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 E. Balaras , C. Benocci , and U. Piomelli , Two-Layer Approximate Boundary Conditions for Large-Eddy Simulation . AIAA J. , vol. 34 , pp. 1111 – 1119 , 1996 .[Crossref] , [Google Scholar]], 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 E. Balaras , C. Benocci , and U. Piomelli , Two-Layer Approximate Boundary Conditions for Large-Eddy Simulation . AIAA J. , vol. 34 , pp. 1111 – 1119 , 1996 .[Crossref] , [Google Scholar]) a fully developed turbulent channel flow with a heated top wall, (2 W.-W. Kim and S. Menon , Application of the Localized Dynamic Subgrid-Scale Model to Turbulent Wall-Bounded Flows , AIAA Paper 1997-0210, 35th Aerospace Sciences Meeting & Exhibit , Reno , NV , 1997 .[Crossref] , [Google Scholar]) a backward-facing step flow with a heated bottom wall, and (3 W. Cabot and P. Moin , Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow, Flow . Turbulence and Combustion , vol. 63 , pp. 269 – 291 , 2000 .[Crossref], [Web of Science ®] , [Google Scholar]) 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 W.-W. Kim and S. Menon , Application of the Localized Dynamic Subgrid-Scale Model to Turbulent Wall-Bounded Flows , AIAA Paper 1997-0210, 35th Aerospace Sciences Meeting & Exhibit , Reno , NV , 1997 .[Crossref] , [Google Scholar]] 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.