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The effect of phase angle and wing spacing on tandem flapping wings

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Abstract

In a tandem wing configuration, the hindwing often operates in the wake of the forewing and, hence, its performance is affected by the vortices shed by the forewing. Changes in the phase angle between the flapping motions of the fore and the hind wings, as well as the spacing between them, can affect the resulting vortex/wing and vortex/vortex interactions. This study uses 2D numerical simulations to investigate how these changes affect the leading dege vortexes (LEV) generated by the hindwing and the resulting effect on the lift and thrust coefficients as well as the efficiencies. The tandem wing configuration was simulated using an incompressible Navier-Stokes solver at a chord-based Reynolds number of 5 000. A harmonic single frequency sinusoidal oscillation consisting of a combined pitch and plunge motion was used for the flapping wing kinematics at a Strouhal number of 0.3. Four different spacings ranging from 0.1 chords to 1 chord were tested at three different phase angles, 0°, 90° and 180°. It was found that changes in the spacing and phase angle affected the timing of the interaction between the vortex shed from the forewing and the hindwing. Such an interaction affects the LEV formation on the hindwing and results in changes in aerodynamic force production and efficiencies of the hindwing. It is also observed that changing the phase angle has a similar effect as changing the spacing. The results further show that at different spacings the peak force generation occurs at different phase angles, as do the peak efficiencies.

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Abbreviations

A :

Planform area with unit depth

C L :

Lift coefficient

C P :

Power coefficient

C R :

Resultant coefficient

C T :

Thrust coefficient

f :

Flapping frequency

h 0 :

Plunging amplitude

h(t):

Plunging displacement

L :

Instantaneous lift force

M :

Instantaneous pitching moment

p :

Pressure

t :

Time

T :

Flapping period

u :

Flow velocity

k :

Reduced frequency

St :

Strouhal number

V :

Instantaneous plunge velocity

αave :

Average angle of attack

α0 :

Pitching amplitude

α(t):

Pitching angle

ηL :

Lift efficiency

ηP :

Propulsive efficiency

ν :

Kinematic viscosity

ρ :

Fluid density

φ α :

Pitching phase lag

φ h :

Plunging phase lag

Ψ :

Phase angle

ω :

Instantaneous rotational velocity

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Louisville, Louisville, KY, 40292, USA

    Timothy M. Broering & Yong-Sheng Lian

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  1. Timothy M. Broering
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  2. Yong-Sheng Lian
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Correspondence to Yong-Sheng Lian.

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Broering, T.M., Lian, YS. The effect of phase angle and wing spacing on tandem flapping wings. Acta Mech Sin 28, 1557–1571 (2012). https://doi.org/10.1007/s10409-012-0210-8

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  • DOI: https://doi.org/10.1007/s10409-012-0210-8

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