Conclusions The first draft of the simulation model shows promising results in terms estimating average solid content over dwell time. At least that is the case up until roughly 15 ms. Based in laboratory results, the solid content rate seems to converge to an upper limit value, which is not the case for the simulation model. Hence, experiments indicate that there is a physical limit on the dewatering rate. The surface moisture vaporization needs to by analysed further as theory suggest that there should be an increased resistance to surface vaporization as the moisture level decreases in the porous media. However, since the dryness levels during the TAD molding process ranges about 5-6% from start to finish, it should have a neglectable affect as there is still a lot of bound water in the fibre. Other limiting factors that are not considered at the moment are:
Figure 5. Colour plot representing solid content in in the fibre structure
The averaged solid content for the entire fibre web is presented in Fig. (5)
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Including the TAD wire which add blockage to the airflow as well as absorbs water from the fibres Analysing the TAD molding process in a 3- dimensional space which should have an overall reduction in blockage due to an added dimension where the flow can travel. Including the deformation of the fibre web during the molding process. Perhaps the poroelastic physics interface could be utilized to analyse both the deformation of the fibre web as the fluid transport of the porous media simultaneously.
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Acknowledgements The authors are grateful for the financial support of the Knowledge foundation, Grant No. 2022-0024, as well as generous in-kind contributions from Albany International Inc., Karlstad University and Valmet AB.
Figure 6. Solid content comparison to laboratory trials performed by [20]
The solid content from the simulation model is compared to lab-scale data from [20], for early TAD molding the simulation model show great coherence with the laboratory results. After some time, the laboratory results deviate from the linear behaviour and display diminishing returns. A few additions need to be added to the models to capture the diminishing returns. In a first approach to establish a numerical model of the TAD molding process, the influence of web deformation was excluded which eliminates both compressibility of the sheet which leads to decreasing permeability and also the rewetting phenomena, which are important factors to consider for a comprehensive model [39, 40]. The TAD fabric is likewise excluded from the simulations. According to [12] machine clothing such as forming fabrics affects the dewatering rate and magnitude through three main parameters, fabric caliper, void volume and air permeability. Similar dependence on the process is assumed to be influenced by TAD fabrics. Adding some of these to the numerical models, it is hypothesized to better simulate both laboratory and pilot scale results.
References
[1] Hubbe MA, Sjostrand B, Nilsson L, Koponen A, McDonald JD. Rate-limiting Mechanisms of Water Removal during the Formation, Vacuum Dewatering, and Wet-pressing of Paper Webs: A Review. Bioresources. 15(4) (2020) 9672-755, [2] Ramaswamy S. Vacuum dewatering during paper manufacturing. Dry Technol. 21(4) (2003) 685-717, https://doi.org/10.1081/Drt-120019058 [3] Attwood BW. A study of vacuum box operation. Paper Technology. 3(5) (1962) T144-T53, [4] Neun JA. Performance of High-Vacuum Dewatering Elements in the Forming Section. Tappi J. 77(9) (1994) 133-8, [5] Neun JA. High-vacuum dewatering of newsprint. Tappi J. 79(9) (1996) 153-7,
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