Reactive Shock Research Articles

A global simulation method for obtaining reduced reaction mechanisms for use in reactive blast wave flows

A finite rate chemistry solver usually consumes the largest part of the computing time in the numerical simulation of reactive flows. To reduce these costs, a global simulation method has been developed for systematically simplifying detailed reaction mechanisms and a reduced reaction mechanism for CH4−O2 is presented. This reduced mechanism accurately replicates the associated detailed mechanism whilst significantly reducing the required computing time. A shock induced methane combustion problem is computed by coupling the reduced reaction mechanism to a 1-D viscous compressible flow solver. As a comparison, a simulation of non-reactive shock flow having the same initial conditions is also performed. These calculations reveal some of the key features found in reactive shock flows.

Detonation structures behind oblique shocks

Detonation structures generated by wedge-induced, oblique shocks in hydrogen–oxygen–nitrogen mixtures were investigated by time-dependent numerical simulations. The simulations show a multidimensional detonation structure consisting of the following elements: (1) a nonreactive, oblique shock, (2) an induction zone, (3) a set of deflagration waves, and (4) a ‘‘reactive shock,’’ in which the shock front is closely coupled with the energy release. In a wide range of flow and mixture conditions, this structure is stable and very resilient to disturbances in the flow. The entire detonation structure is steady on the wedge when the flow behind the structure is completely supersonic. If a part of the flow behind the structure is subsonic, the entire structure may become detached from the wedge and move upstream continuously.

Studies of reactive triple shock collision

Experimental studies have been performed on two-dimensional reactive blast waves in a diverging nozzle. Both blast and reaction wave loci have been measured and the results compared with numerical calculations.

Convection of a pattern of vorticity through a reacting shock wave

The passage of a weak vorticity disturbance through a reactive shock wave, or detonation, is examined by means of a linearized treatment. Of special interest is the effect of chemical heat release on the amplification of vorticity, in particular, and on the disturbance pattern generated downstream of the detonation, in general. It is found that the effect of exothermicity is to amplify the refracted waves. The manner in which the imposed disturbance alters the structure of the detonation itself is also discussed.

Von neumann peak from detonation velocity

The passage of a detonation wave through solid explosive can be described as the result of a reactive shock in the crystalline material and the transmission of spalled unreacted explosive across any air spaces which may be present. Calculation of the spall velocity can then be related to a particle velocity which is thought to be the von Neumann peak. This peak particle velocity is roughtly 20% higher than the Chapman-Jouguet (CJ) value at the highest densities and may exceed 30% at low explosive densities.

Detonic research infrared radiometer with nanosecond response

Two infrared radiometers were constructed for use in shock wave and detonation research. Fast detectors were combined with wide-band amplifiers to achieve an overall response of about 5 ns, which was confirmed by experiments on planar shocked copper plates. Detonation experiments show the merits of a new optical technique for probing detonation wave structure and for reactive and nonreactive shock wave research.

A reactive shock in a polytropic gas

We shall consider the progress of a plane-detonation wave in a polytropic gas. Three basic assumptions are made; namely, that the gas is shocked by an infinite piston moving at a constant velocity up, that the shock is sufIicient to start the detonation, and that the detonation iself takes place rapidly throughout a thin but finite-width region, rather than instantaneously across a geometrical surface, as is usually supposed. The main content of the paper centers around this last assumption, which by allowing the energy release to occur in a finite time in a boundary layer, produces a model which is closer to reality. Thus the flow comprises three distinct domains; the unburnt gas ahead of the detonation, the burning zone in the boundary layer, and the burnt gas zone which extends from the back of the boundary layer to the piston. As is usual, the detonation reaction is assumed to transform the undetonated gas into a gas with similar thermodynamical properties, while at the same time releasing a certain amount of heat. The rate at which this heat is released depends on the local thermodynamical conditions and on the progress variable /3 introduced to describe the state of completion of the chemical kinetics of the gas in the burning zone. The equations which will be used to study the burning zone for a

Self-similar solution of the spherical detonation problem

Under polytropic equation of state and strong shock assumptions, group-theoretic methods are used to obtain a class of self-similar solutions to a one-dimensional problem in reactive shock hydrodynamics with spherical symmetry and to characterize the class of all state-dependent chemical reaction rates under which such solutions exist. In the special case that the reaction rate is proportional to the internal energy, the system of ordinary differential equations describing the self-similar solution can be reduced to a single, first-order differential equation for which a phase-plane analysis yields the nature of the solution near the equation's critical points. Further, a modeling parameter which characterizes the flow is identified.

Similarity Solutions for Reactive Shock Hydrodynamics

It is shown how group-theoretic methods, or similarity methods, can be applied to determine the class of self-similar solutions for a one-dimensional, time-dependent problem in shock hydrodynamics,with a chemical reaction taking place behind the shock. The functional form of all reaction rates depending on the state variables is characterized under which the general system of differential equations and boundaryconditions admit self-similar solutions, It is shown that a subclass of these solutions can model certain processes in detonation physics.

