation. This leads to modelling errors andumerical errors that give more or less inaccurate results. Val-dation of the quality and trust of different approaches in CFDalculations are therefore needed.

. Application of the best practice guidelines for CFD

The CFD code validation was focussed mainly on a number ofenchmark cases from the steady-state mixing experiments, slugixing tests and experiments with density differences. So-called

est practice guidelines (BPG) were used for quality assurancef the validation calculations. ERCOFTAC BPG (Casey andintergerste, 2000), which have been specified for nuclear reac-

or safety calculations within the ECORA project (Menter et al.,002) were applied. The BPG are built on the concept of an errorierarchy. The different types of errors in CFD simulations areivided into the two main categories:

Numerical errors, caused by the discretisation of the flowgeometry and the model equations, and by their numericalsolution.Model errors, which arise from the approximation of physicalprocesses by empirical mathematical models.

This concept implies that numerical errors are quantifiednd reduced to an acceptable level, before comparison withxperimental data is made. The BPG contain a set of systematicrocedures for quantifying and reducing numerical errors. Thenowledge of these numerical errors is a prerequisite for theroper judgement of model errors. The separation of numericalrrors from model errors allows then valid conclusions on modelerformance. Numerical errors are minimized by optimising theomputational mesh, numerical schemes, convergence criteriand time step. Another kind of errors are uncertainties risingrom insufficient information about the problem definition andet-up. These uncertainties can be quantified by performingalculations with variations of the unknown parameters andy a subsequent analysis on the influence of these parameters.his belongs to boundary positions, boundary conditions and

nternal geometry modelling. Turbulence models are the mostelevant physical models responsible for model errors. Only ifensitivity tests are made the solution errors and model errorsan be quantified and only then you can get an indication onow good your CFD calculations are. Sensitivity tests for theollowing aspects were considered:

Grid size.Convergence criteria.

Round-off error.Time step size.Turbulence model.Inlet boundary position and inlet boundary condition.

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ig. 1. Mesh and time step refinement to obtain converged numerical solutions—elocity distribution in the downcomer (upper) and time dependent global max-mum of the mixing scalar at the core inlet (lower).

Outlet boundary position.Internal geometry.Code.

Fig. 1 shows examples for computational grid and time stepptimisation using the CFX-5 code. The number of mesh pointsor the discretisation of the solution area has to be increasedntil convergence of the solution has been achieved (meshith about 750,000 elements using the Upwind Discretisationcheme UDS). The same procedure has to be applied concerning

ime step refinement (see also Fig. 1).However, in practical applications with complicated geom-

try and complex flow phenomena like the mixing problemsonsidered, a really grid and time step independent solution canften not be reached by practical reasons (computer resources).n these cases, so-called production meshes were used in thealculations. The production mesh is an optimum between max-mum possible refined grid on the one hand, but with omittingarts of the flow domain, which were found to be of small impactn the results, e.g. the cold leg loops, and neglecting or simpli-ying some geometrical details, e.g. by modelling complicatedtructures as porous body domain. The production mesh is not

et a mesh, for which grid-independent solution was reached.n general, the choice of the production mesh is dependent fromhe process to be simulated. The production mesh for momen-um driven mixing calculations might be different from that one

1642 U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655

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ig. 2. Visualisation of the ROCOM production mesh for the CFX-5 calcula-ions.

or the analysis of buoyancy controlled mixing. The productionesh for the CFX-5 calculations, an unstructured grid with aboutmillion elements, is shown in Fig. 2.Concerning numerical solution schemes, higher order

chemes are preferred due to higher accuracy. Fig. 3 shows theelocity distribution (vertical component) in the core inlet planealculated with the FLUENT code for steady-state conditionsith one running pump in the Vattenfall facility by applying firstrder and second order scheme. Using the first order scheme, theolution is well converging, but physically wrong. The positionf the maximum velocity observed in the experiment is not metn the first order solution. The reason is to be seen in the influ-nce of inlet boundary conditions. The bend in the cold leg pipeot far from the RPV inlet nozzle causes an asymmetric velocityrofile and turbulence parameters distribution at the RPV inlet.his impact of the bend is not well reproduced in the more dif-

usive first order scheme calculation. The disturbance caused byhe bend is not “transported” to the core inlet plane, the diffusivecheme “forgets” about it.

. Post-test calculations of ROCOM steady-state mixing

ests

Fig. 4 shows a comparison between CFD solutions and exper-ment for the steady-state mixing test ROCOM stat01 with four

tzAt

ig. 3. Calculated velocity distribution in the core inlet plane (in m/s)—firstrder (up) and second order (down) solution.

unning pumps. The sector formation and the high maximumixing scalar values are well reproduced in the calculation.he best agreement was achieved, when a transient calcula-

ion for the steady-state conditions was performed, because theelocity field in the flow domain is not really time-independentven with steady-state boundary conditions. Macroscopicuctuations occur, which are averaged from the transientolution.

Parallel to CFX, the CFD code FLUENT has beensed for performing second code calculations for the basicteady-state mixing test ROCOM stat01 and for calculatingdditional steady-state tests with asymmetric operation ofoops (ROCOM stat04, ROCOM stat09). Second code calcu-ations are an important contribution with respect to different

esh structures, specific turbulence models and particularlyor modelling of internal structures. A comparison of the dif-erent FLUENT and CFX-5 results with measurement dataplateau averaged mixing scalar distribution at core inlet)or ROCOM stat01 is also shown in Fig. 4. The results ofhe calculations for the additional tests ROCOM stat04 andOCOM stat09 are described in Hemstrom et al. (2005).

