Abstract

In the present research, a 2D simulation of tandem flapping foil following an elliptical trajectory, i.e., altered from a simple flapping trajectory is performed. The purpose of the research is to evaluate the influence of the trajectory motion of the tandem flapping foil on hydrodynamics characteristics and propulsive efficiency. The study is carried out with tandem foil configurations as in such position, both the foils are subjected to the same flow, which allows the flapping foil to enhance the propulsive efficiencies with proper selection of foil position as well as the foil trajectory. The 2D simulation is carried out with NACA 0012 at Re = 1173 by varying Strouhal number (St) between 0.2 and 0.5. The results show that an elliptical motion trajectory pattern and interfoil spacing of 1cm–2cm (where cm is the mean chord length) between the foils would enhance the propulsive efficiency whereas an unfavorable spacing between the foils causes unfavorable wake interaction, which reduces propulsive efficiency as compared to solo flapping foil. When the results of the current numerical investigation of elliptical trajectory are compared to the results of simple trajectory tandem flapping, the current study shows a significant increase in propulsive efficiency. This study gives new insights in the development of biomimetic propulsors, as it strives to improve propulsive efficiency through the usage of wake vortex.

References

1.
Techet
,
A. H.
,
2008
, “
Propulsive Performance of Biologically Inspired Flapping Foils at High Reynolds Numbers
,”
J. Exp. Biol.
,
211
(
2
), pp.
274
279
.
2.
Buchholz
,
J. H.
, and
Smits
,
A. J.
,
2008
, “
The Wake Structure and Thrust Performance of a Rigid Low-Aspect-Ratio Pitching Panel
,”
J. Fluid Mech.
,
603
, pp.
331
365
.
3.
Jones
,
K. D.
,
Dohring
,
C. M.
, and
Platzer
,
M. F.
,
1998
, “
Experimental and Computational Investigation of the Knoller–Betz Effect
,”
AIAA J.
,
36
(
7
), pp.
1240
1246
.
4.
Lewin
,
G. C.
, and
Haj-Hariri
,
H.
,
2003
, “
Modelling Thrust Generation of a Two-Dimensional Heaving Airfoil in a Viscous Flow
,”
J. Fluid Mech.
,
492
, pp.
339
362
.
5.
Lua
,
K. B.
,
Lim
,
T. T.
,
Yeo
,
K. S.
, and
Oo
,
G. Y.
,
2007
, “
Wake Structure Formation of a Heaving Two-Dimensional Elliptic Airfoil
,”
AIAA J.
,
45
(
7
), pp.
1571
1583
.
6.
Boudreau
,
M.
,
Picard-Deland
,
M.
, and
Dumas
,
G.
,
2020
, “
A Parametric Study and Optimization of the Fully-Passive Flapping-Foil Turbine at High Reynolds Number
,”
Renewable Energy
,
146
, pp.
1958
1975
.
7.
Martín-Alcántara
,
A.
,
Fernandez-Feria
,
R.
, and
Sanmiguel- Rojas
,
E.
,
2015
, “
Vortex Flow Structures and Interactions for the Optimum Thrust Efficiency of a Heaving Airfoil at Different Mean Angles of Attack
,”
Phys. Fluids
,
27
(
7
), p.
073602
.
8.
Floryan
,
D.
,
Van Buren
,
T.
,
Rowley
,
C. W.
, and
Smits
,
A. J.
,
2017
, “
Scaling the Propulsive Performance of Heaving and Pitching Foils
,”
J. Fluid Mech.
,
822
, pp.
386
397
.
9.
Lau
,
T. C.
, and
Kelso
,
R. M.
,
2016
, “
A Scaling Law for Thrust Generating Unsteady Hydrofoils
,”
J. Fluid Mech. Struct.
,
65
, pp.
455
471
.
10.
Moriche
,
M.
,
Flores
,
O.
, and
Garcia-Villalba
,
M.
,
2017
, “
On the Aerodynamic Forces on Heaving and Pitching Airfoils at Low Reynolds Number
,”
J. Fluid Mech.
,
828
, pp.
395
423
.
11.
Van Buren
,
T.
,
Floryan
,
D.
, and
Smits
,
A. J.
,
2018
, “
Scaling and Performance of Simultaneously Heaving and Pitching Foils
,”
AIAA J.
,
57
(
9
), pp.
