摘要One-dimensional detonation waves are simulated with the three-step chain branching reaction model, and the instability criterion is studied. The ratio of the induction zone length and the reaction zone length may be used to decide the instability, and the detonation becomes unstable with the high ratio. However, the ratio is not invariable with different heat release values. The critical ratio, corresponding to the transition from the stable detonation to the unstable detonation, has a negative correlation with the heat release. An empirical relation of the Chapman–Jouguet Mach number and the length ratio is proposed as the instability criterion.
Abstract：One-dimensional detonation waves are simulated with the three-step chain branching reaction model, and the instability criterion is studied. The ratio of the induction zone length and the reaction zone length may be used to decide the instability, and the detonation becomes unstable with the high ratio. However, the ratio is not invariable with different heat release values. The critical ratio, corresponding to the transition from the stable detonation to the unstable detonation, has a negative correlation with the heat release. An empirical relation of the Chapman–Jouguet Mach number and the length ratio is proposed as the instability criterion.
[1] Kailasanath K 2003 AIAA J. 41 145
[2] Erpenbeck J J 1962 Phys. Fluids 5 604
[3] Erpenbeck J J 1964 Phys. Fluids 7 684
[4] Lee H I and Stewart D S 1990 J. Fluid Mech. 216 103
[5] Short M and Stewart D S 1997 J. Fluid Mech. 340 249
[6] He L and Lee J H S 1995 Phys. Fluids 7 1151
[7] Gamezo V N, Desbordes D, Oran E S 1999 Shock Waves 9 11
[8] Han G L, Jiang Z L, Wang C and Zhang F 2008 Chin. Phys. Let. 25 2125
[9] Ng H D, Radulescu M I, Higgins A J, Nikiforakis N and Lee J H S 2005 Combust. Theory Model. 9 385
[10] Short M and Quirk J J 1997 J. Fluid Mech. 339 89
[11] Ng H D and Lee J H S 2003 J. Fluid Mech. 476 179
[12] Toro E F 1999 Riemann Solvers and Numerical Methods for Fluid Dynamics (Berlin: Springer) p 459
2011, Vol. 28 
