Detonation Shock Dynamics Theory Research Articles

Calibration and verification of the reaction rate for an insensitive PBX

To investigate the detonation characteristics of an insensitive Plastic bonded explosive (PBX), the reaction rate was obtained and used in the numerical simulation of diverse case problems in the one-dimensional and two dimensional space. To calibrate the reaction rate, Detonation shock dynamics (DSD) theory was adopted, and two-dimensional steady-state experimental data were used to determine the shock front curvature function D n (κ). The reaction rate was calibrated by numerically integrating the master equation of the DSD theory. For the calibrated reaction rate, the simulation of the Large scale gap test (LSGT) and EIDS CAP test with regard to the shock sensitivity problem were carried out. Two numerical example were investigated using the reaction rate. First, an underwater explosion, which is basically a one-dimensional problem, was solved. Second, to also validate the reaction rate detonation wave progress, a corner turning problem was solved. Considering the results of the simulations and the experimental test, it was concluded that the calibrated reaction rate well describes the detonation characteristics of insensitive PBX with a reasonable degree of accuracy. The present study is the first case to obtain the reaction rate of an insensitive castable PBX using the DSD theory. Moreover the reaction rate obtained was verified using different detonation tests such as the gap sensitivity test, the underwater explosion test and the detonation wave propagation test.

Predictions of Detonation Propagation Through Open Cell Foam Embedded in Chemically Sensitized Nitromethane

We report results of Eulerian hydrodynamic simulations of detonation shock waves propagating through open cell foams constructed of aluminum, polymethylmethacrylate, and lead at approximately 20 % relative density in nitromethane. By varying pore sizes, as well as material impedance, we predict the dynamic responses at the mesoscale using a reactive flow model in the ALE3D software package. We explain predictions of the detonation profile of each explosive system, along with the stress-strain response of the foams therein. Finally, we describe predictions of a radially expanding detonation front and apply the theory of Detonation Shock Dynamics to the expansion rate of the shock front.

Embedded particle size distribution and its effect on detonation in composite explosives

This paper discusses the effects of stochastically varying inert particle parameters on the long-term behaviour of detonation front propagation. The simulation model involves a series of cylindrical high explosive unit cells, each embedded with an inert spherical particle. Detonation shock dynamics theory postulates that the velocity of the shock front in the explosive fluid is related to its curvature. In our previous work, we derived a series of partial differential equations that govern the propagation of the shock front passing over the inert particles and developed a computationally efficient simulation environment to study the model over extremely long timescales. We expand upon that project by randomising several properties of the inert particles to represent experimental designs better. First, we randomise the particle diameters according to the Weibull distribution. Then we discuss stochastic particle spacing methods and their effects on the predictability of the shock wave speed. Finally, we discuss mixtures of plastic and metal particles and material inconsistency among the particles.

Scaling of detonation velocity in cylinder and slab geometries for ideal, insensitive and non-ideal explosives

Experiments were conducted to characterize the detonation phase-velocity dependence on charge thickness for two-dimensional detonation in condensed-phase explosive slabs of PBX 9501, PBX 9502 and ANFO. In combination with previous diameter-effect measurements from a cylindrical rate-stick geometry, these data permit examination of the relative scaling of detonation phase velocity between axisymmetric and two-dimensional detonation. We find that the ratio of cylinder radius ($R$) to slab thickness ($T$) at each detonation phase velocity ($D_{0}$) is such that$R(D_{0})/T(D_{0})<1$. The variation in the$R(D_{0})/T(D_{0})$scaling is investigated with two detonation shock dynamics (DSD) models: a lower-order model relates the normal detonation velocity to local shock curvature, while a higher-order model includes the effect of front acceleration and transverse flow. The experimentally observed$R(D_{0})/T(D_{0})$(${<}1$) scaling behaviour for PBX 9501 and PBX 9502 is captured by the lower-order DSD theory, revealing that the variation in the scale factor is due to a difference in the slab and axisymmetric components of the curvature along the shock in the cylindrical geometry. The higher-order DSD theory is required to capture the observed$R(D_{0})/T(D_{0})$(${<}1$) scaling behaviour for ANFO. An asymptotic analysis of the lower-order DSD formulation describes the geometric scaling of the detonation phase velocity between the cylinder and slab geometries as the detonation phase velocity approaches the Chapman–Jouguet value.

Numerical study of detonation shock dynamics using generalized finite difference method

The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of the level set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of the detonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel problem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain. The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtained conveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSD must be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable any more.

