Investigation of the detonation regimes in gaseous mixtures with suspended starch particles

The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere (1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere (1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles. The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical simulations explain experimental observations made by Peraldi and Veyssiere (1986). Received 5 July 1997 / Accepted 13 July 1998     

On the effect of grain size on shock sensitivity of heterogeneous high explosives

Analysis of available data on dependence of the critical detonation diameter of various heterogeneous condensed explosives on mean size of grains and voids demonstrated that in many cases surprising correlations between and the initial specific surface area of heterogeneous explosives exist, namely, or . The run distance to detonation in wedge test with sustained strong shock of constant amplitude also linearly correlates with , i.e. . At the same time, the shock sensitivity reversal effect is often observed when grain size of HE is reduced. Apart from that Moulard (1989) found that detonation critical diameter of plastic bonded explosive with mono- and bimodal RDX grain size distribution depends nonmonotonously on mean grain size. Complicated dependence of shock sensitivity of heterogeneous explosives on their specific surface area can be explained based on comparison of the critical hot spot size at given characteristic pressure behind shock wave with the mean heterogeneity size . At high characteristic pressure (relative to the critical ignition pressure) is small compared with and all specific surface area of heterogeneous explosive is available for the hot spot growth process in accordance with the grain burn concept. However, when characteristic pressure of shock wave decreases, increases and can become comparable with . In this case only relatively large potential hot spots with size can result in self-supported hot spot growth process and shock sensitivity is controlled by the specific surface area which corresponds to only larger heterogeneities and can be significantly smaller than initial specific surface area. Received 18 July 1996 / Accepted 6 November 1996     

Detonation wave initiation of ram accelerator propellants

The current ram accelerator operations have shown that data on the ability of the propellants to detonate are required. Previous studies examined the efficacy of initiation techniques based on piston impact. The purpose of the present work is to analyze the effects of detonation wave transmission from a detonating mixture into a low sensitivity mixture. One-dimensional modeling based on the analysis of pressure vs particle velocity for the mixtures is used to interpret experimental data. Furthermore, calculations based on chemical kinetics (CHEMKIN code) are provided. Experimental data together with the modeling of the detonation transmission provide some new insight into the limiting conditions necessary to establish a Chapman-Jouguet (CJ) wave in a detonable mixture. Received 11 January 2000 / Accepted 15 September 2000     

Detonation properties of dense methane-oxygen-diluent gaseous mixtures: application to ram accelerators

Using a 90mm-bore, 3.15 m long detonation tube, experimental detonation characteristics (detonability limits, detonation velocities and peak pressures) of stoichiometric methane-oxygen-diluent mixtures at an initial pressure up to 3.5 MPa have been experimentally investigated. A parametric study has been carried out as a function of both amount and nature of diluent, namely carbon dioxide, nitrogen and helium. The experimental results allowed the adjustment and validation of computations of the Chapman-Jouguet characteristics by means of a thermochemical code. These experimental data associated with validated computations provide a valuable tool, among others, for the choice of the most appropriate mixture composition in the superdetonative combustion mode for ram accelerator (ramac) experiments. The investigations were organized to determine the upper detonable areas of dense ternary mixtures, and to provide detonation velocity data in order to adjust a series of intermolecular parameters involved in the thermochemical code. Received 8 May 1997 / Accepted 15 December 1997     

