Gap effect on the initiation of detonation in gas mixtures in cylindrical combustion chambers. II. Triggering of detonation within a turbulent flame

Schlieren moving-picture photography is used to study the burnup of oxygen gaseous mixtures in a cylindrical chamber with a gap at its periphery. It is found that a flame penetrating from the chamber into the gap can accelerate up to detonation speeds. The reaction wave in the gap precedes the primary combustion front propagating through the chamber and the reaction products escaping the gap create secondary combustion sources in the chamber. A process occurs in which a detonation wave that appears in the gap near one flank of the flame enters the main volume through the opposite flank, first triggering an explosion in the turbulent combustion zone (“an explosion within an explosion”) and then a detonation wave in the unreacted gas charge (“knock” in an engine). An interpretation is provided for the gas-dynamic structure of the secondary combustion source which is created in the cylindrical combustion chamber by a detonation wave propagating in the gap. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 4, pp. 77–87, July–August 1998     

共轭爆轰模型及其数值解

按照CJ和ZND模型．在所有可能的终点状态中CJ面爆轰产物的熵最低．而且系统永远达不到热力学平衡态．不符合热力学基本定律。为克服这些缺点,取热力学平衡态作为爆轰过程终点,建立了一种新的共轭爆轰模型。在共轭爆轰模型中．阵面激发化学反应释放出的能量。使得爆轰产物粒子朝不同的方向运动。每一对分别向前和向后运动的粒子被称为共轭对。共轭对在做爆炸中产生并在膨胀中湮没。将此过程与爆轰波传播相关联．建立了共轭爆轰模型。它从守恒定律和热力学定律导出．没有类似于cJ似设之类的附加条件。共轭爆轰模型方程组封闭且有唯一解。对于理想气体,由该模型得出的爆轰参数与CJ-ZND模型相近。     

Effect of the degree of dispersion on the detonation wave structure in pressed TNETB

A VISAR interferometer was used to study the reaction zone in steady-state detonation waves in pressed TNETB at different initial densities (1.23–1.71 g/cm³) and degrees of dispersion (5 and 80 μm) of the initial powdered high explosive (HE). The initial density range in which a pressure rise was observed instead of the theoretically predicted chemical spike is shown to depend on the degree of dispersion of the HE. The unusual change in the parameters in the reaction zone is explained by the heterogeneous structure of pressed HEs, whose decomposition has a local nature and proceeds partially at the compression wave front. A technique for recording wave profiles using LiF windows was developed, which confirmed that all qualitative features observed when using aluminum foils ≈200 μm thick and a water window reliably reflect the detonation wave structure. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 5, pp. 90–95, September–October, 2007.     

Energy release of mixed explosives during propagation of a nonideal detonation under conditions similar to the operation conditions of a blasthole charge

Detonation experiments were performed in a specially developed explosive device simulating a blasthole using charges of fine-grained and coarse-grained (granular) 30/70 TNT/ammonium nitrate mixtures of identical density 0.89 g/cm³ in steel shells with an inner diameter of 28 mm and a wall thickness of 3 mm at detonation velocities of 4.13 and 2.13 km/sec, respectively. Despite significant differences in detonation velocity (pressure), identical expansion of the charge shells was observed. On the other hand, numerical simulations of detonation propagation in the explosive device with the corresponding velocities ignoring the possibility of energy release behind the shock front show that the expansion of the charge shell is always greater in the case of a high-velocity regime. It is concluded that under the conditions simulating detonation propagation and the work of explosion products in a blasthole, effective additional energy release occurs behind the low-velocity (nonideal) detonation front. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 4, pp. 111–120, July–August, 2007.     

Propellant performance of organic explosives and their energy output and detonation velocity limits

Methods for determining the propellant performance of high explosives (HEs) are considered. The common and distinguishing features of the techniques of end acceleration of plates and shell expansion are shown. Experimental data on the propellant performance of individual explosives are given. The influence of metal additives on the brisance (propellant performance) and blast effect of explosive compositions is considered. A theoretical method for estimating the propellant performance is proposed, and the propellant performance of hydrogen-free HEs is calculated using experimental data on the enthalpies of formation and densities of single crystals. The energy output and detonation velocity limits of organic HEs are considered and estimated. Promising directions in the investigation of the properties of HEs are considered. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 1, pp. 99–111, January–February, 2007.     

