Investigating thermal mixing and reverse flow characteristics in a T-junction using CFD methodology

Applied Thermal Engineering 102 (2016) 733–741

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Research Paper

Investigating thermal mixing and reverse flow characteristics in a T-junction using CFD methodology C.H. Lin a, Y.M. Ferng b,c,⇑ a

Center of Energy and Environment, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC Dept of Engineering and System Science, Inst of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC c Dept of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong Special Administrative Region b

h i g h l i g h t s
CFD simulates the thermal mixing and reverse in a T-junction.
Steady-state turbulence models are adopted in this paper.
Reverse flow in the T-junction decreases with increasing flowrate in main pipe.
v2f turbulence model can capture the reverse flow from the branch injection.
RKE model can reproduce the thermal mixing characteristics in a T-junction.

a r t i c l e

i n f o

Article history: Received 24 October 2015 Accepted 24 March 2016 Available online 7 April 2016 Keywords: Thermal mixing Reverse flow T-junction CFD Steady-state turbulence model

a b s t r a c t A three-dimensional (3-D) computational fluid dynamics (CFD) methodology is developed to simulate the thermal mixing and reverse flow characteristics in an in-house T-junction. Different steady-state turbulence models are adopted in the simulations and assessed against the measured data of temperature distributions at various cross-sections of the main pipe. The unsteady-state turbulence models may be suitable for resolving the amplitude and frequency of temperature oscillation in a T-junction. However, T-junctions are just one component in an entire complex piping system. The steady-state turbulence models therefore attract some interest for T-junction simulations in engineering applications. Two cases, with the flowrate combinations of 30/200 and 30/400 in the branch/main pipes, are used to validate CFD simulations with different turbulence models. The reverse flow from the branch back upstream of the T-junction intersection is more significant for the lower flowrate of the main pipe, which can be confirmed by both measured data and predicted results. Based on the temperature comparison of the measurements and the predictions, the v2f turbulence model is most suitable for capturing the flow reversal characteristics in the T-junction, while the realizable k—e turbulence model reproduces the measured data more accurately for the T-junction with the higher flowrate in the main pipe and the lesser reverse flow. The present results can provide a useful reference for simulating the thermal mixing and reverse flow in a T-junction with various steady-state turbulence models. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction T-junctions are commonly used in piping systems and multichannel networks in various industries, including petrochemical plants, electronic cooling applications, molecular biological processes, power plants, etc. It is crucial to comprehensively understand the thermal–hydraulic characteristics in a T-junction ⇑ Corresponding author at: Department of Engineering and System Science, Institute of Nuclear Engineering and Sceince, 101, Sec. 2, Kuang-Fu Rd., Hsinchu 30013, Taiwan, ROC. E-mail address: [email protected] (Y.M. Ferng). http://dx.doi.org/10.1016/j.applthermaleng.2016.03.124 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

for piping design. Many simulations using computational fluid dynamics (CFD) with different turbulence models have been conducted to investigate the mixing characteristics of T-junctions. Hu and Kazimi [1] studied temperature fluctuations caused by thermal mixing in T-junctions using the large eddy simulation (LES) turbulence model. The results showed that the calculated maximum temperatures were somewhat higher than the measurements. Wang and Mujumdar [2] developed a three-dimensional (3-D) model with the standard k—e turbulence model to predict the flow and mixing characteristics of multiple and multi-set opposing jets. Good agreement between the simulated and the

