Flutter Instability of a Fluid-Conveying, Fluid-Immersed Pipe Affixed to a Rigid Body

Abstract

Studies of fluid-conveying pipes typically consider systems with an anchor at one or more boundaries, such as pinning or clamping. These types of conditions are satisfactory in the study of many common engineering applications, such as pipelines or heat exhangers. However, a small, fish-like submersible propelled by a fluttering fluid-conveying pipe requires boundary conditions which account for the relative freedom at both ends of the pipe. A submersible of this type achieves its propulsion by a combination of jet action and thrust produced by the fluttering pipe. A simple model of this type of vehicle was devised, consisting of a rigid body affixed to a fluid-conveying pipe. The applicable linearized boundary conditions were derived, and this rigid-free case can be shown to be a generalization of both the free-free and cantilever conditions. The equation of motion of this rigid-free system approaches that of the cantilever and free-free systems for appropriately large and small rigid body masses, respectively. “Intermediate” values of (non-dimensional) rigid body mass, in the range corresponding to a proposed physical realization of the system, were investigated. Consistent with prior work, it was found that, with the addition of external flow generated by the forward motion of the submersible through still water, the onset of flutter instability can be achieved for lower values of conveyed (internal) velocity than would be required in the absence of external flow. Furthermore, the onset of flutter for certain rigid body masses can be achieved at a lower internal velocity than the cantilever case at the same external speed. This point is critical; since it is the internal velocity which must be “paid for”, by powering the system’s prime mover, reduction of the required velocity to achieve flutter has the potential to improve the submersible’s efficiency.