Detached eddy simulation of turbulent and thermal mixing in a T-junction

Annals of Nuclear Energy 124 (2019) 245–256

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Detached eddy simulation of turbulent and thermal mixing in a T-junction Dong Gu Kang a,b, Hanbee Na a, Chi Young Lee c,⇑ a

Korea Institute of Nuclear Safety, 62 Gwahak-ro, Yuseong-gu, Daejeon 34142, Republic of Korea Nuclear and Radiation Safety Department, University of Science and Technology, 217 Gajeong-ro Yuseong-gu, Daejeon 34113, Republic of Korea c Department of Fire Protection Engineering, Pukyong National University, 45 Yongso-ro, Nam-gu, Busan 48513, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 11 May 2018 Received in revised form 5 September 2018 Accepted 1 October 2018

Keywords: DES Vattenfall T-junction test CFD Turbulent thermal mixing Mixing tee

a b s t r a c t Turbulent thermal mixing is one of the major degradation mechanisms of thermal fatigue, called high cycle thermal fatigue, and a mixing tee has been known as typical component susceptible to high cycle thermal fatigue. From a numerical analysis point of view, accurate prediction of turbulent flow and associated thermal fields in a T-junction is an essential task; that requires computational fluid dynamics (CFD) with advanced turbulence modeling. The detached eddy simulation (DES) model is hybrid turbulence model which combines classical Reynolds Averaged Navier-Stokes (RANS) formulations with elements of large eddy simulation (LES) method. The DES model has a benefit from computational cost point of view, but the studies of its applicability to industrial problems seem to have been conducted relatively insufficiently. Therefore, in this study, transient CFD analysis using the DES model was performed against Vattenfall T-junction test, and the applicability of DES model to turbulent thermal mixing was evaluated by comparing with its experimental data. For the comparison of velocities, the DES results were in good agreement with the experimental data. For the comparison of temperature, the calculated results were generally in good agreement, but at separation region, a large difference of mean temperature was observed. For the locations where the wall temperature variation is large in which the risk of thermal fatigue is expected to be higher, it was seen that the low frequency oscillations are dominant and the energy begins to decrease from
4 Hz. In conclusions, it was confirmed that the DES turbulence model has a capability to simulate turbulent thermal mixing phenomenon in a mixing tee and the CFD analysis using that model can provide reliable results for the assessment of the structural integrity of such a piping system. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Thermal fatigue is a significant degradation mechanism affecting structural failure of various components and systems, and it mainly occurs in the piping system where fluids with different temperature meet together; these thermal loads generate cyclic mechanical stresses on the pipe wall over a long period and it can lead to crack initiation and propagation. Most of thermal fatigue stresses are caused by following thermal loads. (1) thermal shock induced by significant temperature gradient along the axial direction of the pipe, which occurs at the coolant injection with high flow rate such as safety injection into reactor coolant system or spray in the pressurizer

⇑ Corresponding author. E-mail address: [email protected] (C.Y. Lee). https://doi.org/10.1016/j.anucene.2018.10.006 0306-4549/Ó 2018 Elsevier Ltd. All rights reserved.

(2) thermal stratification due to the fluid density difference with low flow rate, which mainly results in global bending deflection and local pear-type deformation in horizontal portions of piping system such as surge line and spray line of the pressurizer (3) turbulent thermal mixing characterized by random fluid motion and temperature variation, which occurs in certain piping system such as T-junction where two flows with different temperature mix together. Since the thermal fatigue due to thermal shock loading and thermal stratification have been well understood through a lot of research, they have been considered in design process and can be monitored by plant instrumentation systems. However, turbulent thermal mixing is difficult to be taken into account in conventional simplified fatigue analysis due to its irregularity and complexity.

