Effects of Cowl-Induced Expansion on the Wave Complex Induced by Oblique Detonation Wave Reflection

Oblique detonation wave (ODW) reflection on the upper wall leads to a sophisticated wave complex, whose stability is critical to the application of oblique detonation engines. The unstable wave complex characterized with a continuous moving Mach stem has been observed, but the corresponding re-stability adjusting method is still unclear so far. In this study, the cowl-induced expansion wave based on the model with an upper-side expansion wall is introduced, and the ODW dynamics have been analyzed using the reactive Euler equations with a two-step induction–reaction kinetic model. With the addition of a cowl-induced expansion wave, the re-stabilized Mach stem has been distinguished. This re-stability is determined by the weakened secondary reflection wave of lower wall, while the final location of Mach stem is not sensitive to the position of the expansion corner. The re-stabilized ODW structure is also basically irrelevant to the expansion angle, while it may shift to unstable due to the merging of subsonic zones. Transient phenomena for the unstable state have been also discussed, clarifying fine wave structures further.

Numerical study of wedge-induced oblique detonations in unsteady flow

Oblique detonation waves (ODWs) have been studied widely to facilitate their employment in hypersonic propulsion, but the effects of continuous unsteady inflow have never been addressed so far. Thus, the present study investigates wedge-induced oblique detonations in unsteady flow via numerical simulations based on the reactive Euler equations with a two-step induction–reaction kinetic model. As a first step, the chemical and flow parameters are chosen for the simplest structure such that the ODW initiation occurs under a smooth transition with a curved shock. After a steady ODW with smooth initiation transition is established, the inflow is then subject to a continuous sinusoidal density/temperature disturbance. Cases with single-pulse inflow variation are also simulated to clarify whether the observed phenomena are derived solely from the continuous disturbance. Two aspects are analysed to investigate the features of ODWs in unsteady flow, namely, the formation of triple points on the surface, and the movement of the reactive front position. On the formation of triple points, the continuous disturbance generates at most one pair of triple points, less than or equal to the number of triple points in single-pulse cases. This indicates that the effects of continuous disturbance weaken the ability to generate the triple points, although there appear more triple points convected downstream on the surface at any given instant. On the movement of the reactive front, oscillatory behaviours are induced in either single-pulse or continuous disturbance cases. However, more complicated dynamic displacements and noticeable effects of unsteadiness are observed in the cases of continuous disturbance, and are found to be sensitive to the disturbance wavenumber, $N$. Increasing $N$ results in three regimes with distinct behaviours, which are quasi-steady, overshooting oscillation and unstable ODW. For the quasi-steady case with low $N$, the reactive front oscillates coherently with the inflow disturbance with slightly higher amplitude around the initiation region. The overshooting oscillation generates the most significant variation of downstream surface in the case of modest $N$, reflecting a resonance-like behaviour of unsteady ODW. In the case of high $N$, the disturbed ODW surface readjusts itself with local unstable features. It becomes more robust and the reactive front of the final unstable ODW structure is less susceptible to flow disturbance.

On a stabilization mechanism for low-velocity detonations

We use numerical simulations of the reactive Euler equations to analyse the nonlinear stability of steady-state one-dimensional solutions for gaseous detonations in the presence of both momentum and heat losses. Our results point to a possible stabilization mechanism for the low-velocity detonations in such systems. The mechanism stems from the existence of a one-parameter family of solutions found in Semenko et al. (Shock Waves, vol. 26 (2), 2016, pp. 141–160).

Evolution of detonation formation initiated by a spatially distributed, transient energy source

Detonations usually form through either direct initiation or deflagration-to-detonation transition (DDT). In this work, a detonation initiation process is introduced that shows attributes from each of these two processes. Energy is deposited into a finite volume of fluid in an amount of time that is similar to the acoustic time scale of the heated fluid volume. Two-dimensional simulations of the reactive Euler equations are used to solve for the evolving detonation initiation process. The results show behaviour similar to both direct initiation and DDT. Localized reaction transients are shown to be intimately related to the appearance of a detonation. Thermomechanical concepts are used to provide physical interpretations of the computational results in terms of the interaction between compressibility phenomena on the acoustic time scale and localized, spatially resolved, chemical energy addition on a heat-addition time scale.

Theory of weakly nonlinear self-sustained detonations

We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier–Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.

Adaptive Multiresolution Computations Applied to Detonations

A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and dynamic space adaptivity is introduced using multiresolution analysis. A time splitting method of Strang is applied to be able to consider stiff problems while keeping the method explicit. For time adaptivity an improved Runge–Kutta–Fehlberg scheme is used. Applications deal with detonation problems in one and two space dimensions. A comparison of the adaptive scheme with reference computations on a regular grid allows to assess the accuracy and the computational efficiency, in terms of CPU time and memory requirements.

Mean structure of one-dimensional unstable detonations with friction

This investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge–Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies.