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.     

某成型装药射流的数值模拟与射流转化率

应用LS-DYNA及示踪点处理技术,对某一球锥罩成型装药结构的射流形成过程及射流侵彻靶板过程进行了研究,获得了有效射流沿其运动方向的速度分布、头部速度、侵彻孔几何描述等多项评估射流微元性能的重要参数。计算结果表明,对于普通强度钢质目标靶,在射流侵彻靶板过程中,常规小锥角药型罩产生的有效射流为2000m/s以上的射流段,杆式射流的临界侵彻速度值为1400m/s,从而进一步得到其射流转化率为29.65%。     

Diffraction estimate of the critical energy for initiation of gaseous detonation

A criterion for the excitation of detonation is proposed: the critical initiation energy equals the work performed by the expanding detonation products along a path length equal to the longitudinal dimension of a cell. The initial radius of the layer is chosen to be equal to the radius of the detonation wave diffracted at 90° edge at the time the axial rarefaction wave converges on the axis of the gaseous charge. Formulas are obtained for estimating the critical energy for initiation of plane, cylindrical, and spherical detonation waves. The calculated values are in good agreement with experiment. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 4, pp. 72–76, July–August, 1998.     

Studies on jet formation and penetration for a double-layer shaped charge

An analysis for liner collapsing and jet/slug formation of a double-layer shaped charge (DLSC) is presented. Variations of the collapse angle, collapse velocity, and jet velocity of the DLSC are discussed. Numerical simulations based on the Lee-Tarver model are performed to have an insight into the jet formation. Ballistic tests are conducted using a conical (60°) metal liner 56 mm in diameter to have a contrast with an ordinary shaped charge jet. It is shown that the collapse angle and velocity are both increased by the convergent detonation wave in the DLSC. The jet velocity, kinetic energy, and ballistic capability are significantly increased by using the DLSC, and the DLSC is an efficient way to improve shaped charge performance.     

Numerical simulation of the formation of shaped-charge jets from hemispherical liners of degressive thickness

The formation of shaped-charge jets from hemispherical copper liners of degressive thickness (decreasing from apex to bottom) is analyzed by numerical simulation of a twodimensional axisymmetric problem of continuum mechanics. The comparison was based on the parameters of the jet formed from a modern standard shaped charge with a conical liner which provides penetration of a steel target to a depth equal to 10 charge diameters. The comparative analysis was performed using calculated mass–velocity distributions and the ultimate jet length–velocity distributions obtained on their basis, from which the potential penetrability of jets was evaluated. It is shown that the shaped-charge jets formed by hemispherical shaped-charge liners of degressive thickness are comparable in head velocity and penetrability to the jets from conical liners.     

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.     

Analysis of the shaped charge jet induced reaction of high explosives

A new optical recording technique for analyzing the initiation of high explosives under the impact of a shaped charge jet is described. This method permits determining, in “one single” test, the type of reaction – i.c. no reaction or reaction or detonation - and the parameters build-up distance Δs run-up time Δt, initiation time t_i and initiation distance Z_i in the acceptor charge by observation of the acceptor charge side-on and, via a mirror, also end-on with simultaneous streak and framing recording.     

Theoretical Study of a Diesel‐Filled Airtight Structure Unit Subjected to Shaped Charge Jet Impact

Diesel composite armor has high penetration resistance and can be used in tank vehicles to improve their protective capability and increase fuel oil storage. This study provides a theoretical calculation method to investigate the interaction between a shaped charge jet and a diesel‐filled airtight structure unit. Disturbance theory can predict the part of the jet that is disturbed by diesel fuel. The lumen radius for the container was varied to study its influence on the disturbance capability. A great lumen radius is found to cause lower maximum and minimum speeds of the disturbance velocity range of the jet, as well as a narrower disturbance velocity range. The reliability of the theoretical results was validated by experiments, and the experimental data show good agreement with the theoretical results.     

大间距两不对称喷嘴对置撞击流驻点偏移规律

采用热线风速仪对大喷嘴间距下两不对称喷嘴形成的对置撞击流的轴线速度分布和驻点偏移规律进行了实验研究.研究结果表明,在大喷嘴间距下,两股射流在发生碰撞前,射流已经进入了充分发展区,当两喷嘴出口动量相等时,驻点位于两个喷嘴轴线中心;在撞击区中,两股射流关于撞击面是对称的.轴线上撞击流驻点受两喷嘴动量比的控制,随着动量比偏离1撞击流驻点向动量小的一侧喷嘴移动,两喷嘴出口动量差别越大,驻点偏离中心距离越大.得到了一个描述大喷嘴间距下驻点偏移的公式,拟合结果与实验结果的平均相对误差为10%.     

