Chapman-Jouguet state

Chapman-Jouguet State. See Detonation, Chapman-Jouguet State... 

Product compositions at the Chapman-Jouguet state and in the subsequent expansion of the detonation gases depend most strongly on the two important equilibria,... 

Gas detonation at reduced initial pressures were studied by Vasil ev et al (Ref 8). They point out the errors in glibly comparing ideal lossless onedimensional computations with measurements made in 3-dimensicnal systems. We quote In an ideal lossless detonation wave, the Chapman-Jouguet plane is identified with the plane of complete chemical and thermodynamic equilibrium. As a rule, in a real detonation wave the Chapman-Jouguet state is assumed to be the gas state behind the front, where the measurable parameters are constant, within the experimental errors. It is assumed that, in the one-dimensional model of the detonation wave in the absence of loss, the conditions in the transient rarefaction wave accompanying the Chapman-Jouguet plane vary very slowly if the... 

Yang We performed model validation at the component level, i.e., Chapman-Jouguet state, supersonic inlet, DDT, etc. 

Thermodynamic cycles are a useful way to understand energy release mechanisms. Detonation can be thought of as a cycle that transforms the unreacted explosive into stable product molecules at the Chapman-Jouguet (C-J) state,15 which is simply described as the slowest steady-state shock state that conserves mass, momentum, and energy (see Figure 1). Similarly, the deflagration of a propellant converts the unreacted material into product molecules at constant enthalpy and pressure. The nature of the C-J state and other special thermodynamic states important to energetic materials is determined by the equation of state of the stable detonation products. 

Figure 1 A thermodynamic picture of detonation The unreacted material is compressed by the shock front and reaches the Chapman-Jouguet point. From there adiabatic expansion occurs, which leads to a high-volume state. Finally, detonation products may mix in air and combust.

Among the experiments which were reported, there were several pertaining to measurements of the C-J (Chapman-Jouguet) particle velocity and sound speed and one experiment concerned with an examination of the polytropic equation of state for reaction products of condensed explosives... 

Accdg to remarks of Dunkle (Ref 8), an ideal detonation can be visualized as a steady-state process, in a frame of reference in which the detonation zone is stationary and time-invariant, with the undetonated explosive being "fed into the front at the detonation velocity D and with laminar flow of the products away from the C-J plane the rear boundary of the reaction zone is at velocity (D-u), where u is the particle velocity of the products in stationary coordinates. By the Chapman-Jouguet rule, D-u = c, the local sonic velocity at the C-J plane. That is, the velocity of the products with respect to the detonation front is sonic at the C-J temperature and pressure. Thus, even if the products were expanding into a vacuum, the rarefaction wave would never overtake the detonation front as long as any undetonated explosive remains... 

IBM-7030 STRETCH Computer using the Becker-Kistiakowsky-Wilson equation of state. These parameters are listed by us under "Detonation (and Explosion), Equations of State Used in . He also detd several Chapman-Jouguet parameters... 

Detonation, Sound Speed Frozen in. Under the heading "Chapman-Jouguet Detonation with Varying Product Composition Frozen Sound Speed , Evans 8t Ablow (Ref 4, pp 150-51) stated the following ... 

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. 

Penney (Ref 1, p 3) stated that in any freely tunning detonation, the velocity must obey the Chapman-Jouguet condition, but if the explosive products are forced forward by a constraint which moves at a velocity greater than (D—c), where D and c are the... 

CA 44, 1032(1950) (Penetrating or piercing jet theory of deton) 39) S.R. Brinkley Jr, "The Theory of Detonation Process , pp 83-8 in the "Summary Technical Report Division 8, NDRC , Vol 1 (1946). It includes Riemann formulation (pp 83-4 86) Rankine-Hugoniot condition ( 84 86) Chapman-Jouguet postulate (84) Becker semiempirical equation of state (85) Rayleigh, solution of the Riemann equation (86) and Hydro-thermodynamic theory, applications (87-8) 40) W. Loring H. 

Dunkle s Lecture at Picatinny Arsenal, 21 Nov 1955, p 3 (One-dimensional steady-state process and Rankine-Hugoniot equation) 78) Ibid, 13 Dec 1955, p 5 (Nature of shock waves) p 8 (Chapman-Jouguet point) pp 8-9 (Basic equations of deton) p 9... 

Reynolds number, p 46), etc 61-72 (Shock relationships and formulas) 73-98 (Shock wave interactions formulas) 99-102 (The Rayleigh and Fanno lines) Ibid (1958) 159-6l(Thermal theory of initiation) 168-69 (One-dimensional steady-state process) 169-72 (The Chapman-Jouguet condition) 172-76 (The von Neumann spike) 181-84 (Equations of state and covolume) 184-87 (Polytropic law) 188, 210 212 (Curved front theory of Eyring) 191-94 (The Rayleigh transformation in deton) 210-12 (Nozzle thepry of H. Jones) 285-88 (The deton head model) ... 

Definition of deton, expln de-flgrn) 44-8 (Ideal deton) 48-50 (Nonideal deton) 50-7 (Transient and unstable deton waves) 57-60 (The jumping deton) 61-90 (Thermohydrodynamic theory of deton) 61-6 (Equation of state in deton of condensed expls) 66-8 (The Chapman-Jouguet postulate) 68-75 (The deton reaction zone in gases) 75-7 (Reaction zone in nonideal deton in gases) 77-9 (Reaction zone in condensed expls) 79-87... 

D<6)- D)/D ° = 3.5 f /S, where D = detonation velocity along the charge axis in the direction of wave propagation D = one-dimensional, steady-state, Chapman-Jouquet deton vel = Chapman-Jouguet point and S = radius of curvature of the shock front... 

Ref 66, p 145). Solutions for the Chapman-Jouguet steady detonation wave are obtd from the equations of conservation of mass, the conservation of momentum, the conservation of energy, an equation of state and the C- J condition. Explicit solutions are reported by Eyring et al (Refs 9 22a) and by Taylor (Ref 26, pp 87-89)... 

---