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Flow control of bluff bodies using Genetic Algorithms:
rotary oscillation of circular cylinder
by
Venkata Kaali Rupesh Telaprolu
Y3101043
Thesis Supervisors:
Prof. Tapan K Sengupta
Department of Aerospace Engineering
Engineering
Prof. Kalyanmoy Deb
Department of Mechanical
Indian Institute of Technology, Kanpur
India
Introduction
Necessity for flow control
 Structural
 Acoustic
noise or resonance
 Increased
 Pressure
vibrations
unsteadiness
fluctuation
 Enhanced
heat and mass transfer
Earlier methodologies of flow control

Simple geometric configurations:

Splitter plate

Use of second cylinder

Inhomogeneous inlet flow

Oscillatory inlet flow

Localized surface excitation by suction and blowing

Vibrating cylinder
Why rotary oscillation ?

Can be employed for bodies with non-circular cross-section.

Promotes drag-crisis at significantly lower Reynolds numbers as
compared to that triggered by surface roughening.
Problem definition
•
The computational simulations for two-dimensional flow past a circular
cylinder that is executing rotary oscillation for a range of Reynolds numbers,
peak rotation rates and frequency of oscillation, are performed and studied.
•
Flow control by rotary oscillation for a circular cylinder is governed by three
major parameters.
• Reynolds number,
• Maximum rotation rate (Ω1) and
• Forcing frequency (Sf)
where,
is the translational speed of the cylinder
d is the diameter of the cylinder
ν is the kinematic viscosity
Amax is the dimensional physical peak rotation rate
f is the dimensional forcing frequency
Problem definition (contd)


All equations have been solved in non-dimensional form with d as the length
and as the velocity scales. A time scale is defined from these two and the
pressure is non-dimensionalized by
.
For the dynamic problem, a novel genetic algorithm based optimization
technique has been used, where solutions of Navier-Stokes equations are
obtained using small time-horizons at every step of the optimization process,
called a GA generation. The objective function is evaluated, followed by GA
determined improvement of decision variables.
where, TH is the time-horizon
for one GA generation.
Literature survey

S. Taneda (1978)



A. Okajima et al (1981)


Forces acting on a cylinder, in the range 40 ≤ Re ≤ 160 and
3050 ≤ Re ≤ 6100, were measure for 0.2 ≤ Ω1 ≤ 1.0 and
0.025 π ≤ Sf ≤ 0.15 π.
P. T. Tokumaru and P. E. Dimotakis (1991)



Flow visualization results for 30 ≤ Re ≤ 300 have been reported.
For Re = 40 and 11.5 π < Sf < 27π, vortex shedding was completely
eliminated.
Carried our experimental studies for Re = 15000, calculated drag based on
wake survey.
Reported drag reduction by more than 80% for Re = 15000.
J. R. Filler et al (1991)

Reported alteration of primary Karman vortex shedding by rotational
oscillation of cylinder in Reynolds number range of 250 and 1200, peripheral
speed due to rotational oscillation was between 0.5 and 3% of free stream
speed.
Literature survey (contd)

X.-Y. Lu and J. Sato (1996)


S. C. R. Dennis et al (2000)




Finite difference simulations of Navier-Stokes equations, by a fractional step
method for Re = 200, 1000 and 3000, 0.1 ≤ Ω1 ≤ 3.0 and 0.5 π ≤ Sf ≤ 4π.
Solved 2-D Navier-Stokes equations using stream function-vorticity
formulation for Re = 500 and 1000 by spectral-finite difference method.
Time-varying grid that becomes less fine with growing shear layer in time is
used.
Presence of co-rotating vortex pair and a time variation of drag coefficient
that switches frequency abruptly at a discrete time for Re = 500, Ω1 = 1 and
Sf = π/2, has been reported.
D. Shiels and A. Leonard (2001)


2-D flows for Re = 15000 using high resolution viscous vortex method have
been studied.
Multi-pole vorticity structures revealing bursting phenomenon in boundary
layer, causing large drag reduction during particular cases of rotary oscillation
have been noted.
Literature survey (contd)

J.-W. He et al (2000)




B. Protas and A. Styczek (2002)



Rotary control of cylinder wake at Re = 75 and 150 using optimal control
approach with adjoint equations over a time interval is reported.
Advantage of velocity-vorticity formulation with usage of more localized and
compact vorticity variable was noted.
M. Milano and P. Koumoutsakos (2002)


Gradient-based classical optimization for 200 ≤ Re ≤ 1000 was performed.
Finite element discretization was used and cost function gradient was
evaluated by adjoint equation approach.
30 to 60% drag reduction reported.
Drag optimization for flow past circular cylinder using two actuation
strategies- belt type and apertures on cylinder, was studied.
R. Mittal and S. Balachander (1995)


