Shock-to-detonation Transition Research Articles

Investigation of system parameters towards safer impact based shock-to-detonation transition in a novel laser driven flyer plate prototype

Laser driven flyer plate technology offers improved safety and reliability for detonation of explosives in industrial applications ranging from mining and stone quarrying to the aerospace and defense industries. This study is based on developing a safer laser driven flyer plate prototype comprised of a laser initiator and a flyer plate subsystem that can be used with secondary explosives. System parameters were optimized to initiate the shock-to-detonation transition (SDT) of a secondary explosive based on the impact created by the flyer plate on the explosive surface. Rupture of the flyer was investigated at the mechanically weakened region located on the interface of these subsystems, where the product gases from the deflagration of the explosive provide the required energy. A bilayer energetic material was used, where the first layer consisted of a pyrotechnic component, zirconium potassium perchlorate (ZPP), for sustaining the ignition by the laser beam and the second layer consisted of an insensitive explosive, cyclotetramethylene-tetranitramine (HMX), for deflagration. A plexiglass interface was used to enfold the energetic material. The focal length of the laser beam from the diode was optimized to provide a homogeneous beam profile with maximum power at the surface of the ZPP. Closed bomb experiments were conducted in an internal volume of 10 cm3 for evaluation of performance. Dependency of the laser driven flyer plate system output on confinement, explosive density, and laser beam power were analyzed. Measurements using a high-speed camera resulted in a flyer velocity of 670 ± 20 m/s that renders the prototype suitable as a laser detonator in applications, where controlled employment of explosives is critical.

Effect of shock impedance of mesoscale inclusions on the shock-to-detonation transition in liquid nitromethane

Two-dimensional, meso-resolved numerical simulations are performed to investigate the effect of shock impedance of mesoscale inclusions on the shock-to-detonation transition (SDT) in liquid nitromethane (NM). The shock-induced initiation behaviors resulting from the cases with NM mixed with randomly distributed, 100-μm-sized air-filled cavities, polymethyl methacrylate (PMMA), silica, aluminum (Al), and beryllium (Be) particles with various shock impedances are examined. In this paper, hundreds of inclusions are explicitly resolved in the simulation using a diffuse-interface approach to treat two immiscible fluids. Without using any empirically calibrated, phenomenological models, the reaction rate in the simulations only depends on the temperature of liquid NM. The sensitizing effect of different inclusion materials can be rank-ordered from the weakest to the strongest as PMMA → silica → air → Al → Be in the hot-spot-driven regime of SDT. Air-filled cavities have a more significant sensitizing effect than silica particles, which is in agreement with the experimental finding. For different solid-phase inclusions, hot spots are formed by Mach reflection upon the interaction between the incident shock wave and the particle. The sensitizing effect increases roughly with the shock impedance of the inclusion material. More details of the hot-spot formation process for each solid-phase inclusion material are revealed via zoom-in simulations of a shock passing over a single particle.

Effects of micrometer-scale cavities on the shock-to-detonation transition in a heterogeneous LX-17 energetic material

Cavities and other fracture structures within energetic materials may have significant impact on their performance. The mechanism on how hot spots induced by cavity collapse affect the detonation initiation process is still not fully understood. In this work, two-dimensional simulations are conducted for heterogeneous LX-17 energetic material containing array-distributed cavities to investigate the detonation initiation process induced by the impaction of the incident shock wave (ISW), and the impacts of cavity size and volume fraction on the shock-to-detonation transition (SDT) are also evaluated. First, we fix the cavity radius to be 40 μm and the cavity volume fraction to be 12.57%, and compare the detonation initiation processes for neat and heterogeneous LX-17 energetic materials. The results indicate that cavities within LX-17 can accelerate the detonation initiation, i.e., shortening the initiation distance and time. Then, the flow characteristics and incident shock wave evolutions during the cavity collapse process are analyzed. The results show that the interaction between the cavity and the incident shock wave results in the local hot spots and causes LX-17 reactant to auto-ignite, so as to accelerate the shock-to-detonation transition. Finally, the influence of the cavity size and volume fraction on the detonation initiation process is assessed. It is found that as the cavity volume fraction increases, the detonation initiation distance and time increase and even become larger than the results predicted of the neat case, i.e., the acceleration effect of cavities on the detonation initiation weakens and the cavities even inhibits the shock-to-detonation transition. When the cavity volume fraction is fixed, it is found cases of small-size cavity predict longer initiation distance and time than cases of large-size cavity. The analysis indicates that increasing cavity volume fraction corresponds to smaller density of LX-17 reactant, and the hot spot duration time is shorter for cases of small-size cavity than cases of large-size cavity. Therefore, the detonation initiation distance and time increase as the cavity volume fraction increases and the cavity size decreases.

