It is well established that natural flyers flap their wings to sustain flight due to poorperformance of steady wing aerodynamics at low Reynolds number. Natural flyers also benefitfrom the propulsive force generated by flapping. Unsteady airfoils allow for simplified study offlapping wing aerodynamics. Limited previous work has suggested that both the Reynoldsnumber and motion trajectory asymmetry play a non-negligible role in the resulting forces andwake structure of an oscillating airfoil. In this work, computations are performed to on this topicfor a NACA 0012 airfoil purely pitching about its quarter-chord point.Two-dimensional computations are undertaken using the high-order, extensivelyvalidated FDL3DI Navier-Strokes solver developed at Wright-Patterson Air Force Base. TheReynolds number range of this study is 2,000-22,000, reduced frequencies as high as 16 areconsidered, and the pitching amplitude varies from 2° to 10°. In order to simulate theincompressible limit with the current compressible solver, freestream Mach numbers as low as0.005 are used. The wake structure is accurately resolved using an overset grid approach.The results show that the streamwise force depends on Reynolds number such that thedrag-to-thrust crossover reduced frequency decreases with increasing Reynolds number at agiven amplitude. As the amplitude increases, the crossover reduced frequency decreases at agiven Reynolds number. The crossover frequency data show good collapse for all pitchingamplitudes considered when expressed as the Strouhal number based on trailing edge-amplitudefor different Reynolds numbers. Appropriate scaling causes the thrust data to become nearlyindependent of Reynolds number and amplitude. An increase in propulsive efficiency isobserved as the Reynolds number increases while less dependence is seen in the peak-to-peak liftand drag amplitudes.Reynolds number dependence is also seen for the wake structure. The crossover reducedfrequency to produce a switch in the wake vortex configuration from von Kármán (drag) toreverse von Kármán (thrust) patterns decreases as the Reynolds number increases. As thepitching amplitude increases, more complex structures form in the wake, particularly at thehigher Reynolds numbers considered. Although both the transverse and streamwise spacingdepend on amplitude, the vortex array aspect ratio is nearly amplitude independent for eachReynolds number.Motion trajectory asymmetry produces a non-zero average lift and a decrease in averagedrag. Decomposition of the lift demonstrates that the majority of the average lift is a result of thecomponent from average vortex (circulatory) lift. The average lift is positive at low reducedfrequency, but as the reduced frequency increases at a given motion asymmetry, an increasingamount of negative lift occurs over a greater portion of the oscillation cycle, and eventuallycauses a switch in the sign of the lift. The maximum value, minimum value, and peak-to-peakamplitude of the lift and drag increase with increasing reduced frequency and asymmetry.The wake structure becomes complex with an asymmetric motion trajectory. A fasterpitch-up produces a single positive vortex and one or more negative vortices, the number ofwhich depends on the reduced frequency and asymmetry. When the airfoil motion trajectory isasymmetric, the vortex trajectories and properties in the wake exhibit asymmetric behavior.
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