A way to improve product performance of tissue grade paper products is to replace the press section with a Through Air Drying (TAD) section which is a technique where paper sheets are moulded into a structured fabric by vacuum boxes and transferred over one or more TAD cylinders with steam heated displacement drying (Tysén 2018, Tysén et al. 2015; 2018). Much like conventional papermaking machines, where the Yankee cylinder is the most energy requiring step, the TAD cylinders have by far the highest energy demand. Hence, improving the drying rate in the molding process is necessary from an energy demand standpoint. The process of sheet molding is modelled with Comsol Multiphysics where the computational model is setup with a 2- dimensional representation of the paper sheet. The tissue sample with randomly distributed fibre positions is generated using a MATLAB script written in the Livelink interface with Comsol. The process is simulated with the Moisture Flow multiphysics interface. The comprising physical modules are the Laminar Flow and the Moisture Transport in Air modules. The purpose of this paper is to gain a better understanding of driving as well as limiting mechanisms of moisture transport in porous media concept of TAD molding system. The aim is to develop a first draft of a computational model that can simulate the change in solid content Theory / Numerical Set Up Wood fibres for papermaking and paper sheets are both hygroscopic materials and, as such, contain bound water within the sheet network structure and within fibre walls. The network of fibres in a sheet as well as the fibres themselves can be viewed as porous media and understanding the physics and characteristics of fluid transport is key in numerically assessing water removal rate. Physical effects such as fluid flow and transport of fluids in different phases is considered. Heat transfer is excluded from these simulations at this stage as evaporative cooling is assumed to have neglectable effects on the drying process. Computational domain The computational model is setup with a 2- dimensional representation of the paper sheet. The tissue sample with randomly distributed fibre positions is generated using a MATLAB script written in the Livelink interface with Comsol. The script creates fibres and randomly position them throughout the domain, which represents the paper, see Fig. 1. The code can be set to create fibres comprising of various basis weights and paper sheet porosities. In this paper, a sheet comprising of a basis weight at 18 g/m 2 and a porosity at approximately 0.7 were simulated and analysed. Ten different structures were created in the Livelink Matlab script.
Figure 1. 2-dimensional representation of paper sheet model in Comsol. The upper SEM image is from the study [20]. The basis weight (g/m 2 ) is a standard measurement in paper manufacturing and it represent the weight of the paper in relation to a standard size. More specifically, it is the ratio between the mass of dry substance and the surface area of the sample.
𝑁𝜌 𝐿 𝑆
𝐵𝑊 =
(1)
Where 𝜌 𝐿 coarseness or length density (kg/m) of a fibre, 𝑁 is the number of fibres, whereas 𝑆 (m) is the height of the sample. Modelling continua in porous media Porous materials such as networks of wood fibres has a complex solid structure and is highly discontinues from a continuum theory perspective, see Fig. (2). This is resolved by viewing the modelled structure as a porous media in several layers, that is, the wood fibres are interpreted as a mixture of different materials (solids and fluids) with measurable quantities in a macroscopic field.
Figure 2. A 2-dimensional schematic representation of the structure of a single wood fibre and, on smaller scales, bundles of microfibrils.
Governing Equations / Numerical Model At the start of the simulation process, the fibres are saturated with water, although surrounded by moist air. As air flows through the paper sheet, the fibres are dried due to moisture mitigation from the core of the fibre to the surface through convection and capillary forces. At the surface, water is evaporated though forced convection and vapour diffusion. The process is simulated with the Moisture Flow Multiphysics interface. The comprising physical modules are the Laminar Flow and the Moisture Transport in Air modules.
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