Publications

Abstract not provided.

Abstract not provided.

A decomposition chemistry and heat transfer model to predict the response of removable epoxy foam (REF) exposed to fire-like heat fluxes is described. The epoxy foam was created using a perfluorohexane blowing agent with a surfactant. The model includes desorption of the blowing agent and surfactant, thermal degradation of the epoxy polymer, polymer fragment transport, and vapor-liquid equilibrium. An effective thermal conductivity model describes changes in thermal conductivity with reaction extent. Pressurization is modeled assuming: (1) no strain in the condensed-phase, (2) no resistance to gas-phase transport, (3) spatially uniform stress fields, and (4) no mass loss from the system due to venting. The model has been used to predict mass loss, pressure rise, and decomposition front locations for various small-scale and large-scale experiments performed by others. The framework of the model is suitable for polymeric foams with absorbed gases.

A decomposition chemistry and heat transfer model to predict the response of removable epoxy foam (REF) exposed to fire-like heat fluxes is described. The epoxy foam was created using a perfluorohexane blowing agent with a surfactant. The model includes desorption of the blowing agent and surfactant, thermal degradation of the epoxy polymer, polymer fragment transport, and vapor-liquid equilibrium. An effective thermal conductivity model describes changes in thermal conductivity with reaction extent. Pressurization is modeled assuming: (1) no strain in the condensed-phase, (2) no resistance to gas-phase transport, (3) spatially uniform stress fields, and (4) no mass loss from the system due to venting. The model has been used to predict mass loss, pressure rise, and decomposition front locations for various small-scale and large-scale experiments performed by others. The framework of the model is suitable for polymeric foams with absorbed gases.

A case study is reported to document the details of a validation process to assess the accuracy of a mathematical model to represent experiments involving thermal decomposition of polyurethane foam. The focus of the report is to work through a validation process. The process addresses the following activities. The intended application of mathematical model is discussed to better understand the pertinent parameter space. The parameter space of the validation experiments is mapped to the application parameter space. The mathematical models, computer code to solve the models and its (code) verification are presented. Experimental data from two activities are used to validate mathematical models. The first experiment assesses the chemistry model alone and the second experiment assesses the model of coupled chemistry, conduction, and enclosure radiation. The model results of both experimental activities are summarized and uncertainty of the model to represent each experimental activity is estimated. The comparison between the experiment data and model results is quantified with various metrics. After addressing these activities, an assessment of the process for the case study is given. Weaknesses in the process are discussed and lessons learned are summarized.

A decomposition model has been developed to predict the response of removable syntactic foam (RSF) exposed to fire-like heat fluxes. RSF consists of glass micro-balloons (GMB) in a cured epoxy polymer matrix. A chemistry model is presented based on the chemical structure of the epoxy polymer, mass transport of polymer fragments to the bulk gas, and vapor-liquid equilibrium. Thermophysical properties were estimated from measurements. A bubble nucleation, growth, and coalescence model was used to describe changes in properties with the extent of reaction. Decomposition of a strand of syntactic foam exposed to high temperatures was simulated.

The investigation of the liquefaction and flow behavior of a thermally decomposing removable epoxy foam (REF) was discussed. It was concluded that the behavior of REF, can vary greatly depending on both physical and thermal boundary conditions as well as on decomposition chemistry. It was shown that the foam regression away from a heated surface generally involves two moving boundaries, a fluid-solid interface and a fluid-vapor interface. During thermal decomposition, the physical and chemical behaviors of the foams were coupled and can significantly affect heat transfer rates to the encapsulated units.

