Steady-state Detonation Research Articles

Detonation in a relaxing gas

One-dimensional steady-state detonation has been theoretically investigated in a gas with internal degrees of freedom (not directly related to irreversible energy release) characterized by a finite relaxation time τ. Relaxing gas is a variant of a system with sound speed dispersion. Detonation in such a system has been studied in detail by Kirkwood and Wood, who have pointed out the difficulties in formulating the Chapman-Jouguet (C-J) condition in such a medium. Self-sustaining (normal) and strong detonations for an arbitrary α  τ τ Q (where τ Q is the characteristic heat release time) have been determined, using an ideal gas with relaxing vibrational energy of molecules. The “topology” of continuous (in α) evolution of normal and strong detonations in the p- ν (pressure and specific volume of gas) plane has been determined with varying α. For normal detonations two values α ∗ and α ∗∗ < α ∗ , both of the order of unity, have been found to exist such that for the equilibrium C f and frozen cf sound speeds and for gas velocity u relative to the detonation wave at the Jouguet point, we have u = c f if c f > α ∗, c f > u > c e if α ∗ > α > α ∗∗, and u c e if α < α ∗∗ . The steady detonation wave zone has been matched with the rarefaction wave. The C-J condition has been generalized and a procedure has been described for calculating the parameters at the Jouguet point and the normal detonation velocity in a real gas mixture with relaxation.

Simple model of detonation in a gas-film system with consideration of mechanical fuel removal

Many studies have been dedicated to investigations of detonation in a system consisting of a fuel film an gaseous oxidizer. Examples of such studies are given. The present study performs an approximate calculation of steady-state detonation parameters with consideration of two mechanisms of mixture formation, mechanical removal of fuel and its evaporation.

Transition of porous explosive combustion into detonation

This article considers the planar one-dimensional motion of a porous medium consisting of solid contacting particles (explosive grains), with space between particles filled with gas. It is established by the numerical analysis performed that if the work of intergranular pressure forces is expended solely in gas heating, then a smooth transition from combustion to detonation is realized in porous explosives. A retonation wave was propagated through the unreacted material between the initial and secondary combustion zones in the majority of experiments performed. It is noted that at the pressure values characteristic of steady-state detonation of porous explosives, it is necessary to consider the compressibility of the particle material as well as the factors of nonthermal ignition and homogeneous burnup of explosives behind the shock front.

Some aspects of nonideal detonation in composite explosives

Abstract A theoretical treatment is formulated for steady-state planar detonation waves in composite explosives such as Amatex 20. This treatment provides a more definitve and realistic description of detonation in such explosives, and extends the classical Zeldovich-von Neumann-Doering model of ideal detonation into a propotype model for nonideal detonation. Incomplete decomposition of the slowest reacting component, and incomplete attainment of chemical equilibrium among the detonation products from the different explosive components were assumed to be the kinetic processes responsible for nonideal behavior. The constitutive relationship for the shocked reacting explosive was constructed with different equations of state for the explosives and their products and enough reaction coordinates to account for this type of nonideality. Detonation parameters and Lagrange particle velocity histories were calculated for nonideal detonation waves in an explosive modeling Amatex 20.

A study of the steady-state reaction-zone structure of a homogeneous and a heterogeneous explosive

The two-dimensional steady-state reaction-zone structure of a homogeneous and a heterogeneous explosive is studied. To do this theoretical results obtained from the Euler equations of compressible flow are combined with experimental data on steady-state detonation shock-wave speed and shape as a function of the explosive charge size. The theoretical results, constrained by the experiments, define an inverse problem for the chemical heat-release function in the reaction zone which follows the shock wave; this problem is solved. The heterogeneous explosive is made from the homogeneous one by adding small quantities of other materials. Because of this, the two explosives were closely related in many respects. In spite of this, quite large differences in the detonation characteristics are observed between the two explosives, both in the wave speed as a function of charge size and in the shape of shock-wave loci near the explosive edge. It is found that a single forward rate exponentially dependent on the inverse of the local shock pressure can ‘‘explain’’ the homogeneous case observations, but that a rate with much less state dependence near the explosive edge is necessary to understand the observations for the heterogeneous material. Near the failure diameter of both materials, prominent structures are found on the experimental shock-wave loci. These structures would seem to be incompatible with a steady flow and call into question whether two-dimensional steady-state detonations occur at all in condensed explosives near their failure diameter.

