A study on leakage-flow-induced vibrations. 1st Report. Fluid-dynamic forces acting on the walls of a one-dimensional, narrow, tapered passage.

Abstract

An analytical study is presented on leakage-flow-induced vibrations in the case of a one-dimensional, narrow, tapered passage. The fluid-dynamic forces acting on the walls of the passage when one of them is vibrating harmonically with a small amplitude are obtained as the sum of two components : one proportional to the wall velocity and the other proportional to the wall displacement, from which fluid-dynamic coefficients are determined as a function of frequency. It is found that if the passage is divergent, both negative fluid-dynamic stiffness and negative fluid-dynamic damping can occur, and that negative fluid-dynamic stiffness can occur in the case of a high exit loss factor even if the passage is parallel or convergent.