The Effect of Inertia on Flow Between Misaligned Rotating Disks

The effect of inertia on flow between a rotating and a stationary disk is studied for the case when the stationary disk is tilted with respect to the rotation axis. Based on the three-dimensional Navier-Stokes equations, an analytical solution is developed, with three perturbation parameters: aspect ratio, Reynolds number and tilt parameter. The noninertial hydrodynamic effect is to produce a moment which acts on the rotor and is perpendicular to both rotation and tilt axes. The effect of the inertia terms is to contribute another moment which acts on the rotor along the tilt axis. This analytical prediction explains qualitatively experimental and numerical results obtained at finite Reynolds numbers.