Optimization and Computational Fluid Dynamics - Department of ...

278 J. Hämäläinen, T. Hämäläinen, E. Madetoja, H. Ruotsalainen
CD Velocity (m/s)
CD Position (m)
HOCS
3D CFD
Fig. 9.10 Comparison of CD velocity for the optimal control (Step 2) between HOCS
Fiber and the 3D CFD model
coupled with optimization by using finite difference approximation for the
cost function gradient, this would lead to computing times of days or weeks,
which is unreasonable. As illustrated in Fig. 9.1, compromises need to be
made and CFD models need to be reduced when developing tools for control
purposes.
9.4 Multi-objective Optimization of Papermaking
As presented in the previous sections, the unit-processes of the paper machine
have been individually modeled and optimized for more than ten years. Nowadays,
focus has extended to handle larger ensembles including the whole papermaking
process. This poses a real challenge since a paper machine consists
of a number of consecutive sub-ensembles as shown in Fig. 9.11. There are four
main parts essential in the papermaking process: the headbox, wire section,
press section and the drying section. Thus, the model of the whole process
represents the combination of different unit-process models as a chain where
the output of one unit-process is an input for the following unit-processes.
In order to decrease the CPU time used, the elaborateness and the accuracy
of the CFD models often have to be significantly reduced. Sometimes, the
CFD model might even need to be replaced with a statistical or stochastic
model. Thus, when handling multiphysical or multidisciplinary problems,
more efficient simulation and optimization procedures are needed.