Eulerian Model Research Articles

Investigating wave shape effect on sediment transport over migrating ripples using an eulerian two-phase model

A Reynolds-averaged two-phase Eulerian model for sediment transport, SedFoam, is utilized in a two-dimensional domain for a given sediment grain size, flow period, and mobility number to study the asymmetric and skewed flow effects on the sediment transport over coarse-sand migrating ripples. First, the model is validated with a full-scale water tunnel experiment of orbital ripple driven by acceleration skewed (asymmetric) oscillatory flow with good agreement in the flow velocity, net sediment transport, and ripple migration rate. The model results showed that the asymmetric flow causes a net onshore sediment transport of both suspended and near-bed load (the conventional bed load and part of the near-bed suspended load, responsible for ripple migration). The suspended load transport is driven by the “positive phase-lag” effect, while the near-bed transport is due to the large erosion of the boundary layer on the stoss flank, sediment avalanching on the lee flank, and the returning flux induced by the stoss vortex. Together, these processes result in a net onshore transport rate. In contrast, for an energetic velocity skewed (skewed) flow, the net transport rate is offshore directed. This is due to a larger offshore-directed suspended load transport rate, resulting from the “negative phase-lag” effect, compared to the onshore-directed near-bed load transport rate. Compared to the asymmetric flow, the onshore near-bed load transport (and migration) rate is limited by the larger offshore directed flux associated with returning flow on the lee side, due to a stronger lee vortex generation during the onshore flow half-cycle. In the combined asymmetric-skewed case, the near-bed load and migration rate are higher than in the asymmetric flow case. Moreover, the offshore-directed suspended load is much smaller compared to the skewed flow case due to a competition between the negative (due to velocity skewness) and positive (due to acceleration skewness) phase-lag effects. As a result, the net transport rate is onshore directed but slightly smaller than the asymmetric flow case.

Numerical and experimental analysis of inelastic and rate-dependent buckling of thin injection-moulded high-density polyethylene structure

Semi-crystalline polymers is an important group of materials that is used in a vast array of products. In this study, the rate-dependent properties of high-density polyethylene (HDPE) are investigated, both experimentally and theoretically. Experimental compression testing of a three-dimensional HDPE structure is performed and analysed numerically by use of the finite element method. In addition, an Eulerian constitutive material model for isotropic, semi-crystalline polymers is proposed. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, pressure-dependence of inelastic deformations, and damage. The proposed material model was implemented in Abaqus as a VUMAT, which is an explicit implementation. The material model was calibrated by use of uniaxial tensile tests performed on HDPE dog-bone shaped samples, and the model was further explored by applying the VUMAT implementation to the compression tests of the HDPE structure. The simulation model was able to reproduce the experimental results well, both the uniaxial tests and the compression tests. In particular, the friction present in the compression tests seems to play an important role in determining the buckling mode of the structure.

Refining the diffusive compressible Euler model

We revisit the molecular arguments underpinning the diffusive compressible Euler model (proposed in Svärd (2018)), and conclude that a heat diffusive term is not accounted for in the energy equation of the original model. The new heat diffusive term complements the diffusion of the conserved variables already present in the model. By studying a diffusive and conductive heat transfer problem, we quantify the new term in the updated model and evaluate it in the context sound attenuation. Although the new diffusive term is important for certain problems, we also demonstrate that it has a negligible effect on the aerodynamic validation cases that the original model has already successfully passed. Furthermore, the updated system is compatible with the weak well-posedness that has previously been established for the original system.

Numerical investigation on critical heat flux for 5 × 5 fuel assemblies with a wide range of working conditions

To determine the safe boundary of fuel assembly operation and improve the heat transfer performance of fuel assembly, it is necessary to accurately calculate the thermohydraulic characteristics and the critical heat flux (CHF) in rod bundles. The Eulerian two-phase model coupled with extended wall boiling model was used to numerically investigate the 5 × 5 fuel rod bundle flows with four sets of mixing vane spacer grids. A wide range of working conditions were analyzed to validate the numerical method. The results indicate that the current numerical model can not only accurately calculate the CHF values but also predict the location of heat transfer crisis. Based on CFD (Computational Fluid Dynamics) results, the detailed two-phase flow distributions were provided to analyze the CHF performance under special structures, such as bowed rod and spacer backward shift. The quantitative results were obtained on the analyses of spacer position influence on CHF and the penalty effect of bowed rod. Furthermore, the prediction of present numerical model under low inlet subcooling conditions and cold rod CHF were discussed. The research of this paper provides support for the design and optimization of fuel assemblies.

