Optimization and Computational Fluid Dynamics - Department of ...

18 Gábor Janiga
2.1 Introduction
Designing optimal shapes or optimal configurations for practical engineering
applications has been the subject of numerous publications during the
last decade. Generic and robust search methods inside the design space, such
as Evolutionary Algorithms (EAs), offer several attractive features for such
problems [38]. The basic idea associated with the EA approach is to search
for optimal solutions using an analogy to the evolution theory. During the
iteration (or “evolution” using EA terminology) procedure, the decision variables
or genes are manipulated using various operators (selection, combination,
crossover or mutation) to create new design populations, i.e., new sets
of decision variables. For simpler optimization problems, more classical optimization
methods, like the Simplex approach, are often better adapted to
find the optimal solution within a small number of iterations [74].
The main goal of this work is to achieve cost-efficient design optimization
of problems involving complex flows with heat transfer or chemical reactions
using Computational Fluid Dynamics (CFD) codes for practical configurations,
while keeping reasonable overall computing times.
Classical optimization techniques, like gradient-based methods are known
for their lack of robustness and for their tendency to fall into local optima.
Generic and robust search methods, such as EAs [16, 34], offer several
attractive features and have been used widely for design shape optimization
[1, 48, 55, 62, 64]. They can, in particular, be used for multi-objective
multi-parameter problems. They have been successfully tested in many practical
cases, for example for design shape optimization in the aerospace
[1, 24, 54, 55, 64] and automotive industry [61]. The use of a fully automatic
EA coupled with CFD for a multi-objective problem still remains limited by
the computing time and is up to now far from being a practical tool for all
engineering applications.
2.1.1 Purpose
The purpose of this chapter is to illustrate possible methodologies for the
fully automatic optimization of various engineering problems involving CFD.
We are not interested here in developing a new algorithm for optimization.
We solely wish to demonstrate that it is possible to reach an optimal configuration
for a case involving coupled fluid flow, heat transfer and chemical
reactions, investigated using CFD within a reasonable computing time, for
configurations very close to practical ones.
In Case A, we consider laminar flows because it corresponds to a realistic
engineering problem, for example for low-power systems. A model configuration
is chosen consisting of a cross-flow tube bank heat exchanger. The
problem is to optimize the positions of the tubes so that the heat exchange is