The dynamic detonation parameters

The extent to which a detonation will propagate from one experimental configuration into another determines the dynamic parameter called critical tube diameter. It has been found that if a planar detonation wave propagating in a circular tube emerges suddenly into an unconfined volume containing the same mixture, the planar wave will transform into a spherical wave if the tube diameter d exceeds a certain critical value dc (i.e., d dc). II d d.. the expansion waves will decouple the reaction zone from the shock, and a spherical deflagration wave results [6], 

Rarefaction waves are generated circumferentially at the tube as the detonation leaves then they propagate toward the tube axis, cool the shock-heated gases, and, consequently, increase the reaction induction time. This induced delay decouples the reaction zone from the shock and a deflagration persists. The tube diameter must be large enough so that a core near the tube axis is not quenched and this core can support the development of a spherical detonation wave. 

Some analytical and experimental estimates show that the critical tube diameter is 13 times the detonation cell size (dc 13 A) [6], This result is extremely useful in that only laboratory tube measurements are necessary to obtain an estimate of dc. It is a value, however, that could change somewhat as more measurements are made. 

As in the case of deflagrations, a quenching distance exists for detonations that is, a detonation will not propagate in a tube whose diameter is below a 

Belles [29] essentially established a pure chemical-kinetic-thermodynamic approach to estimating detonation limits. Questions have been raised about the approach, but the line of reasoning developed is worth considering. It is a fine example of coordinating various fundamental elements discussed to this point in order to obtain an estimate of a complex phenomenon. 

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The next section deals with the calculation of the detonation velocity based on C-J theory. The subsequent section discusses the ZND model in detail, and the last deals with the dynamic detonation parameters. 

This paper centers on the problem of turbulent flame acceleration by obstacles and the prediction of the dynamic detonation parameters of fuel-air mixtures. 

The general U-shaped behaviour is reproduced but the error can be quite significant for off stoichiometric mixtures. The correlation to detailed chemistry in a simple X = A relationship is not of sufficient accuracy for prediction purposes. In other words, using one experimental data point to determine A and compute the cell size henceforth using detailed chemistry is not accurate enough for practical purposes. This is due to the fact that most dynamic detonation parameters are sensitive functions of the cell size (eg., X ). 

Calculation of the dynamic parameters using a ZND wave structure model do not agree with experimental measurements, mainly because the ZND structure is unstable and is never observed experimentally except under transient conditions. This disagreement is not surprising, as numerous experimental observations show that all self-sustained detonations have a three-dimensional cell structure that comes about because reacting blast wavelets collide with each other to form a series of waves which transverse to the direction of propagation. Currently, there are no suitable theories that define this three-dimensional cell structure. 

An excellent description of the cellular detonation front, its relation to chemical rates and their effect on the dynamic parameters, has been given by Lee [6], With permission, from the Annual Review of Fluid Mechanics, Volume 16, 1984 by Annual Reviews Inc., this description is reproduced almost verbatim here. 

The comparison of calculated and experimental characteristics for all investigated molecules is in the Table 1. As one can see the parameters exhibit the same trend as the h values in dependence on the molecule type. On the other hand, the course of values agrees with the course of the detonation energy ED in dependence on the molecule type. Both calculated parameters and obtained from the classical molecular dynamics simulations agree with the experimental characteristic h and calculated values of ED in Ref. 5,16. 

Current state-of-the-art in the understanding of these phenomena, as well as progress made in achieving empirical and quantitative descriptions of these combustion processes, are reviewed. The specific topics discussed are i) the maximum attainable turbulent flame speed in an obstacle array, ii) computer simulation of turbulent flame accelerations, iii) correlation between the detonation cell size and the dynamic parameters of fuel-air detonations, and iv) the transition from deflagration to detonation. Future directions in the investigation of these problems are also discussed. 

Various dynamic methods based on different physical principles are used for the experimental determination of the pressure at the CJ point and the duration of the chemical reactions in the chemical reaction zone. A large number of these methods, especially for the determination of the pressure at the CJ point-detonation pressure, were independently developed in the USA and the former USSR in the 1950s. In the years to follow, the detonation parameters of the solid explosives, equation of state, and adiabatic shock (or Hugoniot) equation of detonation products were the subject of numerous experimental and theoretical investigations. But it should be mentioned that different interpretations of the experimental results were frequent. 

Finally from the space-time diagrcun of the incident pressure wave, which depends on the two parameters X and E, and simultaneously from the modeled pressure load of the reflected wave on a plane surface that only depends on X, it is possible to predict the dynamic loading Ap(t) at any point on the plane surface. In Fig. 11 the predicted arrival times tai and the observed ones texp collected from numerous experiments are compared. The scattering does not exceed 10%. In Fig. 12 the effective measured pressures and the predicted ones on a wall located near the hemispherical detonating charge are compared. The agreement is excellent. 

In ordm to improve our teovdedge on possdble detonation medianisms, we anal3rze energetic and electronic characteristics of an e q>losive molecule by quantum chemistry calculations and spectroscopy data, the crystalline structure of energetic crystals by visualization on micro computers, their effects on experimental detonation parameter, while energy transfer processes are defined and their efficiency, if possible is estimated by molecular dynamics and numerical simulations. 

Other parameters which have been used to provide a measure of a include physical dimensions (thermomechanical analysis, TMA) [126], magnetic susceptibility [178,179], light emission [180,181], reflectance spectra (dynamic reflectance spectroscopy, DRS) [182] and dielectric properties (dynamic scanning dielectrometry, DSD) [183,184], For completeness, we may make passing reference here to the extreme instances of non-isothermal behaviour which occur during self-sustained burning (studied from responses [185] of a thermocouple within the reactant) and detonation. Such behaviour is, however, beyond the scope of the present review. 

As in consideration of deflagration phenomena, other parameters are of import in detonation research. These parameters—detonation limits, initiation energy, critical tube diameter, quenching diameter, and thickness of the supporting reaction zone—require a knowledge of the wave structure and hence of chemical reaction rates. Lee [6] refers to these parameters as dynamic to distinguish them from the equilibrium static detonation states, which permit the calculation of the detonation velocity by C-J theory. 

Jouguet, (Jacques-Charles) Emile (1871 — 1943). French physicist, general inspector of mines and professor of mechanics ficole des Mine, ficole Poly technique, member French Academy of Science (1930). He was the author of Me-canique des Explosifs (1917) and conducted research on wave diffusion, movement of fluids, explosives and fundamental work on the hydro-dynamic theory of detonation. His name is associated with that of Chapman-in the famous Chapman-Jouguet condition. In their honor parameters of a steady detonation wave are usually designated by the subscript CJ... 

Classical molecular dynamics simulations revealed in details the mechanism of the molecular decomposition for four selected molecules RDX, P HMX, DADNE and NQ. Parameters obtained from dynamic trajectories agree with the experimental characteristics h, describing the impact sensitivity and with calculated values of detonation energy for all investigated molecules. The parameters obtained from dynamics simulations could be used for fast effective testing of explosive materials. Anyway the method of testing based on dynamic simulations still needs to be worked out more preciously. That means ... 

The Chapman-Joguet model [113] offers the opportunity to approximate the parameters of the complex dynamic process of a detonation such as detonation velocity, pressure, and transformed energy. For a stoichiometric hydrogen mixture, these parameters are 1968 m/s, 1.6 MPa, and 2.82 MJ/kg, respectively. 

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