Precursors in two-phase detonation: An elementary model for the channel effect

The paper is concerned with the channel effect: detonation-propelled shocks occurring in tubular charges. It is shown that some salient aspects of the phenomenon may be successfully reproduced within a simple one-dimensional model assuming the gas–solid system to be isothermal and the volume fraction of the solid phase to be small. Two modes of the channel effect, dependent on the level of the ignition pressure, are identified. Although the emerging detonations appear to be of the Chapman–Jouguet (CJ) type, their velocities are controlled by the system’s gasification kinetics rather than its thermodynamics. The structure of the emerging CJ detonation differs from that of conventional ZND detonation. There is no shock attached to the reaction zone. The precursor shock is the only shock in the event.     

Multiplicity of detonation regimes in systems with a multi-peaked thermicity

The study investigates detonations with multiple quasi-steady velocities that have been observed in the past in systems with multi-peaked thermicity, using Fickett's detonation analogue. A steady-state analysis of the travelling wave predicts multiple states, however, all but the one with the highest velocity develop a singularity after the sonic point. Simulations show singularities are associated with a shock wave which overtakes all sonic points, establishing a detonation travelling at the highest of the predicted velocities. Under a certain parameter range, the steady-state detonation can have multiple sonic points and solutions. Embedded shocks can exist behind sonic points, where they link the weak and strong solutions. Sonic points whose characteristics do not diverge are found to be unstable, and to be the source of the embedded shocks. Numerical simulations show that these shocks are only quasi-stable. This is believed to be due in part to a feature of the model which permits shocks anywhere behind a sonic point.     

A review of direct numerical simulations of astrophysical detonations and their implications

Multi-dimensional direct numerical simulations (DNS) of astrophysical detonations in degenerate matter have revealed that the nuclear burning is typically characterized by cellular structure caused by transverse instabilities in the detonation front. Type Ia supernova modelers often use onedimensional DNS of detonations as inputs or constraints for their whole star simulations.While these one-dimensional studies are useful tools, the true nature of the detonation is multi-dimensional. The multi-dimensional structure of the burning influences the speed, stability, and the composition of the detonation and its burning products, and therefore, could have an impact on the spectra of Type Ia supernovae. Considerable effort has been expended modeling Type Ia supernovae at densities above 1×10⁷ g·cm^-3 where the complexities of turbulent burning dominate the flame propagation. However, most full star models turn the nuclear burning schemes off when the density falls below 1×10⁷ g·cm^-3 and distributed burning begins. The deflagration to detonation transition (DDT) is believed to occur at just these densities and consequently they are the densities important for studying the properties of the subsequent detonation. This work will review the status of DNS studies of detonations and their possible implications for Type Ia supernova models. It will cover the development of Detonation theory from the first simple Chapman–Jouguet (CJ) detonation models to the current models based on the time-dependent, compressible, reactive flow Euler equations of fluid dynamics.     

Structural characteristics of detonation expansion from a small channel to a larger one

We report on numerical simulations of the evolution of two-dimensional detonation waves that are expanded from a small channel to a larger one. In accordance with experimental data, the simulations predict three different types of evolution, namely, supercritical, critical and subcritical detonations. In a supercritical detonation, the reaction zone remains always attached to the precursor shock, whereas in a critical one it temporarily detaches and then re-attaches to the front. In the subcritical type, the extinction is permanent, i.e., the detonation quenches. The effects of the fuel’s activation energy and the channel-width ratio are studied via a parametric study. It is found that sufficiently large values of these two parameters can result to flows of the critical and even the subcritical type. Finally, three-dimensional simulations have also been performed and are briefly discussed herein.     

Effect of thermal pressure in converging detonation waves

Propagation of converging detonation waves in various explosives is studied using the equation of state, which considers both the thermal and elastic pressures. It is seen that the rate of increase of thermal pressure is higher than that of the elastic pressure during convergence. The present equation of state is better since it also gives the variation of temperature, whereas the polytropic form of the equation of state is independent of temperature. It is seen that the total detonation pressure is slightly greater than the elastic pressure. Results are compared with those reported elsewhere.     

