A study on the focusing phenomenon of a weak shock wave

Abstract

When a plane shock wave reflects from a concave wall or when a curved shock wave reflects from a straight wall, it is focused at a certain location, resulting in extremely high local pressure and temperature. This focusing is due to a non-linear phenomenon of a shock wave. This focusing phenomenon has been extensively applied in a variety of engineering and medical areas. In the current study, the focusing phenomenon of a weak shock wave over a reflector is numerically investigated using a computational fluid dynamics (CFD) method. The total variation diminishing (TVD) scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The Mach number of the incident shock wave is changed in the range from 1.1 to 1.5. Several different types of reflectors are employed to investigate the effect of the reflector on the focusing phenomenon of the weak shock wave. The focusing characteristics of the shock wave are investigated in terms of peak pressure, gas dynamic and geometrical foci. The results obtained are compared with previous experiment results that are available. The results show that the peak pressure of shock wave focusing and its location strongly depend on the Mach number of the incident shock wave and the reflector geometry. The location of the gas dynamic focus is always shorter than that of the geometrical one. This tendency is more remarkable as the incident shock wave becomes stronger. The present computations predict the experimental results with a very good accuracy.