Leakage-flow-induced vibration for a relatively short gap is studied analytically to provide useful information to design structures that include a leakage flow. The relationship between the analysis of a one-dimensional system and that of an annular gap is explained first. Then, the mechanism of flutter-type instability is reproduced from previous study after correcting an error. Finally, the self-excited vibration potential of an engineering system is shown from sample calculations. It is shown that an axial flow becomes dominant in the short-gap approximation, and in this case, the analysis of a one-dimensional flow can be expanded to that of an annular flow. The result that negative damping can occur in the case of a divergent passage owing to the delay induced by fluid inertia was obtained from a previous study. It was suggested analytically that the damping ratio could become negative and its absolute value could become more than 10% in a system that is frequently encountered in a plant, if the natural frequency decreases. The value could be sufficient to generate self-excited vibration.

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