Optimization and Computational Fluid Dynamics - Department of ...

222 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
the result section, all shape-design alternatives become visible at once for
the design engineer, and the set of optimized solutions is obtained in one
optimization run, in contrast to classical single-objective methods.
The use of the Pareto dominance concept has been illustrated, for heat
transfer optimization problems, by Park et al. [33, 34]. In both studies, there
were two variables to be minimized: the pressure drop and the thermal resistance
of a plate exchangers [34], and of a heat-sink [33]. However, the multiobjective
optimization problems were treated as a single objective problem,
using weight coefficients. By performing a series of optimizations with varying
weighting factors, the authors obtained an approximate Pareto front.
8.3 Problem Statement
The problems considered in this work are: I – the multi-objective shape optimization
of two-dimensional (2D) and three-dimensional (3D) convective
wavy channels; II – the multi-objective optimization of Cross-Corrugated
channels. The former is of fundamental nature and is of interest for heat
exchangers and other heat transfer devices. The second problem has a practical
significance since it represents the building block of many gas turbine
recuperators [26].
For both problems, the study is limited to a single module at fully developed
flow and heat transfer conditions. In such a circumstance, channels of
periodic cross section form can be considered periodic in the flow and thermal
fields as well. Therefore, the computational domain of interest becomes a single
periodic module of the entire geometry as depicted in Figs. 8.1 and 8.2 for
the 2D and 3D channels, respectively. CC heat exchanger is formed by stacking
undulated plates at different inclination angles as reported in Fig. 8.3(a).
The geometry obtained is presented in Fig. 8.3(b) while the repeating module
is depicted in Fig. 8.3(c). It can be noticed that, unlike other authors, both
hot and cold fluid domains are included [26, 27].
We have limited the study to the steady, laminar flow regime which is
found in many practical circumstances. The Reynolds number chosen for the
simulation is Re = 200 for both two-dimensional channel and CC module
which corresponds to the typical value found in microturbine recuperators,
while the Prandtl number is assumed as Pr = 0.7, representative of air and
other gases. For computational convenience, a lower value of the Reynolds
number, Re = 100, has been selected for the 3D wavy-channels.