Publications

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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 CO 2 released from the carbonate decomposition. Our modeling simulations show that Sierra Mechanics/Aria code can be used to model a molten corium spreading experiment and the PbO/carbonate experiment. A simplified carbonate decomposition model has been developed to predict thermal decomposition of carbonate mineral in contact with corium. This model has been incorporated into an input model for MELCOR, a severe accident nuclear reactor code developed by Sandia National Laboratories for the U.S. Nuclear Regulatory Commission. A full-plant MELCOR simulation suggests that the ex-vessel accident progression, e.g., core-concrete interaction and core spreading on the containment floor, could be significantly delayed by the introduction of SM to the reactor cavity prior to the reactor pressure vessel failure. Delays of one and half day are suggested with limited SM. Filling the cavity with SM might delay progression by days. Additionally, the modeling suggests that the relative concentration (molar fraction) of hydrogen in containment could be substantially reduced by the non-condensable gas (CO 2 ) generation associated with the SM reaction effectively making the hydrogen concentration below its flammable limit. ACKNOWLEDGEMENTS This research was supported by the Laboratory Directed Research and Development Program of Sandia National Laboratories (Sandia). The authors would like to express thanks to all Sandia staff who helped with this research, including Ms. Denise Bencoe for assisting with the performance of the small-scaled experiments at Advanced Material Laboratories, Ms. Amanda Sanchez and Ms. Lydia Boisvert for grinding all natural carbonate materials and sieving, Dr. Anne Grillet for measuring the microstructure of the samples using X-ray micro CT Scan (SKYSCAN 1272), Dr. Clay Payne for the XRD measurement, Dr. Eric Lindgren for assisting the selection of crucible materials, Dr. Larry Humphries for review this report and Dr. Randall O. Gauntt for reviewing this research, who has retired from Sandia at the time of this publication. The authors like to thank Ms. Laura Sowko for editing this report. Additionally, the authors appreciated the use of the FARO L-26S data information described in Section 4.2.2.1 of this report downloaded from STRESA, Joint Research Centre, European Commission (c) Euratom, 2019.

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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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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.

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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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/ft 3 ) 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/ft 3 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. 2

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An ongoing Sandia National Laboratories’ (SNL) research study is evaluating a potential design of an injectable sacrificial material (SM) system that could contain and cool corium ejected from a reactor vessel lower head failure during a potential severe accident involving melting fuel at a commercial light water nuclear reactor (LWR). An injectable system could be installed at any existing LWR, without significant modification to the cavity or to the drywell pedestal region of the plant. The conceptual design under consideration is a passive system. The SM is being optimized to quickly cool the corium mixture while creating gas to form porosity in the solid, such that subsequent water flooding can penetrate the structure and provide additional cooling. The SM would form a barrier and limit corium-concrete interactions. This three-year project takes a joint experimental and computational approach. In this paper, we will first discuss the success of our small-scale experiments conducted on the interactions between the surrogate corium material (SCM) and SM, used to evaluate the injectable concept. A larger experimental study, currently underway, will further validate the injectable concept, with a focus on accurately measuring interactions. This paper details the modeling study and its progress, including modeling the experiments on a surrogate system and extending the model to bench-scale corium flow from validation experiments. The project’s modeling studies will use the SNL engineering code suite SIERRA Mechanics to understand the interaction of injectable SM and molten corium and predict corium spreading. Spreading is modeled using a level set method to track the front in conjunction with a pressure-stabilized finite element method on the fully three-dimensional mass, momentum, and energy conservation equations. Using this diffuse-interface method, the corium spreading front can be tracked and an appropriate pseudo-solidification viscosity models can be implemented to accurately model the corium spreading physics. Finally, an injectable SM delivery system is discussed along with its deployment to the six-common commercial LWR designs currently operating in the United States. At the end of this project, a simplified model based on SIERRA simulations will be developed for implementation into MELCOR, a severe reactor analysis code, developed at SNL for the U.S. Nuclear Regulatory Commission. This will allow us to demonstrate the ability of the injectable SM system to mitigate the ex-vessel corium spreading, provide containment and negate the release of radionuclides.

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.

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