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A method for intermediate ballistics modelling is presented. The method is used to study the effect of muzzle brakes with a passing projectile. Pressures, velocities and impulses are computed using a thermodynamic interior ballistics code (lumped parameter code) for projectile travel within the barrel. Then Computational Fluid Dynamics (CFD) simulations are used for gas and projectile travel outside the barrel. CFD simulations are performed both with and without a projectile and the results compared. Three generic muzzle brake geometries are used for simulations. Impulses computed from thermodynamic model and CFD model are combined to evaluate the gun recoil. The CFD model, with initial conditions transferred from the thermodynamic model, can further be used to analyse the influence from the muzzle break on the flow.

Instead of the capillary plasma generator (CPG), a discharge rod plasma generator (DRPG) is used in the 30 mm electrothermal-chemical (ETC) gun to improve the ignition uniformity of the solid propellant. An axisymmetric two-dimensional interior ballistics model of the solid propellant ETC gun (2D-IB-SPETCG) is presented to describe the process of the ETC launch. Both calculated pressure and projectile muzzle velocity accord well with the experimental results. The feasibility of the 2D-IB-SPETCG model is proved. Depending on the experimental data and initial parameters, detailed distribution of the ballistics parameters can be simulated. With the distribution of pressure and temperature of the gas phase and the propellant, the influence of plasma during the ignition process can be analyzed. Because of the radial flowing plasma, the propellant in the area of the DRPG is ignited within 0.01 ms, while all propellant in the chamber is ignited within 0.09 ms. The radial ignition delay time is much less than the axial delay time. During the ignition process, the radial pressure difference is less than 5 MPa at the place 0.025 m away from the breech. The radial ignition uniformity is proved. The temperature of the gas increases from several thousand K (conventional ignition) to several ten thousand K (plasma ignition). Compare the distribution of the density and temperature of the gas, we know that low density and high temperature gas appears near the exits of the DRPG, while high density and low temperature gas appears at the wall near the breech. The simulation of the 2D-IB-SPETCG model is an effective way to investigate the interior ballistics process of the ETC launch. The 2D-IB-SPETC model can be used for prediction and improvement of experiments.

An ordinary gun projectile will, after entry into water, be subject to an extremely high drag and will stop after 50 – 100 calibers of travel through the medium. To avoid such a response, supercavitation must take place. By a specially shaped projectile nose, the flow of water around the projectile may escape contact with the surface of the projectile, except at the nose tip. Under these conditions, the projectile is said to be supercavitating. In such a state, the projectile is unstable, but, the stability is maintained by the oscillation caused by the interaction between the rear part of the projectile and the cavity wall. In order to keep the amplitude of this oscillation as small as possible, the size of the cavity should be just slightly larger than the projectile. The cavity size is, however, determined by the size and shape of the nose tip, by the velocity of the projectile, and by the pressure in the ambient water (i.e. the water depth), through Garabedian’s equations. These parameters will also determine the duration of the cavity which determines how far the projectile will travel before the supercavitation ceases, and the projectile stops. The paper outlines the theory for the size, shape, and duration of the cavity. It discusses also the conditions for designing an optimal design of a supercavitating projectile. Special emphasize is put on how to determine the drag on the projectile by observing the size of the bubble.

In order to get the different muzzle velocity in large caliber artillery gun systems, the propellant charge usually have several charge zones. When these charge zones been fired, the different chamber pressure and projectile velocity will happen which can influence the burning rate of propellants. It is very important for getting the burning rate of propellants in different charge zone when predicted the performance of interior ballistics. Usually we can get the burning rate of propellant from experiment results of closed bomb, but these results cannot be directly used in numerical simulation of interior ballistics processes for all charge zones. Now, we use a serial experiment of gun firing for different charge zone to get the performance of interior ballistics. On the basis of the simulation for performance by the IB code, we can get the real burning rate of propellant in IB processes. By using the methods, we can get the accurate results for predict the interior ballistics performance when different charge zones were used. So in this paper, an approach has been developed for getting the real characteristic of burning rate of propellant at different charge zone for large caliber artillery gun systems.

This paper investigated the effect of mid-wall water cooling for the gun barrel under continuous firing. A 2D cross-section model of the gun barrel is adopted and the cooling channel is circular. An interior ballistics code is used to determine the inner wall convection boundary condition, providing gas temperature and heat transfer coefficient. Results of temperature histories of the inner wall and outer wall and temperature distributions are presented. The results show that this cooling method can slow down growth rate of the peak temperature of the inner wall.

