Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

Abstract

The streaky boundary layers have very important roles in laminar-turbulent transition. Streaks of appropriate size can influence stabilities in boundary layers. In this paper, the effect of steady streamwise elongated, spanwise periodic wall heating elements on the first mode instability in supersonic flat plate boundary layers was investigated. For the balance of the efficient and accuracy, the linearized Navier–Stokes equations are used to obtain the base flow and compared with compressible Navier–Stokes equations. A bi-global analysis tool is used for the instability analysis because the heating source has a much larger length-scale in the streamwise direction than that in the spanwise direction, and the streamwise velocity is much larger than the normal velocity and the spanwise one. Results indicated that the distortion caused by the three-dimensional surface heating elements could modify the first mode, resulting in a lower frequency but with an uncertain effect on the higher frequency modes. Additionally, the streaks make the lower spanwise wave number components of the even first mode disturbance in a three-dimensional supersonic boundary layer in the freestream. As a result, the spontaneous radiation of an acoustic wave to the far field was found for the even mode. These findings suggest that laminar-turbulence transition can be suppressed or enhanced by the three-dimensional wall heating.