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Turbulent thermal mixing is often referred to as thermal striping, and fatigue due to that is called high cycle thermal fatigue. In nuclear engineering society, thermal striping was initially issued for liquid metal cooled fast breeder reactors in the 1980s, and interest has shifted into light water reactors after several incidents of piping failure in nuclear power plants such as Civaux Unit 1 in France and Tsuruga Unit 2 in Japan, and so on (Claude, 2003; Hu and Kazimi, 2006; Muramatsu and Ninikata, 1996; Sugano et al, 2000). A mixing tee has been known as typical component susceptible to high cycle thermal fatigue and that of residual heat removal system is seen to be most vulnerable part in nuclear power plants (Hu and Kazimi, 2006). In order to evaluate high cycle thermal fatigue, the magnitudes and frequencies of coolant temperature fluctuations near a piping wall should be identified; to do that many experimental mock-up tests and numerical simulations have been conducted. From a numerical analysis point of view, accurate prediction of turbulent flow and associated thermal fields in a T-junction is an essential task; that requires computational fluid dynamics (CFD) with advanced turbulence modeling. Since the CFD could yield various results depending on the methodologies such as turbulence model, discretization scheme, mesh resolution, and so on, many benchmark studies against experiments have been conducted to confirm the applicability of CFD to thermal striping problem. Among those studies, the Tjunction thermal mixing test carried out by Vattenfall Research and Development, has been paid attention because it was selected as OECD/NEA sponsored CFD benchmark exercise (OECD/NEA, 2009); so the corresponding CFD simulations have been performed (Ayhan and Sökmen, 2012; Frank et al., 2010; Gritskevich et al., 2014; Höhne, 2014; Jayaraju et al., 2010; Kim and Jeong, 2012; Kuczaj et al., 2010; Ndombo and Howard, 2011; Sakowitz et al., 2014). The CFD studies against other various experiments have also been conducted (Hu and Kazimi, 2006; Kuhn et al., 2010; Naik-Nimbalkar et al., 2010; Selvam et al., 2015). The results of these studies can be summarized as follows. (1) Unsteady Reynolds Averaged Navier-Stokes (URANS) based approach has difficulties in simulating fluctuating velocities and temperatures clearly observed in the experiments. (2) large eddy simulation (LES) model has capability to predict flow and temperature field in the T-junction and amplitude and frequency of fluctuations accurately. (3) fluctuations near the wall exhibited dominant frequencies of several Hz or Strouhal number in order of 0.5. (4) wall-resolved approach gives more accurate results than wall function based simulation for predicting fluctuations close to the wall. (5) inlet conditions, especially inlet turbulence doesn’t affect the bulk parameters much, but it has an effect on the near wall flow. However, the accurate prediction of turbulent flow and thermal mixing using CFD is still challenging task, and the validation of CFD method is still required. If only considering the prediction accuracy of turbulent flow, direct numerical simulation (DNS) would be the best approach, but it is not practical to high Reynolds number problem because it requires tremendous number of meshes to directly resolve the whole range of turbulence scales. Therefore, in most of previous studies, the LES method have been widely used. In LES, large eddies are explicitly calculated, while small scales are modeled by using a subgrid-scale model. Since only large eddies are resolved in the LES, much coarser mesh and larger time-step can be used compared with those of DNS. However, for many industrial application, it still requires a large number of meshes and its computational cost is much higher than that of RANS based simulation; especially,

