We propose a novel underwater propulsion system inspired by the jet-propelled locomotion mechanism of squids and other cephalopods. A two-dimensional nonaxisymmetric fluid-structural interaction model is developed to illustrate the physical mechanisms involved in the propulsive performance of this design. The model includes a deformable body with a pressure chamber undergoing periodic inflation and deflation motions enabled by attached springs and a nozzle through which the chamber is refilled and discharged (to form a jet). By using an immersed-boundary algorithm, we numerically investigate the dynamics of this system in the tethered mode. The thrust generation is found to increase with the frequency of body deformation, whereas the efficiency reaches a peak at a certain frequency. Examinations of the surrounding flow field illustrate a combination of vortices shed from the body and the nozzle. The optimal efficiency is reached when the nozzle-generated vortices start to dominate the wake. Our simulations also suggest that steady-state response can only be sustained for a few cycles before the wake is disturbed by a symmetry-breaking instability, which significantly affects the propulsive performance. Special strategies are needed to achieve stable long-distance swimming.

1.
P.
Webb
, “
The biology of fish swimming
,” in
Mechanics and Physiology of Animal Swimming
, edited by
L.
Maddock
,
Q.
Bone
, and
J.
Rayner
(
Cambridge University Press
,
Cambridge
,
1994
), pp.
45
62
.
2.
W.
Harder
,
Anatomy of Fishes
(
E. Schweizerbartsche Verlagsbuchhandlung
,
Stuttgart
,
1975
).
3.
B.
Flammang
and
G.
Lauder
, “
Speed-dependent intrinsic caudal fin muscle recruitment during steady swimming in bluegill sunfish, Lepomis macrochirus
,”
J. Exp. Biol.
211
,
587
598
(
2008
).
4.
B.
Flammang
and
G.
Lauder
, “
Caudal fin shape modulation and control during acceleration, braking and backing maneuvers in bluegill sunfish, Lepomis macrochirus
,”
J. Exp. Biol.
212
,
277
286
(
2009
).
5.
J.
Gosline
and
M.
DeMont
, “
Jet-propelled swimming in squid
,”
Sci. Am.
252
,
96
103
(
1985
).
6.
R.
O’Dor
, “
How squid swim and fly
,”
Can. J. Zool.
91
,
413
419
(
2013
).
7.
H.
Neumeister
,
B.
Ripley
,
T.
Preuss
, and
W. F.
Gilly
, “
Effects of temperature on escape jetting in the squid Loligo opalescens
,”
J. Exp. Biol.
203
,
547
557
(
2000
).
8.
S.
Steele
,
G.
Weymouth
, and
M.
Triantafyllou
, “
Added mass energy recovery of octopus-inspired shape change
,”
J. Fluid Mech.
810
,
155
174
(
2017
).
9.
E.
Anderson
and
M.
Grosenbaugh
, “
Jet flow in steadily swimming adult squid
,”
J. Exp. Biol.
208
,
1125
1146
(
2005
).
10.
M.
DeMont
and
J.
Gosline
, “
Mechanics of jet propulsion in the hydromedusan jellyfish, polyorchis pexicillatus: I. Mechanical properties of the locomotor structure
,”
J. Exp. Biol.
134
,
313
332
(
1988
).
11.
W.
Megill
,
J.
Gosline
, and
R.
Blake
, “
The modulus of elasticity of fibrillin-containing elastic fibres in the mesoglea of the hydromedusa polyorchis penicillatus
,”
J. Exp. Biol.
208
,
3819
3834
(
2005
).
12.
J.
Dabiri
, “
Optimal vortex formation as a unifying principle in biological propulsion
,”
Annu. Rev. Fluid Mech.
41
,
17
33
(
2009
).
13.
B.
Gemmell
,
J.
Costello
,
S.
Colin
,
C.
Stewart
,
J.
Dabiri
,
D.
Tafti
, and
S.
Priya
, “
Passive energy recapture in jellyfish contributes to propulsive advantage over other metazoans
,”
Proc. Nat. Acad. Sci. U. S. A.
