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The gas flow through sheet-like porous materials such as paper can show marked lateral variations due to a heterogeneous, locally varying microstructure. Hence, reliable predictions of such lateral flux variations require an appropriate consideration of local variations in the microstructure. The flow through such sheet-like materials is commonly described with Darcy's law in which permeances are formulated in terms of microstructure properties, such as porosities, tortuosities, or hydraulic radii. This work proposes an extension of existing permeance models that directly considers the variation and the cross-dependence between local microstructure properties. The extended model is applied to local air fluxes through a paper sheet to exemplarily reveal the joint impact of local porosities and local tortuosities on the air flux. The key extension is to consider a joint distribution of porosity and tortuosity. The latter is constructed from the univariate property distributions using a copula approach and yields local tortuosities including their variation for any encountered local porosity. These values jointly enter any permeance model that qualitatively captures the dependence of the air flux on the porosity. To assess the merit of the model, variations in the air flux and in the pore space properties are independently determined from the same measured microstructure of paper. Air flux variations are provided by computational fluid dynamics simulations on multiple, nonoverlapping segments taken from the microstructure. A statistical analysis of the entire microstructure provides the distribution of local porosity, tortuosity, and thicknesses. Our model quantitatively explains that porosity-dependent variations in the tortuosity, in particular the ones associated with high-volume pathways, decisively determine air flux variations. Article Highlights: Computational fluid dynamics simulations determine local variation of air flow through an actual microstructure of paper. Construction and use of the copula approach to model joint distribution of local porosities and tortuosities is explained. Existing permeance models equipped with variations in porosity and porosity dependent tortuosity capture most variations in air flow. [ABSTRACT FROM AUTHOR]

The quality of ambient air attracts considerable, widespread interest. Over the last decades, air purification has become an integral part of HVAC systems, process engineering, automotive and respiratory protection. Efficient separation of micro- and nano- particles is solidly linked with the development of new, sophisticated filtrating materials, as well as generating and validating mathematical models of such porous structures. The paper regards the numerical modeling of various filters. The presented work aims to validate four virtual filtrating materials –the fiberglass HEPA filter, the paper filter used in the automotive industry, knitted wire mesh and polyurethane foam. The pressure drop obtained for the filters under investigation was examined. The CFD results were validated against the data available in the literature. The agreement of the results of numerical and experimental studies proves the suitability of the proposed methods. At the same time, the simplifications employed in the simulations leave room for further improvement in future works.

A numerical model of a vacuum dewatering process was established with a level-set method to simulate two-phase flow in a two-dimensional paper sheet model with constructed volume forces representing flow resistance in a three-dimensional environment. Nine cases of various volume force representations were investigated by comparing numerical and experimental data. Based on the dry content and dwell time relation, the best model is obtained when accounting for in-plane flow resistance at the paper–wire interface. Compared to the other numerical cases, considering the blockage of the pore space, the top layer of the wire plays an essential role in determining the flow resistance during the vacuum process. To validate the maximum dewatering rate obtained in the model, new experimental data with a higher frequency of sampling are needed. The computational time for the two-phase flow models in this study is extensively reduced due to the removal of the internal structure. This distinction enables time-efficient simulations of the vacuum dewatering process in which several dewatering parameters such as the level of the vacuum, the influence of a moving vacuum pulse, and higher basis weights could be investigated. [ABSTRACT FROM PUBLISHER]

The article discusses a study on nitrogen oxide (NOx) formation in recovery boiler in paper making. It states that the study uses a methodolgy of computational fluid dynamics (CFD) combined with a detail reaction mechanism. It mentions that in investigating the origin of nitrogen emissions in this study, they carried out the CFD analysis of a black liquor using a highly detailed model. In conclusion, it mentions that black liquor spray characteristics play an important role in paper making. However, it states that increasing the average particle diameter has an opposite effect.