The
Chapman-Jouguet condition holds approximately in
detonationDetonation is a process of combustion in which a supersonic shock wave is propagated through a fluid due to an energy release in a reaction zone. It is the more powerful of the two general classes of combustion, the other one being deflagration. In a detonation, the shock compresses the material...
waves. It states that the detonation proceeds at a
velocityIn physics, velocity is the rate of change of position. It is a vector physical quantity; both speed and direction are required to define it. In the SI system, it is measured in meters per second: or ms-1. The scalar absolute value of velocity is speed...
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 Döring (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.
The
Chapman-Jouguet condition holds approximately in
detonationDetonation is a process of combustion in which a supersonic shock wave is propagated through a fluid due to an energy release in a reaction zone. It is the more powerful of the two general classes of combustion, the other one being deflagration. In a detonation, the shock compresses the material...
waves. It states that the detonation proceeds at a
velocityIn physics, velocity is the rate of change of position. It is a vector physical quantity; both speed and direction are required to define it. In the SI system, it is measured in meters per second: or ms-1. The scalar absolute value of velocity is speed...
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 Döring (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 explosionA steam explosion is a violent boiling or flashing of water into steam, occurring when water is either superheated, rapidly heated by fine hot debris produced within it, or the interaction of molten metals A steam explosion (also called a littoral explosion, or fuel-coolant interaction, FCI) is a...
s, 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 discontinuously large pressure
gradientIn vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
s 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
rarefactionRarefaction is the reduction of a medium's density, or the opposite of compression.A natural example of this is as a phase in a sound wave or phonon. Half of a sound wave is made up of the compression of the medium, and the other half is the decompression or rarefaction of the medium.Another...
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.