The flow field around a finite-span flat wing in pitch motion is modeled by means of large-eddy simulation. The effect of moderate sweep angles on the stability of the leading-edge vortex (LEV) is investigated. The relative stability of LEVs on flapping profiles can be improved by moderating LEV growth through spanwise vorticity convection and vortex stretching. The LEV growth over an unswept wing and two sweep angles, namely, , is studied by investigating the spanwise flow. The calculated results are in good agreement with experimental data, establishing confidence in the approach. Results show that sweeping the wing profile increases not only the scale of the secondary vortices but also expedites the initiation of the vortices at lower angles of attack. For the sweep angle of , increasing the angle of attack is associated with annihilation of vorticity and thereby limits the vortex growth as a necessary condition for LEV stability. Analysis shows that increasing the sweep angle results in a higher circulation intensity, especially in the inner region of the wing, and significant spanwise flow is observed through the vortex core. The pattern of vorticity remains stable and attached to the surface as the angle of attack continues to grow for the swept wing, while the patterns of vorticity depart the wing surface for the unswept wing. It is suspected that sweeping the wing can control the scale of the vortex by introducing a substantial vortex stretching.
References
1.
W.
McCroskey
, L.
Carr
, and K.
McAlister
, “Dynamic stall experiments on oscillating airfoils
,” AIAA J.
14
, 57
–63
(1976
).2.
K.
Ohmi
, M.
Coutanceau
, O.
Daube
, and T. P.
Loc
, “Further experiments on vortex formation around an oscillating and translating airfoil at large incidences
,” J. Fluid Mech.
225
, 607
–630
(1991
).3.
M.
Ol
, L.
Bernal
, C.-K.
Kang
, and W.
Shyy
, “Shallow and deep dynamic stall for flapping low Reynolds number airfoils
,” in Animal Locomotion
(Springer
, 2010
), pp. 321
–339
.4.
W.
Shyy
and H.
Liu
, “Flapping wings and aerodynamic lift: The role of leading-edge vortices
,” AIAA J.
45
, 2817
–2819
(2007
).5.
T. O.
Yilmaz
and D.
Rockwell
, “Flow structure on finite-span wings due to pitch-up motion
,” J. Fluid Mech.
691
, 518
–545
(2012
).6.
D.
Lentink
and M.
Dickinson
, “Rotational accelerations stabilize leading edge vortices on revolving fly wings
,” J. Exp. Biol.
212
, 2705
–2719
(2009
).7.
T.
Maxworthy
, “Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1. Dynamics of the ‘fling
,’” J. Fluid Mech.
93
, 47
–63
(1979
).8.
Y. S.
Baik
, L. P.
Bernal
, K.
Granlund
, and M. V.
Ol
, “Unsteady force generation and vortex dynamics of pitching and plunging aerofoils
,” J. Fluid Mech.
709
, 37
–68
(2012
).9.
C. P.
Ellington
, C.
van den Berg
, A. P.
Willmott
, and A. L. R.
Thomas
, “Leading-edge vortices in insect flight
,” Nature
384
, 626
–630
(1996
).10.
D.
Rival
, J.
Kriegseis
, P.
Schaub
, A.
Widmann
, and C.
Tropea
, “Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry
,” Exp. Fluids
55
, 1660
(2014
).11.
M. R. A.
Nabawy
and W. J.
Crowther
, “The role of the leading edge vortex in lift augmentation of steadily revolving wings: A change in perspective
,” J. R. Soc. Interface
14
, 20170159
(2017
).12.
J. D.
Eldredge
and A. R.
Jones
, “Leading-edge vortices: Mechanics and modeling
,” Annu. Rev. Fluid Mech.
51
, 75
–104
(2019
).13.
R.
Addo-Akoto
, J.-S.
Han
, and J.-H.
Han
, “Roles of wing flexibility and kinematics in flapping wing aerodynamics
,” J. Fluids Struct.
104
, 103317
(2021
).14.
P.
Ford
and H.
Babinsky
, “Lift and the leading-edge vortex
,” J. Fluid Mech.
720
, 280
–313
(2013
).15.
J.
Wong
and D.
Rival
, “Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles
,” J. Fluid Mech.
766
, 611
–625
(2015
).16.
C. A.
Ozen
and D.
Rockwell
, “Three-dimensional vortex structure on a rotating wing
,” J. Fluid Mech.
707
, 541
–550
(2012
).17.
B.
Cheng
, S. P.
