BRHS /
## Chapman-Jouget detonationOne-dimensional detonation theory was developed independently by Chapman (ChapmanDL:1899) and Jouguet (JougetE:1906) and was based on the preceding shock theory, with the inclusion of an addition energy term corresponding to the energy released by chemical reaction. In this theory, the C-J theory, the chemical reaction is assumed to occur infinitely fast. Further manipulation of equations leads to the following expression q_{CJ} =\frac{\left(M_{CJ}^{2} -1\right)^{2} a_{1}^{2} }{2\left(\gamma _{b} -1\right)M_{CJ}^{2} \left(\gamma _{b} +1\right)},
which relates the resulting wave Mach number M_{CJ}, the corresponding energy release q_{CJ}, the sound speed in the initial reactants a_{1} and the ratio of specific heats of the product gases \gamma_{b}. In a CJ detonation, the reactants at an initial pressure, temperature and density are transformed instantaneously to products at a final pressure, temperature and density. The CJ theory gives a remarkably accurate prediction of detonation velocities based only on a knowledge of the initial conditions and despite the actual complexity of a real detonation.
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