An inflation–deflation propulsion system inspired by the jet propulsion mechanism of squids and other cephalopods is proposed. The two-dimensional squid-like swimmer has a flexible mantle body with a pressure chamber and a nozzle that serves as the inlet and outlet of water. The fluid–structure interaction simulation results indicate that larger mean thrust production and higher efficiency can be achieved in high Reynolds number scenarios compared with the cases in laminar flow. The improved performance at high Reynolds number is attributed to stronger jet-induced vortices and highly suppressed external body vortices, which are associated with drag force. Optimal efficiency is reached when the jet vortices start to dominate the surrounding flow. The mechanism of symmetry-breaking instability under the turbulent flow condition is found to be different from that previously reported in laminar flow. Specifically, this instability in turbulent flow stems from irregular internal body vortices, which cause symmetry breaking in the wake. A higher Reynolds number or smaller nozzle size would accelerate the formation of this symmetry-breaking instability.

1.
Abbott
,
I. H.
and
Von Doenhoff
,
A. E.
,
Theory of Wing Sections, Including a Summary of Airfoil Data
(
Courier Corporation
,
2012
).
2.
Anderson
,
E. J.
and
Grosenbaugh
,
M. A.
, “
Jet flow in steadily swimming adult squid
,”
J. Exp. Biol.
208
,
1125
1146
(
2005
).
3.
Bartol
,
I. K.
,
Krueger
,
P. S.
,
Jastrebsky
,
R. A.
,
Williams
,
S.
, and
Thompson
,
J. T.
, “
Volumetric flow imaging reveals the importance of vortex ring formation in squid swimming tail-first and arms-first
,”
J. Exp. Biol.
219
,
392
403
(
2016
).
4.
Bartol
,
I. K.
,
Krueger
,
P. S.
,
Stewart
,
W. J.
, and
Thompson
,
J. T.
, “
Hydrodynamics of pulsed jetting in juvenile and adult brief squid Lolliguncula brevis: Evidence of multiple jet ‘modes’ and their implications for propulsive efficiency
,”
J. Exp. Biol.
212
,
1889
1903
(
2009a
).
5.
Bartol
,
I. K.
,
Krueger
,
P. S.
,
Stewart
,
W. J.
, and
Thompson
,
J. T.
, “
Pulsed jet dynamics of squid hatchlings at intermediate Reynolds numbers
,”
J. Exp. Biol.
212
,
1506
1518
(
2009b
).
6.
Bartol
,
I. K.
,
Krueger
,
P. S.
,
Thompson
,
J. T.
, and
Stewart
,
W. J.
, “
Swimming dynamics and propulsive efficiency of squids throughout ontogeny
,”
Integr. Comp. Biol.
48
,
720
733
(
2008
).
7.
Bi
,
X.
and
Zhu
,
Q.
, “
Numerical investigation of cephalopod-inspired locomotion with intermittent bursts
,”
Bioinspiration Biomimetics
13
,
056005
(
2018
).
8.
Bi
,
X.
and
Zhu
,
Q.
, “
Dynamics of a squid-inspired swimmer in free swimming
,”
Bioinspiration Biomimetics
15
,
016005
(
2019a
).
9.
Bi
,
X.
and
Zhu
,
Q.
, “
Fluid-structure investigation of a squid-inspired swimmer
,”
Phys. Fluids
31
,
101901
(
2019b
).
10.
Bi
,
X.
and
Zhu
,
Q.
, “
Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer
,”
Phys. Fluids
32
,
081902
(
2020
).
11.
Bungartz
,
H.-J.
,
Lindner
,
F.
,
Gatzhammer
,
B.
,
Mehl
,
M.
,
Scheufele
,
K.
,
Shukaev
,
A.
, and
Uekermann
,
B.
, “
preCICE—A fully parallel library for multi-physics surface coupling
,”
Comput. Fluids
141
,
250
258
(
2016
).
12.
Christianson
,
C.
,
Cui
,
Y.
,
Ishida
,
M.
,
Bi
,
X.
,
Zhu
,
Q.
,
Pawlak
,
G.
, and
Tolley
,
M.
, “
Cephalopod-inspired robot capable of cyclic jet propulsion through shape change
,”
Bioinspiration Biomimetics
(in press) (
2020
).
13.
Costello
,
J. H.
,
Colin
,
S. P.
,
Dabiri
,
J. O.
,
Gemmell
,
B. J.
,
Lucas
,
K. N.
, and
Sutherland
,
K. R.
, “
The hydrodynamics of jellyfish swimming
,”
Ann. Rev. Mar. Sci.
