Eulerian Model Research Articles

Separation Time of Aluminothermic Reduction Products for Sustainable Silicon Production

Background This work was carried out within the framework of the SisAl Pilot project, which is devoted to the environmentally friendly production of silicon. This new method relies on the aluminothermic reduction of quartz in slag, offering a more sustainable alternative to the traditional reduction of silica with carbon in submerged arc furnaces. Methods The process takes place in a rotary kiln producing silicon (Si) and alumina slag (actually, a CaO – Al2O3 slag), which must be separated at the end to extract the silicon. This separation process is analyzed through mathematical modelling and numerical simulation, as it is of industrial interest to know how much time it takes for Si and CaO – Al2O3 slag to separate once the process has ended. Generally, a multiphase flow model is used to estimate the separation time of the two components once aluminothermic reduction has ended. Results Several scenarios are considered for the numerical simulation of the separation time, namely different initial configurations and material properties of both fluids are covered. Moreover, the separation times obtained with two distinct multiphase flow models -VOF (volume of fluid) and Eulerian- are compared. Conclusions The separation times resulting from simulations using the multiphase Eulerian model are more realistic compared to those from the VOF model, which clearly tends to underestimate separation times. Furthermore, apart from the selected multiphase flow model, the density difference between silicon and alumina slag plays a critical role in determining the separation time.

Eulerian multi-fluid simulations of local liquid distribution in a bed packed with cylindrical particles

Packed bed reactors (PBRs) are extensively used in chemical process industries to perform solid-catalyzed gas–liquid reactions. Their performance is significantly influenced by liquid distribution which is a strong function of particle shape and size. In the present work, we simulated the steady-state local liquid distribution, pressure drop (ΔP/L), and overall liquid holdup (〈εL〉) for the beds packed with spherical and cylindrical particles using a three-dimensional (3D) Eulerian multifluid model and validated the predictions using corresponding high-speed imaging measurements performed in pseudo-2D packed beds. We showed that the Eulerian model with existing closures significantly underpredicts the liquid distribution for the bed randomly packed with cylindrical particles. To address this, we proposed a modification in existing mechanical dispersion force (F→D) model as a function of average particle orientation angle (θ). The modification significantly improved agreement between the predictions and the corresponding measurements. Using the modified model, we showed that the increased magnitude of F→D in the lateral direction leads to higher lateral liquid spreading for cylindrical particles as compared to that for the spherical particles. Importantly, the modified model also predicted the local liquid distribution and ΔP/L for beds packed manually with cylindrical particles oriented at different θ in a satisfactory agreement with the corresponding measurements. On increasing θ, the F→D in lateral direction (i.e., perpendicular to flow) as well as liquid–solid interaction force (F→LS) in axial direction (i.e., parallel to flow) found to increase significantly. As a result, the lateral liquid spreading as well as ΔP/L decrease substantially on increasing θ.

Effects of gravity on the cell performance of proton exchange membrane water electrolyzer

Hydrogen is of great significance for building a low-carbon and safe energy system. The proton exchange membrane water electrolyzer (PEMWE) is considered a highly promising hydrogen production device. However, due to the complex physical and chemical processes within the cell, and the impact of gravity effect on the cell characteristic is unclear. Analyzing the impact of gravity on cell performance is critical. In this study, the three-dimensional two-phase flow models are developed for the PEMWE, the models couple many physical fields, including the hydrodynamics, electrochemical reaction kinetics, mass transfer, heat transfer, two-phase flow based on Euler model, and gravity effect. The simulation model is verified through experiment results. The effect of gravity on the cell performance is investigated, the influences of gravity under different placement directions are compared, and the impact of the cell voltage on the transport characteristics is discussed under the gravity effect. Results show that the gas transport and heat transfer are enhanced under the gravity, the active sites in the catalytic layer can be timely released due to the accelerated bubble removal, the polarization performance is accordingly improved. The cell performance with the gravity effect under vertical placement is higher than that with the gravity effect under horizontal placement because of the improved mass transfer, but the mixture velocity at anode flow channel is decreased. Moreover, as the cell voltage increases, the electrochemical reaction rate is enhanced, the heat transfer is increased, and the volume fraction of disperse phase in anode flow channel is accordingly increased. This study provides a theoretical reference for further investigating transport characteristics and optimising the cell performance.

