Search

Three-dimensional wake of an oscillating foil with combined heaving and pitching motion is numerically evaluated at a range of chord-based Strouhal number (0.32≤Stc≤0.56) and phase offset (90∘≤ϕ≤270∘) at Re=8000. The changes in ϕ and Stc reflect a unique route of transition in mechanisms that govern the origin of spanwise instabilities and growth of secondary wake structures. At lower Stc , heave-dominated kinematics demonstrates a strong secondary leading edge vortex (LEV) as the source of growing spanwise instability on the primary LEV, followed by an outflux of streamwise vorticity filaments from the secondary LEV. With increasing heave domination, the origin of stronger spanwise instability is governed by a counter-rotating trailing edge vortex and LEV that leads to growth of streamwise secondary structures. A decreasing heave domination ultimately coincides with an absence of strong LEV undulations and secondary structures. The consistent transition routes are represented on a phase-space map, where a progression of spanwise instability and growth of secondary structures becomes evident within regimes of decreased heave domination. The increasing strength of circulation for the primary LEV, with increasing Stc , provides a crucial reasoning for this newly identified progression. [ABSTRACT FROM AUTHOR]

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 ([Formula: see text]) and phase difference ([Formula: see text]) 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.