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Added-mass force on elliptic airfoils

Published online by Cambridge University Press:  10 September 2021

Eric J. Limacher Open the ORCID record for Eric J. Limacher [Opens in a new window]
Eric J. Limacher*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

Herein, exact algebraic expressions for the non-circulatory (added-mass) forces on elliptic airfoils are derived for any two-dimensional motion – including simultaneous rectilinear acceleration and rotation – embedded in a steady free-stream flow. Despite the lengthy history of the added-mass concept and its widespread application to cylinders of various cross-sections, such closed-form expressions for elliptic cylinders, in terms of kinematic and geometric parameters alone, have remained absent from the literature until now. Inspection of the derived equations reveals that for pure pitching about a point on the chord-line, increasing thickness always decreases the added-mass force magnitude. For any given motion of the chord-line, the difference in force between thick and thin airfoils is proportional to the square of the thickness, although this difference may be positive or negative for the general three-degree-of-freedom case. In the special case of zero thickness and small pitch angles, Theodorsen's added-mass lift force on rigid thin airfoils is recovered; for large pitch angles, an exact generalization of Theodorsen's expression, applicable to the chord-normal direction, is given.

JFM classification

Aerodynamics: Aerodynamics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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