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

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Abstract

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.

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Abbreviations

A :

Control region

\(\partial A\) :

Control region boundary

c :

Airfoil chord length (m)

f :

Plunge frequency (Hz)

h(t):

Transverse displacement of the plate

\(h_0\) :

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

p :

Pressure (Pa)

\(Re_{\rm C}\) :

Chord-based Reynolds number

s :

Airfoil span (m)

\(St=2 f h_0 /U\) :

Strouhal number

U :

Free-stream velocity (m/s)

u :

Component of velocity in x direction

v :

Component of velocity in y direction

x D, y D, Z D :

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

x :

Streamwise coordinate (mm)

y :

Surface-normal coordinate (mm)

z :

Spanwise coordinate (mm)

\(\varGamma\) :

Circulation (mm2/s)

\(\phi\) :

Phase angle (°)

ω :

Vorticity (s−1)

ω 0 :

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

\(\nu\) :

Kinematic viscosity (mm2/s)

\(\zeta\) :

Damping ratio

References

  • Akhtar I, Mittal R, Lauder GV, Drucker EA (2007) Hydrodynamics of a biologically inspired tandem flapping foil configuration. Theor Comput Fluid Dyn 21:155–170

    Article  MATH  Google Scholar 

  • Akkala JM, Eslam Panah A, Buchholz JHJ (2015) Vortex dynamics and performance of flexible and rigid plunging airfoils. J Fluid Struct. doi:10.1016/j.jfluidstructs.2014.10.013

    Google Scholar 

  • Bohl DG, Koochesfahani MM (2009) MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J Fluid Mech 620:63–88

    Article  MATH  Google Scholar 

  • Bridges DH (2010) Toward a theoretical description of vortex wake asymmetry. Progr Aerosp Sci 46:62–80

    Article  Google Scholar 

  • Brunton SL, Rowley CW, Williams DR (2013) Reduced-order unsteady aerodynamic models at low Reynolds numbers. J Fluid Mech 724:203–233

    Article  MATH  Google Scholar 

  • Buchholz JHJ, Green MA, Smits AJ (2011) Scaling the circulation shed by a pitching panel. J Fluid Mech 688:591–601

    Article  MATH  Google Scholar 

  • Cleaver DJ, Wang Z, Gursul I, Visbal MR (2011) Lift enhancement by means of small-amplitude airfoil oscillations at low reynolds numbers. AIAA J 49(9):2018–2033

    Article  Google Scholar 

  • Cohn RK, Koochesfahani MM (1993) Effect of boundary conditions on axial flow in a concentrated vortex core. Phys Fluid A 5(1):280–282

    Article  Google Scholar 

  • Dabiri JO (2009) Optimal vortex formation as a unifying principle in biological propulsion. Ann Rev Fluid Mech 41:17–33

    Article  MathSciNet  Google Scholar 

  • DeVoria AC, Ringuette MJ (2012) Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp Fluid 52:441–462

    Article  Google Scholar 

  • Ellington CP, van den Berg C, Willmott AP, Thomas ALR (1996) Leading-edge vortices in insect flight. Nature 384:626–630

    Article  Google Scholar 

  • Eslam PA (2014) Flow structure and vorticity transport on a plunging wing. Ph.D. thesis, University of Iowa

  • Eslam Panah A, Buchholz JHJ (2014) Parameter dependence of vortex interactions on a two-dimensional plunging plate. Exp Fluid 55(3):1687

    Article  Google Scholar 

  • Freymuth P (1988) Propulsive vortical signature of plunging and pitching airfoils. AIAA J 27(9):1200–1205

    Google Scholar 

  • Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140

    Article  MathSciNet  MATH  Google Scholar 

  • Gopalkrishnan R, Triantafyllou MS, Triantafyllou GS, Barrett D (1994) Active vorticity control in a shear flow using a flapping foil. J Fluid Mech 274:1–21

    Article  Google Scholar 

  • Graftieaux L, Michard M, Grosjean N (2001) Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas Sci Technol 12(9):1422–1429

    Article  Google Scholar 

  • Green MA, Smits AJ (2008) Effects of three-dimensionality on thrust production by a pitching panel. J Fluid Mech 531:211–220

    Article  Google Scholar 

  • Huang H, Dabiri D, Gharib M (1997) On errors of digital particle image velocimetry. Meas Sci Technol 8:1427–1440

    Article  Google Scholar 

  • Hubel TY, Tropea C (2010) The importance of leading edge vortices under simplified flapping flight conditions at the size scale of birds. J Exp Biol 213:1930–1939

    Article  Google Scholar 

  • Jantzen RT, Taira K, Granlund KO, Ol MV (2014) Vortex dynamics around pitching plates. Phys. Fluid 26, art. 053606

  • Kim D, Gharib M (2011) Flexibility effects on vortex formation of translating plates. J Fluid Mech 677:255–271

    Article  MATH  Google Scholar 

  • Lee T, Gerontakos P (2004) Investigation of flow over an oscillating airfoil. J Fluid Mech 512:313–341

    Article  MATH  Google Scholar 

  • Leishman JG, Beddoes TS (1989) A semi-empirical model for dynamic stall. J Am Helicopter Soc 34:3–17

