In previous work, commercially available downward facing exploding bridgewire detonators (EBWs) were exposed to elevated temperatures. These detonators were then initiated using a firing set which discharged a high amplitude short duration electrical pulse into a thin gold bridgewire. Responses of the detonators were measured using photonic doppler velocimetry (PDV) and high-speed photography. A time delay of 4 μs between EBW initiation and first movement of an output flyer separated operable detonators from inoperable detonators or duds. Here, we propose a simple method to determine detonator operability from the calculated state of the detonator at the time the firing set is initiated. The failure criterion is based on the gap distance between the exploding bridgewire (EBW) and the adjacent initiating explosive within the detonator which is low-density pentaerythritol tetranitrate (PETN) that melts between 413-415 K (140-142 ºC). The gap forms as PETN melts and flows to the bottom of the input pellet. Melting of PETN is modeled thermodynamically as an energy sink using a normal distribution spread over a temperature range between the onset temperature of 413 K and the ending temperature of 415 K. The extent of the melt is determined from the average temperature of the PETN. The PETN liquid is assumed to occupy the interstitial gas volume in the lower part of the input pellet. The vacated volume from the relocated liquid forms the gap between the EBW and the PETN. The remaining sandwiched layer consists of solid PETN particles and gas filling interstitial volume. We predict that a threshold gap between 17-27 μm separates properly functioning detonators from duds.
Operability thresholds that differentiate between functional RP-87 exploding bridge wire (EBW) detonators and nonfunctional RP-87 EBW detonators (duds) were determined by measuring the time delay between initiation and early wall movement (function time). The detonators were inserted into an externally heated hollow cylinder of aluminum and fired with current flow from a charged capacitor using an exploding bridge wire (EBW initiated). Functioning detonators responded like unheated pristine detonators when the function time was 4 μs or less. The operability thresholds of the detonators were characterized with a simple decomposition cookoff model calibrated using a modified version of the Sandia Instrumented Thermal Ignition (SITI) experiment. These thresholds are based on the calculated state of the PETN when the detonators fire. The operability threshold is proportional to the positive temperature difference (ΔT) between the maximum temperature within the PETN and the onset of decomposition (∼406 K). The temperature difference alone was not sufficient to define the operability threshold. The operability threshold was also proportional to the time that the PETN had been at elevated temperatures. That is, failure was proportional to both temperature and reaction rate. The reacted gas fraction is used in the current work for the reaction correlation. Melting of PETN also had a significant effect on the operability threshold. Detonator failure occurred when the maximum temperature exceeded the nominal melting point of PETN (414 K) for 45±5 s or more.
This is the Sandia report from a joint NSRD project between Sandia National Labs and Savannah River National Labs. The project involved development of simulation tools and data intended to be useful for tritium operations safety assessment. Tritium is a synthetic isotope of hydrogen that has a limited lifetime, and it is found at many tritium facilities in the form of elemental gas (T2). The most serious risk of reasonable probability in an accident scenario is when the tritium is released and reacts with oxygen to form a water molecule, which is subsequently absorbed into the human body. This tritium oxide is more readily absorbed by the body and therefore represents a limiting factor for safety analysis. The abnormal condition of a fire may result in conversion of the safer T2 inventory to the more hazardous oxidized form. It is this risk that tends to govern the safety protocols. Tritium fire datasets do not exist, so prescriptive safety guidance is largely conservative and reliant on means other than testing to formulate guidelines. This can have a consequence in terms of expensive and/or unnecessary mitigation design, handling protocols, and operational activities. This issue can be addressed through added studies on the behavior of tritium under representative conditions. Due to the hazards associated with the tests, this is being approached mainly from a modeling and simulation standpoint and surrogate testing. This study largely establishes the capability to generate simulation predictions with sufficiently credible characteristics to be accepted for safety guidelines as a surrogate for actual data through a variety of testing and modeling activities.
