Density predictions using a finite element/level set model of polyurethane foam expansion and polymerization

Abstract

Polyurethane foams are used widely for encapsulation and structural purposes because they are inexpensive, straightforward to process, amenable to a wide range of density variations (1–50 lb/ft3), and able to fill complex molds quickly and effectively. Computational models of the filling and curing process are needed to reduce defects such as voids, out-of-specification density, density gradients, foam decomposition from high temperatures due to exotherms, and incomplete filling. This paper details the development of a computational fluid dynamics model of a moderate density PMDI structural foam, PMDI-10. PMDI is an isocyanate-based polyurethane foam, which is chemically blown with water. The polyol reacts with isocyanate to produce the polymer. PMDI-10 is catalyzed giving it a short pot life, meaning that the foam is liquid and flowable only for a short-time; it foams and polymerizes to a solid within 5 min during normal processing. To achieve a higher density, the foam is over-packed to twice or more of its free-rise density of 10 lb/ft3. The goal for modeling is to represent the expansion, filling of molds, and the polymerization of the foam. This model will be used to reduce defects, optimize the mold design, understand processing parameter sensitivities, and predict the final foam properties.A homogenized continuum model for foaming and curing was developed based on reaction kinetics, documented in a recent paper; it uses a simplified mathematical formalism that decouples these two reactions. The chemo-rheology of PMDI is measured experimentally and fit to a generalized-Newtonian viscosity model that is dependent on the extent of cure, gas volume fraction, and temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved using a stabilized finite element method. The equations are combined with a level set method to determine the location of the foam-gas interface as it evolves to fill the mold. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics, viscosity, and other material properties are all sensitive to temperature. Results from the model are compared to experimental flow visualization data to understand the interface evolution with time and post-test X-ray computed tomography (CT) data for the density prediction validation. Several geometries are investigated including two configurations of a mock structural part and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed for future work.