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Research Papers: Fundamental Issues and Canonical Flows

Shear Layer Development, Separation, and Stability Over a Low-Reynolds Number Airfoil

[+] Author and Article Information
Paul Ziadé

Department of Mechanical
& Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: paul.ziade@ucalgary.ca

Mark A. Feero

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: m.feero@mail.utoronto.ca

Philippe Lavoie

Institute for Aerospace Studies,
University of Toronto,
Toronto, ON M5S 1A4, Canada
e-mail: lavoie@utias.utoronto.ca

Pierre E. Sullivan

Professor
Department of Mechanical
& Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada
e-mail: sullivan@mie.utoronto.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 23, 2017; final manuscript received January 5, 2018; published online March 13, 2018. Assoc. Editor: Hui Hu.

J. Fluids Eng 140(7), 071201 (Mar 13, 2018) (12 pages) Paper No: FE-17-1526; doi: 10.1115/1.4039233 History: Received August 23, 2017; Revised January 05, 2018

The shear layer development for a NACA 0025 airfoil at a low Reynolds number was investigated experimentally and numerically using large eddy simulation (LES). Two angles of attack (AOAs) were considered: 5 deg and 12 deg. Experiments and numerics confirm that two flow regimes are present. The first regime, present for an angle-of-attack of 5 deg, exhibits boundary layer reattachment with formation of a laminar separation bubble. The second regime consists of boundary layer separation without reattachment. Linear stability analysis (LSA) of mean velocity profiles is shown to provide adequate agreement between measured and computed growth rates. The stability equations exhibit significant sensitivity to variations in the base flow. This highlights that caution must be applied when experimental or computational uncertainties are present, particularly when performing comparisons. LSA suggests that the first regime is characterized by high frequency instabilities with low spatial growth, whereas the second regime experiences low frequency instabilities with more rapid growth. Spectral analysis confirms the dominance of a central frequency in the laminar separation region of the shear layer, and the importance of nonlinear interactions with harmonics in the transition process.

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Figures

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Fig. 1

Schematic of the experimental setup including the airfoil model and boundary layer traverse (wind tunnel test section not shown)

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Fig. 2

Definition of global and local coordinate systems

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Fig. 3

Airfoil geometry and mesh

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Fig. 4

Near-wall mesh near the leading edge

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Fig. 5

Comparison of pressure coefficient on the upper airfoil surface for AOA = 5 deg between different grids

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Fig. 6

Near-wall mesh spacing in wall units for AOA = 5 deg

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Fig. 7

Kinetic energy ratio, γ, at several locations for AOA = 5 deg

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Fig. 8

Q = 2500 s−2 isosurface contours—(a) AOA = 5 deg and (b) AOA = 12 deg

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Fig. 9

Vortex roll-up at the edge of the shear layer followed by break-down to three-dimensional turbulence. Q = 2500 s−2, AOA = 5 deg.

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Fig. 10

Coefficient of pressure on the airfoil upper surface: (a) AOA = 5 deg and (b) AOA = 12 deg

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Fig. 11

Mean velocity magnitude at midspan for AOA = 5 deg: (a) LES and (b) PIV

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Fig. 12

Mean velocity magnitude at midspan for AOA = 12 deg: (a) LES and (b) PIV

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Fig. 13

Boundary layer profiles. Circles: experiment, solid line: tanh curvefit, dash-dot line: LES—(a) AOA = 5 deg, x′/c=0.35 and (b) AOA = 12 deg, x′/c=0.20.

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Fig. 14

Tangential and wall-normal velocity profiles at x′/c=20% and AOA = 12 deg. Filled markers—PIV and open markers—HW.

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Fig. 15

Solid line: Experimental BL, dash-dot line: LES BL, and circles: measured growth rate. (a) AOA = 5 deg and (b) AOA = 12 deg.

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Fig. 19

Velocity spectra at y′=δ* in the separated shear layer. Dashed and dash-dot lines indicate the peak frequencies determined from the LSA and measured growth rates, respectively: (a) AOA = 5 deg-experiment, (b) AOA = 5 deg-LES, (c) AOA = 12 deg-experiment, and (d) AOA = 12 deg-LES.

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Fig. 18

RMS velocity evolution downstream of separation for (○) AOA = 5 deg and () AOA = 12 deg. Filled markers—LES, open markers—experiments.

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Fig. 17

Standard deviation of peak growth rate. Base flows obtained from perturbations resulting in a set of velocity profiles with a standard deviation of 1% of the nominal shape factor.

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Fig. 16

Growth rate spectra due to base flow deviations

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