CFD-DEM simulation of cyclone self-rotation drying: Particle high-speed self-rotation and heat transfer

Cyclone self-rotation drying (CSRD) has been demonstrated to have the outstanding advantage of low energy consumption in drying field due to the ability of non-phase change separation of liquid in wet particles. Particle high-speed self-rotation are key factors that affect the energy consumption and efficiency of CSRD, but their laws and regulation methods are still unclear. In this study, under the framework of Eulerian-Lagrangian method, Eulerian model and Reynolds Stress Model (RSM) were adopted, and computational fluid dynamics (CFD) and discrete element method (DEM) coupled simulation was established to systematically investigate the effects of operating parameters on sludge particle self-rotation and heat transfer in a 200-mm-diameter CSRD device. The particle self-rotation and revolution speeds were found to decrease with increasing particle size and feeding rate. An average self-rotation speed of 5217.8 rad/s was observed for 1 mm particles at a gas velocity of 10 m/s and a feeding rate of 50 kg/h, when the gas velocity increased to 20 m/s, the self-rotation speed increased about 888.4 rad/s. These operating parameters were also found to affect particle residence time and temperature, smaller particles have better heat transfer performance. This study provides theoretical support for application and optimization of CSRD devices.

Lagrangian and Eulerian modelling of river plumes in the Great Barrier Reef system, Australia

In this paper, we describe methods to verify the adequacy and accuracy of Lagrangian particles from a Lagrangian model to reproduce the concentrations of a passive tracer from an Eulerian-model in river plumes. The modelling simulates plumes from two major rivers discharging in the Great Barrier Reef (GBR), Australia, under real-world scenarios. The study has been a part of a major project to aid in the protection of the GBR system from the impacts of extreme events and climate change. We employ the Regional Ocean Modelling System (ROMS) activated with its built-in Lagrangian model, and forced with wind fields from global models and recorded river volume discharges. The ROMS-Lagrangian model tracks the Lagrangian particles using the spatially interpolated velocities computed on the Eulerian ROMS three-dimensional (3D) grid. The Lagrangian particles are released in the river in proportion to the measured river volume flux. We apply a novel technique that exploits Voronoi polygon areas to convert Lagrangian particle separation into a concentration field. This facilitates comparison with the passive tracer concentrations driven by the Eulerian velocities computed on the ROMS 3D grid. We evaluate the fate of Lagrangian particles activated on a 4-km grid resolution with those of equivalent Eulerian tracer concentrations. For validation, we compare the Lagrangian particles with the Eulerian passive tracer simulated using a higher model grid resolution of 500-m, and found that the computed Lagrangian particle concentrations showed similar overall patterns compared to the passive tracer concentrations from both the coarse 4-km, and high-resolution 500-m Eulerian models. The spatial extent of the particles was in better agreement with the coarse 4-km model than with the higher resolution 500-m model. The clustering of particles resulted in structures at finer scales than the Eulerian model, over the high particle density areas that compared well against observations. The Lagrangian particles are able to capture the general river plume patterns seen in the satellite MODIS images and the satellite derived Chlorophyll-a. We further compare the online ROMS model with an offline particle tracker, OceanPARCELS and determined the similarity of results from both online and offline methods. Overall, our study demonstrates the viability to use Lagrangian particles to reproduce the Eulerian tracer properties, which can be combined with particle properties include tracer age providing to enhance the guidance on the distribution and concentration of effluent from localised flooding river events.

