Efficient thrust enhancement by modified pitching motion

Thrust and/or efficiency of a pitching foil (mimicking a tail of swimming fish) can be enhanced by tweaking the pitching waveform. The literature, however, show that non-sinusoidal pitching waveforms can enhance either thrust or efficiency but not both simultaneously. With the knowledge and inspiration from nature, we devised and implemented a novel asymmetrical sinusoidal pitching motion that is a combination of two sinusoidal motions having periods T1 and T2 for the forward and retract strokes, respectively. The motion is represented by period ratio $\mathrm{\mathbb{T}} = {T_1}/T$ , where T = (T1 + T2)/2, with $\mathrm{\mathbb{T}} > 1.00$ giving the forward strokes (from equilibrium to extreme position) slower than the retract strokes (from extreme to equilibrium position) and vice versa. The novel pitching motion enhances both thrust and efficiency for $\mathrm{\mathbb{T}} > 1.00$ . The enhancement results from the resonance between the shear-layer roll up and the increased speed of the foil. Four swimming regimes, namely normal swimming, undesirable, floating and ideal are discussed, based on instantaneous thrust and power. The results from the novel pitching motion display similarities with those from fish locomotion (e.g. fast start, steady swimming and braking). The $\mathrm{\mathbb{T}} > 1.00$ motion in the faster stroke has the same characteristics and results as the fast start of prey to escape from a predator while $\mathrm{\mathbb{T}} < 1.00$ imitates braking locomotion. While $\mathrm{\mathbb{T}} < 1.00$ enhances the wake deflection at high amplitude-based Strouhal numbers (StA = fA/U∞, where f and A are the frequency and peak-to-peak amplitude of the pitching, respectively, and U∞ is the freestream velocity), $\mathrm{\mathbb{T}} > 1.00$ improves the wake symmetry, suppressing the wake deflection. The wake characteristics including wake width, jet velocity and vortex structures are presented and connected with $S{t_d}( = fd/{U_\infty })$ , ${A^{\ast}}( = A/d)$ and $\mathrm{\mathbb{T}}$ , where d is the maximum thickness of the foil.