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Nuclear Engineering and Design 240 (2010) 23132328

Contents lists available at ScienceDirect

Nuclear Engineering and Design

journa l homepage: www.e lsev ier .com/ locate /nucengdes

imulation of turbulent and thermal mixing in T-junctions using URANS andcale-resolving turbulence models in ANSYS CFX

h. Franka,, C. Lifantea, H.-M. Prasserb, F. Mentera

ANSYS Germany GmbH, Staudenfeldweg 12, D-83624 Otterfing, GermanyETH Zrich, Department Energy Technology, Zrich, Switzerland

r t i c l e i n f o

rticle history:ccepted 10 August 2009

a b s t r a c t

Being of importance for turbulent and thermalmixing and consequently for thermal striping and thermalfatigue problems in nuclear power plants, the turbulent isothermal and thermalmixing phenomena havebeen investigated in two different testcase scenarios. First testcase scenario as proposed by ETHZ (Zborayet al., 2007) comprises of turbulent mixing of two water streams of equal temperature in a T-junction of50mm pipes in the horizontal plane and thereby excluding any buoyancy effects. The second testcase isbased on the Vattenfall test facility in the lvkarleby laboratory and has been proposed byWestin (2007)where water of 15K temperature difference mixes in a T-junction in vertical plane, provoking thermalstriping phenomena. ANSYS CFX 11.0 with Reynolds averaging based (U)RANS turbulence models (SST

and BSL RSM) as well as with scale-resolving SAS-SST turbulence model has been applied to both testcases. CFD results have been compared to wire-mesh sensor, LDV and thermocouple measurements.While the turbulent mixing in the ETHZ testcase could be reproduced in good quantitative agreementwith data, the results of the LES-like simulations were not yet fully satisfying in terms of the obtainedaccuracy in comparison to thedetailedmeasurement data, also the transient thermal stripingphenomena

e struand large-scale turbulenc

. Introduction

Turbulent mixing of fluid of different temperature in T-junctioneometries became of significant importance in the field of nucleareactor safety, since it can lead tohighly transient temperaturefluc-uations at the adjacent pipe walls, cyclic thermal stresses in theipe walls and consequently to thermal fatigue and failure of theipeline. Thermal striping and mixing, in general, is however chal-enging to predict by using commonCFD simulation and turbulenceodeling approaches.Besides the effort spent in former studies for thermal mix-

ng phenomena in T-junctions of the Superphenix reactors, IAEAenchmarksand theEuropeanTHERFATproject, recently twoseriesf experiments have been carried out, which are directly aimedo provide detailed experimental data for thoroughly validation ofFD simulation approaches for the turbulentmixing of fluids of theame temperature aswell as for the thermal striping phenomena in

urbulent thermal fluidmixing in T-junctions. The first experimentas carried out by Vattenfall in 2006 at the lvkarleby Labora-

ory, Vattenfall Research and Development AB, while the seconderies of detailed measurements of turbulent isothermal and ther-

Corresponding author.E-mail address: [email protected] (Th. Frank).

029-5493/$ see front matter 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2009.11.008cture development was well reproduced in the simulations. 2009 Elsevier B.V. All rights reserved.

mal mixing was carried out at the Laboratory for Nuclear EnergySystems, Institute for Energy Technology, ETHZ, Zrich, Switzer-land. Both datasets were used in the present work for CFD modelvalidation.

The present paper describes first the Best Practice Guidelinesrelated investigations on the turbulent mixing of water of equaltemperature in a T-junction in the horizontal plane (ETHZ testcase(Zboray et al., 2007)). The investigations were aimed on investiga-tion of grid independent CFD solutions for traditional RANS/URANSapproaches using SST and BSL RSM turbulence models.

Furthermore it is easy to observe that these traditionalRANS/URANS turbulence modeling approaches are not capable todescribe the phenomenon of thermal striping and high-frequencynear-wall temperature fluctuations in turbulent thermal mixingin T-junctions correctly. Therefore, based on the experiences fromthe first testcase investigations, the scale-resolving SAS-SST modelhas been applied in a transient simulation to the conditions ofthe Vattenfall test facility (Westin, 2007) for one particular set oftestcase conditions. For both testcases a short description of thetest facilities and the testcase conditions are given. The detailed

mesh and setup parameters for the CFD simulations are describedand the CFD results are compared to the experimental data. Fromthat comparison conclusions are formulated for the advantages anddisadvantages of the usedmodeling approaches and recommenda-tions for further investigations are given.

http://www.sciencedirect.com/science/journal/00295493http://www.elsevier.com/locate/nucengdesmailto:[email protected]/10.1016/j.nucengdes.2009.11.008

2314 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

Nomenclature

C turbulence model constantD pipe diameterD kinematic diffusion coefficientF1 blending function of the SAS-SST modelk turbulent kinetic energyL pipe lengthLt turbulent length scalePk turbulence production termQSAS source term of the SAS turbulence modelS shear rateS source term for transport scalar Sct turbulent Schmidt numbert timeT temperatureT* non-dimensionalized temperatureU fluid velocityu, v, w Fluid velocity componentsy+ dimensionless wall distancex, y, z length scales of a hexahedral mesh element

Greek symbols turbulence Eddy dissipation fluid density kinematic viscosityt turbulent eddy viscosity dynamic viscosity Eddy frequency eff effective diffusion coefficient transport scalar vorticity

Subscripts and superscriptscold corresponding to properties of the cold fluid

2

2

tESoit

Table 1Main parameters of the ETHZ T-junction testcase No. 14.

