Unstable inner cylinder whirl of concentric double rotating cylinder system

Abstract

This research investigated unstable inner cylinder whirl in a double rotating cylinder system in which the axis of the inner cylinder is supported elastically in the radial direction and the axis of the outer cylinder is fixed. It was assumed that the two cylinders stay in parallel so that the gap between the cylinders is axially uniform. This paper presents a theory to analyze the complex eigenvalues of the coupled system of the gap flow and the motion of the inner cylinder. The gap flow model takes into account the inertial force and turbulence effect, and derives an equation for the unsteady pressure. The motion of the inner cylinder has two degrees of freedom in the plane normal to the axis, and is coupled with the unsteady pressure of the gap. This theory was compared with experiments carried out by changing the combination of rotational speeds of the inner and outer cylinders, including counter-rotation where two cylinders rotate in opposite directions. The theoretical and experimental results were generally consistent in terms of the whirl frequency, damping ratio, and the boundary of the unstable whirl at the combinations of rotational speeds. In particular, both the theory and experiments indicated that the instability of the whirl increases as the sum of the rotational speeds of the two cylinders rises.

Keywords

• gap flow
• unstable whirl
• rotating cylinder
• counter-rotation
• turbulence
• complex eigenvalue analysis
• unsteady flow