Optimization and Computational Fluid Dynamics - Department of ...

218 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
Since there is no single optimum to be found, we use a multi-objective genetic
algorithm and the so-called Pareto dominance concept.
The results obtained are very encouraging, and the procedure described
can be applied, in principle, to even more complex convective problems.
8.1 Introduction
The common approach when solving thermofluid problems numerically is to
first prescribe the geometry, boundary conditions, and thermophysical properties
and then solve the governing equations for velocity, pressure, temperature,
turbulent kinetic energy, etc. Problems of this type are referred to
here as analysis problems. In design practice, the engineer usually tries different
geometries, chooses other materials with different properties, and so
on until satisfactory performance is obtained. Such cut-and-try method relies
on the experience and skill of the designer to obtain any improvement but
optimal performance is rarely achieved. Furthermore, this simple approach
becomes impractical when the number of design variables is large, when there
is more than one objective, and when there are several constraints to be satisfied.
Therefore, in such cases, it is convenient, if not mandatory, to adopt
an optimization strategy. However, the integration of numerical optimization
techniques as part of the design process is still not very common today,
particularly for complex heat transfer problems. In order to proceed in a systematic
way, a basic requirement in shape optimization is to define the shape
of the system to be optimized in terms of (known) functions and (unknown)
parameters. This task is typically accomplished by means of a parametric
computer-aided design (CAD) system, and by making use of an optimization
procedure, automatic variations of the parameters associated with the geometric
model lead to the creation of a variety of feasible shapes, which are
then subjected to numerical analysis.
The aim of this article is to describe a general strategy for automatic,
multi-objective shape optimization of heat exchanger modules. This represents
a truly multi-objective optimization problem, since it is desired, from a
design point of view, to maximize the heat transfer rate in order to, for example,
reduce the volume of the equipment and to minimize the friction losses
which are proportional to the pumping power required. These two goals are
clearly conflicting, and therefore no single optimum can be found. For this
reason we use a Multi-Objective Genetic Algorithm (MOGA), and the socalled
Pareto dominance which allows us to obtain a design set rather than
a single design.
Optimization of two-dimensional wavy channels is obtained by means of
an unstructured finite-element (FE) solver, for a fluid of Prandtl number
Pr = 0.7, representative of air, assuming fully developed velocity and temperature
fields, and steady laminar conditions. The geometry of the channels