Chemical energy release in one-dimensional detonation waves in gaseous explosives

The Zel'dovich-von Neumann-Doring (ZND) model of a one-dimensional, steady state detonation wave in a gaseous explosive is extended to include the thermal relaxation processes which precede and follow the exothermic chemical reconstitution reactions. In this nonequilibrium model the detonation wave consists of four main zones: a very thin leading shock front in which the unreacted explosive mixture is compressed and accelerated in the direction of shock propagation; a much thicker relaxation zone in which the rotational and vibrational modes of the unreacted explosive gases approach thermal equilibrium; a relatively thin zone in which the chemical energy is released by rapid chain propagation and branching reactions into highly vibrationally excited reaction product gases; and another very thick relaxation zone in which the product gases expand and vibrationally relax toward thermodynamic equilibrium at the Chapman-Jouguet (CJ) state. Quantitative calculations for the H 2Cl 2, O 3, and H 2O 2 systems based on experimental chemiluminescent and crossed molecular beam product energy distribution data show that the amount of chemical energy initially released as product vibrational energy is greater than the sum of CJ equilibrium vibrational energy plus the amount of chemical energy required to sustain the constant velocity shock front. The physical mechanism by which this vibrational energy sustains the shock front is postulated to be the chemical amplification of transverse pressure waves, which propagate through the vibrationally excited products and eventually overtake the leading shock front.

Effect of a chemical inhomogeneity on steady-state detonation velocity

The detonation behavior of the liquid explosive, nitromethane, sensitized by the liquid organic base, diethylene triamine, has been studied experimentally. The work to be described complements earlier work concerning the effect of physical impurities on steady detonation behavior. By interpretation of detonation-velocity measurements, the following three goals are reached: (1) The evidence that physical inhomogeneities (usually voids) produce the downward concave region of the diameter-effect curves of condensed high explosives is enhanced; (2) the hypothesis that homogeneous materials have linear diameter-effect curves is placed on a firmer basis; and (3) the experimental evidence indicates that the sensitizing material has altered the effective chemical kinetics and consequently, has produced an explosive with a shorter one-dimensional reaction zone. A remarkably small amount of the chemical impurity produces a significant reduction of the nitromethane failure diameter; e.g., addition of one molecule of the amine to 5500 molecules of nitromethane reduces the failure diameter by 43%. A discussion is given which attempts to relate this high sensitivity to a molecular isomer of nitromethane (the ’’aci’’ form) whose presence is favored in basic solutions.

Effect of a physical inhomogeneity on steady-state detonation velocity

A set of experiments has been performed which demonstrate that ’’hot spots’’ in an explosive control some aspects of the steady-state detonation process. It is known, from experiments, that the relationship between explosive charge size and steady-state detonation velocity (the ’’diameter-effect curve’’) is qualitatively different for homogeneous and heterogeneous explosives. The experiments to be described strongly indicate that this qualitative difference is due to localized hot regions arising from flow modifications due to the presence of physical inhomogeneities. These local hot regions apparently produce an effective chemical reaction rate which allows a stable steady-state flow at a much smaller charge size than is possible in an analogous homogeneous material. Detonation-velocity measurements were carried out on cylindrical rate sticks at a number of radii thus generating diameter-effect curves. The explosives studied were composed primarily of commercial-grade nitromethane confined in Pyrex tubes. Silica impurities, with a known particle-size distribution, were added to the nitromethane to produce a heterogeneous material. The silica impurities were held in suspension with a guar-gum gelling agent. An attempt is made to interpret the new results by use of earlier numerical and experimental results concerning initiation of detonation at hot-spots.

Asymptotic curve of the scattering of the products of a steady-state detonation

Asymptotic curve of the scattering of the products of a steady-state detonation

Steady-state detonation in a mixture of a gaseous explosive with a finely divided powder

Steady-state detonation in a mixture of a gaseous explosive with a finely divided powder

Theoretical and experimental study of cylindrical shock and heterogeneous detonation waves

A simplified theory of blast initiation of detonations in clouds of fuel in gaseous or droplet form is developed and agrees with the experiments described below. The flow is at first dominated by the strong blast wave but transition from blast to detonation behavior occurs near a critical radius r∗ where the blast energy and the heat of combustion contained in r < r∗ are equal. The complex flow in this transition region cannot be determined analytically. In the simplified theory the details of the transition region are ignored but the flow is represented by the self-similar solution for a strong blast wave for r < r∗ and by the self-similar detonation solution for r > r∗. The development of a sectored shock tube to study cylindrical shock waves and two-phase detonations is described. Data are presented for shock waves as well as for blast initiated detonations of a monodisperse spray of 400 μ kerosene droplets in air at standard conditions. Two regimes of propagation were established experimentally: (1) the subcritical energy regime, where decoupling of shock and reaction zone results in a strong blast wave type decay and, (2) the supercritical energy regime, where the initially overdriven cylindrical detonation decays, at some critical radius, to its Chapman-Jouguet state. Experimentally determined critical radii and steady-state detonation velocity agree very well with theoretical predictions. Detonation velocity was found to be constant at the plane C–J value for radius greater than the critical radius.

