Boundary-Layer Equation-Based Wall Model for Large-Eddy Simulation of Turbulent Flows with Wall Heat Transfer

Abstract

A new thermal boundary-layer model is developed that alleviates the stringent near-wall grid resolution requirement in large-eddy simulations of turbulent flows with wall heat transfer. The model is based on solving the turbulent temperature boundary-layer equation to determine the temperature profile in the near-wall region. The near-wall temperature profile is used to compute the instantaneous wall heat flux, which replaces the temperature (Dirichlet) wall boundary condition specified a priori. This approach is analogous to the wall stress model developed by Balaras et al. [1], in which the instantaneous wall shear stresses replace the no-slip wall boundary conditions. Three benchmark turbulent flows are studied using coarse-grid large-eddy simulations coupled with the new thermal wall model: (1) a fully developed turbulent channel flow with a heated top wall, (2) a backward-facing step flow with a heated bottom wall, and (3) an impinging jet on a heated circular plate. Large-eddy simulations are performed using the commercial code CFD-ACE+, with the localized dynamic subgrid kinetic energy model of Kim and Menon [2] providing the subgrid stresses. Turbulence statistics are compared with benchmark data from direct numerical simulations and experiments and also with data from resolved large-eddy simulations (i.e., near-wall y + ≈ 1). Excellent agreement among the data is obtained.