Flow between rotating disks. Part 1. Basic flow

Abstract

Laser-Doppler velocity measurements were obtained in water between finite rotating disks, with and without throughflow, in four cases: ω 1 = ω 2 = 0; ω 2 /ω 1 = −1; ω 2 /ω 1 = 0; ω 2 /ω 1 = 1. The equilibrium flows are unique, and at mid-radius they show a high degree of independence from boundary conditions in r . With one disk rotating and the other stationary, this mid-radius ‘limiting flow’ is recognized as the Batchelor profile of infinite-disk theory. Other profiles, predicted by this theory to coexist with the Batchelor profile, were neither observed experimentally nor were they calculated numerically by the finite-disk solutions, obtained here via a Galerkin, B -spline formulation. Agreement on velocity between numerical results and experimental data is good at large values of the ratio R Q / Re , where R Q = Q /2πν s is the throughflow Reynolds number and R e = R 2 2 ω/ν is the rotational Reynolds number.