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Nuclear Engineering and Design 240 (2010) 1548–1557

Contents lists available at ScienceDirect

Nuclear Engineering and Design

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

omputational study of conjugate heat transfer in T-junctions

imon Kuhna, Olivier Braillardb, Bojan Nicenoa,∗, Horst-Michael Prassera,c

Paul Scherrer Institute, 5232 Villigen, PSI, SwitzerlandCommissariat à l’Énergie Atomique, CEA Cadarache 13108 St Paul lez Durance Cedex, FranceETH Zürich, Sonneggstrasse 3, 8092 Zürich, Switzerland

r t i c l e i n f o

rticle history:eceived 2 December 2009eceived in revised form 18 January 2010ccepted 19 February 2010

a b s t r a c t

In this work we focus on the numerical prediction of temperature fluctuations induced in solid materialsthrough turbulent mixing processes. As test case we use the mixing of two streams of different tempera-ture in a T-junction. Due to the turbulent mixing of the two streams temperature fluctuations occur whichare also transferred to the solid walls in contact with the fluid. Such fluctuations in the solid materialmay lead to thermal fatigue and are therefore relevant for the lifetime management of components usedin nuclear power plants (NPP).

We investigate the mixing in T-junctions made of different materials and having different pipe wallthicknesses. The temperature difference between the streams in the main and side branch is set to 75 ◦Cand the mass flow rate in the main pipe is three times larger than in the side branch. In a first step weperform a set of simulations by using different formulations of the large-eddy simulation (LES) subgridscale model, i.e. classical Smagorinsky model and dynamic procedure, to identify the influence of the

modeled subgrid scales on the simulation results. The comparison between available experimental dataand the numerical results reveals a good agreement when using the dynamic procedure. In a second stepwe address the temperature fluctuations in the solid wall subject to the wall thickness. The influence ofthe wall thickness is represented as a damping effect on the temperature fluctuations in radial directionin the pipe material. This study shows the capability of LES to predict thermal fluctuations in turbulent mixing.

. Introduction

In T-junctions, especially in the regions where hot and coldtreams are not completely mixed, significant temperature fluc-uations can occur in the whole mixing region and even close tohe solid walls. The presence of these fluctuations may also induceemperature fluctuations in the solid walls, which leads to cyclichermal stresses and eventually to fatigue cracking. To be able toonduct material, structural and damage analysis, knowledge abouthe exact location, amplitude and frequency of those temperatureuctuations is crucial. In this respect computational fluid dynam-

cs (CFD) is used to predict the mixing between hot and cold watern a T-junction and recent studies have shown large-eddy simula-

ions (LES) to be successful (Hu and Kazimi, 2006; Coste et al., 2008;iceno et al., 2008).

Thermal striping leading to thermal fatigue was first investi-ated in the context of liquid-metal-cooled fast breeder reactors

∗ Corresponding author at: Paul Scherrer Institute, Thermal-Hydraulics Labora-ory, Nuclear Energy and Safety Department, 5232 Villigen PSI, Switzerland.el.: +41 563104149.

E-mail address: bojan.niceno@psi.ch (B. Niceno).

029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2010.02.022

© 2010 Elsevier B.V. All rights reserved.

(Muramatsu and Ninikata, 1996). However, this issue is relevantfor various types of nuclear reactors as the incident at the lightwater reactor Civaux-1 revealed (Jungclaus, 1998). With respect toplant life management several experimental and numerical stud-ies were conducted to address thermal fatigue of components innuclear power plants (e.g. Hu and Kazimi, 2003, 2004; Lee et al.,2004, 2009).