The velocity field in the downcomer shows a qualitativelyood agreement between the CFX-4 and CFX-5 calculationsnd the experimental results (LDA measurements at ROCOMPrasser et al., 2003)). Particularly, the calculations confirmhe location of minimum flow velocities below the inlet noz-

les found in earlier experiments (Ulrych and Weber, 1983).

maximum velocity exists at azimuthal positions between thewo inlet, respectively, the two outlet nozzles. A comparison

U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655 1643

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Fig. 4. Comparison of results from th

etween measured and calculated velocity distribution in theower downcomer is shown in Fig. 5.

The calculated and measured velocity distributions agreeostly within the uncertainty band of the measurements, with

xception of the velocity minimum at 45◦ (loop 1). There isbviously a deviation from the symmetry to be expected in theeasured velocity field due to equal mass flow rates in all loops.measurement error of this magnitude in the mass flow rates

an be excluded. However, in loop 1 the mixing device for theracer injection was installed. The mixer creates an additional

ow resistance, which was taken into account by adjustmentf the pump head in this loop. It is assumed, that the mixerffects the velocity profile, distribution of turbulence or occur-ence of swirls induced by the pumps in the corresponding cold

iusa

Fig. 5. Velocity measurements vs. CFX-4

dy-state mixing test ROCOM stat01.

eg pipe, what may have an impact on the velocity distribution.owever, this assumption could not be checked because velocityeasurements near the RPV inlet were not possible.In general, the velocity distribution in the downcomer and

ixing scalar distributions at the core inlet are qualitativelyell predicted in the CFD calculations. The velocity field in

he downcomer has inhomogeneous character with maximumownwards flow components in the regions in-between the inletozzles. A clear sector formation of the flow in the downcomers seen. This leads to maximum mixing scalar values at the core

nlet of 92–99%. That means a part of the fluid remains almostnmixed. The re-distribution of the velocity field and mixingcalar distribution in the case of asymmetric flow conditions islso qualitatively well reproduced in the calculations. However,

results at the end of the downcomer.

1 ing and Design 237 (2007) 1639–1655

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tiwmotmTthe measurements, but the relevant values of maximum mixingscalar (safety relevant minimum boron concentration) are closetogether.

644 U. Rohde et al. / Nuclear Engineer

he mixing along the flow path in the downcomer is under-redicted in all calculations. Disturbance in the inlet boundaryonditions has significant impact on the flow pattern. This cane seen in experiment ROCOM stat01, where a disturbance inurbulence or swirl intensity caused by the mixer is assumedo be responsible for an observed perturbation in the velocityistribution.

Finer grids in the CFD simulation tend to give better results.lso modelling of perforated sheets (such as the drum in

he downcomer) as real structure rather than porous mediummproves quality of results. Influence of porous medium as aubstitute of a perforated sheet can be, in some extent, con-rolled by proper definition of direction-dependent resistancef the porous medium. Other investigated effects (turbulenceodel, wall function, position of outlet boundary) do not have

n unambiguous influence on results.

. CFD calculations for non-buoyant slug mixing tests

.1. The ROCOM slug mixing tests

The CFD calculations for ROCOM slug mixing tests werearried out with the CFD codes CFX-4, CFX-5 and FLU-NT. The transient slug mixing cases ROCOM 01, ROCOM 02,OCOM 03 and ROCOM 08 were calculated. In this paper,

ocus will be put onto CFX calculations for the benchmark caseOCOM 02. A second code calculation was performed for thisase with FLUENT. A detailed description of all the calculationsnd their results is given in Hemstrom et al. (2005).

Based on the meshing studies, finally two grid types (produc-ion meshes) were used for the basic calculations: a tetrahedralroduction mesh (about 7 millions elements) and a hybrid pro-uction mesh (4 million elements). In the CFX-5 productioneshes, all internals were modelled in detail. No porous body

pproach was applied. All the 194 orifices in the core supportlate were modelled. The perforated drum in the lower plenumontains 410 orifices of 15 mm diameter. Inlet boundary positions at the inlet nozzle, outlet boundary at half height of the core.oth production meshes are suitable for the post-test calculationf basically all ROCOM experiments, with slightly preferencesf the tetrahedral production mesh for the steady-state mixingxperiments and the hybrid production mesh for the slug mixingnd density driven experiments. Because no full grid indepen-ence was achieved, there are differences in the results obtainedith different mesh types.Fig. 6 shows streamlines representing the velocity field in the

owncomer and lower plenum (including the perforated drumnd lower support plates as porous media) at the pump start-upcenario calculated with CFX-4. Due to a strongly momentumriven flow at the inlet nozzle the horizontal part of the flowominates in the downcomer. The injection is distributed intowo main jets, the so-called butterfly distribution. In addition,everal secondary flows are seen in various parts of the down-

omer. Especially strong vortices occur in the areas below theon-operating loop nozzles and also below the injection loop.

Fig. 7 shows a quantitative comparison between CFD solu-ions and experiment for the slug mixing test ROCOM 02. The

Fc

Fig. 6. Flow picture (streamlines) at 15 s after the start-up.

ime behaviour of the maximum mixing scalar value at the corenlet is shown. The CFX-4 and CFX-5 solutions are comparedith the measurement. The statistical error of the measure-ent data (error band P2 of two standard deviations) is shown

btained from the averaging of the data from five repetitions ofhe same experiment. This statistical error is not the measure-

ent error, but is caused by macroscopic fluctuations in the flow.he CFD solutions are not always within the uncertainty band of

ig. 7. Comparison of maximum mixing scalar between measurement and CFDalculations for the experiment ROCOM 02.

ing and Design 237 (2007) 1639–1655 1645

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U. Rohde et al. / Nuclear Engineer

Sensitivity studies have shown, that the SST turbulence modelnd the automatic wall functions together with higher orderiscretisation schemes should be used if possible.

