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.

Dynamic Properties of Multi-Lobe Water Lubricated Bearings With Temporal and Convective Inertia Considerations

2017 ◽  
Author(s):  
Saeid Dousti ◽  
Paul Allaire ◽  
Bradley Nichols ◽  
Jianming Cao ◽  
Timothy Dimond
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Added Mass ◽  
Damping Properties ◽  
Inertia Effects ◽  
The Stability ◽  
Water Pumps ◽  
Stiffness And Damping

In this paper, the extended Reynolds equation proposed by Dousti et al. [1] is applied to predict the dynamic behavior of different fixed geometry bearings used in vertical water pumps. The influence of convective and temporal inertia effects is studied in regular and preloaded multi-lobe bearings. It is shown that the convective inertia is more influential at the presence of preload and higher rotational speeds and alters the stiffness and damping properties of the bearing. The temporal inertia leads to the prediction of considerable lubricant added mass coefficients in the order of journal mass. The stability analysis shows depending upon the geometry of the bearing, the new extended Reynolds equation may predict higher or lower logarithmic decrement.

Large-Scale Simulation of Rod Bundles: Coherent Structure Recognition and Stability Analysis

2015 ◽  
Author(s):  
Elia Merzari ◽  
Paul Fischer ◽  
Justin Walker
Keyword(s):  
Stability Analysis ◽  
Coherent Structure ◽  
Large Scale ◽  
Nuclear Reactor ◽  
Axial Flow ◽  
Spectral Element ◽  
Industrial Applications ◽  
Diameter Ratio ◽  
Rod Bundles ◽  
Structure Recognition

The axial flow in rod bundles has been the object of several investigations, since they are relevant for various industrial applications (e.g., heat exchangers, nuclear reactor cores). For tight configurations (pitch-to-diameter ratio smaller than 1.1) the large difference in velocity within the cross section creates the possibility of a Kelvin-Helmholtz instability and the generation of a vortex street in the gap (“gap instability”). While the presence of spacing devices may perturb the flow, simple grid spacers — grids of the type usually encountered in sodium fast reactors — do not prevent this instability. This work seeks to improve our understanding of the gap instability in large rod bundles by using high-fidelity large-eddy simulation (LES). The application of LES methods has been historically limited to single-pin calculations because of the large cost of full-bundle calculations. However, using Nek5000, a massively parallel spectral-element computational fluid dynamics code, we are able to carry out well-resolved LES simulations for this class of geometries. Results are compared with experimental data. For the largest bundle case, over 8 billion collocation points at a polynomial order of 20 are judged necessary to achieve overall excellent accuracy. More than 500,000 processors are used to carry out the simulations (costing approximately 50,000,000 CPU-hours), and 3,000 snapshots of the flow field have been collected to apply several coherent structure recognition techniques, including one of the largest proper orthogonal decompositions carried out to date. Also investigated here is the effect of geometry, including the (presence of spacers, changing pitch-to-diameter ratio, and canister wall. In particular, global linear stability analysis is applied to a series of simplified geometries in order to gain insight into the physics of the gap instability.

Stability of a Submerged Deformable Body

2009 ◽  
Author(s):  
Fangxu Jing ◽  
Eva Kanso
Keyword(s):  
Vortex Shedding ◽  
Deformable Body ◽  
Mass Effect ◽  
Added Mass ◽  
Bending Stiffness ◽  
Body Dimensions ◽  
Fish Model ◽  
The Stability ◽  
Parameter Values ◽  
Stable Passive

We study the stability of passive motion of a fish model. The (articulated body) fish model accounts for the finite dimensions of the fish, its bending stiffness (via the torsional springs at the joints), the unsteadiness of the flow (via the added mass effect) but it does not take into consideration vortex shedding from the trailing edge of the fish. The stability analysis shows that there is a range of parameter values (bending stiffness versus body dimensions) that support stable passive swimming in the direction of the body’s length.

