Hydrodynamic detonation

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

Detonation, hydrodynamic and hydrothermo-dynamic theories of 4 D610... 

Density is an important characteristic of explosives. Raising the density (e.g. by pressing or casting) improves -> Brisance and Detonation Velocity (- Detonation, Hydrodynamic Theory of Detonation). Low-density explosives, in contrast, produce a milder thrust effect (- also Loading Density - Cartridge Density). 

Cook (Ref 21) presents a thermo-hydrodynamic calcn of the detonation parameters and detonation products of two NS expls containing 25/1.5/73.5 NS/A1/AN-SN dope and 27-5/3/ 69.5 NS/A1/AN-SN dope... 

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. 

Characteristics of Explosives and Propellants. See Vol 2, p C149-L and the following Addnl Refs A) W.M. Evans, PrRoySoc 204A, 12-17(1950) CA 45, 10587(1951) (Some characteristics of detonation) B) W.H. Anderson R.B. Parlin, "New Approaches to the Determination of the Thermodynamic-Hydrodynamic Properties of Detonation Processes", Univ of Utah, Inst for Study of Rate Processes, TechRept XXVIII(I953), Contract N7-onr-45107 C) W. Fickett ... 

Many of the unsolved problems of physics and chemistry were concerned with combustion and detonation. A really well-developed scheme of normal combustion is seldom realized in nature. The most common form of gaseous combustion - turbulent combustion - was found to be the result of the hydrodynamic instability of the combustion process in a flow. Even in the simplest system, the physical scheme of turbulent combustion is very far from being perfectly understood. Just as in the analysis of detonative combustion, it is still possible to speak only of the universal instability of the hydrodynamic process accompanying the chemical transformation of matter. Actually, "turbulence is hardly the term for the result of the manifestation of this instability - the appearance of a multifront shockwave in the detonation front. However, the derivation of a complete physical scheme of detonation (especially in relation to condensed expls) will eventually follow from further research in this field... 

I) O.A. Gurton, PrRoySoc 204A, 31-2(1950) (Fading of deton in solid expls) J) A. LeRoux, MP 33, 283-321(1951) (Deton of solid expls by impact with solid shots at high velocities) K) M.A. Cook et al, "Reaction Kinetics and Thermo-Hydrodynamics of 80/20 Tritonal , Univ of Utah, Tech Rept XXIX(1954), Contract N7-onr-45107 (Conf) (Not used by us) L) M.A. Cook, JPhysChem 58, 1114(1954) (A study of the equation of state for EDNA) M) H. Sudo, JlndExplsSocJapan 15, 277-81(1954) (Photographic study of deton of solid expls)... 

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)... 

Cook equation of state, using covolume approximation) 63-4 (Other coyolume equations of state) 65 (Jones, Jones-Miller and Lennard-Jones equations of state) 66 (Cot-trell-Paterson equation of state) 12aj) W. Fickett W.W. Wood, Physics of Fluids 1, 528(1958 (A Detonation-Product Equation of State Observed from Hydrodynamic Data)... 

H) W. Fickett W.W. Wood, The Physics of Fluids 1 (6), 528-34 (Nov-Dec 1958) (Detonation-product equations of state, known as "constant-/ and "constant-)/ , obtained from hydrodynamic data) I) J.J. Erpenbeck D.G. Miller, IEC 51, 329-31 (March 1959) (Semiempirical vapor pressure relation based on Dieterici s equation of state J) K.A. Kobe P.S. Murti, IEC 51, 332 (March 1959) (Ideal critical volumes for generalized correlations) (Application to the Macleod equation of state) Kj) S. Katz et al, jApplPhys 10, 568-76(April 1959) (Hugoniot equation of state of aluminum and steel) K2) S.J. Jacobs, jAmRocketSoc 30, 151(1960) (Review of semi-empirical equations of state)... 

Thus DpJ is the theoretical maximum or hydrodynamic value of the detonation velocity when the initial density and pressure are respectively pdetonation velocity for any other initial density and pressure p and p. respectively /3 is the increase in the hydro-dynamic detonation velocity for a tenfold increase in density or pressure... 

Detonation, Ideal and Nonideal. Accdg to Cook (Ref 2, p 44), an ideal detonation corresponds to the theoretical maximum or hydrodynamic value D. This maximum velocity D is subject to direct experimental determination it is the steady value attained at a sufficiently long distance from the initiator in a tube or charge of diameter sufficiently large that further in-... 

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,... 

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... 

Accdg to Cook (Ref 41, pp 32-5 279), the detonation pressure (p2) cannot be measured directly (at least in condensed explosives), owing to its transient nature and its exceedingly high magnitudes. This pressure can, however, be accurately defined by the following hydrodynamic equation ... 

Detonation - Product Equation of State Obtained from Hydrodynamic Data is discussed by W. Fickett W.W. Wood in the Physics of Fluids 1, 528-34(1958)... 

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-... 

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