A flexible rod in annular leakage flow: Influence of turbulence and equilibrium offset, and analysis of instability mechanisms

Abstract

The linear stability of a flexible, cylindrical rod subjected to annular leakage flow is studied. The mathematical models developed by Li, Kaneko, and Hayama in 2002 and Fujita and Shintani in 2001 are bridged and extended, to account for a flexible rod with equilibrium offset (eccentricity) in laminar or turbulent leakage flow. Stability characteristics are analyzed numerically for a variety of configurations. It is found that simply supported rods may become unstable at a certain critical flow speed by either divergence or flutter, depending on dimensions and fluid/solid properties. It is furthermore found that the critical flow speed is quite insensitive to use of a laminar friction model at high Reynolds numbers in cases of divergence, but sensitive to it in cases of flutter. These findings are verified analytically though analysis of an energy equation. This equation shows that (i) divergence instability is independent of fluid friction; (ii) flutter instability is caused solely by fluid friction. It also suggests a possible explanation to the question of why a ‘wrong’ fluid friction assumption gives a too large critical flow speed in cases of flutter instability at a high Reynolds number.