To examine the effect that body shape plays in the interactions between fish in a dense fish school, fish-like undulating foils are numerically studied in a high-density diamond school. Shape parameters of leading edge radius, boattail angle, and maximum thickness location along the body are independently varied to control the body shape. A traveling wave is prescribed to the body, and the flow around the school is solved using an immersed boundary method-based incompressible Navier–Stokes flow solver. Our findings indicate that body shape does play a significant role in the performance of the school and varies school efficiency and thrust productions by as much as 7% and 40%, respectively, and changes the efficiency in individual swimmers within the school by up to 25%. The leading edge radius drives the scale of the anterior body suction experienced throughout the school. A rounder leading edge generates more suction but consequently consumes more power. Changes to the location of the maximum thickness along the foil significantly impact the wall effect in the school by changing the shape of the “wall.” A maximum thickness that occurs at or in front of the closest point of interaction between the body and tail is favored. Finally, changes to the boattail angle manipulate the shape of the active channels in the school altering vortex–body interactions and the wall effect. A large boattail angle leads to a pinching that prohibits significant flow in the channels, reducing performance.
REFERENCES
1.
Ashraf
,
M. A.
,
Young
,
J.
, and
Lai
,
J. C. S.
, “
Reynolds number, thickness and camber effects on flapping airfoil propulsion
,” J. Fluids Struct.
27
(2
), 145
–160
(2011
).2.
Borazjani
,
I.
and
Sotiropoulos
,
F.
, “
On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming
,” J. Exp. Biol.
213
, 89
–107
(2010
).3.
Boschitsch
,
B. M.
,
Dewey
,
P. A.
, and
Smits
,
A. J.
, “
Propulsive performance of unsteady tandem hydrofoils in an in-line configuration
,” Phys. Fluids
26
(5
), 051901
(2014
).4.
Cong
,
L.
,
Teng
,
B.
, and
Cheng
,
L.
, “
Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow
,” Phys. Fluids
32
, 021903
(2020
).5.
Daghooghi
,
M.
and
Borazjani
,
I.
, “
The hydrodynamic advantages of synchronized swimming in a rectangular pattern
,” Bioinspiration Biomimetics
10
, 056018
(2015
).6.
Dewey
,
P. A.
,
Quinn
,
D. B.
,
Boschitsch
,
B. M.
, and
Smits
,
A. J.
, “
Propulsive performance of unsteady tandem hydrofoils in a side-by-side configuration
,” Phys. Fluids
26
(4
), 041903
(2014
).7.
Di Santo
,
V.
,
Goerig
,
E.
,
Wainwright
,
D.
,
Akanyeti
,
O.
,
Liao
,
J.
,
Castro-Santos
,
T.
, and
Lauder
,
G.
, “
Convergence of undulatory swimming kinematics across a diversity of fishes
,” Proc. Natl. Acad. Sci.
118
(49
), e2113206118
(2021
).8.
Dong
,
G. J.
and
Lu
,
X. L.
, “
Characteristics of flow over traveling wavy foils in a side-by-side arrangement
,” Phys. Fluids
19
, 057107
(2007
).9.
Fields
,
P. A.
, “
Decreased swimming effort in groups of pacific mackerel (Scomber japonicus)
,” Am. Zool.
30
, A134
(1990
).10.
Guo
,
J.
,
Han
,
P.
,
Zhang
,
W.
,
Wang
,
J.
,
Lauder
,
G.
,
Di Santo
,
V.
, and
Dong
,
H.
, “
Vortex dynamics and fin-fin interactions resulting in performance enhancement in fish-like propulsion
,” Phys. Rev. Fluids
8
, 073101
(2023
).11.
Gupta
,
S.
,
Agrawal
,
A.
,
Hourigan
,
K.
,
Thomson
,
M.
, and
Sharma
,
A.
, “
Anguilliform and carangiform fish-inspired hydrodynamic study for an undulating hydrofoil: Effect of shape and adaptive kinematics
,” Phys. Rev. Fluids
7
, 094102
(2022
).12.
Han
,
P.
,
Lauder
,
G.
, and
Dong
,
H.