Sane
, G.
Barbera
, D. R.
Troolin
, T.
Strand
, and X.
Deng
, “Three-dimensional flow visualization and vorticity dynamics in revolving wings
,” Exp. Fluids
54
, 1423
(2013
).18.
C. J.
Wojcik
and J. H. J.
Buchholz
, “Vorticity transport in the leading-edge vortex on a rotating blade
,” J. Fluid Mech.
743
, 249
–261
(2014
).19.
D.
Rival
, R.
Manejev
, and C.
Tropea
, “Measurement of parallel blade-vortex interaction at low Reynolds numbers
,” Exp. Fluids
49
, 89
–99
(2010
).20.
J.
Birch
and M.
Dickinson
, “Spanwise flow and the attachment of the leading-edge vortex on insect wings
,” Nature
412
, 729
–733
(2001
).21.
C.
Ellington
, “The novel aerodynamics of insect flight: Applications to micro-air vehicles
,” J. Exp. Biol.
202
, 3439
–3448
(1999
).22.
T.
Jardin
, “Coriolis effect and the attachment of the leading edge vortex
,” J. Fluid Mech.
820
, 312
–340
(2017
).23.
R.
Lavimi
, M.
Hojaji
, and M. D.
Manshadi
, “Investigation of the aerodynamic performance and flow physics on cross sections of dragonfly wing on flapping and pitching motion in low Reynolds number
,” Proc. Inst. Mech. Eng., Part G
233
, 589
–603
(2019
).24.
J.
Usherwood
, “The aerodynamic forces and pressure distribution of a revolving pigeon wing
,” Exp. Fluids
46
, 991
–1003
(2009
).25.
P.
Wilkins
and K.
Knowles
, “The leading-edge vortex and aerodynamics of insect-based flapping-wing micro air vehicles
,” Aeronaut. J.
113
, 253
–262
(2009
).26.
J.
Birch
, “Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers
,” J. Exp. Biol.
207
, 1063
–1072
(2004
).27.
J.
Zhang
, J.
Hu
, Y.
Yu
, and H.
Xuan
, “On the stabilization of leading-edge vortices with different reduced frequencies over finite-aspect-ratio pitch-up wings
,” AIP Adv.
10
, 025029
(2020
).28.
J. G.
Wong
, J.
Kriegseis
, and D. E.
Rival
, “An investigation into vortex growth and stabilization for two-dimensional plunging and flapping plates with varying sweep
,” J. Fluids Struct.
43
, 231
–243
(2013
).29.
I.
Gursul
, R.
Gordnier
, and M.
Visbal
, “Unsteady aerodynamics of nonslender delta wings
,” Prog. Aerosp. Sci.
41
, 515
–557
(2005
).30.
M. R.
Visbal
and D. J.
Garmann
, “Effect of sweep on dynamic stall of a pitching finite-aspect-ratio wing
,” AIAA J.
57
, 3274
–3289
(2019
).31.
J.
Eldredge
, C.
Wang
, and M.
OL
, “A computational study of a canonical pitch-up, pitch-down wing maneuver
,” in 39th AIAA Fluid Dynamics Conference
(2009
).32.
J.
Weiss
, “The dynamics of enstrophy transfer in two-dimensional hydrodynamics
,” Physica D
48
, 273
–294
(1991
).33.
P.
Roache
, “Perspective: A method for uniform reporting of grid refinement studies
,” J. Fluids Eng.-Trans. ASME
116
, 405
–413
(1994
).34.
C.
Hirsch
, Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows
(Wiley
, 1991
), Vol. 2
.35.
X.
Chai
and K.
Mahesh
, “Dynamic k-equation model for large eddy simulation of compressible flows
,” J. Fluid Mech.
699
, 385
–413
(2012
).36.
R.
Zangeneh
, “Parametric study of separation and reattachment in transonic airfoil flows
,” AIAA J.
59
, 1
–10
(2021
).37.
R.
Zangeneh
, “Development of a new algorithm for modeling viscous transonic flow on unstructured grids at high Reynolds numbers
,” J. Fluids Eng.
143
, 024504
(2021
).38.
R.
Zangeneh
, “Numerical analysis of transonic flow around cones
,” Open J. Fluid Dyn.
10
, 279
–290
(2020
).39.
Y.
Lu
, S.
Gong
, and L.
Guo
, “Dual leading-edge vortices on flapping wings
,” J. Exp. Biol.
209
, 5005
–5016
(2006
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
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