A new methodology for the numerical simulation of wall bounded turbulent flows

Abstract

Research is presented on the development and testing of a new procedure for the time dependent, spatially varying numerical simulation of wall bounded turbulent flows. The Flow Simulation Methodology (FSM), as it is now known, was originally proposed by Speziale (1996a) for the purpose of computing complex, non-equilibrium flows which are currently beyond the reach of Smagorinsky based Large-Eddy Simulations (LES). The new method represents a hybrid approach that combines favorable aspects of Reynolds stress modeling [used for Reynolds Averaged Navier-Stokes (BANS) calculations] with the underlying principles of LES. For instance, Reynolds stress models developed for non-equilibrium, anisotropic, and/or rotational flows can be utilized in the unsteady manner of LES, i.e. where the flow field is decomposed into resolved-scale (calculated) and subgrid-scale (modeled) components, thereby reducing computational requirements. The key to the FSM is a contribution function which provides a degree of local turbulence modeling that is dependent upon the ratio of the numerical resolution to the Kolmogorov length-scale, an estimate for the smallest scales of turbulent motion. With this approach, a calculation resolved to the level of a Direct Numerical Simulation (DNS) can proceed continuously to a Reynolds Averaged Navier-Stokes calculation as the numerical resolution is decreased and/or the Reynolds number is increased. In between these two limits, an "untraditional" LES is recovered. The method is untraditional because it replaces the commonly employed Smagorinsky subgrid-scale model, which is known to have considerable limitations, with a more capable Reynolds stress model. A detailed evaluation of the Flow Simulation Methodology is made for the test case of a transitional and turbulent flat plate boundary layer with zero pressure gradient. The relatively simple geometry is chosen because the technical issues associated with combining elements of RANS calculations and LES must be established and the FSM itself must be validated before more complex flows can be attempted. The Reynolds stresses needed for the new method are computed using the two-equation Algebraic Stress Model (ASM) of Gatski & Speziale (1993) developed for non-equilibrium turbulent flows. Results of FSM calculations are compared with results obtained from coarse grid DNS, traditional LES based on the Smagorinsky subgrid-scale model, and RANS, all of which are implemented using an identical core computer code. This approach is extremely valuable to the evaluation of the FSM since a common code allows for certain behaviors to be more easily attributed to the turbulence models as opposed to numerical effects. Further validation is achieved through comparisons of FSM results with various direct numerical simulations and experiments available in the literature.