Flow rate in main pipe (tap water) 58.6 [l/min]Flow rate in branch pipe (de-ionized water) 59.2 [l/min]

(RANS). The geometry of the investigated testcase is shown in Fig. 2,hot corresponding to properties of the hot fluidt turbulent

. ETHZ testcaseturbulent mixing of isothermal flows

.1. ETHZ T-junction test facility

A series of detailed measurements of turbulent isothermal andhermal mixing was carried out at the Laboratory for Nuclearnergy Systems, Institute for Energy Technology, ETHZ, Zrich,

witzerland (Zboray et al., 2007). The used test section consistsf a horizontal T-junction geometry of Plexiglas pipes of 50mmnner diameter for both the main and the branch pipes. A photo ofhe test section is given in Fig. 1. In the longer run pipe (main pipe,

Fig. 1. ETHZ T-junction test facilAverage velocity in main pipe 0.5 [m/s]Average velocity in branch pipe 0.5 [m/s]Water temperature 25.0 [C]

LM =1.5m), tapwater is flowing from left to right and the deionisedwater flows from the side through the shorter branch pipe (LB =0.5m) as indicated in Fig. 1. The two flows join and mix at and afterthe T-junction and the mixture is drained through a flexible hoseshown on the right side (green).

The lengths of the run and branch pipes allow to have a devel-oped flow profile as the fluids arrive to the T-junction. Besides, atbeginning of both the run pipe and the branch pipe, just behind theinlets, honeycombs are installed to straighten the flow against anyupstream influence. The honeycombs have a cell size of 3.5mmanda length of 60mm in flow direction. In the arrangement shown inFig. 1, the main instrumentation, two wire-mesh sensors (WMS),are installed right behind each other downstream of the T-junctionin the mixing region. Three-dimensional flow field measurements(concentration of de-ionized water) have been carried out by theuse of the 1616 electrode WMS on the basis of difference in liq-uid conductivities of de-ionised and tap water. Applying distanceflanges, the sensors can be also positioned further downstreamof the T-junction. In the experiments the measurement cross-sections for the WMS measurements were located at L=51mm,71mm, 91mm, 111mm, 151mm, 191mm, 231mm, 271mm andL=311mm downstream of the T-junction. It is also possible toinstall a wire-mesh sensor on the branch side of the T-junction.Details of the WMS measurement technique can be found in(Prasser et al., 1998; Prasser et al., 2002; Zboray et al., 2007).

2.2. Selected CFD validation testcase, test geometry, meshes

Several experiments have been carried out at ETHZ by varyingtheflow rates in themain andbranchpipe, by exchanging the injec-tion of tapwater andde-ionizedwater andby changing the locationof theWMSs. For the validation of the ANSYS CFX 11.0 code the testNo. 14 has been selected. Main parameters of testcase No. 14 aregiven in Table 1.

Since the selected testcase is isothermal, so with equal watertemperature in both the main and branch pipes, the mixing of thewater from both pipes characterized by the water quality can betackled by means of Reynolds-averaged NavierStokes equationswhere advantage is taken from the inherent axial symmetry of thesetup wrt. to the symmetry plane of both pipes. Therefore simula-tions were carried out for only one half of the geometry, which ispossible in case of isothermal steady-state flow simulation, where

ity in the horizontal plane.

Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328 2315

dition

bjf

dau

Fig. 2. Geometry and boundary con

uoyancy effects are neglected. The inlet length in front of the T-unction was L=1.0m (20D) for the main pipe and L=0.5m (10D)or the branch pipe.In order to characterize numerical andmodeling errors in accor-ance with the Best Practice Guidelines (BPG) (Menter, 2002),hierarchy of 3 differently refined meshes has been generated,sing the ANSYS ICEM-CFD Hexa mesh generator. Main charac-

Fig. 3. Hierarchy of refined meshes for thes for the ETHZ T-junction testcase.

teristics of the hierarchical grids are given in Table 2. Figuresshowing the cross-sectional mesh refinement and the mesh res-olution of the branch pipe can be seen in Fig. 3(ac) for the coarse,

medium and fine mesh. Quality of the meshes has been care-fully maintained for all three mesh levels, as documented by themin. and max. mesh angles and the max. volume change for meshelements.

ETHZ T-junction testcase geometry.

2316 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

Fig. 4. Profiles of the mixing scalar at two locations downstream of the T-junction for SST turbulence model simulations on 3 different meshes.

Table 2Main parameters of mesh hierarchy for the ETHZ T-junction testcase geometry.

Mesh Nodes Refinement factor Max y+ Max angle Min angle Max. volume change

2

stbitutSflhs

is

Coarse 447,401 22Medium 1,767,491 3.95 7Fine 7,830,664 4.43 4.5

.3. CFD simulation setup and boundary conditions

The simulations on all three meshes were carried out usingteady-state RANS simulation with the shear stress transport (SST)urbulence model (Menter, 1993). The SST model applies a kasedmodel formulation inproximityof thewall and thekmodeln the bulk of the flow, while a blending function ensures a smoothransition between the twomodels. Automaticwall functionsweresed, where a maximum y+ = 4.5 on the finest mesh assures, thathe boundary layer can be fairly well resolved on this fine mesh.ince the flow in the T-junction is highly anisotropic where bothowstreamsmixanddownstreamof theT-junction, further studiesave been carried out by applying the k based baseline Reynoldstress model (BSL RSM) (ANSYS Inc., 2006).