.2. CFD calculations for Vattenfall experiments

CFD calculations have been performed for the VATT-02 testase (see Table 1). It is a slug mixing transient, with a slugith low boron concentration initially present in the cold legipe. Buoyancy forces are negligible. The Vattenfall experimentsre described in detail in Alavyoon et al., 1995. Calculationsave been made by using the CFD codes CFX-5 and FLUENTith two different grids, “Grid 1” with 200,726 cells and “Grid” with 1,605,808 cells. Grid 1 is a quite coarse grid and isonsidered to have about the minimum number of cells requiredo get a fair resolution of the flow field. Grid 2 is a completeefinement of Grid 1, i.e. to get Grid 2 all cells in Grid 1 areplit up into eight cells. However, to be able to check if were close to get a grid-independent solution, one would have toake a calculation with a further refined grid, ideally by a factor

f eight. A calculation with such a grid with about 13 millionells was not possible with the available computer resources.hirteen different turbulence models were tested, six versionsf Reynolds Stress Models (RSM) included:

RNG k-�, Standard k-�, Standard k-� (Kato-Launder) andRealizable k-�.Standard k-� and SST k-�.RSM, with the following versions: LRR-IP, QI, SSG, Omegaand Omega (BSL).

The mean and the minimum dimensionless boron concentra-ions (corresponding to unity minus mixing scalar) are quite well

et in the FLUENT calculations for the VATT-02 slug mixingest. Fig. 8 shows mean and minimum (independently on posi-ion) dimensionless boron concentrations at the core inlet as a

unction of time. The calculated minimum boron concentrationor the Grid 2 calculation with the RNG k-� model is very closeo the measured value (see Fig. 8, bottom). The calculated con-entration is, however, delayed around 0.9 s compared to the

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ig. 9. (a) VATT-02 steady-state radially averaged vertical velocity at the low leveladially averaged tangential velocity at the low level in the downcomer as a function

ration (up) and minimum relative boron concentration (bottom) at core inletindependently of position) as a function of time.

easured concentration. This can to a large extent be due to annaccuracy in the measured flow rate.

However, not only the minimum boron concentration shoulde met well, but also the positions of low boron concentrationsust be captured. Two “islands” of low boron concentrations

re present in both the measurement and in the CFD calculation.owever, there is a displacement of the calculated minimumith respect to the measured minimum. This displacement of

he concentration field is mainly a rotational displacement.

In Fig. 9, comparisons of measured and calculated velocity

omponents are presented. The angular position of angle = 0◦ isefined as the angular position where the main inlet pipe enters

in the downcomer as a function of azimuthal angle. (b) VATT-02 steady-stateof azimuthal angle.

1 ing and Design 237 (2007) 1639–1655

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cwvtdmfliheat release is overestimated, because in reality, the wall will becooled down somewhat, which leads to a reduction of the heatflux. Consequently, the minimum temperature is overestimatedin the calculation. In the case of realistic heat transfer modelling

646 U. Rohde et al. / Nuclear Engineer

he downcomer, which is to the right in the figures. Positivengles are to the right of this position, negative angles are tohe left, when looking at the model from the outside standing atngle = 0◦. Tangential velocity (see Fig. 9b) is defined as beingositive when the flow is directed to the right when looking fromn upright position outside the model, i.e. counter-clockwise.ertical velocity (see Fig. 9a) is positive when directed upwards.nly the radial averages are shown in the figures for each angularosition. One can see that the qualitative agreement is good. Themportant non-symmetry in the flow field found in the experi-

ents is captured quite well.Reasons for not getting a better agreement with measure-

ents, particularly for the concentration distribution at the corenlet, can be found among the following items:

Too few computational cells. Due to limited computerresources it could not be shown that a really grid-independentsolution was achieved.A too long time step might have been used. Due to limitedcomputer resources time step sensitivity tests have not beenmade.Simplifications in geometry can be more important thanexpected. Chamfers, vertical cylinders and the lowest struc-ture in the lower plenum are neglected. Even if these structuresare small they can have a significant influence on the flow fieldand the mixing. A sensitivity test showed that it is very impor-tant to model the horizontal structures in the lower plenum.Sensitivity tests showed big differences in results for differentturbulence models, which indicates that more advanced turbu-lence models will give a better agreement with measurements.

.3. CFD calculations for the Gidropress experiments

NRI simulated two from three slug mixing experiments pro-ided by EDO Gidropress (Logvinov et al., 2000; Bezrukov etl., 2002; Rohde et al., 2005). The experiments simulated slugixing in the reactor vessel of a VVER-1000 reactor. In the tests,

he experimental facility was filled with hot water (temperaturef 71 ◦C in test 1, 73.3 ◦C in test 2) and slug of cold water (tem-erature of 25.8 ◦C in test 1, 27.4 ◦C in test 2) was situated in theoop seal. The loop flow rate was then increased up to 175 m3/htest 1) and 470 m3/h (test 2).

In test no.1 the elliptical perforated bottom with original 1324oles (diameter of 8 mm) was modelled as porous media zonen the first version of the grid (variant 1A), and the number ofoles was decreased to 312 holes with diameter of 16 mm in theecond grid (variant 1B). In test no. 2 the elliptical perforatedottom was modelled with the reduced number of holes. Viewf the grid and calculation domain used in test 1 is shown inig. 10.

At walls, adiabatic (Neumann) boundary condition was usedor the energy equation. For test 2, also adiabatic and constant

emperature boundary conditions were tested (variants 2A andB). Realizable k-� model was used with differential viscos-ty option and standard wall functions. Full buoyancy effectsncluding the effect of buoyancy on � were considered. F

ig. 10. Computational domain with grid used in Gidropress test no. 1—overalliew.

Fig. 11 shows the dimensionless averaged temperature at theore inlet. Calculated minimum of average core inlet tempera-ure is lower than the experimental one. The calculated averagealues are almost independent from the grid option (porousody or reduced number of holes). Grid with perforated bot-om (variant 1B) provides better mixing than grid with porousone (variant 1A). The underestimation of the minimum valuen the calculation is an indication, that heat exchange betweenold slug and walls cannot be neglected.