The present study applies LES to predict the fluid velocity fieldand the temperature field in the fluid and the solid in two differentmixing T-junctions using the commercial CFD software FLUENT.1

The two cases differ by the wall material and its thickness: (i) 1 mmof brass and (ii) 5 mm of steel. The properties of both materialsare listed in Table 1. The first design is based on CEA’s FATHERINO“Skin of Fluid Mockup” experiment and these results are used forthe validation of the computations. For both cases the mixing T-

junction has an inner pipe diameter of 54 mm. We computed forboth designs a case where the hot fluid enters the main pipe witha mean velocity of 2.55 m/s and a temperature of 83 ◦C. The meanvelocity of the cold fluid in the branch pipe was set to 0.85 m/s and

1 FLUENT is a trademark of ANSYS Inc. (http://www.ansys.com).

S. Kuhn et al. / Nuclear Engineering and

Nomenclature

˛ heat transfer coefficientˇ volumetric thermal expansion coefficientBi Biot number, ˛t/�cp heat capacityCS Smagorinsky constant� LES filter width� LES test filter widthd wall distanceg acceleration due to gravity� von Kármán constant� heat conductivity� dynamic viscosity� kinematic viscosity�t turbulent viscosityp filtered pressurePr Prandtl numberPrt Turbulent Prandtl number� fluid densityRe Reynolds number for pipe flow, UmD/�Sij rate of strain tensort pipe wall thicknessT temperature�ij = u

′iu

′j

subgrid turbulent stress

�i = T ′ u′i

subgrid turbulent heat flux

u, v, w resolved velocity components

to(wcTt

bloflrc

2

rt

Um mixed velocityx, y, z Cartesian coordinates

he temperature to 8 ◦C. This results in a temperature differencef 75 ◦C of the pre-mixed fluid streams and a Reynolds numberRe) in the mixed stream of 2.7 × 105. On the outer pipe surfacee applied a convective boundary condition with a heat transfer

oefficient of 2 W/(m2K) and a free stream temperature of 293 K.hese values were chosen to mimic the experimental conditions ofhe FATHERINO setup (Braillard, 2008).

The practical relevance of the performed simulations is giveny the large value of Re and the varying fluid properties due to the

arge temperature difference. We focus in detail on the dynamicsf the mixing and the temperature fluctuation in the solid and theuid with respect to the wall thickness. The generated data areelevant for the subsequent prediction of thermal stresses and theorresponding life span of the T-junctions.

. The FATHERINO 2 facility

The FATHERINO 2 facility (see Fig. 1) is located at CEA Cadaracheesearch center. The FATHERINO facility is designed to performhermo-hydraulic tests in mixing T-junctions. The available tem-

Table 1Properties of the brass and steel mockup (Braillard, 2008).

Properties of brass

Density � (kg/m3) 8522Thermal conductivity � (W/(mK)) 111Heat capacity cp (J/(kg K)) 385

Properties of steel

Density � (kg/m3) 7821Thermal conductivity � (W/(mK)) 16Heat capacity cp (J/(kg K)) 440

Design 240 (2010) 1548–1557 1549

perature difference reaches 75 ◦C with a maximum mixing flow rateof 50 m3/h. The facility is able to create a very turbulent mixing in 2′′

T-junction mockups. The heat transfer coefficient is estimated to be14,000 W/(m2 K) with Re = 4.9 × 105. These physical parametersare similar to industrial mixing T-junctions.

The FATHERINO 2 test procedure consists of mixing the flu-ids from two vessels in the mockup. These vessels are initiallyfilled with water and conditioned at low (5 ◦C) and high temper-ature (80 ◦C). There is a motor pump for each line (cold and hotbranches) and the flow rate is controlled by operating valves. Toensure the boundary conditions in each inlet a homogenizationdevice is installed to control the turbulent flow and to providea known velocity profile. A thin brass mockup (“Skin of FluidMockup”) was designed to visualize the field of mean and fluc-tuating temperature in the fluid with minimized attenuation inreal time. The basic idea is to use the mockup as an envelope ofthe fluid, and to benefit from its thermal properties to efficientlyvisualize the thermal information. Only the interface between thefluid and the structure will be observed, but this represents themost interesting part of the mixing domain which contributesto the assessment of the thermal load for mechanical stresscalculation.

