The Impact of the Dimension of a Mathematical Model of Internal Ballistics on Design Parameters of a Shot for Grain Gunpowder Charges

Abstract

The problem of the impact of the mathematical model dimension on the calculated intraballistic characteristics of a shot for the charges made of granulated powder is considered. Mathematical models of the shot are studied using the spatial (axisymmetric), one-dimensional, and zero-dimensional (thermodynamic) formulations. The thermodynamic model takes into account the distribution of the pressure and velocity of a gas-powder mixture behind the shot for a channel of variable cross-section. Comparison of simulation results is carried out in a wide range of loading parameters. It is shown that there is a range of the loading parameters for a thermodynamic approach to give satisfactory approximation to the parameters obtained using the gas-dynamic approach, which describes the flow of a heterogeneous reacting mixture with a separate consideration of phases and intergranular interactions between them. Notably that in the entire range of the charging parameters studied in this work, the one-dimensional and twodimensional gas-dynamic models only slightly differ from each other. Therefore, in the main pyrodynamic period, the actuation of the charge, made of granulated powder, can be simulated using a one-dimensional gas-dynamic model or a zero-dimensional thermodynamic model with allowance for spatial distribution of the pressure and velocity of the gas-powder mixture.

Numerical Simulation of the Nonstationary Process of the Shot Based on the Navier – Stokes Equations

“…The calculations showed that the upper estimate of the decrease in the muzzle velocity of the projectile due to viscous friction is less than 0.5 %, the increase in the maximum pressure on the bottom of the channel is 1.5 % and the decrease in the maximum pressure on the bottom of the projectile is 1.1 %. The estimates made in [27] showed that one-dimensional and two-dimensional gas-dynamic models of internal ballistics based on the Euler equations differ in muzzle velocity by 1.0 %, in maximum pressure on the channel bottom by 3.0%, and in maximum pressure on the bottom of the projectile by 2.4 %. The level of differences between the studied parameters due to viscosity is less than these values.…”

“…We assume that the particle material is incompressible and the gas parameters inside and outside the powder elements in each section are the same. The system of equations for the internal ballistics of an artillery shot, which describes the flow of a heterogeneous reacting mixture, taking into account intergranular interaction in an axisymmetric formulation based on the Euler equations, is described in the work of the authors [27]. In addition to this model, instead of the Euler equations for the carrier phase, we will consider In Fig.…”

“…The dimensionless equations describing the motion of a viscous heat-conducting gas in the case of an axisymmetric swirling flow have the following form [27]:…”

“…The equations for the solid phase with velocities V p = (u p , v p , w p ) T in a cylindrical coordinate system (x, r, ϕ) are presented in the form [27]…”