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Theoretical Modeling of Unsteady Aerodynamic Loads on Plunging Airfoils in a Subsonic Compressible Flow

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The aerodynamic loads on a plunging flat plate are computed using Mathieu functions for different subsonic compressible Mach numbers and large range of reduced frequency (0-15). The obtained theoretical results are validated against previous theoretical results and simulations of the unsteady inviscid flow. The theoretical aerodynamic loads showed a good agreement to the CFD simulations. Results indicate that for small frequencies, the compressibility effect on the compressible aerodynamic loads is imperceptible. For high oscillation frequencies, the total lift phase approaches zero, in contrast to the behavior of the incompressible fluids. For a constant free stream velocity, the number of the dipole sources, distributed along the plate surface, increases as the reduced frequency K increases. The compressible circulatory and non-circulatory frequency response functions are presented. The high frequency gain K_hf of the circulatory lift frequency response function decreases as the Mach number increases. The non-circulatory lift transfer function magnitude decreases as Mach number increases. Fluid compressibility induces a phase lag between the noncirculatory lift and the fluid motion. Finally, the reduced frequency has an insignificant effect on the non-circulatory transfer function phase lag at high K values.

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