Publications

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Many important engineering and scientific applications such as cement slurries, foams, crude oil, and granular avalanches involve the concept of yield stress. Therefore, modeling yield stress fluids in different flow configurations, including the accurate prediction of the yield surface, is important. In this paper, we present a computational model based on the finite element method to study the flow of yield stress fluids in a thin mold and compare the results with data from flow visualization experiments. We use the level set method to describe the interface between the filling fluid and air. We use polypropylene glycol as a model Newtonian fluid and Carbopol for the model yield stress fluid, as the Carbopol solution demonstrates yielding without thixotropy. To describe the yielding and shear-thinning behavior, we use a generalized Newtonian constitutive equation with a Bingham–Carreau–Yasuda form. We compare the results obtained from the mold filling experiments with the results from the three-dimensional (3D) model and from a reduced-order Hele-Shaw (HS) model that is two-dimensional, including the effect of shear-thinning along the thin direction only approximately. We show that both the 3D and the HS model can capture the experimental meniscus shape reasonably well for all the fluids considered at three different flow rates. This indicates that the shape evolution is insensitive to the dimensionality of the model. However, the viscosity and yield surfaces predicted by the 3D and HS models are different. The HS model underestimates the high viscosity and unyielded regions compared to the estimation by the 3D model.

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Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

We propose developing numerical methods informed by novel experimental diagnostics that transition from solid-to-fluid, while accurately predicting the stress and deformation regardless of phase.

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To mitigate adverse effects from molten corium following a reactor pressure vessel failure (RPVF), some new reactor designs employ a core catcher and a sacrificial material (SM), such as ceramic or concrete, to stabilize the molten corium and avoid containment breach. Existing reactors cannot easily be modified to include these SMs but could be modified to allow injectable cooling materials. Current reactor designs are limited to using water to stabilize the corium, but this can create other issues such as reaction of water with the concrete forming hydrogen gas. The novel SM proposed here is a granular carbonate mineral that can be used in existing light water reactor plants. The granular carbonate will decompose when exposed to heat, inducing an endothermic reaction to quickly solidify the corium in place and producing a mineral oxide and carbon dioxide. Corium spreading is a complex process strongly influenced by coupled chemical reactions, including decay heat from the corium, phase change, and reactions between the concrete containment and available water. A recently completed Sandia National Laboratories laboratory directed research and development (LDRD) project focused on two research areas: experiments to demonstrate the feasibility of the novel SM concept, and modeling activities to determine the potential applications of the concept to actual nuclear plants. Small-scale experiments using lead oxide (PbO) as a surrogate for molten corium demonstrate that the reaction of the SM with molten PbO results in a fast solidification of the melt due to the endothermic carbonate decomposition reaction and the formation of open pore structures in the solidified PbO from CO2 released during the decomposition. A simplified carbonate decomposition model was developed to predict thermal decomposition of carbonate mineral in contact with corium. This model was incorporated into MELCOR, a severe accident nuclear reactor code. A full-plant MELCOR simulation suggests that by the introduction of SM to the reactor cavity prior to RPVF ex-vessel accident progression, e.g., core-concrete interaction and core spreading on the containment floor, could be delayed by at least 15 h; this may be enough for additional accident management to be implemented to alleviate the situation.

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Understanding the stress development in fluids as they transition to solids is not well-understood. Computational models are needed to represent "birthing stress" for multiphysics applications such as polymer encapsulation around sensitive electronics and additive manufacturing where these stresses can lead to defects such as cracking and voids. The local stress state is also critical to understand and predict the net shape of parts formed in the liquid phase. In this one-year exploratory LDRD, we have worked towards a novel experimental diagnostic to measure the fluid rheology, degree of solidification, and the solid stress development simultaneously. We debugged and made viable a "first-generation" Rheo-Raman system and used it to characterize two types of solidifying systems: paraffin wax, which crystalizes as it solidifies, and thermoset polymers, which form a network of covalent bonds. We used the paraffin wax as a model system to perform flow visualization studies and did some preliminary modeling of the experiment, to demonstrate the inadequacy of the current modeling approaches. This work will inform an advanced fluid constitutive equation that includes a yield stress, temperature dependence, and an evolving viscosity when we pursue the full proposal, which was funded for FY20.

