Low Reynolds number aerodynamics has become of interest in conjunction with the emergence of micro air vehicles. Often, the flight of such vehicles experiences an unsteady condition such as flapping, pitching, and yawing. At low Reynolds number, the Karman vortex is formed in the near wake of an airfoil and shed downstream when the angle of attack is small.
In this paper, through an experimental study, we investigate how the shedding frequency changes with the pitching motion of an airfoil. As the vortex shedding is directly influenced by the boundary layer developed over the airfoil surface, both quantitative and qualitative examination of the unsteady nature of the boundary layer is also carried out.
A NACA 0012 airfoil is given the harmonic pitching motion about one-quarter chord axis at reduced frequencies between 0.1 and 0.4. The mean incidence is set to 0˚ and the amplitude of oscillation is varied up to 3˚. The Reynolds number based on the chord length is 27,000. Smoke-wire technique and hot-wire anemometry are employed for the flow visualization and the velocity measurements, respectively. The frequency characteristic of the wake has to be deduced based on very short data segments. The time-varying frequency characteristic is then tracked by examining the variations in spectral estimates from segment to segment. For the spectral estimation of each segment, a short-time autoregressive (AR) method is applied. When only small number of samples are available because of the unsteady nature of the flow, the autoregressive method is more useful and reliable than the Fast Fourier transform (FFT) method for spectral analysis, because its resolution is higher than the FFT method.
For the case of steady airfoil, it is well known that the onset location of separation and the boundary-layer thickness at the trailing edge are proportional to the angle of attack and the Karman vortex shedding frequency decreases with the angle of attack. However, for an oscillating airfoil, these tendencies no longer hold. Even if the instantaneous angle of attack decreases from the maximum angle of attack, the onset location of separation moves continuously toward the leading edge on the upper surface and the shedding frequency continues to decrease. For example, for the case of K=0.2, the minimum shedding frequency is obtained at ωt=150˚ (α=1.5˚, pitch-down stroke). The shedding frequency of an oscillating airfoil (K=0.2) with 3˚ amplitude is found to vary from 130Hz to 160Hz whereas the shedding frequency of a steady airfoil varies from 160Hz and 100Hz as the angle of attack is changed from 0˚ to 3˚. It is found that the range of the shedding frequency variation decreases as the reduced frequency of airfoil oscillation increases.
