# Numerical Simulation of Non-Isothermal Mixing Flow Characteristics with ELES Method
## 5 Conclusions  
In this paper, the mixing flow of non-isothermal fluids in tee pipes upstream is numerically studied in detail. Firstly, three typical flow patterns of thermal mixing in tee pipes (wall jet with \(M_{R}\) = 8.1, deflecting jet with \(M_{R}\) = 0.8, and impinging jet with \(M_{R}\) = 0.2) were simulated using the ELES method, and the results have been compared with the experimental data in reference [5] to prove the validity of the model. Secondly, the flow characteristics of the backflow upstream with different momentum ratios were studied by carrying out 12 groups of simulations using ELES, as well as the temperature characteristics near the wall where the backflow appears. Moreover, in order to evaluate the thermal fatigue, the frequency analysis at specified points near the wall of three typical flow patterns was estimated. The conclusions are summarized below:  
1. ELES is a valid tee pipe numerical turbulent-solving method and aptly predicts the flow patterns of non-isothermal mixing in tee pipes.
2. The characteristics of the backflow in the tee are obviously different with different momentum ratios \(M_{R}\). The relatively general rules are that the eddies caused by the backflow appear near the opposite sidewall of the branch pipe for cases of the impinging jet when \(M_{R}\leq\) 0.1, the eddies appear near the wall at the right-angle structure upstream of the main pipe for cases of the deflecting jet when \(M_{R}\) \(\sim\) 0.8, while the eddies appear near the wall at the right-angle structure upstream of the branch pipe for cases of the wall jet when \(M_{R}\geq\) 11.5. In addition, the size of the eddies caused by the backflow is dependent on \(M_{R}\).  
Figure 15: Power spectrum density of the temperature in Case1, Case7, and Case12.  
3. The characteristics of temperature distribution and the frequency of temperature fluctuations are different under different backflow patterns with different momentum ratios \(M_{\rm R}\). Besides the pipe wall downstream, 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. It seems that an impinging jet with smaller \(M_{\rm R}\) and a wall jet with larger \(M_{\rm R}\) have a greater possibility of fatigue cracks on the wall around the intersection, while the effect of fatigue caused by the deflecting jet on the wall seems less significant.
4. Long-period temperature fluctuations of frequencies lower than 6 Hz upstream (e.g., approximately 0.5 Hz, 1.2 Hz, 3.0 Hz, etc.) from the tee were observed, and they may be related to the periodic variation of the backflow around the attached wall. Besides, this requires further study to validate the long-period fluctuation of a frequency lower than 3 Hz upstream through further experiments.  
Conceptualization, H.W.; methodology, C.S.; software, Z.Z.; validation, Y.J. and F.Z.; investigation, C.S. and Z.Z.; writing--original draft preparation, C.S.; writing--review and editing, C.S.; visualization, H.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.