Centrifugal waves

Abstract

When a hollow circular cylinder with its axis horizontal is partially filled with water and rotated rapidly about its axis, an almost rigid-body motion results with an interior free surface. The emotion is analysed assuming small perturbations to a rigid rotation, and a criterion is found for the stability of the motion. This is confirmed experimentally under varying conditions of water depth and angular velocity of the cylinder. The modes of oscillation (centrifugal waves) of the free surface are examined and a frequency equation deduced. Two particular modes are considered in detail, and satisfactory agreement is found with the frequencies observed.

Experimental study of coating flows in a partially-filled horizontally Rotating cylinder

“…These initial axial instabilities do not grow as in the conventional Rayleigh-Taylor instability because of the fluctuating direction of gravity as observed in a rotating frame. Phillips (1960) and Greenspan (1976) have studied these instabilities theoretically.…”

“…Later Karweit and Corrsin (1975) documented similar observations but without quantifying them. Phillips (1960) analyzed the propagation of disturbances on the free surface of the homogeneous fluid film that coats the cylinder at large angular velocities, while Ruschak and Scriven (1976), Orr and Scriven (1978) and Lin (1986) studied the two-dimensional problem numerically and observed recirculation zones in the flow. All these studies took viscosity, surface tension and inertia into account.…”

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

“…There have been a number of studies concerned with the free vibration characteristics (1)- (3) , the responses of the centrifugal wave to lateral (4), (5) and axial excitations (6) , the self-excited vibration of a system consisting of a tank and its elastic supports (7)- (13) , utilization as a dynamic absorber (14) , and the nonlinear sloshing analysis based on shallow water approximation theory (15)- (19) . These studies are classified into those which consider viscosity (5), (7)- (9), (11)- (13), (15), (16), (18) and those which use inviscid theory (1)- (4), (6), (10), (14), (17), (19) , or into those which consider the coupling with the vibrations of elastic supports (7)- (17) and those which analyze the liquid motion generated by a prescribed tank excitation (4)- (6), (18), (19) . One feature of the earlier works is that they focus on the analyses of the phenomena.…”

Stability of the tubular layer of a deformed material in a rotating horizontal cylinder

“…In the case of the nontubular form of fluid motion, experimental and theoretical studies of the position of a free surface are given in [5] for high viscosity and in [6] for a high degree of filling. The problem of determination of high-speed modes of motion of a tubular layer of an ideal liquid was solved by Phillips [7]. The loss of motion stability of the surface of a viscous liquid which fills a considerable part of the hollow of a rotating cylinder was investigated in [8] with allowance for gravity.…”