The catastrophic nuclear reactor accident at Fukushima damaged public confidence in nuclear energy and a demand for new engineered safety features that could mitigate or prevent radiation releases to the environment in the future. We have developed a novel use of sacrificial material (SM) to prevent the molten corium from breaching containment during accidents as well as a validated, novel, high-fidelity modeling capability to design and optimize the proposed concept. Some new reactor designs employ a core catcher and a SM, such as ceramic or concrete, to slow the molten corium and avoid the breach of the containment. However, existing reactors cannot easily be modified to include these SMs but could be modified to allow injectable cooling materials (current designs are limited to water). The SM proposed in this Laboratory Development Research and Development (LDRD) project is based on granular carbonate minerals that can be used in existing light water reactor plants. This new SM will induce an endothermic reaction to quickly freeze the corium in place, with minimal hydrogen explosion and maximum radionuclide retention. Because corium spreading is a complex process strongly influenced by coupled chemical reactions (with underlying containment material and especially with the proposed SM), decay heat and phase change. No existing tool is available for modeling such a complex process. This LDRD project focused on two research areas: experiments to demonstrate the feasibility of the novel SM concept, and modeling activities to determine the potential applications of the concept to actual nuclear plants. We have demonstrated small-scale to large-scaled experiments using lead oxide (Pb0) as surrogate for molten corium, which showed that the reaction of the SM with molten Pb0 results in a fast solidification of the melt and the formation of open pore structures in the solidified Pb0 because of CO₂ released from the carbonate decomposition.

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Transport of solid particles in blood flow exhibits qualitative differences in the transport mechanism when the particle varies from nanoscale to microscale size comparable to the red blood cell (RBC). The effect of microscale particle margination has been investigated by several groups. Also, the transport of nanoscale particles (NPs) in blood has received considerable attention in the past. This study attempts to bridge the gap by quantitatively showing how the transport mechanism varies with particle size from nano-to-microscale. Using a three-dimensional (3D) multiscale method, the dispersion of particles in microscale tubular flows is investigated for various hematocrits, vessel diameters, and particle sizes. NPs exhibit a nonuniform, smoothly dispersed distribution across the tube radius due to severe Brownian motion. The near-wall concentration of NPs can be moderately enhanced by increasing hematocrit and confinement. Moreover, there exists a critical particle size (∼1 μm) that leads to excessive retention of particles in the cell-free region near the wall, i.e., margination. Above this threshold, the margination propensity increases with the particle size. The dominance of RBC-enhanced shear-induced diffusivity (RESID) over Brownian diffusivity (BD) results in 10 times higher radial diffusion rates in the RBC-laden region compared to that in the cell-free layer, correlated with the high margination propensity of microscale particles. This work captures the particle size-dependent transition from Brownian-motion dominant dispersion to margination using a unified 3D multiscale computational approach and highlights the linkage between the radial distribution of RESID and the margination of particles in confined blood flows.

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Using a multiscale blood flow solver, the complete diffusion tensor of nanoparticles (NPs) in sheared cellular blood flow is calculated over a wide range of shear rate and haematocrit. In the short-time regime, NPs exhibit anomalous dispersive behaviors under high shear and high haematocrit due to the transient elongation and alignment of the red blood cells (RBCs). In the long-time regime, the NP diffusion tensor features high anisotropy. Particularly, there exists a critical shear rate around which the shear-rate dependence of the diffusivity tensor changes from linear to nonlinear scale. Above the critical shear rate, the cross-stream diffusivity terms vary sublinearly with shear rate, while the longitudinal term varies superlinearly. The dependence on haematocrit is linear in general except at high shear rates, where a sublinear scale is found for the vorticity term and a quadratic scale for the longitudinal term. Through analysis of the suspension microstructure and numerical experiments, the nonlinear haemorheological dependence of the NP diffusion tensor is attributed to the streamwise elongation and cross-stream contraction of RBCs under high shear, quantified by a capillary number. The RBC size is shown to be the characteristic length scale affecting the RBC-enhanced shear-induced diffusion (RESID), while the NP submicrometre size exhibits negligible influence on the RESID. Based on the observed scaling behaviours, empirical correlations are proposed to bridge the NP diffusion tensor to specific shear rate and haematocrit. The characterized NP diffusion tensor provides a constitutive relation that can lead to more effective continuum models to tackle large-scale NP biotransport applications.