Explosive dispersal of solid particles

Abstract. The rapid dispersal of inert solid particles due to the detonation of a heterogeneous explosive, consisting of a packed bed of steel beads saturated with a liquid explosive, has been investigated experimentally and numerically. Detonation of the spherical charge generates a blast wave followed by a complex supersonic gas-solid flow in which, in some cases, the beads catch up to and penetrate the leading shock front. The interplay between the particle dynamics and the blast wave propagation was investigated experimentally as a function of the particle size (100–925 m) and charge diameter (8.9–21.2 cm) with flash X-ray radiography and blast wave instrumentation. The flow topology during the dispersal process ranges from a dense granular flow to a dilute gas-solid flow. Difficulties in the modeling of the high-speed gas-solid flow are discussed, and a heuristic model for the equation of state for the solid flow is developed. This model is incorporated into the Eulerian two-phase fluid model of Baer and Nunziato (1986) and simulations are carried out. The results of this investigation indicate that the crossing of the particles through the shock front strongly depends on the charge geometry, the charge size and the material density of the particles. Moreover, there exists a particle size limit below which the particles cannot penetrate the shock for the range of charge sizes considered. Above this limit, the distance required for the particles to overtake the shock is not very sensitive to the particle size but remains sensitive to the particle material density. Overall, excellent agreement was observed between the experimental and computational results. Received 16 August 1999 / Accepted 26 June 2000     

Structure and multiplicity of detonation regimes in heterogeneous hybrid mixtures

The problem of propagation of steady nonideal detonations in heterogeneous hybrid mixtures is studied in the case of a hydrogen-air gaseous mixture with suspended fine aluminum particles. Due to the difference in the order of magnitude of the characteristic induction and combustion times of gaseous mixture and solid particles, the process of energy release behind the leading shock front occurs over an extended period of time and in a nonmonotonic way. An approximate numerical model has been improved to find the steady propagation regimes and investigate their structure. The problem is analyzed in the frame of the theory of the mechanics of multiphase media with mass, momentum and heat exchanges between particles and gases. The one-dimensional ZND model of detonation with losses to the lateral boundaries is used. It is shown that three different steady propagation regimes may exist: the Pseudo-Gas Detonation (PGD), the Single-Front Detonation (SFD) and the Double-Front Detonation (DFD). The numerical results match the available experimental results obtained previously. The influence of the fundamental parameters of the system on the domains of existence of the different regimes is displayed. Moreover, it is shown that, according to the theory of nonideal detonations with nonmonotonic energy release, there may exist a multiplicity of detonation modes. However, the total number of solutions actually obtained by numerical calculations differs from that predicted by the theory. The reasons for these discrepancies are discussed.     

Detonation waves in trinitrotoluene

Fabry-Perot, ORVIS, and VISAR laser interferometry are used to obtain nanosecond time resolved particle velocity histories of the free surfaces of copper and tantalum discs accelerated by detonating trinitrotoluene (TNT) charges and of the interfaces between TNT detonation products and lithium fluoride crystals. TNT detonation reaction zone profiles are measured for self-sustaining detonation and piston supported overdriven (supracompressed) waves. The experimental records are compared to particle velocity histories calculated using very finely zoned meshes of the exact dimensions with the DYNA2D hydrodynamic code. The Ignition and Growth reactive flow model, which is based on the Zeldovich-von Neumann-D?ring (ZND) theory of detonation, yields excellent agreement with the experimental records for TNT using an unreacted von Neumann spike pressure of 25 GPa, a reaction rate law which releases 90% of the chemical energy within 80 ns and the remaining 10% over an additional 200 ns, and a reaction product equation of state fit to cylinder test data assuming a Chapman-Jouguet pressure of 19 GPa. The late time energy release is attributed to diffusion controlled solid carbon particle formation. Received 26 July 1997 / Accepted 29 December 1997     

Detonation interaction with wedges and bends

The paper reports the results of a series of studies on the interaction of gaseous detonations with obliquely inclined surfaces. Interactions of increasing complexity are described in turn: at a planar inclined wall, two-dimensional propagation in a curved channel and finally three-dimensional interaction with a bend in a cylindrical pipe. The role of detonation structure is discussed as well as the magnitude and duration of potentially damaging overpressures. Received 15 December 2000 / Accepted 15 January 2002     

