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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.

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.

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 0.1 cm to 1 cm. 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 1 cm of each other and in some cases the fronts coincided.

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.

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. The response variable was chosen as the steady-state decomposition front velocity. Four different analyses are presented, including (1) an analytical mean value (MV) analysis, (2) a linear surrogate response surface (LIN) using a constrained latin hypercube sampling (LHS) technique, (3) a quadratic surrogate response surface (QUAD) using LHS, and (4) a direct LHS (DLHS) analysis using the full grid and time step resolved finite element model. To minimize the numerical noise, 50 μm elements and approximately 1 ms time steps were required to obtain stable uncertainty results. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model. © 2002 Elsevier Science B.V. All rights reserved.

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.

The decomposition of unconfined rigid polyurethane foam has been modeled by a kinetic bond-breaking scheme describing degradation of a primary polymer and formation of a thermally stable secondary polymer. The bond-breaking scheme is resolved using percolation theory to describe evolving polymer fragments. The polymer fragments vaporize according to individual vapor pressures. Kinetic parameters for the model were obtained from thermal gravimetric analysis (TGA). The chemical structure of the foam was determined from the preparation techniques and ingredients used to synthesize the foam. Scale-up effects were investigated by simulating the response of an incident heat flux of 25 W/cm2 on a partially confined 8.8-cm diameter by 15-cm long right circular cylinder of foam that contained an encapsulated component. Predictions of internal foam and component temperatures, as well as regression of the foam surface, were in agreement with measurements using thermocouples and X-ray imaging.

The decomposition of unconfined rigid polyurethane foam has been modeled by a kinetic bond-breaking scheme describing degradation of a primary polymer and formation of a thermally stable secondary polymer. The bond-breaking scheme is resolved using percolation theory to describe evolving polymer fragments. The polymer fragments vaporize according to individual vapor pressures. Kinetic parameters for the model were obtained from Thermal Gravimetric Analysis (TGA). The chemical structure of the foam was determined from the preparation techniques and ingredients used to synthesize the foam. Scale-up effects were investigated by simulating the response of an incident heat flux of 25 W/cm{sup 2} on a partially confined 8.8-cm diameter by 15-cm long right circular cylinder of foam which contained an encapsulated component. Predictions of center, midradial, and component temperatures, as well as regression of the foam surface, were in agreement with measurements using thermocouples and X-ray imaging.

A database has been created for use with the Jacobs-Cowperthwaite-Zwisler-3 equation-of-state (JCZ3-EOS) to determine thermochemical equilibrium for detonation and expansion states of energetic materials. The JCZ3-EOS uses the exponential 6 intermolecular potential function to describe interactions between molecules. All product species are characterized by r*, the radius of the minimum pair potential energy, and {var_epsilon}/k, the well depth energy normalized by Boltzmann`s constant. These parameters constitute the JCZS (S for Sandia) EOS database describing 750 gases (including all the gases in the JANNAF tables), and have been obtained by using Lennard-Jones potential parameters, a corresponding states theory, pure liquid shock Hugoniot data, and fit values using an empirical EOS. This database can be used with the CHEETAH 1.40 or CHEETAH 2.0 interface to the TIGER computer program that predicts the equilibrium state of gas- and condensed-phase product species. The large JCZS-EOS database permits intermolecular potential based equilibrium calculations of energetic materials with complex elemental composition.

