two different turbulence models in comparison with ... · t=0.9, 0.2 and 0.1 for bsl-rsm turbulence...

Two different turbulence models in comparison with experiments on

thermal mixing phenomenon in a tee piping

CHAO-JEN LI, YAO-LONG TSAI, TAI-PING TSAI, LI-HUA WANG Material and Chemical Research Laboratories

Industrial Technology Research Institute Rm. 637, Bldg. 52, 195, Sec.4, Chung Hsing Rd., Chutung, Hsinchu,

TAIWAN [email protected]

Abstract: - Thermal fatigue failures in reactor cooling systems of nuclear power plants are caused by the fluctuating stresses on a piping system due to the hot and cold flows are mixed together in a mixing piping. The present paper describes BSL Reynolds Stress (BSL-RSM) and k-epsilon (k-ε) simulation data of thermal mixing in a mixing piping compared with results from experimental data. The fluid in the experiment is concentration of de-ionized water and the liquid electrical conductivities are measured by the use of the 16×16 electrode. To verify the mixing phenomenon between de-ionized water with different electrical conductivities and water with different temperatures, the inlet temperatures of the hot and cold water in the simulation process are set to 80℃ and 15℃ respectively. The analytic results calculated by the commercial CFD code ANSYS CFX 11.0 show that the different turbulence models（BSL-RSM, k-ε）and different turbulent Prandtl numbers（0.9, 0.2, 0.1）

will affect the simulation results of temperature fluctuations. Since the coefficient of determination, R2, obtained by using Prt=0.1 for BSL-RSM turbulence mode is between 0.996 and 0.788, which is higher than that by using Prt=0.2 and Prt=0.9, the perditions for smaller turbulent Prandtl number are in better agreement with measurements. The absolute error, β, obtained by using BSL-RSM turbulence model at x=0.025m is smaller than that by using k-ε turbulence model. However, at x=-0.025m, the absolute error, β, obtained by using k-ε turbulence model is smaller than that by using BSL-RSM turbulence model. The computational results are in qualitative good agreement with experimental data that the mixing phenomenon of water with two different temperatures can be explained by de-ionized water with two different electrical conductivities.

Key-Words: - BSL-RSM、k-ε、Thermal Fatigue、Turbulent Prandtl Number、Mixing

1 Introduction In 1998, a leak occurred in the Civaux 1 reactor

residual heat removal system (RHRS) at the extrados of an elbow near the RHR heat exchangers. Temperature fluctuations in pipe systems can lead to thermal fatigue in the pipe walls, since it can lead to highly transient temperature fluctuations at the adjacent pipe walls, cyclic thermal stresses in the pipe walls and consequently to thermal fatigue and failure of the pipeline. The flow in the mixing-tee is a challenging test case, and the CFD-methods based on RANS (Reynolds Averaged Navier-Stokes equations) typically used in industrial applications have difficulties providing accurate results for this flow situation. Recent studies using advanced scale-resolving methods such as the simulated results [1,2,3] have compared LES and DES with the experimental results [4] measured by Vattenfall at the Älvkarleby laboratory, Vattenfall Research and Development AB.

In this study, a isothermal de-ionized water experiment [5] was performed at the Laboratory for

Nuclear Energy Systems, Institute for Energy Technology, ETHZ, Zürich, Switzerland. The electrical conductivity of the fluid is used as a parameter that can investigate the influence of the mixing phenomena in a mixing tee. The computed results [6] show comparisons of parameter variations using three different turbulent Schmidt number（ Sct=0.9, 0.2 and 0.1 ） for turbulence model simulations in comparison to the experimental data [5]. The better agreement with the measurements could be obtained for smaller turbulent Schmidt number.

In order to verify that the mixing phenomenon of water with two different temperatures that can be explained by de-ionized water with two different electrical conductivities, the present paper describes the CFD solutions for traditional RANS approaches using BSL-RSM and k-ε turbulence models simulating the mixing of two fluid streams of different temperatures.

WSEAS TRANSACTIONS on FLUID MECHANICS Chao-Jen Li, Yao-Long Tsai, Tai-Ping Tsai, Li-Hua Wang

ISSN: 1790-5087 45 Issue 2, Volume 5, April 2010

2 Experimental Setup of ETHZ [5] The detailed measurements of turbulent isothermal

mixing was carried out at a perpendicular connection of two pipes of 50mm inner diameter (Fig.1), which were made of acrylic glass. The used test section consists of a horizontal mixing-tee geometry of Plexiglas pipes of 50 mm inner diameter for both the main and the branch pipes. The length of the main branch is 1.5 m whereas the length of the side branch is 0.5 m. Tap water is flowing from left to right and the demineralized water is pumped from a storage tank through the side branch. as indicated in Fig.1. The electrical conductivity difference between tap water and desalinated water was used as the parameter characterizing the changing concentration of salts dissolved in the tap water during the mixing process.

