A conservative level set method for N-phase flows with a free-energy-based surface tension model
Not Available
Howard, Amanda A. (ORCID:0000000264116198)↗
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An efficient level set method for tracking many materials
Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.
97 MATHEMATICS AND COMPUTING↗
Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods
We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.
42 ENGINEERING↗
Level set methods for stochastic discontinuity detection in nonlinear problems
Not provided.
Computer Science↗
Implementing Calving Laws in Ice-Sheet Models using Level Set Methods.
Abstract not provided.
Sockwell, Kenneth Chadwick↗
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.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
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.
36 MATERIALS SCIENCE↗
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.
36 MATERIALS SCIENCE↗
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.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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.
42 ENGINEERING↗
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.
97 MATHEMATICS AND COMPUTING↗
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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems
MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A Conservative Finite-Volume Based Interface-Tracking Algorithm Using the Signed Distance Function
Methods for tracking an interface between two fluid phases are developed to ensure desired fluid properties, conservation, and stability are preserved in a finitevolume (FV) discretization. Here, the interface is tracked using a level set method where the signed distance function implicitly defines the interface. Marching methods are used to evaluate the value of the signed distance function, including a novel initialization method to initialize any implicit function to the signed distance function around sharp corners in the level set. Global conservation and consistency with a set of governing equations is enforced by a compression coefficient that measures the volumetric compression or expansion due to inaccuracies in the level set evaluation. A redistribution method is integrated into the volume correction to eliminate the small-cell instability while maintaining global conservation. This suite of methods is implemented and tested using static uniform velocity, and potential flow cases with multiple interface geometries. Results show these methods achieve up to second order accuracy, and are conservative. The application for these methods is intended to track the interface of a 3D printing filament in a finite-volume discretization of the all-speed Navier-Stokes equations.
42 ENGINEERING↗
Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS
This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.
97 MATHEMATICS AND COMPUTING↗
Pore Resolved Simulations of Joule Heating in Fibrous Media using an Embedded Boundary Method
Joule heating has been regarded as an energy-efficient and sustainable method for heating materials and gases at large scales. The modeling of local temperature effects at pore-resolved scales for such systems, however, has been difficult to achieve due to challenges in coupling thermo-chemical processes in complex porous media and in large representative volume elements (RVEs). To this end, we developed an electro-thermal model at the pore scale to study Joule heating effects in large heterogeneous systems with different microstructures. This was achieved using the level set method to implicitly delineate distinct regions within the domain, and an embedded boundary method to facilitate heat exchange across the fluid-solid interface. Moreover, we applied this method to investigate unsteady non-linear electro-thermal effects in non-woven fibrous graphite conductors for RVEs with characteristic lengths of 2 mm, with different fiber orientations, porosity (80% – 90%) and fiber diameters (10 – 20µm). The coupled equations were solved numerically and they produced peak temperatures greater than 2000 K resulting in heating rates as high as 80,000 K/s. Moreover, the results depended strongly on the microstructure of the fiber skeleton and current density. Geometries with large fibers (∼ 20µm) had the highest average and peak temperatures with the mean temperature increasing by 3.9 % while the peak temperature increased by 9.9 %. Anisotropic domains on the other hand had the lowest mean and peak temperatures with peak and mean temperatures of 2293 K and 1437.7K respectively representing a corresponding 12.1% and 5.1% drop in the temperatures. An increase in porosity from 80% to 90%, however, led to an increase in the peak temperature by 5.1%.
Joule heating↗
Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames
Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.
42 ENGINEERING↗