A Wall Model for Large-Eddy Simulation of Compressible Channel Flows

Abstract

A wall model for the large-eddy simulation (LES) of compressible channel flows with isothermal walls is presented, which extends the incompressible model of Chung and Pullin (Journal of Fluid Mechanics, 2009). The wall model computes the local, instantaneous wall shear stress and heat flux, which are then applied as wall boundary conditions, by solving two time-dependent, parameter-free ordinary differential equations (ODEs) at each time step. These ODEs are obtained by integrating the LES momentum and internal energy equations in the wall-normal direction from the wall to the first grid point placed in the log layer. In contrast to so-called "wall-resolved" LES, employment of this wall model allows use of relatively coarse computational meshes of fixed size, independent of Reynolds number. The wall model is first validated by comparing the LES results at M = 0.15 and friction Reynolds number 2003 to the direct numerical simulation (DNS) results of Hoyas and Jimenez (Physics of Fluids, 2006), and at M = 0.7 and friction Reynolds number 186 to the DNS results of Wei and Pollard (Computers & Fluids, 2011). Results are then presented for LES of channel flows at M = 0.15 and M = 0.7, over a three-order-of-magnitude range of friction Reynolds numbers, on a uniform mesh with 256 x 32 x 128 grid points in the streamwise, wall-normal, and spanwise directions.