13
,
5-1
(
2020
).
14.
Dhondt
,
G.
,
The Finite Element Method for Three-Dimensional Thermomechanical Applications
(
John Wiley & Sons
,
2004
).
15.
Eleni
,
D. C.
,
Athanasios
,
T. I.
, and
Dionissios
,
M. P.
, “
Evaluation of the turbulence models for the simulation of the flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil
,”
J. Mech. Eng. Res.
4
,
100
111
(
2012
).
16.
Gosline
,
J. M.
and
DeMont
,
M. E.
, “
Jet-propelled swimming in squids
,”
Sci. Am.
252
,
96
103
(
1985
).
17.
Gosline
,
J. M.
,
Steeves
,
J. D.
,
Harman
,
A. D.
, and
Demont
,
M. E.
, “
Patterns of circular and radial mantle muscle activity in respiration and jetting of the squid Loligo opalescens
,”
J. Exp. Biol.
104
,
97
109
(
1983
).
18.
Han
,
P.
,
Lauder
,
G. V.
, and
Dong
,
H.
, “
Hydrodynamics of median-fin interactions in fish-like locomotion: Effects of fin shape and movement
,”
Phys. Fluids
32
,
011902
(
2020
).
19.
Hoover
,
A.
and
Miller
,
L.
, “
A numerical study of the benefits of driving jellyfish bells at their natural frequency
,”
J. Theor. Biol.
374
,
13
25
(
2015
).
20.
Hoover
,
A. P.
,
Griffith
,
B. E.
, and
Miller
,
L. A.
, “
Quantifying performance in the medusan mechanospace with an actively swimming three-dimensional jellyfish model
,”
J. Fluid Mech.
813
,
1112
1155
(
2017
).
21et al..
Hou
,
T.
,
Yang
,
X.
,
Su
,
H.
,
Jiang
,
B.
,
Chen
,
L.
,
Wang
,
T.
, and
Liang
,
J.
, “
Design and experiments of a squid-like aquatic-aerial vehicle with soft morphing fins and arms
,” in
2019 International Conference on Robotics and Automation (ICRA)
(
IEEE
,
2019
), pp.
4681
4687
.
22et al..
Jameson
,
A.
,
Schmidt
,
W.
, and
Turkel
,
E. L. I.
, “
Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes
,” in
14th Fluid and Plasma Dynamics Conference
(
American Institute of Aeronautics and Astronautics
,
1981
).
23.
Lauder
G. V., Madden
, P. G. A.
,
Tangorra
,
J. L.
,
Anderson
,
E.
, and
Baker
,
T. V.
, “
Bioinspiration from fish for smart material design and function
,”
Smart Mater. Struct.
20
,
094014
(
2011
).
24.
Liu
,
W.
,
Xiao
,
Q.
, and
Zhu
,
Q.
, “
Passive flexibility effect on oscillating foil energy harvester
,”
AIAA J.
54
,
1172
1187
(
2016
).
25.
Luo
,
Y.
,
Xiao
,
Q.
,
Shi
,
G.
,
Pan
,
G.
, and
Chen
,
D.
, “
The effect of variable stiffness of tuna-like fish body and fin on swimming performance
,”
Bioinspiration Biomimetics
(in press) (
2020a
).
26.
Luo
,
Y.
,
Xiao
,
Q.
,
Shi
,
G.
,
Wen
,
L.
,
Chen
,
D.
, and
Pan
,
G.
, “
A fluid–structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness
,”
J. Fluids Struct.
92
,
102778
(
2020b
).
27.
Megill
,
W. M.
,
Gosline
,
J. M.
, and
Blake
,
R. W.
, “
The modulus of elasticity of fibrillin-containing elastic fibres in the mesoglea of the hydromedusa Polyorchis penicillatus
,”
J. Exp. Biol.
208
,
3819
3834
(
2005
).
28.
Mehl
,
M.
,
Uekermann
,
B.
,
Bijl
,
H.
,
Blom
,
D.
,
Gatzhammer
,
B.
, and
van Zuijlen
,
A.
, “
Parallel coupling numerics for partitioned fluid–structure interaction simulations
,”
Comput. Math. Appl.
71
,
869
891
(
2016
).
29.
Miles
,
J. G.
and
Battista
,
N. A.
, “
Naut your everyday jellyfish model: Exploring how tentacles and oral arms impact locomotion
,”
Fluids
4
,
169
(
2019
).
30.
O’Dor
,
R. K.
, “
How squid swim and fly
,”
Can. J. Zool.