The mockup has to exhibit a good thermal transparency; tem-perature fluctuations in the fluid must be visualized with a verylow level of attenuation. To obtain such a property the structuremust have a very low Biot number (ratio between the heat transfercoefficient and the conductivity of the material). As a consequencethe selected material for the mockup needs to have a large ther-mal conductivity and a thin thickness. In the same time, a toothin mockup increases the risk to be damaged by the inertia ofthe fluid and pressure effects in the flow. Because of all thesedemands the mockup was finally constructed of brass with a wallthickness of 1 mm, which yields a Biot number of Bi=0.126 (seeFig. 2).

The mockup consists of 3 pipes and 1 T-join, the different partsare joined together without any additive material (brazed joint orcement) to avoid undesired thermal effects in the area of interest.A mat black color covers the parts used for infrared visualization(see Fig. 2).

3. Subgrid scale models and numerical details

The equations describing turbulent flows and heat transfer aregiven by the conservation of mass, momentum and thermal energy.The spatially filtered form of the conservation of momentum equa-tion can be written as

∂ (�ui)∂t

+∂(

�ui uj

)∂xj

= − ∂p

∂xi+ ∂

∂xj

[�

∂ (�ui)∂xj

− ��ij

]+ Fi, (1)

and the conservation of thermal energy equation becomes

∂(

�T)

∂t+

∂(

�ujT)

∂xj= ∂

∂xj

[�

Pr

(∂T

∂xj

)− ��j

], (2)

where p is the filtered pressure field, Fi is an external force, �denotes the dynamic viscosity of the fluid, Pr is the Prandtl numberdefined as

Pr = �cp

�, (3)

and �ij, �j represent the unresolved turbulent stress and turbu-

lent heat flux, respectively. The coupling between the temperatureand the velocity fields is accomplished by applying the Boussinesqapproximation:

FB = −�giˇ(

T − Tref

), (4)

1550 S. Kuhn et al. / Nuclear Engineering and Design 240 (2010) 1548–1557

Fig. 1. Schematic of the FATHERINO 2 facility.

n of Fl

waw

S1�b

�

TP

Fig. 2. Detailed view of the T-junction and the “Ski

here ˇ is the thermal expansion coefficient of the fluid, and gi thecceleration due to gravity. The working fluid for this test case isater, its properties are outlined in Table 2.

The LES is performed by using the classical and the dynamicmagorinsky model for the subgrid scales (SGS) (Germano et al.,991). For both models the unresolved traceless subscale stressesij are related to the rate of strain Sij of the resolved velocity fieldy employing the Boussinesq eddy-viscosity concept:

ij − 13

�kkıij = −2�tSij. (5)

able 2roperties of water at 20 ◦C (Wagner and Kruse, 1998).

Property

Density � (kg/m3) 998.2Kinematic viscosity � (m2/s) 1 × 10−6

Thermal conductivity � (W/(m K)) 0.597Heat capacity cp (J/(kg K)) 4182Thermal expansion coefficient ˇ (1/K) 2.07 × 10−4

Prandtl number Pr 7

uid Mockup” used for the FATHERINO experiment.

The eddy viscosity is defined as

�t = (CS�)2|S|, (6)

where � denotes the length scale of the unresolved motion relatedto the volume of the computational cell as: �V

� = (�V)1/3, (7)

and |S| is the magnitude of the strain rate defined as:

|S| =√

2SijSij, Sij = 12

(∂ui

∂xj+ ∂uj

∂xi

)(8)

In the classical formulation of the Smagorinsky model CS is aconstant, which is set to a value of 0.1 in our case (e.g. Piomelliet al., 1988). To ensure correct near wall behavior of the turbulentviscosity wall-damping functions must be applied when using thisclassical Smagorinsky approach. In FLUENT this is implemented bycomputing the turbulent viscosity as

