Basic Study on Classification of Fine Particles in Almost Rigidly Rotating Flow. 2nd Report, Dependence of Ekman Layer and Interior Region on Wall Configuration of Housing and Rotor.

Abstract

We have theoretically considered the condition of a wall configuration necessary for the occurrence of a rigidly rotating region, Hide's prediction for an almost rigidly rotating through-flow between two rigidly rotating concentric spheres, and the relationship between the wall configuration and the flow structure of the interior region and the Ekman layer. The conclusions are as follows. (1) For the occurrence of the rigidly rotating region, it is necessary to make the axial section of the flow field C-shaped. (2) We have supported Hide's prediction theoretically and clarified the details of the flow structure. (3) When either the rotor or the housing walls, or both are disk-shaped, the interior axial velocity component ωI is proportional to the thickness of the Ekman layer δ on the disk and the interior axial vorticity component ωI. On the other hand, when both the rotor and the housing walls have curvatures, ωI depends not only on δ and ωI but also on the interior azimuthal velocity component and the radial change of δ.