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Dynamic Thin-Airfoil Stall and Leading-Edge Stall of Oscillating Wings at Low Reynolds Number

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Abstract

This paper investigates the unsteady aerodynamic characteristics of an oscillating flat plate and the NACA 0012 airfoil around the angle of attack (AoA) close to their static stall angle at a low Reynolds number, 3.2 × 104. The kinematic oscillatory motion is described by a sinusoidal function in which the oscillation frequency and amplitude are variable. Both experimental and numerical methods are applied in the two-dimensional space. The experiment aims at measuring the aerodynamic forces and the moment directly. For numerical simulation, the SST (Shear Stress Transport) gamma theta model is employed to solve the unsteady flow field and to compute the lift coefficients (CLs). Good qualitative agreement between the experimental and numerical results for CL is obtained, which demonstrates the feasibility of the modified RANS model in the flow transition case. In general, NACA 0012 is greatly influenced by the dynamic effect in contrast with the flat plate. For a given reduced frequency, the shape of the hysteresis loop of CL shows some distinguishing features; the process of flow reattachment of NACA 0012 is slower than that of the flat plate in the downstroke phase, so that a smooth transition of CL is observed; there are still vortices shedding from the trailing edge even at small angles of attack, which results in a local instability of CL. By studying the effects of the reduced frequency (K) and the amplitude, it is found that the AoA corresponding to the maximum CL is more sensitive to the former and the reduced pitch rate (a') is the main parameter determining the dynamic stall angle for both flat plate and NACA 0012. In addition, the results for K = 0.07 show that the lift and drag coefficients at a maximum angle of attack are close to their static values for the discussed amplitudes and wing geometries.

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Abbreviations

a :

pivot point

c :

chord, m.

K :

reduced frequency, ωc/2U.

U :

mean wind tunnel velocity, ms−1

s :

span of the wing geometry, m

t :

blade thickness, m

α:

angle of attack, deg

ά:

reduced pitch rate, deg

α0 :

mean angle of attack, deg

α1 :

oscillation amplitude, deg

αmax :

maximum angle of attack, deg

αmaxCL :

angle of attack corresponding to the maximum lift coefficient

ω :

oscillation frequency, Hz

t :

physical time, s

τ:

dimensionless time, tc/2U.

AoA:

angle of attack, deg

AR:

aspect ratio

CL:

aerodynamic lift coefficient

CD:

aerodynamic drag coefficient

CM:

aerodynamic moment coefficient

LEV:

leading-edge vortex

Re:

Reynolds number

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Acknowledments

The first author thanks Prof. Xavier Amandolese for his guidance on unsteady aerodynamics during the internship in France.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Chengwei Fan, Yadong Wu & Anjenq Wang

  2. Gas Turbine Research Institute/School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yuelong Yu

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  1. Chengwei Fan
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  2. Yadong Wu
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  3. Yuelong Yu
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Correspondence to Yadong Wu.

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The Authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 5, pp. 102–116.

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Fan, C., Wu, Y., Yu, Y. et al. Dynamic Thin-Airfoil Stall and Leading-Edge Stall of Oscillating Wings at Low Reynolds Number. Fluid Dyn 54, 691–704 (2019). https://doi.org/10.1134/S0015462819040128

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  • DOI: https://doi.org/10.1134/S0015462819040128

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