�t = L2S |S|, (9)

where the characteristic length scale LS is computed from

LS = min(�d, CS�), (10)

ng and Design 240 (2010) 1548–1557 1551

wdc

�

w

C

C

w

o

Meatotbfl

ssptbwmbseabmaTf

4

tSMcspstfl

eitfIlt

4

r

S. Kuhn et al. / Nuclear Engineeri

here � denotes the von Kármán constant (� = 0.42) and d theistance to the closest wall. The subgrid turbulent heat flux is cal-ulated from the simple gradient diffusion hypothesis as

i = − �t

Prt

∂T

∂xi(11)

here Prt = 0.85 is the turbulent Prandtl number.For the dynamic procedure used with the Smagorinsky model

S is no longer a constant but evaluated with the expression

S = −12

LijMij

MklMkl, (12)

here Lij = uiuj − uiuj represents the resolved turbulent stress

f the scales between � and a coarse � (where � = 2�), and

ij = �2 |S|Sij −�2|S|Sij represents the contribution of the mod-led stress of those scales. The value of CS is clipped at zero tovoid numerical instabilities. The dynamic procedure to obtainhe Smagorinsky constant ensures correct near wall behaviorf the turbulent viscosity eliminating the necessity to includehe wall-damping functions. The SGS turbulent Prandtl num-er is obtained by applying the dynamic procedure to the SGSux.

The computations were performed by using the commercialoftware package FLUENT, which provides a finite-volume basedecond-order accurate solver. The PRESTO algorithm was used forressure–velocity coupling, the diffusive and convective terms ofhe discretised equations were approximated by a second-orderounded central differencing scheme (BCD), and time integrationas performed by a fully implicit second-order method. Theodeled flow domain covered 8 hydraulic diameters of both inlet

ranches before the junction and 8 hydraulic diameters down-tream. The mesh for this domain consisted of 1,900,800 volumelements for the fluid and 288,000 volume elements for the solidnd yielded a maximum y+ of 5 in the mixing zone. The inletoundary conditions were specified as velocity inlets with a vortexethod to add random fluctuations, on the outer pipe surfaceconvective boundary condition was applied (˛ = 2 W/(m2K),

∞ = 293 K). A total of 4 s of flow time (real time) was computedor each case.

. Comparison to the FATHERINO experiment of CEA

In a first step we address the influence of the SGS model onhe simulation results. Therefore we apply LES with the classicalmagorinsky model and dynamic procedure to the “Skin of Fluidockup”, which is made of brass with a wall thickness of 1 mm, and

ompare the predictions with the experimental results. The mea-urements are performed by applying infrared thermography to theipe surface, i.e. an ensemble of infrared images is recorded andtatistically analyzed to obtain the distribution of the mean surfaceemperature and the root mean square (RMS) of the temperatureuctuations.

For the case of mixing two fluid streams in a T-junction differ-nt flow regimes are observed. Upstream of the junction the flows fully developed in the main branch and the side branch. Behindhe intersection of the two branches intensive mixing occurs andurther downstream the flow returns to the fully developed state.n the next section this region of intense mixing is addressed, fol-owed by an investigation of the mean temperature field and theemperature fluctuations in the solid pipe wall.

.1. Velocity and temperature field in the mixing zone

Contours of the mean streamwise velocity component in theegion of intensive mixing are depicted in Fig. 3 for both SGS mod-

Fig. 3. Contour of the mean streamwise velocity in the mixing zone of the T-junction.

els. The two branches intersect at an angle of 90◦, and the coldfluid (blue in Fig. 3(a) and (b)) enters the junction from the bot-tom. Consequently the side flow has zero momentum in x-direction(streamwise direction of the main branch) and exerts blockageeffects on the main flow. This blockage can be observed in Fig. 3(a)and (b) by the distortion of the mean streamwise velocity compo-nent distribution. Both SGS models predict the same velocity fieldupstream of the intersection of the pipe branches. However, a majordifference is observed downstream: For the classical Smagorinskymodel (Figs. 3(a) and 4) a zone of flow separation and reversalis found between the streamwise coordinates x ≥ 0.04 mm andx ≤ 0.065 mm in the vicinity of the lower pipe wall. This region offlow reversal is not predicted by the dynamic procedure (Fig. 3(b)).This difference between the two SGS models in the near wallregion can be explained by the usage of the turbulent viscos-ity wall-damping function which must be applied in the classicalSmagorinsky approach.