Discussion of the Experimental Findings from the initiation of covered,but unconfined high explosive charges with shaped charge jets

The results of experiments on the initiation of covered, but unconfined high explosive charges with shaped charge jets from Chick and Hatt, which have been diagnosed by the flash X-ray technique, as well as the author's own experiments in which the build-up distances and the run-up times have been recorded by means of a rotating-mirror camera in the framing and streak modes, are analyzed and explained in detail in this paper. Build-up distances and run-up times versus the residual jet velocity, or versus the dynamic pressure, are in fairly good agreement, despite the somewhat different shaped charges and acceptor charges that have been used in the two approaches. The greater initiability of an acceptor charge behind a barrier, but with an air gap between, is attributed less to a precursor shock that desensitizes the high explosive charge which is in contact with a barrier, but rather to the higher velocity of the free shaped charge jet and, particularly, to the area loading on a high explosive charge with an air gap in front.     

Influence of Drift Velocity and Distance Between Jet Particles on the Penetration Depth of Shaped Charges

The penetration depth of shaped charge jet into target is strongly affected by the stand‐off. The penetration process terminates even when the jet velocity is still high, and the penetration capability of jet particles degrades after jet breakup at a large stand‐off. This work presents an analytical model to describe the radial drift velocity and distance between jet particles, which leads to decreased penetration depth. The results show that jet particles with low drift velocity impact the crater wall easily. Furthermore, the jet particles cannot reach the crater bottom to increase depth because the crater diameter generated by the jet is quite small. Moreover, the distances between jet particles also play an important role in penetration depth under the influences of strain hardening of target, as well as tumbling and dispersion of jet particles. The radial drift velocity and distance between jet particles are investigated by applying the model to non‐precision charge and precision charge penetrations into target at different stand‐offs. The cutoff jet velocity and cutoff penetration velocity also are determined based on the analytical model. With increased stand‐off, the cutoff jet velocity increases, and the cutoff penetration velocity is almost constant. This result is proven by a number of experiments. The stand‐off curves of two charges are also calculated, and results are in good agreement with experiments. The stand‐off curve can be determined with only two or three experiments using the proposed method. Notably, jet particles should have a slow drift velocity and great penetration capability after breakup for suitable shaped charge.     

Hypervelocity Jet Initiation Threshold Criteria of Nitromethane and Nitromethane Mixtures

The experimental hypervelocity jet initiation threshold criteria for neat nitromethane and homogeneous- and heterogeneous-sensitized nitromethane mixtures have been determined over a range of failure diameters, jet velocities from 2–9 mm/μs, and jet diameters in two test configurations. These criteria were used to define detonation and failure conditions in nitromethane and the nitromethane mixtures as a function of contact- and bow-shock conditions. These data were compared with data reported by others in the literature on bare solid explosives. A favorable comparison of threshold values is achieved by normalization of the criteria with the failure diameters. The effect on the initiation of the confinement proximity to the jet axis was also investigated. Experimental results have shown that high impedance boundaries near the jet axis induced conditions that allowed initiation to occur at lower jet velocities than those determined by the criteria. Tests also were performed on both homogeneous and heterogeneous nitromethane mixtures, having the same failure diameters, to determine if the same or similar jet penetration distances were required for initiation. The results, within experimental error, do not show any definitive differences in initiation conditions between the two types of mixtures.     

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.     

Detonation velocity deficit and curvature radius of flexible detonation fuses

The detonation velocity deficit in bending flexible detonating fuses is studied, based on the detonation wave’s corner effects and delay time phenomenon. A physical model and a theoretical mathematical equation of the detonation velocity deficit are established by using the dimensional analysis. Based on experimental data, a semi-empirical formula of the detonation velocity deficit for bending fuses in the same charge size is derived. It is shown that the detonation velocity deficit and the reciprocal of the curvature radius are in an exponential relationship.     