110
,
17904
17909
(
2013
).
14.
W.
Huang
and
H.
Sung
, “
An immersed boundary method for fluid-flexible structure interaction
,”
Comput. Methods Appl. Mech. Eng.
198
,
2650
2661
(
2009
).
15.
H.
Zhao
,
J.
Freund
, and
R.
Moser
, “
A fixed-mesh method for incompressible flow–structure systems with finite solid deformations
,”
J. Comput. Phys.
227
,
3114
3140
(
2008
).
16.
G.
Herschlag
and
L.
Miller
, “
Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish
,”
J. Theor. Biol.
285
,
84
95
(
2011
).
17.
M.
Wilson
,
J.
Peng
,
J.
Dabiri
, and
J.
Eldredge
, “
Lagrangian coherent structures in low Reynolds number swimming
,”
J. Phys.: Condens. Matter
21
,
204105
(
2009
).
18.
S.
Alben
,
L.
Miller
, and
J.
Peng
, “
Efficient kinematics for jet-propelled swimming
,”
J. Fluid Mech.
733
,
100
133
(
2013
).
19.
S.
Park
,
B.
Kim
,
J.
Lee
,
W.
Huang
, and
H.
Sung
, “
Dynamics of prolate jellyfish with a jet-based locomotion
,”
J. Fluids. Struct.
57
,
331
343
(
2015
).
20.
S.
Park
,
C.
Chang
,
W.
Huang
, and
H.
Sung
, “
Simulation of swimming oblate jellyfish with a padddling-based locomotion
,”
J. Fluid Mech.
748
,
731
755
(
2014
).
21.
A.
Hoover
,
B.
Griffith
, and
L.
Miller
, “
Quantifying performance in the meedusan mechanospace with an actively swimming three-dimensional jellyfish model
,”
J. Fluid Mech.
813
,
1112
1155
(
2017
).
22.
A.
Hoover
and
L.
Miller
, “
A numerical study of the benefits of driving jellyfish bells at their natural frequency
,”
J. Theor. Biol.
374
,
13
25
(
2015
).
23.
A.
Hoover
,
A.
Porras
, and
L.
Miller
, “
Pump or coast: The role of resonance and passive energy recapture in medusan swimming performance
,”
J. Fluid Mech.
863
,
1031
1061
(
2019
).
24.
E.
Anderson
,
H.
Jiang
, and
M.
Grosenbaugh
, “
Jet flow in steadily swimming squid
,”
Am. Zool.
41
,
1380
1381
(
2001
).
25.
H.
Jiang
and
M.
Grosenbaugh
, “
Numerical simulation of vortex ring formation in the presence of background flow
,”
Theor. Comput. Fluid Dyn.
20
,
103
123
(
2006
).
26.
I.
Bartol
,
P.
Krueger
,
W.
Stewart
, and
J.
Thompson
, “
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
(
2009
).
27.
I.
Bartol
,
P.
Krueger
,
R.
Jastrebsky
,
S.
Williams
, and
J.
Thompson
, “
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
).
28.
S.
Spagnolie
and
M.
Shelley
, “
Shape changing bodies in squid: Hovering, ratcheting, and bursting
,”
Phys. Fluids
21
,
013103
(
2009
).
29.
G.
Weymouth
and
M.
Triantafyllou
, “
Ultra-fast escape of a deformable jet-propelled body
,”
J. Fluid Mech.
721
,
367
375
(
2013
).
30.
M.
Triantafyllou
,
G.
Weymouth
, and
J.
Miao
, “
Biomimetic survival hydrodynamics and flow sensing
,”
Annu. Rev. Fluid Mech.
48
,
1
26
(
2016
).
31.
G.
Weymouth
,
V.
Subramaniam
, and
M.
Triantafyllou
, “
Ultra-fast escape maneuver of an octopus-inspired robot
,”
Bioinspiration Biomimetics
10
,
016016
(
2015
).
32.
F.
Renda
,
F.
