Numerical study of wall cooling effects on transition between shock structures in a rocket propulsion nozzle

A numerical study is performed to study the effect of nozzle wall cooling on transition between two different shock structures such as free shock separation and restricted shock separation in an axisymmetric thrust-optimized contour nozzle. In this study, cooling of nozzle wall which is associated to the first half of nozzle length is concerned, and at different cooling rates, the transition between shock structures, hysteresis cycle, and also plateau pressure ratio at which the transition occurs are characterized. To do this, a two-dimensional numerical calculation is accomplished utilizing the commercial CFD software, FLUENT. Validity of current numerical model is confirmed by comparison of nozzle wall pressure, hysteresis cycle, and plateau pressure ratio with experimental and previously published works as well as applying simple energy balance. Numerical results show that the increase in cooling rate causes the transition between shock structures and thus hysteresis cycle to appear at lower values of pressure ratio. It is found that, in the case of nozzle wall cooling, a single point could be realized for transition between shock structures. It is also shown that the effect of nozzle wall cooling is to reduce the plateau pressure ratio at which the transition happens.