Harmonically pitching airfoil in a periodic streamwise superimposed flow

The unsteady lift of a NACA (National Advisory Committee for Aeronautics) 0015 airfoil with harmonic pitching frequency fα encountering periodic streamwise superimposed flow is investigated via a wind tunnel test. An extended method for predicting the unsteady lift characteristics of a pitching airfoil under incoming flow superimposed of various sinusoidal flow with multiple frequencies fu is presented and experimentally verified. The spectral result of the experiment confirms the existence of the sum frequency fα+fu and the difference frequency |fα−fu|, indicating that the pitch motion frequency and the sinusoidal flow frequency interact as Greenberg's theory. The amplitude and phase of unsteady lift in the frequency of pitching motion would not change with the change of sinusoidal streamwise flow. In the situation of periodic superimposed flow, it is seen that the sinusoidal inflow components of various frequencies do not interact with the pitching frequency together. This means that there were neither |fα−fu1−fu2| nor fα+fu1+fu2 present in an incoming flow superimposed of two sinusoidal flow with different frequencies, fu1 and fu2. The results of all cases indicate that the amplitude and phase of a frequency combined of pitching frequency and fu1 or fu2 in a periodic superimposed flow are the same as those of corresponding frequency in a sinusoidal streamwise flow under the condition of small disturbance. The Fourier amplitude spectra further corroborate this result by showing that superposition can be used to estimate the unsteady lift in the situation of periodic superimposed flow.