Calculated cold slug lags behind the experimental one. Theeason for this time shift could not be clarified finally.

The transient of the average dimensionless temperature at theore inlet for the test 2 is shown in Fig. 12. In variant 2A zeroall heat fluxes are assumed as in the simulations of test 1. Inariant 2B, constant wall temperature, equal to temperature ofhe hot water outside the cold slug, is assumed. In both cases,etailed model of the perforated bottom and realizable k-epsilonodel are used. In case 2A, no heat release from the wall to theuid is considered. The minimum temperature is underestimated

n the calculation. In the case of constant wall temperature, the

ig. 11. Test 1—average dimensionless temperature at the core inlet vs. time.

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Table 4Quantitative deviations between measurement and calculation for the test caseROCOM stat01

Averagedperturbation (%)

DEV3 SIGNrel

Eq. C.4.7 (%)DEV3 ABSrel

Eq. C.4.6 (%)

EXP 25.45 – –

ig. 12. Dimensionless average core inlet temperature for variant 2A with zeroall heat fluxes and variant 2B with constant wall temperature.

solution of the coupled fluid dynamics–heat conduction prob-em), a better agreement between measurement and calculationould be expected.

. Quantitative comparison of CFD results witheasurement data for the ROCOM non-buoyant

xperiments

For the assessment of agreement between calculation andeasurement, not only visual and qualitative comparisons have

o be performed, but also a quantitative estimation of the devi-tions. Deviations between calculation and measurement occurue to model errors, e.g. in turbulence modelling, but also dueo uncertainties in conditions of the experiment, e.g. uncertain-ies in geometry, boundary conditions or measurement error.omparison between calculation and experiment should be per-

ormed after minimizing numerical errors according to bestractice guidelines (Menter et al., 2002). So-called “best practiceolutions” were included into the comparison, where numericalrrors are reduced to maximum possible extend. Target valuesnd comparison criteria have been evaluated in Hemstrom etl. (2005). This methodology is applied in the following foruantitative assessment of deviations between calculation andxperiment.

For the quantitative comparison of the experimental and cal-ulation results, three stationary experiments and one transientxperiment at the ROCOM test facility were selected. The com-arison was made between the calculated and measured data ofhe mixing scalar in the core inlet plane of the test facility. Inhis plane, 193 measurement positions are installed, one at thentry into each fuel assembly. Exactly at these positions, thealculated values for the mixing scalar were extracted from thealculations.

For the quantitative comparison different types of deviationsere defined. These are

EV1i,t = cc,i,t − cm,i,t (1)

here cc is the calculated and cm the measured value of the mix-ng scalar or the velocity at the position i and the time t. DEV2 isn accumulated deviation at the certain position i over the impor-

nd Design 237 (2007) 1639–1655 1647

ant time span, i.e. when the perturbation is moving throughhe measurement plane. Two representations of the accumulatedeviation were selected, the first is the absolute deviation.

EV2i ABS =t=t2∑

t=t1

|DEV1i| (2)

When considering the sign, also the direction of deviationeveals:

EV2i SIGN =t=t2∑

t=t1

DEV1i (3)

The averaging of the deviation DEV2 over all measure-ent positions leads to the average accumulated deviationEV3 ABS and DEV3 SIGN. These values are absolute ones

nd are in same units as the mixing scalar (%). The relativeeviations DEV3rel are calculated relating the absolute deviationEV3 to the integral perturbation introduced in the experiment

nto the core inlet plane.

.1. Comparison for the stationary experimentOCOM stat01

Four CFD solutions obtained by different project partnersere included into the comparison between measurement and

alculation. Besides the three steady-state calculations, one tran-ient calculation was included into the comparison (FZR 01tr).his calculation was performed with constant velocity bound-ry conditions at the inlet into the reactor pressure vessel. Thealculated mixing scalar at the core inlet was averaged at theuasi-stationary concentration level in the same way as in thexperiment. The results of the four calculations are shown inig. 4.

Table 4 shows the relative averaged deviation DEV3 forhe different CFD solutions. The averaged perturbation shoulde close to 25% in the case of 100% perturbation in onef the four loops. However, the exact value of the perturba-ion depends on the velocity profile at the core inlet, which isnknown, but should be close to homogeneous in our case. Theelative deviation considering the sign is very low for all calcu-ations in comparison to the absolute deviation. That indicates,

FZR 25.40 −0.345 26.1AEKI 24.95 −2.046 28.5VUJE 25.26 −0.906 25.1FZRtr 24.53 −3.810 24.4

1648 U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655

Table 5Measured and calculated maximum values of the mixing scalar (including time of appearance)

Total maximum (%) Time of total maximum (s) Maximum of the average (%) Time of maximum of the average (s)

ECC

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Quantitative comparisons are also performed for thexperiments ROCOM stat04 and ROCOM stat09. FLUENTalculations have been performed for these experiments byUJE and AEKI. The results are presented in Hemstrom

t al. (2005). The tendencies are the same as observed forOCOM stat01.

.2. Comparison for the slug mixing experimentOCOM 02

Two solutions using the codes CFX-4 and CFX-5 werencluded into the comparison between measurement and cal-ulation. Both calculations are obtained with the correspondingroduction mesh (tetrahedral mesh for CFX-5). In Table 5, theaximum values and the time point of maximum are compiled

or the experiment and the two calculations. Both calculationsredict the maximum of the mixing scalar slightly too early, 1 or.5 s, respectively. The value calculated by CFX-4 of the maxi-um is in good agreement with the measured one, while being

verestimated in the CFX-5 calculation. Further, the accumu-ated normalized perturbation PERT was calculated accordingo:

ERT = 1

(t2 − t1)

t=t2∑

t=t1

1

n

n∑

i=1

Θi(t) (4)

The integral perturbation is normalized in this way, that aalue of PERT0 = 1.0 would be reached, when the mixing scalarver the whole considered time would be unity at all measure-ent positions, in other words we would have a full deboration

ver the full considered time. The integral perturbation was.146 in the experiment, 0.1566 in the CFX-5 calculation and.1124 in the CFX-4 calculation. In the CFX-4 calculation thentroduced perturbation was underestimated in comparison tohe experiment, whereas it was slightly overestimated in theFX-5 calculation.

