M.P. Païdoussis

Dynamic Stability of Pipes Conveying Fluid

This paper deals with the dynamics and stability of flexible pipes containing flowing fluid, where the flow velocity is either entirely constant, or with a small harmonic component superposed. An extensive historical review of the subject is given. In the case of constant flow velocity, the dynamics of the system is examined in a general way and it is shown that conservative systems are subject not only to buckling (divergence) at sufficiently high flow velocities, but also to oscillatory instabilities (flutter) at higher flow velocities. Also presented are some new results for cases of systems subjected to internal dissipative forces. In the case of harmonically varying flow velocity, the equation, of motion derived here exposes an error in a previous derivation. Stability, maps are presented for parametric instabilities, computed by Bolotins method, for pipes with pined or clamped ends, as well as for cantilevered pipes. It is found that the extent of the instability regions increases with flow velocity for clamped-clamped and pinned-pinned pipes, while a more complex behaviour obtaines in the case of cantilevered pipes. In all cases, dissipation reduces the extent of, or entirely eliminates, parametric instability zones.

Flow-pattern identification for two staggered circular cylinders in cross-flow

The flow around two circular cylinders of equal diameter, arranged in a staggered configuration, was investigated using flow visualization and particle image velocimetry for centre-to-centre pitch ratio P / D = 1[ratio ]0 to 5.0 and angle of incidence. α = 0° to 90°. Experiments were conducted within the low subcritical Reynolds number regime, from Re = 850 to 1900. Nine flow patterns were identified, and processes of shear layer reattachment, induced separation, vortex pairing and synchronization, and vortex impingement, were observed. New insight was gained into previously published Strouhal number data, by considering the flow patterns involved. The study revealed that vortex shedding frequencies are more properly associated with individual shear layers than with individual cylinders; more specifically, the two shear layers from the downstream cylinder often shed vortices at different frequencies.

Dynamics of flexible slender cylinders in axial flow Part 1. Theory

A general theory is presented to account for the small, free, lateral motions of a flexible, slender, cylindrical body immersed in fluid flowing parallel to the position of rest of its axis. The cylinder is either clamped or pinned at both ends, or clamped at the upstream end and free at the other; it lies in a horizontal plane wherein all motion is considered to be confined. It is shown that for sufficiently large flow velocities the cylinder may be subject to buckling and oscillatory instabilities in its first and higher flexural modes, respectively. It is shown that for cylinders with both ends supported the oscillatory instabilities are specifically caused by lateral frictional forces, and that in the absence of hydrodynamic-drag effects only buckling is possible. The same applies for cylinders supported at the upstream end and with a very long, gradually tapering free end. The critical conditions of stability, expressed in dimensionless form, are evaluated extensively for clamped-free and pinned-pinned cylinders, illustrating the effect of the various system parameters on stability.

Dynamics of cylindrical structures subjected to axial flow

A general theory is presented for the dynamics of slender cylindrical beams immersed in purely axial, uniform and steady flow. The cylinders may be either isolated or be part of a cluster of identical cylinders. Gravity and pressurization effects are taken into account. It is shown that small flow velocities damp free motions, but that at sufficiently high flow velocities hydroelastic instabilities are possible. Typically, pinned-pinned (simply supported) cylinders are subject to buckling in their first mode, and then at higher flow velocities in their second mode; at slightly higher flow velocities, coupled-mode flutter is shown to occur. Close spacing in a cluster severely destabilizes the system. Cantilevered cylinders, on the other hand, may be subject to buckling in their first mode and to flutter in their higher modes. Finally, the case of cylinders in axial flow subjected to an arbitrary force field is discussed, and a method is developed by which the response may be obtained.

Flutter of thin cylindrical shells conveying fluid

Abstract When the flow velocity in a finite, thin, circular cylindrical shell, either clamped at both ends or cantilevered, exceeds a certain critical value, the system is observed to lose stability by flutter in its second circumferential mode. This paper describes the phenomenon, and presents a theory for its analysis which is based on Flugges equations for the description of shell motion and a classical potential-flow theory for the coupled hydrodynamic forces. Complex frequency calculations reveal the existence of flutter in the case of cantilevered shells; for clamped-clamped shells the theory predicts buckling instability followed by coupled-mode flutter. Theory and experiment are in adequately close agreement.

