High-order LES of turbulent heat transfer in a rotor–stator cavity

Abstract

The present work examines the turbulent flow in an enclosed rotor–stator system subjected to heat transfer effects. Besides their fundamental importance as three-dimensional prototype flows, such flows arise in many industrial applications but also in many geophysical and astrophysical settings. Large eddy simulations (LES) are here performed using a spectral vanishing viscosity technique. The LES results have already been favorably compared to velocity measurements in the isothermal case (Séverac, E., Poncet, S., Serre, E., Chauve, M.P., 2007. Large eddy simulation and measurements of turbulent enclosed rotor–stator flows. Phys. Fluids, 19, 085113) for a large range of Reynolds numbers 10 5 ⩽ Re = Ω b 2 / ν ⩽ 10 6 , in an annular cavity of large aspect ratio G = ( b - a ) / H = 5 and weak curvature parameter R m = ( b - a ) / ( b + a ) = 1.8 ( a , b the inner and outer radii of the rotor and H the interdisk spacing). The purpose of this paper is to extend these previous results in the non-isothermal case using the Boussinesq approximation to take into account the buoyancy effects. Thus, the effects of thermal convection have been examined for a turbulent flow Re = 10 6 of air in the same rotor–stator system for Rayleigh numbers up to Ra = 10 8 . These LES results provide accurate, instantaneous quantities which are of interest in understanding the physics of turbulent flows and heat transfers in an interdisk cavity. Even at high Rayleigh numbers, the structure of the iso-values of the instantaneous normal temperature gradient at the disk surfaces resembles the one of the iso-values of the tangential velocity with large spiral arms along the rotor and more thin structures along the stator. The averaged results show small effects of density variation on the mean and turbulent fields. The turbulent Prandtl number is a decreasing function of the distance to the wall with 1.4 close to the disks and about 0.3 in the outer layers. The local Nusselt number is found to be proportional to the local Reynolds number to the power 0.7. The evolution of the averaged Bolgiano length scale 〈 L B 〉 with the Rayleigh number indicates that temperature fluctuations may have a large influence on the dynamics only at the largest scales of the system for Ra ⩾ 10 7 , since 〈 L B 〉 remains lower than the thermal boundary layer thicknesses.