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Abstract Mixing can vary based on the scale at which the system is observed, and a mixing index that can capture the features at different length scales is desirable. In this article, we analyze the scale dependence of the mixing indices developed for Eulerian multiphase models. Relevant length scales are distinguished by filtering solid fraction fields. The scale‐dependence study is first done on manufactured fields of solid fraction to assess the performance of the mixing indices. The study is extended to a two‐dimensional CFD simulation of the segregation of a bidisperse gas–solid mixture. The local mixing index performs well in capturing the spatial variation of mixing at different scales. The scale dependence of two global mixing indices is considered in the study, where the state of mixing is defined based on statistical measures. We demonstrate that the choice of measures influences the sensitivity of mixing indices to mixing at different scales.
OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.
If a CO 2 reservoir or transmission pipeline were to leak, both the surrounding ecology and maritime traffic safety could be put at risk. To better understand and prepare for this risk, multiphase Computational Fluid Dynamics (CFD) models were built in ANSYS Fluent to capture the behavior of a leak once it enters the water. A 3D Eulerian–Eulerian model was used for validation, while a simplified 2D model was applied to simulate conditions at a 50-m depth. The models integrate bubble dynamics, gas holdup, CO 2 dissolution, dissolved species transport, and seawater acidification into a unified CFD framework. Mass transfer was calculated using the Hughmark correlation, and local seawater temperature and salinity were factored in to determine dissociation behavior and the relevant Henry’s Law constant. To confirm the 3D model’s accuracy, results were checked against two experimental datasets: the QICS field study and the Hauser Tank experiments. The team also modeled a hypothetical release scenario at the High Island 10L site and compared the results with earlier published work. The results show that at a depth of 50 m, the surrounding water column can completely absorb a CO 2 release at a rate of 35 kg/s, since the gas dissolves into the seawater as it rises toward the surface. Beyond confirming this mitigation capacity, the simulations shed light on how a leak would actually unfold in the environment, including the shape and movement of the rising bubble plume, how much CO 2 dissolves along the way, and the resulting shifts in seawater pH and pCO 2 . Together, this provides a practical framework for assessing how CO 2 leaks could affect marine environments in the Gulf of Mexico.
The vertical source-sink distribution of air pollutants within and above forested canopies is necessary for describing the biological, physical, and chemical processes influencing the soil-vegetation-atmosphere exchange. Here, this study implemented inverse modeling methods to estimate the source-sink and flux profiles of reactive nitrogen (N) and sulfur (S) compounds from measurements of the mean concentration profiles of ammonia (NH 3 ), nitric acid (HNO 3 ), sulfur dioxide (SO 2 ), and particulate ammonium (NH 4 + ), nitrate (NO 3 − ), and sulfate (SO 4 2− ) at a forest site in the southern Appalachian Mountains. Three inverse approaches utilizing different approximations to scalar transport within the canopy were developed and evaluated against sensible heat flux measurements. The Eulerian model (EUL), which incorporates vertical velocity skewness, performed well in reproducing the turbulent heat fluxes and was subsequently used to calculate the chemical source-sink and flux profiles. Above-canopy fluxes of NH 3 were downward, indicating that the forest was a net sink of NH 3 . The soil/litter layer was both a source and a sink for NH 3 but the exchange rate at the forest floor was small. Fluxes of HNO 3 , SO 2 , NO 3 − , NH 4 + , and SO 4 2- were uni-directional (deposition only) between the air and the canopy/ground and increased monotonically from the forest floor to the canopy top. Crown foliage dominated the uptake of reactive N and S during the growing season, accounting for 80–90% of the total canopy-scale flux. Fluxes and canopy-ground partitioning estimated using the resistance-based Surface Tiled Aerosol and Gas Exchange (STAGE) model were generally comparable to EUL. The comparison highlights the need for improved parameterizations of litter exchange and NH 3 compensation points in resistance models for forest ecosystems. The findings here benefit the application of critical loads in forest ecosystems and guide further development of resistance-based exchange models.
