Hydrodynamic cloaks, a type of metamaterials possessing zero-drag properties, show fascinating potential for aerospace, marine engineering, and high-speed transportation. However, achieving zero drag with hydrodynamic cloaks in viscous flows is challenged by the complexity of the Navier–Stokes equations. This study designs spherical hydrodynamic cloaks based on machine learning, which allow objects to move in a viscous fluid without disturbing the flow fields. These cloaks merely require the supply of uniform external forces, unaided by metamaterials, allowing objects wrapped in the cloak to move unimpeded through viscous flow fields. Numerical simulations show that these cloaks provide significant drag reduction efficiency (up to 96.26%) and enhance flow stability by eliminating lift fluctuations. These findings provide new insights into flow control and expand the applicability of hydrodynamic metamaterials to high Reynolds number environments, with promising applications in multiphysics fields such as thermal-hydrodynamic coupling and acoustic-hydrodynamic coupling.
REFERENCES
1.
F. E.
Fish
and
G. V.
Lauder
, “
Passive and active flow control by swimming fishes and mammals
,” Annu. Rev. Fluid Mech.
38
, 193
–224
(2006
).2.
H.
Choi
,
W. P.
Jeon
, and
J.
Kim
, “
Control of flow over a bluff body
,” Annu. Rev. Fluid Mech.
40
, 113
–139
(2008
).3.
D.
Greenblatt
and
D. R.
Williams
, “
Flow control for unmanned air vehicles
,” Annu. Rev. Fluid Mech.
54
, 383
–412
(2022
).4.
S.
Jeon
,
J.
Choi
,
W. P.
Jeon
,
H.
Choi
, and
J.
Park
, “
Active control of flow over a sphere for drag reduction at a subcritical Reynolds number
,” J. Fluid Mech.
517
, 113
–129
(2004
).5.
L. N.
Cattafesta
III and
M.
Sheplak
, “
Actuators for active flow control
,” Annu. Rev. Fluid Mech.
43
, 247
–272
(2011
).6.
S.
Chae
,
S.
Lee
,
J.
Kim
, and
J. H.
Lee
, “
Adaptive-passive control of flow over a sphere for drag reduction
,” Phys. Fluids
31
, 015107
(2019
).7.
V. M.
Shalaev
, “
Transforming light
,” Science
322
, 384
–386
(2008
).8.
H.
Chen
,
C. T.
Chan
, and
P.
Sheng
, “
Transformation optics and metamaterials
,” Nat. Mater.
9
, 387
–396
(2010
).9.
J. B.
Pendry
,
D.
Schurig
, and
D. R.
Smith
, “
Controlling electromagnetic fields
,” Science
312
, 1780
–1782
(2006
).10.
D.
Schurig
,
J. J.
Mock
,
B. J.
Justice
,
S. A.
Cummer
,
J. B.
Pendry
,
A. F.
Starr
, and
D. R.
Smith
, “
Metamaterial electromagnetic cloak at microwave frequencies
,” Science
314
, 977
–980
(2006
).11.
D.
Shin
,
Y.
Urzhumov
,
Y.
Jung
,
G.
Kang
,
S.
Baek
,
M.
Choi
,
H.
Park
,
K.
Kim
, and
D. R.
Smith
, “
Broadband electromagnetic cloaking with smart metamaterials
,” Nat. Commun.
3
, 1213
(2012
).12.
L.
Zigoneanu
,
B. I.
Popa
, and
S. A.
Cummer
, “
Three-dimensional broadband omnidirectional acoustic ground cloak
,” Nat. Mater.
13
, 352
–355
(2014
).13.
C. Z.
Fan
,
Y.
Gao
, and
J. P.
Huang
, “
Shaped graded materials with an apparent negative thermal conductivity
,” Appl. Phys. Lett.
92
, 251907
(2008
).14.
S.
Guenneau
,
C.
Amra
, and
D.
Veynante
, “
Transformation thermodynamics: cloaking and concentrating heat flux
,” Opt. Express
20
, 8207
–8218
(2012
).15.
G.
Dai
and
J.
Wang
, “
Transformation hydrodynamic metamaterials: Rigorous arguments on form invariance and structural design with spatial variance
,” Phys. Rev. E
107
, 055108
(2023
).16.
Y. A.
Urzhumov
and
D. R.
Smith
, “
Fluid flow control with transformation media
,” Phys. Rev. Lett.
107
, 074501
(2011
).17.
M.
Chen
,
X.
Shen
, and
L.
Xu
, “
Realizing the thinnest hydrodynamic cloak in porous medium flow
,” Innovation
3
, 100263
(2022
).18.
C.
Jiang
,
H.
Nie
,
M.
Chen
,
X.
Shen
, and
L.
Xu
, “
Achieving environmentally-adaptive and multifunctional hydrodynamic metamaterials through active control
,” Adv. Mater.
36
, e2313986
(2024
).19.
J.
Park
,
J. R.
Youn
, and
Y. S.
Song
, “
Hydrodynamic metamaterial cloak for drag-free flow
,” Phys. Rev. Lett.
