On the issue of accuracy of the solution of the direct problem of external ballistics

S. A. Korolev ; A. M. Lipanov ; I. G. Rusyak

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 47 (2017), pp. 63-74

Résumé

The paper is devoted to the possibility to increase the accuracy of the solution of the direct problem of external ballistics by means of solving a more comprehensive system of projectile motion equations and calculating the coefficients of aerodynamic forces and moments based on the hydrodynamic simulation of the flow around the projectile. The mathematical modl of external ballistics presented in this article takes into account rotation of the projectile and oscillation of the latter in relation to the center of mass. Simulation of the flow around the projectile has been performed by solving the Favre averaged Navier–Stokes equations (FANS), using the $k-\varepsilon$ turbulence model including compressibility. The numerical method has been implemented with the application of the ANSYS Fluent computational fluid dynamics module. Calculation of aerodynamic characteristics of the projectiles has been carried out in a wide range of parameters: Mach number, $\mathrm{M} = 0.5$–$5.0$; angle of attack, $\alpha = 0$–$20^\circ$; and rotation speed, $\omega x = 500$–$2000$ rad/s. Based on numerical simulation results, the approximate dependences for coefficients of aerodynamic force and moment have been obtained using the least square method. The effect of the considered factors on the solution of trajectory problem has been investigated for three types of projectiles: the high explosive rotating projectile, the high explosive feathered projectile, and the armor-piercing subcaliber feathered projectile.

Détail

Keywords: external ballistics, trajectory, aerodynamic coefficients, Navier–Stokes equations, turbulence model, numerical method, accuracy of the solution.