Modelling and Simulation of Multiscale Problems in Industrial Filtration Processes

Introduction. Filtering out solid particles from fluids is essential for many industrial and environmental applications, such as automotive engines, drinking and waste water purification, air filtration etc. A filter can be described shortly as a filter box (which could be of complicated shape) with inlet/s for dirty fluid, and outlet/s for filtrated fluid. The inlet/s and outlet/s are separated by a filtering medium, which is usually a single layer or a multilayer porous media. The filtering medium itself is a complicated porous medium. In our considerations we deal not only with filter media manufactured from nonwoven technical textiles but also consider a variety of other materials such as ceramics, zeolites, sand, paper, etc. Optimal shape design for the filter housing, achieving optimal pressure drop - flow rate ratio, optimal time performance of a filter etc., require not only the detailed knowledge about the flow field through the filter but also information of the particles being captured by the filtering medium. Most research on modeling and simulation of filtration processes is done separately on different scales, namely the micro- and the macro-scales. On the microscale, one deals with individual dirt particles and completely resolved geometries of the filter media [1,2]. On the other hand, macroscale considers complete filter elements, concentration of particles, and porous media approximations for the filter media [3,4]. Apparently, the processes on different scales are not independent from each other: the microscale geometry changes due to the deposited particles and therefore changes the macroscopic parameters such as permeability and absorption rate, which further depend on the micro scale equations. Conversely, the macroscopic velocities and pressure influence the filtration processes on the microscale. Earlier, Fraunhofer ITWM has presented algorithms and softwares for simulations on independent micro- and macro-scales. For microscale, see e.g. [1, 2], and for simulations on macroscale, see e.g. [3, 4]. Following, we shortly discuss the independent macroscale and the microscale models followed by two approaches for multiscale modelling: a subgrid approach, and an approach for coupling continuous macroscale modeling with discrete microscale modeling.