123
, 074502
(2019
).20.
J.
Park
and
Y. S.
Song
, “
Laminar flow manipulators
,” Extreme Mech. Lett.
40
, 100908
(2020
).21.
H.
Pang
,
Y.
You
, and
K.
Chen
, “
Hydrodynamic metamaterial redirector for steering fluid flow in pipelines with arbitrary curvatures
,” J. Fluid Mech.
984
, A18
(2024
).22.
F.
Tay
,
Y.
Zhang
,
H.
Xu
,
H.
Goh
,
Y.
Luo
, and
B.
Zhang
, “
A metamaterial-free fluid-flow cloak
,” Natl. Sci. Rev.
9
, nwab205
(2022
).23.
B.
Wang
,
T. M.
Shih
,
L.
Xu
,
G.
Dai
, and
J.
Huang
, “
Intangible hydrodynamic cloaks for convective flows
,” Phys. Rev. Appl.
15
, 034014
(2021a
).24.
E.
Boyko
,
V.
Bacheva
,
M.
Eigenbrod
,
F.
Paratore
,
A. D.
Gat
,
S.
Hardt
, and
M.
Bercovici
, “
Microscale hydrodynamic cloaking and shielding via electro-osmosis
,” Phys. Rev. Lett.
126
, 184502
(2021
).25.
C. L.
Wu
,
B.
Wang
,
N. Z.
Yao
,
H.
Wang
, and
X.
Wang
, “
Meta-hydrodynamics for freely manipulating fluid flows
,” Phys. Fluids
36
, 063613
(2024
).26.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based on the square of the velocity gradient tensor
,” Flow Turbul. Combust.
62
, 183
–200
(1999
).27.
A. G.
Tomboulides
and
S. A.
Orszag
, “
Numerical investigation of transitional and weak turbulent flow past a sphere
,” J. Fluid Mech.
416
, 45
–73
(2000
).28.
A.
Wächter
and
L. T.
Biegler
, “
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
,” Math. Program.
106
, 25
–57
(2006
).29.
T. A.
Johnson
and
V. C.
Patel
, “
Flow past a sphere up to a Reynolds number of 300
,” J. Fluid Mech.
378
, 19
–70
(1999
).30.
J. L. R.
d'Alembert
, Essai d'une nouvelle théorie de la résistance des fluides
(
David l'aîné
, 1752
).31.
V.
Kalro
and
T.
Tezduyar
, “
Parallel 3d finite element computation of unsteady flows past a sphere
,” in Advances in High Performance Computing
(
Springer
, 1997
), pp. 335
–352
.32.
S.
Lee
, “
A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate reynolds numbers
,” Comput. Fluids
29
, 639
–667
(2000
).33.
R.
Campregher
,
J.
Militzer
,
S. S.
Mansur
, and
A. D.
Silveira Neto
, “
Computations of the flow past a still sphere at moderate Reynolds numbers using an immersed boundary method
,” J. Braz. Soc. Mech. Sci.
31
, 344
–352
(2009
).34.
T. M.
Wang
,
B.
Shih
, and
J.
Huang
, “
Transformation heat transfer and thermo-hydrodynamic cloaks for creeping flows: Manipulating heat fluxes and fluid flows simultaneously
,” Appl. Therm. Eng.
190
, 116726
(2021b
).35.
H.
Wang
,
N. Z.
Yao
,
B.
Wang
,
T. M.
Shih
, and
X.
Wang
, “
Homogeneous venturi-effect concentrators for creeping flows: Magnifying flow velocities and heat fluxes simultaneously
,” Appl. Therm. Eng.
206
, 118012
(2022
).36.
S.
Dong
,
G. S.
Triantafyllou
, and
G. E.
Karniadakis
, “
Elimination of vortex streets in bluff-body flows
,” Phys. Rev. Lett.
100
, 204501
(2008
).37.
S. J.
Kim
and
C. M.
Lee
, “
Investigation of the flow around a circular cylinder under the influence of an electromagnetic force
,” Exp. Fluids
28
, 252
–260
(2000
).38.
H.
Xu
,
Y.
He
,
K. L.
Strobel
,
C. K.
Gilmore
,
S. P.
Kelley
,
C. C.
Hennick
,
T.
Sebastian
,
M. R.
Woolston
,
D. J.
Perreault
, and
S. R.
Barrett
, “
Flight of an aeroplane with solid-state propulsion
,” Nat.
563
, 532
–535
(2018
).39.
Z.
Chen
and
N.
Aubry
, “
Active control of cylinder wake
,” Commun. Nonlinear Sci.
10
, 205
–216
(2005
).40.
A.
Goldburg
and
B.
Florsheim
, “
Transition and Strouhal number for the incompressible wake of various bodies
,” Phys. Fluids
9
, 45
–50
(1966
).41.
H.
Sakamoto
and
H.
Haniu
, “
A study on vortex shedding from spheres in a uniform flow
,” J. Fluids Eng.
112
, 386
–392
(1990
).© 2025 Author(s). Published under an exclusive license by AIP Publishing.
2025
Author(s)
You do not currently have access to this content.