To investigate the effect of the presence or absence of flow rever-sal on the momentum and scalar field we plot instantaneous andmean velocity components together with the temperature field ina cross-section downstream of the junction at x = 120 mm. Fig. 5depicts an instantaneous realization of the velocity componentsin y and z directions together with a contour of the instantaneoustemperature for both models in this cross-section. In case of theclassical Smagorinsky model (Fig. 5(a)) this region of mixing is char-acterized by a pair of counter-rotating vortices at the bottom of thepipe and two separate larger vortices in the upper part. In addi-tion the two fluid streams of different temperature are still sharply

distinguishable, the cold fluid is accumulated in the lower pipe sec-tion and a steep temperature gradient is found. These results areattributed to the zone of flow reversal upstream which entraps thecold fluid in the vicinity of the bottom wall. For the dynamic proce-dure (Fig. 5(b)) a more chaotic picture is observed. There are several

1552 S. Kuhn et al. / Nuclear Engineering and Design 240 (2010) 1548–1557

ofiles

vcdet

tvctolalrstswtb

r

Fig. 4. Mean streamwise velocity pr

ortices of different sizes in the instantaneous velocity field whichontribute to the mixing process. Consequently the two streams ofifferent temperature are mixed more efficiently, fluid packets oflevated temperature are found in the lower part of the pipe andhere is no pronounced temperature gradient.

Fig. 6 depicts the mean velocity components in y and z direc-ions and the contour of the mean temperature. The statistical meanerifies the observations made for the instantaneous cases. For thelassical Smagorinsky model (Fig. 6(a)) the velocity field is charac-erized by a pair of counter-rotating vortices in the lower sectionf the pipe and two separate vortices in the upper section. Theatter transport some cold fluid into the stream of high temper-ture, however the lower part of the pipe is still filled with fluid ofow temperature and a large temperature gradient between theseegions is observed. In case of the dynamic procedure (Fig. 6(b)) thecalar mixing is more efficient. The temperature gradient betweenhe two fluid streams is not so steep as for the classical Smagorin-ky model. The mean velocity field is similar to the results obtained

ith the classical Smagorinsky model, the only difference is that the

wo vortices in the upper section of the pipe are less pronouncedut still present.

The findings of this section revealed a major difference in theesults of the two SGS models. The classical Smagorinsky model

Fig. 5. Instantaneous snapshots of the velocity and the temperatu

at positions x = −0.05 and x = 0.05.

predicts a region of flow reversal downstream of the junction whichalso affects the scalar mixing. In the next section we will address theresulting temperatures and temperature fluctuations in the wall forboth models.

4.2. Mean and fluctuating temperature fields on the outer wall

The failure mechanism of thermal fatigue is connected to tem-perature fluctuations in the solid induced by the mixing processesin the fluid. This means that the computations need to capture thesetemperature fluctuations and their frequency properly in order tocalculate the resulting thermal stresses in the pipe material accu-rately. In addition, some available results from the FATHERINOexperiments carried out by CEA could be used for qualitative codevalidation (Braillard, 2008). In case of FATHERINO’s “Skin of FluidMockup” (1 mm brass wall) special attention is paid to the cou-pling with the heat conduction in the T-junction wall. Infraredthermography images are available for the mean and fluctuating

temperature on the outer pipe surface.