1
12
.
12.
Van Buren
,
T.
,
Floryan
,
D.
,
Wei
,
N.
, and
Smits
,
A. J.
,
2018
, “
Flow Speed Has Little Impact on Propulsive Characteristics of Oscillating Foils
,”
Phys. Rev. Fluids
,
3
(
1
), p.
013103
.
13.
Ashraf
,
M. A.
,
Young
,
J.
, and
Lai
,
J. C. S.
,
2011
, “
Reynolds Number, Thickness and Camber Effects on Flapping Airfoil Propulsion
,”
J. Fluid Mech. Struct.
,
27
(
2
), pp.
145
160
.
14.
Von Ellenrieder
,
K. D.
,
Parker
,
K.
, and
Soria
,
J.
,
2003
, “
Flow Structures Behind a Heaving and Pitching Finite-Span Wing
,”
J. Fluid Mech.
,
490
, pp.
129
138
.
15.
Dong
,
H.
,
Mittal
,
R.
, and
Najjar
,
F. M.
,
2006
, “
Wake Topology and Hydrodynamic Performance of Low-Aspect-Ratio Flapping Foils
,”
J. Fluid Mech.
,
566
, pp.
309
343
.
16.
Taira
,
K.
, and
Colonius
,
T. I. M.
,
2009
, “
Three-Dimensional Flows Around Low-Aspect-Ratio Flat-Plate Wings at Low Reynolds Numbers
,”
J. Fluid Mech.
,
623
, pp.
187
207
.
17.
Visbal
,
M.
,
Yilmaz
,
T. O.
, and
Rockwell
,
D.
,
2013
, “
Three Dimensional Vortex Formation on a Heaving Low-Aspect-Ratio Wing: Computations and Experiments
,”
J. Fluid Mech. Struct.
,
38
, pp.
58
76
.
18.
Lee
,
J.
,
Park
,
Y. J.
,
Cho
,
K. J.
,
Kim
,
D.
, and
Kim
,
H. Y.
,
2017
, “
Hydrodynamic Advantages of a Low Aspect-Ratio Flapping Foil
,”
J. Fluid Mech. Struct.
,
71
, pp.
70
77
.
19.
Xiao
,
Q.
,
Liao
,
W.
,
Yang
,
S. C.
, and
Peng
,
Y.
,
2012
, “
How Motion Trajectory Affects Energy Extraction Performance of a Biomimic Energy Generator With an Oscillating Foil
,”
Renewable Energy
,
37
(
1
), pp.
61
75
.
20.
Sun
,
M.
, and
Lan
,
S. L.
,
2004
, “
A Computational Study of the Aerodynamic Forces and Power Requirements of Dragonfly Aeschnajuncea Hovering
,”
J. Exp. Biol.
,
207
(
11
), pp.
1887
1901
.
21.
Lai
,
G. J.
, and
Shen
,
G. X.
,
2016
, “
Experimental Investigation on the Wing–Wake Interaction at the Mid Stroke in Hovering Flight of Dragonfly
,”
Sci. China Phys. Mech. Astron.
,
55
(
11
), pp.
2167
2178
.
22.
Wang
,
H.
,
Zeng
,
L. J.
,
Liu
,
H.
, and
Yin
,
C. Y.
,
2003
, “
Measuring Wing Kinematics, Flight Trajectory and Body Attitude During Forward Flight and Turning Maneuvers in Dragonflies
,”
J. Exp. Biol.
,
206
(
4
), pp.
745
757
.
23.
Eloy
,
C.
,
2012
, “
Optimal Strouhal Number for Swimming Animals
,”
J. Fluids Struct.
,
30
, pp.
205
218
.
24.
Triantafyllou
,
M. S.
,
Triantafyllou
,
G. S.
, and
Gopalkrishnan
,
R.
,
1991
, “
Wake Mechanics for Thrust Generation in Oscillating Foils
,”
Phys. Fluids A
,
3
(
12
), pp.
2835
2837
.
25.
Xu
,
G. D.
,
Duan
,
W. Y.
, and
Xu
,
W. H.
,
2017
, “
The Propulsion of Two Flapping Foils With Tandem Configuration and Vortex Interactions
,”
Phys. Fluids
,
29
, p.
09710229
.
26.
Esfahani
,
J. A.
,
Barati
,
E.
