Optimization and Computational Fluid Dynamics - Department of ...

8 Multi-objective Optimization in Convective Heat Transfer 249
f/f 0
10
8
6
4
2
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Pareto
front
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1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
Nu/Nu 0
Fig. 8.12 Pareto front for the 2D linear piecewise optimization process
The results are expressed in terms of the ratios Nu/Nu0 and f/f0, where
Nu0 and f0 are the Nusselt number and the friction factor for a parallel plate
channel, taken as reference geometry.
8.8 Results and Discussion
8.8.1 Linear Piecewise Optimization
The first analysis has been conducted on the linear piecewise geometry type.
The variables are small in number and clearly related to the shape of the
channel: the depth of the asperity, the forward side angle, the backward side
angle, the length of the channel and the translation of the upper wall.
The Full Factorial algorithm [14] with three levels has been used (DOE)
to sample the design space. This method gives the best homogeneous distribution
of the samples. The number of Full Factorial samples is 243 and the
parameters ranges are given in Table 8.1. In a GA optimization, the size of
the population within the design space affects the convergence ratio. After
having performed the numerical simulation on this set, its Pareto front has
been chosen as the initial population of multi-objective optimization with GA.
This preliminary Pareto front is a good selection in order to limit the number
of starting channels. The optimization has been performed with MOGA-II
along 30 generations of 20 individuals each: so the total number of designs
evaluated is 600. The results are sketched in Fig. 8.12 where the Pareto front
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