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Quantifying Macro-Descriptors of Dynamic Fragmentation with Thick Level-Set Method Approach.
Abstract not provided.
An Interpolative Particle Level Set Method for Interfacial Physics.
Abstract not provided.
Implementation of a High-Fidelity Interface Resolving Method in Nek5000
The development and utilization of computational fluid dynamics (CFD) models for large, high-temperature electric melters in the Waste Treatment and Immobilization Plant (WTP) in eastern Washington State have proven to be valuable for various purposes. These models allow for a better understanding of the physio-chemical processes occurring within the melter vessels and can contribute to improving operational efficiency, throughput, and addressing operational issues related to vitrification. The CFD models employed for these melter vessels incorporate multiphase fluid flow and heat transfer simulations in different regions, including the plenum, cold cap, and molten glass regions. As the tank waste and glass formers are introduced into the melter, a reacting batch layer known as the cold cap forms on top of the molten glass. To enhance the melt rate, forced convection bubblers located at the bottom of the melters generate convection currents that help homogenize the molten glass and provide heat to the cold cap. As the bubbles rise through the highly viscous glass, they adopt a spherical-cap shape [1]. Meanwhile, the conversion of the batch to glass generates significant amounts of gases (such as water vapor, carbon dioxide, sulfur dioxide, and NOx) due to thermal decomposition [2]. These gases become trapped between the cold cap and molten glass, forming a foam layer [3]. For modeling multiphase flow in CFD and heat transfer simulations of waste glass melters at different scales, efforts are underway to augment the capabilities of the Nek5000 [4] and NekRS [5] open-source codes [6]. Nek5000/NekRS is a scalable and efficient spectral element code that has been successfully applied to a wide range of fluid dynamics problems. By leveraging the Nek5000/NekRS software, it becomes possible to model the melter systems more affordably and with lower computational requirements compared to currently utilized commercial CFD software. The specific objectives of this ongoing effort include: 1. Implementation of a level set method in Nek5000/NekRS: The level set method is a numerical technique commonly employed in CFD simulations to track and represent the interface between different phases or materials accurately. By incorporating this method into Nek5000/NekRS, the ability to simulate multiphase flows in waste glass melters at a high level of fidelity can be achieved. 2. Demonstration of capability for air bubbling through molten glass: As part of the development process, a specific case of air bubbling through molten glass will be simulated using the augmented Nek5000/NekRS code. This demonstration aims to showcase the ability of the software to accurately capture and analyze the complex phenomena involved in the multiphase flow within waste glass melters. By achieving these objectives, the improved Nek5000/NekRS code will offer a powerful computational tool for simulating and analyzing waste glass melter systems, enabling better understanding, optimization, and troubleshooting of these vitrification processes. The ability to accurately model and simulate multiphase flows has broad relevance across many industries and scientific domains, and the improved functionality can contribute to advancements in various fields beyond waste glass melter simulations.
Extending continuum models for atom probe simulation
Highlights: • Demonstration of 3D curvature level set methods for APT simulations • Demonstration of non-rotationally symmetric tip shape simulations • Optimised speed for simulations, calculations achievable on minute timescales This work describes extensions to existing level-set algorithms developed for application within the field of atom probe tomography (APT). We present a new simulation tool for the simulation of 3D tomographic volumes, using advanced level set methods. By combining narrow-band, B-Tree and particle-tracing approaches from level-set methods, we demonstrate a practical tool for simulating shape changes to APT samples under applied electrostatic fields, in three dimensions. This work builds upon our previous studies by allowing for non-axially symmetric solutions, with minimal loss in computational speed, whilst retaining numerical accuracy.
Microstructural and infiltration properties of woven preforms during chemical vapor infiltration
Interface-resolved direct numerical simulations (DNSs) of chemical vapor infiltration (CVI) have been performed over a range of furnace-operating conditions (Thiele moduli) and for practical woven preform geometries. A level-set method is used to resolve the geometry of the initial preform at tow scale. The interface between the vapor and solid phase is then evolved in time through the entire CVI densification cycle, fully resolving the time-varying topology between the two phases. In contrast to previous level-set methods for CVI simulation, the physical reaction and diffusion processes govern the level-set movement in the current approach. The surface deposition kinetics is described by the usual one-step model. In this paper, the DNS data are used to study the evolving porosity, surface-to-volume ratio, and flow infiltration properties (permeability and effective diffusivities). Additionally, comparisons are made to popularly-assumed structure functions and the standard, Kozeny–Carmen porous media model commonly employed in modeled CFD simulations of CVI. The virtual DNS experiments reveal a Thiele modulus and preform geometry (fabric layup) dependence which the existing microstructural and infiltration models are not able to describe throughout the entire densification process. The DNS-based, woven geometry-specific correlations can be applied directly to mean-field, furnace-scale CFD simulations.
