Inertia Effects on the Dynamics of a Disk Levitated by Incompressible Laminar Fluid Flow

Abstract

This paper develops a nonlinear ordinary differential equation (O.D.E.) of motion for a disk parallel to a flat plate and levitated by incompressible laminar flow of fluid supplied from a central orifice. The fluid’s inertia, reflected in high mass flow rates, is accounted for. The transient flow velocity and pressure field are found by iterative integration of the Navier-Stokes equation to determine the O.D.E. for the time-dependent height of the disk (or fluid film thickness). The film thickness is found by not only numerically integrating the O.D.E., but also by linearizing the equation to obtain a closed-form solution. The results of this combined squeeze-film, source-flow case compare favorably with experimental data presented which span cases from negligible inertia (viscous dominance) to cases of inertia dominance. Fortunately, the closed-form solution differs only slightly from the numerical solution; this provides relatively accurate expressions for the frequencies and damping coefficients in terms of the geometry, load (or weight of disk), mass flow rate, and the fluid properties.