Fig. 7 depicts contours of the mean temperature on the outerpipe wall for both models. By comparing the results obtained withthe classical Smagorinsky model (Fig. 7(a)) with the dynamic pro-cedure (Fig. 7(b)) major differences in the distribution of the mean

re field in a cross-section located 120 mm after the junction.

S. Kuhn et al. / Nuclear Engineering and Design 240 (2010) 1548–1557 1553

e in a

ttAo

Fm

Fig. 6. Mean velocity field and mean temperatur

emperature are found, which can be explained by the prediction ofhe separated flow region using the classical Smagorinsky model.s already observed in the cross-section at x = 120 mm the mixingf the two fluid streams with different temperature is less efficient

ig. 7. Contours of the mean temperature on the outer pipe wall for the two SGSodeling approaches.

cross-section located 120 mm after the junction.

due to this separated region predicted by the classical Smagorin-sky model. This finding is verified for the mean temperature on theouter surface where the imprints of the flow reversal are seen inthe amount of fluid with lower temperature accumulating in the

Fig. 8. Contours of the temperature fluctuations on the outer pipe wall for the twoSGS modeling approaches.

1554 S. Kuhn et al. / Nuclear Engineering and Design 240 (2010) 1548–1557

Ft

ldj

ldstcnptpad

Ftbmano(Tdem

sharp distinction between the two streams of different temperature

ig. 9. Contours of the mean temperature on the pipe surface. Top: numerical solu-ion. Bottom: infrared thermography.

ower pipe section after the junction. The dynamic procedure pre-icts a more efficient mixing at the location and downstream of the

unction.Due to these mechanisms we also observed differences in the

ocation of the maximum temperature fluctuations, which areepicted as contours on the outer pipe wall in Fig. 8. For the clas-ical Smagorinsky model (Fig. 8(a)) we observe the maximum ofemperature fluctuations downstream of the junction in a regionlose to the upper pipe section and further downstream in a regionear the center of the pipe. In the zone where the flow reversal isredicted no temperature fluctuations occur since the fluid of loweremperature is entrapped in the vicinity of the wall. The dynamicrocedure (Fig. 8(b)) predicts the maximum of temperature fluctu-tions in the junction in the region where the two fluid streams ofifferent temperature meet.

We validate the numerical results with data available from theATHERINO experiment of CEA (Braillard, 2008). Fig. 9 depicts con-ours of the mean temperature field on the pipe surface obtainedy LES using the dynamic SGS model (top) and by infrared ther-ography (bottom). As it can be observed from this figure a good

greement between the measured mean temperature and theumerical result is obtained. Fig. 10 depicts contours of the RMSf the fluctuating pipe wall temperature. The numerical resultstop in Fig. 10) agree well with the experiment (bottom in Fig. 10).

he region of maximum RMS downstream of the intersection pre-icted by LES corresponds to the region of maximum RMS in thexperiment. However, a slight difference in the exact location of theaximum RMS value is observed, for the LES results this location is

Fig. 11. Contours of the mean tempe

Fig. 10. Contours of the RMS of the fluctuating temperature on the pipe surface.Top: numerical solution. Bottom: infrared thermography.

found closer to the intersection. In addition, the numerical resultspredict another location of increased RMS at the upstream roundedge of the T-junction. This is also observed in the infrared ther-mography, but not as pronounced as for the LES. As it was shownby Coste et al. (2008) the RMS of temperature in this region is sen-sitive to the inlet boundary conditions. The maximum value of theRMS is found to be 3.5 in the simulations and 3.0 in the experi-ment, thus also a good quantitative agreement in the magnitudeof the fluctuating temperature is obtained. Therefore we concludethat LES with the dynamic SGS model is able to capture both meanand fluctuating temperatures in the mixing region and in the pipewall for the mixing in T-junctions.

