Supersonic boundary-layer transition prediction under the effect of compressibility using a correlation-based model

Abstract

The effect of compressibility on supersonic boundary layer transition is simulated by modifying a standard γ-Reθt correlation-based transition model under two-dimensional (2D) approximation. First, the γ-Reθt model’s empirical correlations derived for low Mach numbers are validated against some well-known subsonic flat plate experiments. Second, the same empirical correlations are tested against a direct numerical simulation (DNS) dataset closely approximating a supersonic flat plate experiment at M = 2.25. Finally, the present empirical correlations are extended for supersonic speeds using a known compressibility correlation. For this, the free stream turbulence level is assumed to remain constant and the free stream velocity is increased up to a supersonic speed of Mach 2.7 using adiabatic wall conditions. Numerical results show that the modified γ-Reθt transition model is capable of predicting the downstream movement of the transition onset location in good agreement with the linear theory, experiments, and DNS data up to Mach 2.25. The length of the transition region is observed to grow with higher Mach numbers, and destabilizing effect of compressibility after Mach 2.0 is also predicted, in a limited sense, under the 2D approximation.