Hydrodynamic detonation theory

The hydrodynamic detonation theory allows to correlate the detonation parameters on the basis of the laws of mass, impulse and energy conservation and to calculate them independently of p and V ... 

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. 

Detonation, Nonlinear Theory of Unstable One-Dimensional. J.J. Erpenbeck describes in PhysFluids 10(2), 274-89(1969) CA 66, 8180-R(1967) a method for calcg the behavior of 1-dimensional detonations whose steady solns are hydrodynamic ally unstable. This method is based on a perturbation technique that treats the nonlinear terms in the hydro-dynamic equations as perturbations to the linear equations of hydrodynamic-stability theory. Detailed calcns are presented for several ideal-gas unimol-reaction cases for which the predicted oscillations agree reasonably well with those obtd by numerical integration of the hydrodynamic equations, as reported by W. Fickett W.W. Wood, PhysFluids 9(5), 903-16(1966) CA 65,... 

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... 

Detonation theories leading to development of hydrodynamic and hydrothermodynamic theories, history of 4 D602... 

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]. 

State For Gases at Extremely High Pressure And Temperatures From the Hydrodynamic Theory of Detonation , JChemPhys 15, 518-24 (1947) CA 41, 6047 (1947) 54) W.D. Crater,... 

Hydrodynamic Theory of Detonation, I. Thermochemistry And Equation of State of The Explosion Products of Condensed Explosives , Res (London) 1, 132-44 (1947) CA 44, 10321 (1950) 66) J. Svadeba, Impact Sens -... 

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 major difficulty in applying this hydrodynamic theory of detonation to practical cases lies in the calculation of E2, the specific internal energy of the explosion products immediately behind the detonation front, without which the Rankine-Hugoniot curve cannot be drawn. The calculations require a knowledge of the equation of state of the detonation products and also a full knowledge of the chemical equilibria involved, both at very high temperatures and pressures. The first equation of state used was the Abel equation... 

Extension of the hydrodynamic theory to explain the variation of detonation velocity with cartridge diameter takes place in two stages. First, the structure of the reaction zone is studied to allow for the fact that the chemical reaction takes place in a finite time secondly, the effect of lateral losses on these reactions is studied. A simplified case neglecting the effects of heat conduction or diffusion and of viscosity is shown in Fig. 2.5. The Rankine-Hugoniot curves for the unreacted explosive and for the detonation products are shown, together with the Raleigh line. In the reaction zone the explosive is suddenly compressed from its initial state at... 

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. 

In "concluding remarks", Lutzky stated that the calculation of C-J T with the help of LSZK equations, assuming cv=0.3cal/g (approx average value for deton products), gave results which were too low at high densities (See Table 2). The reason for this is not known - probably it is due to incompleteness of LSZK theory. In any case, it is believed that in all applications where the ealen of T is not needed, and only an (e, p, v) equation of state is required (such as the calculation of the non-reactive, isentropic expansion of detonation products by means of hydrodynamic computer codes), the LSZK equation of state, in particular ... 

Vol 1 (1946), Chapter 5, "The Theory of Detonation Process (Based on Summary by S.R. Brinkley, Jr) lh) G.J. Su C.H. Chang, JACS 68, 1080-83 (1946) (Equation of state for real gases) li) Ibid, IEC 38, 800-02 802-03(1946) (Equations of state for real gases) lj) M.A. Cook, jChemPhys 15, 518-24(1947 (An equation of state at extremely high temperatures and pressures from the hydrodynamic theory of detonation)... 

Detonation, Hydrodynamic and Hydrothermo-dynamic Theories of. See under Detonation (and Explosion), Theories of... 

There were two steps in Jones determination of equations of his theory. He first solved the perturbed hydrodynamic equations for D, using a constant covolume equation of state. Then, using an expression for the ideal deton velocity D, he obtd the equation ... 

Hydrodynamic theory of deton did not explain the above properties... 

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-... 

On the basis of the hydrodynamic theory, the characteristics of detonation have been calculated and values for temperature of detonation, pressure of detonation and velocity of detonation are given for four explosives in Table 5... 

The fundamental hydrodynamic theory of deton refers to a chge of infinite diam or a cylindrical chge encased in a perfectly rigid tube. Of course, ideal lateral confinement can never be realized completely since even massive metal tubes are compressible under the internal pressure developed during deton... 

Deal s values of p2 for Comp B are higher than computed results (0.233 mega-bars) by the hydrodynamic theory of detonation (Ref 3, p 116)... 

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

Important work on the theory of detonation process was performed during WWII in the US by-Division 8 of NDRC under G.B. Kistiakowsky, by.E.B. Wilson Jr and others. Summary of this work was given by S.R. Brinkley-Jr in Ref 39, pp 83-88 and we are using this important work in compiling this section of the Encyclopedia The NDRC review begins with. a qualitative discussion of the building up of a "discontinuous shock front . Then the Riemann formulation of the equation of hydrodynamics is introduced. This formulation was published in 1860 (Ref 1)... 

Only the temperature of detonation, T2, is influenced sufficiently by differences in the form of a(T,v), leading to relatively large differences in pj, to allow one to determine, from the hydrodynamic theory and experimental measurements, the correct form of a(T,v). In this eq one obtains (in final form) ... 

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