Coupled Macro and Micro-Scale Modeling of Polyurethane Foaming Processes

Abstract

Polyurethane foam is used for manufacturing different kinds of products, such as refrigerators, car dashboards or steering wheels. First, we developed a macro-scale simulation tool that is able to predict foam flow in such complex molds. Depending on the location within a product, final properties of polyurethane foams may vary significantly. These properties (e.g. thermal conductivity or impact strength) are strongly dependent on local foam structure. Modeling complex geometries like refrigerators completely on bubble scale is neither possible nor would it be efficient. The computational effort would be enormous. Therefore, we developed a micro-scale model describing bubble growth and the evolution of the foam microstructure in polyurethane foams considering a limited number of bubbles in a representative volume. Finally, we coupled our macro and micro-scale simulation approaches. For that purpose, we introduced tracer particles into our mold filling simulations. We are able to record information about density and temperature changes or varying flow conditions along particle trajectories. This information is then used to set up corresponding simulations on bubble scale. Through this coupling, a basis for studying the evolution of the local foam microstructure in complex geometries is provided.

Foaming parameter identification of polyurethane using FOAMAT® device

“…Several numerical models have been developed to predict PU foam expansion in industrial mold geometries using both macroscale modeling [ 22, 28‐30 ] and microscale modeling. [ 15, 31‐35 ] In ref. [22] a macroscale numerical simulation of foam expansion using REM3D is applied to the cylindrical geometry of the specially developed RHEOFOAM system, which is very similar to the FOAMAT.…”

Numerical simulation with experimental validation of the structural reaction injection moulding of 3D continuous fibre reinforced polyurethane foam

“…The simulation of expanding PUR foam systems is an area of active research. Trends have shown a systematic development ranging from tracking the temporal evolution of the PUR foam density and temperature [24,25] to simulating the spatio-temporal evolution of associated flow properties such as temperature, propagation of foam front, viscosity as well as the reacting species [26][27][28][29][30][31][32][33][34][35][36][37]. Lefebvre et al developed a two-dimensional numerical framework to predict the evolution of the macroscopic velocity, temperature, stresses and species concentration fields in the flow of a reacting polymer system [26].…”

“…However, the morphology of expanding PUR foams is strongly influenced by the interplay between chemical reactions, temperature generation and evolution of the foam rheology [29]. Geier et al expanded the ideas in [24,26,27] for a systemic analysis of the early stage of product development and presented a workflow for simulating the foaming process in the manufacturing of a refrigerator [30,31]. Rao et al adopted in addition an empirical time and temperature dependent density model to simulate the expansion process of foams in a physically blown reactive PUR foam setup [32].…”

Effects of air vents on the flow of reacting polyurethane foam in a refrigerator cavity

“…Outside the nozzle, the gelling stage begins with the polymerization reactions, which turn the cream into a gel that expands rapidly. In the expansion (blowing) stage, the speed of foam expansion can be increased by adding a liquid blowing agent, which does not participate in the reactions, but, due to its low boiling point, undergoes a phase transition to gas . The blowing phase continues until the surface of the foam becomes dry and, finally, it stops when the foam attains its maximum volume .…”