Thrust-efficiency limits of a swimming tail with variable chordwise flexural rigidity

Emulating oscillations performed by natural swimmers can provide different functionalities than those of propeller-based underwater robots. Yet, to successfully accomplish specific missions under limited power, there is a need to design efficient bio-inspired robots. Adding an appropriate level of flexibility to flapping caudal fins (tails) of robots emulating the thunniform swimming mode has been shown to enhance the thrust generation over a finite range of the flapping frequency. Still, in many cases, adding flexibility to increase thrust generation may require increased input power, which may cause a significant reduction in the efficiency. These observations lead to the concept of enhanced performance by varying the stiffness of the tail as in the case of natural swimmers. This study is concerned with assessing the impact of varying the chordwise stiffness on the tail deflection and flow dynamics, including contributions of added mass and circulation forces to thrust generation and their impact on efficiency. The simulation data are used to identify specific flow dynamics and tail deflections associated with the enhanced thrust generation and/or efficiency, and to define a performance limit expressed as the maximum efficiency as a function of the thrust coefficient.