Transforming polymorphs, melting, and boiling are physical processes that can accelerate decomposition rates during cookoff of PETN and make measurements difficult. For example, splashing liquids from large bubbles filled with decomposition products clog pressure tubing in sealed experiments. Boil over can also extinguish thermal excursions in vented experiments making ignition difficult. For better measurements, we have modified the Sandia Instrumented Thermal Ignition (SITI) experiment to obtain better sealed and vented cookoff data for PETN by reducing the sample size and including additional gas space to prevent clogged tubing and boil over. Ignition times were not affected by 1) increasing the gas space by a factor of 3 in sealed SITI experiments or by 2) venting the decomposition gasses. That is, thermal ignition of PETN is not pressure dependent and the rate-limiting step during PETN decomposition likely occurs in the condensed phase. A simple decomposition model was calibrated using these observations and includes rate acceleration caused by melting and boiling. The model is used to predict internal temperatures, pressurization, and thermal ignition in a wide variety of experiments. The model is also used with SITI data to estimate the previously unreported latent enthalpy (5 J/g) associated with the α (PETN-I) to β (PETN-II) polymorphic phase transformation of PETN.
We have completed a series of both vented and sealed cookoff experiments of black powder and smokeless powder in our Sandia Instrumented Thermal Ignition (SITI) apparatus at bulk densities of 1078 and 729 kg/m3, respectively. The confining aluminum cylinder was ramped from room temperature to a set point temperature and then held at the setpoint temperature until ignition. The setpoint temperatures varied between 495 to 523 K for the black powder and 401 to 412 K for the more sensitive smokeless powder. The vented experiments show a significant delay in thermal ignition, indicating that the ignition is dependent on pressure. Post experimental debris shows greater violence for our smokeless powder experiments than our black powder experiments. A simplified universal cookoff model (UCM) was calibrated using the black powder and smokeless powder SITI data and used to predict pressurization and thermal ignition. The current work presents the first calibration of the UCM with a double base propellant. This work also presents the first pressure-dependent cookoff model for black powder and smokeless powder.
The solubility of RDX (hexahydro-1,3,5-tri-nitro-1,3,5-triazine) in TNT (2,4,6-trinitrotoluene) at elevated temperatures is required to accurately predict the response of Comp-B3 (60:40 RDX:TNT) during accidents involving fire. As the temperature increases, the TNT component melts, the RDX partially dissolves in the liquid TNT, and the remaining RDX melts (203 ∘C) as the Comp-B thermally ignites. In the current work, we used a differential scanning calorimeter (DSC) to estimate the solubility of RDX in TNT at the melting point of RDX. Most DSC measurements of Comp-B3 do not show an RDX melt endotherm. The absence of an endotherm associated with the RDX melt has been interpreted as RDX being completely dissolved in TNT before reaching the melting point. We have observed that the endotherm is not absent, but is masked by exothermic reactions occurring at these elevated temperatures. We have inhibited the exothermic reactions by venting our DSC samples and measuring the RDX melt endotherm in our Comp-B3 samples at about 203 ∘C. Using the measured heat flow associated with the RDX melt and the latent melting enthalpy of RDX, we have approximated the solubility of RDX in TNT to be roughly 50–100 g RDX per 100 g TNT. The broad range is based on corrections for exothermic reactions occurring as the RDX melts.
Thermal conductivity has been determined for a variety of energetic materials (EMs) using finite element analysis (FEA) and cookoff data from the Sandia Instrumented Thermal Ignition (SITI) experiment. Materials studied include melt-cast, pressed, and low-density explosives. The low-density explosives were either prills or powders with some experiments run at pour density (not pressed). We have compared several of our thermal conductivities with those in the literature as well as investigated contact resistance between the confining aluminum and explosive, multidimensional heat transfer effects, and uncertainty in the thermocouple bead positions. We have determined that contact resistance is minimal in the SITI experiment, the heat transfer along the midplane is one-dimensional, and that uncertainty in the thermocouple location is greatest near the heated boundary. Our values of thermal conductivity can be used with kinetic mechanisms to accurately predict thermal profiles and energy dissipation during the cookoff of explosives.
