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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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. 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. 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. 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. 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. 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. 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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