Chapman-Jouguet condition

Hugoniot equation and Chapman-Jouguet condition) 133-34 (Combustion knock)... 

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

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... 

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) ... 

The question considered is a description of the conditions which must be met by a localized initiator if a spherical detonation wave is to be formed. The first problem is a determination of the possibility of the existence of such a wave. Taylor analyzed the dynamics of spherical deton from a point, assuming a wave of zero-reaction zone thickness at which the Chapman-Jouguet condition applies. He inquired into the hydrodynamic conditions which permit the existence of a flow for which u2 +c2 = U at a sphere which expands with radial velocity U (Here U = vel of wave with respect to observer u2 = material velocity in X direction and c -= sound vel subscript 2 signifies state where fraction of reaction completed e = 1). Taylor demonstrated theoretically the existence of a spherical deton wave with constant U and pressure p2equal to the values for the plane wave, but with radial distribution of material velocity and pressure behind the wave different from plane wave... 

Ddring s treatment of the Chapman-Jouguet condition) 27) C.M. Mason,... 

Jouguet, (Jacques-Charles) Emile (1871 — 1943). French physicist, general inspector of mines and professor of mechanics ficole des Mine, ficole Poly technique, member French Academy of Science (1930). He was the author of Me-canique des Explosifs (1917) and conducted research on wave diffusion, movement of fluids, explosives and fundamental work on the hydro-dynamic theory of detonation. His name is associated with that of Chapman-in the famous Chapman-Jouguet condition. In their honor parameters of a steady detonation wave are usually designated by the subscript CJ... 

It has been mentioned1 that product compositions in the Chapman-Jouguet condition and in the subsequent expansion of the detonation gases depend most strongly on the two important equilibria... 

For the problem under consideration we take the minus sign in Eqn (10), substituting D—Uj for Cj (Chapman-Jouguet condition) and eliminating Uj by means of ... 

Of course, the famous Chapman-Jouguet condition also involves u, namely ... 

As is obvious from the previous section, the Chapman-Jouguet conditions, in accord with experiment, select the tangent point B of the line ABC drawn from the point representing the initial state to the dynamic adiabate. 

Wendlandt [10] emphasizes the analogy between the overcompressed detonation wave on the branch BFD and a simple compression shock wave without chemical reaction which is also overtaken and weakened from behind by rarefaction waves. In contrast, a detonation wave at the tangent point, for which the Chapman-Jouguet condition is satisfied, is similar to a sound wave and is transformed into a sound wave when the thermal effect of the reaction goes to zero. 

By using the Chapman-Jouguet condition we then have for the detonation velocity Vu = (vu — Vb) + Vb, where Vu — Vb is known as the particle velocity because it corresponds to the velocity of the burned gases with respect to the unburned gases. Alternatively, we have... 

Numerical solutions of the jump conditions have been obtained using Starling s equation of state to represent the thermodynamics of equilibrium and metastable states of hydrocarbon fluids. For simple fluids (small specific heat), only solutions with two-phase downstream states exist. Single-phase downstream states (complete evaporation waves) are predicted for complex fluids with a specific heat comparable to or greater than octane, given a sufficiently superheated initial state. Possible wave velocities range between zero and a maximum value determined by a Chapman-Jouguet condition. 

For a detonation initiated at a fixed wall, the Chapman-Jouguet condition of k equal unity represents a limiting case of K greater than unity. In this hmit, the detonation front itself is an / characteristic and region I disappears. 

Thus from these macroscopic considerations, we find that in a detonation initiated at a wall or a free surface c 1. It is shown below from detailed considerations of the structure of the detonation wave that a steady state solution of the equations exists only if 1. We are thus lead to the Chapman-Jouguet condition that in a free detonation = 1. In principle, however, other steady state detonations are possible. These are piston... 

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