experience has shown that the use of LES in boundary layer flows at high Reynolds numbers is prohibitively expensive (Spalart et al., 1997). Meanwhile, detached eddy simulation (DES) model has been developed to overcome this limitation of LES turbulence model, and it has hybrid approach which combines classical RANS formulations with elements of LES method (Spalart et al., 1997; Strelets, 2001; Spalart et al., 2006; Menter, 2012). However, the studies of its applicability to industrial problems seem to have been conducted relatively insufficiently (e.g. only one out of 29 submissions in OECD/NEA T-junction project). Therefore, in this study, transient CFD analysis using the DES turbulence model was performed against Vattenfall T-junction test, and the applicability of DES model to turbulent thermal mixing was evaluated by comparing with its experimental data. 2. Vattenfall T-junction thermal mixing test The facility of Vattenfall T-junction thermal mixing test is illustrated in Fig. 1. Cold water of 19 °C was supplied through a horizontal pipe with inner diameter 140 mm (Dm in Fig. 1), and hot water of 36 °C was provided from a vertically oriented pipe with inner diameter 100 mm (Db in Fig. 1). The tee section was made from Plexiglas block as shown in Fig. 1. The upstream length of horizontal pipe was more than 80 pipe diameters (fully developed flow), and that of vertical one was approximately 20 pipe diameters (developing flow). The inlet volumetric flow rates of cold and hot water were 0.009 and 0.006 m3/s, respectively. Velocity profiles upstream of the test section were measured using laser doppler velocimetry (LDV) at 3 and 3.1 diameters upstream of cold and hot inlet pipes, respectively. For downstream velocity, particle image velocimetry (PIV) measurements have been used at 1.6, 2.6, 3.6, and 4.6 diameters downstream of the test section. Temperature fluctuations near the pipe walls were measured using thermocouples located 1 mm from the wall at 2, 4, 6, 8, 10, 15, and 20 diameters and around circumference of the pipe such as 0°, 90°, 180°, and 270° (OECD/NEA, 2009). 3. Turbulence model and CFD methodology 3.1. DES turbulence model The DES model has been originally proposed by Spalart et al. (1997). The DES model functions as a subgrid-scale model in regions where the maximum grid spacing is much smaller than the flow turbulence length-scale, and as a RANS model in regions where it is not (Strelets, 2001). In original Spalart-Allmaras (S-A) model (Spalart et al., 1997), the distance to the closest wall, dw , is replaced by new DES length scale, l;

l ¼ minðdw ; C DES DÞ

ð1Þ

D ¼ maxðDx ; Dy ; Dz Þ

ð2Þ

where C DES is a constant and D is the maximum length of local grid cell. Therefore, in the attached boundary layer, due to the significant grid anisotropy (Dx  Dy  Dz ), in accordance with (1), l ¼ dw , and the model reduces to the RANS model. Otherwise, once a field point is far enough from wall ðdw > C DES DÞ, the model performs as a subgrid-scale version of the S-A model (Strelets, 2001). Strelets (2001) has proposed new idea of the model that the DES length scale can be obtained by turbulent length predicted by RANS model instead of dw . In that work, the k  x shear stress transport (SST) model was adopted, because it is consistently considered as one of the best two-equation RANS models, particularly for separation prediction (Menter, 1993; Strelets, 2001). In the

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Fig. 1. Vattenfall T-junction thermal mixing test facility (Angele, 2009).

k  x shear stress transport (SST) model, turbulent length scale lt is expressed as; 1

lt ¼ k2 =ðb xÞ

ð3Þ

where k, x, and b are turbulent kinetic energy, turbulent eddy frequency and constant of SST model, respectively. Therefore, lt is replaced by the DES length scale as follows;

l ¼ minðlt ; C DES DÞ

ð4Þ

This modification would affect the dissipation term in kequation as follows;

qb kx ¼ q

3 3 3
 k2 k2 k2 lt !q ¼ q max 1; lt min ðlt ; C DES DÞ lt C DES D

ð5Þ

where q is the density. In the region where the grid is refined below the turbulent length from SST model, the DES limiter is activated and the SST model switches to the LES mode. However, for both S-A (DES-SA) and Strelets (DES-SST) models, the DES limiter can be activated by grid refinement inside attached boundary layer. This can cause grid-induced separation, where the boundary layers can separate at arbitrary locations depending on the grid spacing (Menter, 2012). In order to overcome this limitation, Spalart et al. (2006) has proposed the concept of delayedDES (DDES), similar to one proposed by Menter and Kuntz for the SST model (Menter and Kuntz, 2004). The DDES extension was also applied to the DES-SA formulation resulting in the DDES-SA model, as well as to the DES-SST model giving the DDES-SST model (Menter, 2012). In the DDES-SST model, the dissipation term in k-equation is re-formulated as follows;

