(a)
(b)
Figure 5: The pressure distributions and airfoil shapes for
the initial and optimized designs for case 2.
Case 3 starts with a different initial design,
namely, the NACA 0010. Here, both algorithms
match the target closely. The basic algorithm
requires 16 equivalent highfidelity function calls,
whereas the improved algorithm 7.
In case 4, the target pressure distribution is the
one of NACA 3210 at M
= 0.75 and α = 1°. The
initial design is NACA 0012 and the minimum
crosssectional area is A
min
= 0.065. The improved
algorithm is able to match the target closely in less
than 12 equivalent highfidelity model evaluations.
The basic algorithm and the direct patternsearch are
both unable to match the target closely.
7 CONCLUSIONS
Computationally efficient variablefidelity design of
transonic airfoils is presented. The algorithm replaces
the direct optimization of a CPUintensive high
fidelity CFD model by iterative updating and re
optimization of its fast surrogate. The surrogate is
constructed using a shapepreserving response
prediction technique with the underlying lowfidelity
CFD model, which is replaced—after a few
iterations—by its local response surface
approximation. The operation and performance of our
algorithm is demonstrated using several transonic
airfoil design cases with the optimized designs
obtained at a low cost corresponding to a few high
fidelity CFD simulations. Our results indicate that the
algorithm presented here is computationally much
more efficient than its basic version that only exploits
the corrected CFD lowfidelity model but not the
response surface one.
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0 0.2 0.4 0.6 0.8 1
1
0.5
0
0.5
1
1.5
/

p
Initial
Optimized
0 0.2 0.4 0.6 0.8 1
0.05
0
0.05
0.1
/c
z/c
TRANSONIC AIRFOIL DESIGN BY THE INVERSE METHOD USING VARIABLEFIDELITY MODELLING
481