The Effects of an Annular Fluid on the Vibrations of a Long Rotor, Part 1—Theory

Analysis and tests were made to investigate the hydrodynamic mass and damping effects of a liquid in a thin annulus surrounding a vibrating rotor. The analytical results are described in this report and the test results in Part 2. The analysis determines the fluid forces for the general case of a vibrating rotor. Vibrational amplitudes and the limits of dynamic stability are then determined for a constant-speed rotor excited by unbalance. Fluid flow was assumed incompressible and tangential and to be in the Taylor vortex regime or in the turbulent regime. The Taylor vortex regime is considered a natural convection process resulting from centrifugal force gradients, while the turbulent regime is a forced convection process. As a result, annular flow around a rotor is considered an inherent combination of forced and natural convection. Fluid damping is estimated for each process separately and for the case where the vortex and turbulent process are predicted to occur simultaneously.