Large-Eddy Simulation of High Reynolds Number Flows in Complex Geometries
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Large-eddy simulation (LES) of wall-bounded flows is limited to moderate Reynolds number flows due to the high computational cost required to resolve the near wall eddies. LES can be extended to high Reynolds number flows by using wall-layer models which bypass the near-wall region and model its effect on the outer region. Wall-layer models based on equilibrium laws yield poor prediction in non-equilibrium flows, in which Wall-Modeled LES (WMLES) that model the near wall region by Reynolds-Averaged Navier-Stokes (RANS) equation and the outer region by LES, has the potential to yield better results. However, in attached equilibrium flows, WMLES under-predicts the skin friction due to slow generation of resolved eddies at the RANS/LES interface; application of stochastic forcing results in faster generation of resolved eddies and improved predictions. In this work, wall-layer models based on equilibrium laws and WMLES are tested for four non-equilibrium flows. Flow over a contoured ramp, with a shallow separation followed by a recovery region, was studied. LES using equilibrium laws was unable to resolve the shallow separation. WMLES predicted the mean velocity reasonably well but over-predicted the Reynolds stresses in the separation and recovery region; application of the stochastic forcing corrected this error. Next, the flow past a two-dimensional bump, in which curvature and pressure-gradient effects dictate the flow development, was studied. WMLES predicted the mean velocity accurately but over-predicted the Reynolds stresses in the adverse pressure gradient region; application of the stochastic forcing also corrected this error. Same trends were seen in a three-dimensional flow studied. A turbulent oscillating boundary layer was also investigated. WMLES was found to be excessively dissipative, which resulted in incorrect prediction of the flow development. LES calculation based on equilibrium laws and dynamic models predicted the flow development correctly. In summary, in flows that are steady in the mean, WMLES with stochastic forcing gave more accurate results than the logarithmic law or RANS. For the oscillating boundary layer, in which stochastic forcing could not be applied, the logarithmic law yielded the best results.