Classical Theory of Plane Detonation Wave

Detonation, Classical Theory of Plane Detonation Wave. The mechanism by which a detonation wave maintains itself and progresses thru an expl was investigated by Neumann (Ref 

Support was found for the hypothesis that the deton wave initiates deton in the neighboring layer of the intact expl by the discontinuity of material velocity which it produces. This acts like a very vehement mechanical blow — a mass-velocity of approx 1500 m/sec — and is probably more effecting at high temp 

The velocity of the deton wave was detd by investigating all phases of the reaction. 

The results showed when the Chapman-Jouguet hypothesis was applicable and what formulas were to be used when it did not hold 

The work of von Neumann was limited to plane waves in absolutely confined explns and to determinations that had reached a stationary state 

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See Detonation, Classical Theory of Plane Detonation Wave in Section 2... 

Detonation, classical theory of plane detonation wave 4 D237... 

In the abstract of the paper (Ref 36a, p 1920) it is stated The limiting slope of he detonation velociry-wave front curvature locus for small- velocity deficits is obtained under an assumption concerning the "reaction zone length as related to the charge diameter and the radius of curvature of the wave front. The model is an extension to two dimensions of von Neumann s classical theory of the plane wave detonation... 

The above classical detonation theory was proposed by Zebdovich [529, 530, 534] (see also [334]), Doring [113] and Grib [169] on the basis of a unidimensional model of a stationary detonation wave. Further studies showed (for references see Strehlow s review [458, 535]) that the real gas-kinetic and the chemical-kinetic pattern of a detonation wave are much more complicated than the idealized plane shock wave. Moreover, the flat chemical reaction fronts which follow from the classical theory are non-stationary, thus leading to distortions and discontinuities in the flame front resulting in the violation of the idealized detonation wave pattern. 

Delayed-, After-, or Post-Reactions in Detonation. There are two general types those which occur within a confined space such as in a closed bomb, and those which involve reaction with external air and are known as "afterburning". Accdg to classical one-dimensional detonation theory, chemical equilibrium is achieved and reaction ceases at the CJ (Chapman-Jouguer) plane, which terminates the reaction zone. In some cases, however, as noted by Craig (Ref 3, p 863), the sharp shock wave and the reaction zone of falling pressure are followed by a further rapid pressure drop which is not predicted by an extrapolation of the one-dimensional theory... 

According to Rivin and Shchelkin, if one considers a wider interval of pressures and diameters (i.e., of values of the Reynolds number) than that with which Breton [39] worked, the relation between the spin and the limit ceases to be single-valued. Such a single-valued relation would necessarily follow from a theory with only the Rivin-Sokolik criterion Dr /d in which we make only the wave front width concrete, replacing it with the tube diameter d or the braking distance d/ = df (Re). One might think that when the Rivin-Sokolik criterion is increased we will move from the classical picture with a narrow plane front and a velocity which does not differ from the calculated value, to appearance of spin at one value of the criterion, and to the detonation limit at an even larger value of Dr /d. Such simple behavior is indeed observed in series of experiments performed in tubes of constant diameter at constant pressure (Breton), i.e., at a practically constant value of the Reynolds number. 

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