Rigid polyurethane foams are used as encapsulants to isolate and support thermally sensitive components within weapon systems. When exposed to abnormal thermal environments, such as fire, the polyurethane foam decomposes to form products having a wide distribution of molecular weights and can dominate the overall thermal response of the system. Decomposing foams have either been ignored by assuming the foam is not present, or have been empirically modeled by changing physical properties, such as thermal conductivity or emissivity, based on a prescribed decomposition temperature. The hypothesis addressed in the current work is that improved predictions of polyurethane foam degradation can be realized by using a more fundamental decomposition model based on chemical structure and vapor-liquid equilibrium, rather than merely fitting the data by changing physical properties at a prescribed decomposition temperature. The polyurethane decomposition model is founded on bond breaking of the primary polymer and formation of a secondary polymer which subsequently decomposes at high temperature. The bond breaking scheme is resolved using percolation theory to describe evolving polymer fragments. The polymer fragments vaporize according to individual vapor pressures. Kinetic parameters for the model were obtained from Thermal Gravimetric Analysis (TGA) from a single nonisothermal experiment with a heating rate of 20 C/min. Model predictions compare reasonably well with a separate nonisothermal TGA weight loss experiment with a heating rate of 200 C/min.

A summary of multidimensional modeling is presented which describes coupled thermals chemical and mechanical response of reactive and nonreactive materials. This modeling addresses cookoff of energetic material (EM) prior to the onset of ignition. Cookoff, lasting from seconds to days, sensitizes the EM whereupon combustion of confined, degraded material determines the level of violence. Such processes are dynamic, occurring over time scales of millisecond to microsecond, and thus more amenable for shock physics analysis. This work provides preignition state estimates such as the amount of decomposition, morphological changes, and quasistatic stress states for subsequent dynamic analysis. To demonstrate a fully-coupled thermal/chemical/quasistatic mechanical capability, several example simulations have been performed: (1) the one-dimensional time-to-explosion experiments, (2) the Naval Air Weapon Center`s (NAWC) small scale cookoff bomb, (3) a small hot cell experiment and (4) a rigid, highly porous, closed-cell polyurethane foam. Predictions compared adequately to available data. Deficiencies in the model and future directions are discussed.

Cookoff modeling of confined energetic materials involves the coupling of thermal, chemical and mechanical effects. In the past, modeling has focussed on the prediction of thermal runaway with little regard to the effects of mechanical behavior of the energetic material. To address the mechanical response of the energetic material, a constitutive submodel has been developed which can be incorporated into thermal-chemical-mechanical analysis. This work presents development of this submodel and its incorporation into a fully coupled one-dimensional, thermal-chemical-mechanical computer code to simulate thermal initiation of energetic materials. Model predictions include temperature, chemical species, stress, strain, solid/gas pressure, solid/gas density, yield function, and gas volume fraction. Sample results from a scaled aluminum tube filled with RDX exposed to a constant temperature bath at 500 K will be displayed. The micromechanical submodel is based on bubble mechanics which describes nucleation, decomposition, and elastic/plastic mechanical behavior. This constitutive material description requires input of temperatures and reacted fraction of the energetic material as provided by the reactive heat flow code, XCHEM, and the mechanical response is predicted using a quasistatic mechanics code, SANTOS. A parametric sensitivity analysis indicates that a small degree of decomposition causes significant pressurization of the energetic material, which implies that cookoff modeling must consider the strong interaction between thermal-chemistry and mechanics. This document consists of view graphs from the poster session.

The Becker-Kistiakowsky-Wilson equation of state (BKW-EOS) has been calibrated over a wide initial density range near C-J states using measured detonation properties from 62 explosives at III total initial densities. Values for the empirical BKW constants {alpha}, {beta}, {kappa}, and {theta} were 0.5, 0.298, 10.5, and 6620, respectively. Covolumes were assumed to be invariant. Model evaluation includes comparison to measurements from 91 explosives composed of combinations of Al, B, Ba, C, Ca, Cl, F, H, N, 0, P, Pb, and Si at 147 total initial densities. Adequate agreement between predictions and measurements were obtained with a few exceptions for nonideal explosives. However, detonation properties for the nonideal explosives can be predicted adequately by assuming partial equilibrium. The partial equilibrium assumption was applied to aluminized composites of RDX, HMX, TNETB, and TNT to predict detonation velocity and temperature.

