Analytical Solution of the Type IV Shock Interaction

Abstract

An analytical model for the type IV shock interaction in high Mach number, calorically perfect air is developed. The model solves the e owe eld around the transmitted shock, using the oblique shock relations, and the e ow inside the jet, using Prandtl ‐ Meyer waves. The length of the transmitted shock and jet geometry are derived explicitly by calculating the shape of the bow shocks using a continuity methodology. Unlike previous analytical methods, no empirical or experimental data on the interaction are required. The model for the jet impingement gives a prediction for the location and value of the peak pressure on the cylinder. Comparison with experimental results shows good agreement for the impingement location, peak pressure, and shock shapes, and the calculation is performed very quickly with minimal computing resources. A parametric study is conducted, demonstrating the variation of key interaction results such as peak pressure, impingement location and lengths of the transmitted shock, and the terminating shock of the jet, as a result of impinging shock location and strength, freestream Mach number, or cylinder radius. Many trends between the dependent and independent variables in this study were apparent, providing useful and insightful results for design purposes.