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

Abstract

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.

On association of lift generation, wake topology and kinematics of oscillating foils

“…This further coincides with a decrease in trailing edge amplitude as described by. 15,22 We also observe that the range of f* between 0.24 and 0.40 shows a delayed wake transition from 2P+2S to 2P within heave-dominated regime compared to the pitch-dominated regime at ϕ<180∘, for example. This could again be an implication of weak or no interaction (and merging) near the trailing edge of the foil due to lower strength of generated vorticity.…”

“…The reduction of trailing edge amplitude within the heave-dominated regime corresponds to decreasing relative vorticity generated at the trailing edge compared to the leading edge. 22 This characteristic feature thus yields a paired configuration of leading and trailing edge vortical structures, even at high f* for the heave-dominated kinematics, thereby explaining the 2P mode configuration.…”

“…blueThe detailed analyses of the coinciding wake and performance characteristics with the heave-and pitch-dominated kinematics is further limited to a chord-based Reynolds number of Re = 1000, where transition of wake modes are more clearly evident. 22,23 This choice of Re also followed closely with assessments of. 9,10,24,17 These studies described transitions in the wake of purely pitching foils and provided a insight into the quasi-two-dimensional and three-dimensional characteristics of wake structures.…”

An Explicit-Correction-Force Scheme of IB-LBM Based on Interpolated Particle Distribution Function

“…The relevant studies are the prime motivators for the new technology in this regard, such as marine, aerial, and energy territory [ 64 ]. Using numerical methods to simulate and analyze relevant experimental conditions, such as wake state, has become an effective research method at present [ 65 ].…”

“…When Re = 1000, 2000, we found that at the vertical line of the wake with the same horizontal position, vortex eyes appeared two to three times. This unstable vortex shedding is a common phenomenon and can be simulated by improving the model to realize the dual Karman vortex street [ 65 ].…”