Experiments on vertical slender flexible cylinders clamped at both ends and subjected to axial flow

2007 ◽  
Vol 366 (1868) ◽  
pp. 1275-1296 ◽  
Author(s):  
Y Modarres-Sadeghi ◽  
M.P Païdoussis ◽  
C Semler ◽  
E Grinevich
Keyword(s):  
Axial Flow ◽  
Quantitative Agreement ◽  
Dynamical Behaviour ◽  
High Flow ◽  
The Third ◽  
Theoretical Predictions ◽  
Series Of Experiments ◽  
Linear And Nonlinear ◽  
Theory And Experiment ◽  
Flow Velocities

Three series of experiments were conducted on vertical clamped–clamped cylinders in order to observe experimentally the dynamical behaviour of the system, and the results are compared with theoretical predictions. In the first series of experiments, the downstream end of the clamped–clamped cylinder was free to slide axially, while in the second, the downstream end was fixed; the influence of externally applied axial compression was also studied in this series of experiments. The third series of experiments was similar to the second, except that a considerably more slender, hollow cylinder was used. In these experiments, the cylinder lost stability by divergence at a sufficiently high flow velocity and the amplitude of buckling increased thereafter. At higher flow velocities, the cylinder lost stability by flutter (attainable only in the third series of experiments), confirming experimentally the existence of a post-divergence oscillatory instability, which was previously predicted by both linear and nonlinear theory. Good quantitative agreement is obtained between theory and experiment for the amplitude of buckling, and for the critical flow velocities.

Dynamics of Tubular Cantilevers Conveying Fluid

1970 ◽  
Vol 12 (2) ◽  
pp. 85-103 ◽  
Author(s):  
M. P. Paidoussis
Keyword(s):  
Quantitative Agreement ◽  
Dynamical Behaviour ◽  
Oscillatory Instability ◽  
Complex Frequency ◽  
Buckling Instability ◽  
Gravity Forces ◽  
Stability Maps ◽  
Conditions Of Stability ◽  
Conveying Fluid ◽  
Flow Velocities

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 may have either a stabilizing or a destabilizing effect on the system, partly depending on the magnitude of these forces themselves. The experiments described in Part 2 were designed to illustrate the dynamical behaviour of vertical tubular cantilevers conveying fluid. The experiments were conducted with rubber tubes conveying either water or air. The tubes were either hanging down or standing upright. It was observed that for sufficiently high flow velocities both hanging and standing cantilevers become subject to oscillatory instability. It was also observed that standing cantilevers which would buckle under their own weight in the absence of flow, in some cases are rendered stable by flow within a certain range of flow velocities. Qualitative and quantitative agreement between theory and experiment was satisfactorily good.

Paper 15: Vibration of Flexible Cylinders with Supported Ends, Induced by Axial Flow

1965 ◽  
Vol 180 (10) ◽  
pp. 268-279
Author(s):  
M. P. Paidoussis
Keyword(s):  
Cross Flow ◽  
Axial Flow ◽  
High Flow ◽  
Flexible Cylinder ◽  
Empirical Expression ◽  
Flexible Material ◽  
Amplitude Vibration ◽  
Critical Velocities ◽  
Flow Components ◽  
Flow Velocities

A flexible cylinder with pinned ends in axial flow of sufficiently high flow velocity is subject to buckling and oscillatory hydroelastic instabilities. These instabilities are discussed briefly and it is shown that they occur at such high flow velocities that they are not likely to be encountered in practice, unless the cylinder is made of very flexible material such as rubber. The cylinder is subjected to small amplitude vibration, however, even at flow velocities very much smaller than the critical velocities for hydroelastic instabilities. The mechanism of energy transfer from the fluid to the cylinder is examined and it is postulated that this vibration is excited by cross-flow components of flow and other departures from steady, uniform and perfectly axial flow. Experimental evidence supporting this postulate is presented. An empirical expression is given for the amplitude of vibration based on reported experimental observations covering a variety of geometries, fluids and cylinder materials.