Physically evocative meso-informed sub-grid source term for energy localization in shocked heterogeneous energetic materials

Reactive burn models for heterogeneous energetic materials (EMs) must account for chemistry as well as microstructure to predict shock-to-detonation transition (SDT). Upon shock loading, the collapse of individual voids leads to ignition of hotspots, which then grow and interact to consume the surrounding material. The sub-grid dynamics of shock-void interactions and hotspot development are transmitted to macro-scale SDT calculations in the form of a global reactive “burn model.” This paper presents a physically evocative model, called meso-informed sub-grid source terms for energy localization (MISSEL), to close the macro-scale governing equations for calculating SDT. The model parameters are explicitly related to four measurable physical quantities: two depending on the microstructure (the porosity ϕ and average pore size D¯void), one depending on shock–microstructure interaction (the fraction of critical voids ξcr), and the other depending on the chemistry (the burn front velocity Vhs). These quantities are individually quantifiable using a small number of rather inexpensive meso-scale simulations. As constructed, the model overcomes the following problems that hinder the development of meso-informed burn models: (1) the opacity of more sophisticated surrogate/machine-learning approaches for bridging meso- and macro-scales, (2) the rather large number of high-resolution mesoscale simulations necessary to train machine-learning algorithms, and (3) the need for calibration of many free parameters that appear in phenomenological burn models. The model is tested against experimental data on James curves for a specific class of pressed 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane materials. The simple, evocative, and fast-to-construct MISSEL model suggests a route to develop frameworks for physics-informed, simulation-derived meso-informed burn models.

Shock-to-detonation transition behavior of functionally graded energetic materials

The behavior of energetic materials is significantly influenced by the spatial distributions of microstructure heterogeneities and voids. We pursue the concept of Functionally Graded Energetic Materials whose microstructure features (e.g., grain size, grain volume fraction, void size, and void volume fraction) change spatially such that they may allow the behavior of the materials to be tailored. We explore using gradients in the density of voids to alter the detonation behavior of a polymer-bonded explosive (PBX) echoing PBX9501 with HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) grains and Estane binder. Five cases, two graded void distributions from 1% to 10% and 10% to 1% by volume along the length of the sample, and three uniform distributions matching the lowest (1%), average (5.5%), and highest (10%) void densities are considered. An Arrhenius reaction burn model is used to account for the chemical kinetics of HMX. Different detonation behaviors are obtained from the same graded sample when impact loading is from 1% void end and from the 10% void end as well as from the uniform cases. The SDT (shock to detonation transition) behaviors are analyzed in terms of the run distance, the time duration and shock velocity changes over the SDT process. The computational results are presented in the context of available experimental data for PBX9501 with which agreement is obtained through a parametric study. Overall, it is shown that gradients in microstructures of PBX can lead to SDT behaviors different or not obtainable from microstructures without gradients, thereby offering a mechanism for designing and tailoring new materials.

A Physics‐Aware Deep Learning Model for Energy Localization in Multiscale Shock‐To‐Detonation Simulations of Heterogeneous Energetic Materials

AbstractPredictive simulations of the shock‐to‐detonation transition (SDT) in heterogeneous energetic materials (EM) are vital to the design and control of their energy release and sensitivity. Due to the complexity of the thermo‐mechanics of EM during the SDT, both macro‐scale response and sub‐grid mesoscale energy localization must be captured accurately. This work proposes an efficient and accurate multiscale framework for SDT simulations of EM. We introduce a new approach for SDT simulation by using deep learning to model the mesoscale energy localization of shock‐initiated EM microstructures. The proposed multiscale modeling framework is divided into two stages. First, a physics‐aware recurrent convolutional neural network (PARC) is used to model the mesoscale energy localization of shock‐initiated heterogeneous EM microstructures. PARC is trained using direct numerical simulations (DNS) of hotspot ignition and growth within microstructures of pressed HMX material subjected to different input shock strengths. After training, PARC is employed to supply hotspot ignition and growth rates for macroscale SDT simulations. We show that PARC can play the role of a surrogate model in a multiscale simulation framework, while drastically reducing the computation cost and providing improved representations of the sub‐grid physics. The proposed multiscale modeling approach will provide a new tool for material scientists in designing high‐performance and safer energetic materials.

