The wake stabilization of a triangular cluster of three rotating cylinders is investigated. Experiments are performed at Reynolds number Re ∼ 2200. Flow control is realized using rotating cylinders spanning the wind-tunnel height. The cylinders are individually connected to identical brushless DC motors. Two-component planar particle image velocimetry measurements and constant temperature hot-wire anemometry were used to characterize the flow without and with actuation. Main open-loop configurations are studied and different controlled flow topologies are identified. Machine learning control is then implemented for the optimization of the flow control performance. Linear genetic algorithms are used here as the optimization technique for the open-loop constant speed-actuators. Two different cost functions J are considered targeting either drag reduction or wake symmetrization. The functions are estimated based on the velocity from three hot-wire sensors in the wake. It is shown that the machine learning approach is an effective strategy for controlling the wake characteristics. More significantly, the results show that machine learning strategies can reveal unanticipated solutions or parameter relations, in addition to being a tool for optimizing searches in large parameter spaces.

1.
D.
Sumner
,
S. J.
Price
, and
M. P.
Païdoussis
, “
Flow-pattern identification for two staggered circular cylinders in cross-flow
,”
J. Fluid Mech.
411
,
263
303
(
2000
).
2.
M. M.
Zdravkovich
, “
Smoke observations of the wake of a group of three cylinders at low Reynolds number
,”
J. Fluid Mech.
32
(
2
),
339
351
(
1968
).
3.
K.
Lam
and
W. C.
Cheung
, “
Phenomena of vortex shedding and flow interference of three cylinders in different equilateral arrangements
,”
J. Fluid Mech.
196
,
1
(
1988
).
4.
A. T.
Sayers
, “
Vortex shedding from groups of three and four equispaced cylinders situated in a cross flow
,”
J. Wind Eng. Ind. Aerodyn.
34
(
2
),
213
221
(
1990
).
5.
M. S.
Bansal
and
S.
Yarusevych
, “
Experimental study of flow through a cluster of three equally spaced cylinders
,”
Exp. Therm. Fluid Sci.
80
,
203
217
(
2017
).
6.
K.
Lam
,
J. Y.
Li
, and
R. M. C.
So
, “
Force coefficients and Strouhal numbers of four cylinder in cross flow
,”
J. Fluids Struct.
18
(
3-4
),
305
324
(
2003
).
7.
A.
Nicolle
and
I.
Eames
, “
Numerical study of flow through and around a circular array of cylinders
,”
J. Fluid Mech.
679
(
May 2011
),
1
31
(
2011
).
8.
A. T.
Sayers
, “
Flow interference between four equispaced cylinders when subjected to a cross flow
,”
J. Wind Eng. Ind. Aerodyn.
31
(
1
),
9
28
(
1988
).
9.
C. J.
Apelt
,
G. S.
West
, and
A. A.
Szewczyk
, “
The effects of wake splitter plates on the flow past a circular cylinder in the range 104<R<5×104
,”
J. Fluid Mech.
61
(
01
),
187
198
(
1973
).
10.
M. F.
Unal
and
D.
Rockwell
, “
On vortex formation from a cylinder. Part 2. Control by splitter-plate interference
,”
J. Fluid Mech.
190
,
513
529
(
1987
).
11.
K.
Kwon
and
H.
Choi
, “
Control of laminar vortex shedding behind a circular cylinder using splitter plates
,”
Phys. Fluids
8
(
2
),
479
(
1996
).
12.
C.
Raibaudo
, “
Characterization of the transient of a separated turbulent boundary layer under control and applications to advanced closed-loop controllers
,” Ph.D. thesis,
École Centrale de Lille
,
2015
.
13.
C.
Raibaudo
,
M.
Stanislas
, and
F.
Kerhervé
, “
Transient characterization of the reattachment of a massively separated turbulent boundary layer under flow control
,”
Flow, Turbul. Combust.
98
(
4
),
1039
1063
(
2017
).
14.
K.
Roussopoulos
, “
Feedback control of vortex shedding at low Reynolds numbers
,”
J. Fluid Mech.
248
(
-1
),
267
(
1993
).
15.
L. W.
Sigurdson
, “
The structure and control of a turbulent reattaching flow
,”
J. Fluid Mech.
298
(
-1
),
139
(
1995
).
16.
G.
Artana
,
R.
Sosa
,
E.
Moreau
, and
G.
Touchard
, “
Control of the near-wake flow around a circular cylinder with electrohydrodynamic actuators
,”
Exp. Fluids
35
,
580
588
(
2003
).
17.
K. T.
Hyun
and
C. H.
Chun
, “
The wake flow control behind a circular cylinder using ion wind
,”
Exp. Fluids
35
,
541
552
(
2003
).
18.
