Copyright © 2012 by JSME

Proceedings of ICONE20

20th International Conference on Nuclear Engineering

July 30- August 03, 2012, Anaheim, California, USA

ICONE20-54981

LES and URANS predictions of thermal load in piping systems; T-Junction

Yacine Addad

Khalifa University of Science,

Technology and Research, Abu Dhabi,

United Arab Emirates Phone : +971 2 501 8515

Email: Yacine.addad@kustar.ac.ae

Jeong Ik Lee

Khalifa University of Science,

Technology and Research, Abu Dhabi,

United Arab Emirates

& Korea Advanced Institute of Science and

Technology, Daejeon, S. Korea

Phone : +82 42 350 3829

Email: jeongiklee@kaist.ac.kr

Keywords: Heat transfer, LES, Thermal Striping, T-Junction, URANS.

ABSTRACT

The present numerical study focuses on the predictions of

thermal mixing in a T-junction using two types of approaches;

the Large Eddy Simulation (LES) and the Unsteady RANS

technique. The numerical predictions are compared to the

experimental reference data of Westin et al. (2008).

Beforehand, the LES using the commercial code Star-CD are

across validated with the open source Code_Saturne in a

simple academic channel flow case at Re=395. For this case,

both codes predictions are found in a satisfactory agreement

with the DNS data which provides sufficient evidence, from a

numerical dissipation related issues point of view, that any of

these codes can be used for the LES runs of the more complex

T-Junction test case. For the later, in agreement with previous

findings reported in the open literature the LES approach is

found capable to mimic correctly the flow behavior and to

provide valuable instantaneous data needed for the thermal

stress fatigue analysis for instance. The URANS technique on

the other hand, even with an advanced non-linear

eddy-viscosity model, is not only incapable of predicting

correctly the mean variables, but also largely dumping the

flow turbulence.

1. INTRODUCTION

At areas of incomplete mixing of high and low temperature

fluid in components and pipes, inhomogeneous temperature

fluctuations can occur. This induces complex variations of

local temperature gradient on both the flow and the structure

of the pipe walls, which then leads to cyclic thermal stress. In

severe cases with large cyclic thermal stresses applied over

long periods of time, high-cycle thermal fatigue crack

initiation and propagation can occur. This coupled

thermal-hydraulic and thermal-mechanical phenomenon is

known as thermal striping.

Recently, high-cycle thermal fatigue failures have occurred

in several light water reactors and fast reactors throughout the

world. Incomplete mixing of high and low fluid temperature

has lead to partial or complete shutdown of the reactors in

question. Hence, this subject has begun to receive a

considerable amount of attention in the recent years and there

are a number of projects currently underway to study this

category of thermal fatigue numerically (Metzner et al., 2005,

Hannink et al., 2008 and Prunier, 2009).

Due to its’ non negligible not only economic, but also

reactors safety related consequences; this geometry has been

a subject of several experimental studies. For example, Costa

et al. (2006) conducted pressure drop, mean and turbulent

velocities measurements of a turbulent Newtonian fluid in a

diverging tee junction to investigate the effects of sharp and

round corner design on the flow characteristics. The study

revealed that rounding the corner lead to an increased

turbulence levels in the branch pipe. As a result, the

momentum is diffused more efficiently thus reducing the

recirculation size. The momentum correction coefficient (K)

was also measured by Ji et al. (2009) and a relationship

between K and the momentum flux ratio (M), independent of

the physical properties of jet flows, was deduced.

Hosseini et al. (2009) investigated experimentally the

structure and mixing mechanism of turbulent flow in a

converging T-junction area with a 90˚ bend upstream by

Copyright © 2012 by JSME

means of PIV technique. The paper describes three main

regions with the highest velocity fluctuations in the

T-junction; the first surrounding the branch nozzle, the

second region is distributed between the branch nozzle and

the reattachment area and the third region is located in the

re-attached flow region. These effects were studied

previously by Ogawa et al. (2005) and Yuki et al. (2003).

