Supersonic Reacting Jet Flows from a Three-Dimensional Divergent Conical Nozzle

The study of supersonic jet flows from a nozzle is significant in practical applications in jet engine and rocket technology. This paper studies supersonic reacting jet flows from a three-dimensional (3D) divergent conical nozzle. We assume that the flow is governed by 3D steady Zeldovich–von Neumann–Döring combustion equations with cylindrical symmetry and that the state of the flow is given at the inlet of the nozzle. When the nozzle is surrounded by a vacuum, we obtain a global continuous and piecewise smooth supersonic reacting jet flow expanding into the vacuum from the nozzle. When the nozzle is surrounded by a static atmosphere with a lower pressure than the pressure of the flow at the exit of the nozzle, we obtain a local continuous and piecewise smooth supersonic reacting jet flow expanding into the atmosphere from the nozzle. Moreover, we also give an explanation for the formation of intercepting shocks in supersonic jets expanding into a lower pressure environment, which is stated in section 148 in the famous book Supersonic Flow and Shock Waves and is verified by physical experiments. The flow patterns constructed in the paper may be used as background solutions for more general supersonic jet flow problems. The result in the paper is also suitable for nonreacting supersonic jet flows.