“…We further limited the detailed analyses of the wake characteristics to the cases Re = 1000 and 4000, where the wake features and transition effects were more profound without the additional complexities associated with higher Reynolds number flows (Zurman-Nasution, Ganapathisubramani & Weymouth 2020). This choice of Re also followed closely with assessments conducted by Godoy-Diana et al (2008), Schnipper et al (2009), Deng, Sun & Shao (2015), Das et al (2016), Lagopoulos et al (2019) and Cimarelli et al (2021).…”
Section: Methodsmentioning
confidence: 80%
“…(2019) and Cimarelli et al. (2021). Figure 1.Schematics of the foil kinematics and resultant velocity at the leading edge during the motion.…”
Section: Methodsmentioning
confidence: 95%
“…The wake then attained the mode again (Cimarelli et al. 2021). These studies either had focused on oscillations with a single degree of freedom, or were limited to pitch-dominated mixed motions.…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, these phase angles characterized primarily a pitch-dominated oscillatory motion, where the trailing edge amplitude was higher compared to the leading edge. Most recently, Cimarelli, Franciolini & Crivellini (2021) conducted two-dimensional numerical simulations of pure heaving foil in order to investigate the role of kinematic and flow parameters in prompting smooth and sharp transition in configurations of wake. In the range of Reynolds numbers between 50 and 5000, they determined that increasing beyond the critical value 200 led to a transition in configuration of wake from to a stable deflected mode.…”
Section: Introductionmentioning
confidence: 99%
“…In the range of Reynolds numbers between 50 and 5000, they determined that increasing Re beyond the critical value 200 led to a transition in configuration of wake from rBvK to a stable deflected mode. The wake then attained the rBvK mode again (Cimarelli et al 2021). These studies either had focused on oscillations with a single degree of freedom, or were limited to pitch-dominated mixed motions.…”
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.
“…We further limited the detailed analyses of the wake characteristics to the cases Re = 1000 and 4000, where the wake features and transition effects were more profound without the additional complexities associated with higher Reynolds number flows (Zurman-Nasution, Ganapathisubramani & Weymouth 2020). This choice of Re also followed closely with assessments conducted by Godoy-Diana et al (2008), Schnipper et al (2009), Deng, Sun & Shao (2015), Das et al (2016), Lagopoulos et al (2019) and Cimarelli et al (2021).…”
Section: Methodsmentioning
confidence: 80%
“…(2019) and Cimarelli et al. (2021). Figure 1.Schematics of the foil kinematics and resultant velocity at the leading edge during the motion.…”
Section: Methodsmentioning
confidence: 95%
“…The wake then attained the mode again (Cimarelli et al. 2021). These studies either had focused on oscillations with a single degree of freedom, or were limited to pitch-dominated mixed motions.…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, these phase angles characterized primarily a pitch-dominated oscillatory motion, where the trailing edge amplitude was higher compared to the leading edge. Most recently, Cimarelli, Franciolini & Crivellini (2021) conducted two-dimensional numerical simulations of pure heaving foil in order to investigate the role of kinematic and flow parameters in prompting smooth and sharp transition in configurations of wake. In the range of Reynolds numbers between 50 and 5000, they determined that increasing beyond the critical value 200 led to a transition in configuration of wake from to a stable deflected mode.…”
Section: Introductionmentioning
confidence: 99%
“…In the range of Reynolds numbers between 50 and 5000, they determined that increasing Re beyond the critical value 200 led to a transition in configuration of wake from rBvK to a stable deflected mode. The wake then attained the rBvK mode again (Cimarelli et al 2021). These studies either had focused on oscillations with a single degree of freedom, or were limited to pitch-dominated mixed motions.…”
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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