On the instability of H 2-Cl 2 gaseous detonations

Experimental results are presented to confirm the existence of steady state detonation waves in H2 Cl2 mixtures. It is observed that cylindrical and spherical detonation waves in H2-Cl2 mixtures exhibit the same qualitative features and dynamics as waves in hydrocarbon-oxygen mixtures to the extent of possessing a similar characteristic “regular” multi-headed micro-structure.

Two-dimensional steady-state detonation waves

Exact relationships have been derived for the steady-state Zeldovich-von Neumann-Doering flow in a cylindrically symmetric detonation behind a curved shock. The equations of motion are integrated along the axis of symmetry without approximating the radial particlevelocity gradient to obtain conservation relationships as generalized Rankine-Hugoniot equations. The Chapman-Jouguet (C-J) condition is formulated with these relationships for a polytropic equation of state to obtain exact expressions for C-J parameters on the axis of symmetry. An inverse method is developed for constructing exact solutions for the axial reaction zone, as the diameter of the charge increases from its critical value to infinity and the flow becomes one dimensional. A particular solution is constructed and examined to demonstrate the dependence of the reaction zone on flow divergence in two-dimensional detonation.

Calculation of the Characteristics of Detonation Waves in Real Materials

The physical model and mathematical methods used in computing the behavior of detonation waves in real materials are described and used to study the detonation behavior of TNT. Data needed as input to the problem are the equation-of-state parameters of the reacted and unreacted phases and the reactionrate parameters. The equation-of-state data are derived from experimentally obtained Hugoniots of the explosive and from experimentally determined steady-state detonation velocities. Values for the rate parameters are obtained by matching the growth trajectories of computed waves with experimentally determined curves over a range of initiation pressures. Good agreement is found between calculated and observed reaction-zone thicknesses, and a trajectory computed for an initiation pressure significantly removed from those at which the rate parameters were evaluated showed fair agreement with experiment.

Explicit solutions for the buildup of an accelerating reactive shock to a steady-state detonation wave

A general method is presented for constructing explicit solutions for the flow of a reactive, polytropic, fluid behind a strong shock supported by a piston. The initial value problem is formulated by prescribing the shock path, and its solution is obtained in terms of the Lagrange particle-velocity gradient. Integration of the continuity equation gives the density field, integration of the momentum equation gives the pressure field, and the energy equation defines the corresponding energy-release rate field. The method of integration provides exact solutions for testing numerical schemes of integrating the flow equations, and forms the basis for modeling the energy-release rate in condensed explosive directly from the observable properties of shock waves. To construct a particular solution, it is sufficient to prescribe a shock path and particle-velocity gradient. The simple solution given for buildup to detonation is analyzed to demonstrate the dependence of initiation on the rear-boundary condition.

Detonation Wave Structure near the Hot Boundary

The solutions of Wood and Adamson for steady state detonation wave structure are discussed with particular attention given to the hot boundary where combustion is complete. Unimolecular, irreversible reaction kinetics, with an ignition temperature, and small rate parameter are assumed. An alternate solution based on Wood's analysis is presented which agrees with Wood's and Adamson's results when the hot boundary Mach number is less than unity. The solution presented here does not agree with that of Wood when the hot boundary Mach number is unity. We find that u ∼ 1 + const (log x)−1 as x → 0 when the hot boundary Mach number is unity. u is the reduced velocity; x is the mass concentration of combustible.