5. Influence of wall thickness

5.1. Mean and fluctuating temperature fields on the outer wall

In this section we address the influence of wall thickness onthe resulting temperature fields. Therefore we computed the thin(brass, 1 mm) and the thick wall (steel, 5 mm) case of the T-junction.Fig. 11 depicts the comparison of the mean temperature on theouter pipe wall for both cases. For the thin wall (left in Fig. 11) a

rature on the outer pipe wall.

is observed. In the whole simulation domain the upper part of thepipe surface remains at the main branch inlet temperature of 356 K.A temperature gradient is only found in the mixing region after theintersection of the two branches. Thus for the thin wall the mixing

S. Kuhn et al. / Nuclear Engineering and Design 240 (2010) 1548–1557 1555

ure flu

ptFatpaj

Fs

the pipe wall for both cases. The locations of maximum RMS differbetween the thin (left in Fig. 12) and the thick wall (right in Fig. 12)case. For the latter, the region of maximum fluctuations is shifted

Fig. 12. Contours of the temperat

rocess inside the pipe is reflected in the temperature contours onhe pipe surface. This is different for the thick wall case (right inig. 11). Due to conduction in the solid material the mean temper-ture is smeared over the pipe surface in the region of mixing after

he branch intersection. Thus the mean quantity is affected by theipe wall thickness and measurements of the pipe surface temper-ture yield no information about the mixing processes inside theunction for thick walls.

ig. 13. Fluctuating temperatures on the pipe inner and outer wall 120 mm down-tream of the junction.

ctuations on the outer pipe wall.

Fig. 12 shows the RMS values of the fluctuating temperature on

in positive z-direction, which is also caused by conduction in the

Fig. 14. Amplitude spectra of the temperature fluctuations for the thin wall case.

1 ing an

sioi

tojFtdew

5

ptqf

t

F

556 S. Kuhn et al. / Nuclear Engineer

olid wall. In addition, the magnitude of the obtained RMS valuess different. The damping effect of the thicker wall is seen in valuesf the temperature RMS that are an order of magnitude lower thann the case of the thin brass wall.

To visualize this damping effect further we plot the fluctuatingemperature on the inner and outer pipe wall on the perimeterf the pipe in a cross-section located 120 mm downstream of theunction. Fig. 13(a) shows the RMS profiles for the thin wall andig. 13(b) for the thick wall. The distribution and the magnitude ofhe RMS values on the inner pipe surface are similar for the twoifferent wall thicknesses. However, for both cases the dampingffect of the wall is observed in the lower RMS values on the outerall. This effect is more pronounced for the thick wall.

.2. Amplitude spectra of the temperature fluctuations

In this section we address the amplitude spectra of the tem-erature fluctuations in the solid pipe material. In addition to

he location of the maximum temperature fluctuations their fre-uency and amplitude is also of interest for the analysis of thermalatigue.

As first step we investigate the coupling between the tempera-ure fluctuations in the fluid close to the wall and the temperature

ig. 15. Amplitude spectra of the temperature fluctuations for the thick wall case.

d Design 240 (2010) 1548–1557

fluctuations in the wall. Therefore we plot the amplitude spectra ofthe fluctuations in the fluid close to the wall (i.e. the center of thefirst computational cell adjacent to the wall) as well as at the innerand outer surfaces of the wall in top of Fig. 14 for the thin case andtop of Fig. 15 for the thick wall. The data for these plots are extractedin the cross-section 120 mm downstream of the junction. For bothcases it is observed that the amplitude of the temperature fluctu-ations in the fluid close to the wall is larger than inside the wallwhich is due to the presence of the thermal boundary layer. In thethin case the influence of the wall thickness itself is negligible, sincethe amplitude spectra for the inner and outer surface collapse andthe shape of the spectra in the wall follows the shape of the spectrain the fluid. The influence of the thick wall is observed in the cor-responding spectra, the amplitude of the spectra on the outer pipesurface is lower compared to the inner surface and it is completelysmoothed out, i.e. the fluctuations are damped throughout the pipewall.

