Dynamics of the detonation-wave front in solid explosives

The important role of the shape of the front during detonation wave propagation in gas mixtures was substantiated by K. I. Shchelkin during construction of the theory of spinning detonation. Subsequently, a unique relationship between the curvature of the front and detonation wave parameters has been repeatedly confirmed in experiments, including for condensed high explosives (HEs). The existence of this relationship formed the basis of the theory of the dynamics of the detonation front which had been developed by the end of the 20th century. This paper presents the results of a study of detonation front propagation in cylindrical samples of a low-sensitivity HE of different diameters with one-point and plane-wave initiation. A unique relationship between the detonation velocity and the curvature of the detonation wave front has been found. Ordinary differential equations describing two-dimensional steady-state detonation front profiles for HE charges in the form of a plate, a cylinder, and a ring were derived assuming that the detonation velocity depends on the curvature of the front. It was taken into account that the boundary angle between the normal to the front and the HE edge is unique for each combination of HE and liner material. It was found that the same detonation front profile corresponds to several combinations of liner material and the determining size of the charge (plate thickness, radius of the cylinder or the inner radius of the ring). A comparison of experimental front profiles near the edges of HE charges for these combinations provides data on the dependence of detonation velocity on the curvature of the front at low velocities corresponding to shock-induced detonation regimes. Analysis of previously obtained data for detonating ring charges of low-sensitivity HEs shows that as the detonation velocity decreases, the total front curvature tends to a limit of about 0.05 mm⁻¹, i.e., of the order of the inverse critical diameter. The limit of the front curvature allows predicting the critical detonation diameter.     

LX‐17 Corner‐Turning

We have performed a series of highly‐instrumented experiments examining corner‐turning of detonation. A TATB booster is inset 15 mm into LX‐17 (92.5% TATB, 7.5% kel‐F) so that the detonation must turn a right angle around an air well. An optical pin located at the edge of the TATB gives the start time of the corner‐turn. The breakout time on the side and back edges is measured with streak cameras. Three high‐resolution X‐ray images were taken on each experiment to examine the details of the detonation. We have concluded that the detonation cannot turn the corner and subsequently fails, but the shock wave continues to propagate in the unreacted explosive, leaving behind a dead zone. The detonation front farther out from the corner slowly turns and eventually reaches the air well edge 180° from its original direction. The dead zone is stable and persists 7.7 μs after the corner‐turn, although it has drifted into the original air well area. Our regular reactive flow computer models sometimes show temporary failure but they recover quickly and are unable to model the dead zones. We present a failure model that cuts off the reaction rate below certain detonation velocities and reproduces the qualitative features of the corner‐turning failure.     

Size Effect and Detonation Front Curvature

A simple theory relates the size effect (decrease of the detonation velocity with decreasing radius) of a cylinder with its average sonic reaction zone length, 〈x_e〉, i.e. the distance from first reaction to the sonic plane. The size effect is described by where R₀ is the radius, U_s and D the detonation velocities at R₀ and at infinite size and σ is a function describing the extent of wall motion, which is calibrated using four explosives. In this theory, the cylindrical symmetry imposes a quadratic shape to the detonation front. The lag distance at the edge of the cylinder, L₀, is related to the reaction zone length by 〈x_e〉 ≈︁ L₀. Collected results are presented for 56 measured curvatures on 26 explosives, with reaction zone lengths varying from 0.1 mm to 30 mm.     

Corner Turning of Detonation Waves in an HMX‐based Paste Explosive

Detonation wave profiles have been determined for RX‐08‐HD (74% HMX paste) loaded in 3 mm square troughs after turning both acute 90° bends and bends with a 1.5 mm inner radius turn and a 4.5 mm outer radius. The explosive troughs were confined with either lucite or copper. We show that the shape of the detonation wavefront can be explained in terms of a Huygens' construction from the leading point to the outer radius. Turbulent behavior occurs between the leading point and the inner edge. The turbulence appears enhanced for the curved samples with copper confinement. The distance the detonation wave has to travel past the turn in order to regain its original symmetry was found to be governed by an exponential time constant of 0.6 µs. Analysis suggests that the leading point alone stays at the straight‐ahead detonation velocity throughout the turn.     

