Detonation wave, hydrodynamic theory

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. 

The hydrodynamic theory of detonation, based on physical theories of shock waves and the chemical theory of absolute reaction rates, utilizes the established laws of conservation of mass, energy, and momen-... 

Report on the Hydrodynamic Theory of Detonation and Shock Waves , OSRD 114... 

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)... 

A new relationship in the hydrodynamic theory of expl waves) 95) W.W. Wood J.G. Kirkwood, JChemPhys 29, 956(1958) (Present status of deton theory) 95a) W. Fickett 8t W.W. Wood, Phys of Fluids 1 (6), 528-34 (Nov-Dec. 1958) (A detonation-product equation of state obtained from hydrodynamic data) 96) Cook... 

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)... 

G.B. Kistiakowsky E.B. Wilson, Jr1. "Final Report on die Hydrodynamic Theory of Detonation and Shock Waves OSRD 114(1941) 6) J. von Neumann "Theory... 

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,... 

G. B. Kistiakowsky and E. B. Wilson, Jr., The Hydrodynamic Theory of Detonation and Shock Waves, OSRD Rept. 114, 1941. 

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... 

Chapmann developed a hydrodynamic theory of detonation along the lines used earlier by Riemann, Rankine and Hugoniot to construct a theory of shock (explosive) waves in a chemically inert gas. 

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. 

Aeeording to the hydrodynamic theory of reaction waves propagating in one dimension (see references to the Introduction. Volume I) the detonation velocity is expected to be less than ideal in samples of diameter d such that the observed velocity D will approach the ideal velocity, > as J oo. Eyring et al. [25] developed a model based on a curved shock front bounded by a burned... 

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. 

The detonation theory developed by Chapman, Michelson and Jouguet is based on the hydrodynamic theory of shock waves in a chemically inert gas proposed earlier by Riemann (in 1860), Rankine (in 1870) and Hugoniot (in 1887, 1889) (see [230]. 

The close agreement between the calculated and measured detonation velocities is in favour of the basic prerequisite of the hydrodynamic detonation theory which implies that the chemical reaction rate is sufficiently high to ensure the onset of thermodynamic equilibrium in the detonation wave front. Rich mixtures display the greatest discrepancy between calculated and measured velocities. This is probably due to the insufficient rate of the chemical reaction preventing completion of the latter in the detonation wave. In reality, under the assumption of a completed reaction, the detonation velocity is lower than the calculated one. This indicates that at high detonation velocities the chemical reaction is the limiting factor. 

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. 

Explosion temperature is the calculated temperature of the fumes of an explosive material which is supposed to have been detonated while confined in a shell assumed to be indestructible and impermeable to heat the calculation is based on the -> Heat of Explosion and on the decomposition reaction, with allowance for the dissociation equilibria and the relevant gas reaction (- Thermodynamic Calculation of Decomposition Reactions). The real detonation temperature in the front of the shock wave of a detonating explosive can be estimated on the strength of the hydrodynamic shock wave theory, and is higher than the calculated explosion temperature. 

Zeldovich, J. B. und Kompaneets, A. S. Theory of Detonation (Translation), Academic Press, New York und London 1960 Berger, J. und Viard, J. Physique des explosifs, Dunod, Paris 1962 Andrejev, K.K. Thermische Zersetzung und Verbrennungsvorgange bei Explosivstoffen (Translation), Barth, Mannheim 1964 Andrejev, K.K. und Beljajev, A.F. Theorie der Explosivstoffe (Translation), Svenska National Kommittee for Mekanik, Stockholm 1964 Zeldovich, J.B. und Raizer, J. Physics of Shock Waves and High Temperature, Hydrodynamic Phenomena (Translation), Academic Press, New York, London 1966... 

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