Flutter of long flexible cylinders in axial flow

International audienceWe consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the upstream end only. A linear stability analysis of transverse motion aims at determining the risk of flutter as a function of the governing control parameters such as the flow velocity or the length of the cylinder. Stability is analysed applying a finite-difference scheme in space to the equation of motion expressed in the frequency domain. It is found that, contrary to previous predictions based on simplified theories, flutter may exist for very long cylinders, provided that the free downstream end of the cylinder is well-streamlined. More generally, a limit regime is found where the length of the cylinder does not affect the characteristics of the instability, and the deformation is confined to a finite region close to the downstream end. These results are found complementary to solutions derived for shorter cylinders and are confirmed by linear and nonlinear computations using a Galerkin method. A link is established to similar results on long hanging cantilevered systems with internal or external flow. The limit case of vanishing bending stiffness, where the cylinder is modelled as a string, is analysed and related to previous results. Comparison is also made to existing experimental data, and a simple model for the behaviour of long cylinders is proposed

Blocking in the rotating axial flow in a corotating flexible shell

International audienceBy coupling the Donnell-Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall, the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up. Copyright © 2009 by ASME

Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part I: stability

The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell´s shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin´s method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence

Flutter of rotating shells with a co-rotating axial flow

It is shown that, in certain regions of parameter space, travelling wave solutions in rotating shells containing co-rotating inviscid fluid become indeterminate. This may render the determination of the flutter speed impossible, or the solution nonphysical

An experimental study of dynamics of towed flexible cylinders

In this paper, some experiments are described which were designed to illustrate the dynamical behaviour of towed flexible cylinders and to test the theory. A silicone rubber cylinder was manufactured such that it was almost neutrally buoyant when immersed in water. The cylinder was terminated by plexiglas end-pieces and was held in horizontal water flow by a length of nylon thread (towrope). Video capturing along with image processing techniques were used to measure the transverse displacement of the cylinder in the horizontal plane. For the cylinder with relatively streamlined nose and tail end-pieces, non-flexural (rigid-body), as well as flexural instabilities developed as the flow velocity was increased; shortening the towrope was not very effective for stabilizing the system, but a sufficiently blunt tail end-piece had a very significant stabilizing effect. The experimental observations are generally in qualitative agreement with the available nonlinear theory. Quantitative comparison of various quantities, e.g. the instability thresholds, between experiment and theory, based on the estimated values of some of the theoretical nondimensional parameters, is also fairly good