The Study of Mach Waves Generated by a Roughness Element

In this paper, a simplified inviscid boundary condition is applied to solve the problem of Mach waves generated by a roughness element on the wall surface of a supersonic wind tunnel. The geometry of the roughness element is simplified by a parabolic function, to which mathematical formulas are introduced to model the boundary condition. These techniques help simplify the problem and minimize the required computer resources for the simulation performance. Using the direct numerical simulation (DNS) method while employing the above-mentioned techniques, the authors can simulate the generation and the propagation of Mach waves from a roughness element at a Mach number of 2.5. The result shows that a pair of Mach waves are generated at the leading and trailing edges of the roughness element and oscillate with small amplitudes. We also study the effect of the height of the element, the flow speed, the Reynolds number, and the unsteadiness of the flow on the simulation result. The numerical result is compared with published experimental data for the validation. © 2022, The Author(s), under exclusive licence to The Korean Society for Aeronautical & Space Sciences.