# Numerical Simulation of Non-Isothermal Mixing Flow Characteristics with ELES Method
## 1 Introduction  
Since several leakages caused by thermal striping in industrial tee pipes have occurred, notably the accidents that happened in the light water reactor of French PWR Civaux 1, 1998 [1], and in the sodium-cooled fast reactor of PHENIX, 1991 [2], they have aroused wide attention of scholars to focus on the thermal fatigue caused by turbulent thermal mixing. In order to study the relationship between temperature and crack, various experiments have been conducted for temperature fluctuation in the mixing tees. For example, [PERSON] et al. [3] and [PERSON] et al. [4] have conducted a scaled model experiment related to Civaux 1. Furthermore, water experiments (WATLON) have been conducted by [PERSON] et al. [5] in the Japan Atomic Energy Agency (JAEA) to study the mixing behavior in tee pipes using particle image velocimetry (PIV) and thermocouples. However, due to the limitations of the experimental conditions and the means of observation, computational fluid dynamics (CFD) has become a cheaper and more efficient method to study the flow characteristics of thermal mixing. So far, many numerical methods have been used to study the turbulence characteristics of mixing flows. Undoubtedly, the Reynolds-Averaged Navier-Stokes (RANS) turbulencemodels are the most classical and basic. [PERSON] et al. [6], for example, employed RANS turbulence models to simulate the non-isothermal mixing flows in tee pipes using ANSYS CFX software. It was found that the RANS model can accurately simulate the turbulent mixing of isothermal fluids in tee pipes but failed in non-isothermal mixing flows. Additionally, throughout the past few decades, the large eddy simulation (LES) model has been the most used model to simulate free shear flow. For example, [PERSON] and [PERSON] [7] carried out a numerical study with LES to investigate the impact of the temperature difference between the mixing flows on temperatures downstream of the tee pipes. [PERSON] et al. [8] performed an LES analysis of turbulent mixing in a tee pipe with different flow ratios. [PERSON] et al. [9] and [PERSON] et al. [10] ran numerical simulations with LES approaches for WATLON of a mixing tee in JAEA to investigate the mechanism of thermal fatigue based on the work of [PERSON] et al. [5]. Other studies using LES were performed by [PERSON] et al. [11], [PERSON] et al. [12], and [PERSON] et al. [13] on different aspects of mixing flows. In recent years, several kinds of hybrid RANS-LES models such as Delayed Detached Eddy Simulation (DDES) and Scale-Adaptive Simulation (SAS) were developed for resolving turbulent structures. [PERSON] et al. [14], [PERSON] et al. [15], and [PERSON] et al. [16] employed different hybrid RANS-LES models to simulate the mixing flows in tee pipes. It was found that the results of hybrid RANS-LES models are very close to the experimental data and that of LES. However, the RANS model, the LES model, and the two hybrid RANS-LES models (DDES and SAS) have their own limitations. Compared with the LES model, there are two main limitations of the RANS model. The first one is the lack of additional information obtained from the RANS simulation, especially for unsteady mixing flows with different temperatures. The second one is related to accuracy. According to the previous study, it is evident that the performance of LES models for free shear flows is significantly more consistent than that of RANS [17; 18]. As for the LES model, the high computational cost required for LES at high or even at moderate Reynold numbers is unacceptable [19] because the turbulence scales in LES formulations are of the order of the shear layer thickness, which makes the turbulence length scale extremely small in relation to the thickness of the boundary layer close to the wall [20]. With regard to the hybrid RANS-LES models (DDES and SAS), they may not always be suitable, particularly for flows without strong enough instability to produce turbulent structures on their own [21].