Physics-Informed Scaling Laws for the Performance of Pitching Foils in Schooling Configurations

TL;DR

This paper develops physics-based scaling laws to predict the propulsive performance of pitching foils in schooling configurations, accounting for hydrodynamic interactions and validated across multiple foil arrangements.

Contribution

It introduces generalized scaling equations incorporating both pure-pitching and induced velocity effects, extending their applicability from two-foil to multi-foil systems.

Findings

Scaling laws accurately predict thrust and power coefficients.

Induced velocity effects are crucial for performance estimation.

Law validity confirmed with three-foil configuration.

Abstract

This study introduces novel physics-based scaling laws to estimate the propulsive performance of synchronously pitching foils in various schooling configurations at Re=4000. 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-foils systems, exhibiting foil arrangements over a wide range of parameter space, including Strouhal number (0.15 \leq St \leq 0.4), pitching amplitude (5 deg \leq \theta_0 \leq 14 deg), and phase difference (0 deg \leq \phi \leq 180 deg). 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. Validity of the approach is further assessed by testing it with a three-foil configuration, which displays a collapse. This indicates that the scaling laws are not only applicable to two-foils systems but also extend their effectiveness to multi-foil arrangements.