On the Similarity of the Pseudo-Shock Structure

We experimentally investigate the dependence of the steady state structure, such as pressure rise and length, of shock trains on the conditions approaching a pseudo-shock generated by mechanically imposing a range of pressure ratios across a supersonic isolator. A range of Ma, θ, Re_θ and confinement ratio C_θ approaching the pseudo-shock are considered. A combination of wall static pressure measurements, schlieren and PIV is used. It is found that the impact of approach conditions can adequately be captured by the Waltrup and Billig correction factor Q = (Ma² − 1)Re_θ¼C_θ^-½ based on local approach conditions. Once corrected by Q, the axial length of the shock train is nearly constant and the pressure raise is nearly a constant fraction of the value across a normal shock at the approach Ma. Therefore, the additional pressure raise has to be provided by the mixing region, which ineffectively provides flow compression, resulting in an elongation of the pseudo-shock. Overall, the pressure raise per unit length along the shock train is independent of approach conditions and approximately three times larger than that along the mixing region, which still exhibits some Ma dependence.