However there remain a number of difficulties principally

related to turbulence modeling and the coupling between the

turbulence and the heat flux. Consequently, several

experiments have recently produced reliable data, for CFD

codes validation, in the core of the flow (Westin et al. 2008,

Zboray et al. 2007, Walker et al. 2009, and Zboray et al.

2011) and/or near wall layer (Pasutto et al. 2007, Kamide et

al. 2009, and Kimura et al. 2010).

Large Eddy Simulation is currently the preferred modeling

approach (Benhamadouche et al., 2003, Pasutto et al., 2007,

Ohtsuka et al., 2003, Hu et al. 2003, Lee et al., 2009 among

others) and more recent studies, in fact, conducted in parallel

to the present work (Kucjaz et al. 2010, Ndombo 2011, Galpin

et al. 2011), but the high Reynolds numbers do not allow wall

resolved LES. Furthermore, using this approach with

wall-functions or the detached eddy simulations DES

technique have been already proved unsuitable for the present

T-junction test case by Jayaraju et al. 2010 (LES) and

Nakamura et al. 2010 (DES). Hence, in this study it is

intended to revisit the U-RANS (Unsteady RANS) approach

with higher order models. For instance, the non-linear cubic

model of Craft et al. (1996) is tested herein.

The present work will follow the same approach as the

papers cited above in which both commercial and/or industrial

codes are used to carry out the numerical study. Thus, the

present work is divided into two parts; the first part will be

dedicated to a detailed cross validation study for LES

predictions of the relatively simple academic and well

documented channel flow test case at Re=395 as predicted by

two different codes, namely, the open source unstructured

industrial Code_Saturne developed at EDF and the

commercial code Star-CD. It has to be mentioned that both

codes are being actively used for LES simulations in nuclear

field (see for example the literature review conducted by

Simoneau et al. 2010 for the Star-CD code and the papers

published by the EDF R&D and D. Laurence research team at

Manchester University (www.cfdtm.org) for Code_Saturne

which further justifies the actual cross validation section. This

is then followed by a T-Junction test case runs using the code

Star-CD in which comparisons are made between the different

approaches, named above, and the recently available

experimental data of Westin et al. 2008. The main aim of the

present paper is to draw some conclusions on the suitability of

the LES and URANS approaches to mimic the flow physics

while shedding some light on LES restrictions related to grid

resolution and inlet boundary conditions.

2. NUMERICAL METHODS

The codes used to conduct the LES computations are the

Code_Saturne (an open source code developed at EDF) and the

commercial code Star-CD. Both codes are co-localized cell

centered incompressible Navier-Stokes solvers. Code_Saturne

simulations (Version 1.3.2) make use of a second order central

difference scheme for the convection and a second order scheme

for the time advancement. The divergence condition is solved

using an iterative conjugate gradient scheme. Similarly, the LES

and URANS simulations using the commercial code Star-CD

(Version 4.10) are carried out with a second order central

difference scheme for the convection of velocities and the

second order MARS scheme for temperature. The three time

level implicit second order scheme is used for the time

advancement. The resulting linear algebraic equations are then

solved with the Conjugate Gradient CG-type solver.

The classical Smagorinsky/Lilly SGS model (Lilly, 1966) is

employed in the present series of Large Eddy Simulations

(LES) with the model constant, Cs, being set to 0.065. The

sub-grid filter width, Δ is notionally defined as twice the cube

root of local cell volume. The Sub-Grid-Scale (SGS)

expression for eddy viscosity may be written as:

SCst2

(1)

where S , the resolved strain rate is defined as 2/1

ijij SS . To

account for near-wall effects, in the commercial code

implementation, the definition of the sub-grid filter width is

modified to read as (Lilly, 1966):

),min( my (2)

where κ = 0.42, y is the distance from the nearest wall, and

m is the mesh filter. While in the open source code

implementation, the more common Van Driest damping

function is used, expressed as:

)26/exp(1 ym (3)

where y+ is the dimensionless value of y.

Figure 1 illustrates the dumping effects of these two

functions on the sub-grid viscosity. For instance, Eq.3 induces

more dumping up to y+=100, while the simpler, i.e. with a

lower computational cost (i.e. the wall distance is computed at

the beginning of the run only and stored for the subsequent

iterations), Eq. 1 induces a more local near-wall dumping.

