Chapman-Jouguet detonations stability

Pukhnachev (Ref 26) made a stability analysis of Chapman-Jouguet detonations to clarify the development of spinning detonations. The phenomena leading to them cannot be described by solution of simple hydrodynamic and reaction-kinetic equations for flat detonation fronts. The analysis was based on previous detonation stability analyses by Shchelkin et al with constant supersonic flow postulated along the z-axis at z <0. There is a sharp discontinuity at z=0, followed by the combustion zone. 

It was found also that the front of the reaction zone coincides with the front of self-ignition of gas warmed by the shock wave) 26) V.V. Pukhnachev, ZhPrikl-Mekhan i TekhnFiz No 6, 66-73(1963) (Stability of Chapman-Jouguet detonation)... 

It should be understood that since the stability predictions involve reaction-rate properties, planar Chapman-Jouguet detonations are stable for suitable rate functions. For example, if the rate of heat release decreases monotonically with an increasing extent of reaction behind the shock, then the mechanism for the instability is absent. The failure to find Chapman-Jouguet detonations without transverse structures reflects the inability to encounter real chemical systems with reaction-rate properties suitable for stability. 

Chapman-]ouguet Stability Condition. See Detonation, Chapman-Jouguet Stability Condition... 

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