Theoretical approach to one-dimensional detonation instability

• Published in: Applied mathematics and mechanics 2016-09, Vol.37 (9), p.1231-1238
• Main Authors: Wang, Chun, Xiang, Gaoxiang, Jiang, Zonglin
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Chemical reactions; Classical Mechanics; Detonation waves; Difference equations; Equilibrium; Fluid- and Aerodynamics; Mach number; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Oscillators; Partial Differential Equations; Rarefaction
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-016-2124-6

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 equilib- rium 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. Key words detonation wave, detonation instability, shock wave, chemical reaction