A Numerical Investigation on the Dynamics of Two-Dimensional Cantilevered Flexible Plates in Axial Flow

2006 ◽  
Author(s):  
Liaosha Tang ◽  
Michael P. Pai¨doussis
Keyword(s):  
Flow Velocity ◽  
Pressure Difference ◽  
Axial Flow ◽  
Equation Of Motion ◽  
Current Theory ◽  
Vortex Model ◽  
Flexible Plates ◽  
Flutter Boundary ◽  
The Stability ◽  
The Time Domain

A cantilevered plate immersed in an otherwise uniform flow may lose stability at a high enough flow velocity; flutter takes place when the flow velocity exceeds a critical value. In the current research, a nonlinear equation of motion of the plate is developed using the inextensibility condition. Also, an unsteady lumped vortex model is used to calculate the pressure difference across the plate. The pressure difference is then decomposed into a lift force and an inviscid drag force. The fluid loads are coupled with the plate equation of motion and a numerical model of the fluid-structure system is developed. Analysis of the system dynamics is carried out in the time-domain. Both the stability and the post-critical behaviour of the system are studied. The flutter boundary and the vibration modes predicted by the current theory are found to be in good agreement with published experimental data.

Nonlinear Dynamics of Supported Cylinder Subjected to Axial Flow

2011 ◽  
Vol 243-249 ◽  
pp. 4712-4717
Author(s):  
Ji Duo Jin ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Velocity ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Equation Of Motion ◽  
Flexible Cylinder ◽  
Chaotic Motions ◽  
Flutter Instability ◽  
The Stability

In this paper, the stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are only the additional axial force induced by the lateral motions of the cylinder. Using six-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the quasiperiodic motion around the buckled position occurs, and this evolves into chaotic motions at higher flow.

Stability of a String in Axial Flow

1985 ◽  
Vol 107 (4) ◽  
pp. 421-425 ◽  
Author(s):  
G. S. Triantafyllou ◽  
C. Chryssostomidis
Keyword(s):  
Stability Analysis ◽  
Frictional Coefficient ◽  
Axial Flow ◽  
Added Mass ◽  
Equation Of Motion ◽  
Bending Stiffness ◽  
Diameter Ratio ◽  
Constant Speed ◽  
Hamilton’S Principle ◽  
The Stability

The equation of motion of a long slender beam submerged in an infinite fluid moving with constant speed is derived using Hamilton’s principle. The upstream end of the beam is pinned and the downstream end is free to move. The resulting equation of motion is then used to perform the stability analysis of a string, i.e., a beam with negligible bending stiffness. It is found that the string is stable if (a) the external tension at the free end exceeds the value of a U2, where a is the “added mass” of the string and U the fluid speed; or (b) the length-over-diameter ratio exceeds the value 2Cf/π, where Cf is the frictional coefficient of the string.

scholarly journals Flutter of Long Flexible Cylinders in Axial Flow

2006 ◽  
Author(s):  
E. de Langre ◽  
M. P. Paidoussis ◽  
Y. Modarres-Sadeghi ◽  
O. Doare´
Keyword(s):  
Stability Analysis ◽  
Axial Flow ◽  
Equation Of Motion ◽  
External Flow ◽  
Transverse Motion ◽  
Control Parameters ◽  
Limit Case ◽  
Finite Region ◽  
Flexible Cylinder ◽  
The Stability

We consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the up-stream 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 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. A simple model for the behaviour of long cylinders is proposed.

Viscous and inviscid centre modes in the linear stability of vortices: the vicinity of the neutral curves

2008 ◽  
Vol 603 ◽  
pp. 1-38 ◽  
Author(s):  
DAVID FABRE ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Axial Flow ◽  
Neutral Curve ◽  
Numerical Results ◽  
Asymptotic Results ◽  
Asymptotic Description ◽  
Vortex Model ◽  
Neutral Curves ◽  
Trailing Vortices ◽  
The Stability ◽  
Wave Limit

