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The ultra-low Reynolds number airfoil wake

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Abstract

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re c ), 5.3 × 103–5.1 × 104, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re c . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re c  ≥ 1.05 × 104 but is absent at Re c  = 5.3 × 103. The observation is connected to the presence of the separation bubble at high Re c but absence of the bubble at ultra-low Re c , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re c .

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Abbreviations

c :

Chord length of airfoil

C L :

Time-averaged lift coefficient

f n :

Natural frequency of the airfoil-fluid system

f v :

Vortex shedding frequency

h b :

Wake bubble width

K–H:

Kelvin–Helmholtz

L f :

Vortex formation length

P b :

Base pressure

Re c :

Chord Reynolds number, \( \rho U_{\infty } c/\mu \)

St :

Strouhal number, f v c/U ∞

U ∞ :

Free-stream velocity

x, y, z:

Cartesian coordinates

\( \overline{U}_{\text{s}} \) :

Mean velocity at boundary layer separation

\( d^{\prime} \) :

Wake width

\( \overline{U} \) :

Mean streamwise (x-component) velocity

\( \overline{V} \) :

Mean cross-stream (y-component) velocity

\( u_{\text{rms}} \) :

Root-mean-square value of streamwise velocity

\( v_{\text{rms}} \) :

Root-mean-square value of cross-stream velocity

(#)* :

Normalized by c and/or U ∞

(#)max :

Maximum value

(#)min :

Minimum value

α:

Angle of attack

μ:

Viscosity of fluid

ω:

Instantaneous vorticity

\( \overline{\omega } \) :

Mean vorticity

ρ:

Density of fluid

λK–H :

Wavelength of K–H vortices

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Acknowledgments

The work described in this paper was supported by a grant from The Hong Kong Polytechnic University (Project No. G-YD83). YZ wishes to acknowledge support given to him from Research Grants Council of Hong Kong Special Administrative Region through grant PolyU 5334/06E.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Md. Mahbub Alam & Y. Zhou

  2. Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    H. X. Yang

  3. School of Aeronautical Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, China

    H. Guo

  4. College of Engineering, Peking University, Beijing, China

    J. Mi

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  1. Md. Mahbub Alam
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Correspondence to Y. Zhou.

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Alam, M.M., Zhou, Y., Yang, H.X. et al. The ultra-low Reynolds number airfoil wake. Exp Fluids 48, 81–103 (2010). https://doi.org/10.1007/s00348-009-0713-7

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