Abstract The process of glaciation in mixed-phase stratiform clouds was investigated by a novel Lagrangian–Eulerian model (LEM) in which thousands of adjoining Lagrangian parcels moved within a turbulent-like velocity field with statistical parameters typical of the Arctic boundary layer. We used detailed bin microphysics to describe the condensation/evaporation processes in each parcel, in which droplets, aerosols, and ice particles were described using size distributions of 500 mass bins. The model also calculated aerosol mass inside droplets and ice particles. Gravitational sedimentation of droplets and ice particles was also accounted for. Assuming that droplet freezing is the primary source of ice particles, the Arctic clouds observed in Indirect and Semi-Direct Aerosol Campaign (ISDAC) were successfully simulated. The model showed that at a low ice particle concentration typical of ISDAC, large vortices (eddies) led to a quasi-stationary regime, in which mixed-phase St existed for a long time. The large eddies controlled the water partitioning in the mixed-phase clouds. Droplets formed and grew in updrafts, typically reaching the cloud top, and evaporated in downdrafts. Ice particles grew in updrafts and downdrafts. The Wegener–Bergeron–Findeisen (WBF) mechanism was efficient in downdrafts and some parts of updrafts, depending on ice concentration and vertical velocity. At low ice concentrations, the effect of ice on the phase partitioning was negligible. In this regime, liquid droplets were found near the cloud top, whereas ice particles precipitated through the cloud base. When ice concentration exceeded about 10 L −1 , the WBF mechanism led to glaciation of almost the entire cloud, with the exception of narrow cloud regions associated with strong updrafts. At ice particle concentrations of a few tens per liter, the oscillatory regime took place due to the ice–liquid interaction. The microphysical structure of mixed-phase St forms as a combined effect of cloud dynamics (large eddies) and the WBF mechanism.
In Eulerian finite element simulations, the mesh moves relative to the material. After every change of position between the mesh and the material, the state variables are interpolated to the new mesh position, which is referred to as advection. Large strain crystal plasticity models are based on the multiplicative decomposition of the total deformation gradient. Further, the stress is evaluated as a function of the thermoelastic strain, temperature, and other state variables. Advection of tensor quantities, such as the strain, is coupled with possibly significant advection errors. In an effort to reduce the advection errors, we develop two rate forms of an established dislocation density-based continuum model. To that end, we replace the multiplicative decomposition of the deformation gradient with the additive decomposition of the velocity gradient, and define the stress rate instead of the total stress. The Eulerian implementation is compared with Lagrangian calculations, and two numerical examples with severe deformation levels are presented.
Hydrogen is a promising component of a future energy-secure and efficient economy, but its competitiveness depends on reducing production costs. One strategy is to operate alkaline water electrolyzers at higher current densities to increase output. However, this intensifies performance losses due to gas bubble accumulation, which blocks transport pathways and deactivates electrochemically active surfaces. Enhancing bubble evacuation through electrode design is therefore essential. Previous studies have explored various approaches — such as modifying surface morphology, applying sonication or pressure modulation, and introducing surfactants — but these efforts have addressed a limited range of conditions due to the complexity of two-phase flow and electrode geometries. Experiments have also largely been focused on either cell level improvements, which lack the information necessary to isolate each contributing factor, or on modified geometries that are not relevant to practical cell operation. From a modeling perspective, conventional Eulerian multiphase models do not track the complex gas–liquid interfacial dynamics and often neglect surface tension and contact angle effects, reducing their predictive accuracy. To provide insights on the effects of different electrode geometries on the performance of alklaine water electrolyzers this work employs an immersed boundary volume-of-fluid method to simulate bubble behavior in 3D porous electrodes. Multiple base electrode geometries, typically used in practice, with varying porosity are evaluated under a constant surface gas generation rate. Simulation data is analyzed to quantify electrode gas coverage, bubble size dynamics and other relevant metrics. Results show that porosity strongly influences bubble accumulation on electrode surfaces, with higher porosity reducing gas coverage, and its not strictly dependent on the electrode geometry. However, the electrode’s base geometry significantly affects gas accumulation at the separator gap, independent of porosity. A foam electrode geometry resulted in the lowest gas coverage of all electrodes with a median volumetric gas coverage of 11%, but at the cost of a 70% reduction in active area compared with the largest surface area electrode, while gyroid electrodes showed the best trade-off between gas coverage, particularly at the separator surface, and electrochemically active area. In conclusion, the results highlight the need for holistic electrode design strategies.
