Restricted Shock Separation in Rocket Nozzles

In overexpanded rocket nozzles the e ow separates from the nozzle wall at a certain pressure ratio of wall pressure to ambient pressure. Flow separation and its theoretical prediction have been the subject of several experimental and theoretical studies in the past decades. Two distinctive e ow separation phenomena, the freeshock and restricted-shock separation, were observed in experiments with nozzles. Both phenomena are discussed in detail, and the system of recompression shocks and expansion waves is described. For the free-shock case three different shock structures in theplume can occur, namely the regular shock ree ection, the Mach disk, or a cap-like shock pattern. Theappearanceofthesedifferentplumepatternsis discussed. Theseshock structuresareconserved for the full-e owing, but overexpanded, nozzle. Numerical results obtained for existing rocket nozzles, e.g., Space ShuttleMain EngineorVulcain, show a qualitativegood agreement with experimental photographs.Furthermore, an explanation for the appearance of restricted shock separation, which has been widely unknown up to now, is given, analyzing why and under what conditions it occurs. The type of nozzle contour strongly ine uences this form of e ow separation, and restricted shock separation also occursin full-scale, thrust-optimized rocket nozzles. Based on the results established for e ow separation, an outlook on the generation of side loads is given.