The concentration of the de-ionized water has been simulatedn both cases by solving a transport equation of a passive transport

calar :

t()+

xj(Uj) =

xj

(eff

xj

)+ S (1)

Fig. 5. Streamlines of the turbulent mixing behind the T-junction. Double-vo144 41 1.74135 44.5 2.0141 40.9 2.08

where

eff = D +tSct

(2)

and D is the kinematic diffusivity, S is a source term for (equal to zero in the present case) and Sct is the turbulentSchmidt number. The later term arises from the application ofthe eddy viscosity hypotheses in the Reynolds averaging pro-cess of this transport equation. Usually it is assumed, that theturbulent Schmidt number Sct 0.9. But it is known from lit-erature, that other values have to be applied, e.g. for freejet flows in order to achieve numerical simulation resultsin close agreement to experiments. Therefore in the presentstudy the turbulent Schmidt number was varied in the range0.1 Sct 0.9.

In the simulations 1/6 power law velocity profiles in accordancewith the specifiedmean water velocity of 0.5m/s in both main and

branch pipes have been specified. The given inlet length of morethan 10D allows for a fairly well developed turbulent velocity pro-file at the mixing point of both water streams in the T-junction.In addition a medium turbulence intensity level of 5% is specifiedat each inlet. For the mixing scalar a value of 0.0 was set at the

rtex system is developing on the inner pipe wall behind the T-junction.

Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328 2317

f the T

baNcg

Fig. 6. Profiles of the mixing scalar for 4 different distances downstream oranch pipe inlet and 1.0 for the main pipe. For the outlet a zeroverage static pressure outlet boundary conditionhasbeenapplied.o slip conditions are set at the walls and a symmetry boundaryondition has been assumed for the central symmetry plane of theeometry (see Fig. 2).-junction for SST and BSL RSM turbulence model and different Sct values.2.4. CFD simulations and comparison to WMS measurements

First of all sensitivity studieswith the SST turbulencemodel andthe default value of Sct =0.9 have been carried on all three differ-ent mesh levels for varying characteristic timescales of the false

2318 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

M tur

tutacoacbi

Fig. 7. Cross-sectional distribution of the mixing scalar: BSL RS

imestep integration of ANSYS CFX, which is used as a means ofnder-relaxing the equations as they iterate towards the final solu-ion. Because the solver formulation is robust and fully implicit,relatively large time scale can typically be selected, so that theonvergence to steady-state is as fast as possible. No sensitivity

f the numerical algorithm was found with respect to the char-cteristic timescale, which was set to t=1.0 s. The convergenceriterion was set to 105 for the maximum residuals, which coulde obtained in all simulation runs. Furthermore the mesh sensitiv-ty was found to be not very large as well, as can be seen in Fig. 4bulence model predictions (Sct =0.2) vs. WMS measurements.

from the comparison of profiles of the mixing scalar at L=51mmand L=191mm behind the T-junction for an SST turbulence modelsimulation with Sct =0.2. Coarse and medium mesh results differonly slightly in location of large gradient of the mixing scalar, sothat the fine mesh results can be regarded as mesh independent

solutions.

For the comparison of the established CFD results with the1616 wires WMS measurements the experimental data wereread into the ANSYS CFX solver and were assigned to a so-calledadditional variable. By that means the experimental data are avail-

Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328 2319

cility i

atls

ntgwswmt

wgoBidRwurh

mLsbjt

Fig. 8. Side view of the Vattenfall T-junction test fa

ble for any kind of post-processing in ANSYS CFX-Post, also it haso be kept in mind, that the spatial resolution of the WMS data isimited and restricted to the area between the first and last mea-urement cross-section.

During sensitivity analysis with respect to turbulent Schmidtumber in the mixing scalar transport equation (1.1) it was found,hat the default value of Sct =0.9 resulted in substantially to largeradients of the mixing scalar, i.e. a too sharp separation of theater stream of high and low mixing scalar values and a sub-tantially underpredicted mixing of the two fluids. This resultas established almost independently from the applied turbulenceodel and occurred in the CFD results for the SST and BSL RSM

urbulence model as well (Fig. 5).By variation of the turbulent Schmidt number best agreement

ith the WMS measurements could be obtained for the investi-ated testcase for Sct =0.2. Fig. 6 shows corresponding comparisonf parameter variation study using Sct =0.9, 0.2 and 0.1 for SST andSL RSM turbulencemodel simulations in comparison to the exper-mental data at L=51mm, L=91mm, L=191mm and L=311mmownstream of the T-junction. Results obtained by using the BSLSM turbulence model are generally in slightly better agreementith the experimental data. But the established increase in sim-lation accuracy for the mixing process seems not to be in a goodelationship to the substantially higher computational effort for theigher order turbulence model.Finally Fig. 7 shows representative cross-sectional plots of the

ixing scalar distribution for the measurement cross-sections at

=51mm and L=191mm downstream of the T-junction. Pictureshow, that the high mixing scalar concentration is transportedy the forming and counter-rotating double-vortex behind the T-unction along the lower and upper pipe walls, while low values ofhe mixing scalar (indicating water from the branch pipe) remains

Fig. 9. Side view of flow visualization test inn the vertical plane (dimensions are given in mm).

for quite a long distance behind the T-junction at the right side ofthe main pipe, where the vortex cores induced by the branch pipeflow are located. Looking at figures for L=191mm it seems that themixing process is despite the used Sct =0.2 still slightly faster in theexperiment where the high mixing scalar concentration values atthe left side of themain pipe are alreadymore dissolved then in theCFD simulation.

