Nonlinear optimal suppression of vortex shedding from a circular cylinder
File(s)
Accepted version
Author(s)
Mao, X
Blackburn, HM
Sherwin, SJ
Type
Journal Article
Abstract
This study is focused on two- and three-dimensional incompressible flow past
a circular cylinder for Reynolds number Re 6 1000. To gain insight into the
mechanisms underlying the suppression of unsteadiness for this flow we determine
the nonlinear optimal open-loop control driven by surface-normal wall transpiration.
The spanwise-constant wall transpiration is allowed to oscillate in time, although
steady forcing is determined to be most effective. At low levels of control cost,
defined as the square integration of the control, the sensitivity of unsteadiness with
respect to wall transpiration is a good approximation of the optimal control. The
distribution of this sensitivity suggests that the optimal control at small magnitude is
achieved by applying suction upstream of the upper and lower separation points and
blowing at the trailing edge. At high levels of wall transpiration, the assumptions
underlying the linearized sensitivity calculation become invalid since the base flow
is eventually altered by the size of the control forcing. The large-magnitude optimal
control is observed to spread downstream of the separation point and draw the shear
layer separation towards the rear of the cylinder through suction, while blowing
along the centreline eliminates the recirculation bubble in the wake. We further
demonstrate that it is possible to completely suppress vortex shedding in two- and
three-dimensional flow past a circular cylinder up to Re = 1000, accompanied by
70 % drag reduction when a nonlinear optimal control of moderate magnitude (with
root-mean-square value 8 % of the free-stream velocity) is applied. This is confirmed
through linearized stability analysis about the steady-state solution when the nonlinear
optimal wall transpiration is applied. While continuously distributed wall transpiration
is not physically realizable, the study highlights localized regions where discrete
control strategies could be further developed. It also highlights the appropriate range
of application of linear and nonlinear optimal control to this type of flow problem.
a circular cylinder for Reynolds number Re 6 1000. To gain insight into the
mechanisms underlying the suppression of unsteadiness for this flow we determine
the nonlinear optimal open-loop control driven by surface-normal wall transpiration.
The spanwise-constant wall transpiration is allowed to oscillate in time, although
steady forcing is determined to be most effective. At low levels of control cost,
defined as the square integration of the control, the sensitivity of unsteadiness with
respect to wall transpiration is a good approximation of the optimal control. The
distribution of this sensitivity suggests that the optimal control at small magnitude is
achieved by applying suction upstream of the upper and lower separation points and
blowing at the trailing edge. At high levels of wall transpiration, the assumptions
underlying the linearized sensitivity calculation become invalid since the base flow
is eventually altered by the size of the control forcing. The large-magnitude optimal
control is observed to spread downstream of the separation point and draw the shear
layer separation towards the rear of the cylinder through suction, while blowing
along the centreline eliminates the recirculation bubble in the wake. We further
demonstrate that it is possible to completely suppress vortex shedding in two- and
three-dimensional flow past a circular cylinder up to Re = 1000, accompanied by
70 % drag reduction when a nonlinear optimal control of moderate magnitude (with
root-mean-square value 8 % of the free-stream velocity) is applied. This is confirmed
through linearized stability analysis about the steady-state solution when the nonlinear
optimal wall transpiration is applied. While continuously distributed wall transpiration
is not physically realizable, the study highlights localized regions where discrete
control strategies could be further developed. It also highlights the appropriate range
of application of linear and nonlinear optimal control to this type of flow problem.
Date Issued
2015-06-23
Date Acceptance
2015-05-24
Citation
Journal of Fluid Mechanics, 2015, 775, pp.241-265
ISSN
1469-7645
Publisher
Cambridge University Press (CUP)
Start Page
241
End Page
265
Journal / Book Title
Journal of Fluid Mechanics
Volume
775
Copyright Statement
The final publication is available via Cambridge Journals Online at https://dx.doi.org/10.1017/jfm.2015.304
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
drag reduction
instability control
vortex shedding
LOW REYNOLDS-NUMBERS
NAVIER-STOKES EQUATIONS
BLUNT TRAILING-EDGE
DRAG REDUCTION
BLUFF-BODY
FEEDBACK-CONTROL
SPLITTER PLATES
BOUNDARY-LAYERS
PASSIVE CONTROL
STENOTIC FLOW
Publication Status
Published