Influence of kinematics on the growth of secondary wake structures behind oscillating foils

Abstract

The wake of an oscillating hydrofoil in combined heaving and pitching motion is numerically evaluated at a range of phase offset (90∘≤ϕ≤270∘) and chord based Strouhal number (0.32 ≤Stc≤ 0.64), while the main analysis is currently reported at Stc=0.32. The Reynolds number is fixed at Re=8000. At ϕ=90∘, a dominant spanwise elliptic instability feature is observed due to the presence of a paired primary and secondary leading edge vortex (LEV) roller over the foil boundary. Subsequent outflux of vorticity from the secondary LEV leads to the formation of streamwise hairpin structures that evolve downstream on account of straining in the braid vorticity region. The spanwise wavelength (λz) of the growing streamwise secondary hairpin legs is approximately 0.86c before the LEV structures shed from the foil. This is followed by a reduction in λz, which coincided with continuous ejection of vorticity from the secondary leading edge structures, and the rearrangement of growing hairpin legs. However, the dominant association between spanwise instability and growth of secondary streamwise structures at ϕ=90∘ reduces with increasing ϕ towards 270∘. At ϕ=180∘, there is a delay in the emergence of dominant secondary hairpin structures that evolve through deformed trailing edge vortex rather than the secondary leading edge structure. Further increase in ϕ to 225∘ and 270∘ depicts the absence of secondary hairpin structures, despite the apparent local instability features on the leading edge rollers.