Modified turbulent Prandtl number model for helium-xenon gas mixture with low Prandtl number

Gas-cooled space nuclear-reactor systems generally adopt the helium-xenon mixture (He-Xe) as a working fluid and coolant, the Prandtl number (Pr) of which is low for recommended mixing ratios. Many studies have shown that the turbulent Pr (Pr-t) is not constant and that it is greater than 0.85 for low-Pr fluids. However, the Pr-t in the Reynolds-averaged Navier-Stokes model is generally set to 0.85 by default, which inevitably results in large prediction errors with respect to the flow and heat transfer of low-Pr He-Xe. In this paper, the Pr-t model of He-Xe is examined using theoretical analysis and numerical simulations. Based on the existing models applicable to liquid metals, the spatial distribution of the Pr-t model is modified. The Pr-t of turbulent core region is expressed as a function form, in which the local Reynolds number (Re) is introduced to characterize the trend of Pr-t in the near-wall region. With the undetermined coefficients obtained using numerical simulation, a new modified Pr-t model for low-Pr He-Xe is proposed. The results suggest that the new model can better reflect changes in Pr-t with Re, Pr, and the distance from the wall. The numerical predictions of Pr-t distribution at different radial positions are consistent with the analytical results, especially the distribution of the near-wall region. For the convective heat transfer simulation, the new Pr-t model has optimal numerical accuracy. In the future, the proposed Pr-t model can be used to further study the flow and heat transfer characteristics of He-Xe.