3. Vattenfall testcasethermal striping in thermal fluidmixing

In contrary to the turbulentmixing of two fluid streams of equaltemperature, which can obviously quite accurately be described bytraditional RANS models, the thermal mixing of two fluid streamsof different temperature is a rather challenging testcase for com-putational fluid dynamics (CFD). The CFDmethods based on RANS,which are typically used in industrial applications, have difficul-ties to provide accurate results for this flow situation. In manycases the high turbulent viscosity predicted from the RANS-basedturbulence models in the mixing zone due to the locally highshear rates suppress any transient flow development and the CFDresults tend to a steady-state solution. On the other hand sideexperimental observations clearly state strong and high-frequencytemperature transients at pipewalls downstreamof the T-junction,the so-called thermal striping effect, which can lead to high-cyclethermal fatigue, crack formation and pipeline break in practi-cal applications, e.g. in pipelines in power plants. Recent studies

using advanced scale-resolving methods such as LES and DES haveshown promising results (Braillard et al., 2005; Hu and Kazimi,2003; Igarashi et al., 2003; Kuszaj and Komen, 2008; Ohtsukaet al., 2003; Westin et al., 2006; Westin et al., 2008). However,detailed validation of the tools and methods is still required in

the Vattenfall T-junction test facility.

2320 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

itions

oa

3

Lcvissw1tsth(ei

(at3taswctrw

wpwnta(

Fig. 10. Geometry and boundary cond

rder to determine their range of validity and their expectedccuracy.

.1. Vattenfall T-junction test facility

The model tests were carried out during 2006 at the lvkarlebyaboratory, Vattenfall Research andDevelopment. The related test-ase conditionshavebeendocumentedandprovided forCFDmodelalidation by Westin et al., Vattenfall (Westin, 2007). The test rigs illustrated in Figs. 8 and 9, and was designed in order to obtainimple and well-defined inlet boundary conditions. The setup con-ists of a horizontal pipe with inner diameter 140mm for the coldater flow (Q2), and a vertically oriented pipe with inner diameter00mm for the hot water flow (Q1). The hot water pipe is attachedo the upper side of the horizontal coldwater pipe. The length of thetraight pipes upstream of the T-junction is more than 80 diame-ers for the coldwater inlet, andapproximately 20diameters for theot water inlet. A stagnation chamber with flow improving devicestube bundles and perforated plates) is located at the entrance toach of the two inlet pipes. The origin of the coordinate system isn the centre of the T-junction.

The temperature fluctuations near the walls were measured byAnderson et al., 2006; Westin, 2007) with thermocouples locatedpproximately 1mm from the pipe wall. Two different types ofhermocoupleswereused,withanestimated frequency responseof0Hzand45Hz, respectively. Velocityprofilesweremeasuredwithwo-component laser Doppler velocimetry (LDV) in each inlet pipes well as in cross-sections located 2.6 and 6.6 diameters down-tream of the T-junction. The mixing process has also been studiedith single-point laser-induced fluorescence (LIF) at isothermalonditions. The pipes near the T-junction were made of plexiglassubes surrounded by rectangular boxes filledwithwater in order toeduce the diffraction when the laser beams pass the curved pipealls.The tests were carried out with a constant flow ratio Q2/Q1=2,

hich implies approximately equal flow velocities in the two inletipes. The temperature difference between the hot and cold water

as 15 C (hot water temperature T1 =30 C), and the Reynoldsumber in both inlet pipes were approximately 1.9105 for theest case considered in the present paper with bulk velocities ofpproximately 1.53m/s in the hot leg and 1.56m/s in the cold legcorresponding to Q1=12 l/s and Q2=24 l/s). Tests were also car-for the Vattenfall T-junction testcase.

ried out (Anderson et al., 2006)with the sameflowratio but varyingReynolds number (0.5105 and 1105) showing similar results.

As mentioned earlier for the provided testcase it was appliedsignificant care to establishwell-defined inlet boundary conditionsfor CFD model validation tests. The LDV measurements in the coldwater pipe just upstream of the T-junction showed mean veloc-ity and turbulence profiles in good agreement with experimentaldata on fully developed pipe flow at similar Reynolds numbers. Thelength of the hot water inlet pipe was too short (20 diameters) toobtain fully developed flow conditions, but the inlet velocity pro-filesweremeasured inorder to obtain inlet boundary conditions forthe simulations. Therefore for the following CFD investigations themeasured velocity profiles were used for both inlet cross-sections.

When comparing computational and experimental results forthe observed temperature fields non-dimensional quantities arecompared, such as

T = T TcoldThot Tcold

(3)

The normalization reduces the influence of small temperaturevariations between different test days. In the results part of thepresent paper the mean temperatures near the pipe walls arereported at the left, right, top and bottom side of the pipe. Due toa mistake when assembling the T-junction, the thermocouples incross-sections z=2D, 4D, 6D and 8D are rotated 4 as compared tothe design specifications, which must be taken into account wheninterpreting the data (Fig. 10).

3.2. Selected CFD validation testcase, test geometry, meshes

From the three different experiments as provided in (Andersonet al., 2006; Westin, 2007) for the validation investigation the so-called 200% testcase has been selected, referring to the Reynoldsnumbers, mean bulk velocities and volume flow rates as given inSection 2.1. Main parameters of the testcase are given in Table 3.

Since it is well-known from literature, that the thermal stripingphenomena cannot be accurately predicted by RANS- or URANS-based simulation approaches, the goal of the current investigation

was the application of scale-resolving turbulence modeling to thetestcase. For this purpose a high spatial and temporal resolutionof the flow is necessary, which assures CFL numbers in the orderof 1 everywhere in the geometry, where dominating turbulentlength and time scales have to be resolved. Twohexahedralmeshes

Th. Frank et al. / Nuclear Engineering an

Table 3Main parameters of the thermal mixing Vattenfall T-junction testcase.