Experimental investigation of shock response to an insensitive explosive under double-shock wave

A new integrated velocimetry system that includes terahertz-wave-based Doppler velocimetry (TDV) and a multiplied electromagnetic particle velocity gauge (EMV) is demonstrated by measuring the particle velocity history and the corresponding shock-to-detonation transition (SDT) distance in double-shock experiments of insensitive explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)-2. This system overcomes the defects in resolution, testing distance, particle velocity measurement history, and shock-wave capture when TDV or EMV are used separately in double-shock experiments. The effectiveness of the integrated velocimetry system is verified via double-shock experiments, and the deviation of shock wave displacement is less than 6%. Furthermore, the desensitization effects of TATB-2 are determined by comparing the initiation behavior for the double-shock and sustained-pulse experiments. Results indicate that the longer the time of the unreactive preshock wave, the stronger the desensitization effects. Further, the reactive main shock wave in the double-shock experiment can weaken the desensitization effects of the double-shock wave.

Effects of Dense Inert Particle Loading in Shocked Energetic Materials

AbstractMetal particles are often added to solid‐fuel rocket motors and weapon systems to boost detonation propagation or to increase impact energy. Aside from the chemical effects of reactive particles, even inert particle effects can be significant on detonation properties due to the momentum and the energy exchanges between the phases. Therefore, a study of inert particles, that can exhibit direct effects on shock‐to‐detonation‐transition (SDT) depending on particle loading and its material properties, is needed. This work numerically investigates the effects of dense inert particle loading on SDT in energetic material (EM). The focus here is on local non‐equilibrium (NE) effects in particle‐added EM mixture and its correspondence to observed parametric trends on detonation. An Eulerian‐Eulerian (EE) framework capable of modeling dense‐dilute particles is used within a well‐established multi‐phase solver to capture dispersed motion in a reactive condensed phase. The numerical approach is first validated against available experimental data, and this is followed by an investigation of particle effects over a range of parameters where a condition‐dependent trend is observed. Focusing on the two‐phase NE effects, the dynamic and the thermal disparities between particles and EM are quantified to demonstrate the effect of relaxation parameters on the observed detonation quantities. The reduction in peak pressure and detonation velocity is observed to follow NE strengths and corresponding relaxation rates. An assessment of the effects of various particle loading parameters, i. e., concentration, size, density, and specific heat, on SDT is performed along with quantifying the relaxation process. All particle loading parameters show a range‐dependent effect on detonation properties, and the observed results demonstrate the relevance of two‐phase NE and corresponding relaxation processes.

Effects of Reversed Shock Waves on Operation Mode in H2/O2 Rotating Detonation Chambers

Operation modes are an important topic in the research of Rotating Detonation Chamber (RDC) as it can affect the stability of RDC. However, they have not been discussed in detail due to the limitation of measurement means in experiments. The aim of this research is to investigate the mechanism of different operation modes by numerical simulation. In this paper, a numerical simulation for RDCs with separate injectors is carried out. Different operation modes and mode switching are analyzed. There is a series of reversed shock waves in the flow field. It was found that they have great effects on operation mode and mode switching in RDCs. A reversed shock wave can transit into a detonation wave after passing through isolated fresh gas region where fresh gas and burnt gas distribute alternatively. This shock-to-detonation transition (SDT) phenomenon will influence the ignition process, contra-rotating waves mode and mode switching in RDCs. SDT makes the number of detonation wave increases, resulting in multi-wave mode with one ignition. Moreover, quenching of detonation waves after collision and SDT after passing through isolated fresh gas region are the mechanism of contra-rotating waves mode in RDCs with separate injectors. In addition, when the inlet total temperature increases, a shock wave is easier to transit into a detonation wave. The distance that a shock wave travels before SDT decreases when temperature increases. This will result in mode switching. Therefore, SDT determines that there is a lower bound of detonation wave number.

Research on the SDT technology based on a two-stage structure

The SDT (shock to detonation transition) technology based on a two-stage structure has been researched. The models of mass block’s velocity and shock-wave convergence produced from mass block impacting charge have been built, which reveal the mechanism of detonation caused by the impact. The influence characteristics of some parameters on the shock-wave convergence have been obtained. According to the analysis, the related parameters have been decided and the grope experiments were carried out. The result shows that the detonator employing the SDT structure, whose igniting time is less than 2ms, has good environmental adaptability. The technique of reliable and fast detonation of high explosive without using sensitive explosive has been realized.