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Nomenclature Cp d D p Q T T⁄ u U⁄ ~ v x y

specific heat capacity, J/kg-K diameter of branch, m diameter of main pipe, m pressure, N/m2 volmetric flowrate, L/min temperature, K b normalized temperature, TTT m T b local velocity, m/s u/um velocity vector, m/s axial distance from the center of T-junction intersection, m ‘vertical distance from the center of main pipe, m

experimental results was obtained. Le and Hassan [3] analyzed the gas mixing phenomenon in a T-shape micromixer using the Direct Simulation Monte Carlo (DSMC) simulation. Vicente et al. [4] used the standard k—e turbulence model to reproduce the measured profiles of the transport scalar and the pressure drop in an X-junction. Using the LES turbulence model, Lee et al. [5] simulated the coolant temperature fluctuations at a mixing T-junction of equal pipe diameters. The calculated normalized mean temperatures and fluctuating temperatures were in good agreement with the measurements. Frank et al. [6] first applied the Best Practice Guidelines (BPGs) on simulating the turbulent mixing of water in a T-junction. The investigations essentially aimed on grid independent CFD solutions for traditional Reynolds-Averaged Navier–Stokes (RANS) and Unsteady RANS (URANS) approaches using the Shear Stress Transport (SST) and Best Straight Line (BSL) Reynolds Stress Model (RSM) turbulence models. Walker et al. [7] used the data obtained from an adiabatic T-junction experiment to validate the steadystate CFD calculations from the following turbulence models: k—e, SST k—x and BSL RSM. Naik-Nimbalkar et al. [8] carried out thermal mixing experiments on a T-junction with water, and used 3-D steady state CFD to predict the velocity/temperature fields. Good agreement with the experimental data was obtained. Aulery et al. [9] performed both RANS and LES simulations of thermal–hydraulic characteristics in a T-junction of a Phoenix reactor. Their analyses confirmed the re-attached jet flow in this configuration. They also reported that RANS models can lead to valuable simulations in relatively short amounts of time, and that LES methods can partially resolve flow scales at a larger computational cost. Ayhan and Sökmen [10] simulated the turbulent thermal mixing of two water streams in a T-junction by way of CFD with the LES model with the eddy-viscosity Sub-Grid Scale (SGS) approach. Sakowitz et al. [11] performed LES simulation for the flow in a T-junction to analyze the mixing quality, secondary structure and flow modes. Different flow ratios of the main pipe/branch were also considered. Smith et al. [12] provided an international benchmarking exercise to test the ability of CFD codes to predict the important parameters affecting turbulent mixing in T-junctions. The simulation results were compared to measured data from experiments performed by Vattenfall’s research and development team. Using the LES model, Sakowitz et al. [13] studied the turbulent mixing process for the two T-junction geometries of square and circular cross-sections in the intake manifolds of Internal Combustion (IC) engines. Gritskevich et al. [14] investigated different turbulence Scale-Resolving Simulation (SRS) modeling approaches for flow in a T-junction, including Scale-Adaptive Simulation (SAS), Delayed Detached Eddy Simulation (DDES) and Embedded Large Eddy Simulation (ELES).

Greek symbols viscosity, kg/m-s k thermal conductivity, W/m-K q density, kg/m3

l

Subscripts b inlet value in the branch m inlet value in the main pipe t turbulent property

As mentioned in the previous simulation research, the unsteady-state turbulence models, including LES, URANS or SAS, and so forth, are suitable for resolving the amplitude and frequency of temperature oscillation in a T-junction. However, the simulations of T-junctions using these unsteady-state turbulence models are time consuming and T-junctions are just one component of an entire complex piping system. In the engineering applications, steady-state turbulence models remains interesting for T-junctions, since they can also provide accurate predictions for capturing the time-averaging thermal–hydraulic characteristics of such junctions [2,4,7]. Therefore, a 3-D CFD methodology is developed in this research to simulate the thermal mixing and flow reversal characteristics of an in-house T-junction [15]. Different steady-state turbulence models are adopted in the simulations and validated against the measured temperature distribution data from the main pipe. Through the comparison of measurements and predictions, the applicability of different steady-state turbulence models for reproducing the thermal–hydraulic characteristics in a T-junction can be obtained. 2. Mathematical model The mathematical model used to investigate the thermal mixing and reverse flow characteristics in a T-junction includes governing equations, turbulence models, and appropriate boundary conditions. Details regarding the mathematical model are described in the following sections. 2.1. Governing equations Continuity equation

