Strong and Weak Detonation

Detonation, Strong and Weak. This subject is discussed by Evans 8t Ablow (Ref 2, pp 141-42), but prior to this it. is necessary to discuss the existence and uniqueness of classes of reaction waves for specific boundary conditions , as given in the book of Courant 8c Friedrichs (Ref 1, pp 215-22) and in Ref 2 

Let the rear boundary of reaction wave move with.a specific velocity Up along the line P in the x,t-plane as in Fig 9 of Ref 2 (our Fig 1). Then initial data are prescribed along two lines. One is the x-axis, which is spacelike with. respect to the material behind it and carries the quantity u = 0 (if. the material is initially at rest), and p=p0. The other line is P, which is timelike, or subsonic to the gas flow, since it is identical with the path of the adjacent gas particles it carries velocity Up. The discontinuity of the reaction wave is represented by the line W. The deductions on uniqueness which. can be Used for non-reactive flow (See Ref 2, pp 136-37) cannot be applied here directly because of the interference of the unknown discontinuity W. 

They can, however, be applied separately to the sectors between the x-axis and W, and betw W and P. There are four cases, according to whether the flow relative to W is supersonic or subsonic before or behind the front. The directions of the character -istics on either side of W relative to the 

Thus the sound speed along the piston for this solution of the flow will have the value 

35 up 2 + c2 an pressure pp and ensity will have appropriate values of state, such as detd by eq  

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Strong and weak detonation waves are described in our writeup under Detonation, Strong and Weak , p D576... 

FIGURE 6.2. Schematic diagram illustrating the properties of various Rayleigh lines. End states at points a, b, c, d correspond to strong and weak detonations and weak and strong deflagrations, respectively. 

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