Computational Method for Almost Rigidly Rotating Flow

Abstract

When the relative flow motion of an incompressible viscous fluid is very small compared with the basic system rotation, the flow field forms an almost rigidly rotating flow. In the present paper, we have constructed a computational method for the almost rigidly rotating flow between the coaxially rotating rotor and housing. The basic equations are axisymmetric continuity and Navier-Stokes equations, which are written with respect to the velocity and the pressure in a cylindrical coordinate system that rotates around the axial coordinate with a constant angular velocity. Coordinate transformation from the physical plane to the computational plane is incorporated to enable simulation of the flow between an arbitrarily shaped rotor and housing. The present computational method is based on the SIMPLE algorithm for colocated grids, and incorporates some devices to stably solve flow fields in strongly rotating systems. Two examples of computational analysis are presented. In the first example of source-sink flow between two rotating disks, the applicability of the present method to the strongly rotating system has been confirmed by a close agreement of the computational velocity profile with the analytical solution of a linear theory. In the second example of the almost rigidly rotating flow between the rotating disk and cylindrical tank, we have numerically considered the flow structure consisting of the Ekman layer, interior region, Stewartson layer and rigidly rotating region.