Equilibrium Wall Model Implementation in a Nodal Finite Element Flow Solver JENRE for Large Eddy Simulations
NAVAL RESEARCH LAB WASHINGTON DC WASHINGTON United States
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The equilibrium wall model is implemented in a nodal finite element flow solver JENRE developed at the Naval Research Laboratory. The Crocco-Busemann relation is used to account for the compressibility. In this wall-model implementation, the first cell adjacent to the wall is used to estimate the shear stress on the wall. The no-slip adiabatic boundary condition is applied to the inviscid and viscous fluxes on the wall to satisfy the surface physical condition, but a non-zero surface tangential velocity is used in the calculation of the volume and surface integrals in a cell adjacent to the wall. This is because using a zero-surface velocity will grossly underestimate these integrals due to the linear basis function used in JENRE. This implementation is validated in a subsonic boundary-layer flow over a flat plate and a supersonic flow in a converging and diverging nozzle used frequently in our jet noise simulations. Skin frictions, velocity profiles and turbulence quantities predicted by the current wall-model implementation agree well with available experimental data and theoretical models. The grid convergence is excellent. Grid sizes much larger than those recommended in other wall-model implementations can be used. The current wall-model implementation has not encountered the numerical problem associated with using the first cell as reported in other wall-model implementations. The volume and surface integrals based on the non-zero surface velocity in a cell adjacent to the wall show a good agreement with those derived from the equilibrium boundary-layer velocity profile and the density profile based on the Crocco-Busemann relation.
- Fluid Mechanics