q

3
 k2 lt max 1; ð1  F DDES Þ ; with F DDES ¼ 0; F 1 ; F 2 lt C DES D

ð6Þ

The F DDES ¼ 0 recovers the Strelets (DES-SST) model. The F1 and F2 are the two blending functions of the SST model which are set to be unity close to the wall and to be zero away from the wall. The F2 offers the highest level of protection against grid-induced separation and is therefore the preferred default (ANSYS, 2015). The definition of F2 is as follows;

2" !#2 3 pffiffiffi 2 k 500 m 5 F 2 ¼ tanh4 max  ; b xy y 2 x

ð7Þ

where m is kinematic viscosity and y is the distance from the wall. In this study, among those DES models, the DDES-SST model was used.

3.2. CFD methodology All CFD calculations in this paper have been conducted using ANSYS CFX-16 (ANSYS, 2015). The computational domain under consideration in this study is depicted in Fig. 2. The inlet boundaries were located at 3 and 3.1 diameters upstream of horizontal and vertical pipes, respectively, which were consistent with the locations of LDV in Vattenfall T-junction test. The outlet boundary was located at
20.7 diameters downstream of horizontal pipe. In addition, many monitoring points were adopted at the locations of thermocouples and velocity measurements to obtain the transient data. The solution domain was discretized into about 4.3 million hexahedral cells as shown in Fig. 3. The boundary layer was resolved using a very fine mesh, so the value of y+ was less than unity in most of the domain. The independency test for grid were performed for two different number of cells (i.e., 2.43 million and 4.3 million cells). Fig. 4 shows the comparison of x-component mean and RMS velocities (i.e., Umean and Urms) at 1.6 diameters downstream (i.e., x/Dm = 1.6) between two different grid systems. As shown in this figure, there are little change in velocity profile even though the number of cells are increased from 2.43 to 4.3 million. Therefore, the results of the grid independency test were successful and it was confirmed that the grid system of 4.3 million cells are acceptable to utilize for this calculation. The physical time step was set to be 103 s and corresponded to the root mean square (RMS) Courant number of about 0.43 in the domain. The transient simulation was started from the steady state result of preceding calculation using the SST turbulence model. Then it has been carried out for 26 s and unsteady data was averaged for later 20 s to obtain mean flow and thermal field characteristics. This duration time for averaging corresponds to
6.7Ld =U b where Ld and U b are the length and bulk velocity of downstream, respectively. Convergence of the iterative computations for each time-step was determined when the RMS residuals of all the major parameters are less than 104. The actual iterative computation at each time-step converged after only three or four iterations. The property (density, viscosity, thermal conductivity, etc.) variations in water according to the variations in temperature were taken into account from the reference (OECD/NEA, 2009). For inlet boundary conditions, preliminary CFD simulations were performed for horizontal and vertical pipes which are connected to cold and hot water inlet, respectively, using the scaleadaptive simulation (SAS) model (Egorov et al., 2010; Menter and Egorov, 2010). For cold inlet boundary, the velocity profiles based on the fully developed flow condition were applied. On the hot

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Fig. 2. Modeling of Vattenfall T-junction test.

Fig. 3. Mesh in the calculation domain.

inlet boundary, the velocity profiles at the cross section where calculated centerline velocity matches with experimental data were specified. For outlet boundary condition, the zero averaged relative static pressure was applied. No slip with automatic wall treatment were specified at the wall and an adiabatic condition was applied on the wall since the pipe wall was Plexiglas with low thermal conductivity. 4. Results and discussion Based on the previous studies (Igarashi et al., 2003; Hu and Kazimi, 2006), the types of mixing flow can be classified using the momentum ratio of the main and branch entering flow,

