Chapman–Jouguet condition

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 explosions, 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 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.

References

• Cooper, Paul W., Explosives Engineering, New York: Wiley-VCH, 1996. ISBN 0-471-18636-8

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