Optimization and Computational Fluid Dynamics - Department of ...

48 Gábor Janiga
y [mm]
18
16
14
12
10
8
6
4
2
0
-2
CO
0.085
0.08
0.075
0.07
0.065
0.06
0.055
0.05
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
HCO
8.4E-05
7.9E-05
7.4E-05
6.9E-05
6.4E-05
5.9E-05
5.4E-05
4.9E-05
4.4E-05
3.9E-05
3.4E-05
2.9E-05
2.4E-05
1.9E-05
1.4E-05
9E-06
4E-06
-10 -5 0 5 10
x [mm]
Fig. 2.18 Mass fraction field of CO (left) and HCO (right) in the worst feasible case for
the EA optimization
erence. In this way, the optimization problem involves several concurrent
objectives that must be fulfilled simultaneously. Generic and robust search
methods, such as EA, can be used for such problems as demonstrated here.
The present optimization problem consists of finding the best group of values
for the model constants of the k–ω turbulence model [79] leading to the most
accurate prediction of the velocity distribution, in agreement with the DNS
data. The k–ω model is widely used in CFD, demonstrating the importance
of this issue. In a first investigation, the shear-stress profiles have been also
examined, but the differences were quite small compared with DNS. It was
observed that the constants producing a good velocity profile automatically
lead to an accurate shear-stress distribution as well, which is not unexpected,
since the shear-stress directly depends on the velocity gradients. Therefore,
the shear-stress profiles are dropped from the objectives and the number of
reference cases is increased, involving different Reynolds numbers.
2.5.1 Governing Equations
The Reynolds-averaged governing equations that describe turbulent flow motion
are summarized here following Wilcox [79]. An incompressible flow with
constant thermodynamic properties is now assumed, unlike Case B.