Copyright © 2012 by JSME

Fig. 1 Representation of the dumping functions effect in a

channel flow at Reynolds number, Re=395.

Finally, in regards to the thermal field predictions, the

turbulent Prandtl number used to determine the sub-grid

thermal conductivity is set to 0.9.

The URANS runs were conducted using the low-Reynolds

non-linear eddy-viscosity model of Craft et al. (2006) where

details about this model along with the different modeling

constants can be found. The same numerical schemes as for

the LES are used without any calculations instability

problems.

3. VALIDATION TEST CASE

The first test case considered is the relatively simple

academic and well documented turbulent channel flow at

Reynolds number Re( u ) = 395 (based on the friction velocity

u ). As presented in Fig. 2, an unstructured grid with 440,000

control cell volumes was generated, to use in both codes, for

this cross validation study.

Fig. 2 The unstructured grid used for the Channel flow LES

runs

Figures 3 and 4 illustrate mean and fluctuating velocities.

As it can be observed in the figures, in general, the LES

predictions are in a reasonably good agreement with the

reference DNS data of (Kim et al. 1987) and with each other.

A remarkable feature is that the over-prediction of the mean

velocity and streamwise component of fluctuating velocity,

usually encountered in LES, are not very pronounced in these

simulations. However, some under-prediction of the wall

normal and spanwise fluctuating velocities occurs, chiefly in

the centre of the channel.

Fig.3 Mean streamwise velocity comparison of LES

predictions with the reference DNS data.

Observed also in the figure, somewhat small discrepancies

are obtained between the two codes predictions which can be

partially rooted to the different dumping functions described

in the previous section. Nevertheless, the velocity profile

results, from both runs, very closely follow DNS results. As

reported in (Addad et al. 2008), this is mainly due to the

more appropriate mesh for the present flow which satisfies

the grid resolution restrictions in the whole domain.

Fig.4 Averaged Reynolds stresses; a) and d)

''vu .

Effectively, according to the present findings either of the

two codes can be used for the remaining of the numerical

investigation. In the present numerical study, the commercial

code has been selected.

4. THE T-JUNCTION CASE DESCRIPTION:

The T-Junction test case selected for the present benchmark

a) b)

c) d)

Copyright © 2012 by JSME

study (see Fig. 5) is the one considered by (Westin et al. 2008).

The flow rate ratio between hot and cold fluids is 0.5 with

different diameters (hot diameter, Dh=0.1m and the cold

diameter Dc=0.15m) to achieve a same Reynolds number at

both inlets of approximately 105. The temperature difference

between hot and cold is 15°c.

Fig.5 A sketch of the T-junction geometry illustrating the

computational domain size used in both; the LES and

URANS runs.

Two fully hexahedral meshes with an average cell-size in

the centre of the pipes of 3 and 2 mm were used for the

URANS and the LES runs respectively. Following the work of

Addad et al. (2008), the LES grid resolution was estimated

about one fifth of the integral scale, , computed from the

URANS calculation. Near the walls, the grids were further

refined in the normal direction to avoid using wall-functions

(see Fig. 6). The resulting grids size was about 2.56 million

for the coarse grid and 8.25 million for the finer mesh.

The mean inlet velocity profile for the cold inlet was

obtained from a RANS-calculation based on a fully developed

straight pipe with cyclic conditions matching the experimental

measurements. For the hot inlet, the mean velocity profile,

presented in Fig. 7, is taken from a RANS calculation (using

the non-linear eddy-viscosity model of Craft et al. 1996)

under development in order to fit the experimental setup.

Fig.6 Zoom on the coarse structured grid used for URANS

runs and the initial LES tests, 2.56 M cells.

Fig. 7 The developing mean velocity profile at physical time

t=1.778s used for the hot inlet boundary.