.3. Conclusions on quantitative comparison betweeneasurement and CFD-calculations

A detailed quantitative comparison of the results of CFD-alculations with measurements in the complex geometry of theodel of a pressure vessel was performed. Different steady-state

nd transient experiments and calculations were considered. Theomparison was mainly concentrated on the core inlet plane.

dditionally, the velocity distribution in the downcomer was

ompared.In the steady-state experiments, the different codes show the

ame global tendencies. The quantitative analysis revealed, that

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he spreading of the tracer in radial direction is underestimatedn all presented calculations. The transient calculation with con-tant velocity in time shows the best agreement in the shapef the distribution of the mixing scalar in the core inlet planend in the calculated maximum value. Further, the comparisonf measurement positions, for which the coolant should flowhrough the sieve drum or around the sieve drum revealed greatifferences.

The pump start-up experiment ROCOM 02 was calculatedy the codes CFX-4 und CFX-5. The time behaviour of theaximum and the average perturbation calculated by both codes

s inside the confidence interval of 2σ during the main part ofhe considered time interval.

. CFD calculations for the buoyancy-driven mixingxperiments

CFD simulations have also been performed for the buoy-ncy driven mixing tests. Three of the Fortum PTS tests andne ROCOM generic buoyancy driven mixing case have beenalculated.

CFX-5 calculations of the buoyancy mixing test D10M05ere performed by M. Scheuerer and Hohne et al. (2006). The

xperiment was performed with injection of water with 10%ncreased density into the cold leg with 5% of nominal flow rate.he calculational grid includes detailed models of the sieve bar-

el, the core support plate and the rods modelling the core inhe ROCOM test facility. The cold leg with the ECC-injectionozzle was added in order to capture the flow stratification inhe cold leg which also influences mixing in the downcomer.he injection of water with higher density was performed fromto 15 s. Calculations were made using second order discreti-

ation schemes in space and time. Two constant time steps (0.1nd 0.05 s) were used in combination with the SST turbulenceodel and scalable wall functions. Fig. 13 (up) shows the flow

treamlines in the cold leg and the downcomer during and afterhe injection of the glucose solution. Fig. 13 (bottom) showshe distribution of glucose solution, detected by the tracer con-entration, at the same time points. It can be seen, that duringhe injection, when the heavier water did not yet arrive in theowncomer, there is a more or less homogeneous distribution ofelocity and tracer concentration around the RPV inlet nozzle.fter the fluid with higher density has moved to the downcomer,

he fluid motion is accelerated downwards, and a jet of heavierater is formed in the downcomer. The glucose solution flows

ownwards directly below the inlet pipe. These phenomena werelso observed in the experiment.

Investigations on the influence of the turbulence model wereerformed by using a Reynolds Stress model (RST), based on

U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655 1649

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ig. 13. Streamlines representing the fluid flow (up) and tracer concentration (zefore injection takes place (T = 4 s) and after injection (T = 23 s).

he omega equation. The RST model, although calculated withhe larger time step (due to higher computer resources require-

ents), shows better agreement with measurement data.However, quantitative comparison between measurement and

alculation is difficult especially for the buoyancy driven mixingases because of the fluctuating nature of the flow field and mix-ng pattern. It might be more useful to compare some averagedr integral parameters. This was done, e.g. for the Fortum PTSxperiments.

The buoyancy driven turbulent flow with stratification andixing in selected Fortum mixing tests was modelled by T. Top-

ila with the commercial CFD code FLUENT. The computationrid used for Fortum mixing test simulations is shown in Fig. 14.

The comparison was mainly based on the tempera-ure/concentration data from the thermocouple locations nearhe pressure vessel wall and in the main (middle one) cold leg.he stratification and mixing in the main loop was studied usingackflow ratio Q* = Qh/QHPI where QHPI is the cold-water injec-ion flow rate and Qh is the flow rate from back the downcomer

o the main loop. The mixing of the cold water plume in theowncomer was studied using time-dependent maximum andverage injection water concentrations at RPV wall at differentertical levels.

2Pmt

mixing scalar Θ in the range 0.0–0.2, bottom) in cold leg and RPV at the time

Fig. 15 shows a comparison of the measured and calculatedhe backflow ratio (up) and the maximum concentration of theold HPI water in the downcomer (down) for the experiment #10rom Table 3. The main features of flow and mixing were quiteell simulated; stratification in the main cold leg and the down-

omer, backflow from the downcomer and side loops to the mainoops and the flow field in the downcomer. However, the mixingf the cold water plume was not as effective in simulations as ineal experiments. More grid size tests with transient simulationsre needed to test the grid-independency of simulations.

Preliminary turbulence models tests with Realizable k-� (For-um) and RNG k-� models (NRI) did not bring out any significantifferences between models.

. CFD simulation mixing tests at Paks NPPVVER-440 reactor)

Additional test data were made available by Paks NPP andEKI for the FLOMIX-R project (Elter, 2002; Rohde et al.,

005). The data have been gained from commissioning tests ofaks NPP performed in years 1987–1989. The tests addressedixing among coolant loop flows in the downcomer and up to

he core inlet in forced flow conditions. The goal of the tests

1650 U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655

Fig. 14. Computation grid used for Fortum mixing test simulations.

Fig. 15. Backflow ratio (up) and cold HPI water concentration at pressure vesselwall at level z = −1460 (down) during simulations of experiment #10.

