RT Journal Article
T1 Effect of flexibility on the self-propelled locomotion by an elastically supported stiff foil actuated by a torque.
A1 López-Tello, Pablo Esteban
A1 Fernández-Feria, Ramón
K1 Mecánica de fluidos
K1 Hidrodinámica
K1 Locomoción
K1 Natación
AB A theoretical model is presented for the locomotion of an aquatic vehicle propelled by a flexiblefoil elastically mounted to translational and torsional springs and dampers at an arbitrary pivotaxis and actuated by a harmonic torque. The work extends a previous model by the authors for anelastically mounted rigid foil [1], allowing for a passive flexural motion of the foil in addition to thepassive pitching and heaving motions of the rigid foil, all of them generated by the actuating torqueand the fluid-foil interaction. The Euler-Bernoulli beam equation is used together with linearizedresults from the potential flow theory, valid for small pitch, heave and flexural deflection amplitudes.The problem is governed by four ordinary differential equations (ODEs) for the temporal evolutionsof the swimming velocity, and the pitch, heave and flexural motions of the flexible foil. In addition tonumerical results of these ODEs, we also present an analytical perturbation solution which providesa valuable quick insight about the propulsion performance, but which is additionally restricted tovery small swimming velocities. The vehicle’s propulsion performance is discussed in terms of thefoil stiffness ratio and the remaining non-dimensional parameters, particularly the translational andtorsional spring constants, the pivot axis location and the Lighthill number. It is found that, exceptfor very low Lighthill numbers, the maximum swimming velocity is reached for a rigid foil actuated atthe leading edge with the resonant combination of the translational and torsional springs constantsfor the given frequency. However, higher propulsive efficiencies and lower costs of transport, butwith slightly smaller swimming velocities, are obtained for flexible foils with the same resonantcombination of the elastic supports at the leading edge. As a validation of the model, the Strouhalnumber for optimal propulsion efficiency is found in a narrow band around 0.32, in agreement withmany experimental and numerical works on optimal propulsion by flapping foils. Additionally, therelation between Strouhal and Lighthill numbers for optimal propulsion is favorably compared withexperimental data for fishes where the primary mechanism for producing thrust is an oscillatoryprominent caudal fin.
PB American Physical Society
YR 2023
FD 2023-06-20
LK https://hdl.handle.net/10630/38824
UL https://hdl.handle.net/10630/38824
LA eng
NO PHYSICAL REVIEW FLUIDS 8, 063102 (2023)
NO Junta de Andalucía, Spain, through Grants No. UMA18-FEDER-JA-047 and No. P18-FR-1532.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026