A Computational Study of the Focusing Phenomenon of Weak Shock Wave

약한 충격파의 포커싱 현상에 관한 수치해석적 연구

When a plane shockwave reflects ken a concave wall, it is focused at a certain location, resulting in extremely high local pressure and temperature. This focusing is due to a nonlinear phenomenon of shock wave. The focusing phenomenon has been extensively applied to many diverse folds of engineering and medical treatment as well. In the current study, the focusing of shock wave over a reflector is numerically investigated using a CFD method. The Harten-Yee total variation diminishing (TVD) scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The incident shock wave Mach number $M_{s}\;of\;1.1{\~}l.3$ is applied to the parabolic reflectors with several different depths. Detailed focusing characteristics of the shock wave are investigated in terms of peak pressure, gasdynamic and geometrical foci. The results obtained are compared with the previous experimental results. The results obtained show that the peak pressure of shock wave focusing and its location strongly depend on the magnitude of the incident shock wave and depth of parabolic reflector. It is also found that depending up on the depth of parabolic reflector, the weak shock wave focusing process can classified into three distinct patterns : the reflected shock waves do not intersect each other before and after focusing, the reflected shock waves do not intersect each other before focusing, but intersect after focusing, and the reflected shock waves intersect each other before and after focusing. The predicted Schlieren images represent the measured shock wave focusing with a good accuracy.