DOI: 10.1002/adem.201000222 Modeling of Ceramic Foams for Filtration Simulation By Claudia Redenbach * , Oliver Wirjadi, Stefan Rief and Andreas Wiegmann Ceramic foams are widely used in the foundry industry for filtering metal melts. The objectives are two-fold—on the one hand inclusions and precipitations shall be removed from the melt, on the other hand the flow shall be smoothed. The most common way to produce these filters is to coat polyurethane foams with a ceramic suspension. [1] Subsequently, the foam is baked to yield mechanical strength and temperature resis- tance. In this step, the polyurethane core burns away leaving hollow struts of the resulting ceramic foam (see Fig. 1). Producers as well as users of the ceramic filters are of course interested in finding a foam structure leading to an optimal behavior of the filter w.r.t. both filtration and flow smoothing. One way to investigate the flow properties of a filter is to simulate numerically the flow in a reconstructed tomographic image of the foam. For a deeper understanding of relations between the geometry of a foam and its flow properties, however, a large variety of different foam structures should be investigated. Instead of the time- consuming and costly approach of producing and imaging a large number of prototypes, we propose the use of (stochastic) geometric models. Using such a model, a variety of different foam structures can be generated virtually and their flow properties can be studied by simulation. In order to get realistic simulation results, a good starting point is a model fitted to the microstructure observed in a real foam. For the ceramic foam studied here, the most important features are – the struts are considerably thicker near the vertices and get thinner toward their center, – some facets are closed during the coating procedure, and – an anisotropy in the orientation distribution of the closed facets due to the fact that the polyurethane foam is pressed when soaked with the fluid ceramic. In ref. [2] a first modeling approach for the ceramic foam investigated here was introduced: First, the strut cores were modeled as the edge system of a random Laguerre tessella- tion, then the coating was simulated by a complex morpho- logical transform, namely a locally adaptable dilation with balls of varying size. This way, the variations in the strut thickness could be reproduced. The modeling of the closed walls, however, was still ad hoc. Here, we present a refined version of the model discussed in ref. [2] In particular, we introduce methods for the estimation of the intensity and orientation of the closed walls in the foam which can then be used to build a more realistic model. Finally, by simulation of the permeability of the foam in different directions, we show that the orientation distribution of the walls indeed plays a role for the filtration behavior of the material. Image Analysis and Modeling The analysis of the material is based on tomographic gray value images of both the polymer foam and the ceramic foam. The images have a size of 670  670  270 voxels with a voxel edge length of 70.88 mm, which corresponds to 47.49  47.49  19.14 mm 3 of material. Figure 1 shows visua- lizations of both datasets. Since the hollow areas in the struts are not expected to play a role for the filtration behavior of the COMMUNICATION [*] Dr. C. Redenbach Department of Mathematics, University of Kaiserslautern 67653 Kaiserslautern, (Germany) E-mail: redenbach@mathematik.uni-kl.de Dr. O. Wirjadi, Dr. S. Rief, Dr. A. Wiegmann Fraunhofer Institute for Industrial Mathematics ITWM Fraunhofer-Platz 1, 67663 Kaiserslautern, (Germany) We present a stochastic model for the microstructure of a ceramic foam filter which is produced by coating an open polymer foam with liquid ceramic. First, we fit a random Laguerre tessellation to the polymer foam skeleton. Then, the coating is modeled using locally adaptable morphology which allows for the reproduction of the ceramic foam’s locally varying strut thickness. Furthermore, we introduce methods for the estimation of the intensity and orientation distribution of the closed facets which are formed during the coating process. By computation of the permeability of the foam in different directions we show that the anisostropic behavior of the material is reproduced correctly in the model. ADVANCED ENGINEERING MATERIALS 2011, 13, No. 3 ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 171