ANALYTICAL SOLUTION OF THE TYPE-IV SHOCK INTERACTION

An analytical model for the type IV shock interaction in high Mach num ber, calorically perfect air is developed. The model solves the flowfi eld around the transmitted shock, using the oblique shock relations, a nd the how inside the jet, using Prandtl-Meyer waves, The length of th e transmitted shock and jet geometry are derived explicitly by calcula ting the shape of the bow shocks using a continuity methodology, Unlik e previous analytical methods, no empirical or experimental data on th e interaction are required, The model for the jet impingement gives a prediction for the location and value of the peak pressure on the cyli nder, Comparison with experimental results shows good agreement for th e impingement location, peak pressure, and shock shapes, and the calcu lation is performed very quickly with minimal computing resources. A p arametric study is conducted, demonstrating the variation of key inter action 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 numbe r, or cylinder radius. Many trends between the dependent and independe nt variables in this study were apparent, providing useful and insight ful results for design purposes.