Ballistic Equations Research Articles

Study on Evolution Characteristics of Gas–Liquid Interaction in a New Gas-Curtain Launcher

For the new idea of a gas-curtain launcher with a grooved tube, the gas-curtain flow field and interior ballistic characteristics are mainly investigated in this paper. The coupling of the gas–liquid interaction model and interior ballistic equations is realized by solving the gas flow equation. Analyses have focused on the morphological evolution of the gas-curtain, pressure distribution, turbulence intensity evolution, and interior ballistic performance. The results show that multiple groove jets first expand independently of each other, and their shape changes from rectangular to triangular. The groove jets then come into contact with each other and form a gas-curtain. Meanwhile, the gas-curtain expansion results in complex changes in the pressure and turbulence intensity of the flow field in the tube. The parameters distribution in the flow field gradually have a simple tendency as the gas-curtain increases and the projectile moves. The moment the projectile starts moving, the gas volume fraction reaches 83%, indicating that the gas-curtain has made remarkable achievements in drag reduction. Significantly, under the calculated conditions in this paper, an initial velocity of 360.58 m/s was obtained at a maximum chamber pressure of 86.34 MPa.

Баллистическая оценка полетов серии «Аполлон» к Луне

Materials from the US sources on the Apollo program were considered, and the presented data were evaluated from the point of view of external ballistics equations, flights of spacecraft to the Moon and their return to the Earth. The evaluation made it possible to determine inconsistency of the data (mass characteristics) in different documents relating to one object in the Apollo 11 mission. Inconsistencies were also found in the ballistic schemes for launching into the departure trajectory to the Moon, mooning, undocking and docking in the lunar orbit, braking maneuver to enter the lunar orbit, acceleration maneuver for returning to the Earth and braking maneuver for landing on the Earth’s surface. Analysis of the lunar missions’ documents formed the basis to ask questions that were not previously raised in such a formulation, and no answers were given to them. In particular, significant discrepancies in the initial data were found in the official documents on the US lunar missions. Reference orbit altitude before the second activation of the Saturn-5 3rd stage, the first space velocity at the Florida peninsula inclination and the second space velocity seem to be strange. Significant doubts are caused by acceleration schedule, projection of the flight path to the Earth and remoteness of the first stage impact area from the launch pad. In terms of the F-1 engines of the Saturn-5 launch vehicle first stage, thrust indicators of one engine and the total thrust of the first stage are not consistent. A conclusion is made that at present it is almost impossible to put into practice some of the maneuvers demonstrated in the US documents.

Internal Ballistic Modeling and Simulation Analysis of High-low Pressure Low-overload Launch of Unmanned Aircraft

The low-overload launch is an important research direction in weapon launch. In this paper, a new low-overload launch method is designed by using the piston-type high-low pressure launch principle combined with the secondary launch principle. Based on the classical internal ballistic equations and multi-body dynamics equations, the internal ballistic model of this low overload launch system is established. A joint simulation model based on MATLAB and RecurDyn is constructed to simulate the internal ballistic state during the launch process. The sensitivity of each parameter change of the high-low pressure system to the launch overload is also studied. The results show that the maximum low-pressure chamber pressure of the low overload launcher in this paper is reduced by 62% compared to the conventional internal ballistic pressure, the saturation of the pressure curve is also improved, and the muzzle velocity is accelerated; the maximum overload is reduced by 65%, which can meet the requirements of muzzle initial velocity and low overload when launching unmanned aircraft.

Research on the launch safety test of explosive charge under simulated launch environment

Aiming at the launch safety problems of breech blow caused by the current harsh artillery launch environment, the mechanism of breech blow caused by explosive charges and the current research status of explosive charge launch safety tests are summarized. In order to consider the influence of friction on the ignition of the explosive due to the relative movement between the explosive and the shell caused by the high-speed rotation of the projectile during the launch process, the simulation of the explosive charge launch environment was carried out based on the projectile launch dynamics equations and the internal ballistic equations, and then a new device for the launch safety test of explosive charges is established to comprehensively simulate the longitudinal overload and high-speed rotation launch environment of explosive charges in the bore. The test results show that the test device can simulate the maximum rotating speed of the projectile in the bore and the stress process at the bottom of the explosive charge during the launch process, which truly reproduces the launch environment of explosive charge. The research in this paper provides a new means for the launch safety test and evaluation of explosive charges.