The instantaneous two dimensional electrical conductivity distributions from measuring planes in the common exit branch of the mixing-tee were obtained by the main instrumentation, two 16×16 electrode wire-mesh sensors (WMS), installed right behind each other downstream of the mixing-tee in the mixing region. The sensors can be also positioned further downstream of the mixing-tee by inserting distance rings and pipe segments. The measurement cross-sections in the experiments for the WMS measurements were located at L=51mm, 71mm, 91mm, 111mm, 151mm, 191mm, 231mm, 271mm and L=311mm downstream of the mixing-tee. Details of the WMS measurement technique can be found in [5,7,8].

Fig.1 Mixing-Tee test facility of ETHZ [5]

3 Numerical Approach Description 3.1 Geometry Setup

The three-dimensional mixing-tee models that represent the ETHZ experiments, as shown in Fig.2, are constructed with ANSYS DesignModeler, a pre-processor of the ANSYS CFX 11.0 code. Several experiments have been carried out at ETHZ by varying the flow rates in the main and branch pipe, exchanging the injection of tap water and de-ionized water, and changing the location of the WMSs. To verify that the mixing phenomenon of water with two different temperatures can be explained by using de-ionized water with two different electrical

conductivities, the ANSYS CFX 11.0 code has been selected and the main parameters of the simulation are given in Table 1.

For the sake of achieving convergence and minimizing the computational time, three different mesh levels are used in the simulation (see Fig.3). Mesh Coarse consists of approximately 320000 hexahedral cells, mesh Intermediate consists of approximately 1600000 hexahedral cells, and mesh Fine consists of approximately 2350000 hexahedral cells.



Fig.2 Geometry for the Mixing-Tee test of ETHZ

Table 1 Simulation Conditions

Main Pipe

(Hot Water) Branch Pipe (Cold Water)

Water Temperature(℃) 80 25 Average Velocity(m/s) 0.5 0.5

Inner Diameter(m) 0.05 0.05 Length(m) 1.5 0.5

Fig.3 Levels of Mesh Coarse, Intermediate, Fine

Hot Water

Cold Water

Main Pipe Branch Pipe51m m

91m m

191m m3 11m m

Hot Water

Cold Water


91m m

191m m3 11m m

Hot Water

Cold Water

Main Pipe Branch Pipe

Hot Water

Cold Water

Hot Water

Cold Water


91m m

191m m3 11m m

(1) Hexahedral-Coarse

(2) Hexahedral-Intermediate

(3) Hexahedral-Fine

(1) Hexahedral-Coarse

(2) Hexahedral-Intermediate

(3) Hexahedral-Fine



3.2 Boundary Conditions Based on the Reynolds Averaged Navier-Stokes

（RANS）equations, a number of models have been developed that can be used to approximate turbulence. The models can be classified as either Reynolds-Stress Models or Eddy-viscosity Models. In order to compare the difference between Reynolds-Stress Models and Eddy-viscosity Models, BSL Reynolds Stress（BSL-RSM）and Shear Stress Transport（k-ε）turbulence models are used in the simulation process.

The temperature of water can be simulated in both turbulence models by solving the governing equation of temperature, Eqn. (1). Prt is the turbulent Prandtl number arising from the application of the eddy viscosity hypotheses in the Reynolds averaging process of this equation. The default value of the turbulent Prandtl number in Ansys CFX 11.0 set to 0.9. For the sake of comparing the computed results with the investigations [6], three different turbulent Prandtl number（Prt=0.9, Prt=0.2, Prt=0.1）in the two turbulence models are used. No slip conditions are set at the walls and zero average static pressure outlet boundary condition has been applied.

( ) 0)Pr

( =

∇+•∇−•∇+

∂

∂TUT

t

T

t

tµραρ

ρ (1)

in which α is the thermal diffusivity, µt is the turbulent viscosity, and Prt is the turbulent Prandtl number.

To compare the computational and experimental results, the computed data are normalized as follows:

Mixing Scalar = coldhot

cold

TT

TT

−

− (2)

where T is the instantaneous mixing temperature at a given location, Thot is the temperature of the hot water(353 K), and Tcold is the temperature of the cold water(298 K).

