On preform impregnation process simulation while transfer molding of composite products

Metallurgy and Material Science

Powder metallurgy and composite materials


DOI: 10.34759/vst-2020-1-233-245

Аuthors

Bodunov N. M.*, Khaliulin V. I.**, Sidorov I. N.***, Kostin V. A.****

Kazan National Research Technical University named after A.N. Tupolev, 10, Karl Marks str., Kazan, 420111, Russia

*e-mail: bodunov_nm@mail.ru
**e-mail: pla.kai@mail.ru
***e-mail: insidorov1955@mail.ru
****e-mail: VAKostin@kai.ru

Abstract

This article envisages an analytical approach to transfer molding simulation as applied to production of articles from composite materials. Navier-Stokes equations, modified by Brinkman, with corresponding initial and boundary conditions are used to describe the flow of incompressible liquid through porous media for two-dimensional unsteady and steady flows. The authors suggest a numerical-analytical method based on the sought solution approximation by linear combination of polynomial basic functions for the flow velocity components. This method novelty consists in selection of generalized variables and finding concrete basic functions, which in some cases allow obtaining analytical solutions, identically satisfying the initial equations, and reducing non-linear boundary problems in other cases. The unknown coefficients contained in the found solutions are determined from the corresponding initial and boundary conditions by the collocation method, or weighted residuals method while solving concrete applied problem.

Partial analytical solutions of Navier-Stokes equations, describing a slow flat flow of a viscous liquid, which basis is formed by the polynomial solution of the linear bi-harmonic equation, were found without accounting for the inertial forces. The external parameters included into solutions are being determined from boundary conditions by the collocation method, or weighted residuals method, while internal parameters, expanding the class of solutions, are selected from mathematical and physical reasons, as well as comparing theory with experimental data and other exact solutions. These solutions can be employed for describing slow flow of a viscous liquid through the porous medium. Approbation of the obtained partial analytical solutions was performed on the examples of solving two test problems, i.e. the problem of a plate flow-around, and Couette problem on liquid flow movement located between two planes under the impact of the pressure difference, whereas one plane is immovable, and the other moves at constant speed. Computational results demonstrated acceptable accuracy of the obtained solutions.

Keywords:

Navier-Stokes-Brinkman equations, porous medium, plate flow-around, polynomial basis functions

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