T. E.
Mclaughlin
,
M. D.
Munska
,
J. P.
Vaeth
,
T. E.
Dauwalter
,
J. R.
Goode
, and
S. G.
Siegel
, “
Plasma-based actuators for cylinder wake vortex control
,” in
2nd AIAA Flow Control Conference
,
Portland, USA
,
2004
.
19.
S. V.
Gordeyev
and
F. O.
Thomas
, “
A temporal proper decomposition (TPOD) for closed-loop flow control
,”
Exp. Fluids
54
(
3
),
1477
(
2013
).
20.
C.-J.
Wu
,
L.
Wang
, and
J.-Z.
Wu
, “
Suppression of the von Karman vortex street behind a circular cylinder by a travelling wave generated by a flexible surface
,”
J. Fluid Mech.
574
,
365
391
(
2007
).
21.
L. N.
Cattafesta
and
M.
Sheplak
, “
Actuators for active flow control
,”
Annu. Rev. Fluid Mech.
43
(
1
),
247
272
(
2011
).
22.
G. B.
Schubauer
and
H. K.
Skramstad
, “
Laminar boundary-layer oscillations and transition on a flat plate
,”
J. Res. Natl. Bur. Stand.
38
(
2
),
251
(
1947
).
23.
C.
Homescu
,
I. M.
Navon
, and
Z.
Li
, “
Suppression of vortex shedding for flow around a circular cylinder using optimal control
,”
Int. J. Numer. Methods Fluids
38
(
March 2001
),
43
69
(
2002
).
24.
M.
Bergmann
and
L.
Cordier
, “
Optimal rotary control of the cylinder wake using pod reduced order model
,”
Phys. Fluids
17
(
9
),
097101
(
2005
).
25.
S.
Mittal
, “
Control of flow past bluff bodies using rotating control cylinders
,”
J. Fluids Struct.
15
(
2
),
291
326
(
2001
).
26.
J. W.
He
,
R.
Glowinski
,
R.
Metcalfe
,
A.
Nordlander
, and
J.
Periaux
, “
Active control and drag optimization for flow past a circular cylinder I. Oscillatory cylinder rotation
,”
J. Comput. Phys.
163
(
1
),
83
117
(
2000
).
27.
B.
Protas
and
J. E.
Wesfreid
, “
Drag force in the open-loop control of the cylinder wake in the laminar regime
,”
Phys. Fluids
14
(
2
),
810
826
(
2002
).
28.
P. T.
Tokumaru
and
P. E.
Dimotakis
, “
Rotary oscillation control of a cylinder wake
,”
J. Fluid Mech.
224
,
77
90
(
1991
).
29.
S.
Choi
,
H.
Choi
, and
S.
Kang
, “
Characteristics of flow over a rotationally oscillating cylinder at low Reynolds number
,”
Phys. Fluids
14
(
2
),
2767
2777
(
2002
).
30.
J. E. F.
Williams
and
B. C.
Zhao
, “
The active control of vortex shedding
,”
J. Fluids Struct.
3
,
115
122
(
1989
).
31.
N.
Fujisawa
,
Y.
Kawaji
, and
K.
Ikemoto
, “
Feedback control of vortex shedding from a circular cylinder by rotational oscillations
,”
J. Fluids Struct.
15
,
23
37
(
2001
).
32.
N.
Fujisawa
,
K.
Ikemoto
, and
K.
Nagaya
, “
Vortex shedding resonance from a rotationally oscillating cylinder
,”
J. Fluids Struct.
12
,
1041
1053
(
1998
).
33.
S.
Müller
,
M.
Milano
, and
P.
Koumoutsakos
, “
Application of machine learning algorithms to flow modeling and optimization
,” in
Center for Turbulence Research Annual Briefs
(
Stanford University
,
Stanford, CA
,
1999
), pp.
169
178
.
34.
M.
Milano
and
P.
Koumoutsakos
, “
A clustering genetic algorithm for cylinder drag optimization
,”
J. Comput. Phys.
175
,
79
107
(
2002
).
35.
N.
Gautier
,
J. L.
Aider
,
T.
Duriez
,
B. R.
Noack
,
M.
Segond
, and
M.
Abel
, “
Closed-loop separation control using machine learning
,”
J. Fluid Mech.
770
,
442
457
(
2015
).
36.
A.
Debien
,
K. A. F. F.
von Krbek
,
N.
Mazellier
,
T.
Duriez
,
L.
Cordier
,
B. R.
Noack
,
M. W.
Abel
, and
A.
Kourta
, “
Closed-loop separation control over a sharp edge ramp using genetic programming
,”
Exp. Fluids
57
(
3
),
40
(
2016
).
37.
T.
Duriez
,
S.