Flow rate in branch pipe (Q1, hot water) 12 [l/s]Flow rate in main pipe (Q2, cold water) 24 [l/s]Mean bulk velocity in branch pipe 1.53 [m/s]Mean bulk velocity in branch pipe 1.56 [m/s]Reynolds number for hot leg 1.9105

wFcmMaiohtrC

gaccdcv

3

tme

behavior theURANSSSTsolutionwasquicklyapproachingasteady-Reynolds number for cold leg 1.9105Hot water temperature 30.0 [C]Cold water temperature 15.0 [C]

ere generated for the geometry of the Vattenfall testcase (seeig. 11), startingwith a rather coarse grid (ANSYS TGrid) and finallyoming upwith amesh showing reasonably good near-wall refine-ent with about 2.2 Mill. mesh nodes (ANSYS ICEM-CFD Hexa).eshes were generated scalable with minimum mesh angles ofbout 35. The maximum y+ values of about 33.2 on the finer meshs comparable to the near-wallmesh refinement of the coarsemeshbtained for the ETHZ testcase, which ismainly due to the requiredigher homogeneity of mesh elements for the LES-like computa-ions. Unfortunately the results on mesh 2 could not be obtainedight in time for comparison in this paper, so further discussion ofFD results refer to the results as obtained for the mesh 1.It is worthmentioning, that unfortunately the orientation of the

eometry in the CFDmodelwas not the same as for the experiment,lso the origin of the coordinate system has been placed in theenter of the T-junction as well. Further on we will refer to theoordinate system used in the CFD simulations, showing its z-axisirected along the axis of the main pipe and its y-axis along theenterline of the branch pipe. Accordingly velocity components u,and w are referring to these coordinate axes as well.

.3. CFD simulation setup and boundary conditionsFor the CFD investigation the inlet geometry was shortened tohe locations of the LDVmeasurements in the cross-sections in theain and branch pipe in front of the T-junction (see Fig. 10), sincexactly the measured mean velocity profiles from the experimen-

Fig. 11. Hexahedral meshes generated for thed Design 240 (2010) 23132328 2321

tal data were prescribed here as inlet boundary conditions for theCFD simulation. Therefore inlet BCs have been prescribed at theupstream cross sections at z=3D2 for the cold leg (main pipe)and at y=3.1D1 for the hot leg (branch pipe). Profiles of turbu-lent kinetic energy and turbulent dissipation were derived fromthe LDV data for both inlets. No transient inflow boundary condi-tions, e.g. generation of unsteady velocity fluctuations according toturbulence spectra or use of unsteady pipe flow data, has been pre-scribed at the inlets. As for the ETHZ testcase a zero averaged staticpressure outlet BC has been used for the outlet cross-section andnon-slip BCs with automatic wall treatment are used for all wallsof the domain. Since the meshes were generated for the full 3Dgeometry there was no more need for a symmetry boundary con-dition. Additionally so-called monitoring points were introducedat all locations of thermocouples, as can be seen from Fig. 10, inorder to monitor the transient history of main characteristics, i.e.fluid temperature at these locations for comparison with the data.

For meshes 1 and 2 some basic investigations have been carriedout for the verification of the CFD setup, the investigation of meshindependency of the CFD solution and for the quantification of thenumerical error in steady-state and transient simulation using theshear strain transport (SST) turbulence model in RANS and URANSmode.The temperaturedependentfluidproperties (density, viscos-ity) have been taken into account by defining the water propertiesfrom the industry standard IAPWS-IF97. Based on resulting fluiddensity differences fluid buoyancy has been taken into account.

For the transient URANS SST and SST-SAS simulations a second-order backward Euler time discretization with a timestep oft=0.001 s was used and a convergence criterion based on themaximumresidualsof104 was reachedatevery timestepwith35coefficient loops (sub-iterations) per timestep. The high-resolutionadvection scheme has been applied for the spatial discretization ofmomentumequations. Itwas found, that after some initial transientstate solution in terms of velocity and temperature fields. Thisresult is as expected from the experience of other researchers andunderlines the strong requirement for scale-resolving turbulencemodels for this type of applications. The solution obtainedwith the

Vattenfall T-junction testcase geometry.

2322 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

e T-ju

UfS

rmlomaflvadtat

wt

Q

ApCaos

Fig. 12. Vortex structure developing downstream of the Vattenfall testcas

RANS SST model furthermore has been used as an initializationor the further transient investigations using the scale-resolvingST-SAS turbulence model.The so-called scale-adaptive simulation (SAS) model was

ecently proposed by Menter and Egorov (2004, 2005) as a newethod for the simulation of unsteady turbulent flows. The formu-

ation canoperate in standard (U)RANSmode, but has the capabilityf resolving the turbulent spectrum in unsteady flow regions. Theethod is termed scale-adaptive simulation (SAS) modeling, as itdapts the length-scale automatically to the resolved scales of theow field. The distinguishing factor in the model is the use of theon Karman length-scale, LK, which is a three-dimensional gener-lization of the classic boundary layer definition U (y)/U (y) (foretails see (Egorov andMenter, 2007)). The governing equations ofhe SST-SAS model differ from those of the SST RANS model by thedditional SAS source term QSAS in the transport equation for theurbulence eddy frequency :

k

t+ (Uk) = Pk ck +

[(+ t

k

)k]

(4)

t+ (U) =

kPk 2 + QSAS +

[(+ t

)]

+ (1 F1)22

1k (5)

here 2 is the value for the k regime of the SST model andhe source term QSAS reads:

SAS = max[2S

2(

L

LvK

)2 C 2k

max

(22

,

k2k2

),0

]

(6)

complete description of the SST-SAS model can be found in the

ublications (Egorov andMenter, 2007; Menter and Egorov, 2005).ontrary to standard URANSmodels, the SAS formulation providesturbulent length-scale, which is not proportional to the thicknessf the turbulent (shear) layer, but proportional to the local flowtructure. The SAS solution automatically applies the RANS modenction as visualized by isosurfaces of the Q-criteria (mesh 1, Q=1001/s2).

in the attached boundary layers, but allows a resolution of the tur-bulent structures in the detached regime. This behavior is in muchbetter agreement with the true physics of the flow, as was alsoshown for other cases by Menter and Egorov (Egorov and Menter,2007; Menter and Egorov, 2004, 2005). The LES-like capability ofthe model is achieved without an explicit dependency on the gridspacing, contrary to classical LES methods.

