Detonation wave, hydrodynamic

These are the basic equations of the hydrodynamic theory of detonation. If p2 and v2 can be determined, they enable the remaining features of the detonation wave to be calculated. Unfortunately p2 and v, relate to conditions in the detonation wave and not to the lower pressure conditions which the explosion products would reach at equilibrium in, for example, a closed vessel. Therefore, further calculations are needed to determine p2 and v2. 

Detonation, TDBP Wave (Taylor- Doring-Burkhardt-Pfriem Wave). Accdg to discussion given by Cook in Chapter 5, under "Theoretical Wave Profiles (Ref 4, pp 92ff), Taylor (Ref 3) studied theoretically the p(x) and W (x) distributions behind plane and spherical detonation waves for gaseous expls and TNT, using the hydrodynamic equation ... 

Hydrodynamic theory of deton and shock waves) 29c) J.O. Hirschfelder et al, OSRD 547(1942) (Thermochemistry and the equation of state of the propellant gases) 30) J. von Neumann, OSRD 549(1942) (Theory of deton waves)... 

The book includes among other topics Definition of expln and classification of expln processes, pp 9-l6 Theory of shock waves, which includes "shock adiabat on p 190 (pp 182-224) Theory of deton waves (pp 225-27) Hugoniot curve for detonation waves (p 228) Hydrodynamic Theory of deton (p 226) Explosion in air. (pp 555-663) Theory of point initiation of deton, called in Rus "Teoriya tochechnago vzryva (pp 598-624) Theory of spherical expln (pp 624-40) Explosion in condensed medium (pp 664-81) Propagation of shock waves in water (pp 681-90) Some problems of theory of deton in liquids (pp 690-98) Propagation of waves in solids (pp 708-18) and Theory of deton in earth. (pp 718-44)... 

Summarizing the work done to ca 1950, Taylor (Ref 5, p 142) stated that the results show that the max or hydrodynamic vel of deton is approached as the diam is increased, but as the diam is reduced the vel fails. Eventually the vel becomes so low that die deton wave is not strong enough to maintain its own propagation. There is, therefore, a critical minimum diam for any expl below which a self-sustained deton wave will not propagate. The critical vel and critical diam bear no direct relation to.the hydrodynamics of deton. They are dependent on an ill-defined prop of the expl which is called sensitiveness . ... 

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... 

Andreev Belyaev (I960), pp 230-43 (Hydrodynamic theory of detonation waves) 250-52 and Fig 4.61 (Interruption and reformation of detonation wave thru inert solid plates) 63) J.A. Nicholls E-K. Dabora, "Standing Detonation Waves, USDept Commerce, OfcTechServ PBRept 148528,... 

CottrelUPoterson Equation of State, An equation of state, applicable to gases at densities near that of the solids and to temps far above the critical, is derived by Cottrell Paterson (Ref 1). It is shown that this equation is likely to hold in the range of density temperature characteristics of the detonation wave in condensed expls. The hydrodynamic equations of deton are developed on the basis of the equation of state. They were applied to PETN and the theory predictions were shown to agree with observations. Murgai (Ref 2) extended the application of the equations to oxygen-deficient expls, specifically TNT... 

This also characterizes the very style of the experimental studies. Even until recently the hydrodynamic theory of the detonation velocity, which was excellently confirmed in experiments, created a sense of contentedness and did not inspire the search for the chemical reaction mechanism or investigation of the conditions at the detonation wave front. If our paper brings about new experimental studies which penetrate deeper into the essence of the phenomenon, then our task will have been accomplished. 

A recent review of detonation theory is given elsewhere [12]. Models of the phenomenon envisage a detonation wave propagating into unreacted material with a sharp discontinuity in temperature and pressure at the detonation front. A reaction zone of a millimeter or smaller dimensions and yielding the equilibrium quantities of reaction products at high temperature and pressure abuts the up-stream side of the front. Using macroscopic hydrodynamic-thermodynamic theory, the energy released, and an equation of state for the assumed products, detonation velocities, pressures, and temperatures may be calculated in certain cases. 

Radial losses of mass, momentum, and energy through the lateral surface of the cylinder do not occur. The detonation wave propagates along the axis of the cylindrical charge and is confined laterally by the infinite diameter explosive (the minimum diameter which can support hydrodynamic detonation at its maximum steady-state rate). 

As was covered earlier under deflagration and detona Vion, the detonation velocity of an explosive is the speed at which the detonation wave moves through the explosive. For most of today s (x>nimercial explosives, detonation velocity ranges from about 5,000 fps for ANFO to more than 22,000 fps for high explosives such as cast 50/50 Pentolite. It should also be noted that eveiy explosive compound v/ill have a maxxmuin or ideal detonation velocity, which is referred to as its hydrodynamic velocity. 

The detonation process may be described mathematically applying thermodynamic and hydrodynamic laws. The state and the motion of the matter in the detonation wave may be expressed by means of the laws of conservation of mass, momentum, and energy. These laws can be written in the form... 

A shock wave propagation, as well as a detonation wave propagation, is a hydrodynamical process that can be mathematically described by means of the conservation laws... 

Figure 21. Hydrodynamic history for Cell B, Fig. 1. Curve identifications are the same as in Fig. 17. Quench comes 1.2 is after the detonation wave. This cell is expected to be closer to equilibrium than Cell A.

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