Buoyancy-Induced Flow in Open Rotating Cavities

2007 ◽  
Vol 129 (4) ◽  
pp. 893-900 ◽  
Author(s):  
J. Michael Owen ◽  
Hans Abrahamsson ◽  
Klas Lindblad
Keyword(s):  
Tangential Velocity ◽  
Axial Flow ◽  
Quantitative Agreement ◽  
Turbine Engines ◽  
The Third ◽  
Commercial Code ◽  
Heated Disk ◽  
Induced Flow ◽  
Cooling Air ◽  
Buoyancy Induced Flow

Buoyancy-induced flow can occur in the cavity between the co-rotating compressor disks in gas-turbine engines, where the Rayleigh numbers can be in excess of 1012. In most cases the cavity is open at the center, and an axial throughflow of cooling air can interact with the buoyancy-induced flow between the disks. Such flows can be modeled, computationally and experimentally, by a simple rotating cavity with an axial flow of air. This paper describes work conducted as part of ICAS-GT, a major European research project. Experimental measurements of velocity, temperature, and heat transfer were obtained on a purpose-built experimental rig, and these results have been reported in an earlier paper. In addition, 3D unsteady CFD computations were carried out using a commercial code (Fluent) and a RNG k‐ε turbulence model. The computed velocity vectors and contours of temperature reveal a flow structure in which, as seen by previous experimenters, “radial arms” transport cold air from the center to the periphery of the cavity, and regions of cyclonic and anticyclonic circulation are formed on either side of each arm. The computed radial distribution of the tangential velocity agrees reasonably well with the measurements in two of the three cases considered here. In the third case, the computations significantly overpredict the measurements; the reason for this is not understood. The computed and measured values of Nu for the heated disk show qualitatively similar radial distributions, with high values near the center and the periphery. In two of the cases, the quantitative agreement is reasonably good; in the third case, the computations significantly underpredict the measured values.

Experiments on Fluidelastic Instability of Cylinder Clusters in Axial Flow

1982 ◽  
Vol 104 (3) ◽  
pp. 342-347 ◽  
Author(s):  
M. P. Paidoussis ◽  
LI. R. Curling ◽  
J. O. Gagnon
Keyword(s):  
Natural Frequencies ◽  
Axial Flow ◽  
High Flow ◽  
Strain Gauges ◽  
Critical Flow ◽  
Water Tunnel ◽  
Random Vibrations ◽  
General Behavior ◽  
Good Agreement ◽  
Flow Velocities

This paper presents a summary of the general behavior of cylinder clusters in axial flow and especially of the fluidelastic instabilities which occur at high flow velocities. Experiments were conducted in a water tunnel with three- and four-cylinder clusters, and the behavior was monitored either optically or by instrumenting one of the cylinders with strain gauges. With increasing flow, the amplitude of small random vibrations of the cylinders increased; simultaneously, the natural frequencies, as a group, decreased, which is in good agreement with theory. The cylinders eventually lost stability by buckling (divergence), and at higher flow by flutter. Agreement between theoretical and experimental critical flow velocities for these fluidelastic instabilities has been found to be good.

Dynamics of Slender Tapered Beams With Internal or External Axial Flow—Part 2: Experiments

1979 ◽  
Vol 46 (1) ◽  
pp. 52-57 ◽  
Author(s):  
M. J. Hannoyer ◽  
M. P. Paidoussis
Keyword(s):  
Axial Flow ◽  
Internal Flow ◽  
Quantitative Agreement ◽  
External Flow ◽  
Critical Conditions ◽  
Experimental Program ◽  
Water Tunnel ◽  
Elastic Instabilities ◽  
Theoretical Predictions ◽  
Flow Part

This paper describes the experimental program which was conducted in parallel with the theoretical investigation presented in Part 1 of this study. Experiments were conducted in a special water tunnel with silicone rubber cantilevers which, in the case of external flow, were truncated cones, the free ends of which were streamlined; in the case of internal flow the beams were tubular, conical inside, and either conical or cylindrical outside, immersed either in still air or water. Experiments were also conducted with uniform tubular cylinders, and some with simultaneous internal and external axial flow. Qualitatively these experiments support theoretical predictions very well. The critical conditions for the various fluid-elastic instabilities which these systems can develop were measured and compared with theory. Quantitative agreement ranged from excellent to fair, the former for internal flow in conical tubes, and the latter for very slender cones in external flow.