Fig. 16. VUJE model of VVER 440 V-213 reactor (left) and reactor internals (right).

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U. Rohde et al. / Nuclear Engineer

as investigation of potential loop temperature asymmetry thatight occur and significantly affect power distribution in the

ore. Paks mixing experiments were calculated by VUJE (FLU-NT), AEKI (FLUENT) and TU Budapest (CFX5). It must beointed out, that the calculations were performed for real planteometry. Because of the 1:5 scaling of the test facilities, theomputational cells are five times bigger, if the same number ofells is used in the real plant calculations as in the calculations

or the test facilities. Moreover, the Reynolds numbers are muchigher under the real plant conditions. This is an additional chal-enge for the real plant calculations. More detailed descriptionsf the CFD analyses are given in Hemstrom et al. (2005).

ciht

Fig. 17. Comparison of calculated dimensionless core inlet temperatures with me

nd Design 237 (2007) 1639–1655 1651

Comprehensive computer models of VVER 440 reactor ves-el were developed. They include all six loops with inlet nozzlesnd three baffles, whose purpose is to deflect the coolant injectednto the reactor vessel from the safety injection tanks. Eight sup-ort consoles for the core barrel alignment were modelled asell. The production mesh used in the calculations of VUJE is

hown in Fig. 16.The sensitivity tests of the meshing showed that the cal-

ulation meshes did not meet the grid-independency criteria,nspite of the large node number. It was concluded thatybrid tetrahedral–hexahedral meshing which is available inhe CFX-10 code seems to be more suitable for the pres-

asured data for loop one (up) and deviations from measurement (bottom).

1652 U. Rohde et al. / Nuclear Engineering and Design 237 (2007) 1639–1655

Table 6Basic assumptions used in the calculations of Paks mixing tests

AEKI TU Budapest VUJE

CFD code used FLUENT 6.1.22 CFX 5.5.1 FLUENT 6.1.18Mesh 1,172,618 1,838,991 1,609,231Elliptical perforated plate Porous medium Porous medium Structure with 227 holesGuide tubes No No Yes (with perforations)DW

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iscretisation scheme First orderall function Non-equilibrium

ure vessel geometry because of the lower number of meshlements.

Comparison of the calculation results with the measure-ents was done only for those simulations which gave the

est agreement (“production calculations”). Summary of basicssumptions used in the production calculations of Paks mixingests performed by AEKI, TU Budapest and VUJE is presentedn Table 6.

All calculations were performed as steady state. Results arehown in Fig. 17 in the form of temperature fields expressedn terms of dimensionless mixing scalars at the core inlet andompared with experimental data. For assessment of deviationsetween calculated results and measurements, maps of errorsre presented as well.

The performed calculations showed that the coolant flows inectors downwards in the downcomer, and the sectors remainlso at the core inlet. The maximum of the mixing scalar is notocated directly below the inlet nozzle, but an azimuthal shift ofhe maximums can be observed because of the asymmetric loca-ion of the inlet nozzles and because of the hydro-accumulatoraffles. The effect of the baffles can be observed even at the corenlet.

The results show qualitatively good accordance with theeasured data. However, the mixing is underestimated in the

alculations (the calculated maximums of the mixing scalarsre larger than the measured ones). Following conclusions onhe CFD modelling of the flow distribution in the RPV of aVER-440 type reactor were drawn:

Good numerical convergence was achieved with basic solverand solver settings based on residuals of continuity andmomentum equations (using first order upwind discretisationscheme and k-� or RSM turbulence model).Some numerical fluctuations of the flow field were observedbelow the ECC baffles in the downcomer, possibly due tosome non-stationarity of the flow field.Modelling of detailed internal geometry (e.g. flow baffles)may have a noticeable influence on results.ECC water baffles guide the main flow and generate turbu-lence effects in the downcomer.The alignment drifts have only local effect.

Accurate model of the perforated elliptical bottom (modellingthe elliptical perforated bottom as solid structure rather thanusing a porous medium) provides more realistic flow patternand improves the accuracy of the calculation.

tpga

Second order Second orderScalable Standard

Using pressure outlet boundary condition gives better numer-ical convergence than outflow boundary.Boundary layer at the walls of downcomer should be less then3 mm, to keep y+ parameter less than 1000.High order methods decrease the numerical stability of thesolution.

. Conclusions

.1. Conclusions from sensitivity tests according to thePG

The most important conclusions from the sensitivity testsade in the CFD simulations of steady-state mixing and flow

istribution, transient slug mixing and buoyancy driven mixingithin the EC project FLOMIX-R are presented below. Sensi-

ivity tests are an important part of applying the best practiceuidelines for CFD in terms of quality assurance. However, ashe test facilities for which the validations were made are quiteifferent, it is in some cases difficult to draw general conclu-ions. The conclusions are also based on calculations that haveot been shown to be grid independent.

.1.1. Grid sizeThe aim is to make CFD calculations that give grid-

ndependent solutions, i.e. results that do not change whenhe grid is refined further. A grid-independent solution can beefined as a solution that has a solution error that is within aange that can be accepted by the end-user, in view of the pur-ose of the calculations. According to the BPG, calculationsust be made with at least three different grids in order to

e able to quantify the grid-dependence of the calculations.he two finer grids also have to be made using a complete

efinement of the nearest coarser grid, to get an objective mea-ure of the grid-dependency. For example, if a calculation isade with 200,000 cells, calculations also have to be madeith 1,600,000 cells and 12,800,000 cells. Due to limited com-uter resources, this procedure has not been possible to followor any of the slug mixing test cases in FLOMIX-R. A tran-ient calculation for a coarse grid of around 200,000 cellsakes in the order of 1 week to perform. The solution errorsave therefore not been quantified. Developments in computer

echnology will make these quantifications of solution errorsossible within a few years. The number of cells required forrid-independency can only be guessed. Several million cellsre probably needed for most of the transient test cases in

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U. Rohde et al. / Nuclear Engineer

LOMIX-R. Inspite of fully grid-independent solutions, solu-ions on so-called production meshes were used to assess thegreement between measurement and calculations. The produc-ion meshes were an optimum in mesh refinement what coulde reached.

