On unsteady shock wave reflections from wedges with straight and concave tips

Abstract

The present paper is devoted to numerical and experimental studies of shock wave reflection from wedges with straight and concave tips. The numerical model is based on the Euler equations and the assumption of an ideal gas with constant specific heats. A locally adaptive unstructured Godunov-type second-order TVD finite-volume flow solver is used. The numerical simulations confirm the previous finding (Lau-Chapdelaine & Radulescu, Shock Waves, 23(6):595-602) that the resulting shock reflection pattern may be of regular or irregular type for the same wedge angle, incident shock Mach number Ms and ratio of specific heats γ, depending on whether the tip of the reflecting wedge is straight or initially curved in a concave manner. Furthermore, it is established by subsequent parametric studies (Ms from 1.5 to 3.0, γ = 1.4) that the effect is observed within the most part of the dual solution (regular reflection and Mach reflection) domain on the wedge angle/shock Mach number diagram. More specifically, when increasing the wall angle of straight wedges Mach reflection reverts to regular reflection when the angle exceeds the sonic/detachment angle, but if the wedge tip is rounded, Mach reflection persists almost till the von Neumann angle. In other words, the Mach reflection pattern necessarily induced by the concave cylindrical surface at the initial stages of reflection does not revert to regular reflection provided that the wedge angle is within the dual solution domain (with the exception of a small part of it adjacent to the von Neumann line) where a Mach reflection solution is physically admissible. Shock-tube experiments with time-resolved flow imaging confirm that the predicted effect does take place. The experimental movies show that, for the same shock Mach number and wedge angle, regular reflection or irregular (Mach) reflection develop along the wedge depending on whether the wedge tip is straight or rounded with a concave cylindrical surface, respectively.