To perform microstructure simulations to predict paperboard properties represent a new approach to product and process development in paper industry.

The software resulting from the project will make it possible to perform a larger portion of product development by computer simulation.

Substantial progress in the fundamental understanding of the papermaking process can be achieved, which is particularly important to be able to develop products with increased functionality but with less material and energy input. This is crucial for the competitiveness of renewable packaging materials in order to meet the increasing threat from fossil fuel based packaging materials such as plastics.

The software is based on an object oriented C++ framework and consists of the following tightly coupled modules: PaperGeo for virtual structure generation, IBOFlow for fluid dynamics simulation, and FeelMath for structural dynamics. The IPS platform is used for pre- and post-processing.

Specifically, the software will be used to investigate how the build-up of the fiber web in the forming section, and certain properties of paperboard packages such as resilience to edge penetration and structural dynamics, depend on fiber properties and process conditions.

In the longer term this means that paperboard packages with better functional properties can be developed.

Paper Forming

In the paper forming section of the paper machine a fiber suspension in the form of a free jet leaves the headbox and impinges on a permeable belt called a forming fabric. The initial forming influences the properties of the fiber web and the subsequent dewatering, and depends on fiber characteristics, chemical additives, forming fabrics and other process conditions.

Since the effective paper properties depend on the micro-structure a continuum model is inadequate.

The fluid-structure interaction of flow and moving fibers and flocs needs to be accurately modeled in this application. The fact that the fibers are buoyant with the same density as the surrounding water makes this a very challenging problem.

Our in-house Navier-Stokes software, IBOFlow, is perfectly suited for this application. The flow around the moving fibers is resolved by the adaptive octree grid and immersed boundary methods are used to model the presence of fibers in the flow. The fibers are approximated as slender bodies represented by hollow elliptical segments. The fluid force on each fiber segment is calculated by integrating the pressure and the viscous stress tensor around the segment surface. An Euler-Bernoulli beam model in co-rotational formulation is used and discretized in a FEM framework to calculate the large fiber deformations. The fiber-fiber and fiber-fabric couplings are modeled by Langrangean multipliers.

In the simulation software, individual fibers are generated and visualized in the process of laying down onto the forming fabric.

The buildup of surface density of paper material across the forming fabric as well as fiber orientations are computed and used as a measure for comparison with experiments. The first version of the paper forming simulation software will be delivered to the industrial partners during the spring 2011.

Product Quality – Edge Wicking

During startup of the Tetra Brik Aseptic (TBA) filling machine after a short stop the bath is filled with a liquid mixture of water and peroxide, and the liquid starts to penetrate the open edge of the paperboard. Only a few millimeters penetration can be allowed otherwise a tube break might occur that destroys the aseptic environment in the filling machine. The resulting penetration depends on fiber properties, chemical additives, sheet structure and other process parameters.

To simulate the edge penetration a multi-scale framework has been developed. Small pieces of 3D paper microstructure are generated using PaperGeo. For these microstructures a pore-morphology model generates active pore radius and saturation levels for different pressure drops. One-phase flow simulations are then performed on active pores to calculate relative permeabilities. These results are validated with two-phase flow simulations using the Volume of Fluids (VoF) module in IBOFlow. A virtual macro sheet (2D distribution of surface weight and anisotropy) is then generated based on the micro properties.

Simulations on the macro sheet give the water front as a function of time.

The first version of the edge wicking simulation software will be delivered to the industrial partners during the summer 2011.