Numerical Study on Droplet Splashing Behavior of Slag‐Splashing for Converter Protection Using Volume of Fluid‐Discrete Phase Model Two‐Way Conversion Model

Limited quantitative research exists on the complex phenomenon of slag splashing in converters. A comprehensive modeling framework is developed to fill this gap, integrating a 3D two‐phase flow model with a volume of fluid‐discrete phase model two‐way conversion model. This framework explores droplet behavior during splashing for converter protection, encompassing the mutual conversion between slag and discrete droplets induced by top‐blowing oxygen. It also tracks the trajectories of all droplets, enabling a detailed quantitative analysis of the splashing process. The Eulerian wall film model is used to simulate liquid film formation on the converter wall. Model predictions are validated against 1:10 scale experimental data from a 50 t converter. This assessment covers splashing rates, droplet locations, and size distribution under various operating conditions. Parametric studies identified an optimal top‐blowing flow rate of 8.80 Nm3 h−1 and an oxygen lance height of 233.2 mm, balancing splashing effectiveness with production cost and safety.

Integrating an urban fire model into an operational wildland fire model to simulate one dimensional wildland–urban interface fires: a parametric study

Background Wildland fires that occur near communities, in the wildland–urban interface (WUI), can inflict significant damage to urban structures. Although computational models are vital in wildfires, they often focus solely on wildland landscapes. Aim We conducted a computational study to investigate WUI fire spread, encompassing both urban and wildland landscapes. Methods We developed a 1D landscape-scale semi-physical model by integrating a semi-physical urban fire spread model into an Eulerian level set model of wildfire. The model includes ignition and spread through radiation, direct flame contact and ember deposition. Key results Through a parametric study, we compare the relative change of spread rate from various structural properties and landscape layouts represented by model parameters, highlighting the significant impact of fire-resistant structure materials over surface treatments. Layout configurations play a pivotal role in fire spread, with isolated islands of combustibles effective in reducing spread rate, aligning with existing mitigation strategies. Conclusion Despite using a 1D domain and limitations on spatial and temporal variability, our model provides insights into underlying phenomena observed in WUI fires and their mitigation. It offers early-stage development of strategies for managing structure materials and landscape layouts. Implications Our model and findings provide insights into WUI fire dynamics, paving the way for advanced mitigation strategies.

Impact of methane and other precursor emission reductions on surface ozone in Europe: scenario analysis using the European Monitoring and Evaluation Programme (EMEP) Meteorological Synthesizing Centre – West (MSC-W) model

Abstract. The impacts of future methane (CH4) and other precursor emission changes are investigated for surface ozone (O3) in the United Nations Economic Commission for Europe (UNECE) region excluding North America and Israel (the EMEP region, for European Monitoring and Evaluation Programme) for the year 2050. The analysis includes a current legislation (CLE) and maximum feasible technical reduction (MFR) scenario, as well as a scenario that combines MFRs with an additional dietary shift that also meets the Paris Agreement objectives with respect to greenhouse gas emissions (LOW). For each scenario, background CH4 concentrations are calculated using a probabilistic Earth system model emulator and combined with other precursor emissions in a three-dimensional Eulerian chemistry-transport model. While focus is placed on peak season maximum daily 8 h average (MDA8) O3 concentrations, a range of other indicators for health and vegetation impacts are also discussed. Our analysis shows that roughly one-third of the total peak season MDA8 reduction achieved between the 2050 CLE and MFR scenarios is attributable to CH4 reductions, resulting predominantly from CH4 emission reductions outside of the EMEP region. The impact of other precursor emission reductions is split nearly evenly between the reductions inside and outside of the EMEP region. However, the relative importance of CH4 and other precursor emission reductions is shown to depend on the choice of O3 indicator, though indicators sensitive to peak O3 show generally consistent results. The analysis also highlights the synergistic impacts of CH4 mitigation as reducing solely CH4 achieves, beyond air quality improvement, nearly two-thirds of the total global warming reduction calculated for the LOW scenario compared to the CLE case.