Hysteresis-corrected calibration of manganin under shock loading

The coefficient of electrical resistance of manganin was measured under shock loading and ramp unloading. We made 64 measurements of loading stress in the 1.3–40.5-GPa range and 22 measurements of unloading stress in the 1.9–23.2-GPa range. The average loading coefficient was 14% larger than the average unloading coefficient—a clear measure of resistance hysteresis. The source of the hysteresis is attributed to an irreversible resistance change in manganin caused by shock damage. We present techniques to correct for the effects of this irreversible resistance change. With this correction, both loading and unloading levels showed the same average coefficient of resistance 0.0221±0.004 per GPa. Our unified calibration procedure can be very useful for analyzing complex stress signals that are produced, for example, by reactive shock waves.

Constant velocity reactive shock waves for testing numerical methods

Piston driven reactive shock waves with constant velocity fronts are constructed for use in testing numerical methods. Explicit solutions are obtained for underdriven, Chapman-Jouguet and overdriven waves in which the reaction rate is proportional to the fraction of material unreacted.

Application of time-dependent numerical methods to the description of reactive shocks

The coupling of the hydrodynamics and the chemical kinetics in a reactive mixture ignited by the passage of a shock is examined using a time-dependent numerical model. The fluid dynamic and chemical rate equations are integrated self-consistently on their own characteristic time-scales using the flux-corrected transport and selected asymptotic methods, respectively. Results are presented for a shock in an H 2 −O 2 mixture. The detailed calculations of the chemical and fluid structure of the shocked region clearly how the chemical energy released is partitioned between the fluid motion and the internal energy. A calculation is also shown for a reactive shock reflected from a rigid wall.

Electron-spin-resonance studies of HMX pyrolysis products

Chemical transformations that occur at the reactive shock front of energetic materials determine many aspects of material properties and performance. One major shortcoming of current explosive models is the lack of chemical kinetics data of the reacting explosive at the high pressures and temperatures experienced under detonation conditions. In the absence of experimental data, long time-scale atomistic molecular dynamics simulations with reactive chemistry provide insight into the decomposition mechanisms of explosives and allow us to obtain effective reaction rates. These rates can then be incorporated into a thermochemical continuum code for accurate and predictive description of grain- and continuum-scale dynamics of reacting explosives. During the course of the past decade, we have examined the chemistry of several reacting explosive materials, such as the high-performing HMX and the very insensitive TATB explosives, both of which are organic molecular solids at ambient conditions. We have used quantum-based, self-consistent charge density functional tight-binding method to calculate the interatomic forces in molecular dynamics simulations either for thermal decomposition studies (constant volume–temperature) or dynamical shock studies using the multiscale shock simulation technique (MSST). These studies allow us to investigate the chemical reactivity of explosives and to examine electronic properties at extreme conditions of temperature and pressure for a relatively long timescale on the order of several hundreds of picoseconds. In this chapter, we discuss challenges in simulating the reactions of shocked energetic materials and review specific examples of our recent simulations on HMX, PETN, and shocked TATB. Each of these studies revealed interesting aspects associated with known macroscopic properties of these materials. We also discuss simulations on nonenergetic materials such as shocked carbon and methane.

On hydrodynamic effects of exothermic power in condensed explosives

The initial flow produced in an explosive by the impulsive action of a constant velocity rear-boundary is considered to provide a better understanding of the coupling between hydrodynamic flow and chemical reaction and the shock initiation of detonation in explosives impacted by flying plates. Equations determining the initial shape of the reactive shock are derived from the equations of motion for an arbitrary specific energy-pressure-specific volume-extent of reaction equation of state and an arbitrary energy release rate. These expressions for the flow derivatives define the relationship between hydrodynamic flow and energy release rate induced by a constant velocity rear boundary, and demonstrate the dependence of the shock initiation process on the equation of state of an explosive and its energy release rate. The equations for the first derivatives show that the shock accelerates with a positive particle velocity gradient; those for the second derivatives show that the wave can develop with a positive, negative, or zero pressure gradient and account for the flows observed by Bernier, Wackerle and Johnson, and Kennedy respectively. The equation determining the pressure gradient was used to check the results of numerical studies of initiation and to determine the relationship between the pressure gradient and the initial shock pressure for a series of condensed explosives. Calculations on cast TNT, PBX9404, and Composition B based on reasonable assumptions about their equations of state and energy release rates predict that the sign of the initial pressure gradient in these explosives will change from negative to positive as the initial shock pressure is increased in a series of shock initiation experiments.

Ionization measurement in reactive shock and detonation waves using microwave techniques

The use of microwave cavity techniques in the study of ionization in detonation waves and shock waves in reactive gas mixtures is discussed. Absorption measurements were conducted using a cavity oscillating in the TM010 mode at S band frequency and the shift in resonant frequency of a TE011 mode cavity, operating at X band frequency, was obtained by repetitively sweeping the frequency through the cavity resonance and displaying the response by means of a raster scan generator. The results are compared with microwave free-propagation experiments obtained at X and Q band frequencies in which both the microwave power absorbed by the ionized medium and the power transmitted through and reflected from the medium are monitored. Some results obtained by dc probes are also included for comparison.Equilibrium conductivities measured for the oxyhydrogen and oxyacetylene detonation waves are in reasonable accord with theoretical values. For the reactive shocks, however, the results obtained from the microwave reflection techniques yield far higher values of electron density than those obtained by the absorption methods; this is attributed to the inhomogeneous nature of the ionized medium.