, “
Hydrodynamics of median-fin interactions in fish-like locomotion: Effects of fin shape and movement
,” Phys. Fluids
32
, 011902
(2020
).13.
Han
,
P.
,
Pan
,
Y.
,
Liu
,
G.
, and
Dong
,
H.
, “
Propulsive performance and vortex wakes of multiple tandem foils pitching in-line
,” J. Fluids Struct.
108
, 103422
(2022
).14.
Hemelrijk
,
C. K.
,
Reid
,
D. A. P.
,
Hildenbrandt
,
H.
, and
Padding
,
J. T.
, “
The increased efficiency of fish swimming in a school
,” Fish
16
, 511
–521
(2015
).15.
Herskin
,
J.
and
Steffensen
,
J. F.
, “
Energy savings in sea bass swimming in a school: Measurements of tail beat frequency and oxygen consumption at different swimming speeds
,” J. Fish Biol.
53
(2
), 366
–376
(1998
).16.
Johansen
,
J. L.
,
Vaknin
,
R.
,
Steffensen
,
J. F.
, and
Domenici
,
P.
, “
Kinematics and energetic benefits of schooling in the labriform fish, striped surfperch Embiotoca lateralis
,” Mar. Ecol. Prog. Ser.
420
, 221
–229
(2010
).17.
Kelly
,
J.
,
Khalid
,
M. S. U.
,
Han
,
P.
, and
Dong
,
H.
, “
Geometric characteristics of flapping foils for enhanced propulsive efficiency
,” J. Fluids Eng.
145
, 061104
(2023a
).18.
Kelly
,
J.
,
Pan
,
Y.
, and
Dong
,
H.
, “
Body shape effects on the hydrodynamic performance of bio-inspired undulating swimmers
,” in ASME Fluids Engineering Division Summer Meeting
, 2022
.19.
Kelly
,
J.
,
Pan
,
Y.
, and
Dong
,
H.
, “
Wake interactions between groups of undulating foils
,” AIAA Paper No. AIAA 2023-2292, 2023b
.20.
Kelly
,
J.
,
Pan
,
Y.
,
Menzer
,
A.
, and
Dong
,
H.
, “
Hydrodynamics of body–body interactions in dense synchronous elongated fish schools
,” Phys. Fluids
35
, 041906
(2023c
).21.
Khalid
,
M.
,
Wang
,
J.
,
Dong
,
H.
, and
Liu
,
M.
, “
Flow transitions and mapping for undulating swimmers
,” Phys. Rev. Fluids
5
, 063104
(2020
).22.
Killen
,
S. S.
,
Marras
,
S.
,
Steffensen
,
J. F.
, and
McKenzie
,
D. J.
, “
Aerobic capacity influences the spatial position of individuals within fish schools
,” Proc. R. Soc. B
279
, 357
–364
(2012
).23.
Kulfan
,
B. M.
, “
Universal parametric geometry representation method
,” J. Aircr.
45
(1
), 142
–158
(2008
).24.
Kulfan
,
B. M.
and
Bussoletti
,
J. E.
, “
“Fundamental” parametric geometry representations for aircraft component shapes
,” AIAA Paper No. AIAA 2006-6948, 2006
.25.
Li
,
C.
and
Dong
,
H.
, “
Three dimensional wake topology and propulsive performance of low-aspect-ratio pitching-rolling plates
,” Phys. Fluids
28
, 071901
(2016
).26.
Li
,
C.
,
Dong
,
H.
, and
Liu
,
G.
, “
Effects of a dynamic trailing-edge flap on the aerodynamic performance and flow structures in hovering flight
,” J. Fluids Struct.
58
, 49
–65
(2015
).27.
Li
,
X.
,
Gu
,
J.
,
Su
,
Z.
, and
Yao
,
Z.
, “
Hydrodynamic analysis of fish schools arranged in the vertical plane
,” Phys. Fluids
33
, 121905
(2021
).28.
Lucas
,
K. N.
,
Lauder
,
G. V.
, and
Tytell
,
E. D.
, “
Airfoil-like mechanics generate thrust on the anterior body of swimming fishes
,” Proc. Natl. Acad. Sci. U. S. A.
117
(19
), 10585
–10592
(2020
).29.
Mittal
,
R.
