# Numerical Simulation of Non-Isothermal Mixing Flow Characteristics with ELES Method
## 4 Results and Discussion
### Temperature Characteristics near the Wall Where Backflow Appears
From the distribution of temperature fluctuation along line3 in Figure 13, we can see that although the axial range affected by the thermal striping is narrow, the temperature fluctuation intensity is relatively higher compared with that of Case1 and Case7. With the penetration depth, the temperature fluctuation intensity tends to increase and then decrease, and a peak of approximately 0.32 appears at the location of \(Y=-1.55\,D_{b}\). Figure 14d shows the temperature distributions at \(Y=-1.55\,D_{b}\). It can be seen that the phenomenon of thermal striping is very significant, and the radial range affected by the thermal striping is wide as it is from \(-90^{\circ}\) to \(90^{\circ}\). Meanwhile, the fluctuation peak appears at \(\theta=45^{\circ}\) in Figure 14d. Figure 13: Axial distribution of temperature fluctuation intensity along corresponding lines. In order to analyze the frequency characteristics (PSD), the FFT method was applied to the data extracted over a period of 74.8 s and presented in Figure 15. The prominent frequency components were observed in all analyses in Figure 15. At \(Z=-0.5\,D_{m}\), \(\theta=180^{\circ}\) of Case 1 in Figure 15, frequency peaks appeared at 0.5 Hz, 0.8 Hz, 1.2 Hz, 1.97 Hz, 2.53 Hz, 3.3 Hz, 6.31 Hz, etc. ; at \(Z=-0.2\,D_{m}\), \(\theta=105^{\circ}\), frequency peaks appeared at 0.47 Hz, 1.26 Hz, 2.63 Hz, 5.68 Hz, etc. ; while at \(Z=-0.2\,D_{m}\), \(\theta=180^{\circ}\), frequency peaks appeared at 0.48 Hz, 1.27 Hz, 2.60 Hz, 5.78 Hz, etc. Although the peaks did not exactly match, they were similar in the three locations. Besides, it is generally known that the frequency approaching 6 Hz in Figure 15 corresponds to the frequency of the Karman vortex street. In addition, the characteristic frequency was not very significant, at approximately 6 Hz downstream shown in references [5; 10], but long-period temperature fluctuations of frequencies lower than 6 Hz upstream from the tee were found, which had also been observed by [PERSON] et al. [10] downstream. As described in [PERSON] et al. [41] and [PERSON] [42], long-period temperature fluctuations of a low frequency (0.1-10 Hz) would cause the most harmful thermal loads. Hence, the conditions may require more attention. At \(Z=-0.18\,D_{m}\), \(\theta=0^{\circ}\) of Case 7 in Figure 15, frequency peaks appeared at 0.49 Hz, 0.89 Hz, 1.47 Hz, 2.75 Hz, 6.0 Hz, etc., while at \(Y=-1.5\,D_{b}\), \(\theta=45^{\circ}\)of Case 12, frequency peaks appeared at 0.95 Hz, 1.55 Hz, 3.2 Hz, 5.76 Hz, etc. The characteristic frequency of approximately 6 Hz in the two cases seems more obvious than that in case1, which is because the phenomena that occurred at the points in case7 and case12 are more similar to the phenomena of the Karman vortex street. Moreover, a long-period temperature fluctuation of a frequency lower than 6 Hz upstream (e.g., approximately 0.5 Hz, 1.2 Hz, 3.0 Hz, etc.) from the tee was observed, too. This may be related to the periodic variation of the backflow around the attached wall. The long-period temperature fluctuation of a frequency lower than 6 Hz downstream from the T-junction was also seen in the experimental investigation by [PERSON] et al. [43] and the numerical study by [PERSON] et al. [10]. However, it requires further study to validate the long-period fluctuation of a frequency lower than 6 Hz upstream through more experiments. Figure 14: Temperature distribution upstream (the upper figures show temperature \(T^{*}\) distribution and the lower figures show temperature \(T_{sd}^{*}\) distribution): (**a**) A cross-section at \(Z=-0.2\,D_{m}\) in case1; (**b**) a cross-section at \(Z=-0.5\,D_{m}\) in case1; (**c**) a cross-section at \(Z=-0.18\,D_{m}\) in case7; (**d**) a cross-section at \(Z=-1.55\,D_{b}\) in case12. In sum, by analyzing the temperature distribution of three different flow patterns with different \(M_{R}\) values, three more regions are found to be prone to thermal fatigue at the intersection of the tee upstream. The effects of fatigue are different in the three regions.