Numerical modelling of detonation structure in two-phase flows

A one-dimensional physical model and a numerical method for the simulation of heterogeneous detonation were proposed based on an Eulerian approach for heterogeneous flows. The combination of modern shock-capturing schemes in combination with a dynamically moving, adaptive grid ensure the properresolution of both reaction zones and flow discontinuities. Numerical examples illustrate the effect of the heat release due to heterogeneous combustion. Received August 4, 1995 / Accepted December 12, 1995     

Some observations of detonation propagation through a gas containing dust particles in suspension

An experimental study of the influence of low concentration particle suspensions on the propagation of detonation waves in a combustible gaseous mixture is presented. In all cases the particles have an effect on the propagation of the detonation but at certain concentrations, both with inert and combustible particles, a zone of reduced pressure is observed following the detonation front. At the end of this zone there is a sharp pressure increase, which, in some instances, resembles a second shock or detonation front. The paper considers the possible origins of this second pressure rise.R.O. Carvel, Present address: Department of Civil and Offshore Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK     

Detonation and deflagration initiation at the focusing of shock waves in combustible gaseous mixture

Abstract. Detonation and deflagration initiation under focusing conditions in a lean hydrogen-air mixture was experimentally investigated. The experiments were carried out in a shock tube equipped with the laser schlieren system and pressure transducers. Two-dimensional wedges (53° and 90°), semi-cylinder and parabola, were used as the focusing elements. The peculiarities of mild and strong ignition inside the reflector cavity were visualized. A hydrogen-nitrogen mixture was taken for comparison between reactive and inert mixture. It was found that mild ignition inside the reflector cavity can lead to detonation initiation outside the cavity. Schlieren pictures of the process were obtained and the dependence of the distance of detonation initiation on Mach number of the incident shock wave was established. Received 30 August 1999 / Accepted 23 February 2000     

A numerical simulation of reflection processes of a detonation wave on a wedge

Abstract. A two dimensional numerical simulation has been performed to study reflection processes of detonation waves on a wedge. The numerical scheme adopted is the flux corrected transport scheme and a two-step chemical reaction is assumed for a stoichiometric oxyhydrogen mixture diluted with argon. Transverse wave structures of the detonation are produced by artificial disturbances situated in front of a one-dimensional Chapman-Jouguet detonation wave. Numerical grids are generated by solving a Laplace equation. Results show that in the case where Mach reflection occurs, the cells in the Mach stem are smaller than those in the incident wave and are distorted in shape. There is also an initiating stage during which the cells in the Mach stem are created. The critical angle beyond which Mach reflection cannot occur is discussed. Received 15 October 1999 / Accepted 27 March 2000     

Mechanism of detonation of emulsion explosives with microballoons

A mechanism of detonation of emulsion explosives containing microballoons in finite-diameter charges is described. A parametric dependence of the detonation velocity on the charge characteristics is obtained. The fact that the reaction-zone width increases with decreasing charge porosity is explained. It is shown that the emulsion does not completely burn out at the Chapman-Jouguet point. Final formulas for calculating the reaction time and reaction-zone width are given.

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Critical radius of explosive gaseous mixtures with initial concentration gradients

A synthetic review of works concerning detonation of non-uniform explosive mixtures allows to retain a criterion of detonation onset. This criterion is due to Zel'dovich and then Makhviladze. The present study proposes to adapt Makhviladze's criterion to define the formation point of a quasi-stationary detonation in spatially non-uniform, non-stationary and non-preheated gaseous mixtures. The temperature increase of gaseous mixture is due to the travelling shock. This point is compared to the critical radius defining the distance for which the Chapman-Jouguet conditions are attained. The detonability of a non-uniform medium (propane/oxygen mixtures) is characterized by a small scale experimental investigation and by application of a simple advection-diffusion model. Accepted 3 March 1996     

Ignition and detonation of solid explosives: a micromechanical burn model

This paper describes a new computational framework for modeling splid explosives and proof-of-concept calculations. Our goal is to expand predictive model capability through the inclusion of various micro-mechanical burn processes. We propose a model which is complicated enough to represent underlying physics, but simple enough for engineering scale computations. Key components of the model include energy localization, the growth of hot spots, micro-mechanics in/around hot spots, and a phase-averaged mixture equation of state. The nucleation and growth of locally heated regions is treated by a statistical model based on an exponential size distribution. Proof-of-concept calculations are limited to shock loading, but show the capability of simulating Pop-plots, initial temperature effect, detonation waves in 2D, detonation shock confinement test, and multi-dimensional effects in a unified fashion based on micro-physics.