,
Dong
,
H.
,
Bozkurttas
,
M.
,
Najjar
,
F.
,
Vargas
,
A.
, and
von Loebbecke
,
A.
, “
A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries
,” J. Comput. Phys.
227
, 4825
(2008
).30.
Novati
,
G.
,
Verma
,
S.
,
Alexeev
,
D.
,
Rossinelli
,
D.
,
Van Rees
,
W.
, and
Koumoutsakos
,
P.
, “
Synchronisation through learning for two self-propelled swimmers
,” Bioinspiration Biomimetics
12
, 036001
(2017
).31.
Pan
,
Y.
and
Dong
,
H.
, “
Computational analysis of hydrodynamic interactions in a high-density fish school
,” Phys. Fluids
32
, 121901
(2020
).32.
Pan
,
Y.
and
Dong
,
H.
, “
Effects of phase difference on hydrodynamic interactions and wake patterns in high-density fish schools
,” Phys. Fluids
34
, 111902
(2022
).33.
Pavlov
,
D. S.
and
Kasumyan
,
A. O.
, “
Patterns and mechanisms of schooling behavior in fish: A review
,” J. Ichthyol.
40
(2
), S163
–S231
(2000
).34.
Quinn
,
D. B.
,
Lauder
,
G. V.
, and
Smits
,
A. J.
, “
Flexible propulsors in ground effect
,” Bioinspiration Biomimetics
9
, 036008
(2014a
).35.
Quinn
,
D. B.
,
Moored
,
K. W.
,
Dewey
,
P. A.
, and
Smits
,
A. J.
, “
Unsteady propulsion near a solid boundary
,” J. Fluid Mech.
742
, 152
(2014b
).36.
Seo
,
J.
and
Mittal
,
R.
, “
Improved swimming performance in schooling via leading-edge vortex enhancement
,” Bioinspiration Biomimetics
17
, 066020
(2022
).37.
Tytell
,
E.
,
Borazjani
,
I.
,
Sotiropoulos
,
F.
,
Baker
,
T.
,
Anderson
,
E.
, and
Lauder
,
G.
, “
Disentangling the functional roles of morphology and motion in the swimming of fish
,” Integr. Comp. Biol.
50
, 1140
(2010
).38.
van Rees
,
W.
,
Gazzola
,
M.
, and
Koumoutsakos
,
P.
, “
Optimal shapes for anguilliform swimmers at intermediate Reynolds numbers
,” J. Fluid Mech.
722
, R3
(2013
).39.
Videler
,
J. J.
and
Hess
,
F.
, “
Fast continuous swimming of two pelagic predators, Saithe (Pollachius Virens) and Mackerel (Scomber Scombrus): A kinematic analysis
,” J. Exp. Biol.
109
, 209
(1984
).40.
Wang
,
Y.
,
Sun
,
X.
,
Huang
,
D.
, and
Zheng
,
Z.
, “
Numerical investigation on energy extraction of flapping hydrofoils with different series foil shapes
,” Energy
112
, 1153
–1168
(2016
).41.
Weihs
,
D.
, “
Hydromechanics of fish schooling
,” Nature
241
, 290
(1973
).42.
Xu
,
G. D.
,
Duan
,
W. Y.
, and
Xu
,
W. H.
, “
The propulsion of two flapping foils with tandem configuration and vortex interactions
,” Phys. Fluids
29
, 097102
(2017
).43.
Xu
,
W.
,
Xu
,
G.
,
Li
,
M.
, and
Yang
,
C.
, “
Bio-inspired wake tracking and phase matching of two diagonal flapping swimmers
,” Phys. Fluids
35
, 031902
(2023
).44.
Yu
,
M.
,
Wang
,
Z. J.
, and
Hu
,
H.
, “
High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion
,” J. Fluids Struct.
42
, 166
–186
(2013
).45.
Zhang
,
W.
,
Pan
,
Y.
,
Wang
,
J.
,
Di Santo
,
V.
,
Lauder
,
G. V.
, and
Dong
,
H.
, “
An efficient tree-topological local mesh refinement on Cartesian grids for multiple moving objects in incompressible flow
,” J. Comput. Phys.
479
, 111983
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
