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On the unsteady motion and stability of a heaving airfoil in ground effect

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Abstract

This study explores the fluid mechanics and force generation capabilities of an inverted heaving airfoil placed close to a moving ground using a URANS solver with the Spalart-Allmaras turbulence model. By varying the mean ground clearance and motion frequency of the airfoil, it was possible to construct a frequency-height diagram of the various forces acting on the airfoil. The ground was found to enhance the downforce and reduce the drag with respect to freestream. The unsteady motion induces hysteresis in the forces’ behaviour. At moderate ground clearance, the hysteresis increases with frequency and the airfoil loses energy to the flow, resulting in a stabilizingmotion. By analogy with a pitching motion, the airfoil stalls in close proximity to the ground. At low frequencies, the motion is unstable and could lead to stall flutter. A stall flutter analysis was undertaken. At higher frequencies, inviscid effects overcome the large separation and the motion becomes stable. Forced trailing edge vortex shedding appears at high frequencies. The shedding mechanism seems to be independent of ground proximity. However, the wake is altered at low heights as a result of an interaction between the vortices and the ground.

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Abbreviations

a :

heaving amplitude

c :

airfoil chord

C D :

drag coefficient

C L :

downforce coefficient

h :

airfoil ride height

ĥ :

non-dimensional airfoil displacement, 2(h − h 0)/a

h 0 :

mean ride height

f :

heaving frequency

k :

reduced frequency, πf c/U ∞

L :

downforce

Ma :

Mach number

Re :

Reynolds number based on wing chord c, ρU ∞ c/µ

T :

heaving period, f −1

t :

time

U ∞ :

freestream velocity

W :

work done by the fluid on the airfoil

x, y :

cartesian coordinates, x positive downstream, y positive up

y + :

non-dimensional normal wall distance

α :

airfoil incidence

ν :

kinematic viscosity

νT :

turbulent viscosity

ρ :

density

τ :

non-dimensional time, t/T

ω :

vorticity, ∂v/∂x− ∂u/∂y

ξ:

aerodynamic damping

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Authors and Affiliations

  1. School of Engineering Sciences, University of Southampton, Southampton, SO17 1BJ, UK

    Juan Molina, Xin Zhang & David Angland

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  1. Juan Molina
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  2. Xin Zhang
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  3. David Angland
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Correspondence to Xin Zhang.

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Molina, J., Zhang, X. & Angland, D. On the unsteady motion and stability of a heaving airfoil in ground effect. Acta Mech Sin 27, 164–178 (2011). https://doi.org/10.1007/s10409-011-0445-9

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  • DOI: https://doi.org/10.1007/s10409-011-0445-9

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