(A) study on the shock wave propagation past blunt bodies

Abstract

This paper deals with the diffraction of the weak shock wave whose Mach number is $1<M_s<2$ by some blunt bodies. Through experimental, numerical, and theoretical(analytic) studies, qualitative and quantitative results about these phenomena have been deduced, and compared with one another. With the experimental studies which make use of the shock tube, it is demonstrated that the analytic solution of the 1-D Riemann problem is quite resonable, and, about the reflected shock wave in front of a circular cylinder, experimental and numerical values are compared with each other. In addition, we have designed and produced an optical instrument of the holographic interferometry system, and, through the image processing techniques, made them to be used for the future works. In the numerical analysis, the unsteady, 2-D, Euler equation is solved with the TVD high resolution method which has the 2nd order accuracy for the space and the time. As a result, the program using this method is shown to be able to be used for the simulation code of our future experiments. The example cases of circular cylinder, square column, and prismatic column at $M_s=1.34$ are demonstrated here. In the theoretical consideration, at first, we have calculated the transition angle of the regular reflection to the Mach reflection for the pseudo-steady flows with a classical oblique shock theory and a simple coordinate transformation. Then, for these transition phenomena, their physical meaning has been explained with the method of the shock-fitting. For fully unsteady cases, the problem has been solved with use of the Whitham``s ray-shock theory. Trough that theory, the locus of the Mach triple point can be predicted, which almost corresponds with the numerical results. In addition, we have tried to approach some interesting themes - the velocity of the reflected shock waves, the vorticities backward the bodies, and the interaction between the shock wave and the vortex about which no complete the...