.1.2. Inlet boundary position and inlet boundary conditionIt is well known that the choice of inlet boundary position

nd inlet boundary condition (turbulence level, variation in inletelocity field in space and time) can have a big influence onhe flow pattern far downstream from the inlet. Sensitivity testsave been made in some cases, otherwise the inlet was put farpstream from the downcomer at a position where the flowonditions were well known.

For the ROCOM steady-state mixing case, results were notensitive to different turbulence intensities at an inlet positionedlose to the downcomer. Slightly different results were achievedf the tracer concentration profile was changed at the same inletosition. Modelling of the four cold legs, bends included, gavenly slightly different results compared to having an inlet closeo the downcomer.

.1.3. Outlet boundary position and outlet boundaryondition

For the Vattenfall steady-state flow situation the results werenly slightly sensitive to whether the main outlet was put athe core inlet or at the core outlet. For the ROCOM cases itas found that the main outlet should be put above the core

nlet.

.1.4. Modelling of internal geometryInternal structures can have a big influence on flow and

ixing. These structures can either be omitted, be simplifiedr be modelled in detail. One type of simplifying model is aorous media model, with distributed resistances. Especiallyow the structures in the lower plenum are modelled can have aig influence on flow and mixing. There were different experi-nces concerning the importance of modelling the lower plenumtructures. However, for most applications, a detailed modelave results that were in best agreement with measurements.general recommendation is that internal structures should beodelled in detail. One should be very careful with decisions to

mit these structures or to use simple forms of the porous mediapproach.

.1.5. Turbulence modelsFor the Vattenfall slug mixing transient the best results were

chieved with the RNG k-� model, with scalable wall functions,ompared with the k-� SST model and the RSM (Omega (BSL)),ith automatic wall functions. For the ROCOM transient buoy-

nt case, RSM (BSL) gave improved results compared to thetandard k-� and the k-� SST model. For the ROCOM steady-tate mixing and non-buoyant transient mixing, the results were

ot very sensitive to turbulence model (the Standard k-� modelnd the k-� SST model gave similar results). For the (buoyant)ORTUM PTS tests, the Realizable k-� model produced bet-

er results than the RNG k-� model. For the VVER mixing test

sacn

nd Design 237 (2007) 1639–1655 1653

alculations the Standard k-� model with non-equilibrium wallunctions and RSM with standard wall functions gave the bestgreement. RSM with non-equilibrium wall functions and the-� SST model overestimated the mixing.

The conclusions presented above are in some cases contra-ictory. The RSM models should give better agreement witheasurement, as they are more advanced than the two-equationodels. This was not always the case for the calculations inLOMIX-R. The contradictory conclusions make it hard toraw any general conclusion on which turbulence model tose. It should, however, once again be emphasized that theseesults are based on calculations that have not been showno be grid-independent. In general, standard turbulence mod-ls implemented in the codes can be used for turbulent mixingalculations.

.1.6. Double precisionIn general, the use of double precision arithmetic is recom-

ended, but it requires more computer resources.

.1.7. Time stepEspecially if the Courant-Friedrichs-Lewy number (CFL) is

arger than 1, and especially where there are strong gradients,ne can expect problems with time step dependency. For theensitivity tests made for time step, time step independency waseached with time steps which were as long as up to 10 times theFL number (FORTUM PTS) and 50 times the CFL number

ROCOM slug mixing transient). These CFL numbers are forositions where there are large gradients in concentration oremperature.

.1.8. Height of wall-adjacent cellsOne sensitivity test was made for the height of the wall-

djacent cells for the Vattenfall steady-state case. The maximum+ values were very high with the grids used, up to around 5000.he grid was therefore refined at the wall-adjacent cells. How-ver, calculations with these lower and more optimum y+ at thealls gave worse results for the Vattenfall steady-state case. Thisight indicate that the non-equilibrium wall function used does

ot work properly for the type of boundary layers present inhe downcomer, especially those close to the flow-impingementhere the jet from the inlet pipe hits the downcomer wall. For theOCOM production mesh the y+ value in the downcomer was5, and therefore below the recommended value of maximum00.

.1.9. CodeThe commercial codes CFX4, CFX5 and Fluent 6 were used.

or both the Vattenfall slug mixing case and the ROCOM 02lug mixing case the differences between the results from Fluentand CFX5 were significant, inspite of the fact that the calcu-

ations were run with exactly the same grids. For the ROCOM

teady-state mixing case, the differences were smaller. However,s none of the calculations are probably grid-independent, oneannot expect to obtain the same results from the codes, as theumerics in the codes are different. Another difference between

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654 U. Rohde et al. / Nuclear Engineer

he two codes is that exactly the same wall functions could note applied.

.1.10. Numerical schemesAt least second order schemes should be used, both in space

nd time. For some applications there were convergence prob-ems (unstable solutions) when using second order schemes.his might indicate that there are also low-frequency fluctuations

n the measurements, which cannot be resolved by a steady-statealculation. For these cases a time-averaged flow field mightave to be calculated with a transient calculation.

.2. Comparisons with measurements

.2.1. Steady-state mixing and flow distributionIn general, the flow pattern, velocity distribution in the down-

omer and mixing scalar distributions at the core inlet areell predicted in the CFD calculations. The velocity field in

he downcomer has inhomogeneous character with maximumownwards flow components in the regions in-between the inletozzles. A clear sector formation of the flow in the down-omer is seen. This leads to maximum mixing scalar valuest the core inlet of 92–99%. That means a part of the fluidemains almost unmixed. The re-distribution of the velocityeld and mixing scalar distribution in the case of asymmet-ic flow conditions is also qualitatively well reproduced in thealculations.