COMPARATIVE STUDY USING CFD OF COUNTER-CURRENT AND CO-CURRENT HYDROTREATING REACTORS USING JATROPHA CURCAS L VEGETABLE OIL

In this work, mathematical modeling and CFD simulation of two countercurrent and cocurrent hydrotreatment reactors were carried out, validating the results with a drained bed reactor (TBR), a commercial CoMo/γ-Al2O3 catalyst was used, the material the raw material was Jatropha Curcas L vegetable oil. The operating conditions were temperature 380 ° C, pressure 8 MPag. The kinetic model that was used considered 13 reactions that involve processes of decarboxylation, decarbonization, hydrodeoxygenation and hydrocracking reactions for triolein and tristearin triglycerides. The CFD simulation was carried out in Fluent 18.2 in a transient state and in 3D, considering the standard κ - ε turbulence models, Eulerian multiphase model and porous medium model, it was shown that the countercurrent reactor has less pressure drop than the countercurrent, the conversion the countercurrent reactor has a greater conversion of reactants of 99%, the generation of products from the countercurrent reactor has higher concentrations than the cocurrent reactor, this is because it has more contact areas between phases in the reactor.

Enhancing Efficiency in Deep-V Planing Hull Ships: A Study on The Design of Spray Strips to Minimize Resistance

Spray strips are deflectors installed on the hull to decrease the wetted surface area (WSA). By reducing the WSA, the overall resistance of the ship is lowered because it lessens the friction of water flowing against the hull. The purpose of this research is to predict the function of spray strips in an effort to improve ship performance. In this study, the numerical methodology employs the Finite Volume Method (FVM) along with the Reynolds-averaged Navier-Stokes equation (RANS) for resolving fluid dynamics issues. The modeling of the two-phase flow involves the utilization of both the Volume of Fluid (VOF) model and the Eulerian model. The results of this study show that spray strips can reduce the total resistance by about 2.7%. Increasing the number of spray strips can reduce the drag shear value by 3.5%. Spray strips are effective in reducing total drag when the Froude number (Fr) is greater than 1 or when the vessel is in the planing phase. The profile shape of spray strips with dimension 2:1 shows the best performance on ship resistance.

Exact solution of the generalized Riemann problem for the Eulerian droplet model with particle pressure

In this paper, we investigate the generalized Riemann problem for the Eulerian droplet model with particle pressure. By introducing two new state variables, the generalized Riemann problem for a system of balance law (nonhomogeneous system) is neatly transferred into the Riemann problem for a system of conservation law (homogeneous system). Four different kinds of exact solutions are presented in fully explicit forms, which are given in terms of two nonconstant states separated by a shock or a generalized rarefaction wave or by a combination of such wave profiles.

Unraveling the discrepancies between Eulerian and Lagrangian moisture tracking models in monsoon- and westerly-dominated basins of the Tibetan Plateau

Abstract. Eulerian and Lagrangian numerical moisture tracking models, which are primarily used to quantify moisture contributions from global sources to specific regions, play a crucial role in hydrology and (paleo)climatology studies on the Tibetan Plateau (TP). Despite their widespread applications in the TP region, potential discrepancies in their moisture tracking results and their underlying causes remain unexplored. In this study, we compare the most widely used Eulerian and Lagrangian moisture tracking models over the TP, i.e., WAM2layers (the Water Accounting Model – 2 layers) and FLEXPART-WaterSip (the FLEXible PARTicle dispersion model coupled with the “WaterSip” moisture source diagnostic method), specifically focusing on a basin governed by the Indian summer monsoon (Yarlung Zangbo River basin, YB) and a westerly-dominated basin (upper Tarim River basin, UTB). Compared to the bias-corrected FLEXPART-WaterSip, WAM2layers generally estimates higher moisture contributions from westerly-dominated and distant sources but lower contributions from local recycling and nearby sources downwind of the westerlies. These differences become smaller with higher spatial and temporal resolutions of forcing data in WAM2layers. A notable advantage of WAM2layers over FLEXPART-WaterSip is its closer alignment of estimated moisture sources with actual evaporation, particularly in source regions with complex land–sea distributions. However, the evaporation biases in FLEXPART-WaterSip can be partly corrected through calibration with actual surface fluxes. For moisture tracking over the TP, we recommend using high-resolution forcing datasets, prioritizing temporal resolution over spatial resolution for WAM2layers, while for FLEXPART-WaterSip, we suggest applying bias corrections to optimize the filtering of precipitation particles and adjust evaporation estimates.

