Study on Vibration Reduction of a Rotating Cylindrical Tank with Elastic Supports

Abstract

A method for reducing the vibration of a rotating cylindrical tank with elastic supports is studied by considering the case where a stationary circumferential flow relative to the tank is created by inserting rotating ring plates whose rotational speed differs from the tank's rotational speed. It is shown that the vibration can be reduced when the flow's relative velocity is negative. The relative velocity appears not only in the inertial and Coriolis terms of the Navier-Stokes equations but also in the dynamic boundary condition on the liquid surface. It is found that the vibration reduction can be caused by the relative velocity that appears in the dynamic boundary condition on the liquid surface. A semianalytical method is presented for the viscous rotating sloshing problem, for which it is customary to resort to numerical methods. The method is verified by comparing with earlier results available for the case with no stationary circumferential flow relative to the tank. This method transforms the viscous rotating sloshing problem into only several ten ordinary differential equations, thereby reducing computational efforts significantly.

Vibration analysis of a cylindrical rotor partially filled with liquid considering nonlinearity of liquid motion

“…The range of radial basis function number l shown in Tables 1 and 2 was determined as follows. The linear analysis (Utsumi, 2013) confirmed that l was at most 5 for obtaining the stable region agreeing with that given by Saito and Someya (1979) experimentally verified (Saito et al, 1982). For the nonlinear terms, we note that the liquid domain is variable due to the liquid surface displacement  and that the Taylor expansions of il ra R   ( i  1,2,3) (e.g.…”

Vibration analysis of a cylindrical rotor containing liquid with stationary circumferential flow

“…An analysis of a rotor containing liquid with circumferential flow was tried in a previous paper (Utsumi, 2013), where the relative circumferential velocity of the flow was assumed to be equal to that of the ring plates proportional to the radial coordinate r. The present paper presents an improved analysis for conservative estimate of the vibration reduction effect by considering the boundary condition that the relative circumferential flow velocity vanishes at the cylindrical wall (maximum r). Using the semi-analytical method, we examine the influences of the circumferential flow velocity terms appearing in various governing equations.…”