Investigation of thermal performance in dual‐fuel units

AbstractNumerical studies were carried out to investigate the thermal performance of the muzzle flow with strong shock discontinuities and gas–gas heat transfer mechanism in the base bleed unit (BBU) of an aerodynamic vehicle under the combined effects of muzzle flow and depressurization process. The process was modeled using the Navier–Stokes equations with chemical kinetics and interior ballistic equations. The results show that the muzzle phenomena with large temperature gradients and different wave structures appear after the supersonic vehicle enters into the free‐flight stage. The BBU also experiences a strong depressurization process with the release of high‐temperature propellant gas at 2200 K. However, the igniter combustion gas at a higher temperature of 3050 K in the BBU develops downstream and upstream repeatedly under the combined effects of the base wave and depressurization process, which makes the energy conversion process in the unit more complicated. With the projectile leaving the control of the muzzle flow, the BBU is full of the igniter combustion gas and the energy in the unit is uniformly distributed gradually. The high‐temperature area, at approximately 2750 K, propagates downstream along the axial and radial directions simultaneously until it finally dominates the entire unit. The maximum temperature of the combustion gas acting on the propellant surface is always 2740 K and the maximum heat flux remains approximately 1250 W/cm2 at later periods.

Dynamics analysis and experimental validation of the aluminum honeycomb buffer in the tether-net launcher

Aluminum honeycomb is newly introduced in the tether-net launcher device to attenuate the large recoil force and impact generated on the platform. The stress–strain of aluminum honeycomb is first obtained through the quasi-static compression experiment to study the mechanical properties. The compression simulation model is then established using the crushable foam plasticity model. By comparing the simulation and experiment results, the error of plateau stage force is 0.33%, which validates the accuracy of the simulation model. After that, the internal ballistic responses of the launcher are gained by the equivalent classical interior ballistic equations. The dynamic launch model is built through the integration of the above models. It is verified by the dynamic launch experiment, with the average recoil error being 5.9%. Finally, the recoil performance of the launcher with or without aluminum honeycomb buffer is studied. The results show that aluminum honeycomb can reduce the average launch recoil force by 17.23%, with little effect on launch velocity, demonstrating good energy absorption ability.

Monte Carlo-Based Analysis and Experimental Validation of the Interception-Damage Probability of the New Active Interception Net

This study aims to prove the intercepting effectiveness of the new active interception net. According to the timing sequence of intercepting the incoming missile body by the new interception net, the external ballistic equations of the incoming missile body and the interception net are established, respectively, and then the mathematical probability model conforming to the physical characteristics of the interception process is constructed. The process of intercepting the incoming missile by intercepting net is simulated 1000 times by Monte Carlo method on the basis of considering the random parameters such as route shortcut, dive angle, and incoming velocity of the incoming missile. The simulation results under different intercept conditions, including the optimal intercept angle, the power of the payload warhead, and the probability of intercept damage, are analyzed. Through analysis, it is found that with the cooperation of multiple interception nets, the probability of interception and damage to the incoming target can be significantly improved. When the velocity of the incoming missile body is up to 900 m/s, the probability of damage is over 65%. The research content theoretically verifies the effectiveness of ultra-short-range interception of the new active interception net. In order to further verify the reliability of interception, a new interception net was carried out to verify the interception of the incoming missile body. Through the analysis of the test results, it is found that the new interception net can intercept the incoming missile body effectively after launch, which well verifies the Monte Carlo simulation results and further proves the intercepting effectiveness of the new interception net.

Discrete and continuum fundamental solutions describing heat conduction in a 1D harmonic crystal: Discrete-to-continuum limit and slow-and-fast motions decoupling

In the recent paper by Sokolov et al. (Int. J. of Heat and Mass Transfer 176 (2021) 121442) ballistic heat propagation in a 1D harmonic crystal is considered and the properties of the exact discrete solution and the continuum solution of the ballistic heat equation are numerically compared. The aim of this note is to demonstrate that the continuum fundamental solution can be formally obtained as the slow time-varying component of the large-time asymptotics for the exact discrete solution on a moving point of observation.

