Mathematical modeling and computer simulations can assist engineers in designing new filter media and filter elements. Often, modeling and simulation assists the filter media design at microscale (pore and particle scale), whereas, at macroscale (filter element scale) it assists the filter element design. In fact, in many cases the processes at microscale and macroscale are interdependent, and a consideration of the coupled micro and macro models is needed. Moreover, the microscale simulations can provide the macroscopic models with important parameters, e.g. deposition rate, changes in permeability due to the loading, etc. In this way a complete design cycle of filter media and filter element can be performed, embedding all studies in the virtual material design concept. Earlier, Fraunhofer ITWM has presented algorithms and software, independently for simulations on the micro scale, see, e.g. [1, 2], and macro scale, see, e.g., [3, 4]. The goal of this paper is to discuss two approaches where the coupled micro and macro scale simulations are used in CAE.
In the first case, coupled simulation on micro- and macro- scales is discussed. The approach is based on a fractional time step discretization, with subproblems being solved consecutively on the micro and macro scales. The macro scale parameters, permeability and absorption rate, are consecutively upscaled from solutions of micro scale problems. The macroscopic solution at each time step is downscaled to provide input velocity and particles distribution for the micro scale simulations. The changes in the microstructure are monitored in selected locations of the filter media in order to provide proper information for the upscaling procedure.
In the second case, the microscale simulations are used to determine the coefficients for the macroscopic equations, thus significantly reducing the amount of the required measurements data.