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

Abstract

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 (Prt) is not constant and that it is greater than 0.85 for low-Pr fluids. However, the Prt 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 Prt 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 Prt model is modified. The Prt of turbulent core region is expressed as a function form, in which the local Reynolds number (Re) is introduced to characterize the trend of Prt in the near-wall region. With the undetermined coefficients obtained using numerical simulation, a new modified Prt model for low-Pr He–Xe is proposed. The results suggest that the new model can better reflect changes in Prt with Re, Pr, and the distance from the wall. The numerical predictions of Prt 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 Prt model has optimal numerical accuracy. In the future, the proposed Prt model can be used to further study the flow and heat transfer characteristics of He–Xe.