Thermodynamic calculation of ideal and nonideal detonation

Conclusion A method has been proposed for calculating ideal and nonideal detonation, the thermodynamic basis of which is the method of characteristic function extrema, with the integral equations of conservation of the hydrodynamic model of steady-state flow of a continuous medium supplemented by the Chapman-Jouguet condition in the form of a minimum in normal detonation rate.The method has been realized in the form of a package of thermodynamic calculation programs which allow calculation of the composition and thermodynamic parameters of complex chemically reacting systems in the six basic problems of thermodynamics and in steady-state gas dynamic problems under conditions of equilibrium and specified chemical., thermal, and mechanical nonequilibrium of the products with arbitrary equations of state of the phases.Generalized results have been presented from calculations of ideal detonation of a large number of CHNO explosives and compared to experimental data. A new set of coefficients has been proposed for the BKW equation of state called the BKW-RR coefficients, which in combination with proper consideration of the phase state of the condensed carbon in the detonation products permits significant improvement in predicting the detonation rate.Results of nonideal detonation calculations have been presented, with the detonation products being under conditions of chemical, thermal, and mechanical nonequilibrium. It has been shown that the mass fraction of inert condensed phase in the detonation products not in mechanical equilibrium with the remaining products can differ significantly at the Chapman-Jouguet point from the inert content of the original mixture. Therefore, in the thermodynamic calculation of nonideal detonation one should use the equations of conservation of mass fluxes of the chemical elements in place of the equations of mass balance of chemical elements. It has been noted that in the case of nonideal detonation it is possible to use the Chapman-Jouguet condition in the form of equality of the flux velocity of the deoration product mixture as a whole relative to the front to the local speed of sound calculated with consideration of nonequilibrium conditions.Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 23, No. 4, pp. 75–84, July–August, 1987.     

Model for the propagation of a stationary reaction front in a viscoelastic medium

A coupled thermomechanical model for the propagation of a stationary chemical-reaction wave in a condensed medium is developed. Stresses and strains that arise during the reaction as a result of thermal and “concentration” expansion of the material are related by Maxwell’s equations for a viscoelastic medium. The expression for the heat flux is written as a generalized Fourier law with finite relaxation time for the heat flux. It is shown that deformation of the material in the reaction zone can lead to an apparent change in the activation energy, heat effect, and other characteristics of the system. This model allows for the existence of two different — subsonic and supersonic — regimes of propagation of the front, as well as the model in which the stress- and strain-tensor components are related by a generalized Hooke’s law. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 4. pp. 41–51, July–August, 2000.     

Equation of state of the detonation products of RDX

Summary Experimental data and theoretical ideas concerning the detonation adiabat and the thermodynamic properties of real gases have been used to find the equation of state of the detonation products of RDX in the density range 0–2.3 g/cm³. The equation of state relates mainly to the region of thermodynamic parameters corresponding to adiabatic expansion of the explosion mines the pressure at given values of the density and energy in this region correct to 5–10%.Fizika Goreniya i Vzryva, Vol. 2, No. 4, pp. 85–96, 1966     

In the theory of blast waves

The behavior of the blast wave from an exploding spherical volume is investigated mathematically over the entire range of blast-wave propagation. The computational method uses analytical results for a similar problem for a point explosion with counter pressure and the theory of an asymptotically equivalent point explosion. The asymptotic solution of the gas-dynamic equations away from the explosion site is matched to the initial conditions of blast-wave formation due to the disintegration of the detonation shock upon its arrival at the boundary of the exploding volume. The spatial distribution of the blast-front pressure is found for combustible gaseous systems and solid explosives. The theoretical results obtained agree quantitatively with available experimental measurements. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 4, pp. 93–99, July–August, 2006.     

Interaction of Aluminum with Detonation Products

A method of electrical conductivity and an analysis of recovered explosion products are used to study interaction of aluminum with detonation products of condensed high explosives. The electrical conductivity of HMX/Al and RDX/Al mixtures is inhomogeneous; a region with the maximum electrical conductivity is adjacent to the detonation front, whereas the electrical conductivity decreases with distance from the front. If the wave is incident onto a wall, the electrical resistance of the composite high explosive increases, which indicates that the high-conducting zone disappears. The electrical conductivity, resistance of the conducting zone, and the time of resistance growth are found as functions of the particle size of the additive. The results obtained confirm the reaction of the metal additive with detonation products in a microsecond range of time. An analysis of condensed explosion products shows that the reaction of aluminum with detonation products proceeds on the particle surface. The amount of reacted aluminum and the oxide-layer thickness are estimated. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 120–129, Jnuary–February, 2006.     