3.4. CFD simulations and comparison to data

As already mentioned, the SAS-SST solution on the meshes 1and 2 for the Vattenfall testcase geometrywas initialized at T=0.0 swith the quasi steady-state result from the preceding SST URANSsimulation on the same mesh. Then transient simulation by usingthe SAS-SST scale-resolving turbulence model approach has beencarried out for 7.6 s real timewith a time step oft=0.001 s, whereafter a first 1.48 s the transient averaging of mean flow field char-acteristics (e.g. mean velocity and temperature) has been started.

Fig. 12 shows the typical developing vortex structures down-stream of the T-junction at T=7.6 s real time. The visualization isbased on isosurfaces of the so-called Q-criteria, where:

Q = 2 S2 =(

uixj

ujxi

)2(

uixj

+ ujxi

)2(7)

with being the vorticity and S the strain rate of the flow field.The figure clearly shows that the small change in the Vattenfall T-junction geometry in comparison to the ETHZ testcase by choosinga smaller diameter for the branch pipe leads to the formation ofa so-called horseshoe vortex upstream the intruding hot water jetfromthebranchpipe. Furthermore thefigure showsrather irregularturbulent vortex structures forming immediately downstream ofthe T-junction and being convected with the flow along the mainpipe. Further downstream it can be observed, that the length scale

of the vortex structures decreases with turbulent dissipation.

Inorder tomakeanassessment,whether theSAS-SSTsimulationis able to resolve the different turbulent scales on the underlyingmesh and with the used timestep, two different evaluations havebeen carried out. First, the blending function of the SAS-SST model

Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328 2323

ity an

rlamsTltLflp

dp

Fig. 13. Time averaged veloc

esponsible for the blending between the scale-resolving turbu-encemodel and the URANS SST has been analyzed in the geometrynd it shows, that already at the location of the T-junction theethod is fully switching from URANS SST to the scale-resolvingimulation and this state remains unchanged downstream of the-junction up to the outlet cross-section. Second the turbulentength scale Lt =

k/C1/4 of the CFD simulation was compared

o the maximum edge size of the mesh elements =max{x, y,z}. Comparison shows, that for almost the entire flow domain

t/

2324 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

d w v

atst

fl

Fig. 14. Time averaged streamwise w velocity an

t the top of the pipe. In the result the fluid temperature at thehermocouple sensor location on top wall of the pipe at z=2D still

hows rather high fluid temperature close to the branch pipe inletemperature.

Fig. 14 shows the streamwise w velocity and wRMS velocityuctuationsaty=0; z=2.6Dand z=6.6D, respectively indirect com-

Fig. 15. Time averaged crosswise v velocity and v velelocity fluctuations at y=0; z=2.6D and z=6.6D.

parison to the LDV measurement data at these locations. Fig. 15shows the corresponding comparison for the crosswise v velocity

and vRMS velocityfluctuations in the samecorrespondingprofiles. Inboth Figs. 14 and 15 the comparison of SST and BSL RSM turbulencemodel simulation results show, that scale-averaging turbulencemodels like SST or BSL RSM are not able to satisfactory predict

ocity fluctuations at y=0; z=2.6D and z=6.6D.

Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328 2325

tlCai

FSitpt(itceo1aemtctbtfsaisli

mrsiditlmm

aaia

Fig. 16. Development of centerline RMS velocities from z=0 to z=7.5D.

he profiles of mean velocity components w and v in the two ana-yzed cross-sections,while the resultswith SAS-SST scale-resolvingFD simulation shows reasonable good agreement with data. Thegreement with data for the SAS-SST simulation could be slightlymproved on the refined mesh 2.

The streamwise w velocity in the left hand side diagrams ofig. 14 shows reasonable well agreement with data for both SAS-ST simulations on mesh 1 and 2. Further the fluctuation velocityn streamwise direction wRMS is in general good agreement withhe measurements as well, also the pattern of the cross-sectionalrofile shows some asymmetry and some larger deviations fromhe data points for mesh 1 calculation on the right side of the pipepositive x). This could be an indication that the averaging periodn the CFD simulation on mesh 1 of about T6.12 s real time (sta-istical averaging started after 1600 timesteps; averaging periodorresponding to 6120 timesteps) was still too short in order tostablish statistically reliable averaged values. The results obtainedn the refined mesh 2 with a larger averaging period of about2.42 s real time (statistical averaging started after 3000 timesteps;veraging period corresponding to 12420 timesteps) show in gen-ral more symmetric profiles and therefore seem to be statisticallyore reliable from the point of view of statistical averaging of

he SAS-SST transient results. The later start-up of the statisti-al averaging process allowed for a better flow development andherefore the statistical averaged flow properties are less affectedy contributions from the URANS solution used for the initializa-ion of the SAS-SST simulation. Similar situation can be observedor the crosswise v velocity component and its RMS fluctuation ashown in Fig. 15, where the SAS-SST results on mesh 2 are in bestgreement with the experimental data. For the crosswise veloc-ty component it can be observed, that the RMS fluctuations areubstantially higher then the averaged mean values. For both ana-yzed RMS velocity fluctuations can be observed, that the SAS-SSTs slightly underpredicting the measured values.