Numerical Modelling of Shock Initiation of a HNIW‐Based Explosive

AbstractTo investigate shock‐to‐detonation transition (SDT) characteristics of a HNIW‐based explosive, a rate law based on the Forest Fire model was calibrated by conducting five wedge tests. In the wedge tests, initial shock pressure at wedge‐shaped test explosive charges was varied from 5 to 11 GPa. In each test, the shock trajectory along the wedge‐shaped explosive charge was recorded with a streak camera. The streak records showed that sharp SDT occurred in the test explosive. The shock Hugoniot of the test explosive was determined from the free‐surface velocity of PMMA attenuators measured with a VISAR instrument and the early shock velocity in the wedges, determined from the shock trajectories. The Pop plot for the test explosive was obtained from run distances to detonation estimated based on the shock trajectories. The Forest Fire rate of the test explosive was calibrated from the experimental Hugoniot and the Pop plot. The wedge tests were numerically simulated with the calibrated rate by using a one‐dimensional Lagrangian hydrodynamic code. The calculated shock trajectories closely reproduced experimental observations. The rate was further applied to two‐dimensional numerical simulations of large‐scale gap tests (LSGTs). The estimated critical gap thickness by the LSGT simulations was 43.7 mm, which was in good agreement with experimental data of 46.67 mm. The results of these two types of numerical simulations suggested that the calibrated rate could be used to model most SDT‐related applications.

Prediction of Probabilistic Detonation Threshold via Millimeter‐Scale Microstructure‐Explicit and Void‐Explicit Simulations

AbstractWe present an approach and relevant models for predicting the probabilistic shock‐to‐detonation transition (SDT) behavior and Pop plot (PP) of heterogeneous energetic materials (HEM) via mesoscopic microstructure‐explicit (ME) and void explicit (VE) simulations at the millimeter (mm) sample size scale. Although the framework here is general, the particular material considered in this paper is pressed Octahydro‐1,3,5,7‐tetranitro‐1,2,3,5‐tetrazocine (HMX). To systematically delineate the effects of material heterogeneities, four material cases are considered. These cases are homogeneous material, material with granular microstructure but no voids, homogeneous material with voids, and material with both granular microstructure and voids. Statistically equivalent microstructure sample sets (SEMSS) are generated and used. Eulerian hydrocode simulations explicitly resolve the material heterogeneities, voids, and the coupled mechanical‐thermal‐chemical processes. In particular, it is found that both microstructure and voids strongly influence the SDT behavior and PP. The effects of different combinations of microstructure heterogeneity and voids on the SDT process and PP are quantified and rank‐ordered. The overall framework uses the Mie–Grüneisen equation of state and a history variable reactive burn model (HVRB). A novel probabilistic representation for quantifying the PP is developed, allowing the calculation of (1) the probability of observing SDT at a given combination of shock pressure and run distance, (2) the run‐distance to detonation under a given combination of shock pressure and prescribed probability, and (3) the shock pressure required for achieving SDT at a given run distance with a prescribed probability. The results are in agreement with general trends in experimental data in the literature.

Meso-resolved simulations of shock-to-detonation transition in nitromethane with air-filled cavities

Two-dimensional meso-resolved numerical simulations are performed to investigate the complete shock-to-detonation transition (SDT) process in a mixture of liquid nitromethane (NM) and air-filled, circular cavities. The shock-induced initiation behaviors resulting from the cases with neat NM, NM with an array of regularly spaced cavities, and NM with randomly distributed cavities are examined. For the case with randomly distributed cavities, hundreds of cavities are explicitly resolved in the simulations using a diffuse-interface approach to treat two immiscible fluids and graphic processing unit-enabled parallel computing. Without invoking any empirically calibrated, phenomenological models, the reaction rate in the simulations is governed by Arrhenius kinetics. For the cases with neat NM, the resulting SDT process features a superdetonation that evolves from a thermal explosion after a delay following the passage of the incident shock wave and eventually catches up with the leading shock front. For the cases wherein mesoscale heterogeneities are explicitly considered, a gradual SDT process is captured. These two distinct initiation behaviors for neat NM and heterogeneous NM mixtures agree with experimental findings. Via examining the global reaction rate of the mixture, a unique time scale characterizing the SDT process, i.e., the overtake time, is measured for each simulation. For an input shock pressure less than approximately 9.4GPa, the overtake time resulting from a heterogeneous mixture is shorter than that for neat NM. This sensitizing effect is more pronounced for lower input shock pressures. A random distribution of cavities is found to be more effective in enhancing the SDT process than a regular array of cavities. Statistical analysis on the meso-resolved simulation data provides more insights into the mechanism of energy release underlying the SDT process. Possible directions toward a quantitatively better agreement between the experimental and meso-resolved simulation results are discussed.

