Wall modeled LES for variable viscosity turbulence

Modification of turbulence by temperature-dependent fluid properties is not ignorable when a relatively large temperature difference is imposed on the flow fields. It is true particularly for high Prandtl number flows heated/cooled from the wall boundaries. Since most of the algebraic wall models simply assume constant fluid properties, it is required to provide an alternative model to simulate such a flow field. Indeed, models based on the equilibrium logarithmic law cannot describe the effects of variable viscosity. This study hence proposes a wall-modelled LES method by introducing a temperature-dependent near-wall layer for the viscosity. With a simple model function for the viscosity, the steep near-wall variation of the temperature-dependent viscosity is described. We then integrate the Favre averaged thin boundary layer equations for the momentum and the temperature to construct an algebraic non-equilibrium wall model. The present LES shows that the proposed model successfully reproduces the skewed mean velocity and temperature profiles owing to the temperature-dependent variable viscosity.