Effects of Reynolds number and average angle of attack on the laminar scaling of oscillating foils

Verma, Suyash; Freeman, Benjamin; Hemmati, Arman

doi:10.1063/5.0082578

“…Now we introduce coefficients () in each term of , to account for the multiplicative constants similar to the approach followed by Van Buren et al. (2019) and Verma, Freeman & Hemmati (2022 a ). The resulting expression is therefore written as …”

Section: Resultsmentioning

confidence: 99%

Characterization of bifurcated dual vortex streets in the wake of an oscillating foil

Verma

¹

,

Hemmati

²

2022

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Wake evolution of an oscillating foil with combined heaving and pitching motion is evaluated numerically for a range of phase offsets ( $\phi$ ), chord-based Strouhal numbers ( $St_c$ ) and Reynolds numbers ( $Re$ ). The increase in $\phi$ from $90^\circ$ to $180^\circ$ at a given $St_c$ and $Re$ coincides with a transition of pitch- to heave-dominated kinematics that further reveals novel transitions in wake topology characterized by bifurcated vortex streets. At $Re= 1000$ , each of the dual streets constitutes a dipole-like paired configuration of counter-rotating coherent structures that resemble qualitatively the formation of $2P$ mode. A new mathematical relation between the relative circulation of coherent dipole-like paired structures and kinematic parameters is proposed, including heave-based ( $St_h$ ), pitch-based ( $St_{\theta }$ ) and combined motion ( $St_A$ ) Strouhal numbers, as well as $\phi$ . This model can predict accurately the wake transition towards $2P$ mode characterized by a bifurcation, at low $Re= 1000$ . At $Re= 4000$ , however, the relationship was inaccurate in predicting the wake transition. A shear splitting process is observed at $Re= 4000$ , which leads to the formation of reverse Bénard–von Kármán mode in conjunction with $2P$ mode. Increasing $\phi$ further depicts a consistent prolongation of the splitting process, which coincides with a unique transition in terms of absence and reappearance of bifurcated dipole-like pairs at $\phi = 120^\circ$ and $180^\circ$ , respectively. Changes in the spatial arrangement of $2P$ pairs observed consistently for oscillating foils with the combined motion constitute a novel wake transition that becomes more dominant at higher Reynolds numbers.

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“…Three dimensionality is known to dominate outside the intermediate St range (Zurman-Nasution et al 2020), where the finite aspect ratio of the foil tends to decrease the thrust and efficiency (Tang et al 2016, Zurman-Nasution et al 2020. Meanwhile, the high Re effect in the high St regime causes an unsteady boundary layer (Verma et al 2022). These effects will be considered in future work.…”

Section: Discussionmentioning

confidence: 97%

Propulsive performance of a heaving and pitching foil with large amplitudes in unsteady ground effect

Zhang,

Nakamura

2024

Fluid Dyn. Res.

0

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To reveal the effect of ground on the force behavior, propulsion performance, and vortex dynamics of a flapping foil, we numerically study a flapping foil actuated by combined heaving and pitching motions with large amplitudes near a solid ground surface. The instantaneous forces in both streamwise and cross-stream directions undergo a sudden drop during upstroke in close ground effect. The time-averaged thrust is enhanced by the ground but varies non-monotonically with ground distance at high foil oscillating frequencies. Three force regimes are identified in lift production, giving rise to two equilibrium altitudes of zero lift, one stable and another unstable. Moreover, we propose a simple scaling law model by a path-length-based Strouhal number and ground effect for thrust and power performance of a large-amplitude flapping foil. The results of the model are consistent with numerical results and previous experimental studies. The vortex dynamics in the wake structure are largely affected by ground proximity; in particular, the formed vortex pairs and their orientations are sensitive to their initial relative positions. Different sources and mechanisms of satellite vortex formation are then discussed. The ground exerts little effect on the phase angles that optimize the propulsive efficiency. This study is expected to provide new insights into the development and maneuvering of flapping foil-based propulsive systems.

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“…The continuity and Navier-Stokes equations were solved directly using OpenFOAM, which is a numerical package based on the finite-volume method. It is extensively used for simulating wake dynamics of oscillating foils and panels [17,33,38,41,[43][44][45][46][47][48]. The oscillatory foil dynamics was modelled using the Overset Grid Assembly (OGA) method, based on a stationary background grid and a moving overset grid that were merged for the simulation [49].…”

Section: (A) Numerical Detailsmentioning

confidence: 99%

On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils

Verma,

Khalid,

Hemmati

2023

Proc. R. Soc. A.

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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 ≤ S t c ≤ 0.56 ) and phase offset ( 90 ∘ ≤ ϕ ≤ 270 ∘ ) at R e = 8000 . The changes in ϕ and S t c reflect a unique route of transition in mechanisms that govern the origin of spanwise instabilities and growth of secondary wake structures. At lower S t c , 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 S t c , provides a crucial reasoning for this newly identified progression.

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Effects of Reynolds number and average angle of attack on the laminar scaling of oscillating foils

Cited by 13 publications

References 32 publications

Characterization of bifurcated dual vortex streets in the wake of an oscillating foil

Characterization of bifurcated dual vortex streets in the wake of an oscillating foil

Propulsive performance of a heaving and pitching foil with large amplitudes in unsteady ground effect

On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils

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