New experiments examine the interactions between a pair of three-dimensional (AR = 2) non-uniformly flexible pitching hydrofoils through force and efficiency measurements. It is discovered that the collective efficiency is improved when the follower foil has a nearly out-of-phase synchronization with the leader and is located directly downstream with an optimal streamwise spacing of X*=0.5. The collective efficiency is further improved when the follower operates with a nominal amplitude of motion that is 36% larger than the leader’s amplitude. A slight degradation in the collective efficiency was measured when the follower was slightly-staggered from the in-line arrangement where direct vortex impingement is expected. Operating at the optimal conditions, the measured collective efficiency and thrust are ηC=62% and CT,C=0.44, which are substantial improvements over the efficiency and thrust of ηC=29% and CT,C=0.16 of two fully-rigid foils in isolation. This demonstrates the promise of achieving high-efficiency with simple purely pitching mechanical systems and paves the way for the design of high-efficiency bio-inspired underwater vehicles.
Trisections on certain rational elliptic surfaces and families of Zariski pairs degenerating to the same conic-line arrangement
