Intermittent Unsteady Propulsion with a Combined Heaving and Pitching Foil
Inviscid computations are presented of a self-propelled virtual body connected to a combined heaving and pitching foil that uses continuous and intermittent motions. It is determined that intermittent swimming can improve efficiency when the dimensionless heave ratio is $h^* < 0.7$ while it degrades efficiency for $h^* \geq 0.7$. This is a consequence of the physical origins of the force production for pitch-dominated ($h^* < 0.5$) and heave-dominated ($h^* > 0.5$) motions. Based on insight derived from classic unsteady thin airfoil theory, it is discovered that pitch-dominated motions are driven by added-mass-based thrust production where self-propelled efficiency is maximized for high reduced frequencies, while heave-dominated motions are driven by circulatory-based thrust production where self-propelled efficiency is maximized by low reduced frequencies. Regardless of the dimensionless heave ratio the reduced frequency is high for small amplitude motions, high Lighthill numbers, and low duty cycles and vice versa. Moreover, during intermittent swimming, the stopping vortex that is shed at the junction of the bursting and coasting phases becomes negligibly weak for $h^* < 0.5$ and small amplitude motions of $A^* = 0.4$. This study provides insight into the mechanistic trade-offs that occur when biological or bio-inspired swimmers continuously or intermittently use combined heaving and pitching hydrofoils.