Integrated Lagrangian and Eulerian 3D microstructure-explicit simulations for predicting macroscopic probabilistic SDT thresholds of energetic materials

Computational predictions of measures for macroscopic material attributes from the microstructure scale is a fundamental challenge in materials science. Data transfer across scales and physics-based models plays a central role in this highly material-specific process. Here, we present an approach for computationally establishing the probabilistic shock-to-detonation transition (SDT) threshold or “pop plot” (PP, the relation between run-to-detonation distance and applied pressure) of polymer-bonded explosives (PBXs) from three-dimensional (3D) simulations. The approach takes respective advantages of multiphysics Lagrangian and Eulerian modeling frameworks. The combined Lagrangian and Eulerian simulations provide an explicit account of 3D heterogeneous material microstructure at sizes up to tens of mm, mechanisms for the development of hotspots, and the coupled mechanical-thermal-chemical-transport processes which underlie the behaviors being predicted. Data transfers in the form of hotspot intensity fields from the Lagrangian simulations to the Eulerian simulations link the two frameworks. To capture the fundamental nature of the multiphysics processes, the source, and the propagation of the stochastic variations in material behavior, a 3D statistically equivalent microstructure sample set (SEMSS) is designed and used. The approach facilitates an efficient quantification of the probabilistic macroscopic detonation thresholds, leading to an analytical expression for the PP that accounts for both the microstructure effects and uncertainties. The material system modeled tracks the properties of PBX 9501 and the loading conditions studied involve shock pressure Ps in the range of 11–15 GPa. The results are in good agreement with available experimental data.

A mesoscopic reaction rate model for shock-to-detonation of PBX explosives having different mean particle sizes

In order to well predict mean explosive particle size effects on the shock-to-detonation transition (SDT) process of a plastic bonded explosive (PBX), some improvements to a previous three-term mesoscopic reaction rate model that consists of a hot-spot ignition term, a hot-spot growth term, and an overall reaction term are made: A set of new switch conditions, which depend on mean explosive particle size, is proposed for the operations of the three terms; a new expression is obtained for the hot-spot growth term by combining an ignition efficiency factor which depends on mean explosive particle size and replacing the original burning topology geometric factor, which merely describes the characteristic of the outward pore surface burning reaction, by a more reasonable one, which combines the characteristic of inward particle surface burning reaction and that of outward pore surface burning reaction. Furthermore, for verification, the improved reaction rate model is incorporated into the DYNA2D code to simulate numerically the SDT process of three formulations of PBXC03 having the same density but different mean particle sizes, and the numerical results of pressure histories at different Lagrangian locations in the explosive are found to be in good agreement with previous experimental data.

A multi-scale simulation of hot spot initiation of detonation utilizing experimental measurements

Empirical and phenomenological hydrodynamic reactive flow models, such as the ignition-and-growth and Johnson–Tang–Forest models, have been effective in predicting the shock initiation and detonation characteristics of various energetic substances. These models utilize the compression and pressure properties of the reacting mixture to quantify its reaction rate. However, it has long been known that the shock initiation of detonation is controlled by local reaction sites called ‘hot spots’. In this study, a hot-spot model based on the temperature-dependent Arrhenius reaction rate is developed. The complex reaction process of the target explosive is addressed by conducting differential scanning calorimetry experiments whereas the reaction rate is determined using the Friedman isoconversional method. The hot spot is approximated by the region of high pressure accumulation due to multiple shock reverberations within the polymer binder, which is surrounded by the bulk explosive. The mesoscale smoothed particle hydrodynamic simulation is adopted to identify the peak temperatures within the hot spots. These peak temperatures obtained from the mesoscale level are then used to initialize the random sites of heat release prior to conducting the full-scale hydrodynamic simulation of the shock-to-detonation transition (SDT). To validate the simulation, the distance to detonation is compared with the reported experimental value to validate the initiation process of the proposed model and an 18-mm-radius rate stick is experimentally tested to confirm the reproducibility of the detonation properties. The comparison shows that the detonation properties and the initiation process of the explosive are well characterized, while no-go conditions are observed if no mesoscale hot-spot model is included in the hydrodynamic simulation. Therefore, the SDT process can be well described by the present model based on multi-scale hot-spot initiation.

