Optimization and Computational Fluid Dynamics - Department of ...

272 J. Hämäläinen, T. Hämäläinen, E. Madetoja, H. Ruotsalainen
Flow rate (-)
CD Position (-)
Initial
Optimized
Fig. 9.5 Initial and optimized flow rate distribution of the header
shape of the header, and its resulting outflow velocity profile, is illustrated
in Figs. 9.4 and 9.5, respectively. As can be seen, the optimized velocity
profile is notably even across the width of the machine, except for some
minor boundary layer effects at the edges.
In design processes, relatively complex and computationally expensive
models can be coupled with optimization, as shown in this example. In the
header optimization tool, a 2D turbulence model has been used, but when
faster response times are required, more reduced models are needed. An example
of such a control problem is presented in the next section.
9.3 Optimal Control of the Fiber Orientation in the
Slice Channel
9.3.1 On Modeling Fiber Orientation
Modeling of fiber suspension flows involves numerous challenges. Wood fibers
are non-spherical particles with a length-to-diameter aspect ratio typically of
the order of 100. Having approximately the same density as water, they tend
to align with the velocity direction but, because of their flexibility, they also
form accumulations called “fiber flocs”. Moreover, fibers interact with the
carrying phase and turbulence as well. Thus, we face conflicting modeling