Solution of the system of gas-dynamic equations for the processes of interaction of vibrators with the air

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.198501

Keywords:

gas dynamics, system pf differential equations, boundary value problem, grid method, tridiagonal matrix algorithm, velocity field

Abstract

The modern practice of using vibratory machines involving small seeds of low weight faces such an undesirable phenomenon as the effect exerted on the kinematics of vibrational movement of particles of fractions of the seed mixture by the aerodynamic forces and momenta. The periodic movement of air relative to the working planes of a vibratory machine arises due to fluctuations in the packets of these planes, which form flat aerodynamic channels. Consequently, the issues of studying the processes of interaction between the working bodies of vibratory machines and the air environment, aimed to justify their structural improvements, appear relevant. Existing mathematical models, which assess the parameters of air movement relative to the working planes of vibratory machines, produce only a generalized pattern and are flat. This paper proposes a statement, as well as an estimated finite difference scheme, of solving a three-dimensional boundary value problem on calculating the field of velocities and pressures in the region of air, located between two parallel synchronously oscillating planes. The problem employs a system of differential equations to describe the flow of the perfect gas. The finite difference scheme has been solved by a sweep method.

Using the sweep method to solve these kinds of problems makes it possible to ensure the convergence and stability of estimation schemes, regardless of the step and other parameters of the grid applied. A variant of the calculation has been given, which demonstrated the feasibility of the proposed method for the assigned boundary conditions and parameters of the vibrational mode of machine operation. It has been established that in the working space enclosed between two oscillating planes there are both vertical (transverse) and horizontal (longitudinal) components of air velocity, which change over time

Author Biographies

Roman Antoshchenkov, Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Associate Professor, Head of the Department

Department of Mechatronics and Machine Parts

Аnton Nikiforov, Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002

Senior Lecturer

Department of Mechatronics and Machine Parts

Ivan Galych, Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002

Senior Lecturer

Department of Mechatronics and Machine Parts

Victor Tolstolutskyi, State-Owned Enterprise Kharkiv Machine Building Design Bureau named A. A. Morozov Plekhanivska str., 126, Kharkiv, Ukraine, 61001

PhD, Head of Department

Department of Automated Control Systems and Engineering Calculations

Vitalina Antoshchenkova, Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of Economics and Marketing

Sergey Diundik, National Academy of National Guard of Ukraine Zakhysnykiv Ukrainy sq., 3, Kharkiv, Ukraine, 61001

PhD, Associate Professor

Department of Armored Vehicles

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Published

2020-04-30

How to Cite

Antoshchenkov, R., Nikiforov А., Galych, I., Tolstolutskyi, V., Antoshchenkova, V., & Diundik, S. (2020). Solution of the system of gas-dynamic equations for the processes of interaction of vibrators with the air. Eastern-European Journal of Enterprise Technologies, 2(7 (104), 67–73. https://doi.org/10.15587/1729-4061.2020.198501

Issue

Vol. 2 No. 7 (104) (2020): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2020 Roman Antoshchenkov, Аnton Nikiforov, Ivan Galych, Victor Tolstolutskyi, Vitalina Antoshchenkova, Sergey Diundik

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