We have completed a series of vented and sealed cookoff experiments of the ε-polymorph of CL-20 in our Sandia Instrumented Thermal Ignition (SITI) apparatus using both powder and pressed pellets at nominal densities of 313 ± 8 kg/m3 and 1030 ± 4 kg/m3, respectively. The boundary temperature of our aluminum confinement cylinder was ramped in 10 minutes from room temperature to a prescribed set-point temperature ranging between 448 nd 468 K and held at the set-point temperature until ignition. A universal cookoff model (UCM) has been calibrated using the ε-CL-20 SITI data to predict pressurization and thermal ignition of ε-CL-20. The ignition model was validated by using one-dimensional time-to-explosion (ODTX) ignition data from a different laboratory. We found that a thirtyfold increase in the reaction rates due to liquefaction at 520 K could explain the high temperature ODTX cookoff data. The model gives a plausible explanation of why melting is important in fast cookoff events involving CL-20. Our model also gives support to 520 K as the liquefaction point of CL-20, which has different values in the literature.
We have completed a series of small-scale cook-off experiments of ammonium nitrate (AN) prills in our Sandia Instrumented Thermal Ignition test at nominal packing densities of about 0.8 g/cm3. We increased the boundary temperature of our aluminum confinement cylinder from room temperature to a prescribed set-point temperature in 10 min. Our set-point temperature ranged from 508 to 538 K. The external temperature of the confining cylinder was held at the set-point temperature until ignition. We used type K thermocouples to measure temperatures associated with several polymorphic phase changes as well as melting and boiling. As the AN boiled, our thermocouples were destroyed by corrosion, which may have been caused by reaction of hot nitric acid (HNO3) with nickel to form nickel nitrate, Ni(NO3)2. Videos of the corroding thermocouples showed a green solution that was similar to the color of Ni(NO3)2. We found that ignition was imminent as the AN boiling point was exceeded. Ignition of the AN prills was modeled by solving the energy equation with an energy source due to desorption of moisture and decomposition of AN to form equilibrium products. A Boussinesq approximation was used in conjunction with the momentum equation to model flow of the liquid AN. We found that the prediction of ignition was not sensitive to small perturbations in the latent enthalpies.
We have used several configurations of the Sandia Instrumented Thermal Ignition (SITI) experiment to develop a pressure-dependent, four-step ignition model for a plastic bonded explosive (PBX 9407) consisting of 94 wt.% RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine), and a 6 wt.% VCTFE binder (vinyl chloride/chlorotrifluoroethylene copolymer). The four steps include desorption of water, decomposition of RDX to form equilibrium products, pressure-dependent decomposition of RDX forming equilibrium products, and decomposition of the binder to form hydrogen chloride and a nonvolatile residue (NVR). We address drying, binder decomposition, and decomposition of the RDX component from the pristine state through the melt and into ignition. We used Latin Hypercube Sampling (LHS) of the parameters to determine the sensitivity of the model to variation in the parameters. We also successfully validated the model using one-dimensional time-to-explosion (ODTX and P-ODTX) data from a different laboratory. Our SITI test matrix included 1) different densities ranging from 0.7 to 1.63 g/cm3, 2) free gas volumes ranging from 1.2 to 38 cm3, and 3) boundary temperatures ranging from 170 to 190 °C. We measured internal temperatures using embedded thermocouples at various radial locations as well as pressure using tubing that was connected from the free gas volume (ullage) to a pressure gauge. We also measured gas flow from our vented experiments. A borescope was included to obtain in situ video during some SITI experiments. We observed significant changes in the explosive volume prior to ignition. Our model, in conjunction with data observations, imply that internal accumulation of decomposition gases in high density PBX 9407 (90% of the theoretical maximum density) can contribute to significant strain whether or not the experiment is vented or sealed.
A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.