An eXplosive CHEMical kinetics code, XCHEM was developed to solve the reactive diffusion equations associated with thermal ignition of energetic material. This method-of-lines code uses stiff numerical methods and adaptive meshing. Solution accuracy is maintained between multilayered materials consisting of blends of reactive components and/or inert materials. Phase change and variable properties are included in one-dimensional slab, cylindrical and spherical geometries. Temperature-dependent thermal properties was incorporated and modification of thermal conductivities to include decomposition effects are estimated using solid/gas volume fractions determined by species fractions. Gas transport properties are also included. Time varying temperature, heat flux, convective and thermal radiation boundary conditions, and layer to layer contact resistances are also implemented. The global kinetic mechanism developed at Lawrence Livermore National Laboratory (LLNL) by McGuire and Tarver used to fit One-Dimensional Time to eXplosion (ODTX) data for the conventional energetic materials (HMX, RDX, TNT, and TATB) are presented as sample calculations representative of multistep chemistry. Calculated and measured ignition times for explosive mixtures of Comp B (RDX/TNT), Octol, (HMX/TNT), PBX 9404 (HMX/NC), and RX-26-AF (HMX/TATB) are compared. Geometry and size effects are accurately modeled, and calculations are compared to experiments with time varying boundary conditions. Finally, XCHEM calculations of initiation of an AN/oil/water emulsion, resistively heated, are compared to measurements.

Thermochemical data fits for approximately 900 gaseous and 600 condensed species found in the JANAF tables (Chase et al. 1985) have been completed for use with the TIGER non-ideal thermoequilibrium code (Cowperthwaite and Zwisler 1973). The TIGER code has been modified to allow systems containing up to 400 gaseous and 100 condensed constituents composed of up to 50 elements. Gaseous covolumes have been estimated following the procedure outlined by Mader (1979) using estimates of van der Waals radii for 48 elements and three-dimensional molecular mechanics. Molecular structures for all gaseous components were explicitly defined in terms of atomic coordinates in Å (Hobbs and Baer 1992a). The Becker-Kistiakowsky-Wilson equation of state (BKW-EOS) has been calibrated near C-J states using detonation temperatures measured in liquid and solid explosives and a large product species data base. Detonation temperatures for liquid and solid explosives were predicted adequately with a single set of BKW parameters. Values for the empirical BKW constants α, β, κ, and θ were 0.5, 0.174, 11.85, and 5160, respectively. Values for the covolume factors, κi, were assumed to be invariant. The liquid explosives included mixtures of hydrazine nitrate with hydrazine, hydrazine hydrate, and water; mixtures of tetranitromethane with nitromethane; liquid isomers ethylnitrate and 2-nitroethanol; and nitroglycerine. The solid explosives included HMX, RDX, PETN, Tetryl, and TNT. Color contour plots of HMX equilibrium products as well as thermodynamic variables are shown in pressure and temperature space. Similar plots for a pyrotechnic reaction composed of TiH2 and KClO4 are also reported. Calculations for a typical HMX-based propellant are also discussed. © 1992 Springer-Verlag.

Variations of bed void fraction in a full-scale, reacting, fixed-bed coal gasifier have been deduced from measured axial pressure profiles obtained during gasification of seven coal types ranging from lignite to bituminous. Packed-bed pressure correlations were used to calculate the void fractions based on monotonic polynomial fits of measured pressure profiles. Insights into the fixed-bed combustion processes affected by the void distribution were obtained by a one-dimensional, steady-state, fixed-bed combustion model. Predicted temperature profiles from this model compare reasonably well to experimental data. The bed void distributions are not linear but are perturbed by vigorous reactions in the devolatilization and oxidation zones. Results indicate that a dramatic increase in temperature and associated gas release causes the bed to expand and the gas void space to increase. Increased void space localized in the combustion zone causes the steep temperature gradient to decrease and the location of the maximum temperature to shift. Also, large feed gas flow rates cause the void fraction in the ash zone to increase.