ЕКСПЕРИМЕНТАЛЬНІ ДОСЛІДЖЕННЯ МЕТОДУ І ЗАСОБІВ ДІАГНОСТУВАННЯ ТЕХНІЧНОГО СТАНУ КАНАЛІВ СТВОЛІВ ТА БОЄПРИПАСІВ НА ОСНОВІ ІДЕНТИФІКАЦІЇ ХАРАКТЕРИСТИК БАЛІСТИЧНИХ ЕЛЕМЕНТІВ ПОСТРІЛУ

An experimental study of the adequacy of advanced mathematical models of the shot, which are based on solving the equations of internal ballistics, is proposed. The structure and composition of the experimental setup are substantiated, the choice of software and hardware for registration of measuring information in the course of research is made. The experimental setup is based on the ballistic measuring system "Prototypa" in the modification of STZA 12A, and also includes samples of weapons that have acquired defects with known parameters, in particular, in the form of swelling or abrasion of the barrel. A method of conducting experimental research to verify the adequacy of an improved mathematical model of the shot is proposed. The method involves mathematical modeling of the firing process taking into account the presence of a defect with known parameters by numerically solving the equations of internal ballistics and further implementation of experimental shots from a sample of weapons with a defect in the barrel channel and obtaining data on real ballistic elements. An example of the course of experimental research for a separate combination of the type of weapon and the existing defect of the barrel. According to the results of the experiment, data for each of the weapon samples were obtained in the form of curves of powder gas gases and muzzle velocities of methane elements for a series of shots. The results of experimental researches are stated and their analysis is carried out. A comparison of the actual course of shots from a weapon containing a defect in the barrel channel with the corresponding models of shots obtained analytically. Conclusions on the adequacy of the improved mathematical model of the shot and the practical applicability of the method of diagnosing the technical condition of barrels and ammunition to barrel systems based on the identification of the characteristics of ballistic elements of the shot in the implementation of technical weapons control.

Spreading of disturbances in realistic models of transmission grids in dependence on topology, inertia and heterogeneity

The energy transition towards more renewable energy resources (RER) profoundly affects the frequency dynamics and stability of electrical power networks. Here, we investigate systematically the effect of reduced grid inertia, due to an increase in the magnitude of RER, its heterogeneous distribution and the grid topology on the propagation of disturbances in realistic power grid models. These studies are conducted with the DigSILENT PowerFactory software. By changing the power generation at one central bus in each grid at a specific time, we record the resulting frequency transients at all buses. Plotting the time of arrival (ToA) of the disturbance at each bus versus the distance from the disturbance, we analyse its propagation throughout the grid. While the ToAs are found to be distributed, we confirm a tendency that the ToA increases with geodesic distance linearly. Thereby, we can measure an average velocity of propagation by fitting the data with a ballistic equation. This velocity is found to decay with increasing inertia. Characterising each grid by its meshedness coefficient, we find that the distribution of the ToAs depends in more meshed grids less strongly on the grid inertia. In order to take into account the inhomogeneous distribution of inertia, we introduce an effective distance r_{mathrm{eff}}, which is weighted with a factor which strongly depends on local inertia. We find that this effective distance is more strongly correlated with the ToAs, for all grids. This is confirmed quantitatively by obtaining a larger Pearson correlation coefficient between ToA and r_{mathrm{eff}} than with r. Remarkably, a ballistic equation for the ToA with a velocity, as derived from the swing equation, provides a strict lower bound for all effective distances r_{mathrm{eff}} in all power grids. thereby yielding a reliable estimate for the smallest time a disturbance needs to propagate that distance as function of system parameters, in particular inertia. We thereby conclude that in the analysis of contingencies of power grids it may be advisable that system designers and operators use the effective distance r_{mathrm{eff}}, taking into account inhomogeneous distribution of inertia as introduced in Eq. (12), to locate a disturbance. Moreover, our results provide evidence for the importance of the network topology as quantified by the meshedness coefficient beta.