Brunton
, and
B. R.
Noack
,
Machine Learning Control—Taming Nonlinear Dynamics and Turbulence
, Number 116 in Fluid Mechanics and Its Applications (
Springer-Verlag
,
2016
).
38.
R.
Li
,
B. R.
Noack
,
L.
Cordier
,
J.
Borée
, and
F.
Harambat
, “
Drag reduction of a car model by linear genetic programming control
,”
Exp. Fluids
58
(
8
),
103
(
2017
).
39.
C.
Bingham
,
C.
Raibaudo
,
C.
Morton
, and
R.
Martinuzzi
, “
Suppression of fluctuating lift on a cylinder via evolutionary algorithms: Control with interfering small cylinder
,”
Phys. Fluids
30
(
12
),
127104
(
2018
).
40.
N.
Fujisawa
and
T.
Nakabayashi
, “
Neural network control of vortex shedding from a circular cylinder using rotational feedback oscillations
,”
J. Fluids Struct.
16
(
1
),
113
119
(
2002
).
41.
N.
Deng
,
B. R.
Noack
,
M.
Morzyński
, and
L. R.
Pastur
, “
Low-order model for successive bifurcations of the fluidic pinball
,”
J. Fluid Mech.
884
,
A37
(
2020
).
42.
P.
Holmes
,
J. L.
Lumley
,
G.
Berkooz
, and
C. W.
Rowley
,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
, 2nd ed. (
Cambridge University Press
,
2012
).
43.
L.
Sirovich
, “
Turbulence and the dynamics of coherent structures. Part 2: Symmetries and transformations
,”
Q. Appl. Math.
45
(
3
),
573
582
(
1987
).
44.
W.
Terra
,
A.
Sciacchitano
, and
F.
Scarano
, “
Aerodynamic drag of transiting objects by large-scale tomographic-PIV
,” in
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics
,
Lisbon, Portugal
,
2016
, ISBN: 0034801723.
45.
R.
de Kat
and
B. W.
van Oudheusden
, “
Instantaneous planar pressure determination from PIV in turbulent flow
,”
Exp. Fluids
52
(
5
),
1089
1106
(
2012
).
46.
P. A. J.
du Plessix
, “
Low-order representations in the turbulent wake of a normal flat plate
,” Ph.D. thesis,
University of Calgary
,
2015
.
47.
L. V.
King
, “
On the convection of heat from small cylinders in a stream of fluid: Determination of the convection constants of small platinum wires with applications to hot-wire anemometry
,”
Philos. Trans. R. Soc., A
214
,
373
432
(
1914
).
48.
G.
Comte-Bellot
, “
Hot-wire anemometry
,”
Annu. Rev. Fluid Mech.
8
(
1
),
209
231
(
1976
).
49.
M. S.
Bartlett
, “
Periodogram analysis and continuous spectra
,”
Biometrika
37
,
1
16
(
1950
).
50.
C.
Raibaudo
,
P.
Zhong
,
B. R.
Noack
, and
R. J.
Martinuzzi
, “
Open and closed-loop control of a triangular bluff body using rotating cylinders
,”
IFAC-PapersOnLine
50
(
1
),
12291
(
2017
).
51.
A.
Darabi
and
I.
Wygnanski
, “
Active management of naturally separated flow over a solid surface. Part 1. The forced reattachment process
,”
J. Fluid Mech.
510
,
105
129
(
2004
).
52.
G.
Godard
and
M.
Stanislas
, “
Control of a decelerating boundary layer. Part 3: Optimization of round jets vortex generators
,”
Aerosp. Sci. Technol.
10
(
6
),
455
464
(
2006
).
53.
O.
Lögdberg
, “
Turbulent boundary layer separation and control
,” Ph.D. thesis,
Royal Institute of Technology, KTH Mechanics
,
Stockholm, Sweden
,
2008
.
54.
R.
Li
,
B. R.
Noack
,
L.
Cordier
,
J.
Borée
,
E.
Kaiser
, and
F.
Harambat
, “
Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk
,”
Arch. Mech.
70
(
6
),
505
534
(
2018
).
55.
L. A.
Rastrigin
, “
Systems of Extremal Control
,” Ph.D. thesis,
Institute of Technology, KTH Mechanics
,
Stockholm, Sweden
,
1974
.
56.
J. P.
Bons
,
R.
Sondergaard
, and
R. B.
Rivir
, “
Turbine separation control using pulsed vortex generator jets
,”
J. Turbomachinery
123
(
2
),
198
(
2001
).
57.
J.
Ortmanns
,
M.
Bitter
, and
C. J.
Kähler
, “
Dynamic vortex structures for flow-control applications
,”
Exp. Fluids
44
(
3
),
397
408
(
2008
).
You do not currently have access to this content.