Effect of droplet diameter on oblique detonations with partially pre-vaporized n–heptane sprays

Liquid fuels have been widely used in propulsion systems for their higher energy density and easier storage, but there are few studies on oblique detonation engines (ODEs) using the liquid fuels. In this study, oblique detonation waves (ODWs) in partially pre-vaporized n–heptane sprays are simulated, using a hybrid Eulerian–Lagrangian algorithm with a skeletal chemical mechanism, to facilitate liquid fuels applications in ODE. A novel phenomenon has been observed, illustrating that the ODW initiation lengths in pre-vaporized n–heptane sprays firstly increase and then decrease with increasing fuel droplet diameters. It is found out that an increase of droplet diameter can increase the transferred heat amount caused by droplets evaporation and lower the inflow temperature, so leading to the increase of ODW initiation length firstly. However, extremely large droplet diameter can markedly reduce the heat transfer rate of the droplet and its surrounding mixture, and the compressed gas-stream behind oblique shock wave has a higher temperature that accelerate the induction chemical reaction and results in a decrease in the ODW initiation length. Furthermore, the unsteady oscillations of ODW initiation structures are also observed even for a steady inflow, which involves the periodic hot spots, normal detonation waves and their evolutions. Some factors causing the unsteady behavior of ODWs are tested through a sensitivity analysis method of the initiation lengths. Through the analyzation, the fluctuation of the post-shock temperatures is the main factor causing the fluctuation of initiation lengths, revealing that inhomogeneous heat loss by evaporation of dispersed liquid droplets is the main reason causing the unsteady behaviors of ODWs and the competition between heat release by chemical reactions and heat loss by evaporation determines the steadiness of ODWs.