For the URANS calculation, these profiles, of mean and

fluctuating variables, obtained from the precursor calculations

have been prescribed at the test case inlet boundaries, while

different types of unsteady inflow boundary conditions have

been applied during initial LES tests with the coarse grid. In

agreement with the findings of Westin et al. (2008), the LES

results revealed the predictions to be insensitive to the type of

instantaneous fluctuations imposed at the inlet boundaries. i.e.,

no significant discrepancies are observed between runs using

random fluctuations superimposed to fully developed profiles

and the runs using more realistic time and space correlated

fluctuations using the SEM method of Jarrin et al. (2006). As

it will be explained with details in the next section, this

particular advantage in the present case is mainly due to the

fact that large portion of the turbulent structures are generated

at the T-junction position where the two flows encounter each

other.

Within the SEM framework, the turbulent flow field is

seen as a superposition of eddies of assigned spin, position

and size. While spin and position are drawn from a uniform

and appropriately normalized distribution, size is the

characteristic scale of turbulence, limited by the minimum

mesh spacing. The correlation function needed by the method

is then provided by the user-assigned Reynolds Stress tensor

(obtained from the precursor results in the present case). The synthetic eddies generated at the inflow are convected

and recycled in the computational domain with an assigned

convective velocity.

The fluctuating velocity signal is generated as:

(4)

where N is the total number of eddies, ԑ is random eddies

rotation sign, f is a shape function, and is the average eddy

length scale.

Z

Cold

12Dc 3Dc

X

Z

3.1Dh

Hot Top

Right Left

Y

Copyright © 2012 by JSME

The instantaneous velocity field is then computed as:

(5)

where the factors are obtained from the Cholesky

decomposition of the Reynolds Stress tensor. A detailed

description about this boundary type along with its advantage

over the vortex method, used by Westin et al. (2008), is

presented in the paper by Jarrin et al. (2006).

4. RESULTS

4.1 Instantaneous fields and flow characteristics:

Fig. 8 illustrates instantaneous temperature fields as

predicted by the LES and URANS approaches respectively.

As expected the LES approaches generates more small-scale

structures similar to the experimental visualizations reported

in Westin et al. (2008). Indeed for the present case (flow rate

ratio equal to 0.5 and Re=105), the dominant turbulent

structures are mainly generated at the two pipes intersection,

as illustrated in Fig. 9, which explains the case quite particular

insensitivity to the unsteady inlet conditions. An animation of

the figure shows that these co-rotating vortices are originating

at the junction and being convected along the main pipe

before dissipating further downstream. As result, a secondary

flow motion is generated in this region and plays an important

role in the flow mixing between the hot and cold streams. As

illustrated in Fig. 10, the vortices remain apparent in the

averaged velocity field. At first (from X/D=0 to 3), they are

limited to the upper region of the pipe only, but further

downstream their size is increased to occupy the whole pipe

section while their intensity is decreased. From these

observations, its becomes obvious that for a RANS model to

be able to reproduce the secondary flow it has to take in

account the Reynolds stresses anisotropy, hence the choice of

the non-linear eddy viscosity model in the present study.

4.2 Time Averaged Results

Quantitative comparisons between experimental data and

mean velocity profiles from both LES and URANS

approaches at the position X/D= 2.6 are presented in Fig.11.

In agreement with previous findings, the LES predictions are

in a reasonable agreement with the experimental data for both

of the streamwise velocity component, U, and the normal

component W. All results show clearly the effect of the

penetrating hot stream in the main pipe flow causing the “M”

shape on the mean velocity profile. Indeed, as the flow

penetrate in the main pipe from the hot leg; it causes the

incoming cold stream to slowdown in the centre of the pipe

forming this M-shape on the mean velocity component.

Interestingly, the level of this penetration can be easily

measured from the figure showing the streamwise velocity

profile in the z-axis direction as the upper part of the pipe is

marked by a slower flow motion while in the lower part a

more accelerated flow is observed due to the jet presence.

Both approaches, are predicting successfully these physical

phenomena. Actually, the non-linear eddy-viscosity model is

found to be able in returning a good prediction for the large

velocity component at this location, but at the same time the

prediction of the secondary motion is less satisfactory.

