Thermodynamics of Similar Particle-Laden Gas Flows in Convergent-Divergent Nozzles

In integral solid-propellant rocket ramjets, a highly fuel-rich solid-propellant rocket is imbedded or attached to a supersonic combustion ramjet system to act as a fuel-rich hot-gas generator. In connection with the consideration of such ramjets, Thomas (1980) and Billig et al. (1980) have discussed gas-particle flows with high loading ratios. The analysis of such flows becomes particularly simple if a steady, one-dimensional, similar flow is considered under certain additional assumptions. In the present investigation, the assumption of a constant collisional relaxation time, in addition to the assumption of similarity of flow, makes it possible to demonstrate that the gas and particle velocities increase proportional to the axial coordinate x, the temperatures decrease proportional to the square of x, and the gas state changes with a polytropic exponent n which is constant along the flow and can be calculated.