Laminarization effects on the dynamics of a disk levitated by incompressible fluid flow

A nonlinear ordinary differential equation of motion for a disk parallel to a flat plat and levitated by incompressible turbulent fluid flow supplied from a central orifice was developed. The transient flow velocity and pressure field for the turbulent flow are found by integrating the time averaged Navier-Stokes equation with power law velocity and shear stress correlations. The results for the turbulent film are coupled with the study of inertia effects on the dynamics of a disk levitated by incompressible laminar flow to determine the results for a laminarizing flow. The transient pressure field is integrated to use in Newton's second law to determine the O.D.E. for the height of the disk as a function of time when the disk is perturbed from its equilibrium state by a forcing function. The theoretical magnitudes, frequencies, and damping coefficients of oscillation are shown to be within 8% of those measured. The numerical solution differs only slightly from the linearized solution: the latter provides relatively accurate closed form expressions for the frequencies and damping coefficients in terms of the geometry, load, mass flow rate, and the fluid properties.