A study on leakage-flow-induced vibrations. Part 1: Fluid-dynamic forces and moments acting on the walls of a narrow tapered passage

Abstract

Leakage-flow-induced vibrations (instabilities) have been observed in many fields of engineering, but there remain many points to be clarified as to the mechanism of the instability. In the present paper, the viscous fluid-dynamic forces and the moments acting on the walls of a one-dimensional, narrow, tapered passage when one wall is vibrating in coupled translational and rotational modes are analyzed, and fluid-dynamic mass, damping and stiffness matrices are determined, by which the mechanism of instability generated from the flow through a narrow passage is examined. In the case of a single-degree-of-freedom translational or rotational system, only diagonal components of the fluid-dynamic matrices are estimated, and it is found that both negative fluid-dynamic damping caused by the phase delay due to the fluid inertia and negative fluid-dynamic stiffness can occur. In the case of a single-degree-of-freedom translational system, if the passage is divergent, both negative fluid-dynamic damping and fluid-dynamic stiffness can occur. In the case of a single-degree-of-freedom rotational system, the area increment ratio of the passage, at which negative fluid-dynamic damping and fluid-dynamic stiffness can occur, changes remarkably with the location of the pivot. In the case of a two-degree-of-freedom translational and rotational system, it is difficult to conclude directly from the fluid-dynamic matrices whether the fluid-dynamic forces stabilize the system or not. Therefore, in Part 2 of this study the stability of a plate which can vibrate in a coupled mode of translational and rotational motion in a one-dimensional, narrow, tapered passage will be examined.