Finer grids in the CFD simulation tend to give betteresults. Also modelling of perforated sheets (such as therum in the downcomer) as real structure rather than porousedium improves quality of results. Influence of porousedium as a substitute of a perforated sheet can be, in

ome extent, controlled by proper definition of direction-ependent resistance of the porous medium. Other investigatedffects (turbulence model, wall function, position of outletoundary) do not have an unambiguous influence on results.n general, the mixing along the flow path in the down-omer is under-predicted in all calculations. Disturbance in thenlet boundary conditions has significant impact on the flowattern.

.2.2. Slug mixing transientsFor the ROCOM slug mixing transient the qualitative agree-

ent with measurements is good. The position of the lowestoron concentrations was captured fairly well. Quantitativeood agreement with the level of the measured lowest borononcentrations was achieved. Considering the agreement ofhe measured and calculated boron concentration values atocal positions, the deviations are larger than for the global

inimum. For the ROCOM buoyant slug mixing transient,he local concentration was over-predicted, i.e. mixing wasnder-predicted.

For the Vattenfall slug mixing transient, the minimum aver-

ge boron concentration at the core inlet was captured very welly the CFD calculations. Also, the minimum boron concentra-ion at the core inlet was captured very well. The distributionf low boron concentration across the core inlet plane was

nd Design 237 (2007) 1639–1655

ot, however, accurately modelled by the CFD calculation.here is mainly a rotational displacement of the concentrationeld. This could be relevant in reality, as a core is primar-

ly different radially, as far as enrichment and reactivity areoncerned.

In the Gidropress slug mixing transient the calculated mini-um of the average core inlet temperature was lower than the

xperimental one. This was probably a consequence of the facthat the heat exchange between the cold slug and the warm wallsas neglected in the CFD calculation. Other possible reasons are

he pre-mixing in the main coolant pump simulator, which is dif-cult to model, and the not exactly known initial position of thelug boundary.

The CFD calculations for the FORTUM PTS buoyant tran-ient mixing case modelled the main features of the flow quiteell. Quantitatively there was some poor agreement for mixing

n the main loop and for the mixing of the cold plume in theowncomer.

The conclusions from the various calculations made wereot unanimous. The results are promising, however, bettergreement with measurements is needed for a CFD calcu-ation to be an equivalent competitor to model tests. Theontinuous developments in computer capacity and in soft-are capabilities will allow more extensive calculations to beade, enabling a reduction in errors from all sources, and

ncrease the accuracy of CFD calculations. A methodology ofuantitative comparison between measurement and calculationas developed and applied. It provided very useful infor-ation concerning a quantified engineering error assessmenthich can be used, e.g. in reactor physics calculations concern-

ng the consequences of boron dilution transients as a safetyurcharge.

.3. Development needs

This section gives a summary of the conclusions drawn fromhe calculations concerning what is needed in the future to obtain

ore accurate CFD calculations for boron dilution transients andixing in pressurized water reactors. As shown earlier in this

eport agreement with measurements is not satisfactory in allases. In order to get results from CFD calculations that are inetter agreement with measurements, the following points haveo be considered:

More computational cells. No fully grid-independent solu-tions were obtained due to constraints in computer resources.More detailed modelling of internal structures might also beneeded, which leads to additional cells.Shorter time steps might in some cases be needed.More advanced turbulence models, especially models thatcan cope with the specific features of the flow fieldspresent in these applications, such as accelerating flow, flow-impingements and buoyancy. Further-improved Reynolds

Stress Models or LES models (or hybrids between the two)might be needed to get better agreement with measurements.Better models of wall boundary layers (i.e. wall functions)are also probably needed.

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U. Rohde et al. / Nuclear Engineer

Some steady-state cases have to be run as transients, as low-frequency fluctuations cannot be captured by a steady-statecalculation. A transient calculation takes at least an orderof magnitude longer time to perform than the correspondingsteady-state calculation.

The computation time needed for a grid- and time step-ndependent CFD calculation using an advanced turbulence

odel is today too long (in the order of months). To be ableo perform such calculations in a shorter period of time, theollowing aspects are important:

Faster and more accurate solvers and numerical schemes.Automatic time stepping. The CFD code should choose theoptimal time step (within specified limits) and relaxation forminimizing computation time and ensuring convergence tospecified residual levels.Improvements of the grid generation process in order to beable to, in an easier way than today, make high-quality hexa-hedral grids that would produce more accurate solutions withfewer cells.Grid adaptation (refine and coarsen) during transient runsto get refinements where there are strong gradients of(especially) concentration will also produce more accuratesolutions with fewer cells.Refined porosity models can reduce the need for cells.

The best practice guidelines for CFD have increased thewareness for what is needed to produce high-quality CFDalculations. These guidelines should be extended with moreetailed recommendations, for example, which turbulenceodel to use for different types of flow situations. The CFD code

hould also help the user to apply the best practice guidelines,or example, concerning quality checks for grid and solution.

Inspite of the large amount of work performed in FLOMIX-there are still questions unanswered about the capability of

FD codes to model boron dilution transients and mixing inrimary system in pressurized water reactors. The continuousevelopment in computer capacity and in software capabilitiesill continuously increase the ability to make accurate CFD

alculations.In general, it can be concluded, that CFD codes can be applied

or calculations of turbulent mixing in one-phase flow in anngineering way.

T

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nd Design 237 (2007) 1639–1655 1655

eferences

lavyoon, F., Hemstrom, B., Andersson, N.G., Karlsson, R.I., 1995. Experi-mental and computational approach to investigating rapid boron dilutiontransients in PWRs. In: CSNI Specialist Meeting on Boron Dilution Reac-tivity Transients, State College, PA, USA, October 18–20.

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