№75-12

Numerical simulation of an external ballistic problem using analytical approach and atmosphere flow visualization by finite element method

O. Aziukovskyi¹, V. Hryshchak¹, D. Hryshchak²,K. Ziborov¹, S. Fedoriachenko¹, D. Harkavenko¹, V. Korol^1,3

¹ Dnipro University of Technology, Dnipro, Ukraine

² Culver Aviation, Kiev, Ukraine

³ Metinvest Engineering, Dnipro, Ukraine

Coll.res.pap.nat.min.univ. 2023, 75:119-126

https://doi.org/10.33271/crpnmu/75.119

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ABSTRACT

Purpose. Analysis of the dynamic characteristics of the cargo in the presence of the speed of its carrier, taking into account the influence of the external environment and the determination of factors that affect the operational characteristics and parameters for the dynamic system control.

Methodology. An approximate analytical approach to solving the nonlinear problem of external ballistics of a system with time-dependent parameters, which is implemented using the asymptotic perturbation method, and a numerical algorithm for modeling a dynamic process using a 3D software complex and the finite element method, which allows to visualize the nature of the flow around the object under wind load conditions.

Findings. An analytical approach to solving the nonlinear problem of external ballistics of a system with time-varying parameters is proposed, as well as a numerical model, solution and visualization of a dynamic process that can be applied in problems of mathematical physics and engineering calculations.

Originality. The use of an approximate analytical approach to solving the nonlinear problem of external ballistics, which includes a system of time-varying parameters, is a significant innovative step. For the first time, a three-dimensional distribution of the free fall parameters under atmospheric conditions was obtained depending on the time of free fall under the condition of an initial velocity different from zero. Obtaining the characteristics of the distribution, taking into account the aerodynamic quality of the object, made it possible to adapt the methods of analytical mechanics and differential equations with variable coefficients to the solution of the applied problem. The obtained characteristic three-dimensional surface allows to perform a study of the aerodynamic quality of the object under study using numerical methods and to visualize dynamic processes in three-dimensional space in order to obtain a qualitative picture of the perturbation of the object by the air flow. This integrated approach to the study of ballistic characteristics of cargo forms the scientific principle to perform engineering calculations to solve the problem of controlling dynamic systems.

Practical value. An approximate analytical approach and a calculation model of the dynamic process of a mechatronic unmanned system make it possible to increase its efficiency in the presence of an initial speed and ensure the accuracy of the application of ballistic cargo delivery systems in real operating conditions.

Keywords: external ballistics, nonlinear system of differential equations with variable coefficients, 3-D and FEA-modeling, aerodynamic pressure, wind load, visualization of atmospheric flow.

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