Identifying arbitrary parameter zonation using multiple level set functions
In this paper, we extended the analytical level set method [1, 2] for identifying a piece-wisely heterogeneous (zonation) binary system to the case with an arbitrary number of materials with unknown material properties. In the developed level set approach, starting from an initial guess, the material interfaces are propagated through iterations such that the residuals between the simulated and observed state variables (hydraulic head) is minimized. We derived an expression for the propagation velocity of the interface between any two materials, which is related to the permeability contrast between the materials on two sides of the interface, the sensitivity of the head to permeability, and the head residual. We also formulated an expression for updating the permeability of all materials, which is consistent with the steepest descent of the objective function. The developed approach has been demonstrated through many examples, ranging from totally synthetic cases to a case where the flow conditions are representative of a groundwater contaminant site at the Los Alamos National Laboratory. These examples indicate that the level set method can successfully identify zonation structures, even if the number of materials in the model domain is not exactly known in advance. Although the evolution of the material zonation depends on the initial guess field, inverse modeling runs starting with different initial guesses fields may converge to the similar final zonation structure. These examples also suggest that identifying interfaces of spatially distributed heterogeneities is more important than estimating their permeability values.
Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations
Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.
Annular Flow Simulation Supported by Iterative In-Memory Mesh Adaptation
Various flow regimes exist in a boiling water reactor (BWR) as the steam quality increases in the uprising coolant flow, from bubbly flow, slug/churn flow, to annular flow. The annular flow is characterized by the presence of a fast-moving gas core and the surrounding liquid film flowing on the conduit wall. Additionally, entrained droplets can be observed in the gas core with ingested bubbles in the liquid film. The dynamics occurring on the wavy interface between the liquid film and gas core plays a crucial role in affecting the heat transfer rate and pressure drop within the BWR core. However, a fundamental understanding of annular flow is still lacking, partly due to the difficulty in obtaining detailed local data in annular flow experiments. In the current study, a novel simulation framework is developed for the annular flow by coupling a computational fluid dynamics flow solver with state-of-the-art meshing software. The gas-liquid interface is tracked with the level set method. Based on the computed flow solutions, the computational mesh is dynamically adapted in memory to meet the local mesh resolution requirement. This iterative simulation-adaptation framework can ensure the fine mesh resolution across the interface, which not only helps mitigate the mass conservation degradation known to level set methods but also improves the representation of dramatic interface topological changes such as wave breaking and droplet entrainment. The present investigation will shed light onto the complex interfacial processes involved in annular flow and generate much needed simulation data for annular flow modeling.
A phase-field method for boiling heat transfer
Here we present a phase field method for heat transfer in two-phase flow with boiling. The vapor/liquid interface evolution is modeled by the Cahn-Hilliard equation. The phase change rate is determined by accounting for the heat conduction balance on either vapor or liquid side of the interfacial area, depending on which side the temperature is assumed to be maintained at the saturation temperature during boiling. The velocity correction scheme proposed by Dong & Shen [27] is extended to solve the Navier-Stokes equations for a non-solenoidal velocity field, and the entropy viscosity method is employed for stabilization. The phase change model is verified by two-dimensional simulations of a vapor bubble growing in super-heated liquid and in film boiling. In both cases, mesh independence of the results is systematically performed. Subsequently, the method is applied to predict the growth of three-dimensional vapor bubble in a rectangular microchannel with boiling flow, achieving good agreement with experimental measurements and available simulation results using the level-set method. The numerical experiments demonstrate that the required mesh resolution for the phase field method is comparable with that of volume of fluid (VoF) and level-set methods.
Modeling Growth of Nanostructures in Plasmas
As semiconductor circuits shrink to CDs below 0.1 nm, it is becoming increasingly critical to replace and/or enhance existing technology with nanoscale structures, such as nanowires for interconnects. Nanowires grown in plasmas are strongly dependent on processing conditions, such as gas composition and substrate temperature. Growth occurs at specific sites, or step-edges, with the bulk growth rate of the nanowires determined from the equation of motion of the nucleating crystalline steps. Traditional front-tracking algorithms, such as string-based or level set methods, suffer either from numerical complications in higher spatial dimensions, or from difficulties in incorporating surface-intense physical and chemical phenomena. Phase field models have the robustness of the level set method, combined with the ability to implement surface-specific chemistry that is required to model crystal growth, although they do not necessarily directly solve for the advancing front location. We have adopted a phase field approach and will present results of the adatom density and step-growth location in time as a function of processing conditions, such as temperature and plasma gas composition.
