Analysis of Multiple Degree-of-freedom Oscillatory Aquatic Propulsion

Propulsive performance and flow field data were experimentally measured for a two degree-of-freedom fish platform. The fish platform was designed and constructed based on the yellowfin tuna (\textit{Thunnus albacares}) that is known to be both fast and efficient. This work extends the current understanding of oscillatory aquatic propulsion to a three-dimensional fish platform with full volume flow field data and propulsive performance. A parametric sweep of trailing-edge amplitude of the caudal fin ($A$), heave-to-pitch ratio ($h^*$), and phase offset between the two degrees-of-freedom ($\phi$) was used to explore a parameter space that encompasses and extends beyond the known biological domain. It was found that the shape of phase-averaged propulsive performance curves %($\etaQP$, $\bar{C}_T$, and $\bar{C}_P$) can be described in the $\phi$--$h^*$ space where a kinematic case is defined by $(\phi, h^*)$. The magnitude of each curve as a function of time was strongly dependent on the trailing-edge amplitude. Within the biological Strouhal number range of $0.20 \u3c St \u3c 0.40$, the quasi-propulsive efficiency ($\etaQP$) was locally maximized along a diagonal ridge between The platform maintains relatively good performance along the ridge with a quick drop-off in the perpendicular direction. The time-averaged coefficient of thrust ($\CT$) and input power ($\CP$) were found to be optimal along ridges parallel to the high efficiency ridge. For a given $\phi$, the optimal $\CT$ required a larger $h^*$ while the optimal $\CP$ required a smaller $h^*$. The phase-averaged thrust curves were quantified by the timing of peaks ($t_p$) relative to the start of each cycle. It was found that $t_p$ was strongly dependent on the timing motion of the tail angle ($\theta_T$) and the caudal fin angle ($\theta_C$). The vortex structure around the peduncle region, caudal fin, and wake were described in terms of three main vortices. The leading-edge vortex (LEV) forms along the swept leading-edge of the caudal fin and is vital in understanding the physical mechanisms governing propulsive performance. The finlet vortex (FV) is formed along the top and bottom edges of the tail finlets and plays a crucial role in the evolution of the LEV and therefore propulsive performance. The trailing-edge vortex (TEV) forms along the vertical trailing-edge of the caudal fin. Interactions between the TEV and LEV result in complex three-dimensional structures that undergo large-scale deformation downstream of the trailing-edge. Results show that local flow features, such as the LEV and FV, were directly associated with propulsive performance while far field flow features, such as the deforming wake, were vestiges of propulsive performance. This work highlights the importance of the LEV and upstream vortices (\textit{i.e.} FV) in thrust production by associating them, by analogy, with surface pressure on the caudal fin. It is shown that for cases with low $h^*$, vortices on the pressure side of the caudal fin are responsible for the majority of thrust production. The results are then converted to design recommendations for future underwater oscillatory vehicles