Shock Initiation of XTX-8003 and Pressed PETN

Explosively driven, plane shock waves were used to study initiation characteristics of wedge- and pellet-shaped samples of PETN (pentaerythritoltetranitrate) pressed to densities of 1.60 and 1.72 g/cc, and the extrudable explosive XTX-8003, a mixture of PETN and an inert material. In each shot experiment the free-surface motion of the final attenuator element and the buildup to detonation of the reactive shock front through the explosive wedge were observed with a streak camera. Initial shock states of the explosives were determined by using the mirror-image approximation and the impedance-matching technique. Quantitative results include the Hugoniots of the unreacted explosives and curves relating the distance to detonation to the input shock pressure. Buildup to detonation in the lower density PETN samples appears to be controlled by a reaction occurring at or near the shock front, as is usually observed in shock initiation studies of heterogeneous explosives. However, buildup to detonation in the higher density PETN appears to be dominated by a reactive pressure pulse that forms well behind the leading shock, and which accelerates until it overtakes the leading shock, after which detonation occurs. Such an initiation behavior is more characteristic of homogeneous explosives.

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.

Explicit solutions for steady- and unsteady-state propagation of reactive shocks at constant velocity

A general method is presented for constructing explicit solutions for the equations governing reactive, hydrodynamic flow of a polytropic fluid behind a strong, constant-velocity shock when the particle-velocity gradient is assumed to be an arbitrary function of time. This assumption, together with the known boundary conditions along the shock path, defines the particle-velocity field; integration of the equations of motion along particle paths gives the density and pressure fields; and the combination of these solutions with the energy equation defines the corresponding energy-release-rate field. Particular solutions, obtained by specifying the arbitrary function, give general forms of the particle-velocity field for constructing classes of solutions for steady- and unsteady-state flow. By formulating the first law of thermodynamics for the energy distribution in the wave, we show how the shock propagation depends on the work done along the rear boundary and the energy released by chemical reaction. Properties of steady- and unsteady-state waves and details of the energy distribution within them are discussed to exemplify differences between these types of flow. In both cases, the particle-velocity field defines the piston path that initiates the flow with no transient phase; for unsteady flow, this path must always be followed, but for steady flow it must be followed only up to the reaction time when the characteristic from the piston becomes parallel to the shock front. Although these energy-release-rate fields do not necessarily correspond to those that would be determined with known chemical kinetic properties, these explicit solutions for initiating a constant-velocity reactive shock with no transient phase illustrate properties of reactive hydrodynamic flow that are important to understanding shock initiation of detonation in condensed explosives.

Theory of initiation of detonation in solid and liquid explosives

The experimentally observed differences in the growth of shock initiated detonation in liquid and in solid explosives are discussed with the object of deciding upon a reaction rate model for numerical calculations on the growth of reactive shock waves in granular solid explosives. It is suggested that while a strongly temperature dependent bulk reaction rate model is indicated for liquids and homogeneous solids, the behavior of granular solids indicates a reaction rate which is a function of the pressure behind the shock front and not of the average temperature. A pressure dependent energy release rate is shown to result in the reaction building up at the shock front rather that at the explosive/barrier interface. Under this condition it is possible to attempt approximate analytical solutions of the reactive shock equations which illustrate the relation between the initial growth or failure behavior of the wave and the initial shock pressure, shock curvature, and the rate of energy release and its pressure dependence. A pressure dependent energy release rate is shown to be a consequence of a grain burning model for the reaction process where the rate of propagation from ignition surfaces is assumed to be a function of the pressure and flame temperature of the products of reaction. The problems in verifying this hypothesis are briefly discussed. In low bulk density explosive where the shock pressure is low enough for it to be possible to make independent measurements of burning rate and its over-all pressure dependence, it is difficult to make sufficiently precise measurements of shock pressure. In high density explosives where the shock pressure/distance to steady detonation relationship can be determined with some precision, the magnitude of the pressure is greatly in excess of those at which burning rate measurements can be made.

Continuous Oscillographic Method for Measuring the Velocity and Conductivity of Stable and Transient Shocks in Solid Cast Explosives

The continuous monitoring of the position and relative conductivity of reactive shock waves in confined cast explosives is made possible by a new technique. A fine Nichrome wire is cast within and parallel to the long axis of the sample. A record of its resistance during detonation serves to locate the ionization front associated with detonation. The measurement is recorded on an oscillograph. From the photograph of this record, instantaneous detonation velocities are measured to within ±2%. Attenuation of the initiating shock causes a delay in the establishment of a stable detonation in the acceptor. The distance and time required for this transition is confined charges can be measured. The simultaneous use of independent Nichrome and copper wire sensors furnishes additional information about the conductivity of the predetonation zone. Failure of a propagating detonation can also be studied; this permits the measurement of critical diameters, i.e., that diameter below which detonation will not propagate in an unconfined charge. Examples of each use are presented.