Influence of surface imperfections on laminar-turbulent transition of high-speed flows

Abstract

The presence of surface imperfections can have an important effect on the expected laminar-turbulent transition location for supersonic and hypersonic devices, leading to the appearance of highly localised areas of heat flux augmentation. The study presented in this paper investigates numerically the boundary-layer stability characteristics of a supersonic flow (Mach number = 4.5) in the presence of a rectangular backward-facing step (BFS) placed on a semi-infinite flat plate. The location of the step is defined by the synchronisation point (SP) of a reference two-dimensional 2nd mode with a frequency of 90 kHz (synchronisation frequency). The influence of the step height is investigated by considering five different step heights. The stability analysis combines the Parabolized Stability Equations (PSE) and the Adaptive Harmonic Linearized Navier-Stokes (AHLNS) methods. The high-fidelity AHLNS approach simulates the linear spatial evolution of convective instabilities in the presence of surface imperfections, and it has been already extensively used in transonic applications. The AHLNS stability tool is perfectly suited for studies regarding the influence of two-dimensional surface imperfections on the laminar-turbulent transition location. The low computational requirements of the AHLNS method (compared with similar techniques as DNS (Direct Numerical Simulation)) allow the study of a relatively broad band of modes, with frequencies higher and lower than the synchronisation frequency. Similar to previous studies about surface imperfections, the results of the present investigation show that the backward-facing step amplifies the lower-frequency modes and damps the higher-frequency modes (with respect to the synchronisation frequency). This paper describes the first application of the AHLNS methodology for supersonic configurations and sets the path for future applications in the study of the influence of surface imperfections in high-speed flows.