In this chapter, focused on Computational Fluid Dynamics (CFD)-
based optimization for problems involving convective heat transfer, we present
our approach for the multi-objective shape optimization of periodic wavy
channels, representative of the repeating module of many heat exchangers.
The first problem is of fundamental nature and considers the geometric
parametrization and shape optimization of two- and three-dimensional periodic
wavy channels. The geometry of the channel is parametrized either by
means of linear-piecewise profiles or by non-uniform rational B-splines. The
second case, of industrial interest, illustrates the development and application
of an automatic method for the design of gas turbine recuperators.
After a literature review of shape optimization in heat transfer, we describe
in detail both aforementioned problems in terms of physical assumptions and
mathematical formulation. In the numerical methods section we indicate the
CFD codes used and describe the implementation of periodic boundary conditions.
Thereafter in the geometry parametrization section, we illustrate the
different types of numerical geometry representation used in the two problems,
and the corresponding definition of the design variables whose variation
leads to different shapes of the computational domain.
After a comprehensive classification and description of optimization methods
and algorithms, we present the results obtained for the two different
cases. For both problems the objectives considered are the maximization of
heat transfer rate and the minimization of friction factor, with the additional
objective of minimization of heat transfer surface for the recuperator module.
