Optimization and Computational Fluid Dynamics - Department of ...

102 Kyriakos C. Giannakoglou and Dimitrios I. Papadimitriou
(a) (b)
Fig. 4.6 Total pressure losses minimization in a 2D compressor cascade. Structured computational
grid and Mach number distribution over the optimal compressor cascade
Total Pressure Losses
0.024
0.023
0.022
0.021
0.02
0.019
0.018
0 5 10 15 20 25 30 35 40
(a)
Cycle
Constraint
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
0 5 10 15 20 25 30 35 40 45
Fig. 4.7 Total pressure losses minimization in a 2D compressor cascade (a) convergence
rate of total pressure losses and (b) sum of violated geometrical constraints (total penalty
value)
control points (first nine values) are greater than the corresponding gradient
components for the pressure side points (remaining nine values). Note, also,
that the gradient values at the optimal solution are not zeroed due to the
thickness constraint imposition.
The initial and optimal set of design variables and the corresponding blade
airfoil contours are shown in Fig. 4.9. It is evident that, due to their greater
(positive) gradient values, the suction side control points move towards the
pressure side and tend to reduce the blade thickness. Once the airfoil becomes
too thin, penalization due to the constraint violation is activated. So the
(b)
Cycle