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Previous studies have demonstrated the benefits of the log-conformation formulation to model viscoelastic fluids; it increases stability at high Weissenberg numbers and ensures that the conformation tensor remains positive-definite. Many studies have applied the log-conformation tensor formulation to benchmark cases; however, relatively few studies investigate using the formulation on more complex flows. In this paper, we extend the log-conformation formulation to the manufacturing-relevant flow of blade coating. We first verify the log-conformation formulation on the benchmark problem of flow past a cylinder using the finite element method, and then apply it to the blade-coating process, in which a viscoelastic fluid entrained by a moving substrate passes under a blade at a constant web speed. We investigate various rheological effects and the resulting film thickness for the blade-coating problem, and compare the results from the log-conformation formulation to those of the original stress formulation. We show that the log-conformation formulation agrees well with other established methods, and also increases the maximum achievable web speed in the blade-coating problem.

When the core is breached during a severe nuclear accident, a molten mixture of nuclear fuel, cladding, and structural supports is discharged from the reactor vessel. This molten mixture of ceramic and metal is often referred to as “corium”. Predicting the flow and solidification of corium poses challenges for numerical models due to the presence of large Peclet numbers when convective transport dominates the physics. Here, we utilize a control volume finite-element method (CVEM) discretization to stabilize the advection dominated flow and heat transport. This CVFEM approach is coupled with the conformal decomposition finite-element method (CDFEM), which tracks the corium/air interface on an existing background mesh. CDFEM is a sharp-interface method, allowing the direct discretization of the corium front. This CVFEM-CDFEM approach is used to model the spreading of molten corium in both two- and three-dimensions. The CVFEM approach is briefly motivated in a comparison with a streamwise upwind/Petrov-Galerkin (SUPG) stabilized finite-element method, which was not able to suppress spurious temperature oscillations in the simulations. Our model is compared directly with the FARO L26 corium spreading experiments and with previous numerical simulations, showing both quantitative and qualitative agreement with those studies.

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The biotransport of the intravascular nanoparticle (NP) is influenced by both the complex cellular flow environment and the NP characteristics. Being able to computationally simulate such intricate transport phenomenon with high efficiency is of far-reaching significance to the development of nanotherapeutics, yet challenging due to large length-scale discrepancies between NP and red blood cell (RBC) as well as the complexity of nanoscale particle dynamics. Recently, a lattice-Boltzmann (LB) based multiscale simulation method has been developed to capture both NP–scale and cell–level transport phenomenon at high efficiency. The basic components of this method include the LB treatment for the fluid phase, a spectrin-link method for RBCs, and a Langevin dynamics (LD) approach to capturing the motion of the suspended NPs. Comprehensive two-way coupling schemes are established to capture accurate interactions between each component. The accuracy and robustness of the LB–LD coupling method are demonstrated through the relaxation of a single NP with initial momentum and self-diffusion of NPs. This approach is then applied to study the migration of NPs in micro-vessels under physiological conditions. It is shown that Brownian motion is most significant for the NP distribution in 20μm venules. For 1 ∼ 100 nm particles, the Brownian diffusion is the dominant radial diffusive mechanism compared to the RBC-enhanced diffusion. For ∼ 500 nm particles, the Brownian diffusion and RBC-enhanced diffusion are comparable drivers for the particle radial diffusion process.

In this report, we investigate how manufacturing conditions result in the warpage of moderate density PMDI polyurethane foam (12-50 lb/ft³) when they are released from a mold. We have developed a multiphysics modeling framework to simulate the manufacturing process including resin injection, foaming and mold filling, gelation of the matrix, elevated cure, vitrification, cool down, and demolding. We have implemented this framework within the Sierra Mechanics Finite Element Code Suite. We couple Aria for flow, energy conservation, and foaming/curing kinetics with Adagio for the nonlinear viscoelastic solid response in a multi-staged simulation process flow. We calibrate a model for the PMDI-10S (10 lb/ft³ free rise foam) through a suite of characterization data presented here to calibrate the solid cure behavior of the foam. The model is then used and compared to a benchmark experiment, the manufacturing and warpage over 1 year of a 10 cm by 10 cm by 2.5 cm foam "staple". This component features both slender and thick regions that warp considerably differently over time. Qualitative agreement between the model and the experiment is achieved but quantitative accuracy is not.

