Physics-informed scaling laws for the performance of pitching foils in schooling configurations

Abstract

This study introduces novel physics-based scaling laws to estimate the propulsive performance of synchronously pitching foils in various schooling configurations. These relations are derived from quasi-steady lift-based and added mass forces. Hydrodynamic interactions among the schooling foils are considered through vortex-induced velocities imposed on them, constituting the ground effect. Generalized scaling equations are formulated for cycle-averaged coefficients of thrust and power. These equations encompass both the pure-pitching and induced velocity terms, capturing their combined effects. The equations are compared to computational results obtained from two-foil systems, exhibiting foil arrangements over a wide range of parameter space, including Strouhal number (0.15 ≤ St ≤ 0.4), pitching amplitude (5° ≤θ0≤14°) and phase difference (0° ≤φ≤180°) at Re = 1000-10 000. The individual contributions of pure-pitching and induced velocity terms to propulsive performance elucidate that solely relying on the pure-pitching terms leads to inadequate estimation, emphasizing the significance of the induced velocity terms. The validity of the approach is further assessed by testing it with three-foil and five-foil configurations, which displays a collapse of estimated and measured results. This indicates that the scaling laws are applicable to multi-foil arrangements.