A four-way coupled numerical investigation of draft tube baffled crystallizer

In the present paper, the liquid–solid two-phase turbulent flow in a Draft Tube Baffled crystallizer has been simulated using Computational Fluid Dynamics. In this respect, multiphase Eulerian model along with population balance equations were applied. To implement four-way coupling, aggregation and breakage were considered. The RNG k-ε and RSM turbulence models were employed to conduct numerical simulation of two phase turbulent flow. Results demonstrated that applying RNG k-ε and RSM turbulence models, a significant difference in axial velocity profiles along the x-axis is observed, while those along the z-axis exhibit less difference. Moreover, a significant difference in volume fraction between the two models was observed which mostly concerns the region within the draft tube and the distance between the baffle and crystallizer wall. Furthermore, changing the propeller speed from 165 to 495 rpm, the speed of 330 rpm showed to be optimal in terms of particles residence time. The results also showed that a rise in impeller speed is one of the major contributors to mass exchange enhancement between the liquid and the solid phases. Accordingly, as the impeller speed rises, the rate of mass exchange increases from 9.92 kg/h for 165 rpm to 29.07 kg/h for 495 rpm.

Modeling gas holdup in a multiphase oxygen slurry bubble column reactor for Cu-Cl hydrogen production using CFD

The hydrodynamics of the oxygen bubble column reactor is investigated numerically using CFD analyses to predict the values of the gas holdup using Eulerian model and k−ε turbulence method. It is shown that, at any given static liquid height and solid concentration, increasing the superficial gas velocity leads to a higher gas holdup. Also, the gas holdup reduces when the static liquid height increases and/or the solid concentration increases at any given superficial gas velocity. All gas holdup findings were verified by experimental results from prior literature, showing excellent agreement and validating the models' applicability to this kind of a slurry bubble column system. Profiles of gas holdup obtained from CFD simulations were shown to generally under-predict the experimental data. Also, it is shown that CFD models accurately anticipated the experimental effects of the superficial gas velocity, static liquid height, and solid concentration on gas holdup.

Atmospheric Bubbling Fluidized Bed Risers: Effect of Cone Angle on Fluid Dynamics and Heat Transfer

Abstract In this paper, a comparative study of fluid flow behavior and thermal characteristics of sand particles has been carried out numerically and experimentally in bubbling fluidized beds for five-cone angles of the riser wall having 0 deg, 5 deg, 10 deg, 15 deg, and 20 deg. An Eulerian model with a k–ε turbulence model is used to explore the numerical analysis, and the findings are compared to those of the experiments. For the study, the inlet air velocity is fixed at 1.5 m/s with sand particles filled up to 30 cm to maintain bubbling conditions in the risers. The results indicate that increasing the cone angle up to 10 deg while maintaining the amount of bed materials constant leads to a reduction in pressure drop. The expansion of particles along the riser is observed to decrease with the increase in the cone angle up to 10 deg. The radial solid volume fraction profile transforms to a U shape from the W-type profile as the cone angle increases up to 10 deg. Correspondingly, the solid velocity is found to have an inverted U-type and W-shaped profile for the risers. The granular temperature is also found to increase with a decrease in the solid percentage at any location. The average bed temperature, interphase, and bed-to-wall heat transfer coefficient at a location of 10 cm axial height also increase with the cone angle increase up to 10 deg. As a result, the conical riser, when designed with a greater cone angle up to 10 deg, exhibits more efficiency in terms of heat transfer characteristics. The 3D simulation results are in strong concurrence with the experimental results in all investigations.

A meshless model for three-dimensional direct numerical simulation of local scour around cylinder bridge foundation

