Optimization and Computational Fluid Dynamics - Department of ...

234 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
part centered on the wall. Therefore, the value of parameter x2 is equal to
(L − Lwave)/2. The number of DOFs is now 10.
8.5.1.3 Channel Construction
In Figs. 8.5(a) and 8.5(b) both types of channel are depicted, i.e., linear piecewise
channel and NURBS channel, and they are constructed in the same way.
Once the lower wall profile has been obtained, the upper one, as illustrated
in Fig. 8.1, is made first by a simple translation in y-direction of the former
in order to obtain the height of the channel, followed by a translation in
x-direction. This guarantees the realistic desire to construct the channels of
e.g., a finned heat exchanger, by simple juxtaposition of identical wavy plates.
This action introduces in both cases another DOF which defines the x translation
of the upper profile, variable transl in Tables 8.1 and 8.4. In order
to avoid linear-dependent channels, the translation range is bounded to one
half-period in both the positive and negative x-direction. The y-translation is
instead fixed: in this way the average height of the channel is set to 0.5, that
is half of the non-dimensional hydraulic diameter (Dh). Finally the periodic
duct module is cut by two straight lines, representing the inlet and the outlet
section, as sketched in Fig. 8.1. Overall, we are left with 5 DOFs for the linear
piecewise model, and 11 DOFs for the NURBS channel.
8.5.1.4 Three-dimensional Extension
Once the two-dimensional results have been obtained, it has been tried to
encourage further mixing in the flow, and therefore an augmentation of the
heat transfer rate by forcing a non-zero value of the z-component of the velocity
vector [47]. Three-dimensional analysis has been performed by simple
extrusion from two-dimensional modules. For this purpose, the best twodimensional
optimized channels in terms of low friction factor and high Nusselt
number have been selected first, and one new additional variable was
introduced such as the extrusion angle. The constructing procedure is described
in Fig. 8.2. Due to the exploratory nature of this study, the extrusion
length is fixed to the same value as the channel height.
8.5.2 CC Module
The CAD package CATIA [11] has been utilized to describe the heat transfer
surface geometry, thanks to its key feature of allowing the generation of
parametric drawings. In Fig. 8.6, the parameters required to describe the geometry
of a CC surface are presented. Points P1, P2, P3 and P4 define the