, and
Karbasian
,
H. R.
,
2017
, “
Fluid Structures of Flapping Airfoil With Elliptical Motion Trajectory
,”
Comput. Fluids
,
108
, pp.
142
155
.
27.
Akbari
,
M. H.
, and
Price
,
S. J.
,
2003
, “
Simulation of Dynamic Stall for a NACA 0012 Airfoil Using a Vortex Method
,”
J. Fluids Struct.
,
17
(
6
), pp.
855
874
.
28.
Von Kármán
,
T.
,
1935
, “
General Aerodynamic Theory-Perfect Fluids
,”
Aerodyn. Theory
,
2
, pp.
346
349
.
29.
Godoy-Diana
,
R.
,
Aider
,
J. L.
, and
Wesfreid
,
J. E.
,
2008
, “
Transitions in the Wake of a Flapping Foil
,”
Phys. Rev. E
,
77
(
1
), p.
016308
.
30.
Godoy-Diana
,
R.
,
Aider
,
J. L.
, and
Wesfreid
,
J. E.
,
2009
, “
A Model for the Symmetry Breaking of the Reverse Bénard–von Kármán Vortex Street Produced by Flapping Foil
,”
J. Fluid Mech.
,
622
, pp.
23
32
.
31.
Cleaver
,
D. J.
,
Wang
,
Z.
, and
Gursul
,
I.
,
2012
, “
Bifurcating Flows of Plunging Aerofoils at High Strouhal Numbers
,”
J. Fluid Mech.
,
708
, pp.
349
376
.
32.
He
,
G.-Y.
,
Wang
,
Q.
,
Zhang
,
X.
, and
Zhang
,
S.-G.
,
2012
, “
Numerical Analysis on Transitions and Symmetry-Breaking in the Wake of a Flapping Foil
,”
Acta Mechanica Sin.
,
28
(
6
), pp.
1551
1556
.
33.
Kozłowski
,
T.
, and
Kudela
,
H.
,
2014
, “
Transitions in the Vortex Wake Behind the Plunging Profile
,”
Fluid Dyn. Res.
,
46
(
6
), p.
061406
.
34.
Zheng
,
Z. C.
, and
Wei
,
Z.
,
2012
, “
Study of Mechanisms and Factors That Influence the Formation of Vertical Wake of a Heaving Airfoil
,”
Phys. Fluids
,
24
(
10
), p.
103601
.
35.
Akhtar
,
I.
,
Mittal
,
R.
,
Lauder
,
G. V.
, and
Drucker
,
E.
,
2007
, “
Hydrodynamics of a Biologically Inspired Tandem Flapping Foil Configuration
,”
Theor. Comput. Fluid Dyn.
,
21
(
3
), pp.
155
170
.
36.
Swain
,
P. K.
, and
Dora
,
S. P.
,
2021
, “
Experimental and Numerical Investigation of Wing–Wing Interaction and Its Effect on Aerodynamic Force of a Robotic Dragonfly During Hovering and Forward Flight
,”
Arch Appl. Mech.
,
91
(
5
), pp.
2039
2052
.
37.
Swain
,
P. K.
,
Dora
,
S. P.
,
Suryanarayana
,
M. B.
, and
Barik
,
A. K.
, “
Numerical Investigation of Wing–Wing Interaction and Its Effect on the Aerodynamic Force of a Hovering Dragonfly
,”
Proc. Inst. Mech. Eng. G: J. Aerosp. Eng.
,
235
(
12
), pp.
1648
1663
.
38.
Williamson
,
C.
, and
Roshko
,
A.
,
1988
, “
Vortex Formation in the Wake of an Oscillating Cylinder
,”
J. Fluids Struct.
,
2
(
4
), pp.
355
381
.
39.
Anderson
,
J.
,
Streitlien
,
K.
,
Barrett
,
D.
, and
Triantafyllou
,
M.
,
1998
, “
Oscillating Foils of High Propulsive Efficiency
,”
J. Fluid Mech.
,
360
, pp.
41
72
.
40.
Hover
,
F. S.
,
Haugsdal
,
Ø
, and
Triantafyllou
,
M. S.
,
2004
, “
Effect of Angle of Attack Profiles in Flapping Foil Propulsion
,”
J. Fluids Struct.
,
19
(
1
), pp.
37
47
.
You do not currently have access to this content.