American Institute of Aeronautics and Astronautics
1
Fluid Dynamic Forces on Plunging Spanwise-Flexible
Elliptical Flat Plates at Low Reynolds Numbers
Jonathan M. Rausch
1
, Luis P. Bernal
2
, Carlos S. Cesnik
3
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109
,
Wei Shyy
4
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109
,
Department of Mechanical Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong
and Lawrence Ukeiley
5
Department of Mechanical and Aerospace Engineering, University of Florida, Shalimar, FL, 32579
We consider the aerodynamic performance of flexible isotropic elliptical wings
undergoing periodic plunge motions. Experiments were conducted in the Low Turbulence
Water Channel at the University of Michigan using a pitch-plunge apparatus. Experimental
results include dye flow visualization, laser Doppler vibrometer (LDV) wing deformation
measurements, particle image velocimetry (PIV) flowfield quantification, and direct force
measurements establishing a novel experimental framework for investigating pitching-
plunging and flapping flexible wings. This investigation focuses on the effect of wing stiffness
parameter,
, defined as the ratio of elastic to fluid dynamic forces. A parameter sweep is
performed that spans four orders of magnitude from order 10
1
to 10
4
. The
-parameter is
varied by changing the plate thickness and material properties. The effects of structural
density to fluid density, �, and the thickness to chord ratio,
�
, are shown to be small. The
wings have elliptical planform with aspect ratio 6.1. Sinusoidal plunging kinematics are used
in forward fight at a low Reynolds number (5,300) with a neutral mean effective angle of
attack. The plunging motion has large reduced frequency (1.82) and modest chord-
normalized plunge amplitude (0.175). Deformation measurements show that for the present
conditions the wings bend without twisting. PIV measurements at the 50%- and 75%-
spanwise locations show that large deflections at the wing tip result in a stronger outboard
leading edge vortex due to the increased effective angle of attack for increased flexibility.
The force measurements proved that the prescribed parametric configuration is not thrust
producing due to small wing cross-sectional thickness, motion kinematics, and lack of
aerodynamic-twist. The lift (normal) force coefficient for moderate wing stiffness parameter
(Π
1
of order 10
2
I. Nomenclature
) is larger compared to the rigid wing results. The most flexible wing
produced a lift coefficient history below the rigid wing and lags the rigid wing phase. For the
rigid cases the force measurements show good agreement with quasi-steady two-dimensional
potential flow theory, suggesting that for the present conditions tip vortex effects are small.
aspect ratio [1]
1
Graduate Research Assistant, Department of Aerospace Engineering, AIAA Student Member,
rauschjm@umich.edu
2
Associate Professor, AIAA Member, lpb@umich.edu.
3
Professor, Department of Aerospace Engineering, University of Michigan, AIAA Associate Fellow
4
Professor Clarence L. "Kelly" Johnson Collegiate Professor, Department of Aerospace Engineering, University of
Michigan; currently, Provost & Chair Professor, Department of Mechanical Engineering, Hong Kong University of
Science and Technology, AIAA Fellow, AIAA Fellow
5
Assistant Professor, AIAA Associate Fellow
41st AIAA Fluid Dynamics Conference and Exhibit
27 - 30 June 2011, Honolulu, Hawaii
AIAA 2011-3435
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.