Dynamics of Tubular Cantilevers Conveying Fluid

In Part 1 a general theory is presented to account for the small, free, lateral motions of a vertical, uniform, tubular cantilever conveying fluid, with the free end being either below the clamped one (‘hanging’ cantilever) or above it (‘standing’ cantilever). Gravity forces are not considered to be negligible.It is shown that, when the velocity of the fluid exceeds a certain value, the cantilever in all cases becomes subject to oscillatory instability. In the case of hanging cantilevers buckling instability does not occur. Standing cantilevers, on the other hand, may buckle under their own weight; it is shown that in some cases flow (within a certain range of flow velocities) may render stable a system which would buckle in the absence of flow.Extensive complex frequency calculations were conducted to illuminate the dynamical behaviour of the system with increasing flow. The conditions of stability have also been extensively calculated and stability maps constructed. It is shown that dissipative forces m...

An improved mathematical model for the stability of cylinder rows subject to cross-flow

Abstract Linearized, quasi-static, fluid force coefficient data obtained from wind tunnel tests are used in an analysis of the fluidelastic stability of a double row of flexible circular cylinders subject to a cross-flow. Although the analysis is quasi-static, frequency dependent terms are obtained in the aerodynamic stiffness and damping matrices; the origin of these terms is twofold: firstly, because of the time lag between flow leaving an upstream row and arriving at a downstream row, which becomes important at low values of the non-dimensional flow velocity U fd ; secondly, because of retardation of the flow approaching the cylinder, which is particularly important when small displacements of the cylinder result in large changes in the fluid force coefficients. This analysis is used to investigate the effects of a number of parameters on the critical flow velocity and the theoretical results are compared with those available in the literature. In general, agreement between theory and experiment is reasonably good, indicating the validity of this analysis.

Fluidelastic vibration of cylinder arrays in axial and cross flow--state of the art

Abstract In this paper a critical assessment is presented of the state of the art for flow induced vibrations of cylinder arrays in cross and axial flow. The paper begins with a short historical review for cross flows in which the milestone contributions which have advanced our understanding of the flow induced vibration phenomena involved and/or our predictive ability are highlighted. The main conclusions from the study are as follows. In the case of axial-flow-induced vibration, the absence of separated flow regions has contributed towards the development of analytical predictive tools. Despite this, the designers ability to predict vibration amplitude—in the absence of any special supporting information—is not much better than within one order of magnitude. The designer may predict the onset of fluidelastic instabilities, which generally occur at very high flow velocities, with greater confidence. In contrast, in the case of cross-flow-induced vibration, the complexity of the flow has encouraged more heuristic approaches to be adopted. In an attempt to unify and clarify the sometimes contradictory researchers claims facing the designer, the state of the art in this case is discussed with the aid of a new classification of the flow induced vibration phenomena involved. It is concluded that, although the physical understanding of cross-flow-induced vibration phenomena is not good, useful design guidelines do exist. These, despite being based on insufficiently tested precepts, are capable of predicting vibration characteristics—in the absence of special supporting data—to within a factor of 2–10.

Dynamics and stability of coaxial cylindrical shells containing flowing fluid

Abstract This paper presents an analytical model for the dynamics and stability of coaxial cylindrical shells conveying incompressible or compressible fluid in the inner shell and in the annulus between the two shells. Shell motions are described by Flugges thin-shell equations and the fluid forces are determined by means of linearized potential flow theory and formulated with the aid of generalized force Fourier transform techniques. Calculations have been conducted with two flexible shells or with one replaced by an identical rigid cylinder, with inner or annular flow, or both, mainly with incompressible flows but also with compressible ones; with steel or rubber shells conveying either water or air. It is found that, for the systems studied, annular flow destabilizes the system at lower flow velocities than flow in the inner shell and that the stability threshold is lower when both shells are flexible. The critical flow velocities are in the range of interest for industrial systems. The effect of compressibility is found to be small.

The aerodynamic forces acting on groups of two and three circular cylinders when subject to a cross-flow

Abstract The fluid drag and lift forces in the in-flow and cross-flow directions, respectively, have been measured on one cylinder in a group of either two or three cylinders, when the group was subject to a uniform cross-flow. This was done for a variety of geometrical patterns, and the effect of static cylinder displacements on the fluid forces investigated. The cross-flow spacing between cylinders was varied from 0.75 to 2.0 cylinder diameters and the in-flow spacing from 1.5 to 5.0 cylinder diameters. In general it was found that the effect of cylinder displacement on the fluid forces for one cylinder in a group of three is very similar to that obtained with one cylinder in a group of two. This led to an attempt to use a superposition principle to determine the fluid forces in the former arrangement from a knowledge of the fluid forces in the latter arrangement. Remarkable success was obtained using this superposition for the above range of cylinder spacings.