Using the FLAG hydrocode, hypervelocity plasma jets observed in miniature explosively–driven shock tube experiments have been modeled with a relative error in velocity of less than 5% (a reduction from previous attempts which yielded errors of 37%). This suggests that FLAG may be well-suited to model HE systems involving the acceleration of gases through complex crack systems in HE devices: A phenomenon not accurately captured using current modeling capabilities. The Eulerian hydrocode model presented here leverages AMR to reduce computational cost and, importantly, it was found that mesh resolution and model geometry each significantly affected the average jet velocity. The model and the results are detailed here together with comments on challenges during its development and avenues for future work.
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Increasing engine efficiency is essential to reducing emissions, which is a priority for automakers. Unconventional modes such as boosted and highly dilute operation have the potential to increase engine efficiency but suffer from stability concerns and cyclic variability. To aid engineers in designing ignition systems that reduce cyclic variability in such engine operation modes, reliable and accurate spark-ignition models are necessary. Here, in this article, a Lagrangian–Eulerian spark-ignition (LESI) model is used to simulate electrical discharge, spark channel elongation, and ignition in inert or reacting crossflow within a combustion vessel, at different pressures, flow speeds, and dilution rates. First the model formulation is briefly revisited. Then, the experimental and simulations setups are presented. The results showcase the model’s ability to predict the secondary circuit voltage, current, and power signals, in addition to the spark channel elongation, for the inert cases, or flame front growth, for the reacting cases. The results also compare simulation spark channel and flame growth plots to experimental Schlieren images at different instants in time. This work serves to highlight LESI’s ability to predict the characteristics of discharge and ignition across a variety of operating conditions.
Here, this paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response.
Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient multiphysics modeling of advanced reactors, has been used recently to model both high-temperature gas-cooled and fluoride-salt-cooled pebble bed reactors (PBRs). Griffin uses deterministic methods for solving neutron transport and an Eulerian approach to model pebble movement. An Eulerian approach is also used to directly compute burnup instead of using a pass approach like other tools such as VSOP or PANGU. This work discusses verification efforts and numerical method improvements related specifically to the Eulerian modeling approach implemented for directly computing pebble burnup.
LOKI is a simulation code that models weakly-coupled plasma evolution using Eulerian kinetic models in four phase space dimensions. The code is useful to understand basic plasma nonlinear plasma physics phenomena - in particular, wave-particle and wave-wave resonances that occur in laser plasma interactions. LOKI can simulate fundamental physical process in low-density plasmas on a scale of hundreds of light wavelengths. It does so by solving the relativistic Vlasov and Valsov-Fokker-Planck differential transport equations describing the collision less and low-collisionality evolution of charged particles in electromagnetic fields in two configuration space and two velocity space dimensions. Two principle electromagnetic models are provided: electrostatic (Poisson's Equation) and electromagnetic (Maxwell's equations).
