A study on leakage-flow-induced vibrations. 2nd report. Calculations of fluid-dynamic forces acting on the walls of a one-dimensional, narrow passage by the transfer matrix method.

Abstract

The transfer matrix method is applied to the calculations of fluid-dynamic forces acting on the walls of a one-dimensional, narrow passage when one of them is vibrating harmonically with a small amplitude. First, the fluid-dynamic coefficients in the case of a tapered passage are calculated to check the accuracy of this method. The results show a good agreement with those by theoretical solutions obtained in the first report. Second, fluid-dynamic coefficients in the case of the passage with a step are also calculated. It is found that if the cross sectional area of the upstream passage is smaller than the downstream one, both negative fluid-dynamic stiffness and negative fluid-dynamic damping can occur, and that when the effective pressure loss factor of the passage is nearly equal to unity, the area ratio of the downstream passage to the upstream one, where negative fluid-dynamic damping occurs, decreases with increasing upstream passage length.