and Computational Methods

doi: 10.18698/2309-3684-2023-2-6789

The problems of mathematical modeling of three–dimensional laminar and turbulent motion of a viscous incompressible fluid in multilayer permeable structures – porous mesh materials are considered. Each layer of the material is a woven metal mesh with square cells of micron sizes. Porous mesh materials are widely used in space, chemical, oil and gas, nuclear and other industries, for example, as hydraulic filters. Such materials have a complex internal structure and a variety of possible geometric configurations. Therefore, in the general case, the nature of the functional dependence of the hydraulic resistance that a material sample exerts on the flow of fluid flowing in its pore channels from the Reynolds number is not known. To determine this dependence on the existing material, as well as to create a material with a predetermined hydraulic resistance, computational fluid dynamics tools were used. The domestic engineering analysis system "Logos" and the author's program code developed in Keldysh Research Center were used. The physical parameters of liquid mass transfer in a porous filter material and its hydraulic resistance are determined by the methods of control volumes on an unstructured computational grid for integrating the Navier-Stokes equations and Lattice Boltzmann Method. It is established that the theoretical methods used allow us to estimate from above the functional dependence of the hydraulic resistance of a porous mesh material on the Reynolds number in the range of values from 0.01 to 500. To verify the mathematical model an experimental setup was made with the help of which a cycle of hydraulic spills of sample of porous mesh material was performed. The numerical solutions obtained are consistent with the available analytical dependencies obtained in the works of domestic and foreign scientists and the results of experimental studies.

Городнов А.О., Лаптев И.В., Сидоренко Н.Ю., Иванов М.Ю., Малахов А.С., Реш Г.Ф. Математическое моделирование процессов ламинарной и турбулентной фильтрации жидкой несжимаемой среды в пористых сетчатых материалах. Математическое моделирование и численные методы, 2023, № 2, с. 67–89.