To address the influence of the wall thickness on the temper-ature fluctuations in more details, we plot the amplitude spectraof the temperature in 6 points throughout the wall (P1–P6) in thebottom of Fig. 14 for the thin case and in the bottom of Fig. 15for the thick wall. These data are also extracted in the cross-section120 mm downstream of the junction and P1 denotes a point locatedat the inner surface and P6 at the outer wall, respectively. For thethin case the spectra for the different points throughout the wallcollapse, i.e. no influence of the wall thickness on the heat transfercan be extracted. For the thick wall the damping effect is clearlyvisible in the amplitude and shape of the temperature spectra. Theamplitude decreases with increasing radial position and the spectragradually level out.

6. Conclusions

In this study we numerically investigated the mixing of hotand cold water streams in a T-junction with a temperature dif-ference of 75 ◦C of the pre-mixed fluid streams and a Reynoldsnumber in the mixed stream of 2.7 × 105. We studied two differ-ent designs of the T-junction: (i) a thin wall of 1 mm made of brassand (ii) a thick wall of 5 mm made of steel. These two differentdesigns are aimed at identifying the influence of the wall thicknesson conjugate heat transfer. We applied a LES with different SGSmodels, i.e. the classical Smagorinsky model and the dynamic pro-cedure. The main difference between these SGS models lies in thenear wall treatment. The classical Smagorinsky model needs wall-damping functions to correct the turbulent viscosity in the vicinityof walls. In addition, the unresolved turbulent heat flux is modeledby the simple gradient diffusion hypothesis which aligns it withthe gradient of the mean temperature field. In the dynamic pro-cedure the need of wall-damping functions is eliminated and thedynamic procedure to obtain CS ensures correct near wall behav-ior of the turbulent viscosity. The subgrid scale turbulent Prandtlnumber is obtained by applying the dynamic procedure to theSGS flux.

This difference in the SGS models is seen in the results of thesimulations. The T-junction of the FATHERINO setup features roundedges at the connection of the main and the side branch. As a con-sequence there is no sharp edge which clearly defines the point offlow separation, this has to be treated by the near-wall behaviorof the model. This prediction of flow separation and reversal is themain difference between the two models. The results of the clas-

sical Smagorinsky model show a separated flow region betweenthe streamwise coordinates x ≥ 0.04 mm and x ≤ 0.065 mm in thevicinity of the lower pipe wall. This is not the case when usingthe dynamic procedure. This difference in the computed momen-tum field affects the scalar mixing efficiency downstream of the

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stmaotT

S. Kuhn et al. / Nuclear Engineeri

unction, which results in different predictions of the mean tem-erature distribution and the location of maximum temperatureuctuations of the two models. In comparison with available exper-

mental data the results of the dynamic procedure agree well witheasurements. Thus we conclude that the quality of the numeri-

al results depends heavily on the proper choice of the SGS model,hich needs to be adapted to the geometrical constraints of thearticular test case.

The influence of the wall on the temperature fields is well rep-esented in the numerical solutions. For the thin wall case thealues of the RMS of the temperature fluctuations are reduced byfactor of 3 between the inner and outer pipe surface, however

he distribution of maximum and minimum values on the pipeerimeter is identical. The amplitude spectra of the temperatureuctuations inside the thin wall at different radial locations are sim-

lar. For the thick wall case the wall influence is more expressed.he magnitude of the RMS of the temperature fluctuations reducesy a factor of 10 between inner and outer pipe surface and theistribution on the pipe perimeter is smeared out. This effect islso seen in the shape of the amplitude spectra throughout theall.

The comparison with this single experiment in the present studyhows the potential use of LES to predict the location of maximumemperature fluctuations in the solid wall material induced by the

ixing processes inside the pipe. In addition their frequency andmplitude can also be studied. The generated results can be passedn to a structural analysis tool for the subsequent prediction ofhermal stresses and the corresponding life span of the considered-junctions.

Design 240 (2010) 1548–1557 1557

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