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Analytical model of gromeka — beltrami flow МОДЕЛЬ ТЕЧЕНИЯ ГРОМЕКИ — БЕЛЬТРАМИ
The authors provide a summarized overview of the analytical model of the Gromeka — Beltrami helical flow of nonviscous incompressible fluid in a cylindrical channel. The model is developed on the basis of the method of decomposition for Fourier — Bessel equations. The authors discuss the analytical distribution function for axial, azimuthal and radial fluid velocities and the flow function depending on the length and radius of the cylindrical channel. The analysis of the proposed solution demonstrates that the properties of the flows inside the channel depend on the value of the scalar coefficient. When the value of the coefficient is within the zero-order Bessel function of the first kind, the velocity distribution is characterized by significant reverse currents in the axial zone of the channel. The findings comply with the results of laboratory and field tests. The authors have identified that this type of flow has components of the wave. Similar flows have high angular velocity. The authors assume that these conditions correspond to the emergence of toroidal Taylor — Gertler vortices. Therefore, the analytical model of the Gromeka — Beltrami flow complies with the phenomena observed in the course of experiments and in the natural environment.
Рассмотрена аналитическая модель винтового течения невязкой несжимаемой жидкости в цилиндрическом канале. Модель основана на решении уравнений Громеки методом разложения Фурье — Бесселя. Получены аналитические функции распределения по длине и радиусу цилиндрического канала аксиальных, азимутальных и радиальных скоростей движения жидкости и функции тока. Выполнен анализ полученного решения.
Analytical model of gromeka — beltrami flow МОДЕЛЬ ТЕЧЕНИЯ ГРОМЕКИ — БЕЛЬТРАМИ
The authors provide a summarized overview of the analytical model of the Gromeka — Beltrami helical flow of nonviscous incompressible fluid in a cylindrical channel. The model is developed on the basis of the method of decomposition for Fourier — Bessel equations. The authors discuss the analytical distribution function for axial, azimuthal and radial fluid velocities and the flow function depending on the length and radius of the cylindrical channel. The analysis of the proposed solution demonstrates that the properties of the flows inside the channel depend on the value of the scalar coefficient. When the value of the coefficient is within the zero-order Bessel function of the first kind, the velocity distribution is characterized by significant reverse currents in the axial zone of the channel. The findings comply with the results of laboratory and field tests. The authors have identified that this type of flow has components of the wave. Similar flows have high angular velocity. The authors assume that these conditions correspond to the emergence of toroidal Taylor — Gertler vortices. Therefore, the analytical model of the Gromeka — Beltrami flow complies with the phenomena observed in the course of experiments and in the natural environment.
Рассмотрена аналитическая модель винтового течения невязкой несжимаемой жидкости в цилиндрическом канале. Модель основана на решении уравнений Громеки методом разложения Фурье — Бесселя. Получены аналитические функции распределения по длине и радиусу цилиндрического канала аксиальных, азимутальных и радиальных скоростей движения жидкости и функции тока. Выполнен анализ полученного решения.
Analytical model of gromeka — beltrami flow МОДЕЛЬ ТЕЧЕНИЯ ГРОМЕКИ — БЕЛЬТРАМИ
Zuykov Andrey L’vovich (author) / Orekhov Genrikh Vasil’evich (author) / Volshanik Valeriy Valentinovich (author)
2013
Article (Journal)
Electronic Resource
Unknown
helical flow , ideal fluid , Gromeka equation , Fourier — Bessel decomposition , axial , azimuthal and radial velocity , vorticity , circulation , винтовое течение , идеальная жидкость , уравнения Громеки , разложение Фурье — Бесселя , аксиальные , азимутальные и радиальные скорости , вихрь скорости , циркуляция , функция тока , Architecture , NA1-9428 , Construction industry , HD9715-9717.5
Metadata by DOAJ is licensed under CC BY-SA 1.0
СОВЕРШЕНСТВОВАНИЕ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ЛАМИНАРНОГО КОНТРВИХРЕВОГО ТЕЧЕНИЯ
| DOAJ | 2018
РАСЧЕТ СПИРАЛЬНЫХ КАМЕР ГИДРОТУРБИН ПО УРАВНЕНИЯМ ТЕЧЕНИЯ, ВЫЗЫВАЕМОГО ВИХРЕВЫМ СТОКОМ - ОКРУЖНОСТЬЮ
| DOAJ | 2015