Response of removable epoxy foam (REF) to high heat fluxes is described using a decomposition chemistry model [1] in conjunction with a finite element heat conduction code [2] that supports chemical kinetics and dynamic radiation enclosures. The chemistry model [1] describes the temporal transformation of virgin foam into carbonaceous residue by considering breakdown of the foam polymer structure, desorption of gases not associated with the foam polymer, mass transport of decomposition products from the reaction site to the bulk gas, and phase equilibrium. The finite element foam response model considers the spatial behavior of the foam by using measured and predicted thermophysical properties in combination with the decomposition chemistry model. Foam elements are removed from the computational domain when the condensed mass fractions of the foam elements are close to zero. Element removal, referred to as element death, creates a space within the metal confinement causing radiation to be the dominant mode of heat transfer between the surface of the remaining foam elements and the interior walls of the confining metal skin. Predictions were compared to front locations extrapolated from radiographs of foam cylinders enclosed in metal containers that were heated with quartz lamps [3,4]. The effects of the maximum temperature of the metal container, density of the foam, the foam orientation, venting of the decomposition products, pressurization of the metal container, and the presence or absence of embedded components are discussed.

An efficient polymer mass loss and foam response model has been developed to predict the behavior of unconfined polyurethane foam exposed to fire-like heat fluxes. The mass loss model is based on a simple two-step mechanism using distributed reaction rates. The mass loss model was implemented into a multidimensional finite element heat conduction code that supports chemical kinetics and dynamic enclosure radiation. A discretization bias correction model was parameterized using elements with characteristic lengths ranging from 0.1cm to 1cm. Bias corrected solutions with these large elements gave essentially the same results as grid-independent solutions using 0.01-cm elements. Predictions were compared to measured decomposition front locations determined from real-time X-rays of 9-cm diameter, 15-cm tall cylinders of foam that were heated with lamps. The calculated and measured locations of the decomposition fronts were well within 1cm of each other and in some cases the fronts coincided. © 2004 Elsevier Ltd. All rights reserved.

A Simple Removable Epoxy Foam (SREF) decomposition chemistry model has been developed to predict the decomposition behavior of an epoxy foam encapsulant exposed to high temperatures. The foam is composed of an epoxy polymer, blowing agent, and surfactant. The model is based on a simple four-step mass loss model using distributed Arrhenius reaction rates. A single reaction was used to describe desorption of the blowing agent and surfactant (BAS). Three of the reactions were used to describe degradation of the polymer. The coordination number of the polymeric lattice was determined from the chemical structure of the polymer; and a lattice statistics model was used to describe the evolution of polymer fragments. The model lattice was composed of sites connected by octamethylcylotetrasiloxane (OS) bridges, mixed product (MP) bridges, and bisphenol-A (BPA) bridges. The mixed products were treated as a single species, but are likely composed of phenols, cresols, and furan-type products. Eleven species are considered in the SREF model - (1) BAS, (2) OS, (3) MP, (4) BPA, (5) 2-mers, (6) 3-mers, (7) 4-mers, (8) nonvolatile carbon residue, (9) nonvolatile OS residue, (10) L-mers, and (11) XL-mers. The first seven of these species (VLE species) can either be in the condensed-phase or gas-phase as determined by a vapor-liquid equilibrium model based on the Rachford-Rice equation. The last four species always remain in the condensed-phase. The 2-mers, 3-mers, and 4-mers are polymer fragments that contain two, three, or four sites, respectively. The residue can contain C, H, N, O, and/or Si. The L-mer fraction consists of polymer fragments that contain at least five sites (5-mer) up to a user defined maximum mer size. The XL-mer fraction consists of polymer fragments greater than the user specified maximum mer size and can contain the infinite lattice if the bridge population is less than the critical bridge population. Model predictions are compared to 133-thermogravimetric analysis (TGA) experiments performed at 24 different conditions. The average RMS error between the model and the 133 experiments was 4.25%. The model was also used to predict the response of two other removable epoxy foams with different compositions as well as the pressure rise in a constant volume hot cell.