Accordingly, the resolved fluctuations obtained by the

URANS model do not follow the same trend as the

experimental data. Presented Fig.12, the actual URANS

averaged resolved fluctuations profiles form less than 50 % of

the total experimental data with most of the turbulence being

dumped by the physical model.

Fig. 8 Instantaneous temperature field, a) LES predictions, b)

URANS predictions.

Fig.9 Iso-values of normalized Q colored by the temperature.

Further downstream, at the position X/D=6.6 (see Fig.13), the

experimental data and the LES show the flow to recover to a

nearly fully developed straight pipe type of profile, while the

URANS predict the mean velocity component to be still

altered by this jet-like effect of the hot stream. This delayed

response of the model is certainly affecting the predictions of

the normalized temperature presented in Fig. 14. Actually, the

URANS model predicts a convex profile for the temperature

instead of concave one showed by the experimental and LES

data. Also in the z-axis, the URANS predictions show a much

sharper temperature gradient from the upper side of the pipe

(z/R=1) to the lower one compared to the experiment and LES

a)

b)

Copyright © 2012 by JSME

data. The later agrees with the experiment on the fact that the

flow is still not fully mixed at this position X/D=6.6 while

providing more near wall information.

a)

b)

c)

d)

Fig. 10 Representation of the flow secondary motion colored

by the averaged temperature as obtained from the LES

predisction at a) X/D=1, b) X/D=2, c) X/D=3, and d) X/D=6.

Fig.11 Mean velocities at X/D=2.6. a) Mean streamwise

velocity along the y-axis, b) Mean streamwise velocity along

the z-axis, c) averaged normal velocity component along

y-axis, and d) averaged normal velocity component along

z-axis.

Figure 15 and Figure 16 show the spectra of the

temperature fluctuations near the left pipe wall. Also in this

graph the agreement between the experimental and LES data

is good. The URANS spectra are omitted from the figure but

it can be easily shown that these are largely under-predicted

by this approach due to the turbulence dumping induced by

the model.

5. CONCLUSIONS

In the present paper, LES predictions of one academic test

case using two different unstructured finite volume codes and

one more complex T-junction test case with both LES and

URANS techniques is reported.

First, the benchmark test case reveals the codes to be very

suitable for the LES approach.

The results from URANS and LES computations of

T-junction test case show that:

- For this case, the LES predictions are insensitive to the

type of inlet boundary condition fluctuations used.

- The LES calculations with a wall-resolved grid returns

results in a satisfactory agreement with the experimental

data.

- A fairly qualitative agreement is obtained between the

URANS model and the experimental data, but some

noticeable differences are observed in the prediction of

the mean flow transversal distribution and the

wall-jet-like flow deflection which entails noticeable

differences in the flow field temperature distribution. A

conclusion can then be drawn, that further investigation

is needed to achieve satisfactory predictions of the flow

using this type of Unsteady RANS. One way, would be

to change the model’s physical parameters and constants

to account more for the flow secondary motion and

unsteadiness.

Acknowledgments

The numerical computations presented in this paper have

been conducted at the University of Manchester while the

author was working as a research associate in the Mechanical,

Aerospace, and Civil Engineering (MACE) department.

Fig. 12 Velocity fluctuations at x/D=2.6. a) streamwise

velocity fluctuations along the y-axis, b) streamwise velocity

fluctuations along the z-axis, c) normal velocity fluctuations

along the y-axis, and d) normal velocity fluctuations along the

z-axis.

a) b)

c) d)

a) b)

c) d)

Copyright © 2012 by JSME

REFERENCES

Metzner K.-J., Wilke U., 2005, Nuclear Engineering and

Design, Vol. 235, pp 473–484.

Hannink M.H.C., et al., Eurosafe, 2008.

Prunier V., 2009, NULIFE bulletin, number 2, 2009.

Costa N. P. et al., 2006, J. of Fluids Eng., Vol. 128, pp

1204-1217.

Ji L. et al., 2009, Chemical Eng. Research and Design, Vol.

87, Issue 8, pp 1065-1068.

