Invented by Otto Bayer in 1937, Polyurethane (PUR) foam is an extremely common material, especially in our cars (bumpers, dashboards, seats, etc.) and in our homes (as insulating material for walls, pipes and refrigerators). PUR is produced by mixing alcohol and isocyanates. The resulting reaction generates gas bubbles which become trapped in the curing compound.

Pre-formed foam plastics are produced by casting processes, where the reactants are mixed just before they enter the mould. When foaming large structures, the curing process may start while the reactants are still being fed into the form, which can result in poor product quality with undesirable voids. To ensure successful filling, both the filling and foaming processes must therefore be optimized together.

To verify that CFX-5 could simulate PUR foaming, we set up Bayer’s original experiment: a beaker is partly filled with the reactants; after a while the chemical reaction starts, generating CO2 bubbles while solidifying. The process can be modeled with different levels of sophistication, ranging from a single-phase simulation with prescribed variations of density and viscosity, to complex multiphase models including chemical reactions.

While CFX-5 can handle all these models, we chose the simple approach with two variations: firstly, density and viscosity as specified functions of time, and then as functions of the local mixture age. The first approach is appropriate for Bayer’s experiment, while the latter is capable of modeling the filling and curing processes in the moulds.

It took us only two weeks to make things work with CFX-5, which handled the calculations very well, the viscosity increasing by 3 orders of magnitude without adversely affecting convergence rates. Bayer’s engineers were very impressed with the results. We could prove that CFX-5 is robust and accurate and very well suited to this kind of simulation. However, the run times were fairly high and they felt that they could not yet use the method as a standard tool for the optimization of their processes. We are now investigating how to reduce the CPU requirements without affecting the results, to make the method viable for real applications.

Cell structure of rigid polyurethane foam. Picture courtesy of Bayer AG.

"PUR mushroom" experiment. Picture courtesy of Bayer AG.

CFX-5 simulation of the growth of the "PUR mushroom" over time. The color shows the exponential increase of viscosity. After a few seconds the viscosity becomes so large that the fluid flow comes to a complete stop.