Functional mathematical model of a hydrogen-driven combustion chamber for a scramjet

A functional mathematical model of a hydrogen-driven combustion chamber for a scramjet is described. The model is constructed with the use of one-dimensional steady gas-dynamic equations and parametrization of the channel configuration and the governing parameters (fuel injection into the flow, fuel burnout along the channel, dissipation of kinetic energy, removal of some part of energy generated by gases for modeling cooling of channel walls by the fuel) with allowance for real thermophysical properties of the gases. Through parametric calculations, it is found that fuel injection in three cross sections of the channel consisting of segments with weak and strong expansion ensures a supersonic velocity of combustion products in the range of free-stream Mach numbers $\mathrm{M}_\infty = 6-12$. It is demonstrated that the angle between the velocity vectors of the gaseous hydrogen flow and the main gas flow can be fairly large in the case of distributed injection of the fuel. This allows effective control of the mixing process. It is proposed to use the exergy of combustion products as a criterion of the efficiency of heat supply in the combustion chamber. Based on the calculated values of exergy, the critical free-stream Mach number that still allows scramjet operation is estimated.