Energy release of mixed explosives during propagation of a nonideal detonation under conditions similar to the operation conditions of a blasthole charge

Detonation experiments were performed in a specially developed explosive device simulating a blasthole using charges of fine-grained and coarse-grained (granular) 30/70 TNT/ammonium nitrate mixtures of identical density 0.89 g/cm³ in steel shells with an inner diameter of 28 mm and a wall thickness of 3 mm at detonation velocities of 4.13 and 2.13 km/sec, respectively. Despite significant differences in detonation velocity (pressure), identical expansion of the charge shells was observed. On the other hand, numerical simulations of detonation propagation in the explosive device with the corresponding velocities ignoring the possibility of energy release behind the shock front show that the expansion of the charge shell is always greater in the case of a high-velocity regime. It is concluded that under the conditions simulating detonation propagation and the work of explosion products in a blasthole, effective additional energy release occurs behind the low-velocity (nonideal) detonation front. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 4, pp. 111–120, July–August, 2007.     

The Effects of Containment on Detonation Velocity

Reactive flow cylinder code runs on six explosives were made with rate constants varying from 0.03 to 70 μs⁻¹. Six unconfined/steel sets of original ANFO and dynamite data are presented. A means of comparing confinement effects both at constant radius and at constant detonation velocity is presented. Calculations show two qualitatively different modes of behavior. For U_s/C_o≥1.2, where U_s is the detonation velocity and C_o the zero‐pressure sound speed in steel, we find a sharp shock wave in the metal. The shock passes through the steel and the outer wall has a velocity jump‐off. For U_s/C_o≤1.04, we find a pressure gradient that moves at the detonation velocity. A precursor pulse drives in the explosive ahead of the detonation front. The outer wall begins to move outward at the same time the shock arrives in the explosive, and the outer wall slowly and continuously increases in velocity. The U_s/C_o≥1.2 cylinders saturate in detonation velocity for thick walls but the U_s/C_o<<1.04 case does not. The unconfined cylinder shows an edge lag in the front that approximately equals the reaction zone length, but the highly confined detonation front is straight and contains no reaction zone information. The wall thickness divided by the reaction zone length yields a dimensionless wall thickness, which allows comparison of explosives with different detonation rates. Even so, a rate effect is found in the detonation velocities, which amounts to the inverse 0.15–0.5 power.     

A Contribution to the Analysis of Corner Turning Rib Problems

The detonation process was studied theoretically and experimentally for circularly curved charges with both square and circular cross sections. Velocities of the front of the detonation wave along the inner and outer edge were monitored. For comparison with numerical simulations, the results of experiments from Lawrence Livermore National Laboratory (LLNL), USA and Department of Theory and Technology of Explosives (DTTX), Czech Republic were used. The ribs were simulated with LS‐DYNA code utilizing beta burn model for the explosives. The results of the numerical simulations were in a very good agreement with the experimental data.     

JBO-9021炸药初始密度对爆轰波阵面曲率效应的影响

采用高速扫描相机及电探针,在室温环境下对不同初始密度(1.894~1.901g/cm3)、不同半径(5.0、7.5、15.0mm)的钝感炸药JBO-9021药柱开展了曲率效应实验,获取了拟定态爆轰波阵面形状及波速,分析了其随炸药柱密度及半径的变化。结果表明,随着炸药JBO-9021的初始密度由1.894g/cm3增至1.901g/cm3,3种不同半径JBO-9021药柱的爆轰波拟定态波速均增大,拟定态波阵面形状变得更为平坦,波阵面中心点与边界点之间的波到达时间差降低;在小曲率范围内(κ0.2mm-1),JBO-9021药柱爆轰波波阵面法向波速Dn与当地曲率κ的关系(Dn(κ)关系)不受药柱半径及密度的影响,当曲率κ0.2mm-1时,Dn(k)关系随药柱半径及炸药密度呈现离散趋势,药柱半径及初始密度共同影响爆轰波波阵面大曲率的Dn(κ)关系。     

Air Gap Effects in LX‐17

Three experiments done over twenty years on gaps in LX‐17 are described. For the detonation front moving parallel to the gaps, jets of gas products were seen coming from the gaps at velocities 2 to 3 times greater than the detonation velocity. A case can be made that the jet velocity increased with gap thickness but the data are scattered. For the detonation front moving transverse to the gap, time delays were seen. The delays roughly increase with gap width, going from 0–70 ns at “zero gap” to around 300 ns at 0.5–1 mm gap. Larger gaps of up to 6 mm width almost certainly stopped the detonation, but this was not proved. Real‐time resolution of the parallel jets and determination of the actual re‐detonation or failure in the transverse case needs to be achieved in future experiments.     

