Jouguet Wave and Flow Behind it

Detonation, Chapman-Jouguet Wave and Flow Behind It. Accdg to Evans Ablow (Ref 6), the C-J hypothesis is supported by the agreement betw calcd and observed deton properties under exptl conditions which make the one-dimensional approxi- 

In a somewhat similar thermodynamic argument, Scorah (Ref 2) stated that the work content for the C-J detonation state corresponds to a maximum degradation of energy. Zel dovich (Ref 4) demonstrated the unsatisfactory nature of the thermodynamic arguments by remarking that the increase in entropy across a shock is not sufficient to guarantee that a shock will form. A piston which compresses the gas is also necessary (Ref 6, p 142) 

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) 

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F ow Laws of Detonation. See J.F. Roth, Explosi vst 1958, 23-31 45—54, "Die ele-mentare Ableirung der StrSmungsgesetze der Detonation" (The elementary derivation of the flow laws of detonation). See also Detonation, Chapman-Jouguet Wave and Flow Behind It in Vol 4, pp D236-L to D237-L... 

Detonation, Chapman-Jouguet wave and flow behind it 4 D236... 

For the purpose of studying the pressures and temperatures caused by a detonation, it is sufficient to ignore the detonation wave structure and consider it as a thin surface, a discontinuity. Chapman and Jouguet assumed that the detonation traveled at a speed such that the flow behind the detonation was sonic relative to the detonation. With this assumption one can compute a unique detonation speed for each hydrogenrair mixture, and find the corresponding temperature and pressure behind the detonation wave. The results are shown in Figures 4 6-12 and 4.6-13. It is an experimental fact that the measured speeds of detonations are... 

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