The development of high accuracy rifle has uncovered a need for understanding the movement of the bullet in muzzle flow. Recent researches have always been focused on computational fluid dynamics (CFD) and experimental research on the muzzle flow, which released many data, such as velocity and base pressure drop of projectile. Due to CFD tests are timeconsuming, a dynamic model for spatial motion of projectile is established. In this model an empirical relationship is utilized for the base pressure of projectile, and the model is assumed that the base pressure is along the axis of barrel which applied on the tail cone of the bullet; The spatial motion equations deduced from the mass center motion equations and Euler equations of motion are solved with Runge-Kutta method. A 7.62 caliber bullet is tested to verify the dynamic model. The result agrees with the CFD and experimental data, which shows that the model is applicable in predicting the translational motions, besides the angular motion of projectile is also presented, which can be the initial condition of exterior ballistics to analyses the firing accuracy.

In the present work experimental data from seven perforated (7PF) JA2 propellant combustion in a micro closed bomb is presented and the linear burning rate of the JA2 propellant is determined. The burn rate measurement is based on a sophisticated lumped parameter model which accounts among other things for arbitrary cross sectional propellant geometries with the help of the ICT-Cellular-Combustion-Algorithm (ICCA), pressure dependent thermophysical parameters and heat loss. The model is used to construct a vivacity based objective function which depends on the parameters of the empirical law for the linear burning velocity. With the Nelder-Mead downhill simplex optimization algorithm the objective function is minimized and the burn rate parameters determined. The comparison of the results to published data show that with the new burn rate measurement method the linear burning rate can be determined with great accuracy even when only a few propellant grains with a total propellant mass of less than 8 g per shot are used.

We explore two initial conditions on the same numerical grid to simulate blast overpressure at crew locations in the far-field. The first utilizes a 2D axisymmetric simulation mapped into a 3D quarter symmetry domain (2D-IC) as an initial condition for the exterior blast overpressure simulation. The purpose of this method is to reduce runtime from days to hours where the simulation lends itself to axisymmetric (i.e. the interior of a cannon). The second utilizes a full 3D quarter symmetry simulation (3D-IC) started from propellant ignition to propagation to the position of interest in the exterior of the tube. These results are then compared to experimental blast overpressure results for the same position. The conclusions from the study are that both the 2D-IC and 3D-IC are valid methods for numerically determining blast overpressure. However, the two initial condition approaches vary significantly compared to one another.

This work is a continuation of the research presented at the 29th ISB, concerning an analysis of the dynamic vivacity function determined on the basis of closed vessel tests results. The main conclusion of the analysis was that the form of the vivacity function strongly depends on the loading density. In order to analyze this dependence for the loading densities ranging from 300 to 700 kg/m3, the valved closed vessel (VCV) was used. The maximum value of the time derivative of pressure was attributed to the end of the pyrostatic period. The dynamic vivacity curves for this period were determined. The strong dependence on the loading density was revealed. This was explained by differences in the temperature distribution inside propellant grains. The effect of this distribution on the values of the burning rate was analyzed. Conclusions concerning the method of analyzing closed vessel test data were formulated.

The replacement of plastrite by Hexomax leads to determinate and validate the equation of state parameters of the detonation products, in the goal to make performances numerical calculations of this energetic material. The Chapman- Jouguet state is calculated using two ways, firstly from simulations with the thermo-chemical code named SIAME developed by the CEA for the French DGA and conventional defense applications, secondly from an approach based on empirical relations available in the literature. The hypothesis of a mean value for the polytropic coefficient in the ambient state of detonation products and also for exponential decreasing members coefficients of JWL equation allows to reach to other parameters according the strength to respect the detonation CJ state. Inside SIAME, these coefficients are obtained by minimization of the JWL equation isentropic form of the detonation products CJ expansion. Used in a hydrodynamical calculation code (OURANOS, LS-DYNA), JWL parameters allow to compare the numerical simulation results to experimental results of the cylinder test. The correlation is very good with parameters from the thermo-chemical simulation. The empirical method looks like a FREM (« Fast Running Engineer Model ») leading to a good approximative solution of JWL parameters when the necessary enthalpy of formation for the thermo-chemical simulation is not available. The JWL parameters are used afterwards to evaluate the Hexomax blast effects for aerial detonation.

Shock initiation of explosives has been at the focus of many important studies over the years. One of the interesting topics in this field deals with the ability of a projectile, or jet, to initiate an explosive through impact. To this end, Held introduced the critical v2d initiation criterion, which has shown great success for the case of bare explosives. However, recent experimental results have questioned the generality of this criterion for cases of covered explosives. In this work we employ the Lee-Tarver model, to numerically explore the shock initiation of PBX9404 explosive, subjected to the impact of long rods. We demonstrate the generic difference between bare and covered explosives and identify the crossover between these two cases. We conclude by mapping the run to detonation distance, for rods of different velocities and diameters, for covered explosives.