Calculation of the detonation velocity of porous water-containing RDX-based charges

A nomographic method for predicting the detonation velocity of a porous explosive mixture prepared from RDX powder and water is proposed. It is shown that, in contrast to the existing calculation methods for predicting the detonation velocity, the use of the proposed nomogram greatly simplifies the procedure and requires knowledge of only two parameters: the mass fraction of RDX and the density of the mixture in the charge. At the same time, the nomogram is a coordinate system that enables to place and to compare on one field experimental data obtained at different parameters of the charge. It is shown that RDX powder-water hand-prepared charges can have a detonation velocity of 6–8 km/s. The detonation velocity of cylindrical water-containing charges 10–36 mm in diameter and 120–1000 mm in length with RDX mass fractions of 0.6–1.0 is measured.     

Calculation of shock wave propagation in water containing reactive gas bubbles

The entry of a shock wave from air into water containing reactive gas (stoichiometric acetylene–oxygen mixture) bubbles uniformly distributed over the volume of the liquid has been numerically investigated using equations describing two-phase compressible viscous reactive flow. It has been demonstrated that a steady-state supersonic self-sustaining reaction front with rapid and complete fuel burnout in the leading shock wave can propagate in this bubbly medium. This reaction front can be treated as a detonation-like front or “bubble detonation.” The calculated and measured velocities of the bubble detonation wave have been compared at initial gas volume fraction of 2 to 6%. The observed and calculated data are in satisfactory qualitative and quantitative agreement. The structure of the bubble detonation wave has been numerically studied. In this wave, the gas volume fraction behind the leading front is approximately 3–4 times higher than in the pressure wave that propagates in water with air bubbles when the other initial conditions are the same. The bubble detonation wave can form after the penetration of the shock wave to a small depth (~300 mm) into the column of the bubbly medium. The model suggested here can be used to find optimum conditions for maximizing the efficiency of momentum transfer from the pressure wave to the bubbly medium in promising hydrojet pulse detonation engines.     

Computational study of pyrazine‐based derivatives and their N‐oxides as high energy materials

Gas‐phase heats of formation (HOF), solid‐phase HOF, detonation properties, electronic structure and thermal stability for a series of polynitro pyrazine derivatives containing three heterocycles have been investigated using density functional theory. It is found that the nitro group is an efficient tool to improve HOF of pyrazine derivatives. Furthermore, detonation velocities and detonation pressures of these compounds are evaluated using empirical Kamlet–Jacobs equations. As a result, it indicates that the nitro group is useful to enhance detonation properties. Detonation velocities of five compounds are 9.67, 9.20, 9.74, 9.76 and 9.87 km/s, respectively, which are significantly larger than that of HMX (9.10 km/s). Bond dissociation energy is also performed to investigate their thermal stability, showing that thermal stability of these compounds is little affected by nitro groups or the position of substituent groups. Considering solid‐phase HOF, detonation properties and thermal stability, some of pyrazine derivatives can be potential high energy density materials. Copyright © 2013 John Wiley & Sons, Ltd.     

固体炸药爆轰的一种考虑热学非平衡的反应流动模型

基于固体炸药爆轰过程中化学反应混合区内的固相反应物与气相生成物处于力学平衡状态及热学非平衡状态的事实,提出一种考虑热学非平衡效应的反应流动模型来描述固体炸药的爆轰流动现象.该爆轰流动模型的主要特点是,在反应混合物Euler方程和固相反应物质量守恒方程的基础上,通过附加一套关于固相反应物的组分物理量的流动控制方程来表达固相反应物与气相生成物之间的热学非平衡效应.根据反应混合区内固相反应物与气相生成物这两种化学组分保持各自内能守恒的混合规则,并借助它们具有压力相等的性质以及满足体积分数总和为1的条件,推导获得的附加方程有：固相反应物的内能演化方程、体积分数演化方程及反应混合物的压力演化方程.这样,建立的爆轰模型包括：反应混合物的质量守恒方程、动量守恒方程、总能量守恒方程、压力演化方程,以及固相反应物的质量守恒方程、内能演化方程、体积分数演化方程.对所获得的爆轰模型方程组采用一个时空二阶精度的有限体积法进行数值求解,典型爆轰问题算例结果表明本文提出的固体炸药爆轰模型是合理的.     

