Modeling Heat Transfer and Pressurization of Polymeric Methylene Diisocyanate (PMDI) Polyurethane Foam in a Sealed Container
Polymer foam encapsulants provide mechanical, electrical, and thermal isolation in engineered systems. It can be advantageous to surround objects of interest, such as electronics, with foams in a hermetically sealed container to protect the electronics from hostile environments, such as a crash that produces a fire. However, in fire environments, gas pressure from thermal decomposition of foams can cause mechanical failure of the sealed system.
In this work, a detailed study of thermally decomposing polymeric methylene diisocyanate (PMDI)-polyether-polyol based polyurethane foam in a sealed container is presented. Both experimental and computational work is discussed. Validation experiments, called Foam in a Can (FIC) are presented. In these experiments, 320 kg/m3 PMDI foam in a 0.2 L sealed steel container is heated to 1073 K at a rate of 150 K/min and 50 K/min. FIC is tested in two orientations, upright and inverted. The experiment ends when the can breaches due to the buildup of pressure from the decomposing foam. The temperature at key locations is monitored as well as the internal pressure of the can. When the foams decompose, organic products are produced. These products can be in the gas, liquid, or solid phase. These experiments show that the results are orientation dependent: the inverted cans pressurize, and thus breach faster than the upright. There are many reasons for this, among them: buoyancy driven flows, the movement of liquid products to the heated surface, and erosive channeling that enhance the foam decomposition.
The effort to model this problem begins with Erickson’s No Flow model formulation. In this model, Arrhenius type reactions, derived from Thermogravimetric Analysis (TGA), control the reaction. A three-step reaction is used to decompose the PMDI RPU (rigid polyurethane foam) into CO2, organic gases, and char. Each of these materials has unique properties. The energy equation is used to solve for temperature through the domain. Though gas is created in the reaction mechanism, it does not advect, rather, its properties are taken into account when calculating the material properties, such as the effective conductivity. The pressure is calculated using the ideal gas law. A rigorous uncertainty quantification (UQ) assessment, using the mean value method, along with an analysis of sensitivities, is presented for this model. The model is also compared to experiments. In general, the model works well for predicting temperature, however, due to the lack of gas advection and presence of a liquid phase, the model does not predict pressure well.
Porous Media Model is then added to allow for the advection of gases through the foam region, using Darcy’s law to calculate the velocity. Continuity, species, and enthalpy equations are solved for the condensed and gas phases. The same reaction mechanism as in the No Flow model is used, as well as material properties. A mesh resolution study, as well as a calibration of parameters is conducted, and the model is compared to experimental results. This model, due to the advection of gases, produces gravity dependent results that compare well to experiment.
However, there were several properties that had to be calibrated, and replacing these calibrated parameters with physically derived values is desired. To that end, Vapor Liquid Equilibrium (VLE) equations are added to the Porous Media model. These equations predict the vapor/liquid split of the organic decomposition products based on temperature and pressure. UQ for the parameters in the model as well as a sensitivity study is presented, in addition to comparison to experiment. The addition of the VLE improved temperature and pressure prediction, both qualitatively and quantitatively.