Influence of Joule effect on thermal response of nano FinFET transistors

Integrated circuits based on FinFET nanodevices suffer from thermal processes related to heat dissipation caused by phonon transport bottlenecks. In this work, we report a numerical study of quasi-ballistic transport behavior in 20 nm FinFET transistors. Using a mathematical formulation, numerically implemented by the finite element method , we successfully validate the transfer characteristics and temporal temperature evolution compared with experimental and numerical works. We found that the proposed model, given by a calibrated charge drift-diffusion model coupled with the enhanced ballistic diffusive heat transport equation, predicts the experimental I–V characteristics and the transient temperature evolution well. The error given by this comparison is less than 10% in the I DS -V GS and T-t characteristics, respectively. We show that the proposed equations provide an improved approximation compared to the dual-phase lag and the Cattaneo-Vernotte models. From an engineering viewpoint, we found that the self-heating is concentrated at the end of the channel region at the drain side; this phenomenon was confirmed from literature by experimental results. • We report a numerical study of the quasi-ballistic transport behavior in 20 nm FinFET devices. • The model is able to predict the I(V) characteristics and heating phenomenon compared to experimental and numerical data. • The self-heating is concentrated at the end of the channel region at the drain side of the devices.

Heat conduction in 1D harmonic crystal: Discrete and continuum approaches

In this work the energy transfer in a one-dimensional harmonic crystal is investigated. In particular, a comparison between the discrete approach presented by Klein, Prigogine, and Hemmer with the continuum approach presented by Krivtsov is made. In the pioneering work of Klein and Prigogine the transfer of thermal energy is considered. In particular, an expression is obtained, which allows to calculate the thermal energy of each particle as a function of time. Later, Hemmer derived and used similar expressions to solve several particular problems in context of heat conduction. In the work of Krivtsov—in contrast to the discrete approach—a partial differential continuum equation is derived from the lattice dynamics of a 1D harmonic crystal. This so-called ballistic heat equation describes the propagation of heat at a finite speed in a continuous one-dimensional medium. The current work compares analyses based on the discrete equation of Klein, Prigogine, and Hemmer with those from the continuum-PDE-based one by Krivtsov. There is an important difference between the approaches. The continuum approach is derived from the dynamics of the crystal lattice, in which only kinetic degrees of freedom were excited and then thermal equilibration occurred. In contrast to that we consider in the discrete approach explicitly given equal kinetic and potential initial energies. Several exactly solvable initial problems are studied by using both methods. The problem of point perturbation shows a discrepancy in the results obtained in the framework of the continuous and discrete approaches. It is caused by the fact that the smoothness conditions of the initial perturbation is violated for the continuum approach. For other problems it is shown that at large spatial scales, where the one-dimensional crystal can be considered as a continuous medium, the discrete and the continuum relations converge. The asymptotic behavior of the difference between two aforementioned approaches is analyzed.

Study on Engraving Resistance Characteristic of Band Based on Different Structure Parameters of Rifling

The gun barrel working in complex environments is prone to damage, including the wear and ablation of the bore in the gun barrel. These changes cause changes in the rifling structure, which in turn affects the combustion law of gunpowder gas, which affects the pressure in the bore and changes the internal ballistics of the gun performance. This article takes a large caliber howitzer as the research object, considers the frictional force change during high-speed and high-pressure sliding, and also considers the energy conservation criterion during the engraving process. The initial ballistic equations are established during the initial movement period and Coupled solution with band engraving process. Considering the large deformation, high strain rate, temperature softening effect and cumulative damage effect, an explicit dynamic algorithm is used to compare the differences of the elastic band engraving process under different rifling structure parameters. The influence of different rifling structure parameters on the force state of the belt is analyzed. The influence of the main structural parameters of the engraving system on the belt engraving process is obtained. It provides a useful reference for the integrated analysis of the ammunition and the gun and the optimization of the barrel structure.

Quantitative analysis for affecting factors of firing dispersion of tank

To improve the firing dispersion of the tank, the influences of random factors on firing dispersion are analyzed quantitatively. Based on the six-degree-of-freedom rigid-body ballistic equation, considering the influences of processing and assembly errors, initial disturbances and the wind on flight, using the Sobol’ global sensitivity analysis method, the weights of affecting factor are obtained. The analysis results show that, under the current manufacturing and measuring conditions, the initial disturbance of projectile is the premier factor that takes effect on the firing dispersion of the straight shooting weapon (such as a tank) with small elevation angle.

Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity.

