Turbulent Prandtl Number Analysis of Helium-Xenon Gas Flow and Heat Transfer in the Parallel Channel

The helium-xenon gas mixtures (15-40 g/mol) are used in various designs of small gas-cooled nuclear reactor systems with Prandtl number (Pr) from 0.2 to 0.3. The low Pr values have an effect on the selection of models in the Reynolds-Averaged Navier-Stokes (RANS) simulation, one of which is turbulent Prandtl number (Pr t ) model. However, the existing Pr t models depict different variations of Pr t , which indicates that there are deficiencies in the understanding of Pr t . In this paper, the Direct Numerical Simulation (DNS) method was chosen to simulate turbulent flow and heat transfer of helium-xenon in a parallel channel and to obtain the profile of Pr t . Then, the laws of Pr t with Re, Pr and wall-normal distance were analyzed. The results show that Pr t increases and then decreases with increasing y + , peaking at y + ≈45. With fixed Pr, Pr t increases with increasing Re in the region of y + <10 and y + >90, but decreases in the region between these two. under fixed Re, Pr t increases with increasing Pr in the region of y + < 10, but decreases in the remaining region. The reasons for the phenomena above were analyzed. A comparison between DNS data and existing Pr t models was performed, which showed none of the models could depict the variation of Pr t along the wall-normal direction in DNS data, especially in the region of y + <50. This indicates that the current Pr t models need to be improved to be applied in RANS simulations of helium-xenon better. The DNS results will be regarded as benchmarks for developing an improved Pr t model of helium-xenon mixtures.