Experimental and modeling analysis of detonation in circular arcs of the conventional high explosive PBX 9501

We examine the diffraction dynamics of a two-dimensional (2D) detonation in a circular arc of the conventional HMX-based, high performance, solid explosive PBX 9501, for which the detonation reaction zone length scale is estimated to be of the order of 100–150 µm. In this configuration, a steady propagating detonation will develop, sweeping around the arc with constant angular speed. We report on results from three PBX 9501 arc experiments, exploring the variation in linear speed on the inner and outer arc surfaces for the steady wave along with the structure of the curved detonation front, as a function of varying inner surface radius and arc thickness. Comparisons of the properties of the motion of the steady wave for each arc configuration are then made with a spatially-distributed PBX 9501 reactive burn model, calibrated to detonation performance properties in a 2D planar slab geometry. We show that geometry-induced curvature of the detonation near the inner arc surface has a significant effect on the detonation motion even for conventional high explosives. We also examine the detonation driving zone structure for each arc case, and thus the subsonic regions of the flow that determine the influence of the arc geometry on the detonation propagation. In addition, streamline paths and reaction progress isolines are calculated. We conclude that a common approximation for modeling conventional high explosive detonation, wherein the shock-normal detonation speed is assumed equal to the Chapman–Jouguet speed, can lead to significant errors in describing the speed at which the detonation propagates.     

Deflagration-to-detonation transition in spiral channels

The deflagration-to-detonation transition in hydrogen–air mixtures that fill spiral channels has been studied. A spiral channel has been produced in a cylindrical detonation tube with a twisted ribbon inside. The gas mixture has been ignited by means of a spark gap switch. The predetonation distance versus the twisted ribbon configuration and molar ratio between the gas mixture components has been determined. A pulling force exerted by the detonation tube after a single event of hydrogen–air mixture burnout has been found for four configurations of the twisted ribbon. Conditions under which the use of a spiral tube can be more effective (increase the pulling force) have been formulated.     

Self-force of a charge in a real current

The analysis of the EM radiation from a single charge shows that the radiated power depends on the retarded acceleration of the charge. Therefore for consistency, an accelerated charge, free from the influence of external forces, should gradually lose its acceleration, until its total energy is radiated. Calculations show that the self force of a charge, which compensates for its radiation, is proportional to the derivative of the acceleration. However, when using this self force in the equation of motion of the charge, one gets a diverging solution, for which the acceleration runs away to infinity. This means that there is an inconsistency in the solution of the single charge problem. However, in the construction of the conserved Maxwell charge density, there is implicitly an integral over the corresponding world line which corresponds to a collection of charged spacetime events. One may therefore consistently think of the “self force” as the force on a charge due to another charge at the retarded position. From this point of view, the energy is evidently conserved and the radiation process appears as an absorbing resistance to the feeding source. The purpose of this work is to learn about the behavior of single charges from the behavior of a real current, corresponding to the set of charges moving on a world line, and to study the analog of the self force of a charge associated with the radiation resistance of a continuum of charges.     

New technique for electrostatic charge measurement in gas–solid fluidized beds

Electrostatic charge generation within gas–solid fluidized bed reactors has been a concern to industry for many years. Over the years, numerous methods for measuring this phenomenon within a fluidization column have been proposed. This paper focuses on the design of a new method that minimizes effects such as extra charging due to particle handling and bed hydrodynamic disruption due to the location of the measurement device. In addition, the new method provides the bulk charge of the bed particles rather than a local measurement. The device is flexible and can be adapted to a range of fluidization columns. The new method developed consisted of a Faraday cup placed within the windbox of a fluidization column. The distributor plate was designed in such a way that it can be automatically opened to drop the charged fluidizing particles into the Faraday cup below. The new measurement technique was validated by conducting fluidization experiments in a system consisting of a 0.10 m in diameter carbon steel column with glass beads as the fluidizing particles. The technique was proven to be suitable for measuring the total net electrostatic charges in gas–solid fluidized beds.     