r  ðq~ vÞ ¼ 0

ð1Þ

Momentum equation

r  ðq~ v~ v Þ ¼ rp þ r  ðl r~ vÞ

ð2Þ

where

l ¼ effective viscosity ¼ l þ lt

ð3Þ

Energy equation

r  ðqCp~ v TÞ ¼ r  ðk rTÞ

ð4Þ

where

k ¼ effective conductivity ¼ k þ kt

ð5Þ

lt and kt are the turbulence-induced viscosity and conductivity, respectively, and can be evaluated based on the turbulence models adopted in the simulations.

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2.2. Turbulence models

Table 1 Dimensions of T-junction and test boundary conditions.

Adopting steady-state turbulence models in T-junction simulations also attracts attention in the industry applications, since T-junctions are generally only one component of an entire piping system, and unsteady-state turbulence models are time consuming. Therefore, four kinds of steady-state turbulence models are used in this paper, including the standard k–e (SKE) [16], realizable k–e (RKE) [17], SST k–x(SST-KW) [18], and v2f [19]. The adoption of the SKE will provide the base results for comparison with the predictions from the other turbulence models. The RKE model is selected owing to its superior performance for flows with a strong adverse pressure gradient, separation, and recirculation, all of which may occur in the T-junction layout. The SST-KW model is used herein for its similar good behavior for adverse pressure gradients and separating flows. The v2f model is a general low-Reynolds number turbulence model, and can be accurately applied to flows dominated by separation. Therefore, this model is also selected in the present work. In addition, these steady-state turbulence models are typically adopted for industry engineering applications.

D (cm)

Qb (L/min)

Qm (L/min)

Tb (°C)

Tm (°C)

2.1

20.8

30

200/400

20

90

test conditions are based on experiments performed by the authors, the results of which were presented in a previous paper [20]. 2.4. Numerical treatments The governing equations presented above essentially belong to the class of non-linear partial differential equations (PDEs), which are discretized into their finite-difference forms for numerical calculations. The second-order upwind scheme is used to handle the convection terms in the PDEs. The SIMPLE scheme is used to solve the finite difference equation for velocity coupled with pressure. The Algebraic MultiGrid (AMG) linear solver is adopted for all the finite differencing equations. Fig. 2 shows the typical mesh (2.35 million cells) model adopted in the simulations. The mesh model in 3-D view and from the top view is presented in the central and upper portions, respectively. The mesh distribution on the cross-section in the main pipe is shown in the right portion. Based on the requirements of the BPG [21], the mesh errors should be estimated for the CFD simulations. Therefore, calculations with different mesh sizes (1.8 (coarse), 2.35 (standard), and 3.1 (fine) million cells) for the simulations with the SST-KW turbulence models are performed in this study. The effective grid refinement ratio for these mesh models is about 1.3, which is the minimum value suggested by the ASMS V&V [22]. The deviation in the local maximum velocity and temperature is less than 1.0%. In addition, according to the ASME V&V [22], the values of the fine Grid Convergence Index (GCI) for the local maximum velocity and temperature are 1.4% and 2.0%,

2.3. Geometry and boundary conditions Fig. 1(a) and (b) are a photograph of the test T-junction and a schematic of the CFD simulation domain, respectively. Hot water flows in the horizontal main pipe and cold water is injected from the vertical branch. For simulation, uniform distributions of velocity and temperature are set as the inlet boundary conditions for both the main pipe and the branch. The pressure is employed at the outlet of the main pipe. No-slip and adiabatic conditions for both the momentum and the energy equations are applied to the wall. The dimensions of this test T-junction, as well as the boundary conditions, are listed in Table 1. These dimensions and

Inlet of main pipe

d (cm)

(a) Inlet of branch pipe

Pipe wall

(b)

Outlet of main pipe

Fig. 1. Photo of test T-junction (a); schematic of CFD simulation domain (b).