In this paper, the multiple factors in the transition process is comprehensively analyzed. When the armature is sliding at a very high speed, the velocity skin effect will generate the melt-wave. Then the melt-wave will produce a reversed electromagnetic force, which will leads to the armature separating from the rail. The larger the erosion area, the stronger the separating force. Besides, the mechanical force is much smaller than electromagnetic force. When the contact area cannot meet the conductivity capacity of large current, there will appear transition. The prediction formula of transition is given. The calculation results are almost in consistent with the experimental data. Finally, this paper proposes a key criterion coefficient of j2V, defined as the transition criterion. From the quantitative analysis and experimental data, its value is about 4E20 (A/m/s). When the contact power is greater than this criterion coefficient, there will be transition. It makes the prediction to be more convenient and quickly, which will be very useful for the railgun design.

Aerodynamic coefficients are predicted by traditional, uncoupled computational fluid dynamics (CFD) and coupled CFD/rigid body dynamics simulations on a complex, canard-controlled projectile. The projectile is considered in its uncontrolled state as well as for canard deflection angles such that pure pitching motion is induced. Static and dynamic aerodynamic coefficients are considered for each of the component contributions (i.e. body-fin with interference effects and individual canards). For the non-deflected canards, the aerodynamic model is equally well described by either method. The coupled simulations are completed in roughly the same total CPU time with greater angular resolution than the traditional, uncoupled CFD. For the cases with deflected canards, the traditional, uncoupled CFD was able to isolate additional dependencies: (1) angle of attack as well as canard deflection angle dependency for the body-fin interference effect, and (2) a deflection angle as well as a local angle-ofattack dependency on the canard aerodynamic coefficients.

Previous studies have shown that "sandwich" explosive reaction armor (ERA) has a large interference effect on definite EFPs. However, it is unclear whether the conclusion is applicable to different calibers EFP warheads. To investigate this issue, the processes of copper EFPs formed by various charge diameters warheads penetrating into 1/1/1mm ERA were simulated by AUTODYN-3D software. The shape, deflection angle, velocity, and residual depth of penetration of EFPs after passing through ERA were obtained. The results showed that the interference degree of EFP was nonlinearly decreasing with the increase of charge diameter. Its causes were analyzed from the perspective of interaction time. In order to verify the correctness of the numerical simulation, the pulsed X-ray photographs of the interaction between ERA and EFPs formed by 56mm shaped charges were obtained and DOP was measured. It turned out that the numerical simulation results agreed well with the experimental.

In order to study the bending failure of projectile during high-speed normal penetration into concrete, a dimensionless bending factor is introduced according to the failure modes of projectile, and the dimensionless stress of dangerous cross section is calculated according to Forrestal’s resistance formula. Further, bending failure criterion of the normal penetrating projectile is proposed, i.e., when dimensionless bending factor is greater than 6.8 and dimensionless stress of dangerous cross section is greater than 0.70, the bending failure of the projectile occurs. According to the failure criterion and the no upsetting condition of hollow part, optimization of maximum charge volume and the corresponding projectile structure without bending failure are given, then, the bending failure criterion and the optimized structure of the projectile are verified by numerical simulation.

Combining the results of combustible cartridge and propellant in closed bomb, the classical interior ballistic theory was used to calculate interior ballistic process of the charge with combustible cartridge. The influence of burning rate of the combustible cartridge on the interior ballistic performance parameters was studied. The matching relationship between the burning rate of the combustible cartridge and the different charge structure is confirmed, which provides references for the design of interior ballistic and charge structure.

Thermal stimuli through slow cook-off heating are particularly interesting, since underlying phenomena are very complex, responses depend upon various parameters and they may have a significant impact on warhead system design. A standardized test device with cast-cured or pressed plastic-bonded high explosive charges is used at TDW for investigating such slow thermal stimuli that allows evaluating reaction levels and decomposition temperatures of high explosives. It provides a confined environment and also permits temperature measurements inside the high explosive charge. Experimental tests results of KS57, KS22, and P31 charges varied between burn and deflagration reactions depending on high explosive charges and charge confinements. Such experimental data provide a profound basis for thermal modeling of slow cook-off responses. Multi-physics coupling of transient heat conduction with Arrhenius reaction kinetics form a system of coupled partial differential equations. AKTS-Thermokinetics software deliver corresponding input functions that were determined through differential scanning calorimetry tests of small explosive samples. The recently enhanced model implemented in MATLAB considers additional boundary conditions such as heat conduction through the casing, convection of the turbulent oven heat flow into the casing, and end cap venting effects. Predicted self-heating times, rates, and peak temperatures approach well experimental data. Using this proposed multi-physics model in finite element simulations like COMSOL provides spatial temperature distributions over time and allows future application to full-scale warheads.

