Abstract

A combined experimental-numerical study was conducted to determine the effect of bleeding on the propagation of plane and converging cylindrical shock waves. A fully 3-D Finite Element code was written for simulating inviscid unsteady flow in various cases of shock tube geometry. The scheme used was implicit time-marching with the Galerkin discretization for spatial coordinate derivatives and multi-step finite difference formulation for time derivatives. Initial trials with 1-D radial flow have shown good agreement with the analytical power law of shock propagation derived by Guderley. The numerical code was first applied to the test case of shock wave strengthening through its reflection from a 15 ̕ramp. The numerical results of the shock front shape were found to be in good agreement with the Schlieren photographs taken for the flow at different time intervals. The numerical code was then applied to the test case of a plane shock interaction with a transverse slit. Experiments were carried out in this case to determine the degree of shock attenuation for shock Mach numbers ranging between 1.2 and 2.5, and slit-duct width ratios varying between 0.25 to 1.0. For this test case, a simplified model--based on the Method of Characteristics and the Chester-Chisnel-Whitham (CCW) theory--was also introduced. Numerical results for the attenuated shock Mach number were found to be in excellent agreement with the experimental results and the approximate analytical model. For the 2-D axisymmetric flows, domains similar to the plane flow cases were used to account for the radial convergence effect. Pressure measurements were also carried out at various radii to determine the pressure time history. The transmitted shock, past the slit, was found to undergo attenuation as in the 2-D case, but combined with strengthening due to area convergence. At the same location downstream of the slit, attenuation was found to be higher than in the 2-D case of similar slit-chamber width ratios.