    Article  Google Scholar 

  • Lentink D, Dickinson MH (2009) Rotational accelerations stabilize leading edge vortices on revolving fly wings. J Exp Biol 212:2705–2719

    Article  Google Scholar 

  • Lewin GC, Haj-Hariri H (2003) Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J Fluid Mech 492:339–362

    Article  MATH  Google Scholar 

  • Li G-J, Lu X-Y (2012) Force and power of flapping plates in a fluid. J Fluid Mech 712:598–613

    Article  MathSciNet  MATH  Google Scholar 

  • Lighthill MJ (1963) Introduction: boundary layer theory. In: Rosenhead L (ed) Laminar boundary layers. Oxford University Press, London, pp 46–113

    Google Scholar 

  • Lua KB, Lim TT, Yeo KS, Oo GY (2007) Wake-structure formation of a heaving two-dimensional elliptic airfoil. AIAA J 45(7):1571–1583

    Article  Google Scholar 

  • Maxworthy T (1979) Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight: part 1. Dynamics of the ‘fling’. J Fluid Mech 93(1):47–63

    Article  Google Scholar 

  • Monnier B., Naguib AM, Koochesfahani MM (2013) Investigation of the wake vortex pattern of rigid and flexible airfoils undergoing harmonic pitch oscillation. In: 51st AIAA Aerospace sciences meeting. Dallas, TX, AIAA Paper 2013–0841

  • Mulleners K, Kindler K, Raffel M (2012) Dynamic stall on a fully equipped helicopter model. Aerospace Sci Technol 19:72–76

    Article  Google Scholar 

  • Ol MV, Gharib M (2003) Leading-edge vortex structure of nonslender delta wings at low Reynolds number. AIAA J 41(2):16–26

    Article  Google Scholar 

  • Pitt Ford CW, Babinsky H (2012) Lift and the leading edge vortex. In: 50th AIAA aerospace sciences meeting. Nashville, TN, AIAA Paper 2012–911

  • Potter MC, Foss JF (1982) Fluid mechanics. Great Lakes Press Inc, Okemos, MI

    Google Scholar 

  • Ramesh K, Gopalarathnam A, Granlund K, Ol MV, Edwards JR (2014) Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding. J Fluid Mech 751:500–538

    Article  MathSciNet  Google Scholar 

  • Rival D, Prangemeier T, Tropea C (2009) The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight. Exp Fluid 46:823–833

    Article  Google Scholar 

  • Rockwell D (1998) Vortex-body interactions. Ann Rev Fluid Mech 30:199–229

    Article  MathSciNet  Google Scholar 

  • Shyy W, Lian Y, Tang J, Liu H, Trizila P, Stanford B, Bernal L, Cesnik C, Friedmann P, Ifju P (2008) Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications. Acta Mech Sin 24:351–373

    Article  MATH  Google Scholar 

  • Visbal MR (2009) High-fidelity simulation of transitional flows past a plunging airfoil. AIAA J 47(11):2685–2697

    Article  Google Scholar 

  • Visbal MR (2011) Numerical investigation of deep dynamic stall of a plunging airfoil. AIAA J 49(10):2152–2170

    Article  MathSciNet  Google Scholar 

  • Wang C, Eldredge JD (2013) Low-order phenomenological modeling of leading-edge vortex formation. Theor Comput Fluid Dyn 27:577–598

    Article  Google Scholar 

  • Wojcik CJ (2012) The dynamics of spanwise vorticity on a rotating flat plate in a starting motion. Master’s thesis, University of Iowa

  • Wojcik CJ, Buchholz JHJ (2014a) Parameter variation and the leading-edge vortex of a rotating flat plate. AIAA J 52(2):348–357

    Article  Google Scholar 

  • Wojcik CJ, Buchholz JHJ (2014b) Vorticity transport in the leading-edge vortex on a rotating blade. J Fluid Mech 743:249–261

    Article  Google Scholar 

  • Wu JZ, Ma HY, Zhou MD (2006) Vorticity and vortex dynamics. Springer, Berlin

    Book  Google Scholar 

  • Wu JZ, Wu JM (1993) Interactions between a solid surface and a viscous compressible flow field. J Fluid Mech 254:183–211

    Article  MathSciNet  MATH  Google Scholar 

  • Wu JZ, Wu JM (1996) Vorticity dynamics on boundaries. In: Hutchison JW, Wu TY (eds) Adv Appl Mech Vol 32. Academic Press, London, pp 119–275

  • Yilmaz TO, Rockwell D (2012) Flow structure on finite-span wings due to pitch-up motion. J Fluid Mech 691:518–545

    Article  MATH  Google Scholar 

Download references

Acknowledgments

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).

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Author notes

  1. Azar Eslam Panah

    Present address: Penn State University, Berks, PA, USA

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering IIHR - Hydroscience and Engineering, University of Iowa, Iowa City, IA, 52242, USA

    Azar Eslam Panah, James M. Akkala & James H. J. Buchholz

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  1. Azar Eslam Panah
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  2. James M. Akkala
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Correspondence to James H. J. Buchholz.

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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Eslam Panah, A., Akkala, J.M. & Buchholz, J.H.J. Vorticity transport and the leading-edge vortex of a plunging airfoil. Exp Fluids 56, 160 (2015). https://doi.org/10.1007/s00348-015-2014-7

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