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Research Papers

Aeroelastic Analysis of Membrane Microair Vehicles—Part II: Computational Study of a Plunging Membrane Airfoil

[+] Author and Article Information
Peter J. Attar

School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019peter.attar@ou.edu

Raymond E. Gordnier

 Air Force Research Laboratory, Wright-Patterson AFB, OH 45433-7913

Jordan W. Johnston, William A. Romberg, Ramkumar N. Parthasarathy

School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019

J. Vib. Acoust 133(2), 021009 (Mar 17, 2011) (6 pages) doi:10.1115/1.4002134 History: Received June 03, 2010; Revised June 30, 2010; Published March 17, 2011; Online March 17, 2011

In the second paper of the two part study of membrane microair vehicles, computations are performed for a plunging membrane airfoil. The computational model uses a sixth-order finite difference solution of the Navier–Stokes equations coupled to a finite element solution of a set of nonlinear string equations. The effect, on the structural and fluid response, of plunging Strouhal number, reduced frequency, and static angle of attack is examined. Qualitatively, the flow field is found to be very complex with interactions of vortices shed from various locations along the chord of the airfoil. At a low angle of attack and a low Strouhal number, increasing reduced frequency results in a decrease and an increase in the mean sectional lift and drag coefficients, respectively. Also, at a low angle of attack, increasing the Strouhal number has minimal effect at high and low values of reduced frequencies, but a significant effect is found at an intermediate value of reduced frequency. When the effect of angle of attack is studied for fixed values of Strouhal number and reduced frequency, it is found that the act of plunging gives improved mean sectional lift when compared with the case of a fixed flexible airfoil. The improvement does not increase monotonically with the angle of attack but instead is maximum at an intermediate value. Finally, increasing the value of the membrane prestrain, which stiffens the airfoil, results in a reduced value of the sectional lift coefficient for a given Strouhal number, reduced frequency, and angle of attack.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Membrane wing geometry of Rojratsirikul (17)

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Figure 2

Sectional lift coefficient versus plunging reduced frequency for St=0.2 and 0.5 at an angle of attack of 2 deg

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Figure 3

Sectional drag coefficient versus plunging reduced frequency for St=0.2 and 0.5 at an angle of attack of 2 deg

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Figure 4

Distribution of membrane airfoil mean z position (normalized by chord)

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Figure 5

Distribution of membrane airfoil mean z force per unit span

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Figure 6

Phase-averaged contours of y vorticity at eight points in plunging cycle; St=0.2; k=1.5

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Figure 7

Phase-averaged contours of y vorticity at eight points in plunging cycle; St=0.5; k=1.5

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Figure 8

Sectional lift coefficient versus normalized (by plunging period) time for St=0.2 and St=0.5

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Figure 9

Sectional lift coefficient response reduced frequency spectrum for St=0.2 and St=0.5

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Figure 10

Instantaneous contours of y vorticity for St=0.2 and St=0.5

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Figure 11

Phase-averaged pressure coefficient distributions for the angles of attack of 2 deg, 6 deg, and 10 deg

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Figure 12

Phase-averaged y vorticity distribution at t/T=0 for α=6 deg and α=10 deg

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Figure 13

Instantaneous y vorticity contours at nine points during plunging cycle for airfoil at fixed α=10 deg

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Figure 14

Time-averaged z position versus chord normalized x position along the flexible airfoil for 5% and 20% prestrain values

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Figure 15

Time-averaged z force per unit span versus chord normalized x position along the flexible airfoil for 5% and 20% prestrain values

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Figure 16

Contour of phase-averaged y vorticity at the point t/T=0 in the plunging cycle for the 20% prestrain model

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