Transport-Equation-Based Shock Sensor for Shock–Turbulent Boundary-Layer Interaction

Abstract

High-speed flows are often associated with shock–boundary-layer interaction (SBLI), which causes excessive vehicle surface heating and total pressure loss. Therefore, precise computational prediction of shock interactions becomes essential. Commonly used simulation techniques, including numerical schemes and turbulence models, give erroneous results at shock discontinuities. Local modifications are applied at shocks based on their location and strength. Most shock sensors in the literature predict shock location but do not give shock properties. We propose a shock function to locate shocks and estimate their strength in terms of density ratio by solving a transport equation, along with the governing equations of fluid flow. The sensitivity of the shock function to the transport equation’s parameters and grid resolution are explored. The shock function is used to define a shock sensor that can identify thin and sharp shocks. The shock function and shock sensor are then applied to an oblique shock impinging on a turbulent boundary layer. We use the shock unsteadiness modified [Formula: see text] model, which uses the estimated shock strength to predict the turbulence levels at shocks accurately. We study the effect of nonadiabatic wall temperature on the SBLI region, and the results are compared with available Direct Numerical Simulation (DNS) data.