The penetration of Armor Piercing, Capped (APC) projectiles into Special Treatment Steel is not new [1]. Many years ago the means of calculating the ballistic limit, residual velocity, etc. were based on semi-empirical formulae garnered from actual tests [2]. Major geometric changes in the design of a projectile, cap and windscreen made some difference in the ability of the shell to penetrate armor plate. The purpose of this paper is to attempt to determine a reasonable method to model the mechanical properties of the target material as well as the projectile components to reasonably match the test data and compare with the semi-empirical models. The projectile chosen is a U.S. Navy 14 inch Mark 16 Model 8 projectile depicted in Figure 1. This projectile has been modeled using the Abaqus finite element software. It is believed that the triaxiality of the target material has a great effect on the results [3]. This was compared to the semi-empirical formulae of Lambert and Thompson as well as that of Okun [4]. The modifications to the mechanical properties in the Abaqus model to incorporate triaxiality are discussed. The models were in very good agreement over a fair range of target thicknesses and impact obliquities but not at high obliquities and large target thicknesses.

To study the characteristics of flow field in combustion chamber of continuous rotating detonation engine (CRDE), based on Two-dimensional Conservation Element and Solution Element (CE/SE) method, the numerical simulation was carried out to the effects of combustor axial length on the flow fields and propulsive performances of CRDE. Results show that the CE/SE method is quite efficient to capture the detonation wave. The flow field structure of the combustor is qualitatively consistent with the experimental results of kerosene/air/oxygen mixture detonation. With the increase of the axial length, the length of oblique shock wave and the average values of the axial velocity increase, while the fluctuation at exit, the peak values and average values of the exit pressure and exit density decrease. In addition, the peak values of the axial velocity rise first and then fall, and the circumferential velocity decreases. With the axial length increasing, the flow field needs more time to reach quasi-steady state, the specific impulse first increases and then remains constant.

In order to study reason of the barrel damage, one-dimensional two-phase flow trajectory model was used to study the pressure distribution law in the gun, to study the movement law of the projectile with different resistance in the bore and the pressure distribution. Effects on the tube strength and projectile strength are also studied, to provide a reference for the analysis of the cause of the barrel damage.

The combustion light gas gun (CLGG) uses combustible low molecular weight gas as propellant to burn, expand and propel the projectile out of the barrel with higher muzzle velocities. Previous researches had revealed that the deflagration to detonation transition (DDT) process easily occurred in oxy-hydrogen mixture. The great energy released detonation can cause the bore premature accidents. Large eddy simulation (LES) methodology and a detailed chemistry model with 9 components of 18 reactions are applied to investigate the process of flame acceleration (FA) and DDT in CLGG. The mole concentration ratio of oxy-hydrogen gas mixture plays an important role on the interior ballistic process, especially the phenomenon of DDT. Therefore, some typical simulation cases with different charging ratios are carried out to study the abnormal combustion process in the chamber so as to direct the safety operations in experiments.

The numerical simulation of the interaction between spherical tungsten fragments and cylindrical Comp-B explosive covered by steel casing was carried out by using AUTODYN-3D software. The influences of the fragment impact angle θ and cylindrical charge curvature radius r on the impact initiation characteristics of the explosive are analyzed, and the critical initiation velocity of cylindrical-shell charge (CSC) is obtained. The results show that the impact initiation mechanism of CSC coincides with that of planar-shell charge (PSC). For CSC, the critical initiation velocity increases exponentially with the increase of the sine value of θ and increases nonlinearly with the increase of r, which indicates that the CSC is easier to detonate. In addition, another high-precision simulation software SPEED was used to carry out the initiation process of the insensitive explosive PBXN-109 under the impact of fragments, hoping to provide a reference for further study of impact initiation in reality.

High pressure is applied to concrete target by the projectile in hypervelocity penetration. Moreover, concrete material which undergoes large deformation is incompressible and can be depicted by liquid constitutive model. The present work modifies the cavity expansion theory by characterizing the incompressibility with Bingham liquid constitutive model considering the viscosity of the incompressible material according to Cleja-Tigoiu’s work. The analytic expression for the relationship between the pressure on the cavity boundary and the velocity of the cavity expansion is derived in this paper. Then, the effects of material parameters in the modified model are studied, which is the basis of the calculation of the drag force in hypervelocity penetration. At last, some penetration depth results of long rod impact concrete target on hypervelocity are predicted based on the modified model, which are in good agreement with the experiments.

