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

• Main Authors: Roman Antoshchenkov, Аnton Nikiforov, Ivan Galych, Victor Tolstolutskyi, Vitalina Antoshchenkova, Sergey Diundik
• Format: Article
• Language: English
• Published: PC Technology Center 2020-04-01
• Series: Eastern-European Journal of Enterprise Technologies
• Subjects: gas dynamics; system pf differential equations; boundary value problem; grid method; tridiagonal matrix algorithm; velocity field
• Online Access: http://journals.uran.ua/eejet/article/view/198501

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