Optimization and Computational Fluid Dynamics - Department of ...

276 J. Hämäläinen, T. Hämäläinen, E. Madetoja, H. Ruotsalainen
z, CD
Fig. 9.7 The coordinate frame of the full 3D model
y
x, MD
9.3.4 Validation of the Depth-averaged Navier-Stokes
Equations
The reduced model, that is, the depth-averaged Navier-Stokes equations, has
been validated by comparing the results to a complete CFD model which
includes the headbox slice channel and its free jet in 3D. The coordinate
frame of the model is shown in the sketch in Fig. 9.7. The x-axis follows the
main flow direction, while the z-axis lies in the span-wise direction. The 3D
CFD model utilized has been validated using wind tunnel experiments [31].
The fiber orientation angle profile is mostly determined by the CD velocity
component, because variations in the MD velocity are only of the order of
one per mille. Thus, the CD velocity is the most important component in
the validation. The CD velocity profiles at the slice opening for Step 1 are
presented in Fig. 9.8 (Step 1 is the diagnostics step determining flow rate
profiles inside the headbox which creates the measured fiber orientation profile).
The whole CD velocity field is presented in Fig. 9.9 to illustrate how the
cross-directional flows develop in the slice channel. As can be seen in Fig. 9.8,
the prediction given by HOCS Fiber agrees well with the result calculated
using the whole 3D model, even though the reduced model does not take into
account the effect of the jet.
After the diagnostics step, the fiber orientation is optimized. The CD profiles
obtained from Step 2 are presented in Fig. 9.10. As can be seen, the
difference between the reduced and the full model is now slightly bigger than
in Step 1, but both models predict very small CD velocities resulting in optimal
fiber orientation angle profile.