The muzzle flow of aircraft gun is significantly influenced by the flight speed. Based on the Naiver-Stokes equation and k-epsilon model, the Roe Flux Differencing Scheme was used to simulate the muzzle flowfield of embedded aircraft gun in four different states, viz. inflow velocity of 0, 1.25, 1.5 and 2.5Ma. The structures of the muzzle flowfield were shown clearly, including the interaction process between the muzzle flow and supersonic inflow. The structure features were discussed in detail by comparing the parameters in the static and supersonic flight state. Furthermore, the influence of inflow velocity on the muzzle blast intensity was analyzed.

Numerical study was conducted to analyze the effect of a moving charge on a stationary target. As was found earlier, the shock wave emanating from the moving charge is spherical although the pressures in the direction of movement are much greater than those in the opposite one. The analysis was conducted by running Autodyn 2D and 3D, assuming the target is rigid and either stationary or moves parallel to the charge. The reflected pressures and the overall force on the target were measured for a moving 1 Kg charge at various velocities. The results show that the load on the target increases significantly if the explosion is in air and the intensity of this load depends strongly on the charge velocity.

An active mitigation countermeasure, based on the principle of momentum cancellation of detonating counter-charges against the effect of explosive blast, has been researched. The study was conducted on a small scale and then extrapolated to an intermediate scale. On a small scale it was demonstrated, both theoretically and experimentally, that high orders of momentum cancellation are achievable. Good correlation was obtained between the numerical predictions and the experimental results. Similarly, on the intermediate scale, with a specific choice of experimental setup, good correlation was achieved between the numerical and experimental results. The differences between the results of the small scale and intermediate scale investigations are attributed to variations in the verification methodologies.

Experiments were conducted on cylindrical explosive charge with three different initiation configurations viz., geometric center initiation, single line side initiation and two line side initiation. Blast pressure parameters were measured at different distances from explosive charge. Peak over pressure from single line initiated explosive charges along azimuth direction at 180o is about 40% more than that of point initiated charges at a distance of 1m from point of burst. Over pressure and impulse values of line initiated charges drop down to those values obtained from point initiated charges beyond a distance of 10 times charge diameter from point of burst. Total impulse is observed to be less in case of two-line initiated charge as compared to point initiated and single line initiated charge.

It is assumed that the mechanism of gun propellant gases production is dependent on the knowledge of propellant grains geometry and adoption of a geometric model of propellant grains burning. In the paper, the authors analyse the influence of arrangement of propellant grains in a combustion chamber on the changes of dynamic vivacity. The grains of the propellant charge have been piled up spontaneously at the bottom of a combustion chamber or have been spaced separately, systematically on the whole circuit of a combustion chamber. The investigations were carried out with application of black powder ignition and gas ignition for the same loading density. The results of closed vessel investigations showed that the character of dynamic vivacity is determined not only by geometry of propellant grains but also by the conditions of heat transport between hot ignition gases and available burning surface of propellant grains.

Computational fluid dynamics is used to investigate a bending body projectile as an alternative control methodology to improve gun-launched projectile maneuverability over that of a canard-controlled projectile in the supersonic regime. A fin-stabilized projectile of length-to-diameter ratio 10 is considered. A feasibility study analyzes the aerodynamic performance of a dual bent-body (8° bend at nose-body junction and 8° bend along the body) compared to the straight body and a straight body with 4-10° deflected canards over a range of Mach numbers and angles-of-attack. The resulting aerodynamic coefficients reveal that a projectile that cruises in a straight-body configuration and changes into a bent-body configuration for maneuver control is likely to provide greater control authority than a canardcontrolled projectile. An optimization study seeking to optimize the bentbody geometry of the Air Force Finner for maximum control authority and minimum drag is initiated.

This article is a summary of the first phase of 9x19mm ammunition exploration after the impact. The study included setting the limit of the ammunition ripping angle after hitting the metal barrier. To do the test was used doppler ballistic set, ballistic soap and ballistic gel. The paper is concluded with results analysis that can be used for future work.