MR ¼

qm V 2m Dm Db 2 qb V 2b pðD2b Þ

ð8Þ

where M R is the momentum ratio. q, V, and D are fluid density, velocity, and diameter, respectively. Subscripts of m and b indicate the main and branch pipes, respectively. The three flow patterns are defined as follows; Wall jet: M R > 1:35 Deflecting jet: 0:35  MR  1:35 Impinging jet: M R < 0:35 In this study, M R is 1.05 and the deflecting flow which occurs when the two inlet flows have comparable momentum, was expected. The turbulence structures can be visualized as shown in Fig. 5 based on isosurfaces of Q-criterion defined as follows;

Q¼

 1 2 X  S2 2

ð9Þ

where X is the vorticity and S is the strain rate of the flow field. It is seen that the irregular vortex is formed in the mixing zone where cold and hot water flows meet, which dominates the mixing process in the downstream. Then it gradually dissipates as it goes downstream. The calculated mean and RMS velocities were compared with experimental data along two perpendicular centerlines (yellow line) at several sections (x=Dm = 1.6, 2.6, 3.6, and 4.6) as shown in Fig. 6. Temperature was also compared at four points (red point; 0°, 90°, 180°, and 270°) around circumference of the pipe at several sections (x=Dm = 2, 4, 6, 8, 10, 15, and 20). The velocity and temperature were non-dimensionalized by bulk velocity of downstream (U b ) and temperature difference (T  ¼ ðT  T c Þ=ðT h  T c ÞÞ. Figs. 7 and 8 show the comparison of calculated and experimental mean velocity profiles at four axial locations (x=Dm = 1.6, 2.6, 3.6, and 4.6) along two perpendicular (y- and z-direction) centerlines. The present DES results are in good agreement with the experimental data. As the x=Dm increases, the shape of the xcomponent velocity (U) becomes flatter and the y- and zcomponent velocity (V and W) decreases to almost zero. It shows the process that irregular turbulent mixing flow changes into the fully developed turbulent flow. As shown in Fig. 7(B), the experimental U velocity has negative values near the top wall (z=R ¼ 1:0) at x=Dm = 1.6, which means the existence of separation zone, but the calculation could not simulate it properly (i.e. the calculated U velocity has positive values at that region). The separation results in high turbulence production and affects the heat transfer significantly. As shown in Fig. 8(A) and (B), the calculated V and W velocities also have relatively large difference with experimental data at x=Dm = 1.6. These discrepancies might be caused by that the calculation could not predict secondary flow field properly near the separation region where turbulent mixing occurs actively. The RMS velocity profiles from calculation and experiment are

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Fig. 4. Grid independency test results; (A) Umean along y-direction at x/Dm = 1.6, (B) Umean along z-direction at x/Dm = 1.6, (C) Urms along y-direction at x/Dm = 1.6, (D) Urms along z-direction at x/Dm = 1.6.

Fig. 5. Isosurfaces of Q-criterion (Q = 200 s2) at t = 26 s.

compared, as shown in Figs. 9 and 10. The calculation results show good agreement with experimental data. However, the calculation generally underestimates the RMS velocities compared with experiment. As it goes downstream, the velocity fluctuations decrease. While the U velocity is dominant for mean velocity, the velocity fluctuations in all directions are of similar magnitude.

Fig. 11 shows a comparison of the experimental and calculated the energy spectra of U velocity at four axial (e.g. x=Dm = 1.6, 2.6, 3.6, and 4.6) center points. The calculations are generally in good agreement with experimental data and with the Kolmogorov’s 5=3

law (i.e. the energy density of the flow behaves like
f in some inertial range, where f denotes frequency). A peak can be seen for

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Fig. 6. Locations of comparison between calculated and experimental results.

