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Research Papers: Flows in Complex Systems

Vortex Generation in Low-Speed Flow Over an Oscillating and Deforming Arc Airfoil

[+] Author and Article Information
Majid Molki

e-mail: mmolki@siue.edu

Negin Sattari

Department of Mechanical Engineering,
Southern Illinois University Edwardsville,
Edwardsville, IL 62026-1805

1Corresponding author.

Manuscript received January 17, 2012; final manuscript received August 19, 2012; published online December 21, 2012. Assoc. Editor: Z. C. Zheng.

J. Fluids Eng 135(1), 011102 (Dec 21, 2012) (10 pages) Paper No: FE-12-1019; doi: 10.1115/1.4023075 History: Received January 17, 2012; Revised August 19, 2012

A computational investigation is carried out to study the effect of oscillations on vortex generation and vorticity flux for flow over a deforming arc airfoil. The flow is laminar, incompressible, and two-dimensional at Re = 10,000. The computations are performed using the finite-volume method and a deforming mesh. The vorticity flux is evaluated on the surface of the airfoil. A variety of flow features are observed. Boundary layer flows, vortical structures, rolling vortices, and vortex layers are all present and have some degree of influence on the aerodynamic characteristics of the arc airfoil. Tangential pressure gradient on the surface and tangential acceleration of the airfoil are local sources of vorticity generation, and they result in the flux of vorticity from airfoil into fluid.

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References

Panton, R. L., 2005, Incompressible Flow, 3rd ed., Wiley, Hoboken, NJ.
Wilson, M. M., Peng, J., Dabiri, J. O., and Eldredge, J. D., 2009, “Lagrangian Coherent Structures in Low-Reynolds Number Swimming,” J. Phys.: Condens. Matter, 21, p. 204105. [CrossRef] [PubMed]
Dabiri, J. O., 2009, “Optimal Vortex Formation as a Unifying Principle in Biological Propulsion,” Annu. Rev. Fluid Mech., 41, pp. 17–33. [CrossRef]
Franco, E., Pekarek, D. N., Peng, J., and Dabiri, J. O., 2007, “Geometry of Unsteady Fluid Transport During Fluid-Structure Interactions,” J. Fluid Mech., 589, pp. 125–145. [CrossRef]
Molki, M., and Breuer, K., 2010, “Oscillatory Motions of a Prestrained Compliant Membrane Caused by Fluid-Membrane Interaction,” J. Fluids Struct., 26(3), pp. 339–358. [CrossRef]
Song, A., Tian, X., Israeli, E., Galvao, R., Bishop, K., Swartz, S., and Breuer, K., 2008, “Aeromechanics of Membrane Wings With Implications for Animal Flight,” AIAA J., 46(8), pp. 2096–2106. [CrossRef]
Jones, K. D., and Platzer, M. F., 1997, “Numerical Computation of Flapping-Wing Propulsion and Power Extraction,” AIAA Paper No. 97-0826.
Tuncer, I. H., and Platzer, M. F., 2000, “Computational Study of Flapping Airfoil Aerodynamics,” J. Aircr., 37(3), pp. 514–520. [CrossRef]
Read, D. A., Hover, F. S., and Triantafyllou, M. S., 2003, “Forces on Oscillating Foils for Propulsion and Maneuvering,” J. Fluids Struct., 17(1), pp. 163–183. [CrossRef]
Young, J., and Lai, J. C. S., 2004, “Oscillation Frequency and Amplitude Effects on the Wake of a Plunging Airfoil,” AIAA J., 42(10), pp. 2042–2052. [CrossRef]
Levy, D. E., and Seifert, A., 2009, “Simplified Dragonfly Airfoil Aerodynamics at Reynolds Numbers Below 8000,” Phys. Fluids, 21, p. 071901. [CrossRef]
Bohl, D. G., and Koochesfahani, M. M., 2009, “MTV Measurements of the Vortical Field in the Wake of an Airfoil Oscillating at High Reduced Frequency,” J. Fluid Mech., 620, pp. 63–88. [CrossRef]
Griffin, O. M., 1978, “Universal Strouhal Number for the Locking-On of Vortex Shedding to the Vibrations of Bluff Cylinders,” J. Fluid Mech., 85, pp. 591–606. [CrossRef]
Wu, Z. J., 1992, “Higher Frequency Hydrodynamic Force Components on a Vibrating Cylinder in Current,” Proceedings of the 7th International Offshore and Polar Engineering Conference, San Francisco, CA, pp. 375–382.
Akbari, M. H., and Price, S. J., 2005, “Numerical Investigation of Flow Patterns for Staggered Cylinder Pairs in Cross-Flow,” J. Fluids Struct., 20(4), pp. 533–554. [CrossRef]
Lee, S. J., and Lee, J. Y., 2008, “PIV Measurements of the Wake Behind a Rotationally Oscillating Circular Cylinder,” J. Fluids Struct., 24(1), pp. 2–17. [CrossRef]
Zheng, Z. C., and Zhang, N., 2008, “Frequency Effects on Lift and Drag for Flow Past an Oscillating Cylinder,” J. Fluids Struct., 24(3), pp. 382–399. [CrossRef]
Prasanth, T. K., and Mittal, S., 2009, “Vortex-Induced Vibration of Two Circular Cylinders at Low Reynolds Number,” J. Fluids Struct., 25(4), pp. 731–741. [CrossRef]
Morse, T. L., and Williamson, C. H. K., 2009, “Prediction of Vortex-Induced Vibration Response by Employing Controlled Motion,” J. Fluid Mech., 634, pp. 5–39. [CrossRef]
Wang, Z. J., 2000, “Vortex Shedding and Frequency Selection in Flapping Flight,” J. Fluid Mech., 410, pp. 323–341. [CrossRef]
Gulcat, U., 2009, “Propulsive Force of a Flexible Flapping Thin Airfoil,” J. Aircr., 46(2), pp. 465–473. [CrossRef]
Okamoto, M., and Azuma, A., 2005, “Experimental Study on Aerodynamic Characteristics of Unsteady Wings at Low Reynolds Number,” AIAA J., 43(12), pp. 2526–2536. [CrossRef]
Ferziger, J. H., and Peric, M., 2002, Computational Methods for Fluid Dynamics, 3rd ed., Springer-Verlag, Berlin.
Wu, J. Z., and Wu, J. M., 1993, “Interactions Between a Solid Surface and a Viscous Compressible Flow Field,” J. Fluid Mech., 254, pp. 183–211. [CrossRef]
Wu, J. Z., Wu, X. H., and Wu, J. M., 1993, “Streaming Vorticity Flux From Oscillating Walls With Finite Amplitude,” Phys. Fluids, 5(8), pp. 1933–1938. [CrossRef]
Matlab, 2011, version 7.13.0.564 (R2011b), The MathWorks Inc., Natick, MA.
Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., Coleman, H., and Raad, P. E., 2008, “Procedure for Estimation and Reporting of Uncertainty due to Discretization in CFD Applications,” ASME J. Fluids Eng., 130(7), p. 078001. [CrossRef]
Wu, J. Z., and Wu, J. M., 1996, “Vorticity Dynamics on Boundaries,” Advances in Applied Mechanics, J. W.Hutchinson, and T. Y.Wu, eds., Academic Press, San Diego, CA, pp. 119–275.

