Effect of Injection Mach Number on Penetration in a Supersonic Crossflow

For a transverse gaseous jet in supersonic crossflows, the empirical formula implies that the jet penetration height will monotonically increase with the injection Mach number under a certain crossflow condition. However, due to the high backpressure outside the jet orifice, the penetration height will not go to infinity with further increasing the injection Mach number. In this paper, theoretical derivations and numerical simulations were carried out to investigate the effect of injection Mach number on the jet penetration characteristics of a supersonic jet in an Ma 2.95 crossflow. By proposing an approximation that the backpressure outside the orifice is equal to the pressure of the air inflow passing a normal shock, it is predicted that the jet penetration height reaches its maximum at the Mach number when no shock appears in the Laval nozzle under this backpressure. Furthermore, the distribution characteristics of injectant, the shock structures, and near-wall wake region features were obtained and analyzed. The simulation results show that changing the injection Mach number would significantly influence the structures of shocks and the near-wall wake features, which impacts the spatial distribution of injectant. Similar to the jet penetration height, there also exists a turning point in the variation trend of most structures, rather than monotonously changing with the injection Mach number. For the given condition, the quantitative analysis indicates that the penetration height approximately reaches its peak at injection Mach number (Maj)=2.07, which is consistent with the theoretical assumptions.