scholarly journals Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Abhinav Ravindra Dehadrai ◽  
Ishan Sharma ◽  
Shakti S. Gupta
Keyword(s):  
Stability Analysis ◽  
Governing Equation ◽  
Initial Conditions ◽  
Slenderness Ratio ◽  
Equation Of Motion ◽  
Rate Of Change ◽  
Bending Rigidity ◽  
Stable Regime ◽  
Varying Coefficients ◽  
The Stability

We study the stability of a pre-tensioned, heavy cable traveling vertically against gravity at a constant speed. The cable is modeled as a slender beam incorporating rotary inertia. Gravity modifies the tension along the traveling cable and introduces spatially varying coefficients in the equation of motion, thereby precluding an analytical solution. The onset of instability is determined by employing both the Galerkin method with sine modes and finite element (FE) analysis to compute the eigenvalues associated with the governing equation of motion. A spectral stability analysis is necessary for traveling cables where an energy stability analysis is not comprehensive, because of the presence of gyroscopic terms in the governing equation. Consistency of the solution is checked by direct time integration of the governing equation of motion with specified initial conditions. In the stable regime of operations, the rate of change of total energy of the system is found to oscillate with bounded amplitude indicating that the system, although stable, is nonconservative. A comprehensive stability analysis is carried out in the parameter space of traveling speed, pre-tension, bending rigidity, external damping, and the slenderness ratio of the cable. We conclude that pre-tension, bending rigidity, external damping, and slenderness ratio enhance the stability of the traveling cable while gravity destabilizes the cable.

Spatial stability and the onset of absolute instability of Batchelor's vortex for high swirl numbers

2007 ◽  
Vol 583 ◽  
pp. 27-43 ◽  
Author(s):  
L. PARRAS ◽  
R. FERNANDEZ-FERIA
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Absolute Instability ◽  
Spatial Stability ◽  
The Past ◽  
Trailing Vortices ◽  
The Stability ◽  
Large Aircraft

Batchelor's vortex has been commonly used in the past as a model for aircraft trailing vortices. Using a temporal stability analysis, new viscous unstable modes have been found for the high swirl numbers of interest in actual large-aircraft vortices. We look here for these unstable viscous modes occurring at large swirl numbers (q > 1.5), and large Reynolds numbers (Re >103), using a spatial stability analysis, thus characterizing the frequencies at which these modes become convectively unstable for different values of q, Re, and for different intensities of the uniform axial flow. We consider both jet-like and wake-like Batchelor's vortices, and are able to analyse the stability for Re as high as 108. We also characterize the frequencies and the swirl numbers for the onset of absolute instabilities of these unstable viscous modes for large q.

Stability of a Stationary Flexible Cantilevered Plate in an Axial Flow

2014 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Keiji Matsumoto
Keyword(s):  
Stability Analysis ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Axial Flow ◽  
Complex Eigenvalue ◽  
Flexible Plate ◽  
Moving Plate ◽  
Cantilevered Plate ◽  
The Stability

As the flexible plates, the papers in printing machines, the thin plastic and metal films, and the fluttering flag are enumerated. In this paper, the flexible plate is assumed to be stationary in an axial flow although both the stationary plate and the axially moving plate can be thought. The fluid is assumed to be treated as an ideal fluid in a subsonic domain, and the fluid pressure is calculated using the velocity potential theory. The coupled equation of motion of a flexible cantilevered plate is derived in consideration of the added mass, added damping and added stiffness, respectively. The velocity potential is obtained by assuming the unsteady axial fluid velocity to be zero at the trailing edge of a flexible cantilevered plate, neglecting the effect of a circulation. The complex eigenvalue analysis is performed for the stability analysis. In order to investigate the validity of the proposed analysis, another stability analysis is also performed by using the non-circulatory aerodynamic theory. The comparison between both solutions is investigated and discussed. Changing the velocities of a fluid and the specifications of a plate as parametric studies, the effects of these parameters on the stability of a flexible cantilevered plate are investigated.

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.

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.

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