Extension Of Local Domain-Free Discretization Method To RANS Simulation Of Turbulent Flows

In this paper,a local domain-free discretization(DFD)method is extended to simulate the turbulent flows at high Reynolds numbers in conjunction with the RANS(Reynolds Averaged Navier-Stokes)equations.In the local DFD method,the discretized partial differential equations at an interior mesh node may involve some nodes outside the solution domain,which are called exterior dependent nodes.For the solution of the RANS equations for unsteady compressible flows,Galerkin finite volume method is employed for spatial discretization and the dual time-stepping scheme is adopted in time integration.The Werner-Wengle wall function or Mason wall function is adopted to alleviate the requirement on the near-wall mesh resolution,by transforming the no-slip condition into the no-penetration condition and the prescribed wall shear stress.The normal and tangential velocity components at an exterior dependent node are evaluated via the linear extrapolation in the normal direction in conjunction with the no-penetration condition and the prescribed shear stress,respectively.The pressure at an exterior dependent node is obtained by solving the simplified momentum equation.The temperature,molecular viscosity and density are calculated via the Crocoo-Busemann relation,the law of Sutherland and the state equation respectively.The SST turbulence model and S-A turbulence model are adopted to ensure the closure of the governing equations.By using analytical solutions,appropriate boundary conditions for the SST turbulence model equations are specified and then the turbulence variables at an exterior dependent node are determined.For the S-A turbulence model,the turbulence variables can be evaluated by using eddy viscosity profile in the vicinity of the wall.In order to reduce computational cost,a dynamic mesh adaptation technique is adopted in moving boundary issues.To validate the present developed DFD method,simulations of high-Re turbulent flows over NACA0012,RAE2822 and ONERA M6 have been conducted.The predictions are reasonable compared with the experimental data.