In order to study the detonation stability of continuous rotating detonation engine, an experimental study was carried out on three annular slots of different area ratios, using hydrogen as fuel and air as oxidant. Based on the high frequency pressure signal, the influence of the annular slot area ratio on the detonation parameter stability was analyzed. The experimental results show that when the area ratio is 0.08, the detonation wave propagates in a double-wave colliding mode, and the peak pressure is in the range of 0.3-0.9MPa. When the area ratio is 0.16, the detonation wave propagates in single wave mode, and the pressure peak is around 2.0MPa. When the area ratio is 0.32, the detonation wave propagates in a single-wave/double-wave coexistence mode, and the peak pressure fluctuation ranges from 0.4 to 3.0 MPa. When the area ratio is 0.08, the detonation wave self-sustaining propagation stability is strong, but the detonation wave stability is weak when the area ratio is too large or too small. Therefore, the area ratio of the annular slot has a great influence on the mixing effect of hydrogen and air, which consequently impacts the detonation stability of the continuous rotating detonation engine.

This work deals with numerical simulations of impact problems on fiber-based composite armor using the commercial finite-element-code ANSYS AUTODYN. Having presented some basic knowledge on the theory of numerical simulation in AUTODYN, two recently published approaches for modeling impact on the selected composite (Dyneema® HB26) are explained. While both of them make use of a nonlinear-orthotropic material model implemented in the AUTODYN-code, they differ in the way how the highly inhomogeneous microstructure of HB26 is represented geometrically. Lassig chooses a fully homogeneous description, whereas Nguyen discretizes the composite into sublaminates, which are kinematically joined at the surfaces and breakable when a certain contact-stress is reached. In order to validate the two approaches, the response of HB26- samples impacted by handgun-projectiles was determined experimentally and compared to the corresponding numerical results. Unfortunately, a poor agreement between experimental and numerical results was found, which gave rise to the development of an alternative modeling approach. In doing so, the composite was subdivided into alternating layers of two different types. While the first type of layers was modeled with open-literature properties of UHMWPEfibers, polymer-matrix-behavior was assigned to the second type. Having adjusted some of the parameters, good agreement between experiment and simulation was found with respect to residual velocity and depth of penetration for the considered impact situations.

The strength of components against blast waves has been studied largely especially in the case of the nuclear blast. These works show that the damage is well defined by the pressure level and the recovery time of assemblies or sub-assemblies. In the frame of this work, we studied the effect of an explosive charge on different types of components. The reaction of an explosive charge in a ship breeds a propagating shock wave whose effects can induce severe damages on the different components set inside corridors and rooms. We seeked to determinate the damage level bred on different types of components by the detonation of an explosive charge inside a closed volume. Using the Johnson’s rule, we can establish the iso-damage curve for every type of components. The results show that the mass and the dimensions of the components have the main influence on the behavior of the component against the explosive loading.

The performance of a shaped charge warhead is usually predicted based on an experimentally determined standoff curve valid for a specific target material. However, with the increased variety of target compositions the traditional “shoot and score” approach is not feasible anymore – neither financially nor with respect to time. In this paper, a combined analytical stochastic jet penetration model is presented that permits to predict the penetration process of a shaped charge jet into various target materials. The model combines (semi-) analytical descriptions of jet stretching and breakup with stochastic elements with an extended Walker-Anderson penetration model and an energy-based crater prediction to include the collision of particles with the crater wall.

High Progressivity Rocket Motors (HPRM) are designed to eject an article out of a tube. High burn rate, progressive burn pattern, small burn time and low area expansion ratio are peculiarities of the motor. Initial 200ms of burn time are critical for functionality of motor whereas the test results showed deviations and pressure jumps in first 200ms. The performance further deteriorated when tested after conditioning at higher temperature. The motor test results were studied. Gas flow velocity characteristics inside individual port were studied and found to be on higher side even though the erosive burning constant ‘g’, [1], when calculated, was found to be within limit as specified for normal burn rate motors. Motor configuration was modified to reduce flow velocity and flow interaction. Modified configuration, when tested, was as predicted without any pressure jump. After comparing the flow characteristics, limits for velocity and ‘g’ values were reestablished.

Gurney Velocity of an explosive is a required input into the standard Gurney Model of fragment velocity prediction from a metal cased explosive. It is a critical parameter in the comparison of compositions for performance prediction. Eight empirical Gurney theories discussed in this paper enable prediction of the Gurney Velocity of explosive compositions using differing Detonation parameters. Some parameters are easy to access, whilst others can be difficult to obtain. Only empirical methods are assessed here, being both simple to implement, but also giving reasonable accuracy. Aluminised explosive compositions are treated in an identical manner. Two Gurney Velocities exist for each explosive, ‘prompt’ for rapid case fracture and ‘terminal’ for ductile case expansion. This paper considers only the ‘terminal’ value, being the most important. Analysis of the accuracy of each empirical method is given and statistical comparisons made. Surprisingly some complex methods do not necessarily give any more accurate predictions.

