Existence of three distinct scaling regimes in self-propelled airfoil

We experimentally investigate the self-propulsion of the NACA0015 symmetric airfoil section subject to sinusoidal pitching. A power-spring-based crank–rocker mechanism actuates the airfoil. We employ a rotary apparatus capable of achieving self-propulsion. Self-propulsion across varying pitching frequency, amplitude and pitching-point location is characterised by three distinct scaling relations. These scaling relations relate the self-propulsion Reynolds number ( italic Re Subscript s Re s $\textit{Re}_s$ ) to the frequency Reynolds number ( italic Re Subscript f Re f $\textit{Re}_{\!f}$ ), the pitching amplitude ( theta 0 θ 0 $\theta _0$ ) and the pitching-point location ( p p $p$ ). For p less than 0.4 p < 0.4 $p\lt 0.4$ two scaling relations emerge depending on the pitching amplitude. For theta 0 almost equals 4.6 Superscript ring θ 0 ≈ 4.6 ∘ $\theta _0 \approx 4.6^\circ$ , italic Re Subscript s Baseline tilde left parenthesis 1 minus 2 p right parenthesis left parenthesis italic Re Subscript f Baseline theta 0 right parenthesis Superscript 3 divided by 2 Re s ∼ ( 1 − 2 p ) ( Re