Interpretation of wake instability at slip line in rotating detonation

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 the 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 evolutions 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 main unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilised to analyse 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 differ from the canonical ones in typical mixing layers.

KEYWORDS:

• Rotating detonation
• slip line
• Kelvin–Helmholtz instability
• wake instability

Acknowledgements

The second author is thankful to the discussion with Prof. Frank Lu and Prof. Chiyung Wen.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Ministry of Science and Technology of the People’s Republic of China: [Grant Number 2014CB744100] and National Science Foundation of China: [Grant Number 91541105].

Notes on contributors

Pengxin Liu

Pengxin Liu holds a Ph.D. degree from the Department of Fluid Dynamics. Pengxin Liu's research interests are high-order finite difference scheme and rotating detonation simulation.

Qin Li

Qin Li was once a researcher in State Key Laboratory of Aerodynamics and now is a professor in the School of Aerospace Engineering of Xiamen University.

Zhangfeng Huang

Zhangfeng Huang is Professor in the School of Mechanical Engineering.

Hanxin Zhang

Hanxin Zhang is Academician of Chinese Science Academy.