Multiscale Modeling of Expanding Polyurethane Foams via Computational Fluid Dynamics and Population Balance Equation

This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics during mold filling. The model is formulated upon coupling of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) to predict and simulate the evolution of foam features including apparent density and viscosity, bubble (or cell) size distribution (BSD) during the polymerization, as well as its kinetics. The solution of PBE inside the CFD code is performed with Quadrature Method of Moments (QMOM). The foam, constituted by a liquid polymer and gas bubbles, is simulated as a pseudo-single-phase system, while the interface between the foam and the surrounding air is tracked by a Volume-of-Fluid (VOF) solver within the open-source CFD code OpenFOAM. The modeling is applied for a simple foaming experiment and attention is paid to the effect of the rheological model on the predictions.