Experience of using synchrotron radiation for studying detonation processes

Results of studying detonation processes in condensed high explosives, which are obtained by methods based on using synchrotron radiation, are summarized. Beam parameters are given, and elements of the station and measurement system are described. Data on the density distribution in the detonation front for several high explosives are presented, and values of parameters in the Neumann spike and at the Jouguet point are determined. A method used to reconstruct a complete set of gasdynamic characteristics (density fields, particle velocity vector, and pressure) from the experimentally measured dynamics of the x-ray shadow of the examined flow is described. Results of using this method for studying detonation of a charge of plastic-bonded TATB are presented. A method of measuring small-angle x-ray scattering in the course of detonation conversion is described. Based on results obtained by this method for a number of high explosives with an excess content of carbon, kinetics of condensation of free carbon and dynamics of the mean size of nanoparticles being formed thereby are analyzed.     

Steady-State Detonation Wave Parameters in a FEFO/Nitrobenzene Solution

This paper gives the results of experimental studies of the reaction zone structure during steady detonation in bis-(2-fluoro-2,2-dinitroethyl)-formal (FEFO, C₅H₆N₄O₁₀F₂) and its mixtures with nitrobenzene (NB). For pure FEFO, the pressure and particle velocity at the Chapman—Jouguet point and the characteristic reaction time were measured. For FEFO/NB, the dependence of the detonation parameters of the mixture on the NB concentration was determined, and the detonation front was shown to be unstable in pure and in mixtures containing more than 30% NB.     

Detonation velocity in the transition zone of an explosive charge

Results of an experimental study of the detonation velocity in the transition zone of an acceptor explosive in a cylindrical charge consisting of two different explosives are given. An empirical relation between the length of the transition zone and the ratio of the steady detonation velocities of the donor and acceptor explosives in segmented charges is obtained. Department of the Geodynamics of Explosion of the Institute of Geophysics, Ukrainian National Academy of Sciences, Kiev 252054. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 5, pp. 118–121, September–October, 1997.     

Influence of Longitudinal Gaps on the Detonation Front

Precursor air shocks with velocities that are 50 % higher than the velocity of detonation occur not only in cylindrical holes, but also in flat slits. By attaching to the test charge a sufficiently long plexiglass body with the same hole or slit profiles it is possible to observe the end face of the test charge and, thus, to record the changes in the detonation profile caused by slits, in particular by such that are oblique to the direction of detonation. One result is, that there is no through-detonation across thin slits that are at a flat angle to the detonation wave.     

喷雾多相并存区温湿度测量方法及干燥特性

针对气液固并存区烟气温湿度测量问题,在对几种温湿度测量方法分析的基础上,设计了一种双回路抽气式温湿度测量装置,在喷雾干燥试验平台上,进行了对比和优化研究。在此基础上,分析了干燥塔内的温湿度分布特性。结果表明:内外层抽气速度均存在优化值,较外层抽气,内层抽气对测量值有更显著影响。内层抽气速度在12—24 m/s时,其测量值变化幅度仅为3.3℃;外层抽气速度在4—6 m/s时,其测量值变化幅度小于1℃。得出喷嘴雾化区域内干球温度呈径向双峰分布,湿度呈"W"型分布,且蒸发强度在距喷嘴200 mm处达到最大值。     

The flow of “settling” slurries in tubes with internal spiral ribs

The secondary flows created by an internal spiral rib in an otherwise conventional smooth tube are illustrated by reference to the axial, and combined tangential and radial velocity components for a fluid flowing in a 2-inch diameter tube containing a rib with a pitch-to-diameter ratio of 3 The effect of such secondary flows on the transportability of “settling”(suspensions)was investigated by measuring pressure gradients for the flow of two sand/water slurries in a smooth 2-inch tube and in 2-inch diameter tubes with ribs of pitch-to-diameter ratio 5.15, 3.32 and 1.80. Average flow velocities ranged from 0.5 to 8 feet/sec. and delivered concentrations ranged from 5 to 18 per cent by volume While the ribs were found to be a disadvantage at relatively high average mixture velocities because of increased pressure gradients, they were found to be advantageous at relatively low velocities, i.e. velocities less than the critical deposit velocity for flow in the smooth tube, in that the pressure gradients, for a given sand/water slurry with a given delivered concentration and average velocity, were lower in the ribbed tubes than in the smooth tube. Because of this, the power consumption per unit mass of solid transported was reduced by the presence of a rib. The optimum pitch-to-diameter ratio was estimated to be about 5 Pressure gradients measured for one of the slurries with air added as a third phase showed the presence of air to be a definite disadvantage     