马赫反射效应在炸药爆轰合成金刚石中的应用

 在爆轰法合成超细金刚石中，利用马赫效应提高金刚石得率。用Whitham方法计算马赫杆上的爆轰参数。实验采用中间为TNT药柱、外边包裹TNT/RDX（30/70）的装药，在爆炸罐氮气介质中爆炸，超细金刚石得率为6%，包裹盐后得率超过10%。     

Expansion of detonation products of phlegmatized RDX and its mixtures with dispersed aluminum

Videorecording was used to measure the velocities of expansion of detonation products (DPs) in the axial and radial directions during the detonation of phlegmatized RDX (PRDX) and its mixtures with ASD-4 aluminum powder (PRDXA). It was demonstrated that the initial particle velocities of the DPs in the axial and radial direction for PRDXA are 1–2 km/s higher than those for PRDX for expansion into an atmospheric-pressure air medium and 0.5–2.0 km/s lower for expansion into a low-pressure (10 kPa) air medium. The result of this can be explained by the rapid reaction of aluminum particles during the turbulent mixing of DPs with air due to the formation of cumulative microjets at the surface of the charge.     

Generation of blast waves in a channel by nonideal detonation of aluminum-enriched high-density compositions

The results of experimental studies of the nonideal detonation of high-density, high-energy aluminum-ammonium perchlorate-organic fuel-HE compositions and of the blast waves it generates in a channel filled with air are presented. Aluminum-enriched compositions have high densities (up to 2 g/cm³) and high heats of explosion, nearly twice that for TNT. The studies were performed to work out scientific fundamentals of controlling nonideal detonation and to explore the possibility of creating new high-energy high-density formulations with an enhanced fugacity effect. The factors that enable controlling the nonideal detonation of such charges were determined. It was demonstrated that, at RDX contents above 15%, the detonation velocity increases linearly with the charge density while the critical detonation diameter decreases. Adjusting the density, HE content, ratio of the components makes it possible to vary the detonation velocity in high-density charges over a wide range, from 4 to 7 km/s. The experimental data were compared to the thermodynamically calculated velocity of ideal detonation. For the compositions under study, the pressure- time histories of the blast wave generated in a cylindrical tube by the expanding detonation products at different distances from the charge were measured. The results were compared to analogous data obtained under the same conditions for the detonation of the same mass of TNT (100 g). The parameters of blast waves generated by the test compositions are markedly superior to those characteristic of TNT: the pressure at the leading front of the wave and pressure impulse at a given distance from the charge were found to be 1.5–2.0 (or even more) times those observed for TNT. The TNT equivalency at pressures 30–60 atm has similar values. The TNT equivalencies in pressure and pressure impulse depend nonmonotonically on the distance from the charge, so far unclear why. It was established that the interaction between excess fuel and air oxygen during the expansion of detonation products contributes little to supporting the blast wave.     

Weak detonations,their paths and transition to strong detonation

Previously, a quasi-steady form of the classical Rankine–Hugoniot weak detonation has been shown to play an integral part in describing certain forms of detonation initiation, arising during an intermediate stage between the thermal ignition of the material and the first appearance of a strong detonation with Zeldovich–von Neumann–Döring (ZND) structure. In this paper, we use a parametric variable integration to calculate numerically the path of the weak detonation in two important initiation scenarios, shock-induced and initial disturbance-induced transition to detonation, via a large activation energy induction domain model. The influence that the nature of the path may have on the weak detonation structure is also discussed. In each case these calculations enable us to predict how, where and when the transition to a strong detonation with ZND structure will occur. Explanations for several phenomena observed in both experiments and numerical studies on transition to detonation are also uncovered by these calculations.     

