Towards the simulation of manufacturing effects on multi-layered filter media

Over the years, specialized simulation software for filter elements has proven to be an effective tool for the optimization of the design of filter elements. The complex interplay of fluid flow, dust transport and deposition and flow-induced deformation of the media has to be described in terms of mathematical models and treated with appropriate numerical algorithms. The center of these considerations is the final filter element and therefore, the approach relies on material and model parameters (e.g. flow resistance and stiffness of the filter media) that are either known or that can be obtained from measurements. However, many media are composed of several layers such as filtering nonwovens, protective fleeces, stabilizing meshes etc. The amount of possible or promising combinations can be quite large, so there is a growing interest in finding an optimal layer design in terms of flow resistivity and mechanical stability by using suitable simulation techniques. In general however, knowing the material properties of the components is not sufficient to deduce the corresponding effective material properties of the multi-layered medium. Most manufacturing processes involve compression, stretching and shearing of the materials (e.g. pleating). In particular, when combining nonwovens with meshes, the production process can lead to localized and (at least partially) irreversible changes of the solid volume fraction of the nonwoven layer(s). If the compression is sufficiently strong, this leads to a change in the permeability distribution, and the effective flow resistivity of the resulting medium cannot be assumed to be equal to the sum of the flow resistances of the components. In this paper, we present a simulation technique for the prediction of influences of the production process on multi-layered filtering media with the focus on nonwovens combined with meshes. In a first step, the mechanical interaction between a porous filtering material and the supporting mesh under compression is simulated for a representative elementary volume (REV) of the heterogeneous medium. The influence of the compression on the local flow resistivity distribution in the REV is reflected by models essentially based on the local volume fraction in the porous medium. A flow simulation on the compressed REV is used to compute the effective permeability