Optimization of Insulation Materials

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.

These are, for example, the following materials:

• Metal / plastic foams
• Fiber insulation materials (e.g., glass / stone wool or natural fiber)
• Cellulose insulation materials

The ideal choice of material structure demands  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.

Multiscale Approach for Simulation and Optimization

The focus of our research and development is on multi-scale modeling and simulation. On the micro scale, each fiber of the fiber insulation material or each cell wall of the foam is imaged. On this scale, all the details on the selected calculation grid are resolved so that the properties can be precisely determined.

We simulate in our solution approach:

• The heat conduction
• The heat convection by flow
• The heat radiation

These then flow into a simulation at the macroscopic level on which the individual fibers can no longer be resolved in detail. The macroscopic simulation is embedded in an optimization procedure. The aim of the optimization of the heat transfer coefficient (U-value) is achieved by iteration of the described simulation steps on micro- and macro-scale.

A multi-target optimization is pursued; other properties such as strength or stiffness are also taken into account. Various tools are used, the software FeelMath developed by us at the institute, as well as commercial tools such as ANSYS (on the component level).