Chapman-Jouguet Detonation Velocity

Accdg to Kistiakowsky s eq (10) (listed above ), therefore, they all lie on the same straight line, ab, drawn from the original (unreacted) state of the explosive. Suppose that the R—H curves relating to various extents of the-reaction of. the explosive are as represented in Fig 4. This is certainly true for gaseous expls and has been shown also by Brinkley Wilson (Ref 7a) to be true for ordinary solid granular explosives. Let 

This discussion of von Neumann is important because it presents a definite picture of the structure of deton wave. 

The intact expl is initially subjected to a mechanical shock with a pressure p, which may be considerably in excess of pressure p, calcd for the C—J plane. 

A similar presentation of von Neumann theory is given by Penney in Ref 24a, pp 6-7, where his Fig 2 is similar to Fig 4 shown here 

It is further stated by Kistiakowsky (Ref 24, PP 954-55) that a restatement of above reasoning from a slightly different point of view may be helpful for a correct perspective on the situation existing in a detonation wave. Such wave, from a chem standpoint, starts in the intact explosive certain fast reactions take place in it. which may eventually progress to a state of complete hydro-dynamic equilibrium, controlled by the local pressure and temp in the wave. 

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The minimum value of is the detonation velocity Up at point J (Chapman-Jouguet detonation velocity). 

A second rapid increase in the flame speed occurs at H2 25% for both tubes. This corresponds to a transition to the detonation regime. The detonation velocity in the obstacle field is typically about 1500 m/sec and is practically independent of the H2 concentration up to H2 - 45%. For higher H2 concentrations, the detonation velocity abruptly drops back to the values for deflagration speeds of the order of 800 m/sec. The severe pressure Cor momentum) losses due to the presence of the obstacles accounts for the sub-Chapman-Jouguet detonation velocities observed. The normal velocities are about 2000 m/sec as observed in smooth tubes for H2 concentrations in the range (i.e., 25% H2 45%). 

Chapman-Jouguet detonation velocity (CJDV) Ideal detonation velocity that satisfies Chapman-Jouguet condition at the end of the reaction zone a gas moves at the velocity equal to the difference between the detonation velocity and the sound speed in the combustion products. CJDV in a stationary moving detonation wave is calculated from the thermodynamic equilibrium condition of the reaction products and the mass, impulse, and energy conservation laws. CJDV for typical hydrocarbon fuel + air mixtures lies in the range from 1,400 to 1,900 m/s. 

Chapman-]ouguet Particle Velocity. See Detonation, Chapman-Jouguet Particle Velocity... 

Explosive Chge Prepn Loading Density g/cc Po Chapman- J ouguet Detonation Velocity D in km/sec Chapman -Jouguet Particle Velocity km/ sec UCJ Product Po dD D dp ro S ee Note 1 Shock Velocity in H2O So km/sec Shock Pressure in H2O Ps(H20) km/sec Chapman-J ouguet Pressure, Pr. kbar J Poly- tropic Expo- nent, y Note 3 Term ), See Note 2 Temperature of Detonation T°K ... 

Note 2 Dunkle (Ref 5) remarked that the "ideal or Chapman-Jouguet detonation is a steady-state process, and that the derivation of the Hugoniot equations is based on the process being steady-state, so that the mass velocity. ih (rate of mass flow per unit, area per unit, time) is constant thruout the (one-dimensional) process. 

A Chapman-Jouguet detonation wave may be described as an exothermic supersonic wave that propagates itself at the minimum possible velocity consistent with the conservation laws, whereas a Chapman-Jouguet deflagration is an exothermic subsonic wave that propagates itself at the maximum possible velocity consistent with the conservation laws. 

Calculating Chapman-Jouguet detonations, proceeding at a velocity at which the reacting gases reach sonic velocity. 

A purely thermodynamic treatment of detonation ignores the important question of reaction time scales. The finite time scale of reaction leads to strong deviations in detonation velocities from values based on the Chapman-Jouguet theory.16 The kinetics of even simple molecules under high-pressure conditions is not well understood. 

Detonation, Chapman-]ouguet Particle Velocity. It is one of the CJ Parameters and its values are listed in the Table under Detonation, Chapman-Jouguet Parameters... 

Chapman Jouguet postulated that the detonation velocity D is given by ... 

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