CALCULATING THE VELOCITY OF A VISCOUS FLUID THAT PARTIALLY FILLS A CYLINDRICAL CAVITY
Yu. V. Pivovarov
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
Keywords: конформное отображение, несжимаемая жидкость, уравнения Навье - Стокса, условия проскальзывания, вихрь, функция тока, conformal mapping, incompressible fluid, Navier-Stokes equation, slip condition, vortex, current function
Abstract
Plane-parallel steady motion of a viscous incompressible fluid that partially fills a cylindrical rotating cavity is under consideration. The region occupied by the fluid is simply connected, with two points of a sliding three-phase contact, and the edge angles at which the fluid approaches the walls are specified at these points. The free boundary of the fluid is curvilinear. There is a slip condition at the interface between the fluid and solid wall, which corresponds to proportionality of tangential stresses of a velocity difference of the solid and fluid particles. The flow region is conformally mapped onto a rectangular. The vortex and current function with a given slip coefficient and different rotation velocities of the cylinder are calculated.
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