Improved formulas for velocity, acceleration, and projection angle of explosively driven liners

Chou, Pei Chi; Carleone, Joseph; Flis, William J.; Ciccarelli, Roberto; Hirsch, E.

doi:10.1002/prep.830080602

Cited by 39 publications

(32 citation statements)

References 8 publications

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“…Next, we will talk about the new definition of the deflecting angle proposed in this paper. The performance of fragmentation structures is usually described with characteristics of the fragment dispersion and includes mass, ejection angle, direction angle, velocity, and the distribution density of fragments [22][23][24][25]. The ejection angle ( ) and direction angle (Ω), shown in Figure 11, are studied widely in designing fragmentation structures.…”

Section: End Effectsmentioning

confidence: 99%

Parallel Control to Fragments of a Cylindrical Structure Driven by Explosive inside

Chen¹,

Li²,

Lu³

et al. 2015

Mathematical Problems in Engineering

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By analyzing the fragmentation distributions of a cylindrical structure and a specific structure, the necessity of parallel control to the fragments is presented. The shell shape of structures has an influence on the fragment spatial distribution. A new design method for the shell shape is proposed. To facilitate the establishment of the numerical model and the machining for relative experiments, the mathematical description of the theoretical calculated generatrix of the shell is simplified. The fragment spraying processes of the designed structures are simulated, and end effects are analyzed. Based on the theoretical design and plentiful simulation data, the relationships between the size of the parallel fragmentation structure and the optimized curvature radius of the shell are expressed by an equation. The equation is validated by numerical means and can be a reliable reference to the design of the parallel fragmentation structure.

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Section: End Effectsmentioning

confidence: 99%

Parallel Control to Fragments of a Cylindrical Structure Driven by Explosive inside

Chen¹,

Li²,

Lu³

et al. 2015

Mathematical Problems in Engineering

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“…One way to evaluate this constant is to compare the predictions of the obtained formulas with 2-dimensional codes simulations as done in Ref. 1. The predictions of Eq.…”

Section: Discussionmentioning

confidence: 99%

Simplified and Extended Gurney Formulas for Imploding Cylinders and Spheres

Hirsch

1986

Propellants Explo Pyrotec

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The usefulness of the Gurney formulas in application to one‐dimensional computer codes for shaped charge design has called for their extention to predict the asymptotic velocities of imploding cylinders. Two different approaches by Chou, Carleone, and Flis on 1981 and by Chanteret on 1983 have led to improvements which were shown to predict correctly two‐dimensional code simulations for unconfined charges. Both works did not lead however to simple formulas which retain the conveniency of the original Gurney formulas. In the work presented, closed form analytical solutions for both the cylindrical as well as the spherical geometries are derived. The solution for each geometry is presented in a way in which the symmetry between the inner liner and the confinement is easily recognized. The relation of each solution to the Gurney formula for asymmetrical sandwich is also obvious. The presented solutions reduce to all the known Gurney formulas for the more simple geometries at the appropriate limits. The accuracy of the predictions by the obtained formulas is limited however when the assumptions of the Gurney model do not describe the real physical situation closely. This happens in general in extreme cases, e.g. when the liners are very light comparing to the explosive mass or when the ratio between the confinement radius and the inner liner radius is very large comparing to unity.

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“…Many researchers have done excellent works on this point;s ome formulas are established to assess the driven ability of explosives and to predict velocities of fragments driven by explosives. To give some examples, Waggener estimated the velocities of velocitye nhanced warheads by adding an additional term in Gurney's formula to take into account the enhanced velocity in the target direction [3].P .C.Chou et al developed an improved one-dimensional formula for both the direction and magnitude of the velocity of explosively drivenl iners [4].D .M. Goto et al investigated the fracture and fragmentation of explosively driven rings and cylinders experimentally.F ragmentation processa sw ell as failure mechanisms weref urther discussed [5].F eng et al modified the classic Gurney's formula for cylinder chargestocalculate velocities of velocity enhanced warheads [6].M .W ang et al proposed an umerical model to predict the radiald istribution of the fragment velocities of the velocity enhancedw arheads [7].…”

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confidence: 99%

A Theoretical Analysis about the Driving Mechanism of Mild Detonating Fuse

Wen

Chen

et al. 2015

Propellants Explo Pyrotec

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[a] 1IntroductionIn aerospace applications many devices utilizing explosive, propellant and pyrotechnic compositions play important roles to achieve various functions, such as severance/fracture, release, jettison, switching, and so on. Pyrotechnics are extensively applied because of their high efficiency including high energy delivered per unit weight, small volume and compact, long-term storable energy,a nd controllable initiation and output energies [ 1].T able 1l ists major past and current pyrotechnic applicationsi na stronautics.According to the source of the shock,t hese pyrotechnic devices could generally be classified as point, line, or combined source as shown in Ta ble 2[ 2].S ince internal structural deformationo ften occurredi ne ach firing, pyrotechnics normally are utilizedo nly once. The best assurance of successful operationi st hat the devices are designed with functional margins andh ave beena ccurately manufactured. Meanwhile the explosive, propellant and pyrotechnic-composition energy sources will burn completely and quickly no matter if the ignition input is intentional or inadvertent. Thus selecting the lowest-level energy input to ensure ignition is the main priority.M ild detonating fuse (MDF) can be processed with av arietyo fs pecifications and good consistency,s oi ti sc ommonly used in linear source pyrotechnic devices as actuator. Figure 1s howsa nexample [1].Althoughe xtensivelya pplied, pyrotechnics are used with reservations, because some rocket launchingm ission failAbstract:T wo theoretical models basedo nm omentum conservation, energyc onservation,a nd law of motion were constructed to predict the velocity of fragments driven by mild detonatingf use (MDF). In the models, it is assumed that the driven velocity includes two parts:i nstant velocity coming from the impact of metal sheath and velocity increment caused by detonation products. Twog roups of experiments were designed and carried out to validate the models. The experimentr esults show that the modelb ased on momentum methodb etter describes the fragments driving process. Furthermore, as eries of finite-element simulations using LS-DYNA3D were done to fully verify the model. The simulation results show that the assumption of the fragment velocity composed of instant velocity and velocity increment is reasonable.B oth theoreticalp redictions and simulation results all indicate that instant velocity coming from the impact of the metal sheath accounts for majority( average8 9%)o ft he final velocity,w hich shows that lead sheath playsakey role in the acceleratingp rogress of fragment drivenb yM DF.A saresult, ac ertain distance should bea llowedf or the lead sheath to be accelerated to make full use of the MDF.T his research may relate to the design of linear pyrotechnic separation device in aerospace engineering.

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Improved formulas for velocity, acceleration, and projection angle of explosively driven liners

Cited by 39 publications

References 8 publications

Parallel Control to Fragments of a Cylindrical Structure Driven by Explosive inside

Parallel Control to Fragments of a Cylindrical Structure Driven by Explosive inside

Simplified and Extended Gurney Formulas for Imploding Cylinders and Spheres

A Theoretical Analysis about the Driving Mechanism of Mild Detonating Fuse

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