2-D flow at Re = 200 simulated using Navier-Stokes solver on staggered grid,
using CD2 method in generalized co-ordinates.
50% drag reduction for low Re, for single parameter combination case.
Literature survey (contd)

R. W. Morrison (2004)



J. Branke (2001)


Discussed the capability of evolutionary algorithms (EAs) to find solutions
for dynamic models.
Quantification of attributes to improve detection and response.
Surveyed evolutionary approaches available and applied to various benchmark
problems.
R. K. Ursem et al (2002)


Practical problem of greenhouse control is tried using evolutionary
algorithms.
Role of control-horizons from direct online control point of view has been
discussed.
Genetic Algorithms (GA)s
Essential components of GAs

A genetic representation for potential solutions to the problem.

A way to create the initial population of potential solutions.

An objective (evaluation) function that plays the role of the
environment, rating solutions in terms of their fitness.

Genetic operators that alter the composition of children during
reproduction.

Values of various parameters that the genetic algorithm uses
(population size, probabilities of genetic operators etc.)
Working principle of a Genetic Algorithm
Aims of present investigation

Study the two dimensional simulation of rotationally oscillating
circular cylinder.

Study the disturbance energy creation/exchange mechanism in an
incompressible flow framework.

Study the effects of design parameters on the drag acting on the
body and explore the possibility of using Genetic Algorithms to
implement the investigated problem physically.
Governing Equations
&
Numerical Method
Stream Function-Vorticity Formulation
Navier-Stokes equations, in non-dimensional form are given as,
where,
Flow is computed in the transformed orthogonal grid
plane, where
Grid is stretched smoothly in the radial direction by the transformation,
Navier-Stokes equations in transformed plane
Stream function equation (SFE) is given by,
Vorticity transport equation (VTE) is given by,
Pressure-Poisson equation (PPE) is given by,
Boundary and Initial conditions
No-slip boundary condition on the cylinder wall,
Convective boundary condition on radial velocity at outflow,
The initial condition: impulsive start of cylinder in a fluid at rest.
Solving procedure

Stream function equation (SFE) and PPE are solved using Bi-CGSTAB
variant of conjugate gradient method.

ILUT pre-conditioners used to make Bi-CGSTAB converge fast.

Vorticity transport equation (VTE) is solved by discretizing diffusion
term by second order central difference scheme and time-derivative by
four-stage Runge-Kutta scheme.

Convection terms of VTE are evaluated using compact schemes.

Neumann boundary conditions on the physical surface and in the farstream, required to solve PPE, are given by,
Compact schemes
In the present investigation, the OUCS3 scheme is used. In the periodic
direction, to evaluate first derivates, following form is used.
In the non-periodic direction, additional boundary closure schemes for
j = 1 and j = 2 are used, along with the above equation for j = 3 to N-2.
For boundary closure,
have been
used. To control aliasing and retain numerical stability an explicit fourth
order dissipation term
is added at every point with
Compact schemes compared with CD2 scheme
The region marked in the (kh-θΔt) plane where the numerical group
velocity matches physical group velocity in solving linear wave
equation within 5% tolerance
GA formulation
SFE, VTE and PPE along with boundary conditions, define the system to
be controlled with input as
and the output
is minimized.
Selection operator: Tournament selection with participation size of two.
Crossover operator: Simulated Binary Crossover (SBX) operator.
Mutation operator: Polynomial mutation operator.
GA solution procedure




Randomly generate population for the
first generation in allowed decision
variable space.
Evaluate the cost function of the
members for a user-defined timehorizon, measured from an initial time.
Apply GA to the initial population for
‘G’ number of iterations and the best
solution is recorded.
Using this solution as the initial solution,
another GA generation is started to find
best control strategy for the next timehorizon.
This procedure is continued till the best
control
strategy
of
consecutive
generations are similar to each other or a
maximum number of generations is
reached.
Results and Discussions
Details of present study