Buoyancy-Induced Flow in Open Rotating Cavities

2006 ◽  
Author(s):  
J. Michael Owen ◽  
Hans Abrahamsson ◽  
Klas Lindblad
Keyword(s):  
Tangential Velocity ◽  
Axial Flow ◽  
Quantitative Agreement ◽  
Turbine Engines ◽  
The Third ◽  
Commercial Code ◽  
Heated Disc ◽  
Induced Flow ◽  
Cooling Air ◽  
Buoyancy Induced Flow

Buoyancy-induced flow can occur in the cavity between the co-rotating compressor discs in gas-turbine engines, where the Rayleigh numbers can be in excess of 1012. In most cases the cavity is open at the centre, and an axial throughflow of cooling air can interact with the buoyancy-induced flow between the discs. Such flows can be modeled, computationally and experimentally, by a simple rotating cavity with an axial flow of air. This paper describes work conducted as part of ICAS-GT, a major European research project. Experimental measurements of velocity, temperature and heat transfer were obtained on a purpose-built experimental rig, and these results have been reported in an earlier paper. In addition, 3D unsteady CFD computations were carried out using a commercial code (Fluent) and an RNG k-ε turbulence model. The computed velocity vectors and contours of temperature reveal a flow structure in which, as seen by previous experimenters, ‘radial arms’ transport cold air from the centre to the periphery of the cavity, and regions of cyclonic and anti-cyclonic circulation are formed on either side of each arm. The computed radial distribution of the tangential velocity agrees reasonably well with the measurements in two of the three cases considered here. In the third case, the computations significantly over-predict the measurements; the reason for this is not understood. The computed and measured values of Nu for the heated disc show qualitatively similar radial distributions, with high values near the centre and the periphery. In two of the cases, the quantitative agreement is reasonably good; in the third case, the computations significantly under-predict the measured values.

Stability of a Cluster of Flexible Cylinders in Bounded Axial Flow

1977 ◽  
Vol 44 (3) ◽  
pp. 401-408 ◽  
Author(s):  
M. P. Paidoussis ◽  
S. Suss
Keyword(s):  
Channel Wall ◽  
Cylindrical Channel ◽  
Equations Of Motion ◽  
Axial Flow ◽  
High Flow ◽  
Critical Flow ◽  
Flowing Fluid ◽  
Hydrodynamic Coupling ◽  
Viscous Hydrodynamic ◽  
Flow Velocities

This paper deals with the dynamics of a cluster of parallel flexible cylinders in a cylindrical channel in the presence of an axially flowing fluid. The equations of motion are derived, taking into account inviscid and viscous hydrodynamic coupling of small arbitrary motions of the cylinders. Solutions of the equations of motion yield the eigenfrequencies and modal shapes of the system. For sufficiently high flow velocities the system loses stability by divergence and flutter, similarly to a solitary cylinder in unbounded flow; however, the critical flow velocities are much lower, as proximity to other cylinders and to the channel wall severely destabilize the system.

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory

2014 ◽  
Vol 754 ◽  
pp. 232-249 ◽  
Author(s):  
Marius Ungarish ◽  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Viscosity Coefficient ◽  
Gravity Currents ◽  
Quantitative Agreement ◽  
Flat Bottom ◽  
Special Configuration ◽  
Theoretical Predictions ◽  
Speed Of Propagation ◽  
High Reynolds

AbstractWe investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

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