Interpretation of wake instability at slip line in rotating detonation

TL;DR

This study investigates the wake instability at the slip line in rotating detonation, revealing a unique wake profile caused by transition shocks, and identifies two unstable modes through stability analysis and simulations.

Contribution

It provides a detailed simulation and analysis of wake instability mechanisms at the slip line in rotating detonation, highlighting differences from typical mixing layer instabilities.

Findings

Wake profile is distinct from typical mixing layers.

Transition shock causes wake formation at the slip line.

Two unstable modes with different shapes and velocities were identified.

Abstract

In studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolution exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilized to analyze the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differs from the canonical ones in typical mixing layers.