Optimization and Computational Fluid Dynamics - Department of ...

136 Nicolas R. Gauger
drag, lift, s tres s [ % variation ]
range, stress, C D ,C L [% variation]
0
-10
-20
-30
70
60
50
40
30
20
10
0
-10
-20
stress
C D
C L
eval. grad stress
eval. grad C D
eval. grad C L
10 20 30 40 50 60 70 80 90 100
It
(a)
range
stress
C D
C L
eval. grad range
eval. grad stress
eval. grad C D
eval. grad C L
10 20 30 40 50 60 70 80 90 100
It
(b)
Fig. 5.14 Optimization history (a) for the drag reduction by constant lift while taking
into account the static deformation and (b) for the range maximization (bottom picture)
of the AMP wing (M∞ =0.78, α =2.83 ◦ ). For both optimizations free-form deformation
is considered, 240 design variables are used for parameterization and the optimization
strategy relies on feasible directions
� �
∂I ∂R ∂S
δI = + ψT + φT δX
∂X ∂X ∂X
� � � �
∂I ∂R ∂S ∂I ∂R ∂S
+ + ψT + φT δw + + ψT + φT δZ (5.40)
.
∂w ∂w ∂w ∂Z ∂Z ∂Z