Effect of chemically inert particles on parameters and suppression of detonation in gases

An algorithm for calculating the parameters of a steady one-dimensional detonation wave in mixtures of a gas with chemically inert particles and estimating the detonation-cell size in such mixtures is proposed. The calculated detonation parameters and cell size in stoichiometric hydrogen-oxygen mixtures with W, Al₂O₃, and SiO₂ particles are used to analyze the method of suppression of multifront gas detonation by injecting chemically inert particles ahead of the leading wave front. The ratio between the channel diameter and the detonation-cell size is used to estimate the limit of heterogeneous detonation in the mixtures considered. The minimum mass of particles and the characteristic cloud size necessary for detonation suppression are calculated. The effect of thermodynamic parameters of particles on the detonation suppression process is analyzed for the first time. Particles with a high specific heat and (if melting occurs) a high phase-transition heat are found to exert the most pronounced effect. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 77–88, May–June, 2009.     

Performance Properties of Commercial Explosives

The aquarium test is a proven means of obtaining nonidial performance property data for commercial blasting agents. Optical data on the detonation velocity, shock wave in water, and expansion rate of the pipe enclosing the detonation products (in combination with the equilibrium thermodynamic chemistry code BKW) give the C-J state and degree of chemical reaction at the detonation front, as well as information on additional chemical reaction that occurs as the detonation products expand. Specific explosive systems that are studied are ammonium nitrate-fuel oil mixture (ANFO), aluminized ANFO, flaked trinitrotoluene (TNT), and several other commercial products in 10-cm-diam and 20-cm-diam pipes of Plexiglas and clay. Experimental shock pressure data are obtained with lithium niobate transducers placed in the water surrounding the explosive charge. These data show that the addition of ∼ 100-μm aluminum particles to ANFO significantly increases the initial peak shock pressure delivered to the surrounding medium. Peak shock pressures in the water, calculated from the shock-wave orientation, are also useful in comparing performance properties of various commercial explosives.     

Density distribution at the detonation front of cylindrical charges of small diameter

A synchrotron radiation based technique is use to study the density distribution at the detonation front and its neighborhood for condensed explosives. Particular data are obtained on the structure of the detonation front in TNT, RDX, and an alloy of TNT with RDX; a comparison of the data with those obtained using different techniques confirms the correctness of the technique. It is concluded that adequate information on the structure of the chemical-reaction zone can be obtained for charges of small diameter. At the same time, it is shown that the Chapman-Jouguet parameters for such charges are far from their predicted values for an infinite medium. The results of the work, including those on the curvature of the detonation front in charges of small diameter, supplement the existing knowledge of the detonation transformation in condensed explosives. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 2, pp. 91–99, March–April, 2007.     

Calculation of the Energy of Explosives with a Partial Reaction Model. Comparison with Cylinder Test Data

The energy delivered by explosives is described by means of the useful expansion work along the isentrope of the detonation products. A thermodynamic code (W‐DETCOM) is used, in which a partial reaction model has been implemented. In this model, the reacted fraction of the explosive in the detonation state is used as a fitting factor so that the calculated detonation velocity meets the experimental value. Calculations based on such a model have been carried out for a number of commercial explosives of ANFO and emulsion types. The BKW (Becker‐Kistiakowsky‐Wilson) equation of state is used for the detonation gases with the Sandia parameter set (BKWS). The energy delivered in the expansion (useful work) is calculated, and the values obtained are compared with the Gurney energies from cylinder test data at various expansion ratios. The expansion work values obtained are much more realistic than those from an ideal detonation calculation and, in most cases, the values predicted by the calculation are in good agreement with the experimental ones.     

Comparative brisant characteristics of some classes of industrial emulsion explosives

The four types of mixtures consisting of the two bases (aqueous solutions of ammonium nitrate and ammonium dinitroamide) and the two additions (hollow glass microballoons and gunpowder) are considered in this work. On the base of thermodynamic computations of an ideal detonation and accompanying processes (shock and rarefaction waves) there were obtained not only the dependences of detonation parameters on addition quantities to mixtures, but the pressure versus particle velocity diagrams, too, which in comparison with Hugoniots relatively soft (water) and hard (aluminium) substances allowed to determine values of pressure in the shock waves being produced in surroundings nearby the end-wall and lateral surface of a charge. It is proposed to characterize the brisant effect of an explosive by a value of relative brisance which is calculated as percentage ratio of pressures of shock waves generated in surroundings under the same conditions by detonation products of the given explosive and the standard one. It is shown that the brisant effect of the new emulsion explosives is comparable and even can exceed that of TNT of maximal density. It is shown as well that the brisant ability of industrial emulsion explosives can be raised by 60 and more percents by replacing ammonium nitrate with ammonium dinitroamide and hollow glass microballoons with powders being obtained as a result of military industry conversion and utilization of munitions.     

