Approximate solution for the structure of a detonation

Since detonations propagate at supersonic velocities, while deflagrations propagate at low subsonic velocities, the mass flow rate m is much larger for detonations than for deflagrations. Consequently, the dimensionless reaction-rate function F,(z, p), defined in equation (5-34), is much smaller for detonations typically F (i, p) 10 in a deflagration wave and 

Since the change in e through the detonation wave is Ae 1, equations (15) and (5-33) imply that a representative dimensionless distance scale Ac is large compared with unity for detonations (it is of the order of unity for deflagrations). An estimate of the order of magnitude of the left-hand side of equation (5-19) then shows that dx/d 1 (since the change in x through the wave is At = 1), and therefore equation (5-19) implies that, approximately. 

Since e = i = 0 along curve a, no reaction occurs along this curve, and the structure of the upstream part of the wave is obtained by integrating 

Since the characteristic distance over which properties change appreciably is Ac 1, along curve b (the downstream part of the wave) the 

Since equation (5-27) shows that the temperature T depends on both p and t and equation (7) shows that (p (r) is a fairly complicated function, the integral in equation (19) must generally be evaluated numerically. However, equation (19) shows that the asymptotic dependence of t (as ( - oo) is 

For the highly unrealistic case in which the activation energy is zero (Fj = 0) and the pressure and temperature dependences of A and are such that the 

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