Zeldovich spontaneous wave

A Zeldovich spontaneous wave, also referred to as Zeldovich gradient mechanism, is a reaction wave that propagates spontaneously in a reacting medium with a nonuniform initial temperature distribution when there is no interaction between different fluid elements. The concept was put forward by Yakov Zeldovich in 1980,^[1] based on his earlier work with his coworkers.^[2] The spontaneous wave is different from the other two conventional combustion waves, namely the subsonic deflagrations and supersonic detonations. The wave, although strictly speaking unrealistic because gasdynamic effects are neglected, is often cited to explain the yet-unsolved problem of deflagration to detonation transition (DDT).^[3]^[4]^[5]^[6]

The mechanism behind the spontaneous wave is readily explained by considering a reaction medium at rest with a nonuniform temperature distribution such that the spatial temperature gradients are small or at least it is not sufficiently large (large temperature gradients will evidently lead to interactions between adjacent fluid elements via heat conduction). Corresponding to each fluid element with a definite temperature value, there is an adiabatic induction period, the time it takes to undergo thermal explosion in the absence of any heat loss mechanism. Thus, each fluid element will undergo thermal explosion at a definite time as if it is isolated from the rest of the gas. A sequence of these successive self-ignitions can be identified as some sort of a reaction front and tracked. The spontaneous wave is influenced by the initial condition and is independent of thermal conductivity and the speed of sound.

^ Zeldovich, Y. B. (1980). Regime classification of an exothermic reaction with nonuniform initial conditions. Combustion and Flame, 39(2), 211-214.
^ Zeldovich, Y. B., Librovich, V. B., Makvilaadze, G. M., Sivashinsky, G. I. (1970). On the development of detonation in a nonuniformly heated gas. Astro. Acta, 15, 313-321.
^ Khokhlov, A. M., & Oran, E. S. (1999). Numerical simulation of detonation initiation in a flame brush: the role of hot spots. Combustion and Flame, 119(4), 400-416.
^ Khokhlov, A. M., Oran, E. S., & Wheeler, J. C. (1997). Deflagration-to-detonation transition in thermonuclear supernovae. The Astrophysical Journal, 478(2), 678.
^ Oran, E. S., & Gamezo, V. N. (2007). Origins of the deflagration-to-detonation transition in gas-phase combustion. Combustion and flame, 148(1-2), 4-47.
^ Ivanov, M. F., Kiverin, A. D., & Liberman, M. A. (2011). Hydrogen-oxygen flame acceleration and transition to detonation in channels with no-slip walls for a detailed chemical reaction model. Physical Review E, 83(5), 056313.

[1] Zeldovich, Y. B. (1980). Regime classification of an exothermic reaction with nonuniform initial conditions. Combustion and Flame, 39(2), 211-214.

[2] Zeldovich, Y. B., Librovich, V. B., Makvilaadze, G. M., Sivashinsky, G. I. (1970). On the development of detonation in a nonuniformly heated gas. Astro. Acta, 15, 313-321.

[3] Khokhlov, A. M., & Oran, E. S. (1999). Numerical simulation of detonation initiation in a flame brush: the role of hot spots. Combustion and Flame, 119(4), 400-416.

[4] Khokhlov, A. M., Oran, E. S., & Wheeler, J. C. (1997). Deflagration-to-detonation transition in thermonuclear supernovae. The Astrophysical Journal, 478(2), 678.

[5] Oran, E. S., & Gamezo, V. N. (2007). Origins of the deflagration-to-detonation transition in gas-phase combustion. Combustion and flame, 148(1-2), 4-47.

[6] Ivanov, M. F., Kiverin, A. D., & Liberman, M. A. (2011). Hydrogen-oxygen flame acceleration and transition to detonation in channels with no-slip walls for a detailed chemical reaction model. Physical Review E, 83(5), 056313.

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