Organic materials are an attractive choice for structural components due to their light weight and versatility. However, because they decompose at low temperatures relative to traditional materials, they pose a safety risk due to fire and loss of structural integrity. To quantify this risk, analysts use chemical kinetics models to describe the material pyrolysis and oxidation using thermogravimetric analysis (TGA). This process requires the calibration of many model parameters to closely match experimental data. Previous efforts in this field have largely been limited to finding a single best-fit set of parameters even though the experimental data may be very noisy. Furthermore, the chemical kinetics models are often simplified representations of the true decomposition process. The simplification induces model-form errors that the fitting process cannot capture. In this work, we propose a methodology for calibrating decomposition models to TGA data that accounts for uncertainty in the model-form and experimental data simultaneously. The methodology is applied to the decomposition of a carbon fiber epoxy composite with a three-stage reaction network and Arrhenius kinetics. The results show a good overlap between the model predictions and TGA data. Uncertainty bounds capture deviations of the model from the data. The calibrated parameter distributions are also presented. The distributions may be used in forward propagation of uncertainty in models that leverage this material.
Data from four TGA experiments conducted at Sandia National Laboratories was used for determination of a pyrolysis model using a commercial thermokinetics program developed by Netzsch Instruments (Kinetics NEO, version 2.1). The data measured at 1 K/min and the average of three measurements at 50 K/min were used as input into Kinetics NEO. The model was developed using data in the range 373 to 773 K. An initial estimate of the energy of activation (E) and pre-exponential constant (A) were determined from the model-free Friedman approach.
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 en vironments, such as a crash that produces a fire. However, i n 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. Three models of increasing physics fidelity are presented: No Flow, Porous Media, and Porous Media with VLE. Each model us described in detail, compared to experiment , and uncertainty quantification is performed. While the Porous Media with VLE model matches has the best agreement with experiment, it also requires the most computational resources.
Polymer foam encapsulants provide mechanical, electrical, and thermal isolation in engineered systems. In fire environments, gas pressure from thermal decomposition of polymers can cause mechanical failure of sealed systems. A 3-D finite element conduction-radiation model with porous media flow and a chemistry model was created to investigate the heat transfer and pressurization in such scenarios. Experiments show that the rate of pressurization and the temperature of select thermocouples are dependent on orientation with respect to gravity, indicating buoyancy-driven flow. In this work, the gas velocity is solved by applying the Darcy approximation, and the heat transfer and pressurization are determined by solving the continuity, species, and enthalpy equations in the condensed and gas phases. This work will describe the porous media model, explore material parameters (e.g. phase, permeability, conductivity) for use with PMDI polyurethane, compare predictions to experimental data, and recommend values for material properties. It will use multiple heating rates to validate the data, and show that incorporating gas motion into the model captures the divergent nature of the results in different orientations.
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 in order to protect them from hostile environments or from accidents such as fire. In fire environments, gas pressure from thermal decomposition of foams can cause mechanical failure of sealed systems. In this work, a detailed uncertainty quantification study of polymeric methylene diisocyanate (PMDI)-polyether-polyol based polyurethane foam is presented and compared to experimental results to assess the validity of a 3-D finite element model of the heat transfer and degradation processes. In this series of experiments, 320 kg/m3 PMDI foam in a 0.2 L sealed steel container is heated to 1,073 K at a rate of 150 K/min. The experiment ends when the can breaches due to the buildup of pressure. The temperature at key location is monitored as well as the internal pressure of the can. Both experimental uncertainty and computational uncertainty are examined and compared. The mean value method (MV) and Latin hypercube sampling (LHS) approach are used to propagate the uncertainty through the model. The results of the both the MV method and the LHS approach show that while the model generally can predict the temperature at given locations in the system, it is less successful at predicting the pressure response. Also, these two approaches for propagating uncertainty agree with each other, the importance of each input parameter on the simulation results is also investigated, showing that for the temperature response the conductivity of the steel container and the effective conductivity of the foam, are the most important parameters. For the pressure response, the activation energy, effective conductivity, and specific heat are most important. The comparison to experiments and the identification of the drivers of uncertainty allow for targeted development of the computational model and for definition of the experiments necessary to improve accuracy.
Polymer foam encapsulants provide mechanical, electrical, and thermal isolation in engineered systems. In fire environments, gas pressure from thermal decomposition of polymers can cause mechanical failure of sealed systems. In this work, a detailed uncertainty quantification study of PMDI-based polyurethane foam is presented to assess the validity of the computational model. Both experimental measurement uncertainty and model prediction uncertainty are examined and compared. Both the mean value method and Latin hypercube sampling approach are used to propagate the uncertainty through the model. In addition to comparing computational and experimental results, the importance of each input parameter on the simulation result is also investigated. These results show that further development in the physics model of the foam and appropriate associated material testing are necessary to improve model accuracy.
This study details a methodology for quantification of errors and uncertainties of a finite element heat transfer model applied to a Ruggedized Instrumentation Package (RIP). The proposed verification and validation (V&V) process includes solution verification to examine errors associated with the code's solution techniques, and model validation to assess the model's predictive capability for quantities of interest. The model was subjected to mesh resolution and numerical parameters sensitivity studies to determine reasonable parameter values and to understand how they change the overall model response and performance criteria. To facilitate quantification of the uncertainty associated with the mesh, automatic meshing and mesh refining/coarsening algorithms were created and implemented on the complex geometry of the RIP. Automated software to vary model inputs was also developed to determine the solution’s sensitivity to numerical and physical parameters. The model was compared with an experiment to demonstrate its accuracy and determine the importance of both modelled and unmodelled physics in quantifying the results' uncertainty. An emphasis is placed on automating the V&V process to enable uncertainty quantification within tight development schedules.