There has been much interest in semiconductor superlattices because of their low thermal conductivities. This makes them especially suitable for applications in a variety of devices for the thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometric 1D multilayer systems by considering the separation of ballistic and diffusive heat fluxes, which are both described by Guyer-Krumhansl constitutive equations. The dispersion relations, as derived from the ballistic and diffusive heat transport equations, are used to derive an effective heat conductivity of the superlattice and to explain the minimum of the effective thermal conductivity.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ КОЛЕБАНИЙ СТВОЛА НА УГОЛ ВЫЛЕТА СНАРЯДА ПРИ ВЫСТРЕЛЕ

The problem of longitudinal and transverse vibrations of an artillery gun barrel during firing is considered. Unsteady stress-strain equations for the gun barrel are solved together with equations of internal ballistics. Ballistic parameters and dynamics of the projectile motion inside a gun bore are determined using a thermodynamic approach. Formulation of the vibration problem accounts for the initial gravitational deflection of the barrel, mass forces, varying distribution of the propellant gas pressure, and the effect of moving projectile mass on gun barrel vibrations. To solve the equations for longitudinal and transverse gun barrel vibrations, difference schemes are obtained by integro-interpolation method. It has been revealed that the solution to the problem in a one-dimensional formulation is almost as accurate as the results obtained in a three-dimensional formulation. Moreover, the former case is significantly less time consuming. The decay time of the barrel longitudinal vibrations after shot is shown to be much less than the time between shots in the burst. Deviations of the transverse barrel vibrations from the initial firing angle are more significant, and the vibration decay time is longer than the time between shots, which affects the accuracy of single shots and the dispersion of shells in the burst mode. Thus, when firing from a 30 mm gun at the range of 1 km, lateral vibrations lead to a change in the height of target hit point by 8.7 m.

Interaction between laser-driven high-velocity metal granule and gas

We apply laser-driven launching technique to the interaction between high-velocity metal granule and gas to investigate high speed gas-solid two-phase flow transport. Optimization of target design and adjustment of laser parameters were used to control the laser-driven process. Diagnostic tools with high resolving power of space and time as well as higt accuracy were set up to capture the high-velocity granule. The unsteady flow field of the granule was simulated by solving the the 3-D Reynolds averaged Navier-Stokes equations and six degree of freedom ballistic equation. With the implicit Gauss-Seidel scheme, the code was advanced in time. The results indicated that the laser-driven launching technique was effective and the shadow photographs of high-velocity granule were taken successfully. The aerodynamic drag of high-velocity granule was computed with numerical simulation.

Modified Ballistic–Diffusive Equations for Obtaining Phonon Mean Free Path Spectrum from Ballistic Thermal Resistance: II. Derivation of Integral Equation Based on Ballistic Thermal Resistance

ABSTRACTRebuilding phonon mean free path (MFP) spectra from experimental data is integral to phonon MFP spectroscopy. However, being based on effective thermal conductivity, the current integral equation for this precludes the use of certain heat sources of convenient shapes, such as a cylindrical nanoline. Herein, to enable using diverse specimens exhibiting a ballistic effect, we develop a ballistic thermal resistance-based integral equation, utilizing the ease and accuracy of the modified ballistic–diffusive equations demonstrated in the companion paper. The availability of more diverse shapes of specimens will enhance further development and widen use of phonon MFP spectroscopy.

Numerical Investigations on the Water Entry of Cylindrical Projectiles with Different Initial Conditions

In this paper, coupled with Reynolds-averaged Navier–Stokes equations and ballistic equations, the numerical simulations of high-speed water entry of projectiles under different conditions have been conducted. The water-gas flow was modeled by the mixture multiphase model. The numerical results indicated that the simulations agree well with analytical solutions by two cavity models, which validates the model applied. Then the effects of variations of project length, entry angle and velocity on the entry process of projectiles were further investigated. The results show that, for small water entry angles, the cavity wall interacts with the projectile, affects the trajectory of the projectile, and even ricochets for projectiles with small length (5D). On the other hand, the projectile vibrates during the whole process of water entry; the vibration amplitude decreases with the increase of projectile length and entry angle; however, it is the contrary for the vibration period. Furthermore, after the initial impact period, the influence of these parameters on the drag coefficient is not obvious.

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation.

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.