Fig. 7. Mean velocity profiles at four axial locations; (A) U along y-direction (B) U along z-direction.

the location at x=Dm = 1.6, 2.6 as shown in Fig. 11(A) and (B). Both experiment and calculation almost have the dominant frequency of 3
5 Hz, which corresponds to Strouhal number with an order of O (0.1). However, at the further downstream locations, as shown in Fig. 11(C) and (D), the energy spectra almost decreases with frequency. Fig. 12 shows a comparison of the experimental and calculated the energy spectra of V and W velocities at two axial (e.g. x=Dm = 1.6 and 3.6) center points. The calculations are also in good agreement with experimental data and with the Kolmogorov’s law. As shown in Fig. 12 (A) and (B), a distinct peak is observed for energy spectra of V velocity in the frequency range of 3
5 Hz which is similar to U velocity. On the other hand, for W velocity spectrum, there is a peak around 5
7 Hz as shown in Fig. 12(C) and (D). Fig. 13 shows the comparison of calculated and experimental non-dimensional mean temperatures at four points (0°, 90°, 180°, and 270°) around circumference of the pipe at several locations (x=Dm = 2, 4, 6, 8, 10, 15, and 20) (see Fig. 6). The calculated and

experimental results are generally in good agreement, but there is a large difference especially at top region (0°) of x=Dm = 2. This seems to be caused by that the present DES calculation could not predict separation in that region. As it goes downstream, hot water tends to cool down in the top region, and cold water tends to get hot in the rest of the region. The non-dimensional RMS temperatures (T rms ¼ T rms =DT) from calculation and experiment are compared, as displayed in Fig. 14. The calculation results show good agreement with experimental data. The RMS temperatures have maximum values at around x=Dm ¼ 2
6 for each circumferential positions and decrease as it goes downstream. Since the thermal fatigue is caused by cyclic thermal stress resulting from wall temperature fluctuations, the regions where the RMS temperatures are large might be susceptible to thermal fatigue. The side (i.e., 90° and 270°) regions at x=Dm ¼ 4 have the maximum RMS temperatures. The top (0°) position at x=Dm ¼ 2 where separation is expected to occur, the bottom (180°) region at x=Dm ¼ 6, and the side (90° and 270°) regions at

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Fig. 8. Mean velocity profiles at four axial locations; (A) V along y-direction (B) W along z-direction.

Fig. 9. RMS velocity profiles at four axial locations; (A) U along y-direction (B) U along z-direction.

x=Dm ¼ 2 have relatively high RMS temperatures. Therefore, the risk of thermal fatigue in these areas is expected to be higher than in other regions. Fig. 15 shows a comparison of the experimental and calculated the energy spectra of temperature near wall at three locations mentioned above that the RMS temperatures are relatively high

(Fig. 15(A)–(C)) and one point that the RMS temperature is nearly zero (Fig. 15(D)). For the locations where temperature variation is large, the calculations generally overestimate power spectral density (PSD) compared with experiment but the trends are qualitatively in good agreement. It can be also seen that the low frequency oscillations are dominant and the energy begins to

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Fig. 10. RMS velocity profiles at four axial locations; (A) V along y-direction (B) W along z-direction.

Fig. 11. Energy spectra of U velocity at four axial center points: (A) x=Dm = 1.6, (B) x=Dm =2.6, (C) x=Dm = 3.6, (D) x=Dm = 4.6.

decrease from
4 Hz. Especially, the experimental data at the left (270°) point at x=Dm ¼ 4 (Fig. 15(A)) shows distinct peak in the range of 3
4 Hz, and this peak is also observed at right (90°) point. For the point where temperature variation is hardly visible, the energy density has nearly flat shape with respect to frequency. Fig. 16 shows the wall temperature distributions on top and side view with different physical time from 25 s to 26 s at intervals of 0.1 s. As shown in this figure, the variations of wall temperature are irregular and rapid with respect to time by turbulent thermal mixing. It can be also seen that the hot spot is generated at certain

positions and dissipated as it goes downstream. Especially, the region of x=Dm = 3
5 on the side wall and that of x=Dm = 2
3 on the upper wall have relatively high temperature variations. Since this irregular wall temperature change is inherently occurred in the piping system like a mixing tee, it is considered that obtaining the transient wall temperature distribution for long enough time duration and at small time interval using CFD analysis is the essential prerequisite for the reliable assessment of the structural integrity of such a piping system. It is also confirmed that the DES turbulence model which has a benefit from computational

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Fig. 12. Energy spectra of V and W velocity: (A) V at x=Dm = 1.6, (B) V at x=Dm = 3.6, (C) W at x=Dm = 1.6, (D) W at x=Dm = 3.6.