In a previous paper, We have recently that if the Reynolds number is sufficiently large, all trailing vortices with non-zero rotation rate and non-constant axial velocity become linearly unstable with respect to a class of viscous centre modes. We provided an asymptotic description of these modes which applies away from the neutral curves in the (q, k)-plane, where q is the swirl number which compares the azimuthal and axial velocities, and k is the axial wavenumber. In this paper, we complete the asymptotic description of these modes for general vortex flows by considering the vicinity of the neutral curves. Five different regions of the neutral curves are successively considered. In each region, the stability equations are reduced to a generic form which is solved numerically. The study permits us to predict the location of all branches of the neutral curve (except for a portion of the upper neutral curve where it is shown that near-neutral modes are not centre modes). We also show that four other families of centre modes exist in the vicinity of the neutral curves. Two of them are viscous damped modes and were also previously described. The third family corresponds to stable modes of an inviscid nature which exist outside of the unstable region. The modes of the fourth family are also of an inviscid nature, but their structure is singular owing to the presence of a critical point. These modes are unstable, but much less amplified than unstable viscous centre modes. It is observed that in all the regions of the neutral curve, the five families of centre modes exchange their identity in a very intricate way. For the q vortex model, the asymptotic results are compared to numerical results, and a good agreement is demonstrated for all the regions of the neutral curve. Finally, the case of ‘pure vortices’ without axial flow is also considered in a similar way. In this case, centre modes exist only in the long-wave limit, and are always stable. A comparison with numerical results is performed for the Lamb–Oseen vortex.

Effects of Lumped Masses on the Stability of Fluid Conveying Tubes

1970 ◽  
Vol 37 (2) ◽  
pp. 494-497 ◽  
Author(s):  
J. L. Hill ◽  
C. P. Swanson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fluid Flow ◽  
Flow Velocity ◽  
Equation Of Motion ◽  
Numerical Results ◽  
Fluid Flow Velocity ◽  
The Stability ◽  
The Masses ◽  
Lumped Masses

The effects of adding lumped masses to fluid conveying tubes are studied. The addition of the masses is accounted for by a discontinuous mass distribution. Solutions of the partial differential equation of motion with the discontinuous coefficient are sought approximately using Galerkin’s method. Numerical results are presented for the destabilizing fluid-flow velocity for a cantilevered tube. The numerical results compare favorably with experimental results.

scholarly journals Flutter of long flexible cylinders in axial flow

2007 ◽  
Vol 571 ◽  
pp. 371-389 ◽  
Author(s):  
E. DE LANGRE ◽  
M. P. PAÏDOUSSIS ◽  
O. DOARÉ ◽  
Y. MODARRES-SADEGHI
Keyword(s):  
Axial Flow ◽  
Equation Of Motion ◽  
External Flow ◽  
Transverse Motion ◽  
Control Parameters ◽  
Limit Case ◽  
Finite Region ◽  
Flexible Cylinder ◽  
Linear And Nonlinear ◽  
The Stability

We 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.

Nonlinear Dynamics of a Slender Flexible Cylinder in Axial Flow

2011 ◽  
Vol 130-134 ◽  
pp. 761-765
Author(s):  
Ji Duo Jin ◽  
N. Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Velocity ◽  
Nonlinear Model ◽  
Dynamic Instability ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Flexible Cylinder ◽  
Flutter Instability ◽  
The Stability

The stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the additional axial force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the buckled configuration becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the system is restabilized in the buckled configuration prior to another dynamic instability at higher flow.

Flow through axial-flow-turbomachinery blading

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Flow Velocity ◽  
Compressible Flow ◽  
Dimensional Analysis ◽  
Incompressible Flow ◽  
Compressible Fluid ◽  
Axial Flow ◽  
Linear Cascade ◽  
Dimensional Parameters ◽  
Flow Through

This chapter is concerned primarily with the flow of a compressible fluid through stationary and moving blading, for the most part using the analysis introduced in Chapter 11. The principles of dimensional analysis are applied to determine the appropriate non-dimensional parameters to characterise the performance of a turbomachine. The analysis of incompressible flow through a linear cascade of aerofoil-like blades is followed by the analysis of compressible flow. Velocity triangles for flow relative to blades, and Euler’s turbomachinery equation, are introduced to analyse flow through a rotor. The concepts introduced are applied to the analysis of an axial-turbomachine stage comprising a stator and a rotor, which applies to either a compressor or a turbine.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

Sign in / Sign up

Export Citation Format

Share Document