Numerical simulations were performed to investigate the re-initiation mechanism of a diffracted detonation wave near the critical channel width for a weakly unstable gas. Two scenarios were examined: diffraction of a planar detonation wave and of a cellular detonation wave inside the inlet channel. The results revealed that the critical channel width predicted using a cellular detonation wave is smaller than that predicted using a planar detonation wave. The re-initiation mechanisms are described in detail by tracing massless particles along both the plane of symmetry and the re-initiation path. For planar detonation diffractions, a compression wave is formed in the far field behind the diffracted shock. Re-initiation is closely related to the amplification of this compression wave and its coalescence with the diffracted shock. Depending on the inlet channel width, the strength of the reflected rarefaction wave is responsible for weakening the strength of the compression wave and its coalescence with the diffracted shock, consequently hindering the reaction of particles behind the diffracted shock wave. In cellular cases, the continuous collisions of transverse waves, which generate local explosion sites, sustain detonation wave propagation.

A three-dimensional upwind conservation element and solution element method (CESE) in cylindrical coordinates is first developed to effectively solve the unsteady reactive Euler equations governing a hydrogen–air rotating detonation engine (RDE) with coaxial structures. The effects of the annular width on the structure of the detonation front and the relationship between the thrust and mass flow rate are then investigated. Additionally, RDEs with various injection conditions are systematically analyzed regarding flow patterns and propulsion performance. The results reveal a positive correlation between the specific impulse and the area ratio of the injection slot to the head-end wall. Nevertheless, the specific impulse shows minimal dependence on the injector slot’s location when the area ratio is constant. Ultimately, it is concluded that the area ratio between the injector and the head-end wall is critical in determining the loss of specific impulse.

The linear stability of one-dimensional detonations with one-reaction chemistry coupled with molecular vibration nonequilibrium is investigated using the normal mode approach. The chemical kinetics in the Arrhenius form depend on an averaged temperature model that consists of translational–rotational mode and vibrational mode. The Landau–Teller model is applied to specify the vibrational relaxation. A time ratio is introduced to denote the ratio between the chemical time scale and the vibrational time scale in this study, which governs the vibrational relaxation rate in this coupling kinetics. The stability spectrum of disturbance eigenmodes is obtained by varying the bifurcation parameters independently at a different time ratio. These parameters include the activation energy, the degree of overdrive, the characteristic vibrational temperature, and the heat release. The results indicate that the neutral stability limit shifts to higher activation energy on the vibrational nonequilibrium side with a smaller time ratio, implying that the detonation is stabilized. A similar observation is seen at a lower degree of overdrive. Compared with the above two parameters, the characteristic vibrational temperature plays a minor role in the stabilization of detonation, and no change in the number of eigenmodes is identified throughout the selected range. By plotting the neutral stability curves relating the heat release to the above parameters, the decreases in instability ranges are obviously seen under vibrational nonequilibrium. The thermal nonequilibrium effect on detonation stability is clearly demonstrated. The analysis presented in this paper is ultimately justified by comparing the results with numerical simulation.

In this study, a novel approach for enhancing the stability of rotating detonation waves (RDWs) with the use of a swirling inflow strategy is presented. A series of numerical simulations are carried out by solving the two-dimensional reactive Navier–Stokes equations. The effects of the swirling angle on the stability of the RDWs and the combustion mode are analyzed. The results show that the formation of the burnt gas bumps is suppressed by the implementation of a swirling inflow. The swirling inflow also contributes to an increased homogeneity of the reactant within the fuel refill zone. As a result, a remarkable enhancement of the stability of the RDWs in terms of their oscillations in heights and inclined angles is achieved without an apparent compromise of the heights of the RDWs. The propagation speeds of the RDWs are controllable within a wide range approximately from 81% to 114% of the Chapman–Jouguet detonation speed by adjusting the swirling angle. Moreover, the oscillations in the instantaneous fuel consumption rates of both detonative and deflagrative combustion are dominated by the oscillation in the height of the RDW; hence, the swirling inflow reduces the oscillations in these two fuel consumption rates and subsequently the detonation fraction. Consequently, the smoothness of the performance output in terms of specific impulses can be significantly improved with a reduced standard deviation of oscillation up to 84% by the implementation of swirling inflows, and the averaged specific impulse only encounters a small deficit of no more than 7.4%.