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We generate a wide range of models of proppant-packed fractures using discrete element simulations, and measure fracture conductivity using finite element flow simulations. This allows for a controlled computational study of proppant structure and its relationship to fracture conductivity and stress in the proppant pack. For homogeneous multi-layered packings, we observe the expected increase in fracture conductivity with increasing fracture aperture, while the stress on the proppant pack remains nearly constant. This is consistent with the expected behavior in conventional proppant-packed fractures, but the present work offers a novel quantitative analysis with an explicit geometric representation of the proppant particles. In single-layered packings (i.e. proppant monolayers), there is a drastic increase in fracture conductivity as the proppant volume fraction decreases and open flow channels form. However, this also corresponds to a sharp increase in the mechanical stress on the proppant pack, as measured by the maximum normal stress relative to the side crushing strength of typical proppant particles. We also generate a variety of computational geometries that resemble highly heterogeneous proppant packings hypothesized to form during channel fracturing. In some cases, these heterogeneous packings show drastic improvements in conductivity with only moderate increase in the stress on the proppant particles, suggesting that in certain applications these structures are indeed optimal. We also compare our computer-generated structures to micro computed tomography imaging of a manually fractured laboratory-scale shale specimen, and find reasonable agreement in the geometric characteristics.

Polyurethane foams are used widely for encapsulation and structural purposes because they are inexpensive, straightforward to process, amenable to a wide range of density variations (1 lb/ft3 - 50 lb/ft3), and able to fill complex molds quickly and effectively. Computational model of the filling and curing process are needed to reduce defects such as voids, out-of-specification density, density gradients, foam decomposition from high temperatures due to exotherms, and incomplete filling. This paper details the development of a computational fluid dynamics model of a moderate density PMDI structural foam, PMDI-10. PMDI is an isocyanate-based polyurethane foam, which is chemically blown with water. The polyol reacts with isocyanate to produces the polymer. PMDI- 10 is catalyzed giving it a short pot life: it foams and polymerizes to a solid within 5 minutes during normal processing. To achieve a higher density, the foam is over-packed to twice or more of its free rise density of 10 lb/ft3. The goal for modeling is to represent the expansion, filling of molds, and the polymerization of the foam. This will be used to reduce defects, optimize the mold design, troubleshoot the processed, and predict the final foam properties. A homogenized continuum model foaming and curing was developed based on reaction kinetics, documented in a recent paper; it uses a simplified mathematical formalism that decouples these two reactions. The chemo-rheology of PMDI is measured experimentally and fit to a generalized- Newtonian viscosity model that is dependent on the extent of cure, gas fraction, and temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved via a stabilized finite element method. The equations are combined with a level set method to determine the location of the foam-gas interface as it evolves to fill the mold. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics, viscosity, and other material properties are all sensitive to temperature. Results from the model are compared to experimental flow visualization data and post-test X-ray computed tomography (CT) data for the density. Several geometries are investigated including two configurations of a mock structural part and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed for future work.

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Kinetic models have been developed to understand the manufacturing of polymeric foams, which evolve from low viscosity Newtonian liquids, to bubbly liquids, finally producing solid foam. Closed-form kinetics are formulated and parameterized for PMDI-10, a fast curing polyurethane, including polymerization and foaming. PMDI-10 is chemically blown, where water and isocyanate react to form carbon dioxide. The isocyanate reacts with polyol in a competing reaction, producing polymer. Our approach is unique, although it builds on our previous work and the polymerization literature. This kinetic model follows a simplified mathematical formalism that decouples foaming and curing, including an evolving glass transition temperature to represent vitrification. This approach is based on IR, DSC, and volume evolution data, where we observed that the isocyanate is always in excess and does not affect the kinetics. The kinetics are suitable for implementation into a computational fluid dynamics framework, which will be explored in subsequent articles. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2945–2957, 2017.