Simultaneous material, shape and topology optimization
Using three design fields we develop an optimization environment that can simultaneously optimize material, shape and topology. We use the implicit representation of the boundaries with level-set functions that define the shape and topology. Differentiable R-functions allow us to combine these shapes and topology descriptions with Boolean operations. Additionally, we incorporate design dependent-stiffness materials with another design field. Notably, this framework accommodates design dependent loads, has the ability to introduce holes, and ensures the satisfaction of optimality criteria. It builds upon the fictitious domain, ersatz material, material interpolation and level-set methods. Additionally, it also borrows from parameterized density-based topology optimization methods. Since analytical sensitivities can be computed, we use efficient nonlinear programming algorithms to update the design instead of the Hamilton–Jacobi’s scheme of level-set methods. We illustrate the features of our framework by designing a cantilever beam with octet truss microlattice, a dam with design-dependent loads, and a composite clevis plate.
Computational Study of Droplet Dynamics in Dispersed Flow Film Boiling Regime in PWR Geometries
Dispersed flow film boiling (DFFB) regime is exhibited during low-flooding rate conditions following the postulated Loss-of-Coolant Accident (LOCA) in nuclear reactor flow channels. LOCA is a type of design-basis accident scenario, which is crucial for reactor design and licensing. Accurate models to predict the heat transfer in DFFB regime is critical for the reactor to maintain safety limits. The nominal operating linear heat rate is also set based on the maximum linear heat rate determined for a LOCA transient. It is understood that the behavior of entrained droplets in DFFB regime greatly affects the heat transfer by evaporating and desuperheating the surrounding steam. Furthermore, interaction with flow structures also aids in increasing the evaporation rate of entrained droplets. In order to quantify this enhancement in heat transfer, the size of droplets downstream of flow structures (Spacer Grids and Mixing Vanes) is of crucial importance. Thermal hydraulic analysis codes like COBRA-TF, CATHARE-3 and adopt a three-field equation model that allows them to model the droplet field separately. However, to ensure the accuracy of these field equations, various correlations and physical models are required. This paper proposes a method for characterizing the mean Sauter Diameter of droplets across spacer-grids and mixing vanes in PWR sub-channels using PHASTA - a high fidelity flow solver with multiphase capabilities using the level-set method. The PHASTA code is a finite element based computational fluid dynamics code designed for solving compressible and incompressible turbulent flows. It has been demonstrated to be massively scalable (up to 786,432 cores), which is crucial for simulating large realistic domains. The code incorporates the level-set method for interface tracking of the gas-liquid interface.
A high-order discontinuous Galerkin method for level set problems on polygonal meshes
We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. Here, we analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.
A level-set immersed boundary method for reactive transport in complex topologies with moving interfaces
A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface reactions is tracked by the level-set method, while the immersed boundary method captures the momentum and mass transport at the interface. The proposed method is capable of accurately modeling transport near evolving boundaries in Cartesian grids. The framework formulation guarantees second order accuracy in space. Since the interface velocity is only defined at the moving boundary, an interface velocity propagation method is also proposed. The method can be applied to other moving interface problems of the “Stefan” type. Here, we validate the proposed LS-IBM both for flow and transport close to an immersed object with reactive boundaries as well as for crystal growth. Lastly, the proposed method provides a powerful tool to model more realistic problems involving moving reactive interfaces in complex domains.
Simulation of Etching Profiles Using Level Sets
Using plasma discharges to etch trenches and via holes in substrates is an important process in semiconductor manufacturing. Ion enhanced etching involves both neutral fluxes, which are isotropic, and ion fluxes, which are anisotropic. The angular distributions for the ions determines the degree of vertical etch, while the amount of the neutral fluxes determines the etch rate. We have developed a 2D profile evolution simulation which uses level set methods to model the plasma-substrate interface. Using level sets instead of traditional string models avoids the use of complicated delooping algorithms. The simulation calculates the etch rate based on the fluxes and distribution functions of both ions and neutrals. We will present etching profiles of Si substrates in low pressure (10s mTorr) Ar/Cl2 discharges for a variety of incident ion angular distributions. Both ion and neutral re-emission fluxes are included in the calculation of the etch rate, and their contributions to the total etch profile will be demonstrated. In addition, we will show RIE lag effects as a function of different trench aspect ratios. (For sample profiles, please see http://www.ipt.arc.nasa.gov/hwangfig1.html)
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II
Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I
In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.