Mapping the properties of the vortex-induced vibrations of flexible cylinders in uniform oncoming flow
Flexible structures placed within an oncoming flow exhibit far more complex vortex-induced dynamics than flexibly mounted rigid cylinders, because they involve the distributed interaction between the structural and wake dynamics along the entire span. Hence, mapping the well-understood properties of...
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Published in | Journal of fluid mechanics Vol. 881; pp. 815 - 858 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cambridge
Cambridge University Press
25.12.2019
|
Subjects | |
Online Access | Get full text |
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Summary: | Flexible structures placed within an oncoming flow exhibit far more complex vortex-induced dynamics than flexibly mounted rigid cylinders, because they involve the distributed interaction between the structural and wake dynamics along the entire span. Hence, mapping the well-understood properties of rigid cylinder vibrations to those of strings and beams has been elusive. We show here with a combination of experiments, conducted at Reynolds number,
$Re$
from 250 to 2300, and computational fluid dynamics that such a mapping is possible for flexible structures in uniform flow undergoing combined cross-flow and in-line oscillations, but only when additional concepts are introduced to model the extended coupling of the flow and the structure. The in-line response consists of largely standing waves that define cells, each cell spanning the distance between adjacent nodes, over which stable vortical patterns form, whose features (‘2S’ versus ‘P
$+$
S’) depend strongly on the true reduced velocity,
$V_{r}=U/f_{y}d$
, where
$U$
is the inflow velocity,
$f_{y}$
is the cross-flow vibration frequency and
$d$
is the cylinder diameter, and the phase angle between in-line and cross-flow response; while the cross-flow response may contain travelling waves, breaking the symmetry of the problem. The axial distribution of the highly variable effective added masses in the cross-flow and in-line directions, and the local phase angle between in-line and cross-flow motion determine the single frequency of cross-flow response, while the in-line response vibrates at twice the cross-flow frequency. The cross-flow and in-line lift coefficients in phase with velocity depend strongly on the true reduced velocity but also on the local phase angle between in-line and cross-flow motions. Modal shapes can be defined for in-line and cross-flow, based on the resemblance of the response to conventional modes, which can be in the ratio of either ‘
$2n/n$
’ or ‘
$(2n-1)/n$
’, where
$n$
is the order of the cross-flow response mode. We use an underwater optical tracking system to reconstruct the sectional fluid forces in a flexible structure and show that, once the cross-flow and in-line motion features are known, employing strip theory and the hydrodynamic coefficients obtained from forced rigid cylinder experiments allows us to predict the distributed forces accurately. |
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ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/jfm.2019.738 |