Numerical simulations and theoretical analysis of the forward shock wave in a non-premixed air-breathing rotating detonation combustor

The forward shock wave induced by the detonation wave propagates in the inlet and restrains the air from being injected into the rotating detonation engine, and the stable continuous propagation of the detonation wave is affected. Numerical simulation and theoretical derivation of air flow velocity and detonation wave height were carried out in a rotating detonation combustor. The influence of the forward shock wave on air flow velocity and air flow velocity on detonation wave height was analyzed. A non-premixed air-breathing rotating detonation combustor was numerically simulated with the two-dimensional Navier–Stokes equations and a kerosene/air reaction model based on the RYrhoCentralFoam solver. Analytical equations were derived and validated to calculate the air flow velocity across the forward shock wave and the height of the detonation wave. The results show that the air flow velocity across the forward shock wave is inversely proportional to the detonation wave velocity, incoming flow temperature, and pressure ratio at the forward shock wave. In addition, the angle of the forward shock wave is inversely proportional to the velocity of the detonation wave and incoming flow and is proportional to the incoming flow temperature and the pressure ratio. The forward shock wave leads to a blocked zone of injection in the combustor, as the inflow velocity decreases or even reverses across the shock wave. As a result, the forward shock wave induced by the detonation wave restrains the recovery of the reactant fill zone, which has an influence on the height of the detonation wave.