Furthermore comparison has been made for the axial develop-ent of the centerline vRMS and wRMS fluctuation velocities in the

ange of 1.5D z7.5D in comparison to the LDVmeasurements ashown in Fig. 16. The predicted values from the statistical averag-ng of the CFD result show again a reasonable good agreementwithata and the correct decay in the amplitudeof thefluctuation veloc-ties RMS over pipe length. Results onmesh 1 and 2 show the samerend and evolution of the RMS fluctuation velocities over the pipeength, also the predicted values on the refined mesh 2 show someinor reduced level of velocity fluctuations in correspondence toesh 1 results.

Further comparisons are made for the normalized time aver-

ged wall temperatures at the bottom, left and right side as wells at the top wall of the pipe at the locations of the thermocouplesn the experiment (r=69mm). Comparison to thermocouple datare shown in Figs. 17(ad). The definition of T* corresponds to theFig. 17. Development of timeaveragedwater temperature over pipe length for ther-mocouple locations at top, left and right side wall as well as at the bottom of thepipe.

formula as given in Eq. (3). Comparison to non-dimensionalizedtemperature has been chosen, since it is mentioned by the exper-imentalists, that it was rather difficult and not always possible tokeep a constant temperature level for the inflow conditions overthe time of themeasurement campaign. Furthermore the results ofthe ANSYS CFX SAS-SSTmodel have not only compared to data, butan ANSYS Fluent simulation has been carried out on the identical

mesh 1 using the SAS-SST model implementation in ANSYS Fluent.The mesh 1 has still a rather coarse mesh resolution in the vicinityof the pipe wall. Therefore the different cell-centered vs. vertex-centered discretisation schemes of ANSYS CFX and ANSYS Fluent

2326 Th. Frank et al. / Nuclear Engineering and Design 240 (2010) 23132328

F 4D; d

lamrseoe

rtbfAmfl

podova1

Fd

ig. 18. Temperature fluctuations over time for thermocouples T52 and T58 at z=ata.

ead in that case to rather different locations of data representationnd different resolution of the boundary layer. Consequently theeshwas refined and the ANSYS CFX simulationwith SAS-SSTwas

epeated on the refined mesh 2, also the modified treatment of thetatistical averaging make the results on two different meshes notntirely comparable. For the comparison on the left and right sidef the pipe the agreement with data thereby could be improved,specially on cross-sections between x/D between 2 and 6.It can be observed from Fig. 17b, that the SAS-SST simulation

esults agree very well with data for the thermocouple locations athe bottomwall of the pipe for the full axial range ofmeasurementsetween 2 z/D10. While almost no difference can be observedor the two compared numerical simulations of ANSYS CFX andNSYS Fluent at this location onmesh 1 the solution on the refinedesh shows some smaller mixing with the higher temperatureuid.In Fig. 17(c and d) the normalized time averaged wall tem-

eratures are compared for the left and right pipe wall locationsf the thermocouples. It can be observed, that the experimentalata show a slight asymmetry, especially for 2 z/D6, while for

bvious symmetry reasons the CFD results show almost identicalalues for both sides of the pipe in the long-term statistical aver-ge. It can be remarked, that the solution of ANSYS CFX on meshdelivers slightly higher temperature values in comparison to the

ig. 19. Temperature fluctuations over time for thermocouples T53 and T57 at z=4D; ata.=45 (a) as predicted from ANSYS CFX SAS-SST simulation and (b) experimental

ANSYS Fluent solution, possibly due to the different location of thefirst near-wall mesh vertex in the ANSYS CFX discretization. On therefined mesh 2 the ANSYS CFX result is again in quite good agree-mentwith bothdata and theANSYS Fluent solution. TheCFD resultsare in reasonable good agreement with the thermocouple data atthe left pipe wall, while the experimental temperature data at theright pipe wall are slightly lower. This is resulting in a slightly bet-ter agreement on x/D2 and a slightly worse agreement on largerx/D, but should be addressed to the uncertainty of the experimentaldata. As already mentioned it has to be taken into account and ismentioned in the experimental report (Anderson et al., 2006), thatit was in particular difficult throughout the different realizationsof the experiment to maintain constant thermal boundary condi-tions, which is seen as one of themain reasons for the requirementto normalize the measured temperature values and for possibledifferences to the CFD results.

Finally Fig. 17a shows the comparison for the top wall loca-tion of thermocouples. At these locations the largest differencesbetween the experimental data and CFD results on one hand sideand between the two CFD codes on the other hand side can be

observed. ANSYS CFX is predicting substantially higher fluid tem-peratures especially in the close distance to the T-junction, whilethe agreement with data becomes better with increasing pipelength, especially for z/D>6. The agreement of the ANSYS Fluent

=90 (a) as predicted from ANSYS CFX SAS-SST simulation and (b) experimental

ring an

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Th. Frank et al. / Nuclear Enginee

esults with data for the top wall temperature sensors seems toe better over the entire range of measurement locations in com-arison to the ANSYS CFX results. The reason for the observableifferences are still subject of further investigations, especiallyince even with the mesh refinement on mesh 2 the differencesetween the CFD results could not be substantially decreased. Aossible reason for the differences between the ANSYS Fluent andNSYS CFX results might be themaximum allowed number of onlyhree inner iterations per timestep in the ANSYS CFX simulation.lso the momentum and energy transport RSM residuals matchedhe prescribed convergence target, the resulting temperature fieldight be locally affected by still larger numerical errors. Finally

he plotted temperature values corresponding to the first near-all mesh cell in the CFD simulation do not correspond to the samehysical location onmesh 1 vs.mesh 2 and in ANSYS CFX vs. ANSYSluent due to thedifferent spatial discretizationof bothCFDsolvers.he computation timeof theSAS-SST simulationsunfortunatelydidot allow a repetition of the simulation with a smaller integrationimestep or a larger number of inner iterations for an improvedonvergence level.

