Experiments in Fluids

, 56:160 | Cite as

Vorticity transport and the leading-edge vortex of a plunging airfoil

  • Azar Eslam Panah
  • James M. Akkala
  • James H. J. BuchholzEmail author
Research Article
Part of the following topical collections:
  1. Extreme Flow Workshop 2014


The three-dimensional flow field was experimentally characterized for a nominally two-dimensional flat-plate airfoil plunging at large amplitude and reduced frequencies, using three-dimensional reconstructions of planar PIV data at a chord-based Reynolds number of 10,000. Time-resolved, instantaneous PIV measurements reveal that secondary vorticity, of opposite sign to the primary vortex, is intermittently entrained into the leading-edge vortex (LEV) throughout the downstroke, with the rate of entrainment increasing toward the end of the stroke when the leading-edge shear layer weakens. A planar vorticity transport analysis around the LEV indicated that, during the downstroke, the surface vorticity flux due to the pressure gradient is consistently about half that due to the leading-edge shear layer for all parameter values investigated, demonstrating that production and entrainment of secondary vorticity is an important mechanism regulating LEV strength. A small but non-negligible vorticity source was also attributed to spanwise flow toward the end of the downstroke. Aggregate vortex tilting is notably more significant for higher plunge frequencies, suggesting that the vortex core is more three-dimensional.


Vortex Vorticity Particle Image Velocimetry Strouhal Number Particle Image Velocimetry Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Control region

\(\partial A\)

Control region boundary


Airfoil chord length (m)


Plunge frequency (Hz)


Transverse displacement of the plate


Plunge amplitude (m)

\(k=\pi f c/U\)

Reduced frequency

\(\mathbf {n}_A (=\mathbf {e}_z)\)

Surface normal of the control region

\(\mathbf {n}_{\partial A}\)

In-plane normal to the control region boundary


Pressure (Pa)

\(Re_{\rm C}\)

Chord-based Reynolds number


Airfoil span (m)

\(St=2 f h_0 /U\)

Strouhal number


Free-stream velocity (m/s)


Component of velocity in x direction


Component of velocity in y direction

xD, yD, ZD

Dimensions of the 3D reconstructed flow volume in the x, y, and z directions (mm)


Streamwise coordinate (mm)


Surface-normal coordinate (mm)


Spanwise coordinate (mm)


Circulation (mm2/s)


Phase angle (°)


Vorticity (s−1)


Undamped natural frequency of the pressure measurement system (rad/s)


Kinematic viscosity (mm2/s)


Damping ratio



The authors gratefully acknowledge support for this work from the US Air Force Office of Scientific Research Flow Interactions and Control program managed by Dr. Douglas Smith (Award Number FA9550-11-1-00190).

Supplementary material

Supplementary material 1 (mpg 1708 KB)

348_2015_2014_MOESM2_ESM.mpg (802 kb)
Supplementary material 2 (mpg 802 KB)
348_2015_2014_MOESM3_ESM.mpeg (1.2 mb)
Supplementary material 3 (mpeg 1180 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Azar Eslam Panah
    • 1
    • 2
  • James M. Akkala
    • 1
  • James H. J. Buchholz
    • 1
    Email author
  1. 1.Department of Mechanical and Industrial Engineering IIHR - Hydroscience and EngineeringUniversity of IowaIowa CityUSA
  2. 2.Penn State UniversityBerksUSA

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