How flexibility induces streamlining in a two-dimensional flow

Silas Alben, Michael Shelley, Jun Zhang

Research output: Contribution to journalArticle

Abstract

Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small "tip region" about the flow's stagnation point. The result is a transition from the classical U2 drag scaling of rigid bodies to a new U4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the length-scale of similarity. This analysis predicts that the fiber and wake are quasiparabolic at large velocities, and obtains the new drag law in terms of the drag on the tip region. Under variations of the model suggested by the experiment-the addition of flow tunnel walls, and a back pressure in the wake-the drag law persists, with a simple modification.

Original languageEnglish (US)
Pages (from-to)1694-1713
Number of pages20
JournalPhysics of Fluids
Volume16
Issue number5
DOIs
StatePublished - May 2004

Fingerprint

streamlining
two dimensional flow
drag
Drag
flexibility
wakes
fibers
Fluids
Fibers
fluids
elastic bending
seaweeds
Seaweed
scaling
soaps
Soaps (detergents)
stagnation point
glass fibers
rigid structures
fluid dynamics

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes
  • Condensed Matter Physics

Cite this

How flexibility induces streamlining in a two-dimensional flow. / Alben, Silas; Shelley, Michael; Zhang, Jun.

In: Physics of Fluids, Vol. 16, No. 5, 05.2004, p. 1694-1713.

Research output: Contribution to journalArticle

Alben, S, Shelley, M & Zhang, J 2004, 'How flexibility induces streamlining in a two-dimensional flow', Physics of Fluids, vol. 16, no. 5, pp. 1694-1713. https://doi.org/10.1063/1.1668671
Alben, Silas ; Shelley, Michael ; Zhang, Jun. / How flexibility induces streamlining in a two-dimensional flow. In: Physics of Fluids. 2004 ; Vol. 16, No. 5. pp. 1694-1713.
@article{1fa1c708c03746eab45ab630cf7c7d84,
title = "How flexibility induces streamlining in a two-dimensional flow",
abstract = "Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small {"}tip region{"} about the flow's stagnation point. The result is a transition from the classical U2 drag scaling of rigid bodies to a new U4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the length-scale of similarity. This analysis predicts that the fiber and wake are quasiparabolic at large velocities, and obtains the new drag law in terms of the drag on the tip region. Under variations of the model suggested by the experiment-the addition of flow tunnel walls, and a back pressure in the wake-the drag law persists, with a simple modification.",
author = "Silas Alben and Michael Shelley and Jun Zhang",
year = "2004",
month = "5",
doi = "10.1063/1.1668671",
language = "English (US)",
volume = "16",
pages = "1694--1713",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics Publising LLC",
number = "5",

}

TY - JOUR

T1 - How flexibility induces streamlining in a two-dimensional flow

AU - Alben, Silas

AU - Shelley, Michael

AU - Zhang, Jun

PY - 2004/5

Y1 - 2004/5

N2 - Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small "tip region" about the flow's stagnation point. The result is a transition from the classical U2 drag scaling of rigid bodies to a new U4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the length-scale of similarity. This analysis predicts that the fiber and wake are quasiparabolic at large velocities, and obtains the new drag law in terms of the drag on the tip region. Under variations of the model suggested by the experiment-the addition of flow tunnel walls, and a back pressure in the wake-the drag law persists, with a simple modification.

AB - Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small "tip region" about the flow's stagnation point. The result is a transition from the classical U2 drag scaling of rigid bodies to a new U4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the length-scale of similarity. This analysis predicts that the fiber and wake are quasiparabolic at large velocities, and obtains the new drag law in terms of the drag on the tip region. Under variations of the model suggested by the experiment-the addition of flow tunnel walls, and a back pressure in the wake-the drag law persists, with a simple modification.

UR - http://www.scopus.com/inward/record.url?scp=2442637514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442637514&partnerID=8YFLogxK

U2 - 10.1063/1.1668671

DO - 10.1063/1.1668671

M3 - Article

AN - SCOPUS:2442637514

VL - 16

SP - 1694

EP - 1713

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

ER -