Cost-effective and high-fidelity method for turbulent transition in compressible boundary layer

Abstract

An efficient high-fidelity simulation approach is investigated for laminar-to-turbulent transition in compressible boundary layer flow. This approach combines large-eddy simulation (LES) with the parabolized stability equations (PSE) analysis. LES is chosen for high-fidelity simulation of the transitional flow, whereas the PSE analysis is used for an efficient treatment of instability modes in the flow. Instability modes from the PSE analysis are assigned as forcing at the inlet of the LES computational domain. A framework of LES combined with PSE (PSE+LES) for the turbulent transition is demonstrated in supersonic boundary layer flow at Mach 3. Complete transition to turbulence via oblique-mode breakdown is well resolved in the current study. Detailed flow features associated with the turbulent transition are compared well with previous direct-numerical simulation (DNS) studies, including the growth of instability modes in the pre-transition regime, the transition range shown in the evolution of the skin friction, and the turbulent boundary layer. It is shown that the current PSE+LES approach can reduce the computational cost by two orders of magnitude, compared to the relevant DNS cost. The current study for supersonic flow and the authors' previous study for subsonic flow imply that the PSE+LES approach can be used in boundary layer flows at various speeds.