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Pulsation Analysis of Paper Making Processes
Tiivistelmä:
Pulsation was modeled in the approach flow system and the headbox using the equations of fluid transients, which are the same as the equations of acoustics when friction can be neglected, which is the case in the approach piping. One and threedimensional solutions were compared assuming the structure around the fluid perfectly rigid. In the threedimensional solution, which was obtained using a commercial FEM code, the fluidstructure interaction (FSI) was taken into account. In the coating process, in which it is extremely important to include friction, pulsation was modeled using the equations of fluid transients, the equations of pulsatile flow, and using a CFD code that solves the NavierStokes equations.
Tapered slice channels of the headbox were analyzed in detail. It was found that the shape of the channel can affect the velocity oscillation amplitude and thus machinedirection basis weight variation at the channel outlet significantly. Changing the traditional linear shape to parabolic could decrease basis weight variation almost by one third for the same excitation amplitude.
The fluidstructure interaction must be taken into account to correctly model pulsation in the approach piping and the headbox. The rigid and FSI solutions can yield large differences in the results. Laboratory measurements using particle image velocimetry confirm that FSI needs to be included in the analysis. Modeling of the approach piping and the headbox reveals that with FSI included in the analysis, many experimental findings of basis weight variation of paper can be explained. The relationship between pressure pulsation in the piping system and the machinedirection basis weight variation in paper was shown computationally. No simple relationship was found.
In the paper coating process, modeling friction is extremely important. In the case of Newtonian fluid the approaches of harmonic fluid transients, the method of characteristics, and the analytical solution of pulsatile flow yield similar results because of the long time scale of the problem. In the case of nonNewtonian fluid, which is encountered in the paper coating, the solution is obtained by solving the NavierStokes equations with a CFD code. Also, the approach of harmonic fluid transients gives similar results for velocity pulsation. The relationship between pressure and velocity pulsation and basis weight variation was shown.