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Polyurethane is a complex multiphase material that evolves from a viscous liquid to a system of percolating bubbles, which are created via a CO2 generating reaction. The continuous phase polymerizes to a solid during the foaming process generating heat. Foams introduced into a mold increase their volume up to tenfold, and the dynamics of the expansion process may lead to voids and will produce gradients in density and degree of polymerization. These inhomogeneities can lead to structural stability issues upon aging. For instance, structural components in weapon systems have been shown to change shape as they age depending on their molding history, which can threaten critical tolerances. The purpose of this project is to develop a Cradle-to-Grave multiphysics model, which allows us to predict the material properties of foam from its birth through aging in the stockpile, where its dimensional stability is important.

The recent boom in the oil and natural gas industry of hydraulic fracture of source rocks has caused a new era in oil and gas production worldwide. However, there are many parts of this process that are poorly understood and thus hard to control. One of the few things that can be controlled is the process of injection to create the fractures in the subsurface and the subsequent injection of proppants to maintain the permeability of the fractured formation, allowing hydrocarbons to be extracted. The goal of this work was to better understand the injection process and resulting proppant distribution in the fracture through a combination of lab-scale experiments and computational models.

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Performing experiments in the laboratory that mimic conditions in the field is challenging. In an attempt to understand hydraulic fracture in the field, and provide laboratory flow results for model verification, an effort to duplicate the typical fracture pattern for long horizontal wells has been made. The typical "disks on a string" fracture formation is caused by properly orienting the long horizontal well such that it is parallel to the minimum principal stress direction, then fracturing the rock. In order to replicate this feature in the laboratory with a traditional cylindrical specimen the test must be performed under extensile stress conditions and the specimen must have been cored parallel to bedding in order to avoid failure along a bedding plane, and replicate bedding orientation in the field. Testing has shown that it is possible to form failure features of this type in the laboratory. A novel method for jacketing is employed to allow fluid to flow out of the fracture and leave the specimen without risking the integrity of the jacket; this allows proppant to be injected into the fracture, simulating loss of fracturing fluids to the formation, and allowing a solid proppant pack to be developed.

Performing experiments in the laboratory that mimic conditions in the field is challenging. In an attempt to understand hydraulic fracture in the field, and provide laboratory flow results for model verification, an effort to duplicate the typical fracture pattern for long horizontal wells has been made. The typical "disks on a string" fracture formation is caused by properly orienting the long horizontal well such that it is parallel to the minimum principal stress direction, then fracturing the rock. In order to replicate this feature in the laboratory with a traditional cylindrical specimen the test must be performed under extensile stress conditions and the specimen must have been cored parallel to bedding in order to avoid failure along a bedding plane, and replicate bedding orientation in the field. Testing has shown that it is possible to form failure features of this type in the laboratory. A novel method for jacketing is employed to allow fluid to flow out of the fracture and leave the specimen without risking the integrity of the jacket; this allows proppant to be injected into the fracture, simulating loss of fracturing fluids to the formation, and allowing a solid proppant pack to be developed.

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A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.

We are studying PMDI polyurethane with a fast catalyst, such that filling and polymerization occur simultaneously. The foam is over-packed to tw ice or more of its free rise density to reach the density of interest. Our approach is to co mbine model development closely with experiments to discover new physics, to parameterize models and to validate the models once they have been developed. The model must be able to repres ent the expansion, filling, curing, and final foam properties. PMDI is chemically blown foam, wh ere carbon dioxide is pr oduced via the reaction of water and isocyanate. The isocyanate also re acts with polyol in a competing reaction, which produces the polymer. A new kinetic model is developed and implemented, which follows a simplified mathematical formalism that decouple s these two reactions. The model predicts the polymerization reaction via condensation chemis try, where vitrification and glass transition temperature evolution must be included to correctly predict this quantity. The foam gas generation kinetics are determined by tracking the molar concentration of both water and carbon dioxide. Understanding the therma l history and loads on the foam due to exothermicity and oven heating is very important to the results, since the kinetics and ma terial properties are all very sensitive to temperature. The conservation eq uations, including the e quations of motion, an energy balance, and thr ee rate equations are solved via a stabilized finite element method. We assume generalized-Newtonian rheology that is dependent on the cure, gas fraction, and temperature. The conservation equations are comb ined with a level set method to determine the location of the free surface over time. Results from the model are compared to experimental flow visualization data and post-te st CT data for the density. Seve ral geometries are investigated including a mock encapsulation part, two configur ations of a mock stru ctural part, and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Thoughts on m odel improvements are also discussed.

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