Properties of Chapman-Jouguet waves

Chapman-Jouguet waves assume a special significance in many systems, particularly those involving detonations. It is therefore of interest to investigate the properties of the Chapman-Jouguet points in greater detail. 

Explicit expressions for the dimensionless downstream properties (in terms of a and y) are easily derived for Chapman-Jouguet waves. For example, if equation (27) is solved for v, giving 

Upper signs correspond to the detonation branch, and lower signs correspond to the deflagration branch. Substitution of equation (31) into equation (30) yields 

The temperature ratio may be computed from T /Tq = pv [see equation (18)] the downstream temperature is found to exceed the upstream temperature at both Chapman-Jouguet points. 

Equation (33) may be used to compute the initial Mach number for Chapman-Jouguet waves. The result is 

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FIGURE 2.6. The dependence of the properties of Chapman-Jouguet waves upon the dimensionless heat-release parameter a, as determined by equations (31)-(34) with y = 1.3. 

Detonation. Past investigators have usually considered that a Chapman-Jouguet detonation wave is the only stable detonation wave that normally exists and have expended most of their analytic efforts in describing the change in thermodynamic properties that occurs across this wave. This is accomplished by use of the equations for conser-... 

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