The convergence studies with the BSL-RSM turbulence model using Prt=0.9 have been carried on all three different mesh levels. The convergence criterion was set to 10-5 for the residuals. Fig.4 shows the comparison of profiles of the mixing scalar at L=51mm, L=91mm, L=191mm, and L=311mm behind the mixing-tee for an BSL-RSM turbulence model simulation with Prt=0.9 for three different mesh levels（coarse, intermediate, fine）.

Coarse mesh results differ from intermediate mesh and fine mesh results. The most important region is the temperature near the pipe wall (x=-0.025m and x=0.025m). At x=-0.025m, coarse mesh results are the same as intermediate mesh and fine mesh results. However, at x=0.025m, coarse mesh results are different from intermediate mesh and fine mesh results. For the sake of minimizing the computational time, the intermediate mesh can be used for further numerical analysis since the intermediate mesh results is nearly the same as fine mesh results.

51m m(Hexahed ra l)

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BS L-RS M(I nterm ediate)

BS L-RS M(F ine)

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BS L-RS M(C o arse)

BS L-RS M(I nterm ediate)

BS L-RS M(F ine)

(a)



Fig.4 The Mixing Scalar at four locations for BSL-RSM turbulence model simulations on three different mesh

levels

4 Numerical Simulation Results 4.1 Turbulent Prandtl Number Effect

Fig.5 shows corresponding comparison of parameter variation study using Prt=0.9, 0.2 and 0.1 for BSL-RSM turbulence model simulations with Hexahedral mesh type in comparison with the

experimental data at L=51mm, L=91mm, L=191mm and L=311mm downstream of the mixing-tee. The coefficient of determination（Eqn. (3)）, R2, is a relative comparison criterion between the experimental and predicted values. The accuracy of computational results improves as R2 approaches 1.

91mm (Hexah edral)

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B S L -RS M (F ine )

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(c)

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BS L- RS M( Interm ediate)

BS L- RS M( Fine)

311 mm(Hex ahed ral)

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(d)



( )( )∑

∑Π−Π

Π−Π−=

2

2

2 1measmeas

predmeasR (3)

in which measΠ is the experimental data, measΠ is

the average value of experimental data, predΠ is the

predicted result, and R2 is the coefficient of determination.

Since the coefficient of determination, R2, obtained by using Prt=0.1 is grater than other Prt values as shown in Fig. 5, predicted results obtained by using Prt=0.1 are generally in slightly better agreement with the experimental data.

The most important region is the temperature near the pipe wall (x=-0.025m and x=0.025m). The absolute error（Eqn. (4)） , β, obtained by using Prt=0.1 at x=-0.025m is between 0.1232 and 0.0075, which is smaller than that by using Prt=0.2 and Prt=0.9. Additionally, the absolute error, β, obtained by using Prt=0.1 at x=0.025m is between 0.0066 and -0.0290, which is smaller than that by using Prt=0.2 and Prt=0.9. The correlation improves as β approaches 0.

( )measpred Π−Π=β (4)

51mm-Different Turbulent Prandtl Number (M esh Type:Hexahedral)

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Scala

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Experimental Data

BSL-RSM(Pr=0.9)

BSL-RSM(Pr=0.2)

BSL-RSM(Pr=0.1)

(a) 51mm

Prt=0.9 -> R2=0.966

Prt=0.2 -> R2=0.997

Prt=0.1 -> R2=0.996

51mm-Different Turbulent Prandtl Number (M esh Type:Hexahedral)

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ing

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Experimental Data

BSL-RSM(Pr=0.9)

BSL-RSM(Pr=0.2)

BSL-RSM(Pr=0.1)

(a) 51mm

Prt=0.9 -> R2=0.966

Prt=0.2 -> R2=0.997

Prt=0.1 -> R2=0.996

(a)

91mm -D ifferent Turbulent Prandtl Number (Mesh Type:Hexahedral)

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ing

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E xperime ntal Data

B SL-R SM(Pr=0 .9)

B SL-R SM(Pr=0 .2)

B SL-R SM(Pr=0 .1)

Prt=0.9 -> R2=0.933

Prt=0.2 -> R2=0.991

Prt=0.1 -> R2=0.992

91mm -D ifferent Turbulent Prandtl Number (Mesh Type:Hexahedral)

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E xperime ntal Data

B SL-R SM(Pr=0 .9)

B SL-R SM(Pr=0 .2)

B SL-R SM(Pr=0 .1)

Prt=0.9 -> R2=0.933

Prt=0.2 -> R2=0.991

Prt=0.1 -> R2=0.992

(b)

191mm-Different Turbulent P rand tl Num ber (Mesh Type:Hexah edral)

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BSL -RSM(Pr=0 .9)

