Optimization and Computational Fluid Dynamics - Department of ...

8 Multi-objective Optimization in Convective Heat Transfer 219
is parametrized by means of Non-Uniform Rational B-Splines (NURBS) and
their control points represent the design variables. An alternative and simpler
geometry is described by means of piecewise-linear profiles. An extension to
3D is made by considering channels obtained by extrusion at different angles
of the 2D channels.
A similar strategy has been adopted for the multi-objective optimization of
the periodic module of Cross-Corrugated (CC) compact recuperators. However,
in this case, several widespread industrial codes are linked sequentially
to obtain an automatic procedure for the recuperator design and optimization.
The software tools used are CATIA for the geometric parametrization,
ANSYS ICEM-CFD for the grid generation, and ANSYS-CFX for preprocessing,
solution and post-processing. This study is focused on the development
and validation of an automated calculation methodology for the
thermo-fluid dynamic aspects of a recuperator design. Such a methodology
correlates all the phases throughout the design process, i.e., the different mechanical,
thermal and fluid dynamic aspects according to the concept of Multi
Disciplinary Optimization (MDO). The final objective is to find optimum
configurations for highly effective as well as tightly compact recuperators.
The described optimization procedure is robust and efficient, and the results
obtained are very encouraging. In particular, we show that our approach
is effective in performing genuine multi-objective shape optimizations that
can deal with local minima and does not require knowledge of function gradients.
There are no fundamental reasons, apart from computational costs
and modeling accuracy, which prevent the application of the methodology to
more complex geometries and more complex physics such as, for example,
unsteady or turbulent flow regimes.
8.2 Literature Review
We limit our attention to optimization in heat transfer, and more specifically
to shape optimization for heat transfer problems.
Gradient-based methods seem to be the most common approach for optimization
of heat transfer. For example, Prasad and Kane [42] performed
a three-dimensional design sensitivity analysis using a boundary element
method. A two dimensional shape optimization for the Joule heating of solid
bodies is described by Meric [28]. The sensitivity analysis was performed using
the adjoint variable method and the material derivative technique, with
a FE discretization of the non linear primary problem and the linear adjoint
problem. Cheng and Wu [6], and Lan et al. [25], considered the direct design
of shape for two-dimensional conductive bodies. In their approach the problem
was discretized using a boundary-fitted Finite Volume method, coupled
with a direct sensitivity analysis for minimization of the objective function.