Flow and heat transfer simulation with a thermal large eddy lattice Boltzmann method in an annular gap with an inner rotating cylinder

Abstract

In this study, a thermal Large Eddy Lattice Boltzmann Method (LBM–LES) is applied to Taylor–Couette flow simulations, allowing detailed analysis of local heat transport over a wide range of Taylor numbers, including resolved transient Taylor vortices. The challenge in thermal management of electric motors is to control the temperature in the air gap between rotor and stator due to the gap’s small width and complex geometry, in which Taylor vortices strongly influence the heat transfer. This thin gap — here simplified by an annulus — is solved for the first time by a Thermal Lattice Boltzmann Method with a Smagorinsky sub-grid model. The influence of the rotational velocity of the inner cylinder with Taylor numbers from 36 to 511 — corresponding to a Reynolds number on the inner cylinder of up to 126[Formula: see text]000 — is numerically investigated. The simulations are validated on the basis of the global Nusselt number, where we find good agreement with a published measurement series, an empirical correlation and Finite Volume simulations using the SST turbulence model. Special attention is paid on predicting the critical Taylor number, which is reproduced almost exactly by Direct Numerical Simulations (DNS) with LBM, whereas LBM–LES slightly overestimates and the SST model further overestimates the occurrence of Taylor vortices.