On the Hydrodynamic Thickness of Cellular Detonations

The characterization of the detonation dynamic parameters (detonability limits, direct initiation energy, critical tube diameter, etc.) requires a characteristic length scale for the detonation wave in the direction of propagation. However, most detonations are unstable, their reaction zones are turbulent, and their structure departs significantly from the idealized one-dimensional Zel'dovich-Von Neumann-Doring model. It is argued that the most suitable length scale to characterize a turbulent detonation wave is the location of the sonic surface, which separates the statistically stationary flow of the reaction zone structure from the unsteady expansions behind the wave. Previous real and numerical experiments are reviewed in order to determine the relation between the global location of the mean sonic surface and the chemical, mechanical, and thermodynamic relaxation processes occurring in the detonation wave structure. Based on the experimental evidence, we postulate that the structure of turbulent detonations can be modeled in the one-dimensional Zel'dovich-Neumann-Doring framework, with the turbulence effects as source terms in the momentum and energy equations. These source terms involve the relaxation rates for the mechanical fluctuations, thermal fluctuations and the chemical exothermicity towards equilibrium. In the framework of the idealized one-dimensional structure with source terms, the sonic surface location is governed by the balance between the competing source terms satisfying the generalized Chapman-Jouguet criterion. We recommend that future work in detonation research should be focused at: 1) acquiring a large experimental database for the mean detonation properties (detonation velocity, location of sonic surface and mean reaction zone profiles); 2) the development of the appropriate source terms involving the turbulent fluctuations in the averaged equations of motion. __________ Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 6, pp. 157–180, November–December, 2005.     

Mathematical model of continuous detonation in an annular combustor with a supersonic flow velocity

A two-dimensional unsteady mathematical model of a continuous spinning detonation wave in a supersonic incoming flow in an annular combustor is formulated. The wave dynamics in a combustor filled by a gaseous hydrogen-oxygen mixture is studied. The possibility of continuous spin detonation with a supersonic flow velocity at the diffuser entrance is demonstrated numerically for the first time; the structure of transverse detonation waves and the range of their existence depending on the Mach number are studied. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 6, pp. 83–91, November–December, 2008.     

Afterburn Ignition Delay and Shock Augmentation in Fuel Rich Solid Explosives

We present experimental and computational results that explain some aspects of measured energy release in explosions of unconfined trinitrotoluene [TNT, C₆H₂(NO₂)₃CH₃], and an aluminum‐containing explosive formulation, and show how this energy release can influence shock wave velocities in air. In our interpretation, energy release is divided into early, middle, and late time regimes. An explanation is provided for the interdependence of the time regimes and their influence on the rate at which energy (detonation/explosion and afterburn) is released. We use a merging of the thermodynamic and chemical kinetic processes that predicts how chemical kinetics may determine the time delay of the afterburn of combustible gases produced by the initial detonation/explosion/fast reaction. The thermodynamic computer code CHEETAH is used to predict gaseous and solid products of early time energy release, and a chemical kinetic reaction mechanism (CHEMKIN format) is used to describe the subsequent afterburn of the gas phase products in air. Results of these calculations are compared with field measurements of unconfined explosions of 2 kg charge weights of TNT and an aluminum‐containing explosive formulation.     

Generalized analysis of explosion propagation in condensed systems

The complex problem of the propagation of explosion of condensed explosives in gas media (air) is solved analytically. A generalized model is constructed which describes the following processes: explosion propagation in an explosive charge from the time of initiation to the establishment of the normal detonation regime (explosion transient); proper normal detonation; expansion of explosion products into the medium (air) with the formation of a blast wave and motion of the perturbed medium in the blast wave. Unlike in the well-known formulations of such problems using the classical hypothesis about adiabatic explosive processes, the present study is based on the more natural hypothesis about an exponential density profile of the perturbed medium and explosion products. The method of Salamakhin is extended to real explosion processes.