Numerical study of wedge-induced oblique detonations in unsteady flow

Abstract

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.