Fig. 13. Mean temperature near the pipe wall at several axial locations (see Fig. 6).

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Fig. 14. RMS temperature near the pipe wall at several axial locations (see Fig. 6).

Fig. 15. Energy spectra of temperature near wall at four locations: (A) Left point (270°) at x=Dm = 4, (B) Top point (0°) at x=Dm = 2, (C) Bottom point (180°) at x=Dm = 6, (D) Bottom point (180°) at x=Dm = 2.

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Fig. 16. Wall temperature distributions on top and side view with different physical time.

cost point of view, has a good capability to simulate turbulent thermal mixing phenomenon in T-junction. 5. Conclusions In this study, transient CFD analysis using the DES turbulence model was performed against Vattenfall T-junction test, and the applicability of DES model to turbulent thermal mixing was evaluated by comparing with its experimental data. For the comparison of mean and RMS velocities, the DES results were in good agreement with the experimental data, but the calculation generally underestimated the RMS velocities compared to experiment. For energy spectra of velocity, the calculations were generally in good

agreement with experimental data and with the Kolmogorov’s law, and both almost show to have the dominant frequency which corresponded to Strouhal number with an order of O(0.1). For the comparison of mean and RMS temperatures, the calculated results were generally in good agreement, but at separation region, a large difference of mean temperature was observed. For the locations where the wall temperature variation is large in which the risk of thermal fatigue is expected to be higher, the calculations generally overestimated PSD compared with experiment, but the trends were qualitatively in good agreement. It could be also seen that the low frequency oscillations are dominant and the energy begins to decrease from
4 Hz. In conclusions, it was confirmed that the DES turbulence model has a capability to simulate turbulent ther-

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mal mixing phenomenon in a mixing tee and the CFD analysis using that model can provide reliable results for the assessment of the structural integrity of such a piping system. Acknowledgement The authors like to acknowledge Vattenfall Research and Development for sharing the experimental data.

Declarations of interest None. References Angele, K., 2009. The Vattenfall T-junction test facility May 19. Kick-off Meeting for the OECD/NEA CFD Benchmark Task. NEA headquarters, France. ANSYS, 2015. ANSYS CFX-16 User Manual. ANSYS Inc.. Ayhan, H., Sökmen, C.N., 2012. CFD modeling of thermal mixing in a T-junction geometry using LES model. Nucl. Eng. Des. 253, 183–191. Claude, F., 2003. Thermal fatigue in mixing tees: a step by step simplified procedure. Proceedings of 11th International Conference on Nuclear Engineering (ICONE11). April 20-23 Tokyo Japan. Egorov, Y., Menter, F.R., Lechner, R., Cokljat, D., 2010. The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 2: application to complex flows. Flow Turbulence Combust. 85, 139–165. Frank, Th., Lifante, C., Prasser, H.-M., Menter, F., 2010. Simulation of turbulent and thermal mixing in T-junctions using URANS and scale-resolving turbulence models in ANSYS CFX. Nucl. Eng. Des. 240, 2313–2328. Gritskevich, M.S., Garbaruk, A.V., Frank, Th., Menter, F.R., 2014. Investigation of the thermal mixing in a T-junction flow with different SRS approaches. Nucl. Eng. Des. 279, 83–90. Höhne, T., 2014. Scale resolved simulations of the OECD/NEA-Vattenfall T-junction benchmark. Nucl. Eng. Des. 269, 149–154. Hu, L., Kazimi, M., 2006. LES benchmark study of high cycle temperature fluctuations caused by thermal striping in a mixing tee. Int. J. Heat Fluid Flow 27, 54–64. Igarashi, M., Kimura, N., Tanaka, M., Kamide, H., 2003. LES analysis of fluid temperature fluctuations in a mixing tee pipe with the same diameters. Proceeding of 11th International Conference on Nuclear Engineering (ICONE11). April 20-23 Tokyo Japan.