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Existence of the detonation cellular structure in two-phase hybrid mixtures

The cellular detonation structure has been recorded for hybrid hydrogen/air/aluminium mixtures on 1.0 m 0.110 m soot plates. Addition of aluminium particles to the gaseous mixture changes its detonation velocity. For very fine particles and flakes, the detonation velocity is augmented and, in the same time, the cell width diminishes as compared with the characteristic cell size of the mixture without particles. On the contrary, for large particles, the detonation velocity decreases and the cell size becomes larger than . It appears that the correlation law between the cell size and the detonation velocity in the hybrid mixture is similar to the correlation between the cell size and the rate of detonation overdrive displayed for homogeneous gaseous mixtures. Moreover, this correlation law remains valid in hybrid mixtures for detonation velocities smaller than the value D of the mixture without particles. Received 10 May 2001 / Accepted 12 August 2002 Published online 19 December 2002 Correspondence to: B. Veyssiere (e-mail: veyssiere@lcd.ensma.fr)     

Non-equilibrium model of steady detonations in aluminum particles - oxygen suspensions

Steady-state detonation regimes are studied on the basis of the mathematical model of detonation of aluminum particles in oxygen taking into account differences in velocities and temperatures of the mixture components. The final steady state is analyzed by determining the types of final singularities in the plane of relaxation parameters (the ratios of characteristic times of thermal and velocity relaxations and combustion). The regions of existence of steady-state regimes are found numerically, depending on the detonation wave velocity and relaxation parameters. Numerical illustrations of various flow types are presented, and the properties of the detonation wave structure caused by velocity nonequilibrium are examined. Qualitative agreement of data obtained with frozen relaxation parameters and their dependence on the flow parameters is shown. Received 5 July 1997 / Accepted 13 July 1998     

Detonation interaction with a diffuse interface and subsequent chemical reaction

We have investigated the interaction of a detonation with an interface separating a combustible from an oxidizing mixture. The ethylene-oxygen combustible mixture had a fuel-rich composition to promote secondary combustion with the oxidizer in the turbulent mixing zone that resulted from the interaction. Diffuse interfaces were created by the formation of a gravity current using a sliding valve that initially separated the test gas and combustible mixture. Opening the valve allowed a gravity current to develop before the detonation was initiated. By varying the delay between opening the valve and initiating the detonation it was possible to achieve a wide range of interface conditions. The interface orientation and thickness with respect to the detonation wave have a profound effect on the outcome of the interaction. Diffuse interfaces result in curved detonation waves with a transmitted shock and following turbulent mixing zone. The impulse was measured to quantify the degree of secondary combustion, which accounted for 1–5% of the total impulse. A model was developed that estimated the volume expansion of a fluid element due to combustion in the turbulent mixing zone and predicted the resulting impulse increment.      

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

Turbulent jet initiation of detonation in hydrogen-air mixtures

Large scale experiments (50 m³) have been carried out on the initiation of detonation by means of a jet of hot combustion products. The effects of hydrogen concentration (18–30% vol.), jet orifice diameter (100–400 mm), and the mixture composition in constant volume explosion chamber (25–50%) were investigated. Both high enough hydrogen concentration and large enough jet size are necessary for detonation initiation. The minimum values are within the ranges of 20 to 25% vol. H₂, and of 100 to 200 mm correspondingly. A minimum ratio of jet size and mixture cell width 12–13 is required for detonation initiation.