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The effects of a periodic free-stream velocity on the unsteady aerodynamics of an airfoil in incompressible flow are examined. Existing theories are reviewed, and their simplifications and limitations are properly identified. A new general aerodynamic theory for an airfoil undergoing a combination of harmonic pitching, plunging and fore-aft motion is presented. An extension to arbitrary free-stream velocity variations and arbitrary airfoil motion is also given. The theoretical results are validated against numerical predictions made by a modern Euler code.
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Wall et al. (1994) studied this question.
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