# Numerical Simulation of Non-Isothermal Mixing Flow Characteristics with ELES Method
## 3 Simulations with the Numerical Method ELES
### Validation of the Numerical Method ELES  
#### 3.3.1 The Contours of Temperature and Velocity Distributions Downstream  
The distributions of temperature and fluctuation intensity on a half-cylindrical surface 1 mm apart from the main pipe wall and two cross-sections downstream (as shown in Figure 1) were obtained by simulation. Figures 6-8 show comparisons of these statistical results and the experimental ones. The left sides of Figures 6-8 are the LES results of [PERSON] et al. [5]. using the AQUA code, which is an in-house thermal hydraulic simulation code [35]. The right sides are the ELES simulation results using FLUENT 17.0. Figure 4: Mean axial velocity and velocity fluctuations distributions along a vertical line (\(Z=-0.53\,D_{m}\)) in the W-ref case for four types of grids. Figure 5: Contours of turbulence generation and structure in three cases: (**a**) Vorticity contours, (**b**) \(Q\)-criterion colored with \(V_{z}\) in the cases. Figure 6: Temperature distribution downstream of W-ref case using LES and ELES: (**a**) Temperature \(T^{*}\) distribution distribution using LES; (**b**) Temperature \(T^{*}\) distribution using ELES; (**c**) Temperature \(T_{\text{sd}}^{*}\) distribution using LES; (**d**) Temperature \(T_{\text{sd}}^{*}\) distribution using ELES. Figure 7: Temperature distribution downstream of D-ref case using LES and ELES: (**a**) Temperature \(T^{*}\) distribution using LES; (**b**) Temperature \(T^{*}\) distribution using ELES; (**c**) Temperature \(T_{\text{sd}}^{*}\) distribution using LES; (**d**) Temperature \(T_{\text{sd}}^{*}\) distribution using ELES. The data displayed in Figures 6-8 were normalized with the temperature difference as seen in Equations (21) and (22):  
\[\overline{T}^{*}=\frac{\overline{T}-T_{b}}{T_{m}-T_{b}} \tag{27}\]  
\[T_{sd}^{*}=\frac{1}{T_{m}-T_{b}}\sqrt{\frac{\sum_{i}\left(T_{i}-\overline{T} \right)^{2}}{N}} \tag{28}\]  
Here, \(T_{b}\) is the branch temperature and (\(T_{m}-T_{b}\)) is the temperature difference fixed at 15 \({}^{\circ}\)C, \(T\) is the time-averaged temperature at a certain position on a surface, and \(N\) is the total number of sampling data. Considering that the sampling frequency was 100 Hz and the measurement time period was 480 s in reference [5], just for comparison, the sampling interval was set as 0.01 s (10 time-steps), and a period of approximately 100 s was taken for statistics after calculation convergence in the current work. It can be found that the numerical values and distributions in Figures 6-8 show good agreement. It can be clearly seen in Figures 6-8 that the thermal stripping phenomenon appears and the high fluctuation intensity occurs around the cold fluid in contact with the hot. In the W-ref case, the high-intensity region touched the pipe wall to form a half-circle big-value area at each radial cross-section, while in the deflecting jet case, the high-intensity region was separate from the pipe wall because the cold fluid from the branch pipe flowed into the central part of the main pipe. On the other hand, the cold jet from the branch pipe reached the opposite side pipe wall in the impinging jet case, and the high-intensity region then appeared in the upper half of the main pipe and decreased rapidly in the axial direction. As can be seen from the distribution results in radial cross-sections, along the main flow direction downstream in all three cases, the temperature range narrowed and the  
Figure 8: Temperature distribution downstream of I-ref case using LES and ELES: (**a**) Temperature \(T^{*}\) distribution using LES; (**b**) Temperature \(T^{*}\) distribution using ELES; (**c**) Temperature \(T_{sd}^{*}\) distribution using LES; (**d**) Temperature \(T_{sd}^{*}\) distribution using ELES. maximum fluctuation intensity decreased, which suggested gradually sufficient mixing was obtained with the flow. The main difference between the ELES results and the LES ones conducted by [PERSON] et al.