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Converging–diverging nozzles are common in rocket engine systems to increase the exhaust velocity and improve thrust performance. In this study, we focused on the acceleration of subsonic burned gas without a structural throat via detonation to realize a simple and compact engine. We developed and tested a rotating detonation engine (RDE) without a throat and with a diverging channel (constant diverging angle α=5 deg). Gaseous C2H4 and O2 were used as the propellants, and the mass flow rate ranged from 62 to 134 g/s in the combustion tests under low back-pressure conditions. We measured pressure and thrust, as well as high-speed imaging of self-luminescence of the combustion and imaging of the exhaust plume. The pressure at the exit was less than one-fifth of the maximum pressure in the RDE, significantly below the value for a sonic flow. The results suggested that the exhaust flow was supersonic, with values up to Mach 1.7, without the need of a converging section within the engine. In addition to the estimated Mach number from the measured pressure, the exhaust plume images coherently indicated the existence of supersonic exhaust.

This study evaluated the propulsion performance of a nozzleless, cylindrical rotating detonation engine (RDE). Using a C2H4–O2 mixture, the RDE was tested in a low-back-pressure environment at propellant mass flow rates of 8–45 g/s. In high-speed imaging of the self-luminescence within the combustor, rotating luminous regions were observed at mass flow rates above 22 g/s. Measured pressure distributions suggest that burned gas reached sonic velocity at the combustion chamber outlet. This paper proposes the structure of internal flow in the RDE and confirms that calculated pressure distribution based on the structure was close to the experimental distribution. This study also estimated the RDE’s thrust by pressure and momentum exchange and confirmed it by experimental measurement. Moreover, the theoretical thrust calculated under the assumption that exhaust is a sonic flow agreed with the load cell thrusts, suggesting that RDE combustion is perfectly completed inside the chamber. Specific impulses are 80–90% of specific impulses for ideal correct expanded flow for all mass flow rates, and its value was close to that of an annular RDE. In addition, RDE performance will increase by about 20% if the RDE is equipped with a divergent nozzle and the gas is correctly expanded to back pressure.

Gas dynamics in a simplified pulse detonation engine (PDE) was theoretically analyzed. A PDE was simplified as a straight tube with a fixed cross section. One end of the tube was closed, namely, this end was the thrust wall, and the other end was open. A detonation wave was initiated at the closed end and simultaneously started to propagate toward the open end. When the detonation wave broke out from the open end, a rarefaction wave started to propagate from the open end toward the closed end. This rarefaction wave was reflected by the closed end. By considering this rarefaction wave to be self-similar in the analysis of the interference between this rarefaction wave and its reflection from the closed end, we analytically formulated the decay portion of the pressure history at the closed end (thrust wall) without any empirical parameters. By integrating the obtained pressure history at the thrust wall with respect to time, important performance parameters of a PDE were also formulated. The obtained formulas were compared with numerical and experimental results and agreed with them very well.

An effective nondimensional parameter, referred to as the first Damkohler parameter, is proposed to quantitatively classify the unsteady flow regime of shock-induced combustion around a hypervelocity spherical projectile in the stoichiometric hydrogen-air mixture. The parameter consists of the ratio of the fluid characteristic timescale to the chemical characteristic timescale. The fluid characteristic time is defined as a projectile diameter divided by a speed of sound behind the normal segment of the steady bow shock. The chemical characteristic time is defined as a temperature behind the normal segment of the steady bow shock over the maximum temperature increase per unit time for the exothermicity. The temperature increase for the exothermicity is estimated by the time integration of the species equations in the zero dimension in space. The proposed first Damkohler number can be analytically computed by the chemical and fluid characteristics only, without ballistic range experiments or expensive simulations on high-performance computers. The parameter is quantitatively characterized from the two distinct flow regimes observed in the experimental and numerical results. Also, features of the transition between two regimes are clarified by changing the projectile diameter, the projectile speed, and the test gas pressure.

Unsteady combustion around a spherical projectile in supersonic flows is numerically studied using the simplified two-step chemical reaction model consisting of the induction and the exothermic reactions. A series of simulations indicates that the intensity of the concentration of the heat release is a key parameter to determine the regime of the unsteady flowfield. Flow features of the unsteady combustion with low-frequency and high-amplitude oscillation, which is called the large-disturbance regime, are reproduced when the concentration of the heat release of the chemical reaction is high. Mechanism of the large-disturbance regime is clarified based on the histories of the density and pressure profiles on the stagnation streamline and the flowfield in front of the projectile body. The period and amplitude of the oscillation corresponding to the shock pressure behind the how shock agree with experimental observations, and the reproduction of the large-disturbance regime in the present simulation is confirmed.