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Efficient Global Optimization Applied to Wind Tunnel
Evaluation Based Optimization for
Improvement of Flow Control by Plasma Actuator
○Masahiro Kanazaki(Tokyo Metropolitan University)
Takashi Matsuno (Tottori University)
Kengo Maeda (Tottori University)
Hiromitsu Kawazoe (Tottori University)
Japan-Finland Joint Seminar 2013

Contents
Introduction
 Overview of Active Flow Control by Means of Plasma
Actuator
Objectives
Optimization Method
Efficient Global Optimization (EGO)
Experimental Setup
Formulation
Results
Conclusions
2

Introduction(1/3)
Requirements of flow control around aircraft
Take-off and landing
Pitching, rolling and yawing motion
➔ Large aerodynamic force under
the large scale flow
3
 Complex geometry
 Noise
Improvement of
aerodynamics at
landing and take-off

Introduction(2/3)
Plasma Actuator: PA
Electric device for active flow control
Induced flow (Jet) is appeared by ionization of
the air between exposed electrode and
insulated electrode
Alternating current (AC) is supplied.
Small and light weight device
4

Introduction(3/3)
Pulse Width Modulation(PWM) PA
 Efficient AC supplement for PA
 Optimum values of (T1, T2) or (1/T1, 1/T2) are unknown.
Requirement to find the optimum AC wave form
Flow simulation by CFD*: over 10 hours.
Real time scale in wind tunnel: 1~ sec.
→ Optimization during a wind tunnel
experiment in real time
5
*CFD: Computational Fluid Dynamics

Objectives
Wind tunnel evaluation based optimization
Optimization during a wind tunnel experiment in
real time
Efficient Global Optimization ~ Kriging model based
Genetic Algorithm
Improvement of flow control by PA
Designing AC wave form
6

7
Optimization Method(1/5)
 Surrogate model：Kriging model
 Interpolation based on sampling data
 Standard error estimation (uncertainty)
)()( ii
y xx  
global model localized deviation
from the global model
 EI(Expected Improvement)
 The balance between optimality and uncertainty
 EI maximum point has possibility to improve the model.
Improvement at a point x is I=max(fmin-Y,0)
Expected improvement E[I(x))]=E[max(fmin-Y,0)]
To calculate EI,
Jones, D. R., “Efficient Global
Optimization of Expensive Black-Box
Functions,” J. Glob. Opt., Vol. 13,
pp.455-492 1998.

8
, ：standard distribution,
normal density
：standard errors
Surrogate model construction
Multi-objective optimization
and Selection of additional samples
Sampling and Evaluation
Evaluation of
additional samples
Termination?
Yes
Knowledge discovery
Knowledge based design
No
Kriging model
Genetic Algorithms
Wind tunnel
Exact
Initial model
Initial designs
Additional designs
Improved model
Image of additional sampling based on
EI for minimization problem.

9
 Heuristic search：Genetic algorithm (GA)
 Inspired by evolution of life
 Selection, crossover, mutation
 BLX-0.5
EI maximization → Multi-modal problem
Island GA which divide the population into
subpopulations
Maintain high diversity

Fully automated optimization based on the wind
tunnel evaluation.
Wind tunnel testing is incorporated into EGO.
• NI LabVIEWTM is employed.
10
Design variable (Power supply)
Objective function(Aerodynamic force)

Optimization method(5/5)
Flowfield around semicircular cylinder with two PAs
Drag minimization by controlling two design
variables related to (T1, T2)
 Over 1,000 wind tunnel run will be required if full-
factorial design should be carried out.
11
PA off PA on

12
Formulation
 Modulation frequency：
 Duty ratio： [%]
m
p
x
f
T
f
1
20
1
1
mod 
1
2
100
T
T
Dcycle 
Power supply unit provide frequency fp 9kHz
and 20/fp as a one unit wave.
[Hz]
 Objective function
 Design variables
Minimize CD (Drag coefficient)
2 .0 ≤ xm ≤ 90.0
10.0 ≤ Dcycle ≤ 70.0

13
Result（1/5）
Lower xm = Higher jet energy
10 initial samples

25
Result（1/5）
Local minimum
Global minimum
After 12 additional sampling

26
Result（2/5）
The minimum point could be obtained
about 20 wind tunnel runs.

 Higher Dcycle can achieve lower CD
 Higher Dcycle as DesA provides a higher AC voltage long time to PAs
 Local optimum DesB can also be found
 CD can be also reduced with DesB while the total electrical energy is
relatively low. → PAs can control the flow with lower electrical
energy under proper PWM driving conditions
27
Result（3/5）
DesA
DesB
DesC

28
Result（4/5）
x m [-] D cycle [%] f mod [Hz] C D
DesA 2.0 60.0 400.0 0.2985
DesB 15.0 25.0 53.3 0.3272
DesC 88.0 55.0 9.1 0.4105
DesA
DesB
DesC

29
Result（5/5）
x m [-] D cycle [%] f mod [Hz] C D
DesA 2.0 60.0 400.0 0.2985
DesB 15.0 25.0 53.3 0.3272
DesC 88.0 55.0 9.1 0.4105
DesA
DesB
DesC
 DesA: Separated region was reduced, and the streamline was less deformed
from the uniform flow
 DesB: Separated region was reduced, the streak of smoke far downstream from
the model was blurred

Conclusions
Wind Tunnel Evaluation–Based Optimization
The optimization technique successfully
integrated in the operating system of the wind
tunnel experiment
Automation of the data-acquisition/optimization
process
Improvement of Flow Control by Plasma
Actuator
The cost of optimization based on wind tunnel
evaluation can be drastically reduced
Not only global optimum but also local optimum were
found out.
30

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