Drag increment induced by a small-scale forward-facing step in Mach number 5 turbulent boundary layer flows

Small-scale roughness elements or imperfections are inevitable over the surface of a flight vehicle. The aerodynamics of these small-scale structures is difficult to predict but may play an important role in the design of a flight vehicle at high speed. The forward-facing step is a typical type of roughness element. Many experiments have been conducted to study the aerodynamics of supersonic forward-facing step, especially with a step height larger than boundary layer thickness. However, few studies focus on small steps. To improve the understanding of small-scale forward-facing step flow, we perform a series of simulations to analyze its aerodynamic influence on a Mach number 5 turbulent boundary layer. The general flow structures are analyzed and discussed. Several shock waves can be induced by the step even if the step height is much smaller than the boundary layer thickness. Two significant shocks are the separation shock and the reattachment shock. The influenced area by the step is limited. With the increase of the step height, the non-dimensional influence area decreases and gradually converges when the step height reaches the boundary layer thickness. There are two normalized distributions of the skin friction coefficient and pressure coefficient associated with step height. By using the normalized parameters, a power-law relationship between the step height and the drag increment coefficient is revealed and fits the simulation results well. It is further illustrated that this relationship still holds when changing the inlet angle of attack, but needs slight modification with the angle of attack.