Giorgio-Serchi
,
F.
Boyer
, and
C.
Laschi
, “
Modelling cephalopod-inspired pulsed-jet locomotion for underwater soft robots
,”
Bioinspiration Biomimetics
10
,
055005
(
2015
).
33.
F.
Giorgio-Serchi
,
A.
Arienti
, and
C.
Laschi
, “
Underwater soft-bodied pulsed-jet thrusters: Actuator modeling and performance profiling
,”
Int. J. Rob. Res.
35
,
1308
1329
(
2016
).
34.
X.
Bi
and
Q.
Zhu
, “
Numerical investigation of cephalopod-inspired locomotion with intermittent bursts
,”
Bioinspiration Biomimetics
13
,
056005
(
2018
).
35.
M.
Gharib
,
R.
Rambod
, and
K.
Shariff
, “
A universal time scale for vortex ring formation
,”
J. Fluid Mech.
360
,
121
140
(
1998
).
36.
P.
Linden
and
J.
Turner
, “
Optimal vortex rings and aquatic propulsion mechanisms
,”
Proc. R. Soc. London, Ser. B
271
,
647
653
(
2004
).
37.
P.
Linden
, “
The efficiency of pulsed-jet propulsion
,”
J. Fluid Mech.
668
,
1
4
(
2011
).
38.
J.
Gosline
,
J.
Steeves
,
A.
Harman
, and
M.
DeMont
, “
Patterns of circular and radial mantel muscle activity in respiration and jetting of the squid Loligo Opalescens
,”
J. Exp. Biol.
104
,
97
109
(
1983
).
39.
B.
Griffith
,
X.
Luo
,
D.
McQueen
, and
C.
Peskin
, “
Comparative jet wake structure and swimming performance of salps
,”
Int. J. Appl. Mech.
1
,
137
177
(
2009
).
40.
S.
Xu
and
Z.
Wang
, “
An immersed interface method for simulating the interaction of a fluid with moving boundaries
,”
J. Comput. Phys.
216
(
2
),
454
493
(
2006
).
41.
D.
Golddstein
,
R.
Handler
, and
L.
Sirovich
, “
Modelling a no-slip flow boundary with an external force field
,”
J. Comput. Phys.
105
,
354
366
(
1993
).
42.
W.
Huang
,
S.
Shin
, and
H.
Sung
, “
Simulation of flexible filaments in a uniform flow by the immersed boundary method
,”
J. Comput. Phys.
226
,
2206
2228
(
2007
).
43.
K.
Shoele
and
Q.
Zhu
, “
Leading edge strengthening and the propulsion performance of flexible ray fins
,”
J. Fluid Mech.
693
,
402
432
(
2012
).
44.
K.
Shoele
and
Q.
Zhu
, “
Performance of a wing with nonuniform flexibility in hovering flight
,”
Phys. Fluids
25
,
041901
(
2013
).
45.
C.
Peskin
, “
The immersed boundary method
,”
Acta Numer.
11
,
479
517
(
2002
).
46.
K.
Shoele
and
Q.
Zhu
, “
Flow-induced vibrations of a deformable ring
,”
J. Fluid Mech.
650
,
343
363
(
2010
).
47.
K.
Shoele
and
Q.
Zhu
, “
Performance of synchronized fins in biomimetic propulsion
,”
Bioinspiration Biomimetics
10
,
026008
(
2015
).
48.
E.
Anderson
and
M.
Demont
, “
The mechanics of locomotion in the squid Loligo pealei: Locomotory function and unsteady hydrodynamics of the jet and intramantle pressure
,”
J. Exp. Biol.
203
,
2851
2863
(
2000
).
49.
K.
Sutherland
and
L.
Madin
, “
Comparative jet wake structure and swimming performance of salps
,”
J. Exp. Biol.
213
,
2967
2975
(
2010
).
50.
A.
Leonard
, “
Vortex methods for flow simulation
,”
J. Comput. Phys.
37
,
289
335
(
1980
).
You do not currently have access to this content.