Validation of DSD Relations for RDX‐TNT‐Based Cast Explosives for Lower Diameters and Dn–κ Surface Equation

AbstractIn this paper, we extended our work on RDX and TNT‐based explosives to lower diameter to validate detonation shock dynamics (DSD) first‐order relationships between normal detonation velocity Dn and detonation wave curvature κ. At 25 mm diameter, we observed that Dn–κ relationship approximates, although not perfectly, the relation for 50 mm diameter. Thus to an approximation, the first order DSD theory is independent of geometry. On that basis, a general equation has been proposed, which can predict Dn–κ for RDX/TNT cast explosives in the mixing ratios 60 : 40–40 : 60.

Propagation laws for steady curved detonations with chain-branching kinetics

An extension to the theory of detonation shock dynamics is made and new propagation laws are derived for steady, near-CJ (Chapman-Jouguet), weakly curved detonations for a chain-branching reaction model having two components. The first is a thermally neutral induction stage governed by an Arrhenius reaction with a large activation energy, which terminates at a location called the transition interface, where instantaneous conversion of fuel into an intermediate species (chain radical) occurs. The second is an exothermic main reaction layer (or chain-recombination zone) having a temperature-independent reaction rate. We make an ansatz that the shock curvature is sufficiently large to have a leading-order influence on the induction zone structure, whereupon it is shown that multi-dimensional effects must necessarily be accounted for in the main reaction layer. Only for exactly cylindrical or spherical waves can such multi-dimensional effects be omitted. A requirement that the main reaction layer structure pass smoothly through a sonic plane leads to a propagation law for the detonation front: a relationship between the detonation velocity, the shock curvature and various shock arclength derivatives of the position of the transition interface. For exactly cylindrically or spherically expanding waves, a multi-valued detonation velocity-curvature relationship is found, similar to that found previously for a state-sensitive one-step reaction. The change in this relationship is investigated as the ratio of the length of the main reaction layer to the induction layer is changed. We also discuss the implications of chain-branching reaction kinetics for the prediction of critical detonation initiation energy based on detonation-velocity curvature laws. Finally several calculations that illustrate the important effect that arclength and transverse flow variations may have on the steady propagation of non-planar detonation fronts are presented. Such variations may be important for the propagation of cellular gaseous detonation fronts and for the axial propagation of detonations in a cylindrical stick of condensed-phase explosive. We also show that the arclength variations provide a formal mechanism for the existence of steady non-planar detonation fronts having converging sections, a possibility ruled out for simple irreversible one-step reaction mechanisms where only diverging steady waves are admissible.

Computation of shock acceleration effects on detonation shock dynamics for explosives described by general equation of state

The inclusion of detonation shock acceleration effects leads to an extended theory of detonation shock dynamics (DSD). The shock motion is described by an intrinsic partial differential equation specified in terms of the normal shock velociety, D n , the normal shock acceleration D n , and the curvature, κ . Earlier developments were based on analytical (asymptotic) calculations and carried out for the polytropic equation of state (EOS) that made detailed analysis tractable. But the demands of quantitative accuracy for engineering design require that real EOS constitutive forms be used with more functional complexity. In this paper, we present a numerical approach that can be used to compute the D n -D n -κ -relation for general EOS and rate-law forms.

Detonation shock dynamics and comparisons with direct numerical simulation

Comparisons between direct numerical simulation (DNS) of detonation and detonation shock dynamics (DSD) is made. The theory of DSD defines the motion of the detonation shock in terms of the intrinsic geometry of the shock surface, in particular for condensed phase explosives the shock normal velocity, D n , the normal acceleration, [Ddot] n , and the total curvature, κ. In particular, the properties of three intrinsic front evolution laws are studied and compared. These are (i) constant speed detonation (Huygens construction), (ii) curvature-dependent speed propagation (κ relation) and (iii) curvature- and speed-dependent acceleration ([Ddot] n –D n –κ relation). We show that it is possible to measure shock dynamics directly from simulation of the reactive Euler equations and that subsequent numerical solution of the intrinsic partial differential equation for the shock motion (e.g. a [Ddot] n –D n –κ relation) reproduces the computed shock motion with high precision.

Level Set Methods Applied to Modeling Detonation Shock Dynamics

We give an extension of the level set formulation of Osher and Sethian, which describes the dynamics of surfaces that propagate under the influence of their own curvature. We consider an extension of their original algorithms for finite domains that includes boundary conditions. We discuss this extension in the context of a specific application that comes from the theory of detonation shock dynamics (DSD). We give an outline of the theory of DSD which includes the formulation of the boundary conditions that comprise the engineering model. We give the formulation of the level set method, as applied to our application with finite boundary conditions. We develop a numerical method to implement arbitrarily complex 2D boundary conditions and give a few representative calculations. We also discuss the dynamics of level curve motion and point out restrictions that arise when applying boundary conditions.