Theoretical approach to one-dimensional detonation instability

doi:10.1007/s10483-016-2124-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1231-1238.doi: https://doi.org/10.1007/s10483-016-2124-6

Theoretical approach to one-dimensional detonation instability

Chun WANG, Gaoxiang XIANG, Zonglin JIANG

State Key Laboratory of High Temperature Gas Dynamics, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2015-11-13 修回日期:2016-02-04 出版日期:2016-09-01 发布日期:2016-09-01
通讯作者: Chun WANG E-mail:wangchun@imech.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 90916028) and the Innovation Program of the State Key Laboratory of High Temperature Gas Dynamics of Institute of Mechanics, Chinese Academy of Sciences

Theoretical approach to one-dimensional detonation instability

Chun WANG, Gaoxiang XIANG, Zonglin JIANG

State Key Laboratory of High Temperature Gas Dynamics, Chinese Academy of Sciences, Beijing 100190, China

Received:2015-11-13 Revised:2016-02-04 Online:2016-09-01 Published:2016-09-01
Contact: Chun WANG E-mail:wangchun@imech.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 90916028) and the Innovation Program of the State Key Laboratory of High Temperature Gas Dynamics of Institute of Mechanics, Chinese Academy of Sciences

摘要/Abstract

摘要：

Detonation instability is a fundamental problem for understanding the microbehavior of a detonation front. With the theoretical approach of shock dynamics, detonation instability can be mathematically described as a second-order ordinary difference equation. A one-dimensional detonation wave can be modelled as a type of oscillators. There are two different physical mechanisms controlling the behaviors of a detonation. If the shock Mach number is smaller than the equilibrium Mach number, the fluid will reach the sonic speed before the end of the chemical reaction. Then, thermal chock occurs, and the leading shock becomes stronger. If the shock Mach number is larger than the equilibrium Mach number, the fluid will be subsonic at the end of the chemical reaction. Then, the downstream rarefaction waves propagate upstream, and weaken the leading shock. The above two mechanisms are the basic recovery forces toward the equilibrium state for detonation sustenance and propagation. The detonation oscillator concept is helpful for understanding the oscillating and periodic behaviors of detonation waves. The shock dynamics theory of detonation instability gives a description of the feedback regime of the chemical reaction, which causes variations of the leading shock of the detonation.

关键词: chemical reaction, detonation instability, shock wave, detonation wave

Abstract:

Key words: shock wave, chemical reaction, detonation wave, detonation instability

中图分类号:

Chun WANG, Gaoxiang XIANG, Zonglin JIANG. Theoretical approach to one-dimensional detonation instability[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1231-1238.

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Theoretical approach to one-dimensional detonation instability

Theoretical approach to one-dimensional detonation instability

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