A meshless local scour model for cylinder bridge foundation based on the smoothed particle hydrodynamics (SPH) method is proposed in this paper. Differing from the traditional Eulerian mesh model used for monopile local scour, it overcomes the high requirements of mesh quality and density for capturing large deformations at the fluid interface. Unlike the transient sediment erosion SPH model used for dam-break, sediment flushing, and water jet, the meshless approach is innovatively applied to the continuous simulation of bridge local scour under steady flow conditions. The present SPH model is established based on the SPH multi-phase fluid model, integrating a classical fluid model combined with numerical stabilization algorithms to govern water particle motion and a sediment model from Zhang et al. (2024) to govern sediment evolution, and tests a new scheme for boundary treatment in the model based on DualSPHysics. Furthermore, a novel scour visualization method that aims at extracting both visible and actual bed surfaces from discrete particles is proposed. The model is validated through comparison with rigid bed and live bed experiments, demonstrating favorable agreement in terms of flow and scour simulation. Importantly, the model results reveal a discrepancy between the elevation of the post-scour visible bed surface derived from the conventional Eulerian mesh model and experimental data, compared to the actual bed surface unaffected by water flow erosion. This indicates the necessity for incorporating a safety margin in foundation design when utilizing experimental results to determine the maximum scour depth.

Nonlinear electrodynamics and its possible connection to relativistic superconductivity: an example

Abstract This work presents an illustrative example suggesting a potential connection between the Heisenberg–Euler (HE) model of nonlinear electrodynamics (NLED) and relativistic superconductivity. Within a cylindrical coordinate system, we derive nonlinear Maxwell’s equations from the HE Lagrangian to the fourth order in the electromagnetic (EM) field. By considering static electric and magnetic fields with Gaussian radial profiles, we compute the corresponding HE current density. In parallel, we explore relativistic type-II superconductivity in analogy with the Ginzburg–Landau (GL) theory. We calculate the vortex-supercurrent density of the condensate and propose a link between this current and the HE current. This connection enables the derivation of the relativistic order parameter state. The problem considered in this article may contribute to the understanding of superconductivity in strong EM environments within the broader framework of NLED.

Numerical Simulation of CO Generation and Combustion Efficiency in Sintering Process: Effect of Solid Fuel Particle Size

For sintering pot productive process with various fuel particle size distributions, a transient numerical simulation sintering model based on the computational fluid dynamics approach is developed using Fluent 2021R1. The model combines chemical reaction, mass and heat transfer, Euler–Euler model, and fluid flow in porous media. In this study, CO is employed as the combustion's intermediate product, which is further oxidized by secondary combustion in the high‐temperature zone. Through calculations, the solid fuel combustion behavior of the sintering is explained collectively with the changing bed temperature, CO emission, and solid fuel combustion efficiency of the process under various fuel particle size distribution. In the sintering process, the fuel particle size distribution is crucial for lowering CO emissions and increasing combustion efficiency. The combustion efficiency shows a tendency of increasing initially before decreasing with the reduction of solid fuel particle size, while CO emissions show a trend of reducing first and then increasing. It is advantageous to lower the CO emission in the sintering process, and the combustion efficiency of the sintering process is greatly boosted by 5.13% when the proportion of solid fuel with 5 mm particle size decreases and the proportion of solid fuel with 3 mm particle size increases.

Numerical modelling of the Water-Quenching Process validated through experiments with IN718 Nickel-Based Superalloy

Quenching is often a necessary step during manufacturing to tailor microstructures of metals and alloys for desired applications. Although employed extensively throughout human history, it relies heavily on experience and often trial and error. Therefore, the availability of computational tools, capable of describing the physics of the process during quenching, would help effective design, lower manufacturing costs, and make the process more environmentally friendly.This work analyses and validates a numerical procedure for immersion water quenching using computational fluid dynamics. The methodology employs the partitioned approach. Hence, the heat transfer information is exchanged at the interface of the part and the surrounding environment (i.e., water). An energy equation and an Eulerian two-fluid model describe the solid and fluid regions, respectively.The validation experiment includes water quenching of an IN718 nickel-based superalloy solid cylinder, in axial direction, with embedded thermo-couples for the measurements of cooling curves during the process. As such, no phase transformation within the solid material is assumed. The computational procedure focuses on determining the heat transfer coefficient due to fluid dynamics and the quenchant (i.e., water) phase change during cooling. The cylinder experiences effects of various heat transfer regimes, including film, transition and nucleate boiling, and natural convection intensified by buoyancy forces due to the presence of two fluid phases.A good agreement with validation data is achieved presenting an innovative numerical tool capable of predicting with high accuracy the temperatures and cooling rates of metal alloys during water quenching. Some complications are observed and reported where vapour movement is obstructed. Therefore we highlight further steps to alleviate any issues.