The flow of sand/water slurries in horizontal pipes with internal spiral ribs — effect of rib height

The effect of secondary flows created by an internal spiral rib in an otherwise conventional smooth 2-inch pipe on the transportability of “settling” suspensions of sand in water was investigated with emphasis on the effect of rib height. While the ribs were found to be a disadvantage at relatively high average mixture velocities because of increased pressure gradients, they were advantageous at low velocities. The deposit velocity and the pressure gradient at the deposit velocity in ribbed pipes of several pitch to diameter ratios and rib heights were correlated with respect to the corresponding smooth pipe values. These correlations are useful in pipeline design. The optimum rib geometry was estimated to be a pitch to diameter ratio of about 8 and a rib height in the range of 10–15% of the pipe diameter for the solid-liquid mixtures investigated.     

Studies of shaped charges with built-in asymmetries. Part II: Modelling

A well-characterized shaped charge was used to study the influence of asymmetrical initiation on the jet. An experimental study yielded flash radiographs of the jets from charges fired with the initiation point offset 2, 4, 6, 8 and 10 mm, respectively, from the central axis. The axial and lateral velocities of the jet particles were determined from the sets of radiographs. In a previous paper it was hypothesized that a simple relationship might exist between the departure vectors of the jet particles and the geometry of the impingement of the detonation front on the liner. Any part of the jet from an asymmetrically initiated shaped charge departs at an angle determined by the difference between the current angle between the actual detonation wave where it contacts the liner, and that which would have arisen had the initiation been perfectly axial. We set up a simple computer code which evaluates, for any given initiation offset distance, the instantaneous angles between the detonation front and the successive elements of the liner which are encountered as the wave sweeps along it. Since it is possible to map particle velocities in the jet on to those regions of the liner where they originated, simulated sets of axial and lateral jet velocities were readily generated. Agreement between theory and experiment is sufficiently close to suggest that our approximation is useful and can assist in understanding the jet dynamics of asymmetrically initiated shaped charges.     

FOX-7和RDX基含铝炸药的冲击起爆特性

为研究FOX-7和RDX基含铝炸药的冲击起爆特性,对其进行了冲击波感度试验和冲击起爆试验,结合冲击波在铝隔板中的衰减特性,确定了FOX-7和RDX基含铝炸药的临界隔板值和临界起爆压力,并通过锰铜压阻传感器记录了起爆至稳定爆轰过程压力历程的变化。结果表明,以Φ40mm×50mm的JH-14为主发装药时,FOX-7和RDX基含铝炸药临界隔板值分别为37.51和34.51mm,对应的临界起爆压力为10.91和11.94GPa;起爆压力为11.58GPa时,FOX-7炸药的到爆轰距离为25.49~30.46mm,稳定爆轰后的爆轰压力为27.68GPa,爆轰速度为8 063m/s;起爆压力为14.18GPa时,RDX基含铝炸药的到爆轰距离为17.27~23.53mm,稳定爆轰后的爆轰压力为17.16GPa,爆轰速度为6 261m/s。     

Mathematical modeling of detonation of an aluminum dust in oxygen with allowance for velocity nonequilibrium of the particles

The problem of propagation of a plane detonation wave is studied on the basis of a mathematical model for the detonation of aluminum particles in oxygen with allowance for the difference in velocities and temperatures of components. A qualitative analysis of the final steady state is performed. The domains of existence of steady solutions and the manifold of solutions of various types are determined. Various types of flows are illustrated numerically. The special features of the flow structure behind the front are analyzed, depending on relaxation parameters. We have performed flow calculations taking into account the characteristic times versus the parameters behind the front and have shown agreement between the data obtained and the frozen and variable relaxation parameters. The data obtained are found to correspond to the known experimental results concerning the widths of the ignition and combustion zones. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 6, pp. 80–91, November–December, 1997.     

Experimental Investigation of a Minihydrocyclone

A phase doppler particle analyzer (PDPA) was used to measure the liquid/solid two‐phase flow pattern in a 25 mm minihydrocyclone. The distributions of velocity, concentration, root mean square (RMS) velocities, and especially the average diameter of the particles were evaluated in this work. The measurements showed that in the upper section of the minihydrocyclone the particles accumulated in the outer helical flow near the line of zero velocity value (LZVV), which probably means that the inner helical flow has a more important influence on the separation. Strong turbulence occurred around the air‐core as well as around the zone near the wall. The RMS value indicated that the transformation of the axial flow direction takes place in the lower section of the conical length.