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Unsteady aerodynamics and vortex-sheet formation of a two-dimensional airfoil

Published online by Cambridge University Press:  02 October 2017

X. Xia  and
K. Mohseni Open the ORCID record for K. Mohseni [Opens in a new window]
X. Xia
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250, USA
K. Mohseni*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250, USA Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611-6250, USA
*
†Email address for correspondence: [email protected]
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Abstract

Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modelling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical steady Kutta condition can be extended to unsteady situations by realizing that a flow cannot turn abruptly around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a finite-angle trailing edge, or in the case of flow separation away from a sharp corner, the direction of the forming vortex sheet is ambiguous. To remove any ad hoc implementation, the unsteady Kutta condition, the conservation of circulation as well as the conservation laws of mass and momentum are coupled to analytically solve for the angle, strength and relative velocity of the trailing-edge vortex sheet. The two-dimensional aerodynamic model together with the proposed vortex-sheet formation condition is verified by comparing flow structures and force calculations with experimental results for several airfoil motions in steady and unsteady background flows.

JFM classification

Aerodynamics: Aerodynamics Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 439 - 478
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Copyright
© 2017 Cambridge University Press 

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