In the United States transportation sector, Light-Duty Vehicles (LDVs) are the largest energy consumers and CO 2 emitters. Electrification of LDVs is posed as a potential solution, but SI engines can still contribute to decarbonization. Car manufacturers have turned to unconventional engine operation to increase the efficiency of Spark-Ignition (SI) engines and reduce the carbon emissions of their fleets. Dilute, lean, and stratified-charge engine operation has the potential for engine efficiency improvements at the expense of increased cyclic variability and combustion instability. At such demanding engine conditions, the spark ignition event is key for flame initiation and propagation and for enhanced combustion stability. Reliable and accurate spark ignition models can help design ignition systems that reduce cyclic variability. Multiple computational spark-ignition models exist that perform well under conventional conditions, but the underlying physics needs to be expanded, for unconventional engine operation. In this paper, a hybrid Lagrangian–Eulerian Spark-Ignition (LESI) model is coupled with different turbulent flame propagation models for engine simulations. LESI relies on Lagrangian arc tracking and Eulerian energy deposition. The LESI model is coupled with the Well-Stirred Reactor (WSR), Thickened Flame Model (TFM), and g-equation model and used to simulate several cycles of a Direct-Injection Spark-Ignition (DISI) engine using a commercial Computational Fluid Dynamics (CFD) engine solver. The results showcase the successful coupling of LESI with the combustion models. Global engine metrics, such as pressure and Apparent Heat Release Rate (AHRR), for each simulation setup are compared to experimental engine results, for validation. In addition, results highlight the successful prediction of spark channel movement by comparing simulation images to experimental optical engine images. Finally, the successful coupling of LESI to combustion models, making it a usable model in the engine modeling community, is emphasized and future development details are discussed.
This paper describes and compares some of the advantages and limitations of Eulerian and Lagrangian approaches to water quality modeling and introduces a mixed Eulerian-Lagrangian (or semi-Lagrangian) methodology that captures the strengths of both approaches. The semi-Lagrangian modeling approach is applied to advection-dominated rivers, and flexibly ensures unconditional stability for all time step durations and grid segmentations. The semi-Lagrangian modeling approach is demonstrated by applying it to estimate the dissolved oxygen concentrations in the Sava River in Slovenia, focusing on aspects of the methodology and findings that would be of broad interest to managers of water quality in fluvial water bodies. Results of comparisons of the semi-Lagrangian model with the Eulerian-based QUAL2K model in steady and non-steady scenarios demonstrate that while both models are fully capable of producing satisfactory results when optimally configured, the semi-Lagrangian approach offers accuracy and stability without sensitivity to the interaction of time step size and computational grid segmentation scheme.
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 evolution for molten salt equipment. In FY24, significant developments were made to the code package, enhancing its capabilities in many aspects. The improvements and advancements can be summarized as follows: 1. Implementation of tritium transport capabilities and validation with experimental data: To enable modeling of tritium and other fission gases within MSRs, we implemented gas transport within MOSCATO via inclusion of couple mass transport equations within the salt and structural alloys. Comparisons to experimental data from literature showed good agreement with respect to tritium release rates. 2. Preliminary implementation of two-phase flow models in MOSCATO: To model tritium and other gases above their solubility limits, we implemented preliminary two-phase flow models within MOSCATO to account for bubble transport. The first model adopted was the Level-Set approach, which can handle the high void fraction regime, but with a requirement for high mesh resolution thus high computational expense. In this report, we present a verification of the Level-Set method using a simple benchmark case. We also performed a demonstration of the code as applied to an experimental case involving cover gas flow through salt in an experimental vessel. The second model adopted was the Eulerian-Eulerian dispersed flow model, which is computationally cheaper but limited to low void fraction regimes, such as bubbly flow. Validation and verification have not yet been performed for the Eulerian-Eulerian approach, but a preliminary implementation was completed. 3. Validation with static corrosion experiments: Static corrosion experimental data for stainless steel coupons within molten salts was used to further validate the corrosion model in MOSCATO. To do so, we leveraged the existing models in MOSCATO and simulated the sample mass loss and mass gain phenomena. Several ion species, including Cr 2+ , Fe 2+ and H + , were simulated in salt using the PNP solver, while Cr 0 and Fe 0 were simulated with a diffusion solver in stainless steel. The mass loss of the samples was compared with experimental data, and good agreement was achieved. These combined activities served to further expand the capabilities of MOSCATO and make it more generally applicable to the full range of phenomena that can control chemistry and corrosion in molten salt reactors.