Cumulation jets in microchannels inside explosive materials

Fiber optic light guides with diameters of 0.125 mm are used to measure the velocity of jets formed in microchannels inside plastic explosives. The velocity of the head of a jet can exceed the normal detonation velocity by a factor of two in air-filled microchannels with axes perpendicular to the detonation front. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 3, pp. 140–142, May–June 1999.     

An empirical confinement model for ANFO explosive

Ammonium-nitrate-fuel-oil (ANFO) explosive, one of the most used mining explosives, exhibits highly non-ideal behaviour. The non-ideality of the detonation is manifested in the strong dependence of the detonation velocity on the charge radius and existence and the characteristics of confinement. This can lead to the detonation velocities as low as one-third of the ideal velocity. The literature reported experimental detonation velocities of cylindrical ANFO charges confined in different confiners (aluminium, copper, steel, polymethyl methacrylate, and polyvinyl chloride) are analysed in this paper. An empirical confinement model, which relates the detonation velocity to the charge radius and the mass of the confiner to the mass of explosive ratio per unit length, is proposed. The model predicts the detonation velocity of unconfined and confined ANFO charges with a mean average percentage error of 8.8 %.     

Determination of Critical Conditions for Detonation Initiation in a Finite Volume by a Converging Shock Wave

Direct initiation of spherical and cylindrical detonation in a stoichiometric hydrogen–air mixture under normal conditions by a collapsing low-pressure region (cavity) in a space bounded by a rigid shell is considered. The study of the flow with allowance for the actual mechanism of chemical reactions was performed using the finite-difference method based on the Godunov scheme, with a moving computational grid and explicit capturing of the leading shock wave and contact surface. It is established that, for a fixed pressure in the collapsing region and for its radius equal to or exceeding the known critical radius for an unbounded space, there exists a minimum (critical) shell radius, on exceeding which a detonation wave emerges in the flow field under study. In the case of spherical symmetry, the excess internal energy of the spherical layer between the shell and the low-pressure region to be spent on initiation of detonation burning attains a minimum value that far exceeds the critical energy for detonation initiation by a TNT charge in an unbounded space. Key words: discontinuity decay, hydrogen–air mixture, detonation, shock wave, critical initiation energy.     

Detonation Velocity Deficits and Curvature Radius of Mild Detonation Cords

In order to study the detonation velocity deficits of wound mild detonation cords, a physical model and a theoretical mathematical equation for detonation velocity deficits of wound mild detonation cords were established based on the detonation wave’s corner effects and delay time phenomenon by using non‐dimensional analysis method. Besides, a semi‐empirical formula for detonation velocity deficit of wound mild detonation cords in the same charge size was obtained through experiments and curve fitting. Both the theoretical mathematical equation and the semi‐empirical formula show that the detonation velocity deficit of wound mild detonation cords and the reciprocal of the curvature radius have an exponential relationship.     

INTERACTING JETS IN A FLUIDIZED BED

This work extends the Pitot-tube probe technique to the study of jetting phenomena in a three-dimensional, high-temperature gas-solid fluidized bed. For an isolated jet, the jet height was defined as the intersection of two momentum flux profiles, one along the jet axis and the other in the emulsion phase. A study of two adjacent jets confirmed that the measured jet heights were close to the visual jet heights observed through a window in the bed.

In two adjacent jets, the jets behave like two isolated jets at low nozzle velocities. As the nozzle velocity increases, the jet heights reach a maximum height in the transition zone. The jets begin to interact after the transition zone, and the jet height becomes a constant.

Similar results are obtained for two kinds of perforated-plate distributors. The maximum jet height for multiple, interacting jets is a function only of distributor geometry and is well predicted by a simple geometric model.     

Diagnostic of Superfast Jets with 25km/s Tip Velocities

In so-called cavity charges superfast jets with tip velocities in the range of 25 km/s were found. Such fast jets are strongly eroding by the perforation of the ambient air. The ablated jet material forms a tube around the jet and is optically protecting the core of the jet itself. With tests, where the jet is elongating in a vacuum, this problem does not exist or is drastically reduced. To get enough special resolution, the profile streak technique(PST) was used to obtain the diameter of the stretching jet as a function of the passing time or with respect to its velocity gradient. With this special diagnostic technique the radius of these superfast jets was measured the first time. The used test method with typical results together with the applied evaluation technique will be described.