Stokes Flow Characteristics in a Cylindrical Quadrant Duct With Rotating Outer Wall

Abstract

The Stokes flow in a cylindrical quadrant duct with a rotating wall was analytically and numerically studied. Based on mathematics and fluid dynamics theory, the analytical expressions of three velocity components were achieved by solving a Poisson's equation and a biharmonic equation. Especially, a closed-form analytical expression of axial velocity was obtained, which can greatly improve the calculating accuracy and speed in analyzing Stokes flow. The velocity distributions for different Reynolds numbers were investigated numerically to insure the accuracy of the analytical results at low Reynolds numbers and to confirm the error range of the analytic results at higher Reynolds numbers. The conclusion indicates that there exists an infinite sequence of eddies that decrease exponentially in size towards the sectorial vertex. The width of the first eddy region reached 99.4% of the sector radius; the sum of the width of other eddies is only 0.6% of the sector radius, which cannot be easily displayed graphically, while the sequence of eddies contributes to form the chaotic flow. The maximum deviations of the velocity components between the analytical results and simulated ones are all less than 1% when Re < 0.1, which verifies the validity and accuracy of the analytical expressions in the creeping flow regime. The analytical expressions are not only suitable for creeping flow but also for laminar flow with smaller Reynolds number (Re < 50).