Models of shock wave propagation for diverging metallic structures

In the present study we have considered shock waves propagating freely in some diverging metallic structures. The characteristic equation along with boundary conditions provides a differential equation that is used to evaluate certain flow variables and parameters. The Chisnell-Chester-Whitham (CCW) method forms the basis to obtain the analytical relations for shock velocity, shock strength and pressure behind the shock wave. The variation of pressure with parameter  (compression behind the shock) and propagation distance r is obtained for cylindrical (barrel) shock waves. It is found that shock velocity decreases and the shock strength increases as the shock wave progresses in both the Al and Cu metals. The pressure behind the shock also decays with propagation distance. The rate of decay of pressure in case of Al differs with that in Cu metal. Adiabatic sound velocity c and the parameter  both shows a decreasing trend with propagation distance for both materials but the rate of decay is higher for the former.