Optimization and Computational Fluid Dynamics - Department of ...

2 A Few Illustrative Examples of CFD-based Optimization 41
In previous works [43, 44, 74], the optimization problem was simple (single
objective) and the Simplex method [28, 63] has been used to speed-up the
computational procedure. Here a multi-objective problem is considered and
an EA is employed to investigate the optimization domain for the retained
input parameters. For the present problem, one evaluation is extremely costly
in CPU time.
One possibility to speed-up the evaluation is to perform every numerical
simulation on parallel computers [42] or to use simplified methods to describe
the chemical processes (e.g., the flamelet or tabulated chemistry approach
[11, 25, 26, 27, 41, 52, 65]). In the presented application, the Navier-Stokes
equations are solved for a two-dimensional flow. In the case of detailed chemistry,
29 species conservation equations are solved additionally. Tabulated
chemistry involves only three supplementary transport equations. In UGC + ,
both the detailed reaction mechanism and the tabulated chemistry (FPI, for
Flame-Prolongation of ILDM) are implemented and available for the computations
[41]. In the first case, all chemical parameters are computed using
the standard software CHEMKIN [45] while FPI computations rely on tabulated
values. The computation using detailed chemistry can be performed
either with simple molecular transport using the unity Lewis number assumption
or using detailed transport modeling [39]. The presented investigation is
based on both detailed chemistry and detailed transport computation. This
high level of physical accuracy is important to reduce the modeling uncertainty
associated with the CFD solutions, especially for cases with minor
differences in the objective functions. However, the stability and the speed
of the evaluations are greatly enhanced by starting the simulation using the
simplified method (FPI, see [41]) during 30 time-steps. The corresponding
results are converted into an initial, detailed chemistry solution based on the
tabulated values. The detailed chemistry computation is then continued for
another 40 time-steps, leading to the “final” result of the evaluation, used to
evaluate the objective functions after the necessary post-processing. Unfortunately,
the detailed chemistry computations are extreme stiff. Therefore, in
many cases, the residual values will still be very high after this fixed number
of iterations, indicating convergence problems. Such simulations are marked
as non-feasible results and dismissed from the optimization. “Non-feasible”
means also that either no converged solution can be found or that the CPU
time required until convergence would be unacceptably long.
All CFD evaluations rely on adaptive time-steps in order to stabilize the
solution procedure. A starting value of 0.1 s has been always used here for
the restart of the detailed computation from the tabulated chemistry results.
Further investigations are needed to check if other time-step values would
improve the number of valid evaluations. Although the detailed computations
considerably decrease the number of feasible solutions, they deliver also more
realistic and accurate results.
The smallest grid spacing employed in the present computations is 62.5 μm.
This resolution is needed for very stiff intermediate radicals like HCO and