Figures

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Fig. 1

Schematic view of the arc airfoil in equilibrium position and its deforming motion with time; angle of attack α, chord length C, camber mC, global coordinates XY, and local coordinates xy are shown. The origin of the local reference frame is positioned at (X0, Y0).

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Fig. 2

Grid refinement effect on instantaneous u-component of velocity at streamwise locations X/C = 0.2 (intersecting the boundary layer) and X/C = 0.8 (near the wake) for Re = 10,000 and α = 2  deg at t = 5 s

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Fig. 3

Time-averaged lift and drag coefficients of the stationary arc airfoil are compared with the experimental data of Ref. [22]; the experimental data are for cambers of 0.09C and 0.12C with Re = 7600; computations are for 0.10C and Re = 10,000

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Fig. 4

Vorticity flux determined from vorticity gradient is compared with the tangential pressure gradient (Pa/m) for the stationary airfoil

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Fig. 5

Local tangential acceleration (m/s2) of the oscillating airfoil surface at selected times

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Fig. 6

Vorticity flux determined from vorticity gradient is compared with the combined effect of tangential pressure gradient and tangential wall acceleration for the oscillating airfoil; the ordinate is in Pa/m

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Fig. 7

Pressure and vorticity distribution for flow over the stationary airfoil for α = 0 deg (left) and α = 2 deg (right)

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Fig. 8

Vorticity contours and the corresponding velocity vectors; from top to bottom, first and second rows: stationary airfoil, α = 0 deg,m = 0.1,Re = 10,000; third and fourth rows: oscillating airfoil, α = 10 deg,f = 40,A = 0.1,m = 0.1,Re = 10,000

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Fig. 9

Contours of vorticity from ω = -1000 to +1000 1/s; first row from top (stationary, f = 0,A = 0): α = 0 deg, second row (stationary, f = 0,A = 0): α = 10 deg, third row (oscillating, f = 40,A = 0.1): α = 0 deg, fourth row (oscillating, f = 40,A = 0.1): α = 10 deg; time between frames in each row is 0.01 s; Re = 10,000, m = 0.1

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Fig. 10

Lift and drag coefficients: Re = 10,000,α = 10 deg,m = 0.1,f = 36.55 Hz

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Fig. 11

Frequency response of the lift coefficient to airfoil oscillations at Re = 10,000 and α = 0 deg (upper graph) and α = 10 deg (lower graph)

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