Chapman-Jouguet condition
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The Chapman-Jouguet condition holds approximately in detonation waves. It states that the detonation proceeds at a velocity at which the reacting gases just reach sonic velocity (in the frame of the lead shock) as the reaction ceases.
Chapman and Jouguet originally (c 1890) stated the CJ condition for an infinitesmally thin detonation. A physical interpretation of the condition is usually based on the later modelling (c 1943) by Zel'dovich, Von Neumann and Doring (the so-called ZND model).
In more detail, (in the ZND model) in the frame of the lead shock of the detonation wave, gases enter at supersonic velocity and are compressed through the shock to a high-density, subsonic flow. This sudden change in pressure initiates the chemical (or sometimes, as in steam explosions, physical) energy release. The energy release reaccelerates the flow back to the local speed of sound. It can be shown fairly simply, from the one-dimensional gas equations for steady flow, that the reaction must cease at the sonic ("CJ") plane, or there would be discontinously large pressure gradients at that point.
The sonic plane forms a "choke point" that enables the lead shock, and reaction zone, to travel at a constant velocity, undisturbed by the expansion of gases in the rarefaction region beyond the CJ plane.
This simple one-dimensional model is quite successful in explaining detonations. However, observations of the structure of real chemical detonations show a complex three-dimensional structure, with parts of the wave travelling faster than average, and others slower.
[edit] References
- Cooper, Paul W., Explosives Engineering, New York: Wiley-VCH, 1996. ISBN 0-471-18636-8
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