Reynolds-averaged Navier-Stokes calculations of unsteady turbulent flow

In this study, a combination of the unsteady incompressible Navier-Stokes equations in vorticityvelocity formulation and the Algebraic Stress Model (ASM) of Gatski and Speziale (1996) is employed for Unsteady Reynolds Averaged Navier-Stokes (URANS) calculations of turbulent boundary layer flows. The Navier-Stokes equations are solved using a fourth-order compact difference scheme in space and a fourth-order Runge-Kutta method in time. The highly accurate numerical method greatly reduces the possibility of contamination of the results by second-order artificial dissipation from the numerical schemes. A flat plate boundary layer subjected to a strong adverse pressure gradient with laminar separation and turbulent reattachment is investigated. Performing URANS calculations for this Aow, we found that unsteady vertical structures remain in the flow field despite the large "effective eddy viscosity" produced by the turbulence model (ASM). This is due to the fact that a special function is used in this turbulence model such that the eddy viscosity is strongly coupled with the unsteady flow structures. For comparison, URANS calculations were also carried out employing the standard k - ∈ model, where in contrast no unsteady vertical structures were found in the flow field. For further comparison, results from 2-D "Direct Numerical Simulation (DNS)" and 3-D Large-Eddy Simulation (LES) using the standard Smagorinski model are also presented and discussed.