Al/Pt nanolaminates with a bilayer thickness (tb, width of an Al/Pt pair-layer) of 164 nm were irradiated with single laser pulses with durations of 10 ms and 0.5 ms at 189 W/cm2 and 1189 W/cm2, respectively. The time to ignition was measured for each pulse, and shorter ignition times were observed for the higher power/shorter pulse width. Videographic images of the irradiated area shortly after ignition show a non-uniform radial brightness for the longer pulse, while the shorter pulse shows uniform brightness. A diffusion-limited single step reaction mechanism was implemented in a finite element package to model the progress from reactants to products at both pulse widths. The model captures well both the observed ignition delay and qualitative observations regarding the non-uniform radial temperature.
We have previously developed a PBX 9501 cookoff model for the plastic bonded explosive PBX 9501 consisting of 95 wt% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine (HMX), 2.5 wt% Estane® 5703 (a polyurethane thermoplastic), and 2.5 wt% of a nitroplasticizer (NP): BDNPA/F, a 50/50 wt% eutectic mixture bis(2,2-dinitropropyl)-acetal (BDNPA) and bis(2,2-dinitropropyl)-formal (BDNPF). This fivestep model includes desorption of water, decomposition of the NP to form NO2, reaction of the NO2 with Estane and HMX, and decomposition of HMX [1]. This model has been successfully validated with data from six laboratories with scales ranging from 2 g to more than 2.5 kg of explosive. We have determined, that the PBX 9501 model can be used to predict cookoff of other plastic bonded explosives containing HMX and an inert binder, such as LX-04 consisting of 85 wt% HMX and 15 wt% Viton A (vinylidine fluoride/hexafluoropropylene copolymer), LX-07 (90 wt% HMX and 10 wt% Viton A), LX- 10-0 (95 wt% HMX and 5 wt% Viton A), and LX-14 consisting of 95.5 wt % HMX and 4.5 wt% Estane® 5702-F1 (a polyurethane thermoplastic). Normally our cookoff models are verified using Sandia’s Instrumented Thermal Initiation (SITI) experiment. However, SITI data for LX-04, LX-07, LX-10-0, and LX-14 are not available at pressed density; although, some molding powder SITI data on LX-10-0 and LX-14 exists. Tarver and Tran [2] provide some one-dimensional time-to-explosion (ODTX) data for these explosives. The applicability of the PBX 9501 model to LX-04, LX-07, LX-10-0, AND LX-14 was made using this ODTX data [2]. The PBX 9501 model is applied to these other explosives by accounting for the correct amount of HMX in the explosive and limiting the NP reaction. We have found the PBX 9501 model to be useful for predicting the response of these PBXs to abnormal thermal environments such as fire.
We previously developed a PETN thermal decomposition model that accurately predicts thermal ignition and detonator failure [1]. This model was originally developed for CALORE [2] and required several complex user subroutines. Recently, a simplified version of the PETN decomposition model was implemented into ARIA [3] using a general chemistry framework without need for user subroutines. Detonator failure was also predicted with this new model using ENCORE. The model was simplified by 1) basing the model on moles rather than mass, 2) simplifying the thermal conductivity model, and 3) implementing ARIA’s new phase change model. This memo briefly describes the model, implementation, and validation.
We have used a modified version of the Sandia Instrumented Thermal Ignition (SITI) experiment to develop a pressure-dependent, five-step ignition model for a plastic bonded explosive (PBX 9501) consisting of 95 wt% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine (HMX), 2.5 wt% Estane® 5703 (a polyurethane thermoplastic), and 2.5 wt% of a nitroplasticizer (NP): BDNPA/F, a 50/50 wt% eutectic mixture bis(2,2-dinitropropyl)-acetal (BDNPA) and bis(2,2-dinitropropyl)-formal (BDNPF). The five steps include desorption of water, decomposition of the NP to form NO2, reaction of the NO2 with Estane® and HMX, and decomposition of HMX. The model was fit using our experiments and successfully validated with experiments from five other laboratories with scales ranging from about 2 g to more than 2.5 kg of PBX. Our experimental variables included density, confinement, free gas volume, and temperature. We measured internal temperatures, confinement pressure, and ignition time. In some of our experiments, we used a borescope to visually observe the decomposing PBX. Our observations included the endothermic β–δ phase change of the HMX, a small exothermic temperature excursion in low-density unconfined experiments, and runaway ignition. We hypothesize that the temperature excursion in these low density experiments was associated with the NP decomposing exothermically within the PBX sample. This reactant-limited temperature excursion was not observed with our thermocouples in the high-density experiments. For these experiments, we believe the binder diffused to the edges of our high density samples and decomposed next to the highly conductive wall as confirmed by our borescope images.