A Simple PolyUrethane Foam (SPUF) mass loss and response model has been developed to predict the behavior of unconfined, rigid, closed-cell, polyurethane foam-filled systems exposed to fire-like heat fluxes. The model, developed for the B61 and W80-0/1 fireset foam, is based on a simple two-step mass loss mechanism using distributed reaction rates. The initial reaction step assumes that the foam degrades into a primary gas and a reactive solid. The reactive solid subsequently degrades into a secondary gas. The SPUF decomposition model was implemented into the finite element (FE) heat conduction codes COYOTE [1] and CALORE [2], which support chemical kinetics and dynamic enclosure radiation using 'element death.' A discretization bias correction model was parameterized using elements with characteristic lengths ranging from 1-mm to 1-cm. Bias corrected solutions using the SPUF response model with large elements gave essentially the same results as grid independent solutions using 100-{micro}m elements. The SPUF discretization bias correction model can be used with 2D regular quadrilateral elements, 2D paved quadrilateral elements, 2D triangular elements, 3D regular hexahedral elements, 3D paved hexahedral elements, and 3D tetrahedron elements. Various effects to efficiently recalculate view factors were studied -- the element aspect ratio, the element death criterion, and a 'zombie' criterion. Most of the solutions using irregular, large elements were in agreement with the 100-{micro}m grid-independent solutions. The discretization bias correction model did not perform as well when the element aspect ratio exceeded 5:1 and the heated surface was on the shorter side of the element. For validation, SPUF predictions using various sizes and types of elements were compared to component-scale experiments of foam cylinders that were heated with lamps. The SPUF predictions of the decomposition front locations were compared to the front locations determined from real-time X-rays. SPUF predictions of the 19 radiant heat experiments were also compared to a more complex chemistry model (CPUF) predictions made with 1-mm elements. The SPUF predictions of the front locations were closer to the measured front locations than the CPUF predictions, reflecting the more accurate SPUF prediction of mass loss. Furthermore, the computational time for the SPUF predictions was an order of magnitude less than for the CPUF predictions.

A Chemical-structure-based PolyUrethane Foam (CPUF) decomposition model has been developed to predict the fire-induced response of rigid, closed-cell polyurethane foam-filled systems. The model, developed for the B-61 and W-80 fireset foam, is based on a cascade of bondbreaking reactions that produce CO2. Percolation theory is used to dynamically quantify polymer fragment populations of the thermally degrading foam. The partition between condensed-phase polymer fragments and gas-phase polymer fragments (i.e. vapor-liquid split) was determined using a vapor-liquid equilibrium model. The CPUF decomposition model was implemented into the finite element (FE) heat conduction codes COYOTE and CALORE, which support chemical kinetics and enclosure radiation. Elements were removed from the computational domain when the calculated solid mass fractions within the individual finite element decrease below a set criterion. Element removal, referred to as ?element death,? creates a radiation enclosure (assumed to be non-participating) as well as a decomposition front, which separates the condensed-phase encapsulant from the gas-filled enclosure. All of the chemistry parameters as well as thermophysical properties for the CPUF model were obtained from small-scale laboratory experiments. The CPUF model was evaluated by comparing predictions to measurements. The validation experiments included several thermogravimetric experiments at pressures ranging from ambient pressure to 30 bars. Larger, component-scale experiments were also used to validate the foam response model. The effects of heat flux, bulk density, orientation, embedded components, confinement and pressure were measured and compared to model predictions. Uncertainties in the model results were evaluated using a mean value approach. The measured mass loss in the TGA experiments and the measured location of the decomposition front were within the 95% prediction limit determined using the CPUF model for all of the experiments where the decomposition gases were vented sufficiently. The CPUF model results were not as good for the partially confined radiant heat experiments where the vent area was regulated to maintain pressure. Liquefaction and flow effects, which are not considered in the CPUF model, become important when the decomposition gases are confined.

Abstract not provided.

Abstract not provided.

Sensitivity/uncertainty analyses are not commonly performed on complex, finite-element engineering models because the analyses are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, an analytical sensitivity/uncertainty analysis is used to determine the standard deviation and the primary factors affecting the burn velocity of polyurethane foam exposed to firelike radiative boundary conditions. The complex, finite element model has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state burn velocity calculated as the derivative of the burn front location versus time. The standard deviation of the burn velocity was determined by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation is essentially determined from a second derivative that is extremely sensitive to numerical noise. To minimize the numerical noise, 50-micron elements and approximately 1-msec time steps were required to obtain stable uncertainty results. The primary effect variable was shown to be the emissivity of the foam.