Multi-scale shock-to-detonation simulation of pressed energetic material: A meso-informed ignition and growth model

This work presents a multiscale modeling framework for predictive simulations of shock-to-detonation transition (SDT) in pressed energetic (HMX) materials. The macro-scale computations of SDT are performed using an ignition and growth (IG) model. However, unlike in the traditional semi-empirical ignition-and-growth model, which relies on empirical fits, in this work meso-scale void collapse simulations are used to supply the ignition and growth rates. This results in a macro-scale model which is sensitive to the meso-structure of the energetic material. Energy localization at the meso-scale due to hotspot ignition and growth is reflected in the shock response of the energetic material via surrogate models for ignition and growth rates. Ensembles of meso-scale reactive void collapse simulations are used to train the surrogate model using a Bayesian Kriging approach. This meso-informed Ignition and Growth (MES-IG) model is applied to perform SDT simulations of pressed HMXs with different porosity and void diameters. The computations are successfully validated against experimental pop-plots. Additionally, the critical energy for SDT is computed and the experimentally observed Ps2τs=constant relations are recovered using the MES-IG model. While the multiscale framework in this paper is applied in the context of an ignition-and-growth model, the overall surrogate model-based multiscale approach can be adapted to any macro-scale model for predicting SDT in heterogeneous energetic materials.

Shock-to-detonation transition of RDX, HMX and NTO based composite high explosives: experiments and modelling

HMX, RDX and NTO based cast-cured plastic bounded explosive (PBX) are widely used in insensitive ammunitions. Designing modern warheads needs robust and reliable models to compute shock ignition and detonation propagation inside PBX. Comparing to a pressed PBX, a cast-cured PBX is not porous and the hot-spots are mainly located at the grain-binder interface leading to a different burning behavior during shock-to-detonation transition. Here, we review the shock-to-detonation transition (SDT) and its modeling for cast-cured PBX containing HMX, RDX and NTO. Future direction is given in conclusion.

The Onset of Detonation Behind Shock Waves of Moderate Intensity in Gas Phase

The shock-to-detonation transition (SDT) in gaseous n-heptane/oxygen/argon mixtures has been experimentally studied, using a shock tube, at low initial pressure (2–4 kPa) for a better understanding of the deflagration-to-detonation transition process. The detonation is generated by a precursory shock wave (PSW), with a Mach number smaller than that of the self-sustained detonation. Pressure (P2) and temperature (T2) behind incident shock waves have been accurately determined from the PSW velocity. The transition occurs in the measurement zone located between 3.20 m and 3.65 m from the shock tube diaphragm. The auto-ignition of mixture behind PSW is immediately followed by the onset of a combustion wave, which propagates at near Chapman–Jouguet (CJ) detonation velocity in the mixture carried at P2, T2 conditions. Consequently, the pressure peak can reach 350 times the initial pressure during the transition. The combustion wave merges with the PSW to form an overdriven detonation propagating in the initial mixture at velocity that progressively decreases to a value close to CJ value, of the order of 2 000 m.s−1. The experimental particles heating times are compared with the computed ignition delay times, τI,2, by using a detailed kinetic model of n-heptane oxidation. For stoichiometric n-heptane/oxygen mixtures diluted by 50% Ar, the experimental delay times are compatible with those computed. In this case, τi,2 is governed by the so-called “high temperature mechanism” (T2 > 1000 K) and varies exponentially with temperature. For undiluted mixtures, the particle heating times is much shorter than τi, 2. Then, the chemistry is governed by the “low temperature mechanism” (T2 < 950 K). Between 750 K and 950 K, τi, 2 decreases or small changes with temperature decrease but is sensitive to pressure. Turbulence in boundary layer could also promote the SDT.

Modeling Damage Induced Initiation of Explosives

Sandia National Laboratories developed the DaMaGe Initiated Reaction (DMGIR) model to numerically predict weakly supported shock waves that generate an initiation at energy levels below the shock-to-detonation transition (SDT) of an explosive. The DMGIR model couples the strain energy fluence contribution from damage to the initiation process. It does not attempt to include all possible specific initiation mechanisms at the mesoscale, but instead looks at cumulative damage incurred in the explosive through experimental calibration of a small number of material constants. Both shock pressure (hydrostatic) and shear stress (deviatoric) are accounted for in the summation. The model was designed to be robust and relatively simple to calibrate. The DMGIR model is implemented into the Sandia National Laboratories’ CTH shock wave and large deformation code. The model runs concurrently with the existing History Variable Reactive Burn (HVRB) model currently used for shock initiation.