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Fig. 2. Typical mesh distributions in the simulations.

Fig. 3. Predicted streamlines near the intersection of a T-junction for Qb/Qm = 30/200 with different turbulence models.

respectively, and the corresponding numerical errors are 1.2% and 1.7%, which are estimated using a safety factor of 1.25 and an expansion factor of 1.15. The results presented in the following section were obtained using the mesh size of 2.35 million cells All of the simulation works presented in this paper was performed using the FLUENT code [23] on a PC with an IntelÒ i7 processor and 32 GB RAM. The convergence criteria for all of the governing equations are set such that summation of the relative residual in every control volume is less than 105 . The decay trend in the residual plot for each equation is also considered as an alternative criterion. Both of these criteria should be met to ensure the convergence of the numerical simulations. 3. Results and discussion Fig. 3 shows the streamlines near the intersection of a T-junction for the case with the branch/main pipe flowrates of 30 (L/min)/200 (L/min), which are predicted using the different turbulence models. It can be clearly is seen in this figure that the reverse flow from the branch injection back into the upstream side of the T-junction intersection is captured by all the turbulence models adopted herein. The ranges of reverse flow are slightly different

for various turbulence models, which may influence the temperature distribution upstream of the T-junction intersection, especially near the bottom side. In addition, different predicted results are also shown in the hot/cold water mixing range downstream of a T-junction. This mixing range is predicted to be larger using the v2f model, as shown in the detailed comparison of Fig. 3. The influenced areas of reverse flow and thermal mixing are clearly revealed in the vector plots, as shown in Fig. 4. This figure illustrates the predicted plots of normalized vector distributions on a 2-D plane that is vertically cut from the central plane. The normalized velocity (U⁄) is defined as the calculated local velocity divided by the inlet velocity of the main pipe. It is clearly revealed in Fig. 4 that the cold water from the branch is injected into the T-junction intersection; some of water reverses to flow upstream, while the remaining water flows downstream along the bottom side of the pipe. All the turbulence models capture this flow characteristic, but report different influenced ranges. In addition, detailed observation of these flow plots reveals that only the reverse flow range predicted by the v2f model may be large enough to influence the temperature at the bottom side on the plane of x = 5d. Figs. 5–8 show the 2-D distributions of normalized temperature (T⁄) contours predicted using the SKE, RKE, SST-KW, and v2f

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RKE

SKE

v2f

SST-KW

Fig. 4. 2-D plots of normalized vector distributions with different turbulence models.

-5 d

0

10 d

20 d

⁄

Fig. 5. 2-D distributions of normalized temperature (T ) contours predicted by SKE turbulence model.

-5 d

0

10 d

20 d

Fig. 6. 2-D distributions of normalized temperature (T⁄) contours predicted by RKE turbulence model.

turbulence models, respectively. In these figures, the upper plot is the 2-D distribution plot vertically cut from the central plane of the T-junction, and the lower plots are the 2-D normalized temperature distributions at different cross-sections of the main pipe, i.e. at x = 5d, 0.0, 10d, and 20d. The measured temperature points are illustrated in the left portion and the locations of the different cross-sections in the main pipe are listed in the right portion. Comparison of all the predicted temperature contours on the cross-section at x = 5d for Figs. 5–8 confirms that the reverse flow at x = 5d upstream of the T-junction intersection is only captured

by the v2f turbulence model. As shown in Fig. 5, the secondary flow plays an important role in the thermal mixing after the T-junction intersection, which is revealed in the green area located on both sides of the cross-sections in the main pipe at x = 10, and 20d. This flow circulation characteristic on both side of cross-section in the main pipe can also be shown in the streamline distributions from the side view of Fig. 3. Hot/cold water stratification is seen on the cross-section of the main pipe downstream from the T-junction intersection, as the lower density hot water accumulates in the upper/central regions, while the higher density cold

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-5 d

0

10 d

20 d

Fig. 7. 2-D distributions of normalized temperature (T⁄) contours predicted by SST-KW turbulence model.

