Effect of thermo-mechanical non-equilibrium on the onset of transition in supersonic boundary layers

Abstract

Direct numerical simulations (DNS) for supersonic boundary layers (SBLs) with a free-stream Mach number of M∞ = 2.2 are carried out. Various cases are investigated, involving the adiabatic and the isothermal (cooled and heated) walls. The laminar boundary layer is tripped using a blowing and suction strip with single-frequency and multiple spanwise wave-number excitation. Effects of thermo-mechanical non-equilibrium of thermal boundary layer on laminar-to-turbulent transition (LTT) are presented in detail. Cases with two perturbation intensities are investigated (0.5% and 2.4%). The receptivity analysis of transition onset location towards the thermo-mechanical non-equilibrium is performed using different physical quantities like streamwise evolution of skin-friction coefficient, Stanton number and Dynamic mode decomposition (DMD). The results reveal that thermo-mechanical non-equilibrium tends to advance the transition onset location and also decreases the transition length for the heated walls regardless of the initial perturbation intensity. However, for the cooled walls with 2.4% perturbation intensity, the existence of thermo-mechanical non-equilibrium has a stabilizing effect resulting in delayed transition onset. The flow stays laminar for cooled walls with 0.5% perturbation intensity. The results obtained from DMD analysis uncover two distinct ways of evolution for odd and even harmonics of the perturbation frequency. DMD results also show that the fundamental evolution of the modes is not affected by the physical flow parameters like wall temperature or existence of thermo-mechanical non-equilibrium. It is observed that the imposed frequency mode or the principal mode is dominant in the transition region and eventually breakdown to smaller structures in the turbulent regime.