An entropy viscosity method for large eddy simulation of turbulent thermal flow in a rotor–stator cavity

Abstract

Turbulent flow and heat transfer in a rotor–stator cavity have fundamental importance in both academia of turbulence research and the industry of rotating turbomachinery. The main characteristic of the flow is that there is the centrifugal Ekman layer on the rotor and the centripetal Bödewadt layer on the stator, which are separated by a central rotating core. In this paper, an entropy viscosity subgrid model based on the large eddy simulation (LES) method is proposed to solve the complex flow with heat transfer in a rotating frame at high Reynolds numbers. The method is fully validated by the simulation of turbulent thermal flow in a closed stator–rotor cavity up to Re=106. By performing 12 simulations, the sensitivity of the simulation results to mesh resolution and the free parameters of entropy viscosity are systematically studied, and the proper range for the parameters is determined. In particular, it is found that the prediction on the mean flow and fluctuation from the simple turbulent diffusivity model, which scales linearly with the eddy viscosity, is as accurate as that from the alternative model that is a more computationally complex model. Despite the comparable accuracy, the entropy viscosity-based LES uses the mesh resolution two-order lower than that of direct numerical simulation; therefore, it is feasible to apply the LES to the flow at the practical Reynolds number in an aircraft engine, that is, Re≥107.