Several types of equations are used for modeling the relationship among the state parameters of explosives and computer implementation is mostly needed for predicting the behavior of explosives. During modeling of detonation characteristics of explosives in simulations, Jones-Wilkins-Lee (JWL) equation of state (EOS) is widely used. The parameters of JWL EOS are not always available for newly developed explosive compositions. In this study, cylinder expansion test has been utilized to determine parameters. Cylinder expansion tests have been performed for different Polymer Bonded Explosives (PBX) and TNT with the designed setup and JWL EOS parameters are obtained. Gurney constants are also derived by post-processing the test results. Pressure - specific volume ratio curves for these explosives are compared with the curves available in literature and seen that the results are close for similar compositions. Parameters are also verified with the comparison of open area blast measurement results with numerical simulation.

In-bore failure of a large caliber tungsten heavy alloy long rod penetrator has been studied. A 2D axisymmetric finite element analysis has been carried out to check its in-bore structural integrity. The objective of structural analysis has been to obtain accurate stress field in the penetrator. Three phase approach was adopted to analyze the problem. The analysis involved quasi static analysis of the entire penetrator and fracture mechanics approach. A high stress concentration with steep spatial gradient has been found in the fillet region of rear thread/groove of the penetrator. Although, stresses are very high at the fillet of the rear groove, they reduce to safe limit rapidly. Though bulk failures are not predicted, high axial stresses at thread roots can cause catastrophic failure when cracks are present. Fracture mechanics based approach has been used to find the desired fracture toughness for a given crack size.

Impact experiments with gelatin targets often lack information on the pitch rate of the bullet at the time of impact. Usually, this boundary condition is also ignored in numerical modelling. To investigate the effect of pitch rate on the bullets behavior in gelatin, a numerical study is performed for various impact angles and pitch rates. To enable this study, a constitutive model describing the hyperelastic, nearly incompressible and viscoelastic behavior of gelatin is implemented in a commercial finite element code. We investigate how the pitch rate and impact angle affects the depth where a full metal jacket bullet starts to tumble in a gelatin target. Results indicate that whilst the impact angle dominates the bulletgelatin interaction, large pitch rates (>150 rad/s) should be included in any analysis. However, in most ballistic experiments the pitch rate is low (

Waste projectile recycle means a lot to cost saving and could improve the waste propellant utilization ratio. Simulation analysis was conducted to study the emptying technology of waste projectile by cavitating jet. Twodimensional axial model of angle nozzle was build and the cavitating results under different working condition (different inlet media's pressure and temperature, different temperature in the projectile) was simulated by using of mixture multiphase model. The results indicate that, the velocity contours show “sword shape”, and the gas phase mass fraction shows the “tongue shape” and decay along the axis director. The temperature of inlet media and the temperature in the projectile is not the main factor to influence the cavitation. While the inlet media's pressure affects the cavitation a lot, the bigger the pressure, the better the cavitation intensity. The conclusions could offer references for further study of emptying technology of waste projectile by cavitating jet.

Progressivity, i.e. gain in burning area, of multi-perforated propellant grains is graphically shown to have a maximum for certain dimension ratios. Form functions, amount of slivers, and optimum dimensions for some basic grain types are presented. The effect of finite manufacturing precision on form function, progressivity, and amount of slivers is estimated approximatively. This study of form functions is strictly geometric, no physical effects of combustion, like flame spread, combustion inside perforations, or erosive burn rate, are taken into account.

The investigation in attack angle induced by canards control force is an important issue for trajectory correction technology. This paper focuses on the attack angle response of projectile considering not only durable force but instantaneous force. Following the introduction of the projectile nonlinear dynamic models in the non-rolling reference frame, the equations of attack angle under control are established. The initial angular rate is derived through a model with conservation of angular momentum. The analytical solutions of attack angle under the two conditions are presented. The analytical expression of the relationship between trajectory shift and attack angle is presented. When instantaneous force is taken into consideration, the magnitude of the maximum angle of attack is raised by 10.2%, the steady-state time is extended by 15.2%, whereas the trajectory under two kinds of condition varies little.

In this paper the combined numerical-experimental approach was used to investigate the explosively driven fragmentation of warhead casing . The experimental tests were conducted with the aim of gathering the data which will be useful for verification of the subsequent simulations. During the experiments after the detonation of explosive, the fragments of the ruptured casings were collected. The number and the mass distribution of fragments were examined. Then, the numerical simulations were conducted with the same explosive fragmentation geometry as in experiments. The correctness of the conducted simulations and the applicability of the used numerical technique were verified by comparing the numerical results, especially fragments number and their mass distribution, with the conducted experimental tests outcomes. The reasonable agreement between examined parameters was achieved, what testifies that the technique can be used in the future to predict the fragmentation behavior of warheads casings.

