Performance comparison of tethered and self-propelled models of fish locomotion using unsteady thin airfoil theory
Numerous experimental and computational studies have been conducted in the past few decades to understand the swimming performance of fish, and to identify the optimal kinematic strategies for a swimming fish or fish-like robot. Many of these studies model the swimmer in a `tethered' condition, in which the swimmer is held fixed while it is subjected to a free stream. Its performance is then quantified using power expenditure, thrust generation, and efficiency. However, the dynamics of a tethered swimmer are different from those of a self-propelled swimmer, whose performance is best measured using its steady-state swimming speed in still fluid and its efficiency. It is an open question whether the conclusions drawn from studies of tethered swimmers can be directly applied to free swimmers. In this study, we use an unsteady panel method to systematically compare the swimming performance of a tethered fin and that of a self-propelled fin attached to a virtual drag-producing body to investigate how their performance varies over a set of prescribed kinematics. After validating the numerical model against previous experimental results, we show how the pitch amplitude, heave amplitude and the phase offset between them affect the efficiency and thrust generation in the tethered case, and how they affect the speed and efficiency in the self-propelled case. We find that the kinematic strategies that optimize the performance of a tethered swimmer do not necessarily optimize the performance of a self-propelled swimmer.