The shock-to-detonation transition in solid explosives

The development of a shock wave and its subsequent growth-to-detonation is considered to be a necessary step in the initiation of detonation in any explosive. Using this argument as a basis, it is logical to study in detail, the development of impulse-initiated detonations, to establish the dependence of the growth-to-detonation process on physical, chemical, and geometric variables which appear to be of importance. In this paper, experiments on shock initiation of cast and pressed explosives are discussed. Plane shocks developed by explosive plane-wave generators, and degraded to desired peak amplitudes by the use of intermediate layers of inert materials, were used to initiate detonation in the test explosive sample. The velocity of the shock in each sample was measured as a function of distance into the explosive and as a function of initial shock amplitude. Initial shock pressures ranged from 28 to 140 kilobars. Explosives discussed are TNT and various cyclotols. Both cast and pressed charges were used. In cast charges other than TNT the shock velocity remained essentially constant for a period of time, the length of which depended on the initial shock amplitude, and then rapidly accelerated to normal, steady state detonation velocity. In pressed charges it was found that in the rapid rise, the shock velocity temporarily exceeded the steady detonation value, but decayed thereafter to that of the normal steady detonation. In cast TNT the velocity was found to rise to a value intermediate to that of the initial shock and the final detonation, where it persisted for a time before growth to the normal detonation value. The over-all results can be explained by a hydrodynamic model in which pressure build-up, due to chemical reaction behind the shock, reinforces the shock front as it proceeds through the charge. On the other hand, the detailed results cannot be explained by thermal reactions in homogeneous domains, but require the concept of hotspot initiation. In the discussion our findings will be compared with the work of others who have used various impact and gap-test configurations. Some of the problems and differences of opinion which have arisen in the interpretation of shock initiation will be discussed.

Structure of Detonations in Dilute Sprays

Solutions to the differential equations governing the structure of a steady-state detonation in a spray are obtained both numerically and by means of analytical approximations for the case in which the droplets in the spray burn heterogeneously. It is shown that, for reasonable droplet burning rates, the detonation structure corresponds almost precisely to the spray analog of the von Neumann hypothesis of a shock wave followed by a deflagration zone. The size of the burning region is demonstrated to be large enough to cast doubt upon the stability of a spray detonation not supported to a significant extent by purely gaseous reactions.

Detonation Pressure of Liquid TNT

The plane steady-state detonation pressure behind the reaction zone of liquid TNT is reported. This pressure of 171.8 kilobars was established by measuring free-surface velocity as a function of plate thickness for 2024 aluminum plates placed in contact with the detonating explosive. The zero thickness metal shock pressure, obtained by extrapolating the free-surface velocity data, is corrected to the corresponding detonation pressure by an impedance matching calculation. Recording was done by a sweeping-image camera technique.

Theory of Detonations. III. Ignition Temperature Approximation

This paper is one of a series in which we discuss the effect of viscosity, diffusion, and heat conductivity on the structure of steady-state plane detonation waves. It is shown that the consideration of these phenomena may lead to considerable overlapping of the reaction and shock zones and also to the existence of detonation limits. In order to discuss in more detail the topological nature of the solutions and the nature of the detonation limits, the equations are simplified by idealizing the chemical kinetics in the following manner: At temperatures below an ignition temperature, the reaction rates are taken to be zero; at temperatures above this ignition temperature, the reaction rates are taken to be functions of the chemical composition but independent of the temperature. In order to further simplify the equations, the Prandtl number is taken to be ¾ and the Lewis number to be unity. These idealizations lead to an uncoupling of the detonation equations, although the importance of the transport properties remains unchanged. In the high-temperature range, the fractions of the mass rate of flow, Gi, are functions of the chemical composition only. In the low-temperature range, the Gi are constant. With these simplifications, we consider in detail both flames and detonations involving the unimolecular A→B or the equivalent bimolecular reaction A+X→B+X where X represents either a molecule of A or B. Calculations are made for values of the ignition temperature greater than, equal to, and less than the von Neumann spike temperature. Comparison of these calculations with numerical calculations previously performed, using an Arrhenius type variation of the reaction rate with temperature, gives the best agreement when the ignition temperature is taken to be greater than the von Neumann spike temperature. If the ignition temperature is greater than the von Neumann spike temperature, it is found that the thickness of the detonation wave is of the order of one mean free path. This suggests the conclusion that under the extreme conditions of a detonation the usual concept of chemical equilibrium between activated state and reactant molecules cannot apply. Instead, the molecules gain their energies of activation in successive stages. With this more complicated reaction mechanism, the detonation wave would be much thicker. These conclusions, regardless of the functional form of the rate law, depend upon the existence of a lower limit for the value of the rate constant which can support a steady-state detonation. Such a lower limit was suggested by our previous calculations with the Arrhenius rate law. However, more detailed studies are required to determine under what conditions such a lower limit may exist.