Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)4341210.22363/2658-4670-2024-32-3-319-324DLVHXGPhysics and AstronomyФизикаResearch ArticleLiquid radial flows with a vortex through porous mediaРадиальные потоки жидкости с вихрем через пористые средыhttps://orcid.org/0000-0002-7744-972516454766600S-4813-2018RybakovYuri P.РыбаковЮ. П.

Professor, Doctor of Sciences in Physics and Mathematics, Professor at the Institute of Physical Research and Technologies

rybakov-yup@rudn.ruhttps://orcid.org/0000-0001-6894-625557200754585AAC-8298-2020SemenovaNatalia V.СемёноваН. В.

Junior member of teaching at the Institute of Physical Research and Technologies

semenova-nv@rudn.ruRUDN UniversityРоссийский университет дружбы народов15122024323VOL 32, NO3 (2024)ТОМ 32, №3 (2024)31932425032025Copyright ©; 2024, Rybakov Y.P., Semenova N.V.Copyright ©; 2024, Рыбаков Ю.П., Семёнова Н.В.2024Rybakov Y.P., Semenova N.V.Рыбаков Ю.П., Семёнова Н.В.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/43412

The filtration process is studied for a popular class of filters with radial cartridges that proved their high effectiveness in purification of water. The mass balance equation for radial flows in porous media is obtained by using the lattice approximation method, the transverse diffusion process being taken into account. The Euler dynamical equations are modified by including the Darcy force proportional to the velocity of the filtration flow. The system of equations is written for the stationary axially symmetric radial flow and solved by the perturbation method, if the vertical velocity is supposed to be small.

Изучается процесс фильтрации для популярного класса фильтров с радиальными картриджами, доказавших свою высокую эффективность при очистке воды. Уравнение баланса массы для радиальных потоков в пористых средах получено с использованием метода решёточного приближения с учётом процесса поперечной диффузии. Динамические уравнения Эйлера модифицированы путём включения силы Дарси, пропорциональной скорости фильтрационного потока. Система уравнений записана для стационарного осесимметричного радиального потока и решена методом возмущений, если вертикальная скорость предполагается малой.

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