Optimization and Computational Fluid Dynamics - Department of ...

2 A Few Illustrative Examples of CFD-based Optimization 43
illustrate the full computational procedure, the evaluation of an individual
set of parameters requires four steps:
1. the computation of the composition of the mixture in the primary and
secondary inlet, knowing the specific design variables;
2. the simplified CFD simulation, i.e., the resolution of the governing coupled
equations for the flow variables, the energy and the species conservation
equations, using first tabulated chemistry (FPI);
3. the high-quality CFD simulation using detailed chemistry and transport
models, restarted from the previously obtained FPI solution;
4. the post-processing of the obtained results to extract the values of the objective
functions (average mass flow rate of CO along a horizontal cut and
maximal variation of the temperature profile along this cut, respectively)
for these design variables.
For the case considered here, the configuration is two-dimensional and can
be optimized on a single PC with a high but acceptable computing time,
provided a CFD software as efficient as UGC + is employed. Nevertheless, this
will not always be the case. Therefore, a parallel version of this optimization
procedure has been developed, as already described for another optimization
problem in Sect. 2.3.5. As a whole, 254 configurations have been evaluated
during the optimization procedure and 64 feasible cases have been found.
The total computational time requested by the optimization using 5 PCs is
roughly 3 weeks.
The optimization procedure can now be started with the objectives of
reducing as much as possible the average mass flow rate of CO and reducing
the temperature variations along a horizontal cut through the solution at
y =0.025 m, near the outlet.
The optimization space is defined, as explained before, by two parameters
as shown in Figs. 2.14 and 2.15, where the objective functions are represented
as function of the input parameters using a contour plot representation. The
darker values correspond to a higher mass flow rate of CO and a higher temperature
variation, respectively. The top left corners of these figures contain
no results. Since the corresponding input parameters would yield a configuration
in contradiction with the concept of a central primary inlet with a
surrounding secondary inlet, they are not considered in the procedure.
It can be seen that both objectives improve roughly in the same direction
in parameter space. Differences are only observed when looking at the details
of these evolutions, so that we observe a posteriori that these objectives are
in fact not really concurrent, but approach a nearly identical optimum. The
differences between both optimal solutions are so small (less than 2 K for the
temperature variation) that they probably approach solution accuracy, even
using detailed chemistry.
All EA parameters are listed in Table 2.4.
The two objective values of the feasible cases are shown in Fig. 2.16, in
which 20% of the evaluation results are not shown to improve clarity. This