-5 d

0

10 d

20 d

⁄

Fig. 8. 2-D distributions of normalized temperature (T ) contours predicted by v2f turbulence model.

0.08

0.06

0.04

Y-Direction (m)

water concentrates on the bottom side of the piping. However, the cold water is predicted to be concentrated near the piping bottom below the location of thermocouple # 8, rendering the predicted temperature higher than the measured data, as discussed in the following paragraphs. Similar characteristics are shown in the predicted results using the RKE, SST-KW, and v2f turbulence models, as illustrated in Figs. 6–8. Fig. 9 shows the comparison of the temperature distributions at x = 0 between the measurements and the predictions for the case of Qb/Qm = 30/200. Dashed lines represent the predicted results along the line containing the measured points of T1/4/7; and solid lines are the results along the central line having the measured points of T2/5/8. The notation for T1/4/7 and T2/5/8 is illustrated in the upper portion of the figure. Based on the predicted temperature contour at x = 0 in Figs. 5–8, the cold water is injected into the intersection of the T-junction and doesn’t mix with the hot water from the main pipe until it passes over half a diameter in height in the intersection. The water temperature is predicted to be less from the upper side to the center of the main pipe. However, the measured data from T2/5/8 reveal that there is thermal mixing of cold/hot water near the location of T5 (i.e. the central position), causing the predicted temperature near T5 to be much less than the measured temperature. The predictions by all four turbulence models show this trend. In addition, the cold water is injected into the bottom of the main pipe, mixes with the hot water from the main pipe, and then circulates around both sides of the main pipe, as clearly shown in the streamline

0.02

0.00 Data for T1,4,7 Predictions by SKE

-0.02

Predictions by RKE Predictions by SSTKW

-0.04

Predictions by v2f Data for T2,5,8 Predictions by SKE

-0.06

Predictions by RKE Predictions by SSTKW

-0.08

Predictions by v2f

0

20

40

60

80

100

Temperature (oC) Fig. 9. Comparison of temperature distributions between measurements and predictions at x = 0 for Qb/Qm = 30/200.

C.H. Lin, Y.M. Ferng / Applied Thermal Engineering 102 (2016) 733–741

0.08

0.06

Y-Direction (m)

0.04

0.02

0.00

Data for T1,4,7 Predictions by SKE Predictions by RKE

-0.02

Predictions by SSTKW Predictions by v2f Data for T2,5,8

-0.04

Predictions by SKE Predictions by RKE Predictions by SSTKW

-0.06

-0.08 65

Predictions by v2f

70

75

80

85

90

95

Temperature (oC) Fig. 10. Comparison of temperature distributions between measurements and predictions at x = 20d for Qb/Qm = 30/200.

distributions from the side view in Fig. 3. Therefore, a more uniform temperature distribution is resulted along the vertical line T1/4/7 on the left side of the main pipe cross-section. The present models over-predict the temperature variation in this region; however, the temperature difference predicted by the v2f model is the closet to the measured results of all the predictions. The difference between T1/4/7 is measured to be 8 °C and is predicted to be 16, 21, 18, 12 °C for the SKE, RKE, SST-KW, and v2f turbulence models, respectively. Fig. 10 shows the comparison of the temperature distributions at x = 20d between the measurements and the predictions for the case of Qb/Qm = 30/200. According to the predicted distributions

