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Research Papers: Fundamental Issues and Canonical Flows

Vortex Dynamics and Shedding of a Low Aspect Ratio, Flat Wing at Low Reynolds Numbers and High Angles of Attack

[+] Author and Article Information
Daniel R. Morse, James A. Liburdy

Mechanical Engineering, Oregon State University, Corvallis, OR 9733

J. Fluids Eng 131(5), 051202 (Apr 14, 2009) (12 pages) doi:10.1115/1.3112385 History: Received April 16, 2008; Revised January 26, 2009; Published April 14, 2009

This study focuses on the detection and characterization of vortices in low Reynolds number separated flow over the elliptical leading edge of a low aspect ratio, flat plate wing. Velocity fields were obtained using the time-resolved particle image velocimetry. Experiments were performed on a wing with aspect ratio of 0.5 for velocities of 1.1 m/s, 2.0 m/s, and 5.0 m/s corresponding to chord length Reynolds numbers of 1.47×104, 2.67×104, and 6.67×104, respectively, and angles of attack of 14 deg, 16 deg, 18 deg, and 20 deg. A local swirl calculation was used on proper orthogonal decomposition filtered data for vortex identification and corresponding vortex centers were tracked to determine convective velocities. The swirl function was also analyzed for its temporal frequency response at several discrete points in both the shear layer and in the separated recirculation region. A peak frequency was detected in the shear layer with a corresponding Strouhal number of approximately 3.4 based on the flow direction projected length scale. The Strouhal number increases with both angle of attack and Reynolds number. The shear layer convective length scale, based on the vortex convection velocity, is found to be consistent with the mean separation distance between vortices within the shear layer. This length scale decreases with increasing Rec.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 2

Flow visualization of leading edge Kelvin–Helmholtz instability rollup forming spanwise vortices, Rec=1.47×104, α=20 deg.

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Figure 3

Downstream view (looking upstream) of a low aspect ratio wing using smoke wire visualization for Rec=1.47×104, α=20 deg. The wing outline is highlighted in bold and the separated flow region is outlined with a dashed line. Streamwise tip vortices are shown with smoke lines curving toward the center and leading edge instabilities are observed to disrupt the smoke lines along the centerline increasing smoke diffusion.

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Figure 6

The POD distribution of energy across modes and angles of attack for (a) Rec=1.47×104, (b) Rec=2.67×104, and (c) Rec=6.67×104

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Figure 8

(a) Time trace of Γ∗′ at x/c=0.1 and y/c=0.025 for the first 200 of 2000 total milliseconds of data for the α=14 deg, Rec=1.47×104 case. (b) Corresponding autocorrelation of Γ∗′ shown for time lag values up to 100 ms. (c) Corresponding spectrum of Γ∗′ shown with observed peak near Sth=2.4.

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Figure 9

(a) rms value of Γ∗, σ(Γ∗), for the Rec=1.47×104, α=20 deg case. The solid white line identifies the region of highest amplitude. (b) rms value of the temporal autocorrelation of Γ∗, σ(ρΓ∗). The two areas outlined with dashed lines represent regions of large amplitude cyclic activity of Γ∗.

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Figure 10

Average spectral results using four points in the high cyclic shear region shown in Fig. 9 for Rec=1.47×104, α=20 deg. TR PIV data at 500 Hz over 2 s: (a) averaged spectrum of v′, (b) averaged spectrum of u′, (c) averaged spectrum of Γ∗, and (d) hot wire data spectrum for a single point in the shear region using data at 10 kHz for 10 s.

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Figure 12

Average spectra of Γ∗′ for α=20 deg using TR PIV data at 500 Hz for 2 s of data obtained from (a) the high cyclic shear region shown in Fig. 1 for Rec=1.47×104, (b) the high cyclic shear region shown in Fig. 1 for Rec=2.67×104, (c) the recirculation region shown in Fig. 1 for Rec=1.47×104, and (d) the recirculation region shown in Fig. 1 for Rec=2.67×104

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Figure 13

Average Strouhal number versus angle of attack for the high frequency component determined in the shear region

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Figure 1

Mean flow PIV data obtained at the wing centerline. Streamlines illustrate the extent of the separated region. The light gray region represents an area of no data below the wing. An approximation of the wing contour is shown with a dotted line.

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Figure 4

TR PIV vector field for Rec=1.47×104 at four angles of attack: (a) 14 deg, (b) 16 deg, (c) 18 deg, and (d) 20 deg; grayscale plots of Γ∗ are shown in (e)–(h), which were calculated from the velocity fields in (a)–(d).

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Figure 5

Time sequence of (a)–(e) Γ∗=−0.70 contours and TR PIV vectors for Rec=1.47×104 and α=14 deg from t=64 ms to t=72 ms; (f)–(j) corresponding isolated contours of Γ∗ shown over a larger field of view with vortex center x-position plotted above each contour.

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Figure 7

Detected vortex positions shown for the first 200 ms of a total of 2000 ms with and without filtering. Unfiltered detected vortex positions for Γ∗=−0.70 at =14 deg and (a) Rec=1.47×104, (b) Rec=2.67×104, and (c) Rec=6.67×104. POD reconstructed detected vortex positions filtered for path lifetime greater than 0.05τc for (d) Rec=1.47×104, (e) Rec=2.67×104, and (f) Rec=6.67×104 at α=14 deg.

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Figure 11

Average spectra of selected points in the recirculation region for Rec=1.47×104 and α=20 deg. (a) TR PIV data of v′ at 500 Hz for 2 s, (b) TR PIV data of Γ∗′ at 500 Hz for 2 s, (c) hot wire spectrum of v′ at 10 kHZ for 10 s, and (d) TR PIV data of Γ∗′ at 100 Hz for 10 s.

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