Flow Past A Rotating Porous Circular Cylinder At Small Reynolds Number

The flow past a porous cylinder at small Reynolds number is common in nature and industry,such as the flow around a rotating filter core of a biochemical filter,the flow around a pulverized coal particle in a furnace and the flow around a sediment mixture in a river.The regular pattern of the isothermal flow past a rotating homogeneous porous cylinder at small Reynolds number is studied in this thesis.The homogeneous porous cylinder is considered as isotropic porous media so that the permeability is fixed.Ingeniously,Centrifugal force term and Coriolis force term are considered.The whole flow field is divided into two regions as porous region and exterior region.Darcy model is used in porous region,With the consideration of the centrifugal force term and Coriolis force term caused by rotation.The exterior region is divided into the inner Stokes region and the outer Oseen region.Stokes model and Oseen model are adopted in these two regions.Uniform flow boundary condition is adopted at infinity and Beavers-Joseph slip condition is applied at the interface of the clear fluid and the porous cylinder.Control equations for the corresponding stream functions are established.With the coupling of the Oseen solution and Stokes solution by the method of matched asymptotic expansion(MMAE),theoretical solutions are analyzed and deducted.The solutions are contrasted and verificated with the results of other scholars in three extreme cases as the cylinder is non-rotating and solid,the cylinder is non-rotating porous cylinder and the cylinder is solid but rotating.It is found that the results in this paper are in consistency with others,proving that the results are correct.The effects of Reynolds number,dimensionless rotating speed and permeability on resistance and lift are also analyzed.The analysis shows that when the Reynolds number is very small,the resistance increases with the increase of Reynolds number,increases with the increase of rotation speed and decreases with the increase of permeability,and the lift increases with the increase of rotation speed and decreases with the increase of permeability,and hardly changes with the change of Reynolds number when the permeability is high.The flow past a double layered rotating porous cylinder at small Reynolds number is furtherly studied.And the solutions are solved,the regular pattern of the variation of the drag force and the lift force with diameter ratio is analyzed and obtained.The results show that when the ratio of inner and outer diameter permeability is less than 1,the flow resistance and lift decrease with the increase of inner and outer diameter ratio;when the ratio of inner and outer diameter permeability is equal to 1,the flow resistance and lift do not change with the change of inner and outer diameter ratio;when the ratio of inner and outer diameter permeability is greater than 1,the flow resistance and lift increase with the increase of inner and outer diameter ratio.