Flow patterns and performance optimization of underwater two-phase ramjet engines with convergent–divergent nozzles

In this study, a mathematical model of bubbly flow incorporating choking and internal shock waves is developed. This work presents the first systematic analysis of the flow patterns and their influencing factors of the underwater two-phase ramjet engine. The detailed flow field characteristics of shock-free choked flow inside the engine are obtained, and the effects of structural parameters and operating parameters on the propulsion performance are revealed. The results show that the vehicle speed and initial gas void fraction control the occurrence of choked flow and internal shock waves, thereby altering the internal flow patterns. The nozzle throat-to-inlet area ratio significantly influences the classification of flow patterns and global flow field characteristics under shock-free choked flow. An increase in this ratio extends the operating range of shock-free choked flow, enhances overall pressure and velocity, and reduces the gas void fraction within the divergent section. Compared to convergent nozzle engines, convergent–divergent nozzle engines improve thrust and specific impulse under shock-free choked flow by increasing the mass flow rate and enabling supersonic expansion of the bubbly flow in the divergent section. However, their performance deteriorates under subsonic flow or internal shocks. By controlling the throat area and exit area of the convergent–divergent nozzle, shock-free choked flow can be achieved at various vehicle depths and speeds, enabling optimal propulsion performance.