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of flow vectors for all the turbulence models in Fig. 4, the thermally mixed fluid passes downstream along the bottom side of the piping and some fluid flows backward along the upper side. Therefore, the temperature variation in the vertical direction of the cross-section in the main pipe shows a swaying behavior. This temperature variation revealed in the predictions is not seen in the measurements. The difference between the measured temperature at T2/5/8 along the central line and at T1/4/7 along the left-side line is less than 5 °C. In addition, the hot region is predicted to be near the 1/4 height from the piping bottom, which essentially belongs to the un-mixed hot water. The cold region near the piping bottom is simply the cold water from the branch, which is also not mixed with the hot water in the main pipe. These predicted flow characteristics can also help the experiments describe the thermal mixing in a T-junction. As shown above, the strong flow reversal from the branch back upstream of the main pipe is observed in the test case with Qb/Qm = 30/200. This reverse characteristic decreases with an increasing flowrate in the main pipe. The test case with Qb/Qm = 30/400 is selected to validate the present CFD models. Fig. 11 shows the predicted normalized distributions of the velocity vectors and temperature contours by the RKE turbulence model for the case of Qb/Qm = 30/400. A detailed comparison of Figs. 2, 4 and 11 reveals that the reverse flow phenomenon is much smaller for the higher flowrate of 400 L/min in the main pipe than for 200 L/min. The flow reversal in the upper portion of the main pipe downstream of the T-junction is also smaller for the higher flowrate. Fig. 12 shows the comparison of the temperature distributions at x = 0 between the measurements and the predictions for the case of Qb/Qm = 30/400. Thermal mixing occurs as the cold water is injected into the T-junction intersection, as confirmed by the measured data from T2/5/8 and the predicted temperature distributions along the central line for different turbulence models. In addition, the mixed fluid temperature is higher with the higher flowrate of hot water from the main pipe, causing the temperature in the secondary flow on the cross-section of the main pipe to be more uniform and higher than for Qb/Qm = 30/200. These thermal mixing characteristics are confirmed by the predicted velocity vectors and temperature contours as well as by the measured and predicted temperature distributions.

Fig. 11. 2-D distributions of normalized velocity vectors (a) and temperature contours (b) predicted by RKE turbulence model.

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0.08

0.06 100

80

0.02

Predicted results (oC)

Y-Direction (m)

0.04

0.00 Data for T1,4,7 Predictions by SKE

-0.02

Predictions by RKE Predictions by SSTKW Predictions by v2f

-0.04

Data for T2,5,8

+10 %

60

-35 %

40

Predictions by SKE

20

Predictions by RKE

-0.06

Predictions by SSTKW Predictions by v2f

-0.08

0

20

40

Temperature

60

80

100

(oC)

Predictions by RKE Predictions by SSTKW

0.04

Predictions by v2f Data for T2,5,8

Y-Direction (m)

Predictions by SKE

0.02

60

80

100

Fig. 14. Comparison of predicted accuracy for different turbulence models under Qb/Qm = 30/400.

4. Conclusion

Predictions by v2f

-0.02 -0.04 -0.06 -0.08 70

40

Predictions by RKE Predictions by SSTKW

0.00

20

reproduces the thermal mixing in the T-junction in this case of the higher flowrate in the main pipe and less reverse flow more precisely than the other models. This is confirmed in Fig. 14, which compares predicted accuracy for different turbulence models under Qb/Qm = 30/400. According to the quantitative comparison, the maximum error is about 10% for the RKE model and about 35% for the other models.

Data for T1,4,7 Predictions by SKE

0.06

0

Measured data (oC)

Fig. 12. Comparison of temperature distributions between measurements and predictions at x = 0 for Qb/Qm = 30/400.

0.08

0

75

80

85

Temperature

(oC)

90

95

Fig. 13. Comparison of temperature distributions between measurements and predictions at x = 20d for Qb/Qm = 30/400.

