Optimization and Computational Fluid Dynamics - Department of ...

252 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
f/f 0
10
8
6
4
2
D a
D b
D c
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
Nu/Nu 0
Fig. 8.14 Pareto front comparison between different optimization processes for the 2D
NURBS channels: last Pareto front; see also Fig. 8.13
Table 8.4 Ranges of the variables for the first NURBS optimization
D f
D d
Parameter Range Basis
L [1.00;2.50] 1001
Lwave [0.15 L;0.85 L] 1001
∆x23 [0.01 L;0.20 L] 1001
ρ54 [0.05;1.20] 1001
ϑ54 [70 ◦ ; 300 ◦ ] 501
∆x5 [0.30 L;0.75 L] 1001
∆y5 [0.00;0.50] 1001
ρ56 [0.05;1.10] 1001
ϑ56 [−120 ◦ ; 150 ◦ ] 501
∆87 [0.01 L;0.80 L] 1001
transl [−0.500 L;0.500 L] 1001
could not be obtained by moulding. This constraint can be summarized as
follows. During the construction procedure, after the lower wall profile has
been drawn, it is brushed along x direction by straight lines which progressively
change their slope ([−45 ◦ ;+45 ◦ ] with respect to y axis), Fig. 8.15. The
channel is declared feasible if and only if, there exists at least one direction
at which all the lines encounter the wall profile no more than once. The simulation
has been restarted with the same parameters, but introducing the
fabricability check just described. Results are depicted in Fig. 8.13(b). The
presence of such a constraint makes the optimization process closer to the
channel shapes more common in practice. Its observation reveals the decreas-
D e