Jayaraju, S.T., Komen, E.M.J., Baglitetto, E., 2010. Suitability of wall-functions in large eddy simulation for thermal fatigue in a T-junction. Nucl. Eng. Des. 240, 2544– 2554. Kim, J., Jeong, J.J., 2012. Large eddy simulation of turbulent flow in a T-junction. Numer. Heat Transfer, Part A 61, 180–200. Kuczaj, A.K., Komen, E.M.J., Loginov, M.S., 2010. Large-eddy simulation study of turbulent mixing in a T-junction. Nucl. Eng. Des. 240, 2116–2122. Kuhn, S., Braillard, O., Niceno, B., Prasser, H.M., 2010. Computational study of conjugate heat transfer in T-junctions. Nucl. Eng. Des. 240, 1548–1557. Menter, F.R., 1993. Zonal Two-equation k-x Turbulence Model for Aerodynamic Flows AIAA Paper 1993-2906. Menter, F.R., 2012. Best Practice: Scale-Resoloving Simulations in ANSYS CFD. ANSYS Inc.. Menter, F.R., Egorov, Y., 2010. The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1: theory and model description. Flow Turbulence Combust. 85, 113–138. Menter, F.R., Kuntz, M., 2004. Adaptation of eddy-viscosity turbulence models to unsteady separated flow behind vehicles. Symposium on the Aerodynamics of Heavy Vehicles: Trucks, Busses and Trains. December 2-6, Monterey, USA. Muramatsu, T., Ninikata, H., 1996. Development of thermohydraulics computer programs for thermal striping phenomena. Nucl. Technol. 113, 54–72. Naik-Nimbalkar, V.S., Patwardhan, A.W., Banerjee, I., Padmakumar, G., Vaidyanathan, G., 2010. Thermal mixing in T-junctions. Chem. Eng. Sci. 65, 5901–5911. Ndombo, J., Howard, R.J.A., 2011. Large eddy simulation and the effect of the turbulent inlet conditions in the mixing tee. Nucl. Eng. Des. 241, 2172–2183. OECD/NEA, 2009, OECD/NEA: T-junction benchmark specifications (final version, July 2009), OECD/NEA. Sakowitz, A., Mihaescu, M., Fuchs, L., 2014. Turbulent flow mechanisms in mixing Tjunctions by large eddy simulations. Int. J. Heat Fluid Flow 45, 135–146. Selvam, P.K., Kulenovic, R., Laurien, E., 2015. Large eddy simulation on thermal mixing of fluids in a T-junction with conjugate heat transfer. Nucl. Eng. Des. 284, 238–246. Spalart, P.R. et al., 2006. A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20, 181–195. Spalart, P.R., Jou, W.-H., Stretlets, M., Allmaras, S.R., 1997. ‘‘Comments on the feasibility of LES for Wings and on the hybrid RANS/LES approach. Proceedings of the 1st AFOSR International Conference on DNS/LES. August 4-8, Louisiana, USA. Strelets, M., 2001, ‘‘Detached Eddy Simulation of Massively Separated Flows, In: AIAA Paper 2001-0879, 39th Aerospace Sciences Meeting and Exhibit, January 8-11, Reno, NV. Sugano, T., Sakai, T., Ueno, T., Kutomi, Y., 2000. Leakage from CVCS pipe of regenerative heat exchanger induced by high-cycle thermal fatigue at Tsuruga Nuclear Power Station Unit 2 October 15-18, Fukuoka, Japan. Proceedings of 2nd Japan-Korea Symposium on Nuclear Thermal Hydraulics and Safety (NTHAS-2).