Chapman-Jouguet condition
Encyclopedia
The Chapman–Jouguet condition holds approximately in detonation
waves in high explosives. It states that the detonation propagates at a velocity
at which the reacting gases just reach sonic velocity (in the frame of the lead shock wave
) as the reaction ceases.
Chapman and Jouguet originally (c. 1890) stated the condition for an infinitesimally thin detonation. A physical interpretation of the condition is usually based on the later modelling (c. 1943) by Zel'dovich, von Neumann
and W. 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 explosion
s, physical) energy release. The energy release re-accelerates 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 gradient
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 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.
Biography of David Leonard Chapman (1869–1958):
Biography of Yakov Borissovich Zel'dovich (1914 - 1987):
(2) Wikipedia: http://en.wikipedia.org/wiki/Yakov_Borisovich_Zel'dovich
Neumann, John von, "Theory of detonation waves,"
Biography of John von Neumann (1903–1957):
Biography of Werner Döring (1911–2006):
Detonation
Detonation involves a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations are observed in both conventional solid and liquid explosives, as well as in reactive gases...
waves in high explosives. It states that the detonation propagates at a velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
at which the reacting gases just reach sonic velocity (in the frame of the lead shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
) as the reaction ceases.
Chapman and Jouguet originally (c. 1890) stated the condition for an infinitesimally thin detonation. A physical interpretation of the condition is usually based on the later modelling (c. 1943) by Zel'dovich, von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
and W. 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 explosion
Steam explosion
A 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 re-accelerates 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 gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that 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 rarefaction
Rarefaction
Rarefaction 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.
Chapman-Jouguet model: original research papers
- Chapman, David Leonard, "On the rate of explosion in gases," Philosophical Magazine, Vol. 47, pp. 90–104 (1899).
Biography of David Leonard Chapman (1869–1958):
- Bowen, E. J., "David Leonard Chapman. 1869–1958," Biographical Memoirs of Fellows of the Royal Society, Vol. 4, pp. 34-44 (Nov., 1958)
- Jouguet, Jacques Charles Emile, "Sur la propagation des réactions chimiques dans les gaz" [On the propagation of chemical reactions in gases], Journal des Mathématiques Pures et Appliquées, Series 6, Vol. 1, pp. 347–425 (1905), continued in Vol. 2, pp. 5–85 (1906).
- Biography of Jacques Charles Emile Jouguet (1871–1943) [in French], http://www.annales.org/archives/x/jouguet.html .
ZND model: original research papers
- Zel'dovich, Yakov Borissovich, "On the theory of the propagation of detonation in gaseous systems," Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki [Journal of Experimental and Theoretical Physics, JETP], Vol. 10, pp. 542–568 (1940). Translated into English in National Advisory Committee for Aeronautics Technical Memorandum No. 1261 (1950).
Biography of Yakov Borissovich Zel'dovich (1914 - 1987):
- (1) Ginzburg, V. L., "Yakov Borissovich Zel'dovich 8 March 1914 – 2 December 1987," Biographical Memoirs of Fellows of the Royal Society, Vol. 40, pp. 430–441 (November 1994).
(2) Wikipedia: http://en.wikipedia.org/wiki/Yakov_Borisovich_Zel'dovich
Neumann, John von, "Theory of detonation waves,"
- (1a) Office of Scientific Research and Development, Report No. 549, Ballistic Research Laboratory File No. X-122. Aberdeen Proving Ground, Maryland, 1942.
- (2a) Progress Report to the National Defense Research Committee, Division B, OSRD-549 (April 1, 1942. PB 31090) 34 pages. (4 May 1942).
- (3a) John von Neumann, Collected Works, edited by A. J. Taub, Vol. 6 [N.Y., N.Y.: Macmillan, 1942].
- (4a) John von Neumann, Collected Works, edited by A. J. Taub, Vol. 6 [Elmsford, N.Y.: Permagon Press, 1963], pp. 178–218.
Biography of John von Neumann (1903–1957):
- Wikipedia: http://en.wikipedia.org/wiki/Von_Neumann
- Döring, Werner, "Über Detonationsvorgang in Gasen [On the detonation process in gases]," Annalen der Physik [Annals of Physics], Vol. 43, pp. 421–436 (1943).
Biography of Werner Döring (1911–2006):
- Wikipedia [in German]: http://de.wikipedia.org/wiki/Werner_D%C3%B6ring