Computational study of the effect of Reynolds number and motion trajectory asymmetry on the aerodynamics of a pitching airfoil at low Reynolds number

It is well established that natural flyers flap their wings to sustain flight due to poor performance of steady wing aerodynamics at low Reynolds number. Natural flyers also benefit from the propulsive force generated by flapping. Unsteady airfoils allow for simplified study of flapping wing aerodynamics. Limited previous work has suggested that both the Reynolds number and motion trajectory asymmetry play a non-negligible role in the resulting forces and wake structure of an oscillating airfoil. In this work, computations are performed to on this topic for a NACA 0012 airfoil purely pitching about its quarter-chord point.;Two-dimensional computations are undertaken using the high-order, extensively validated FDL3DI Navier-Strokes solver developed at Wright-Patterson Air Force Base. The Reynolds number range of this study is 2,000-22,000, reduced frequencies as high as 16 are considered, and the pitching amplitude varies from 2° to 10°. In order to simulate the incompressible limit with the current compressible solver, freestream Mach numbers as low as 0.005 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 the drag-to-thrust crossover reduced frequency decreases with increasing Reynolds number at a given amplitude. As the amplitude increases, the crossover reduced frequency decreases at a given Reynolds number. The crossover frequency data show good collapse for all pitching amplitudes considered when expressed as the Strouhal number based on trailing edge-amplitude for different Reynolds numbers. Appropriate scaling causes the thrust data to become nearly independent of Reynolds number and amplitude. An increase in propulsive efficiency is observed as the Reynolds number increases while less dependence is seen in the peak-to-peak lift and drag amplitudes.;Reynolds number dependence is also seen for the wake structure. The crossover reduced frequency to produce a switch in the wake vortex configuration from von Karman (drag) to reverse von Karman (thrust) patterns decreases as the Reynolds number increases. As the pitching amplitude increases, more complex structures form in the wake, particularly at the higher Reynolds numbers considered. Although both the transverse and streamwise spacing depend on amplitude, the vortex array aspect ratio is nearly amplitude independent for each Reynolds number.;Motion trajectory asymmetry produces a non-zero average lift and a decrease in average drag. Decomposition of the lift demonstrates that the majority of the average lift is a result of the component from average vortex (circulatory) lift. The average lift is positive at low reduced frequency, but as the reduced frequency increases at a given motion asymmetry, an increasing amount of negative lift occurs over a greater portion of the oscillation cycle, and eventually causes a switch in the sign of the lift. The maximum value, minimum value, and peak-to-peak amplitude of the lift and drag increase with increasing reduced frequency and asymmetry.;The wake structure becomes complex with an asymmetric motion trajectory. A faster pitch-up produces a single positive vortex and one or more negative vortices, the number of which depends on the reduced frequency and asymmetry. When the airfoil motion trajectory is asymmetric, the vortex trajectories and properties in the wake exhibit asymmetric behavior.