Flow Behind a Chapman-Jouguet Detonation

Fic 1 Flow behind a Chapman-Jouguet detonation for u-/U — 1/3, y = 1.3 (Taylor) 

Fig 2 Pressure in rarefaction wave behind Chapman-Jouguet point according to Taylor and to Langweilcr 

Taylor (Ref 5) obtd a transient flow behind a C-J discontinuity using Riemann equations for polytropic gases. A plot of u/u2 vs x/Ut shown in Fig 12 of Ref 6 (See here Fig 1) is for u2 =U/3, c2 = 2U/3 and y=1.3, where u is material velocity in x direction, u2 is material velocity immediately behind the discontinuity at Ut (U = velocity of C-J wave t = time coordinate) C2 = sound velocity and y = Cj/cv (cp=specific heat at constant pressure and cv = sp heat at constant volume), Taylor calculated pressure in the rarefaction wave behind C-J point and plotted it in F ig given as Fig 12 of Ref 6 (Our Fig 2) 

Langweiler (Ref 3) calculated the flow field behind a C-J detonation by assuming that the products maintain the velocity u2, pressure p2, and density until the passage of a rarefaction shock which reduces the velocity to zero. The rarefaction shock is assigned a velocity of (U +u2)/2. The column of forward-moving gas, which Langweiler calls a detonation head, thus has a length which increases with time and is equal to [U-(U + u2) / 2]t = (U-u t / 2. 

A schematic diagram of the pressure profile accdg to the model is shown as a dotted line in Fig 2 (Ref 6, pp 143-44) 

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