Herald of Technological University Herald of Technological University ВЕСТНИК ТЕХНОЛОГИЧЕСКОГО УНИВЕРСИТЕТА 3034-4689 3033-9219 123082 10.55421/3034-4689_2026_29_4_130 DPZOAW 3. Информатика, вычислительная техника и управление 3. Information teory, computer technology and control 3. Информатика, вычислительная техника и управление MATHEMATICAL MODELING AND COMPUTATIONAL EXPERIMENT OF THE PROCESS OF SEPARATION OF TWO-PHASE NON-NEWTONIAN MEDIUM UNDER NON-ISOTHERMAL CONDITIONS IN SEPARATORS WITH CURVED PLATES МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ И ВЫЧИСЛИТЕЛЬНЫЙ ЭКСПЕРИМЕНТ ПРОЦЕССА РАЗДЕЛЕНИЯ ДВУХФАЗНОЙ НЕНЬЮТОНОВСКОЙ СРЕДЫ В НЕИЗОТЕРМИЧЕСКИХ УСЛОВИЯХ В СЕПАРАТОРАХ С КРИВОЛИНЕЙНЫМИ ТАРЕЛКАМИ Ибятов Равиль Ибрагимович Ibyatov Ravil Ибрагимович

доктор технических наук;

doctor of technical sciences;

 Ахмадиев Ф Г Ахмадиев Ф Г akhmadiev@kgasu.ru Галимов Р А Галимов Р А Казанский государственный аграрный университет Казань Россия Kazan State Agrarian University Kazan Russian Federation КГАСУ ru КГАСУ ru КГАСУ ru КГАСУ ru 05 05 2026 05 05 2026 29 4 130 136 14 01 2026 08 04 2026 https://elibrary.ru/item.asp?id=89321181

Рассмотрено математическое моделирование процессов плоских и осесимметрических неизотермических течений и разделения неньютоновских двухфазных сред в сепараторах с криволинейными стенками. Приведен алгоритм численного расчета геометрических характеристик осесимметрического криволинейного канала. Уравнения сохранения массы, энергии и импульсов двухфазной среды, которые записаны в ортогональной системе координат, связанной с областью течения решаются методом поверхностей равных расходов. Эти уравнения упрощены с учетом особенностей течения и геометрии области течения для произвольной системы координат, которые далее уточняются с учетом коэффициентов Ляме для конкретной области. В результате определено поле скоростей для несущей фазы. Далее по уравнениям движения дисперсной фазы вычислены скорости частиц с учетом соответствующих сил межфазного взаимодействия фаз для неньютоновской двухфазной среды. Вычислены траектории движения частиц в межтарелочном пространстве сепаратора, которые позволяют установить гидродинамическую обстановку в зазоре тарелок сепаратора в зависимости от его режимов работы. Для этого построен алгоритм расчета осаждения дисперсных частиц с учетом переменности длины пути осаждения и направления действия центробежной силы относительно стенок криволинейного канала. Численные расчеты проведены с учетом изменения эффективной вязкости среды от температуры, наличия гидродинамического и теплового начальных участков неизотермического течения при различных свойствах среды и частиц. Проведен вычислительный эксперимент по изучению различных режимов неизотермического течения и процесса разделения двухфазной среды, что позволяет определить эффективные режимы работы сепаратора.

Mathematical modeling of processes of flat and axisymmetric non-isothermal flows and separation of non-Newtonian two-phase media in separators with curvilinear walls is considered. Algorithm of numerical calculation of geometric characteristics of axisymmetric curvilinear channel is given. Equations of conservation of mass, energy and pulses of two-phase medium, which are recorded in orthogonal coordinate system related to flow area, are solved by method of surfaces of equal flow rates. These equations are simplified taking into account the peculiarities of the flow and the geometry of the flow region for an arbitrary coordinate system, which are further refined taking into account the Lyame coefficients for a specific region. As a result, the velocity field for the carrier phase is determined. Further, using the equations of motion of the dispersed phase, particle velocities are calculated taking into account the corresponding interphase interaction forces for the non-Newtonian two-phase medium. Trajectories of particles movement in inter-tray space of separator are calculated, which make it possible to establish hydrodynamic situation in gap of separator trays depending on its operation modes. To this end, an algorithm for calculating deposition of dispersed particles is constructed taking into account the variability of the length of the deposition path and the direction of action of centrifugal force relative the walls of the curved channel. Numerical calculations were carried out taking into account the change in the effective viscosity of the medium from temperature, the presence of hydrodynamic and thermal initial sections of non-isothermal flow at various properties of the medium and particles. A computational experiment was conducted to study various modes of non-isothermal flow and the process of separation of the two-phase medium, which makes it possible to determine the effective operating modes of the separator.

 МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ СЕПАРАТОРЫ С КРИВОЛИНЕЙНЫМИ ВСТАВКАМИ НЕИЗОТЕРМИЧЕСКИЕ ДВУХФАЗНЫЕ ТЕЧЕНИЯ МЕТОД ПОВЕРХНОСТЕЙ РАВНЫХ РАСХОДОВ ТРАЕКТОРИЯ ДИСПЕРСНЫХ ЧАСТИЦ НЕНЬЮТОНОВСКИЕ СРЕДЫ ВЫЧИСЛИТЕЛЬНЫЙ ЭКСПЕРИМЕНТ MATHEMATICAL MODELING SEPARATORS WITH CURVILINEAR INSERTS NON-ISOTHERMAL TWO-PHASE FLOWS METHOD OF SURFACES OF EQUAL FLOW RATES TRAJECTORY OF DISPERSED PARTICLES NON-NEWTONIAN MEDIA COMPUTATIONAL EXPERIMENT

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