Numerical analyses have been performed to investigate how the PG-7M grenade interaction with the net-armor affect the shaped charge jet formation and penetration capability. Two types of three-dimensional computer simulations were carried out. The first one include mechanical interaction between the grenade and two commonly used types of net armors. The deformation rate of the warhead and occurrence of the short circuit in a fuse of penetrating grenade were estimated. The second type of analyses included the phenomena of shaped charge jet formation and penetration into RHA plate. Since the simulations were carried out for both the deformed and undeformed warheads, it was possible to evaluate the influence of the grenade deformations on the shape charge jet penetration performance.

The Eulerian in-house hydrocode has been tested with two major challenging problems: (1) formation of a shaped-charge, and (2) formation of an explosively-formed projectile. Both of the simulations are compared with our field x-ray test data. The code is based on the three-dimensional explicit finite element method written in C++. For better accuracy, 2nd accuracy throughout the code has been maintained with sophisticated handling of the technique. The predictions using the commercial code has also been compared. Currently our code has shown a relatively good prediction for the EFP simulation. However it is necessary to use an improved material model, especially to isolate the accuracy of the numerical scheme itself.

An experimental system, which was composed of a high-pressure gas jet generator, transparent chambers with various interior geometries and a high-speed video recorder, was built for the investigation of interactions between high-pressure gas jet and bulk-loaded liquid. A gas-liquid two-phase turbulent flow model was also developed. The experimental and calculated results indicated that in the multi-stage stepped-wall combustion chamber, the two-phase flow was induced by the step, the radial expansion was enhanced and the axial expansion was retarded, thus the Taylor-Helmholtz instability which generated due to the effect of shear at gas-liquid interface decreased. The chamber geometry and the jet intensity had evident effects on the jet expanding and turbulent mixing processes. The presented work is helpful to better understand the physical processes of combustion gas expanding in bulk-loaded liquid.

Non-axisymmetric arrangement devices in a dual-spin projectile may lead to the asymmetry of the front body, thus affecting the ballistic characteristics. This article presents a 7 Degree-of-Freedom (7-DOF) flight dynamic model which includes a model of additional moment that arises due to asymmetric factors. Two aspects of the ballistic characteristics are studied, namely the first maximum angle of attack and the range of variation. Simulation results indicate that a small asymmetric angle, less than 1 degree, can result in a large change in the angle of attack by up to 6.5 degrees in pitch. But attenuation of the range in the X direction is only 10m. Moreover, when the rotational inertia ratio IA / IF is more than 2, it has little effect on range. The maximum range of attenuation is about 10m at the point where the rotational inertia ratio A F I / I is equal to 1.

To study the key technical issues involved in the field of reconstruction of improvised explosive devices (IEDs), the formation mechanism of natural fragmentation under blast loading was investigated using the finite element code AUTODYN 3D with Mott’s stochastic failure model. The analysis of structural response, critical failure condition, as well as dispersion characteristics including initial angle and velocity of fragments were also carried out. Meanwhile, the effects of charge mass and structure were discussed. The results of the mass and number of fragments, as well as the radius of flight can be used to reconstruct the explosion scene of IEDs.

The study investigated the feasibility of embedding a smear-compensated Over-fly Top Attack (OTA) shaped charge jet, within a penetrating Multiple Effects Warhead (MEW). 3D hydrocode modelling simulations considered a variety of design configurations, under static and dynamic engagements at different over-fly crossing velocities and stand-offs. The need to optimise space and maintain an anti-structures emplacement capability led to the design of a novel side-mounted initiation train. Experimental firings validated the initiation and two design variants, to form smear-compensated shaped charge jets. The 3D pre-trial hydrocode modelling simulations were verified with quantitative and qualitative analysis against ionisation probe, witness plate and multi-plane radiograph experimental results. The work has laid the foundation for follow-on de-risking and development, for progression to MEW anti-armour and anti-structures dynamic trials.

In order to study the forming condition of EFP under radial rotation, the numerical simulation of typical explosively-formed projectile (EFP) charge structure in different positions and rotational speeds are completed by using the finite element simulation software LS-DYNA. Simulation results are verified preliminarily by experiments. Results show that the EFP formed under the radial rotation condition has the lateral deflection speed, and the shape is asymmetrical. When the tip of the EFP has horizontal diversion, the tail of the EFP has vertical diversion, and the infection of radial rotation is most seriously, while the rotation location is in the bottom with middle and the donated pointed rotation location followed. Research results also provide a good example for the study of EFP under the radial rotation condition.