Numerical Model for Fluid Spin-Up From Rest in a Partially Filled Cylinder

Abstract

A numerical investigation is presented for the axisymmetric spin-up of fluid in a partially filled cylindrical cavity. It is an extension of earlier analyses to those cases where the liquid free surface intersects one or both endwalls. Previous models of the laminar Ekman layer pumping are modified heuristically for situations where the layer(s) no longer covers the entire wall. Numerical results for a range of Reynolds number, Froude number, and fill ratio have been obtained. They clearly demonstrae that it is the bottom wall Ekman layer which is primarily responsible for spin-up.