Abstract
Our objective is to develop scaling laws for the thrust and lift coefficients of a pitching wing in a periodic freestream by extending the conventional scaling laws presented in our previous study to account for the variations in the frequency ratio. The periodic freestream is spatially uniform and temporally oscillated in the mainstream direction. We derived scaling laws by considering the added mass and circulatory forces, and experimentally validated them at frequency ratios of 1, 2, and 3 and phase differences of 0-2$\pi$. The results showed that the proposed scaling laws agree well with the experimental data under the present conditions. Our scaling laws indicated that as the frequency ratio increases, the thrust coefficient increases and is independent of the phase difference. At a frequency ratio of 1, the lift coefficient depends on the phase difference, whereas at frequency ratios of 2 and 3, it is independent of the phase difference. Furthermore, using our scaling laws as a guide, we propose the method for streamwise and lateral maneuvers.
