In this Brief Communication, we determine an approximate relation that gives the mean time power required to control the wake flow downstream from a circular cylinder. The control law is the sinusoidal tangential velocity imposed on whole or part of the cylinder surface. The mean control power thus depends on four parameters: the amplitude and the Strouhal number of forcing, the control angle that defines the controlled upstream part of the cylinder, and the Reynolds number. This relation indicates that the control power grows like the square of the forcing amplitude, like the square root of the forcing Strouhal number, linearly with the control angle and varies like the inverse of the square root of the Reynolds number. We show that the values obtained with this approximate relation are in very good agreement with the corresponding values given numerically. Finally, the energetic efficiency of the control is discussed. We claimed that the most energetically efficient control law corresponds a priori to low forcing amplitudes applied to a restricted upstream part of the cylinder for relatively high values of the Reynolds number.

1.
P.
Tokumaru
and
P.
Dimotakis
, “
Rotary oscillatory control of a cylinder wake
,”
J. Fluid Mech.
224
,
77
(
1991
).
2.
J.-W.
He
,
R.
Glowinski
,
R.
Metcalfe
,
A.
Nordlander
, and
J.
Périaux
, “
Active control and drag optimization for flow past a circular cylinder. Part 1. Oscillatory cylinder rotation
,”
J. Comput. Phys.
163
,
83
(
2000
).
3.
C.
Homescu
,
I.
Navon
, and
Z.
Li
, “
Suppression of vortex shedding for flow around a circular cylinder using optimal control
,”
Int. J. Numer. Methods Fluids
38
,
43
(
2002
).
4.
M.
Bergmann
,
L.
Cordier
, and
J.-P.
Brancher
, “
Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduce-order model
,”
Phys. Fluids
17
,
097101
(
2005
).
5.
B.
Protas
and
A.
Styczek
, “
Optimal rotary control of the cylinder wake in the laminar regime
,”
Phys. Fluids
14
,
2073
(
2002
).
6.
C.
Min
and
H.
Choi
, “
Suboptimal feedback control of vortex shedding at low Reynolds numbers
,”
J. Fluid Mech.
401
,
123
(
1999
).
7.
B.
Protas
and
J.
Wesfreid
, “
Drag force in the open-loop control of the cylinder wake in the laminar regime
,”
Phys. Plasmas
14
,
810
(
2002
).
8.
M.
Bergmann
,
L.
Cordier
, and
J.-P.
Brancher
, “
On the generation of a reverse von Kármán street for the controlled cylinder wake in the laminar regime
,”
Phys. Fluids
18
,
028101
(
2006
).
9.
H.
Schlichting
and
K.
Gersten
,
Boundary-Layer Theory
(
Springer
,
New York
,
2000
).
10.
C.
Williamson
, “
Vortex dynamics in the cylinder wake
,”
Annu. Rev. Fluid Mech.
28
,
477
(
1996
).
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