# Numerical Simulation of Non-Isothermal Mixing Flow Characteristics with ELES Method
## 4 Results and Discussion
### Temperature Characteristics near the Wall Where Backflow Appears  
It can be found from the above research that different flow patterns with different momentum ratios have different characteristics of the backflow. In order to study the temperature distributions related to the backflow, detailed studies have been carried out under typical conditions in each flow pattern. From Figure 12, three typical cases with the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Average Main Velocity (\(V_{m}\)) (m/s)** & **Momentum Ratio (\(M_{R}\))** & **Flow Pattern** \\ \hline Case1 & 0.11 & 0.05 & Impinging jet \\ Case2 & 0.16 & 0.1 & Impinging jet \\ Case3 & 0.20 & 0.15 & Impinging jet \\ Case4 & 0.23 & 0.2 & Impinging jet \\ Case5 & 0.46 & 0.8 & Deflecting jet \\ Case6 & 1.46 & 8.1 & Wall jet \\ Case7 & 1.74 & 11.5 & Wall jet \\ Case8 & 1.76 & 11.8 & Wall jet \\ Case9 & 1.78 & 12 & Wall jet \\ Case10 & 1.85 & 13 & Wall jet \\ Case11 & 1.95 & 14.5 & Wall jet \\ Case12 & 2.9 & 32 & Wall jet \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Groups of simulations with different momentum ratios with average branch velocity \(V_{b}=1\) m/s. most obvious characteristics of the backflow were chosen as the representative of each flow pattern, which were Case1 with \(M_{R}\) = 0.05, Case7 with \(M_{R}\) = 0.8, and Case12 with \(M_{R}\) = 32. Additionally, the temperature was recorded at every time step with a sampling frequency of 1000 Hz for a duration of 74.8 s.  
Figure 12: Streamlines in y–z plane of three impinging jet cases, one deflecting jet case, and two wall jet cases at \(X\) = 0: (**a**) Case1 with \(M_{R}\) = 0.05; (**b**) Case2 with \(M_{R}\) = 0.1; (**c**) Case4 with \(M_{R}\) = 0.2; (**d**) Case5 with \(M_{R}\) = 0.8; (**e**) Case7 with \(M_{R}\) = 11.5; (**f**) Case12 with \(M_{R}\) = 32. Axial distributions of the temperature fluctuation intensity of the above cases along corresponding lines are depicted in Figure 13. The corresponding lines of the three cases described in Figure 13 are 1 mm away from the wall. From the distribution of temperature fluctuation along line1 in Figure 13, we can see that the axial range affected by thermal striping is very wide, and it also seems that there exists more than one peak, with a maximum of approximately at \(Z=-0.5\,D_{m}\) upstream, which indicates that the thermal mixing caused by the backflow is complex. In addition, the temperature fluctuation intensity at \(Z=-0.5\,D_{m}\) shown in Figure 13 is close to that of \(0.5\,D_{m}\) downstream plotted in Figures 6-8. In order to further study the mixing behavior, two contours were plotted at the cross-sections of \(Z=-0.5\) and \(-0.2\,D_{m}\) upstream as shown in Figure 14a,b. As we can see from Figure 14a,b, thermal striping appears near the opposite wall of the branch pipe, and the temperature fluctuation intensities in some locations are relatively high such as points near the wall at \(105^{\circ}\) and \(180^{\circ}\) of the cross-section at \(Z=-0.2\,D_{m}\) and the point near the wall at \(180^{\circ}\) of the cross-section at \(Z=-0.5\,D_{m}\). From the distribution of temperature fluctuation along line2 in Figure 13, we can see that the temperature fluctuation intensity is relatively low and the axial range affected by thermal striping is narrow, which indicates that the thermal mixing is not fully developed although there exists a relatively larger eddy as shown in Figure 12d. The main reason for this phenomenon may be that the momentums of the main and branch flows are similar as \(M_{R}=0.8\). When each flow blocks the other one in the tee with \(M_{R}\sim 1\), there is not enough power for one to penetrate upstream of the other one. A contour plotted at the cross-section of \(Z=-0.18\,D_{m}\) upstream as shown in Figure 14c reveals the above view. Therefore, the depth of penetration of one to another is dependent on the momentum ratio.