Fig. 13 shows the comparison of the temperature distributions at x = 20d between the measurements and the predictions for the case of Qb/Qm = 30/400. With a higher flowrate in the main pipe, the hot fluid in the main pipe can carry the cold fluid from the branch downstream of the T-junction. Less fluid reverses in the top portion of the main pipe than for the lower main-pipe flowrate, resulting in the temperatures around the measured points of T1 and T2 being higher for Qb/Qm = 30/400 than for Qb/Qm = 30/200. These flow and thermal mixing behaviors are found with help of the thermal–hydraulic characteristics predicted results shown in Fig. 11. In addition, based on the comparison of measurements and predictions, the CFD with the RKE turbulence model

In this study, a CFD methodology is developed to simulate the thermal mixing and reverse flow in a T-junction. Several steadystate turbulence models are adopted in the simulations. The water temperatures under the two test cases, with different flowrates in the main pipe, are measured at cross-sections upstream, within, and downstream of the T-junction intersection. These temperatures are used to validate the predicted results obtained using the different turbulence models. The reverse flow from the branch injection back upstream of the T-junction is captured by all the turbulence models adopted in this research. The ranges of this reverse flow and the hot/cold water mixing range downstream of the T-junction are slightly different for different turbulence models. This mixing range is predicted to be larger using the v2f models. In addition, the higher flowrate in the main pipe decreases the reverse flow phenomenon, which is confirmed in the measurements and the predictions. Based on the comparisons between the measured and the predicted results, the v2f turbulence captures the reverse flow from the branch injection and the RKE model reproduces the thermal mixing characteristics in the T-junction with less flow reversal behavior. The present simulation results can provide useful information about the applicability of various steady-state turbulence models for predicting the thermal mixing and flow reversal in a T-junction for engineering applications and requirements. Based on the literature survey, the thermal mixing characteristics of a T-junction also depend on the pipe dimension, fluid temperature, and injection angle, which will be investigated in the next series of experiments. The corresponding simulation

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works will be performed at that time. In addition, the thermal striping phenomena in a T-junction will result in cyclic thermal stresses and subsequent thermal fatigue cracking. These thermal fluctuation characteristics in a T-junction can be only captured by unsteady-state turbulence models, which is other future work that can be built on the present research. References [1] L. Hu, M. Kazimi, LES benchmark study of high cycle temperature fluctuations caused by thermal striping in a mixing tee, Int. J. Heat Fluid Flow 27 (2006) 54. [2] S.J. Wang, A.S. Mujumdar, Flow and mixing characteristics of multiple and multi-set opposing jets, Chem. Eng. Process. 46 (2007) 703. [3] M. Le, I. Hassan, DSMC simulation of gas mixing in T-shape micromixer, Appl. Therm. Eng. 27 (2007) 2370. [4] W. Vicente, M. Salinas-Vazquez, C. Chavez, E. Carrizosa, Different numerical methods in the study of passive scalar transport in a pipeline x-junction, Appl. Math. Model. 33 (2009) 1248. [5] J.I. Lee, L. Hu, P. Saha, M.S. Kazimi, Numerical analysis of thermal striping induced high cycle thermal fatigue in a mixing tee, Nucl. Eng. Des. 239 (2009) 833. [6] Th. Frank, C. Lifante, H.M. Prasser, F. Menter, Simulation of turbulent and thermal mixing in T-junctions using URANS and scale-resolving turbulence models in ANSYS CFX, Nucl. Eng. Des. 240 (2010) 2313. [7] C. Walker, A. Manera, B. Niceno, M. Simiano, H.M. Prasser, Steady-state RANSsimulations of the mixing in a T-junction, Nucl. Eng. Des. 240 (2010) 2107. [8] V.S. Naik-Nimbalkar, A.W. Patwardhan, I. Banerjee, G. Padmakumar, G. Vaidyanathan, Thermal mixing in T-junctions, Chem. Eng. Sci. 65 (2010) 5901. [9] F. Aulerya, A. Toutanta, R. Monod, G. Brillant, F. Bataille, Numerical simulations of sodium mixing in a T-junction, Appl. Therm. Eng. 37 (2012) 38.

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