Paper forming is the first step in the paper machine where a fiber suspension leaves the headbox and flows through a forming fabric. Complex physical phenomena occur during paper forming due to the interaction between fibers, fillers and fines as well as chemicals added to the suspension. Understanding this process is important for the development of improved paper products because the configuration of the fibers during this step has a large influence on the final paper quality. Since the effective paper properties depend on the micro-structure of the fiber web, a continuum model is inadequate and the properties of each fiber need to be accounted for in the simulations.
In the present work, a framework for microstructure simulation of early paper forming has been developed. The simulation framework includes a Navier-Stokes solver and immersed boundary methods are used to resolve the flow around the fibers. The fibers are modeled with a finite element discretization of the Euler-Bernoulli beam equation in a co-rotational formulation. The contact model is based on a penalty method and includes friction as well as elastic and inelastic collisions.
The fiber model and the contact model are validated against demanding test cases from the literature with excellent results. The fluid-structure interaction in the model is examined by simulating an elastic beam oscillating in a cross flow. Finally, a simulation of early paper forming is performed to demonstrate the potential of the proposed framework. The unique modeling approach can be used to increase the fundamental understanding of paper forming and support process optimization.
This work was part of the ISOP project with industrial partners Albany International, Eka Chemicals, Stora Enso and Tetra Pak. It was supported in part by the Swedish Foundation for Strategic Research (SSF) through the Gothenburg Mathematical Modeling Centre (GMMC).
Authors and Afillations
- A. Mark, Fraunhofer-Chalmers Centre
- E. Svenning, Fraunhofer-Chalmers Centre
- R. Rundqvist, Fraunhofer-Chalmers Centre
- F. Edelvik, Fraunhofer-Chalmers Centre
- E. Glatt, Fraunhofer ITWM
- S. Rief, Fraunhofer ITWM
- A. Wiegmann, Fraunhofer ITWM
- M. Fredlund, Stora Enso
- R. Lai, Eka Chemicals
- L, Martinsson, Albany International
- U. Nyman, Tetra Pak