BSL -RSM(Pr=0 .2)

BSL -RSM(Pr=0 .1)

Prt=0.9 -> R2=0.332

Prt=0.2 -> R2=0.817

Prt=0.1 -> R2=0.965

191mm-Different Turbulent P rand tl Num ber (Mesh Type:Hexah edral)

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BSL -RSM(Pr=0 .9)

BSL -RSM(Pr=0 .2)

BSL -RSM(Pr=0 .1)

Prt=0.9 -> R2=0.332

Prt=0.2 -> R2=0.817

Prt=0.1 -> R2=0.965

(c)



Fig.5 Effects of three different Prt values for BSL-RSM turbulence model (**** means the predicted results do not correlate well with the experimental values)

4.2 Turbulence Model Effect

Fig.6 shows corresponding comparison of turbulence model variation study using BSL-RSM and k-ε turbulence model simulations with Prt=0.1. The Hexahedral mesh type comparison with the experimental data at L=51mm, L=91mm, L=191mm and L=311mm downstream of the mixing-tee is also shown in Fig.6. Based on the values of R2, at L=51mm, L=91mm, and L=191mm, predicted results obtained by using BSL-RSM turbulence model are generally in slightly better agreement with

the experimental data. However, at L=311mm, results obtained by using k-ε turbulence model are generally in slightly better agreement with the experimental data.

The absolute error, β, obtained by using k-ε turbulence model at x=-0.025m is between 0.0069 and -0.0118, which is smaller than that by using BSL-RSM turbulence model. On the other hand, the absolute error, β, obtained by using BSL-RSM turbulence model at x=0.025m is smaller than that by using k-ε turbulence model.

311m m-Differen t Turb ulent Prand tl Number (Mesh Type:Hexahedral)

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Expe rimental Data

BS L-RSM(Pr=0.9)

BS L-RSM(Pr=0.2)

BS L-RSM(Pr=0.1)

Prt=0.9 -> R2=****

Prt=0.2 -> R2=****

Prt=0.1 -> R2=0.788

311m m-Differen t Turb ulent Prand tl Number (Mesh Type:Hexahedral)

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Expe rimental Data

BS L-RSM(Pr=0.9)

BS L-RSM(Pr=0.2)

BS L-RSM(Pr=0.1)

Prt=0.9 -> R2=****

Prt=0.2 -> R2=****

Prt=0.1 -> R2=0.788

(d)

51mm-Different Turbulent Model (Mesh Type:Hexahedral)

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BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(a) 51mm

BSL-RSM -> R2=0.996

k-εεεε -> R2=0.990


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BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(a) 51mm

BSL-RSM -> R2=0.996

k-εεεε -> R2=0.990

(a)



Fig.6 Effects of two different turbulence models for Prt=0.1 with Hexahedral mesh type 4.3 Cross-Sectional Distribution Comparison

Fig.7 shows representative cross-sectional plots of the temperature distribution for the simulation by using BSL-RSM and k-ε turbulence models and the electrical conductivity distribution for the

measurement by using WMS at L=51mm and L=191mm downstream of the mixing-tee. Predicted results obtained by using the mixing of water with two different temperatures are generally in good agreement with the experimental data by using the mixing of de-ionized water with two different


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Experimental Data

BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(b) 91mm

BSL-RSM -> R2=0.992

k-εεεε -> R2=0.971


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Experimental Data

BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(b) 91mm

BSL-RSM -> R2=0.992

k-εεεε -> R2=0.971

(b)


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Experimental Data

BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(c) 191mm

BSL-RSM -> R2=0.965

k-εεεε -> R2=0.931


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Experimental Data

BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(c) 191mm

BSL-RSM -> R2=0.965

k-εεεε -> R2=0.931

(c)


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Experimental Data

BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(d) 311mm

BSL-RSM -> R2=0.788

k-εεεε -> R2=0.814


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BSL-RSM(Pr=0.1)

k-ε(Pr=0.1)

(d) 311mm

BSL-RSM -> R2=0.788

k-εεεε -> R2=0.814

(d)



electrical conductivities. For quite a short distance behind the mixing-tee (L=51mm), the stratification phenomenon of fluid is obvious.

The high mixing scalar concentration is transported by the forming and counter-rotating double-vortex behind the mixing-tee along the lower and upper pipe walls, while low values of the mixing

scalar, indicating water from the branch pipe, remains for quite a long distance behind the mixing-tee at the right side of the main pipe, where the vortex cores induced by the branch pipe flow are located. The mixing phenomena of the study are the same as literature [6].