Hosseini S. M., Hashizume K. Y. H., 2009, J. Fluids Eng.,

Vol. 131, Issue 5, 051103 (7 pages).

Ogawa H. et al., 2005, 11th Int. Topical meeting on Nuclear

Reactor Hydraulics (NURETH 11).

Yuki K. et al., 2003, 10th

Int. Topical meeting on Nuclear

Reactor Hydraulics (NURETH 10).

Westin J., et al., 2008, 16th

Int. Conf. On Nuclear Engineering

(ICONE-16), Paper No. 48731, pp. 1-11.

Zboray R. et al., 2007, 12th Int. Topical meeting on Nuclear

Reactor Hydraulics (NURETH 12).

Walker C. et al., 2009, Nuclear Eng. and Design, Vol. 239,

Issue 1, pp 116-126.

Zboray R. et al., 2011, Nuclear Eng. and Design, Vol. 241, pp

2881-2888.

Pasutto T., Peniguel C., Stefan J. M., 2007, 15th Int. Conf. On

Nuclear Engineering (ICONE-15), Paper 10410.

Kamide H. et al., 2009, Eng. and Design, Vol. 239, pp 58-67.

Kimura N. et al., 2010, Nuclear Eng. and Design, Vol. 240,

Issue 10, pp 3055-3066.

Benhamadouche S., et al., 2003, Transactions of the 17th Int.

Conf. on Structural Mechanics in Reactor Technology

(SMiRT 17).

Ohtsuka M., et al., 2003, 11th

International Conference on

Nuclear Engineering (ICONE 11).

Hu L-W, Kazimi M. S., 2003, 10th International Conference

on Nuclear Engineering (ICONE 10).

Lee J. Ik, Saha L. Hu, P., Kazimi M. S., 2009, Nuclear Eng.

and Design 239, Vol. 5, pp 833-839.

Kucjaz A. K. et al., 2010, Nuclear Engineering and Design,

Vol. 240, pp 2116–2122.

Ndombo J-M. et al., 2011, Nuclear Engineering and Design,

Vol. 241, pp 2172–2183.

Galpin J. and Simoneau J. P., 2011, Int. J. of Heat and Fluid

Flow, Vol. 32, pp 539–545.

Jayaraju S. T. et al., 2010, Vol. 240, Nuclear Engineering and

Design, Vol. 240, pp 2544–2554.

Nakamura A. et al., 2009, 13th

Int. Topical meeting on Nuclear

Reactor Hydraulics (NURETH 13).

Craft T.J., Launder B.E., and Suga K., 1996, Int. J. Heat Fluid

Flow, Vol. 17. pp. 108-115.

Simoneau J. P. et al., 2010, Nuclear Engineering and Design,

Vol. 240, pp 429–439.

Lilly, D.K., 1966. NCAR Manuscript 123.

Kim, J., Moin, P., and Moser, R., 1987, J. Fluid Mech., Vol.

177, pp133.

Addad Y., Gaitonde U., and Laurence D. 2008, Quality and

reliability of large-eddy simulations. ERCOFTAC Series,

Volume 12, Part I, Springer, pp 93-103.

Jarrin N., et al., 2006, Int. J. Heat and Fluid Flow, Vol. 27, pp.

585-593.

Fig. 13 Mean velocity and rms-profiles at x/D=6.6 along the

y-axis; a) averaged streamwise velocity, b) averaged normal

velocity, c) streamwise fluctuations, and d) normal velocity

fluctuations.

Fig. 14 Normalized mean and fluctuating temperature at

x/D=6.6, a) mean temperature along the y-axis, b) mean

temperature along the z-axis, c) temperature fluctuations

along the y-axis, and d) temperature fluctuations along the

z-axis.

a) b)

c) d)

a) b)

c) d)

Copyright © 2012 by JSME

Fig. 15 Spectra of temperature fluctuations 1 mm from the

pipe wall at the left side of the pipe at the position x/D=2.

Fig. 16 Spectra of temperature fluctuations 1 mm from the

pipe wall at the left side of the pipe at the position x/D=4.