Reynolds numbers range - 500 to 15000.
Orthogonal grid of size 150 X 450 is used.
Outer boundary located at 40 diameter from centre of cylinder.
Surface pressure is obtained from total pressure and drag at any instant is
calculated by,
where p is surface pressure,
τix is viscous tensor on surface of cylinder,
ni is unit normal vector in ith direction
Experimental results of Tokumaru and Dimotakis
Time variation of CD and CL for Re = 15000, Sf = 0.9
(CD)Avg for Ω1 = 1.5, is 0.7878
(CD)Avg for Ω1 = 2.0, is 0.4712
(CL)Avg for Ω1 = 1.5, is 0.4101
(CL)Avg for Ω1 = 2.0, is 0.6164
Time variation of CD and CL for Re = 500, Sf = π/2,
(CD)Avg for Ω1 = 0.25, is 1.3040
(CD)Avg for Ω1 = 0.50, is 1.2590
(CL)Avg for Ω1 = 0.25, is 0.08341
(CL)Avg for Ω1 = 0.50, is 0.09089
Streamline contours for the initial conditions used by (a)
Dennis et al (2000) and (b) present computation
Time variation of CD and CL for Re = 1000, Sf = π/2,
(CD)Avg for Ω1 = 0.5, is 1.3630
(CD)Avg for Ω1 = 1.0, is 0.8917
(CL)Avg for Ω1 = 0.5, is 0.07691
(CL)Avg for Ω1 = 1.0, is 0.2219
Vorticity contours for Re = 1000, Sf = π/2, Ω1 = 0.5
Vorticity contours for Re = 1000, Sf = π/2, Ω1 = 1.0
Streamline contours for Re = 1000, Sf = π/2, Ω1 = 0.5
Streamline contours for Re = 1000, Sf = π/2, Ω1 = 1.0
Fourier transform of CD in log-log scale
Fourier transform of CL in log-log scale
Streamline contours for Re = 15000, Sf = 0.9, Ω1 = 1.5
Vorticity contours for Re = 15000, Sf = 0.9, Ω1 = 1.5
Streamline contours for Re = 15000, Sf = 0.9, Ω1 = 2.0
Vorticity contours for Re = 15000, Sf = 0.9, Ω1 = 2.0
Vorticity contours animated, for Re = 15000, Sf = 0.9, Ω1 = 2.0
Energy creation mechanism

Navier-stokes equation in rotational form for incompressible flows is given
by,

The quantity
, has been identified as mechanical energy (E) of the flow
and its instantaneous distribution can be described by,

Splitting physical quantities into primary and disturbance components by
identifying them with subscripts m and d respectively, the distribution of
disturbance energy component of mechanical energy is given in its linearized
form by,
Disturbance energy plots for Re = 15000, Sf = 0.9, Ω1 = 2.0, Ω0 = 0
Time variation of CD and CL for Re = 1000, Sf = π/2, Ω1 = 1.0, Ω0 = 0.5
(CD)Avg = 0.9068
(CL)Avg = 1.336
Streamline contours for Re = 1000, Sf = π/2, Ω1 = 1.0, Ω0 = 0.5
Vorticity contours for Re = 1000, Sf = π/2, Ω1 = 1.0, Ω0 = 0.5
Disturbance energy plots for Re = 1000, Sf = π/2, Ω1 = 1.0, Ω0 = 0.5
Variation of Ω1 of best member with time
Variation of Sf of best member with time
For ηc = 5; ηm = 10,
For ηc = 5; ηm = 60,
For ηc = 5; ηm = 100,
For ηc = 10; ηm = 100,
For ηc = 2; ηm = 100,
Variation of Ω1 and Sf of best member
with time, for multiple GA iterations
For ηc = 2; ηm = 50, with multiple GA iterations,
Conclusions
Time averaged drag and lift coefficients for all computed cases
Case
Re
(CD)avg
(CL)avg
1
500
0.25
π/2
1.3040
0.08341
2
500
0.50
π/2
1.2590
0.09089
3
1000
0.50
π/2
1.3630
0.07691
4
1000
0.50
π
1.3360
0.1150
5
1000
1.00
π/2
0.8917
0.2219
6
15000
1.50
0.9
0.7878
0.4101
7
15000
2.00
0.9
0.4712
0.6164
Time averaged drag coefficient for uncontrolled case for Re = 15000 is 1.3546.
For steady rotation coupled with rotary oscillation case,
(CD)avg = 0.9068 and (CL)avg = 1.336.
Average drag coefficients for different GA simulations
Case
ηc
ηm
(CD)avg
1
2
100
0.3827
2
5
10
0.4092
3
5
60
0.4108
4
5
100
0.4007
5
10
100
0.4735
For the case with multiple GA iterations, (CD)Avg = 0.3543.
Summary of results

Computational procedure is calibrated by comparing the results with
experimental results of Tokumaru and Dimotakis, for Re = 15000.

Ability of the numerical method for DNS of bluff body flows by twodimensional flow models has been testified.

Rotary oscillation is shown to be equivalent to tripping the wall boundary layer
aerodynamically

A large drag reduction has been achieved, by shear release mechanism on one
side of the cylinder, at comparatively low Reynolds number (Re = 1000).

Efficacy of GA-based optimization strategy, capable of arriving at near-optimal
solutions for a dynamic problem, has been emphasized in the present work.
Scope for future work

Investigate whether rotary oscillation brings a phase shift on resultant
force experienced by the cylinder.

Control strategy of steady rotation coupled with rotary oscillation.

Studying the multi-objective framework of the current problem,
using reduction of flow unsteadiness as a second objective.
Thank You