Fig.7 Cross-sectional distribution comparison between turbulence model predictions (Prt=0.1) and WMS

measurements

5 Conclusion This study develops the numerical simulation of

BSL-RSM and k-ε turbulence models for analyzing the thermal mixing phenomenon in a mixing piping. Some conclusions may be drawn as follows: 1.Different turbulence models and Prt values are the

main factors of the simulation. 2.Compared with the experimental results, predicted

results obtained by using Prt=0.1 are generally in slightly better agreement with the experimental data than other Prt values.

3.The accuracy of temperature near the pipe wall (x=-0.025m and x=0.025m) is the most important region. The absolute error, β, obtained by using Prt=0.1 at x=-0.025m and x=0.025m is smaller than that by using Prt=0.2 and Prt=0.9. β obtained by using BSL-RSM turbulence model at x=0.025m is smaller than that by using k-ε turbulence model. However, at x=-0.025m, β obtained by using k-ε turbulence model is smaller than that by using BSL-RSM turbulence model.

4.Based on the value of R2, the computational results obtained by using BSL-RSM turbulence model are

generally in slightly better agreement with the experimental data, but at L=311mm, results obtained by using k-ε turbulence model are generally in slightly better agreement with the experimental data.

5.This study can verify that the mixing phenomenon of water with two different temperatures can be analogized by de-ionized water with two different electrical conductivities.

6.In order to assess thermal fatigue of pipe in nuclear power plant, the temperature fluctuations of fluid must be predicted correctly as a first step in the procedure. Based on the computational results, the simulation in the study is suitable for this mixing problem. Future work will be devoted to analyzing the stress and fatigue assessment of pipe wall.

References:

[1]

Westin, J., Alavyoon, F., Andersson, L., Veber, P., Henriksson, M. and Andersson, C., Experiments and unsteady CFD-calculations

of thermal mixing in a T-junction, CFD4NRS,

Location：：：：51mm


ExperimentBSL-RSM k-εεεε



ExperimentBSL-RSM k-εεεε



Garching, Germany, 2006. [2]

Westin J., Veber P., Andersson L., ‘ t Mannetje C., Andersson U., Eriksson J., Hendriksson M., Alavyoon F., Andersson C., High-Cycle Thermal Fatigue in Mixing Tees：Large-Eddy Simulations Compared to a New

Validation Experiment, 16th Int. Conf. On Nuclear Engineering (ICONE-16), Florida, Orlando, USA, Paper No. 48731, May, 2008, pp. 1-11, 11-15.

[3] Odemark Y., Green T. M., Angele K., Westin J., Alavyoon F., Lundstrom S., 2009, High-Cycle Thermal Fatigue in Mixing Tees：New Large-Eddy Simulations Compared to a

New Validation Experiment, 17th Int. Conf. On Nuclear Engineering (ICONE-17), Florida, Orlando, Belgium, Paper No. 75962, July, 2009, pp. 1-11, 12-16.

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and List of Available Data for CFDValidation, Report Memo U 07-26, Vattenfall R&D AB, Älvkarleby, Sweden, 2007, pp. 1-17.

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ANSYS-CFX. Experiments and CFD Code Applications to Nuclear Reactor Safety (XCFD4NRS ) OECD/NEA CEA Workshop, Grenoble, France 10-12 Septembre 2008.

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new electrode-mesh tomograph for gas-liquid

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Wire-Mesh Sensors, International Journal of Thermal Sciences, Vol. 41, 2002, pp. 17-28.

[9] ANSYS CFX-11.0 User Manual, ANSYS Inc, USA, 2008.

[10] Anderson U., Westin J., Eriksson J., 2006, Thermal Mixing in a T-Junction Model Tests

2006, Report Number U 06:66, Vattenfall R&D AB, Alvkarleby, Sweden, pp.1-68.

[11] Hu L.W., Kazimi M.S., 2006, LES benchmark

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[12] Ogawa1 H., Igarashi M., Kimura N., and Kamide H., 2005, Experimental Study on Fluid

Mixing Phenomena In T-Pipe Junction with

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[13] Kawamura, T. et al., 2003, Study on high-cycle

fatigue evaluation for thermal striping in

mixing tees with hot and cold water, In:11th Int. Conf. Nuclear Engineering, ICONE-11, Tokyo, Japan, April 20-23.

[14] Ohtsuka, M. et al., 2003, LES Analysis of Fluid

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with the Same Diameters, Proc. 11th Int. Conf. On Nuclear Engineering ICONE-11, Tokyo, Japan April 20-23.

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two different turbulence models in comparison with ... · t=0.9, 0.2 and 0.1 for bsl-rsm turbulence...

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