Numerical simulation of 3D polyurethane expansion during manufacturing process

In this paper, a phenomenological model for the expansion stage of flexible polyurethane foams production is introduced. This model is based on the expansion of a diphasic compressible fluid (quasi-homogeneous liquid/gas mixture). Expansion is illustrated through the evolution of the gas rate in the mixture. Two mechanisms are at the origin of this evolution: difference of pressure between the gas and the liquid, and CO2creation in the mixture. The CO2 creation is considered through an evolution law of the CO2 production rate. Evolutions of rheological properties are taken from literature. Numerical resolution is based on mixed and space-time finite elements, using a splitting technique to decouple kinematics computation from evolution equations. Validations are performed on two simple tests: free expansion and closed expansion. An industrial case is also considered: molding of an automobile seat in flexible polyurethane foam, showing the importance of the prediction of quality defaults in these parts.