Direct and large-eddy simulations of transition in the compressible boundary layer

Abstract

The transition to turbulence in the three-dimensional compressible boundary layer over a semi-infinite insulated flat plate is studied by means of direct and large-eddy simulations. Results are presented in the quasi-incompressible (Mach number equal to 0.5) and high supersonic (Mach number equal to 5) cases, both in temporal and spatial configurations. Simulations of controlled transition, in which a two-dimensional wave corresponding to the primary instability is introduced at the initial stage, allows us to study the secondary instability of the flow. The latter is triggered with the aid of a three-dimensional white-noise perturbation of small amplitude superposed upon the wave. At a low Mach number, a direct-numerical simulation shows that the fundamental mode is selected, leading to the peak-valley structure found by Klebanoff et al. (1962). The complete transition process is then studied, with emphasis on vortex-filament dynamics. It is shown that the development to turbulence is well simulated, at least for the prediction of average quantities of the flow. In the high Mach number case, no direct-numerical simulation is possible, and we use a subgrid-scale model, the structure-function model, in order to perform a large-eddy simulation of the transition. In this case, the subharmonic mode appears, giving rise to a staggered pattern of ∧ vortices. These vortices, which affect the whole thickness of the boundary layer, are more elongated than in the incompressible case.