In many applications of slot injection in supersonic or hypersonic flow, the static pressures of the external and injectant streams are not matched. We have developed a simplified analysis of cases with initial pressure mismatch for tangential slot injection into a hypersonic (or supersonic) external flow having a thick, turbulent initial boundary layer including the effects of turbulent mixing, viscid/inviscid interaction, skin friction and heat transfer and heat release for reactive injectants. The treatment uses hypersonic (or supersonic) small disturbance theory, a power law shape for the initial boundary layer velocity profile and a Crocco integral to get the temperature profile, a turbulent entrainment model including the effect of a Convective Mach Number, a quasi-ID assumption in the mixing and burning region, an instantaneous, one-step heat release model and simple models of skin friction and heat transfer. The initial adjustments at the slot lip and further interactions with the viscous regions by waves reflected off the lower wall are treated with weak, locally inviscid waves. Laminar cases can also be handled. Good agreement of predictions with experiment for several experimental cases for gross flowfield variables such as p(x), A(x), M(x), T 0 (x), etc. was achieved. Both over-and under-expanded cases were treated. The calculations need only about 1-2 seconds of CPU time on an Amdahl 5890 class computer. Lastly, calculations for combustor flowfields for a generic Scramjet vehicle at a flight Mach number of 10 with 0.8 < pj/p t < 1.25 are given and discussed.
Nomenclaturea Slot height A Area ot the 1D viscous region Ci-2 Mixing rate constants Cf Skin friction coefficient based on ID variables C p Specific heat f s Stoichiometric fuel/air ratio hf Heating value of the fuel Η Stagnation enthalpy m 1D average mass flow dm/dx Entrainment rate Μ 1D average Mach number Mj Slot injection Mach number M[ Freest ream Mach number Pr Prandtl number ρ Static pressure q Dynamic pressure q w Wall heat transfer rate St Stanton number Τ 1D average static temperature To ID average total temperature Tw Wall temperature Taw Adiabatic wall temperature u ID average velocity
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