Formulation of the Problem

Insulation materials are highly porous fibre structures or foam structures, which should exhibit as low as possible heat conductivity on the one hand, but on the other hand they have to be permanently stable, too. The ideal choice of material structure demands therefore the determination of the different material properties and the quantitative validation of the conflicting criteria. The part of mathematics dealing with effective material properties of porous media is the theory of homogenization. The effective material properties are computed as solutions of ''cell-problems'', which are formulated on representative elementary volumes.

Method of Resolution

Recently at the Fraunhofer ITWM it we succeeded in developing and analysing an efficient algorithm which allows to compute the effective thermal conductivity for highly porous insulating materials. These material are for example metal- / plastic-foam or glass-/ rock-wool, which are used for modern heat exchangers or rather for insulation. The regarded materials have in common that the portion in the volume of the high conductive components (metal, glass) is small and that they have a complex structure. The insulator (air) has by far the greatest volume content. To solve efficiently the aforementioned ''cell-problems'' the proportions of low (air) and high (metal, glass) conductivity is considered as a small parameter. Then we showed that the effective thermal conductivity can be defined with a good accuracy by solving of the ''cell-problems'' on the high conductive components only. Furthermore we examine in the case of fibre materials (glass-/ rock-wool) a discretization, which unknowns are the nods of the graph, which is implicated by the underlying fibre geometry. The nods are then given by the intersection points of the fibres. For materials with high porosity the number of such nods is relatively small. This new approach enables us to compute the effective conductivity of huge fibre geometries.

Conclusion

After many years highly porous insulating materials, in particular the ones consisting of plastic, are still not allowed to be compressed too much. At the ITWM a fast and combined method of measurement and simulation is designed to predict for a period up to 50 years, how insulating materials deform under mechanical pressure load. By this method conventional measurement processes can be replaced and so the development time of this material can be reduced drastically.

Validation

The developed methods were applied successfully in different projects with our industrial partners. The ITWM offers methods for the insulating materials, which consider and appraise many different physical effects (among other thing also heat radiation and gas diffusion in pores). Analogue design studies are arranged for acoustic and electrical insulating materials.