Computer simulations and analysis of structural and energetic features of crystalline cage energetic compound: 2, 4, 6, 8, 12‐pentanitro‐10‐(3, 5, 6‐trinitro (2‐pyridyl))‐2, 4, 6, 8, 12‐hexaazatetracyclo [5.5.0.03,11.05,9]dodecane

First principles molecular orbital and plane‐wave ab initio calculations have been used to investigate the structural and energetic properties of a new cage compound 2, 4, 6, 8, 12‐pentanitro‐10‐(3, 5, 6‐trinitro (2‐pyridyl))‐2, 4, 6, 8, 12‐hexaazatetracyclo [5.5.0.0^3,11.0^5,9]dodecane (PNTNPHATCD) in both the gas and solid phases. The molecular orbital calculations using the density functional theory methods at the B3LYP/6‐31G(d,p) level indicate that both the heat of formation and strain energy of PNTNPHATCD are larger than those of 2, 4, 6, 8, 10, 12‐hexanitro‐2, 4, 6, 8, 10, 12‐hexaazatetracyclo [5.5.0.0.0] dodecane (CL‐20). The infrared spectra and the thermodynamic property in gas phase were predicted and discussed. The calculated detonation characteristics of PNTNPHATCD estimated using the Kamlet–Jacobs equation equally matched with those of CL‐20. Bond‐breaking results on the basis of natural bond orbital analysis imply that C–C bond in cage skeleton, C–N bond in pyridine, and N–NO₂ bond in the side chain of cage may be the trigger bonds in the pyrolysis. The structural properties of PNTNPHATCD crystal have been studied by a plane‐wave density functional theory method in the framework of the generalized gradient approximation. The crystal packing predicted using the Condensed‐phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force fields belongs to the Pbca space group, with the lattice parameters a = 20.87 Å, b = 24.95 Å, c = 7.48 Å, and Z = 8, respectively. The results of the band gap and density of state suggest that the N–NO₂ bond in PNTNPHATCD may be the initial breaking bond in the pyrolysis step. As the temperature increases, the heat capacity, enthalpy, and entropy of PNTNPHATCD crystal all increase, whereas the free energy decreases. Considering that the cage compound has the better detonation performances and stability, it may be a superior high energy density compound. Copyright © 2015 John Wiley & Sons, Ltd.     

非均匀炸药冲击起爆和起爆后的行为

 介绍并分析了Campbell 等人及其他作者研究非均匀炸药冲击起爆和起爆后行为所获得的实验结果,但不涉及其冲击起爆条件。足够强的冲击波进入非均匀炸药后,爆轰将瞬时（指不经过感应时间）且直接（指不经过其他过程,如爆燃）被引发;非均匀炸药起爆后,其中传播的自始至终是一个不断增长的爆轰波,直至发展为正常爆轰,整个过程都是爆轰的增长（新定义）过程。不存在由反应冲击波不断增长并转变为爆轰波的所谓向爆轰的增长。所谓向爆轰的增长,实际上是爆轰的增长（按新定义）的初期;Craig原定义的爆轰的增长,实际上是爆轰的增长（按新定义）的后期;而所谓反应冲击波,实际上是增长中的初期爆轰波。爆轰的增长（按新定义）是所有猛炸药的特性,炸药反应不充分并逐渐趋于充分是爆轰的增长的化学机制。     

Mean field effects in a lattice gas model of ionic space charge

Lattice gas models of the diffuse space charge layer in liquids and in ionic solids with Schottky or Frenkel disorder are considered with and without mean-field charge-interaction corrections. Even without explicit interaction corrections, the lattice gas model, by taking some account of charge carrier size in the liquid case and the actual lattice structure of the material in the case of single crystal solids, predicts a saturation in local charge density at high potentials, unlike the physically less realistic conventional Gouy-Chapman ideal gas, or independent particle model. Both unmodified and modified mean field corrections to the lattice gas basis are discussed and Coulombic interaction terms are considered in detail. The Monte-Carlo results obtained by other workers show that, as expected, the actual mean-field interaction terms required for fitting must be much smaller than those predicted by the unscreened Coulombic interaction. It is suggested that the mean field approach of Gurevich and Kharkats, who introduce an attractive mean field interaction between charges of like sign, is unlikely to be applicable over the entire space charge region of solid electrolyte systems and thus may not provide an explanation for the conductivity instability observed in α-AgSbS₂. Some possible future directions of investigation for lattice gas models are also briefly discussed.