An improved Arbitrary Lagrangian–Eulerian thermal-fluid model by considering powder deposition effects on melting pool during Direct Energy Deposition processes

Directed Energy Deposition (DED) has emerged notably by offering new possibilities for (re-)manufacturing parts. The multi-phase thermal-fluid models that simulate powder stream deposition are computationally too expensive. The mono-phase Arbitrary Lagrangian–Eulerian (ALE) method are limited in prediction due to exclusion of powder deposition parameters. To address this, we propose an improved 3D mono-phase thermal-fluid model that incorporates powder deposition effects and employs a Moving Thermal-Fluid (MTF) framework to accelerate simulations. Mass, energy, and momentum conservation equations are solved using the finite element method (FEM) and an implicit time integration algorithm, and the ALE method tracks the free surface during deposition. The improved ALE allows considering enthalpy and momentum related to powder deposition through the implementation of new source terms in the energy and momentum conservation equations, leading to more accurate predictions without significantly increasing computing time. Numerical investigations into powder deposition parameters, such as powder distribution, powder enthalpy, and powder momentum, are conducted to identify their impact on melting pool prediction. The in-situ and ex-situ measurements of the melting pool are also performed to check the efficiency of the proposed model. The applications highlight the importance of incorporating powder stream effects and demonstrate the proposed model’s computational efficiency compared to the classical ALE model.

Comparison of the effects on heat transfer through oil oscillation in a steel piston cooling gallery: Friction welding versus laser welding

Piston cooling gallery plays a critical role in managing the temperature of the piston and its performance. This paper aims to study the effect of oscillatory heat transfer within the cooling galleries, focusing on two distinct types: flanged (friction-welded) and smooth structures (laser-welded). To do so, the Eulerian multiphase flow model and the k-ω SST turbulence model were used to simulate the oil and air flow through the cooling gallery. Key parameters such as the oil filling rate, wall heat transfer coefficient, oil outlet flow rate, heat removal rate by the oil, and overall wall heat transfer rate were assessed for both gallery designs at an engine speed of 1800 r/min. The results indicate significant disparities between the two cooling gallery structures: the smooth structure exhibits an oil filling rate that is 5.41% higher and an oil outlet flow rate that is 33.48% greater compared to the flanged structure. The flange structure impedes internal oil movement, which leads to boundary layer separation, secondary wall contact, and the emergence of a double vortex phenomena. Collectively, these factors influence the oil fill ratio. This, in turn, affects the distribution of oil within the gallery and, subsequently, the efficiency of heat transfer. Comparative analyses of heat transfer within both galleries, under the same studied conditions, revealed that the smooth structure outperforms the flanged one. However, the presence of a flange significantly alters the heat contribution from different walls, thereby highlighting the substantial impact of flanges on the overall efficiency of heat transfer.

Study of heat transfer coefficients of multiple high-pressure fan-shaped water impinging on the lower surface of high-temperature steel billets

The lack of research on the boiling heat transfer coefficient on billet surfaces during the high-pressure fan-shaped water descaling process significantly affects the cooling, quality, and rolling efficiency of the billet surface. This paper utilizes the Eulerian multiphase flow model in Fluent 19.0 software to simulate the boiling heat transfer behavior of multiple high-pressure fan-shaped water jets impinging the surface of high-temperature steel billets during descaling. The study highlights the correlation between the boiling heat transfer coefficient and three key parameters: the Reynolds number, dimensionless target distance, and dimensionless temperature. The simulation’s accuracy was validated by comparing the simulation results against experimental data. Findings indicate that the boiling heat transfer coefficients were respectively higher in the stagnation area, the lower side of the overlap zone, and at the edges of the flow strands on the billet surface, reaching up to approximately 6000 W·m−2·K−1. Additionally, the heat transfer coefficients were higher in the downstream region compared to the upstream area. The boiling heat transfer coefficient increased by 13.7 % and 9.38 % as the Reynolds number increased from 278,031 to 340,486 and as the initial temperature increased from 1373.15 K to 1573.15 K, respectively. On the other hand, the boiling heat transfer coefficient decreased by 19.0 % when reducing the target distance from 20 de to 54 de. Finally, a function was established to describe the boiling heat transfer coefficient based on the Reynolds number, dimensionless target distance, and dimensionless temperature.