Shock-wave theory

Detonation and Shock Waves, Theory of Point Detonation. This subject is described by Baum et al (Ref 59, Pp 598- 624), under the title "Teoriya Tochechnago Vzryva . 

A number of authors consider that the reaction is caused by compression of the original substance by a shock wave (Vieille, Nernst and Wendt-landt, Jouguet, Sokolik). Becker, in analogy with shock wave theory, considers that heat conduction is involved in the transfer of the reaction from layer to layer, and he argues against the proposition of ignition by a shock wave. 

In a shock wave, as is known, a change of state occurs on the mean free path of molecules of the gas. The outward analogy between the theory of detonation and the shock wave theory prompted many authors to consider that a detonation front is just as sharp as the front of a shock wave. Jouguet spoke in favor of instantaneous reaction. 

We Eire now able to clearly picture the interrelation between shock wave theory and detonation theory. 

The shock wave theory is easier to understand, if we consider a planar shock wave, such as the one shown in Fig. 11, on the assumption that the tube is indestructible (such shock wave tubes are utilized as research instruments in gas dynamics and in solid state physics the shock sources are explosions or membranes bursting under pressure). 

Equations of the detonation wave theory are denoted by numbers corresponding to the respective equations of the shock wave theory, with a suffix d (for detonation ). 

Chapman and Jouguet are pioneers of the shock wave theory development also Riemann, Hugoniot and Rayleigh. 

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. 

Intense compression wave produced by detonation of explosive. -> Detonation, Shock Wave Theory. 

A detailed report is given by H. Hornberg. The State of the Detonation Products of Solid Explosives, Propellants and Explosives 3, 97-106 (1978). Chapman and Jouguet are pioneers of the shock wave theory development also Riemann, Hugoniot and Rayleigh. 

He had wanted to help oppose Nazism. After the fall of France, he says, I was desperate to do something—to make some contribution to the war effort. First he developed a basic theory of armor penetration. On the recommendation of Theodor von Kdrmdn, whom he consulted at Caltech, he and Edward Teller in 1940 extended and clarified shock-wave theory. In... 

Another approach is the so-called shock-wave theory . The compression of transient bubbles leads to an increasing bubble-wall velocity that may eventually reach the speed of sound of the liquid. In true transient cavitation, the bubble vanishes after collapse, creating a shock wave in the liquid. Particles and macromolecules are accelerated in the steep pressure gradient and are shock fragmented. High-speed particles collide and undergo mechanical damage. 

Jeanloz, R. (1989), Shock Wave Equation of State and Finite Strain Theory, J. Geophys. Res 94, 5873-5886. 

One cannot emphasize too strongly the importance of direct, time-resolved experimental observation of microscale phenomena in establishing sound theories of microstructural effects under conditions of shock-wave compression. 

Underlying all continuum and mesoscale descriptions of shock-wave compression of solids is the microscale. Physical processes on the microscale control observed dynamic material behavior in subtle ways sometimes in ways that do not fit nicely with simple preconceived macroscale ideas. The repeated cycle of experiment and theory slowly reveals the micromechanical nature of the shock-compression process. 

C01 L.C. Chhabildas and R.A. Graham, in Techniques and Theory of Stress Measurements for Shock Wave Applications, edited by R.R. Stout, E.R. Norwood, and M.E. Fourney. (American Society of Mechanical Engineers, New York, 1987) AMD-Vol. 83, pp. 1-18. 

The Chapman-Jongnet (CJ) theory is a one-dimensional model that treats the detonation shock wave as a discontinnity with infinite reaction rate. The conservation equations for mass, momentum, and energy across the one-dimensional wave gives a unique solution for the detonation velocity (CJ velocity) and the state of combustion products immediately behind the detonation wave. Based on the CJ theory it is possible to calculate detonation velocity, detonation pressure, etc. if the gas mixtnre composition is known. The CJ theory does not require any information about the chemical reaction rate (i.e., chemical kinetics). 

Another theory of liquid-liquid explosion comes from Board et al. (1975). They noticed that when an initial disturbance, for example, at the vapor-liquid interface, causes a shock wave, some of the liquid is atomized, thus enhancing rapid heat transfer to the droplets. This action produces further expansion and atomization. When the droplets are heated to a temperature equal to the superheat temperature limit, rapid evaporation (flashing liquid) may cause an explosion. In fact, this theory resembles the theory of Reid (1979), except that only droplets, and not bulk liquid, have to be at the superheat temperature limit of atmospheric pressure (McDevitt et al. 1987). 

The theory of detonation has also been extended to study the process of initiation of reaction by the commonest means used in practice, namely, by the shock wave arising from another high explosive. Campbell, Davis and Travis have studied the initiation by plane shock waves of homogeneous explosives, particularly nitromethane. Initiation occurs at the boundary of the explosive after an induction period which is of the order of a microsecond and which depends markedly on initial temperature. During the induction period the shock wave has proceeded through the explosive and compressed it. The detonation initially in compressed explosive has a velocity some 10% above normal, but the detonation soon overtakes the... 

Requirements 1 and 3 follow immediately from the considerations of the theory of detonation when it is remembered that the purpose of the charge is to obtain maximum effect, both from the shock wave of the explosive and also from the destructive effect of expansion of the explosion products. Requirements 1 and 2 follow from the consideration that any reduction in size and weight of the warhead of a missile, or in a shell, immediately makes it possible to increase the range and therefore the usefulness of the weapon. Requirement 5 relates not only to safety, but also the desirability, particularly for armour-piercing ammunition, for the time of detonation to be determined solely by the functioning of an appropriate fuze. 

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. 

N) E.W. Price, "Recent Advances in Solid Propellant Combustion Instability , Ibid, pp 101-113 O) G.A. Marxman C.E. Wooldridge, "Finite-Amplitude Axial Instability in Solid-Rocket Combustion , Ibid, pp 115-27 P) W.A. Sirignano, "A Theory of Axial-Mode Shock-Wave Oscillations in a Solid-Rocket Combustor ,Ibid, pp 129-37 Q) B.T.Zinn C.T. Saveli, "A Theoretical Study of Three-Dimensional Combustion Instability in Liquid-Propellant Rocket Engines , Ibid, pp 139-47 R) R.J. Priem E.J. Rice, "Combustion Instability with Finite Mach Number Flow and Acoustic Liners , Ibid, pp 149-59 S) M.W. Thring, "Combustion Oscillations in Industrial Combustion Chambers , Ibid, pp 163-68... 

Delayed-, After-, or Post-Reactions in Detonation. There are two general types those which occur within a confined space such as in a closed bomb, and those which involve reaction with external air and are known as "afterburning". Accdg to classical one-dimensional detonation theory, chemical equilibrium is achieved and reaction ceases at the CJ (Chapman-Jouguer) plane, which terminates the reaction zone. In some cases, however, as noted by Craig (Ref 3, p 863), the sharp shock wave and the reaction zone of falling pressure are followed by a further rapid pressure drop which is not predicted by an extrapolation of the one-dimensional theory... 

Dunkle (Ref 7) reports that the CJ Theory deals with adiabatic transformations in steady non-viscous, one-dimensional flows in stress tubes or ducts of constanc cross-section. This theory interprets deton waves as shock waves in which a continuing degradation of mechanical (shock) energy into heat is balanced by... 

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