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Dynamic stall on a pitching and surging airfoil

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Abstract

Vertical axis wind turbine blades undergo dynamic stall due to the large angle of attack variation they experience during a turbine rotation. The flow over a single blade was modeled using a sinusoidally pitching and surging airfoil in a non-rotating frame with a constant freestream flow at a mean chord Reynolds number of \({10^5}\). Two-dimensional, time-resolved velocity fields were acquired using particle image velocimetry. Vorticity contours were used to visualize shear layer and vortex activity. A low-order model of dynamic stall was developed using dynamic mode decomposition, from which primary and secondary dynamic separation modes were identified. The interaction between these two modes was able to capture the physics of dynamic stall and as such can be extended to other turbine configurations and problems in unsteady aerodynamics. Results from the linear pitch/surge frame are extrapolated to the rotating VAWT frame to investigate the behavior of identified flow structures.

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Abbreviations

t :

Time (s)

\(\alpha\) :

Angle of attack (°)

\(\theta\) :

Turbine rotation angle (°)

\(Re_{\rm c}\) :

Chord Reynolds number (\(\frac{Uc}{\nu }\))

\(U_\infty\) :

Wind speed (\(\hbox {m s}^{-1}\))

U :

Effective velocity (\(\hbox {m s}^{-1}\))

\(\bar{U}\) :

Average velocity in experiment (tunnel velocity) (\(\hbox {m s}^{-1}\))

\(\chi\) :

Spanwise vorticity (\(\hbox {s}^{-1}\))

\(\eta\) :

Tip speed ratio (\(\frac{\omega R}{U_\infty }\))

\(\omega\) :

Turbine frequency (\(\hbox {rad s}^{-1}\))

\(\varOmega\) :

Pitch/surge frequency (\(\hbox {rad s}^{-1}\))

R :

Turbine radius (m)

Ro :

Rossby number (\(\frac{U_\infty }{2c \omega }\))

c :

Chord length (cm)

\(\nu\) :

Kinematic viscosity (\(\hbox {m}^2\hbox { s}^{-1}\))

\(\lambda\) :

Transformed DMD eigenvalues (\(\hbox {rad s}^{-1}\))

k :

Reduced frequency (\(\frac{\varOmega c}{2 \bar{U}}\))

\(\varGamma _1\) :

Vortex center criteria

\(\varGamma _2\) :

Vortex boundary criteria

\(x,\, u\) :

Streamwise coordinate [c], streamwise velocity (\(\hbox {m s}^{-1}\))

\(y,\, v\) :

Cross-stream coordinate [c], cross-stream velocity (\(\hbox {m s}^{-1}\))

z :

Spanwise coordinate (c)

xl :

Leading edge position (c)

i :

Imaginary component

r :

Real component

j :

Variable index

\(\pm\) :

Pitch up (+) and down (−)

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Acknowledgments

This work was supported by the Gordon and Betty Moore Foundation through grant GBMF#2645 to the California Institute of Technology. The authors thank Professor Peter Schmid for his assistance in implementing the dynamic mode decomposition algorithm, Professor Morteza Gharib for the use of the free surface water channel facility, Hsieh-Chen Tsai and Professor Tim Colonius for discussion on the Coriolis effect and Professor John Dabiri for his insight from VAWT field research.

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Authors and Affiliations

  1. Mechanical Engineering, California Institute of Technology, 1200 E California Blvd, MC 301-46, Pasadena, CA, 91125, USA

    Reeve Dunne

  2. Graduate Aerospace Laboratories, California Institute of Technology, 1200 E California Blvd, MC 301-46, Pasadena, CA, 91125, USA

    Beverley J. McKeon

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  1. Reeve Dunne
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  2. Beverley J. McKeon
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Correspondence to Reeve Dunne.

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The authors declare that they have no conflict of interest.

Additional information

This article belongs to a Topical Collection of articles entitled Extreme Flow Workshop 2014. Guest editors: I. Marusic and B. J. McKeon.

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Dunne, R., McKeon, B.J. Dynamic stall on a pitching and surging airfoil. Exp Fluids 56, 157 (2015). https://doi.org/10.1007/s00348-015-2028-1

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  • DOI: https://doi.org/10.1007/s00348-015-2028-1

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