91
,
413
419
(
2013
).
31.
Park
,
S. G.
,
Kim
,
B.
,
Lee
,
J.
,
Huang
,
W.-X.
, and
Sung
,
H. J.
, “
Dynamics of prolate jellyfish with a jet-based locomotion
,”
J. Fluids Struct.
57
,
331
343
(
2015
).
32.
Peppa
,
S.
and
Triantafyllou
,
G. S.
, “
Sensitivity of two-dimensional flow past transversely oscillating cylinder to streamwise cylinder oscillations
,”
Phys. Fluids
28
,
037102
(
2016
).
33.
Renda
,
F.
,
Giorgio-Serchi
,
F.
,
Boyer
,
F.
, and
Laschi
,
C.
, “
Modelling cephalopod-inspired pulsed-jet locomotion for underwater soft robots
,”
Bioinspiration Biomimetics
10
,
055005
(
2015
).
34.
Sadeghi
,
M.
,
Parallel Computation of Three-Dimensional Aeroelastic Fluid-Structure Interaction
(
University of California
,
Irvine
,
2004
).
35et al..
Sadeghi
,
M.
,
Yang
,
S.
,
Liu
,
F.
, and
Tsai
,
H.
, “
Parallel computation of wing flutter with a coupled Navier-Stokes/CSD method
,” in
41st Aerospace Sciences Meeting and Exhibit
(
American Institute of Aeronautics and Astronautics
,
2003
), p.
1347
.
36.
Salazar
,
R.
,
Fuentes
,
V.
, and
Abdelkefi
,
A.
, “
Classification of biological and bioinspired aquatic systems: A review
,”
Ocean Eng.
148
,
75
114
(
2018
).
37.
Shi
,
G.
,
Xiao
,
Q.
,
Zhu
,
Q.
, and
Liao
,
W.
, “
Fluid-structure interaction modeling on a 3D ray-strengthened caudal fin
,”
Bioinspiration Biomimetics
14
,
036012
(
2019
).
38.
Spagnolie
,
S. E.
and
Shelley
,
M. J.
, “
Shape-changing bodies in fluid: Hovering, ratcheting, and bursting
,”
Phys. Fluids
21
,
013103
(
2009
).
39.
Steele
,
S. C.
,
Weymouth
,
G. D.
, and
Triantafyllou
,
M. S.
, “
Added mass energy recovery of octopus-inspired shape change
,”
J. Fluid Mech.
810
,
155
174
(
2017
).
40.
Thompson
,
J. T.
and
Kier
,
W. M.
, “
Ontogenetic changes in mantle kinematics during escape-jet locomotion in the oval squid, Sepioteuthis lessoniana lesson, 1830
,”
Biol. Bull.
201
,
154
166
(
2001
).
41.
Thompson
,
J. T.
and
Kier
,
W. M.
, “
Ontogeny of mantle musculature and implications for jet locomotion in oval squid Sepioteuthis lessoniana
,”
J. Exp. Biol.
209
,
433
443
(
2006
).
42.
Ward
,
D. V.
, “
Locomotory function of the squid mantle
,”
J. Zool.
167
,
487
499
(
1972
).
43.
Weihs
,
D.
, “
Energetic advantages of burst swimming of fish
,”
J. Theor. Biol.
48
,
215
229
(
1974
).
44.
Weymouth
,
G. D.
,
Subramaniam
,
V.
, and
Triantafyllou
,
M. S.
, “
Ultra-fast escape maneuver of an octopus-inspired robot
,”
Bioinspiration Biomimetics
10
,
016016
(
2015
).
45.
Weymouth
,
G. D.
and
Triantafyllou
,
M. S.
, “
Ultra-fast escape of a deformable jet-propelled body
,”
J. Fluid Mech.
721
,
367
385
(
2013
).
46.
Wilcox
,
D. C.
,
Turbulence Modeling for CFD
(
DCW Industries La Canada
,
CA
,
1998
).
47.
Xiao
,
Q.
and
Liao
,
W.
, “
Numerical investigation of angle of attack profile on propulsion performance of an oscillating foil
,”
Comput. Fluids
39
,
1366
1380
(
2010
).
48.
Xiao
,
Q.
,
Liao
,
W.
,
Yang
,
S.
, and
Peng
,
Y.
, “
How motion trajectory affects energy extraction performance of a biomimic energy generator with an oscillating foil?
,”
Renewable Energy
37
,
61
75
(
2012
).

Supplementary Material

You do not currently have access to this content.