Investigation of the filtration coefficient of elastic-porous medium at plane deformation

E. A. Mikishanina

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 3, pp. 396-407

Résumé

The value of the filtration coefficient is determined empirically due to its physical and chemical properties of the medium and the filtered liquid. However, the experimental data obtained can vary significantly depending on the applied loads. The paper proposes a new hypothesis about the linear dependence of the medium filtration coefficient on the first invariant of the stress tensor arising in the region due to the hydraulic head at the boundary. Within the framework of this hypothesis, the change of the region filtration coefficient under plane deformation is investigated. The appearance of hydraulic head on the border leads to the appearance of elastic perturbations in the environment. Since the velocity of the latter is much higher than the velocity of the liquid filtration, the change in the stress state of the region will lead to a change in the pore space, and, consequently, to a change in the filtration coefficient. Thus, the initial problem is reduced to the solution of the classical problem of elasticity theory, namely, to the solution of the boundary value problem for the Erie function, and then to the definition of the filtration coefficient as the solution of the boundary value problem for the harmonic equation. A numerical algorithm for solving harmonic and biharmonic equations based on the boundary element method is constructed, which ultimately reduces the original problem to a system of linear algebraic equations. As shown by the numerical results of studies, the change in the filtration coefficient of some materials under operating loads reaches 20 percent at some points of the region. These results are especially relevant when using pipes, hoses, water hoses made of various polymeric materials, fiberglass, as well as in the operation of hydraulic engineering and treatment facilities. The change in the filtering capacity of the medium at low elastic deformations makes it possible at the appropriate pressures to filter even in those environments that are usually considered impervious to the liquid. The paper presents the results of numerical experiments to study the filtration coefficient of polyurethane (flexible irrigation hose) and butyl rubber. Graphs of the required mechanical parameters are constructed. Calculations were performed in the Maple software package.

Détail

Keywords: filter coefficient, plane strain, stresses, harmonic equation, biharmonic equation, numerical algorithm.
Mots-clés : filtration