Occasionally, our well-controlled cookoff experiments with Comp-B give anomalous results when venting conditions are changed. For example, a vented experiment may take longer to ignite than a sealed experiment. In the current work, we show the effect of venting on thermal ignition of Comp-B. We use Sandia's Instrumented Thermal Ignition (SITI) experiment with various headspace volumes in both vented and sealed geometries to study ignition of Comp-B. In some of these experiments, we have used a boroscope to observe Comp-B as it melts and reacts. We propose that the mechanism for ignition involves TNT melting, dissolution of RDX, and complex bubbly liquid flow. High pressure inhibits bubble formation and flow is significantly reduced. At low pressure, a vigorous dispersed bubble flow was observed.
Blast waves from an explosion in air can cause significant structural damage. As an example, cylindrically-shaped charges have been used for over a century as dynamite sticks for mining, excavation, and demolition. Near the charge, the effects of geometry, standoff from the ground, the proximity to other objects, confinement (tamping), and location of the detonator can significantly affect blast wave characteristics. Furthermore, nonuniformity in the surface characteristics and the density of the charge can affect fireball and shockwave structure. Currently, the best method for predicting the shock structure near a charge and the dynamic loading on nearby structures is to use a multidimensional, multimaterial shock physics code. However, no single numerical technique currently exists for predicting secondary combustion, especially when particulates from the charge are propelled through the fireball and ahead of the leading shock lens. Furthermore, the air within the thin shocked layer can dissociate and ionize. Hence, an appropriate equation of state for air is needed in these extreme environments. As a step towards predicting this complex phenomenon, a technique was developed to provide the equilibrium species composition at every computational cell in an air blast simulation as an initial condition for hand-off to other analysis codes for combustion fluid dynamics or radiation transport. Here, a bare cylindrical charge of TNT detonated in air is simulated using CTH, an Eulerian, finite volume, shock propagation code developed and maintained at Sandia National Laboratories. The shock front propagation is computed at early times, including the detonation wave structure in the explosive and the subsequent air shock up to 100 microseconds, where ambient air entrainment is not significant. At each computational cell, which could have TNT detonation products, air, or both TNT and air, the equilibrium species concentration at the density-energy state is computed using the JCZS2i database in the thermochemical code TIGER. This extensive database of 1267 gas (including 189 ionized species) and 490 condensed species can predict thermodynamic states up to 20,000 K. The results of these calculations provide the detailed three-dimensional structure of a thin shock front, and spatial species concentrations including free radicals and ions. Furthermore, air shock predictions are compared with experimental pressure gage data from a right circular cylinder of pressed TNT, detonated at one end. These complimentary predictions show excellent agreement with the data for the primary wave structure.
This report presents plots of specific heat, enthalpy, entropy, and Gibbs free energy for 1439 species in the JCZS2i database. Included in this set of species are 496 condensed-phase species and 943 gas-phase species. The gas phase species contain 80 anions and 112 cations for a total of 192 ions. The JCZS2i database is used in conjunction with the TIGER thermochemical code to predict thermodynamic states from ambient conditions to high temperatures and pressures. Predictions from the TIGER code using the JCZS2i database can be used in shock physics codes where temperatures may be as high as 20,000 K and ions may be present. Such high temperatures were not considered in the original JCZS database, and extrapolations made for these temperatures were unrealistic. For example, specific heat would sometimes go negative at high temperatures which fails the definition of specific heat. The JCZS2i database is a new version of the JCZS database that is being created to address these inaccuracies. The purpose of the current report is to visualize the high temperature extrapolations to insure that the specific heat, enthalpy, entropy, and Gibbs free energy predictions are reasonable up to 20,000 K.
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.
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.
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.