Eddy-Resolving Simulation Coupled with Stability Analysis for Turbulent Transition in Compressible Boundary Layer

An efficient and high-fidelity approach is proposed for laminar-to-turbulent transition in compressible boundary layer flows. The proposed method combines eddy-resolving simulations, such as direct-numerical simulation (DNS) and large-eddy simulation (LES), with stability analysis. The combined approach provides (1) high fidelity for simulating transitional flow and (2) cost efficiency for capturing major instabilities in the pre-turbulent region. Coupling between stability analysis and eddy-resolving simulation is pursued via unsteady inlet condition for eddy-resolving simulation; instability modes from stability analysis are introduced at the inlet with the undisturbed laminar solution. The feasibility of the coupled framework is assessed for turbulent transition in both supersonic and hypersonic boundary layer flows because this framework has been rarely used in such high-speed flows. Detailed flow features associated with the transition are well captured, including the growth of instability modes in the pre-turbulent regime and the skin friction in the overall transitional flows. This study demonstrates that the proposed approach provides high fidelity for transitional boundary layers with a fraction of the computational cost of a full-scale DNS computation. It is recognized that artificial dissipation needs to be adequately controlled inside transitional boundary layer, particularly for the hypersonic case, because a common shock sensor is activated unexpectedly in the viscous boundary layer. A modified shock sensor is investigated in the current study of hypersonic boundary layer.