Compact Scheme with Filtering for Large-Eddy Simulation of Transitional Boundary Layer

Abstract

Bypass transition induced by freestream turbulence is numerically simulated by compressible large-eddy simulation and implicit large-eddy simulation using a compact differencing scheme with spatial filtering. Simulated transitional flowfields qualitatively reproduce the physics of the transition and are appropriate for the discussion of transitional flowfields. Key coherent structures, such as low-speed streaks, longitudinal vortex pairs, and hairpin vortices, which play important roles in determining the behavior of transition, need to be directly resolved to properly simulate the physics of transition. Only a slight numerical damping of these coherent structures by the spatial filtering procedure causes the delay of transition. On the other hand, once the flow develops into a fully turbulent state, the spatial filtering has little influence on the flowfield. At the late stage of transition, the coherent structures break down into finer scales which require finer grid resolution to accurately resolve. However, the underresolution of the finer scale structures has little influence on the overall results if the key coherent structures are adequately resolved. Under the condition examined, the tenth-order filtering with α f = 0.495 does not act as an implicit subgrid-scale model. The present results reasonably illustrate the capability of compact/filter-based compressible large-eddy simulation and the guidelines regarding how to properly simulate transitional boundary layers using the large-eddy simulation.