diameter of a single fibre as well as typical gap distance between adjacent fibres.
•
The forming and deformation of the fibre web during the TAD molding process is excluded Zero unbound water remaining in the paper sheet model.
A direct linear system solver was used coupled with an implicit second order backward differentiation formula (BDF) solver. The direct solver is called PARDISO which handles sparse linear systems using LU factorization to compute a solution. More information on the solver is found in COMSOL documentation. The BDF solver performs time stepping using a backward differentiation with a maximum order of accuracy of 2, which is the degree of the interpolating polynomial.
•
Initial and boundary conditions Initially, the fibres are saturated with water and the pore structure of the paper sheet contains air. The boundary conditions of the 2-dimensional representation is presented in Fig. (3)
Figure 4. Grid resolution and geometrical properties of the paper sheet model.
Figure 3. The properties of the computational domain and boundary conditions.
Results and Discussion The results are comprised by presenting the solid content of the fibre web over time. Fig. (5) presents four snapshots of the solid content at times 0, 5, 10 and 20 ms. Local variations of the solid content are observed at 20 ms which is a result of adjacent fibres blocking the airflow and hence, reducing the influence of convective mass transport. Considering that the fibre web is viewed in two dimensions, the air blockage should be overrepresented and thus, causing larger variations of the airflow. This notion is supported in [33] which concluded that flow resistance in the isotropic fibre arrangement in space is lower than the in-plane isotropic orientation and disordered unidirectional fibre arrangements at creeping flow conditions for low to moderate
Pressure was applied at the inlet and outlet boundary in which the vacuum level was set at 30 kPa at the outlet and reference pressure at 0 Pa was set at the inlet. Symmetry was set at the vertical boundaries as the fibre structure of the domain which was considered characteristic. Key input parameters for the simulation model are presented in Table (1). Table 1 : Key input data to the simulation model Parameter data Size Permeability 4.8e -8 [m 2 ] Porosity 0.55 [-] Vapor-air diffusion 2.6e -5 [m 2 /s] Vacuum pressure -30 [kPa] Density fibre 1340 [kg/m 3 ] Mesh setup and solver settings An unstructured mesh grid containing triangle elements was created for the paper models, see Fig. (4). The grid is solved in a finite element space where a set of basis functions are used to create piecewise linear relations between the mesh elements and convert them to weak formulations for them to be solved. Moreover, geometrical features such as the
4
Made with FlippingBook Online newsletter maker