If we finally look on the time series of recorded thermocoupleeasurements in comparison to the fluid temperature recordedt the corresponding monitoring point locations, then similar pat-erns can be recognized. Fig. 18(a and b) shows the comparison ofransient temperature signals for the thermocouples T52 andT58at/D=4 and =45 and Fig. 19(a and b) for the thermocouples T53nd T57 at z/D=4 and =90. In both the CFD results and exper-mental data no regular frequency of the temperature fluctuationver time can be identified. As already discussed, the CFD result forhe top wall of the pipe at z/D=4 (T52) shows too high mean tem-erature level in comparison to experiments, while the amplitudef temperature fluctuations is about 5 C in both cases. For theide walls of the pipe at z/D=4 (T53) the amplitude of temperatureuctuations from the CFD simulation seems to be even higher thenn the experiment.

. Conclusions

Investigations have shown, that Reynolds averaging basedU)RANS turbulence models like SST or BSL RSM are able to sat-sfactorily predict the turbulent mixing of isothermal fluid in-junctions, while the thermal mixing of water streams of dif-erent temperature in T-junctions is a challenging testcase forFD methods, and advanced scale-resolving turbulence modelingpproaches like LES, DES or SAS are required in order to simulatehe strongly transient flow and temperature fields. The applica-ion of Best Practice Guidelines to these type of transient LES-likeimulations and the thoroughly validation of the scale-resolvingurbulencemodels today still involves a couple of unresolved ques-ions due to the extremely high computational effort in the orderf several weeks for a single transient CFD simulation.In the present investigation two different testcases have been

nvestigated. The turbulent mixing of water streams of equal tem-erature in a T-junction in the horizontal plane (ETHZ testcase) hashown to be satisfactorily predictedwith steady-state computationnd traditional Reynolds averagingbasedRANSmodels like SST andSL RSM. The CFD results have been compared to the detailedwire-esh sensor concentration measurements carried out at ETHZ test

acility, by importing the WMS data into the CFD post-processor.n order to establish the very good comparison to the measure-ents, the turbulent Schmidt number had to be adjusted to values

f about 0.10.2 in order to reflect the strongly accelerated turbu-ent mixing in the pipe T-junction in this case. Unfortunately theppliedmeasurement technology does not provide information forore detailed comparison of predicted velocity fields andReynoldstresses with the CFD simulation results.d Design 240 (2010) 23132328 2327

The second investigated testcasewasprovidedbyWestin (2007)and is aimed to provide detailed experimental validation data andthoroughly prepared and monitored testcase boundary conditionsfor the assessment and validation of LES-like turbulencemodels forthe further study of thermal striping phenomena occurring in ther-malmixing in T-junctions. ANSYS CFX 11.0with the scale-resolvingSAS-SST approach has been applied to one of the provided testcaseconditions. The CFD solutions in fact showed the occurrence of thethermal striping phenomena in the simulations. Predicted generalflow patterns and time averagedmean velocity profiles are in goodagreementwith the experimental observations, alsodue to the longsimulation time the averaging time (6.12 s, 6120 timesteps) for theSAS simulation was probably still too short in order to establishstatistically fully reliable time averaged variable fields for velocityand temperature. The predicted velocity fluctuationRMSvalues arein reasonable good agreement with data as well, compare reason-ably well to measured profile data and show the correct reductionin RMS velocity fluctuation amplitude due to turbulent dissipationwith increasing pipe length downstream of the T-junction.

Transient thermal striping was observable from the SAS-SSTsolution. Measured as well as predicted thermal striping patternsdo not show any recognizable regular pattern in temperature fluc-tuations. While some differences occurred for the predicted walltemperatures at the top wall of the pipe, the predicted normalizedtime averaged temperature values for the side and bottom wallthermocouple locationswere ingoodagreementwith themeasure-ments. The onset of thermal striping for the side and bottom wallsof the main pipe was predicted at about z4D, which is in goodcoincidence with the observable rise in normalized time averagedtemperature from the experiments.

Application of Best Practice Guidelines to LES-like CFD simula-tions is still a challenge due to the extremely large computationtimes. Therefore special care has to be applied to the mesh gener-ation with respect to LES criteria for resolution of turbulent lengthscales andwith respect to the time averaging procedure in order toassure the statistical reliability of the CFD results. Further investi-gations are carried out in order to investigate the influence ofmeshresolution on statistically averaged flow simulation results.

Acknowledgements

The authors like to acknowledge the good collaboration andopen discussions with the team of Prof. H.-M. Prasser at ETHZand with J. Westin at Vattenfall AB, who both have provided theunderlying detailed and very carefully documented sets of valida-tion data. The author thanks F. Carlsson from ANSYS Sweden forthe provision of the ANSYS Fluent simulation result for the Vatten-fall testcase. Further the present investigation has been supportedby the German Ministry of Economy (BMWi) under grant number150 1328 in the framework of the German CFD Network in NuclearReactor Safety.

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Simulation of turbulent and thermal mixing in T-junctions using URANS and scale-resolving turbulence models in ANSYS CFXIntroductionETHZ testcaseturbulent mixing of isothermal flowsETHZ T-junction test facilitySelected CFD validation testcase, test geometry, meshesCFD simulation setup and boundary conditionsCFD simulations and comparison to WMS measurements

Vattenfall testcasethermal striping in thermal fluid mixingVattenfall T-junction test facilitySelected CFD validation testcase, test geometry, meshesCFD simulation setup and boundary conditionsCFD simulations and comparison to data

ConclusionsAcknowledgementsReferences