Physics-based scaling laws for collective swimmers

Physics-based scaling laws are developed for a wide range of parameter space and schooling configurations of pitching foils at Re=4000. A novel approach is utilized to model the hydrodynamic interactions between the swimmers based their proximity (ground effect). Thrust and power coefficients are strongly dependent on both lift-based and added-mass contributions. However, there exists equally substantial contributions from induced velocities due to wake-body interactions. The vertical component of such an induced velocity resembles a heaving motion, suggesting that even purely-pitching foils in a school have similar kinematics to that of simultaneously heaving and pitching foils. Besides the contributions from kinematics (oscillation parameters) and flow dynamics, the introduced novel scaling relations include parameters of schooling configurations, i.e., separation distance, separation angle, and phase difference between the foils. An excellent collapse is obtained by comparing estimated (scaled) and measured data, indicating the strength of our scaling equations in capturing the underlying flow physics. The analyses is accurately extended to the arrangements of multiple foils, revealing the robustness of the scaling laws and their strength in capturing the flow physics properly.