Liquid Sloshing in a Rotating, Laterally Oscillating Cylindrical Container

Abstract

Free surface movement of water in a rotating, laterally oscillating cylindrical container was qualitatively investigated. Time-dependent dynamic pressure was measured instead of free surface displacement. The swirling direction was determined by forcing the frequency and rotating direction of the cylindrical container. The swirling direction was opposite to that of the rotating cylindrical container when the forcing frequency was low, whereas the crest of the free surface swirled in the same direction as that of the rotating cylindrical container when the forcing frequency greatly increased. Unstable swirling occurred when swirling direction changes, but it disappeared as the rotating frequency increased.

Parametric Analysis of Nonlinear Oscillations of the “Rotor-Weakly Conductive Viscous Fluid-Foundation” System under the Action of a Magnetic Field

“…x and 1 y , and the center of gravity of the rotor is denoted by x and y. The coordinates of the center of gravity of the foundation О2 are denoted by 2 x and 2 y , 0 c and 1 c are the coefficients of rigidity of the rotor support (rigidity of the rolling bearing),  and 0  are the coefficients of external friction [4][5][6]. It is assumed that the rotor performs a plane-parallel motion, and there is no rotation of the foundation around the coordinate axes.…”

Parametric Analysis of Nonlinear Oscillations of the “Rotor–Weakly Conductive Viscous Fluid–Foundation” System under the Action of a Magnetic Field

“…The coordinates in the displaced position of the center of the shaft (rotor) O 1 are denoted by x 1 and y 1 , and the center of gravity of the rotor is denoted by x and y. The coordinates of the center of gravity of the foundation O 2 are denoted by x 2 and y 2 , c 0 and c 1 are the coefficients of rigidity of the rotor support (rigidity of the rolling bearing), χ and χ 0 are the coefficients of external friction [4][5][6]. It is assumed that the rotor performs a plane-parallel motion, and there is no rotation of the foundation around the coordinate axes.…”

“…This assumption leads to certain errors in assessing the dynamic and kinematic characteristics of the rotor system [2]. Studies of dynamic systems such as rotary systems show the importance of taking into account the electromagnetic properties of the fluid, the nonlinear properties of the shaft supports, foundation vibration and the need to develop measures to reduce them [3,4]. The intensive development of magnetic and electrohydrodynamics (hereinafter referred to as MEHD) started in the 1960s by the Melcher group in the USA.…”