Numerical Study of the Influence of the Type of Gas on Drag Reduction by Microbubble Injection

In this work, a novel numerical method for studying the influence of gas types on drag reduction by microbubble injection is presented. Aimed at the microbubble drag reduction (MBDR) process for different types of gases, the mass transfer velocity of different types of gases in the gas–liquid phase is defined by writing a user-defined function (UDF), which reflected the influence of gas solubility on the drag reduction rate. An Eulerian multiphase flow model and the Realizable k−ε turbulence model are used for numerical calculation. The population balance model is used to describe the coalescence and breakup phenomena of the microbubble groups. Henry’s theorem is used to calculate the equilibrium concentration of the microbubble mixed flow. The interphase mass transfer rate of the microbubble injection process for different types of gases is studied by using permeation theory. The local mass fraction of the mixed flow is solved by the component transport equation. It is found that the larger the solubility of the gas, the lower the efficiency of MBDR. When the volume flow rate of the same type of gas is the same but the injection speed is different, the larger the solubility of the gas is, the greater the difference in the drag reduction ratio.

Numerical Analysis for Effects of Grid Spacer Vane on Flow-Thermal Characteristics of Two Phase Flow in a 5×5 Rod Bundle

Numerical Analysis for Effects of Grid Spacer Vane on Flow-Thermal Characteristics of Two Phase Flow in a 5×5 Rod Bundle

Thermo-hydraulic analysis of direct steam generation in a 500 m long row of parabolic trough solar collector using Eulerian two-fluid modeling approach

Direct steam generation (DSG) in the parabolic trough solar collectors is a potential alternative for economic and performance improvement of the solar thermal system. This process comprises the preheating, evaporation, and superheating of water/steam in the solar collectors. The modeling and simulation of the evaporation section are challenging because of the complex physics associated with the boiling phase change process. This work describes the Eulerian two-fluid modeling of the once-through mode of the DSG process in solar collectors. The interfacial interactions between phases have been modeled using the appropriate empirical correlations. The experimental data from the Spanish DISS test facility is used to validate the numerical model. Further, the 3-D thermal–hydraulic investigation of DSG in a 500 m long solar collectors' row has been performed for operating pressures of 60 bar and 100 bar; inlet mass flow rates of 0.4 kg/s and 0.6 kg/s; DNI of 750 W/m2 for the solar time at 12:00 h and 13:00 h. It has been observed that the maximum absorber temperature is reduced by 27 % at 60 bar and 20 % at 100 bar operating pressure when the inlet mass flow rate increases from 0.4 kg/s to 0.6 kg/s. Similarly, the maximum circumferential temperature difference reduces by 12 % and 14 %, respectively. Moreover, the fluid temperature, steam quality, absorber temperature distributions, fluid velocity, and pressure loss under the subjected boundary conditions have been summarized.

Impact of Atmospheric Circulation Variability on U.S. Midwest Moisture Sources

Abstract Elevated spring and summer rainfall in the U.S. Midwest is often associated with a strong Great Plains low-level jet (GPLLJ), which transports moist air northward to the region from the Gulf of Mexico. While the intensity of hourly precipitation extremes depends on local moisture availability and vertical velocity, sustained moisture convergence on longer time scales depends on horizontal moisture advection from remote sources. Therefore, the magnitude of moisture convergence in the Midwest depends in part on the humidity in these moisture source regions. Past work has identified the time-mean spatial distribution of moisture sources for the Midwest and studied how this pattern changes in years with anomalous rainfall. Here, using reanalysis products and an Eulerian moisture tracking model, we seek to increase physical understanding of this moisture source variability by linking it to the GPLLJ, which has been studied extensively. We find that on interannual time scales, an anomalously strong GPLLJ is associated with a shift in the distribution of moisture sources from land to ocean, with most of the anomalous moisture transported to—and converged in—the Midwest originating from the Atlantic Ocean. This effect is more pronounced on synoptic time scales, when almost all anomalous moisture transported to the region originates over the ocean. We also show that the observed positive trend in oceanic moisture contribution to the Midwest from 1979 to 2020 is consistent with a strengthening of the GPLLJ over the same period. We conclude by outlining how projected changes in a region’s upstream moisture sources may be useful for understanding changes in local precipitation variability. Significance Statement In this work, we study how the origin of moisture that forms precipitation in the U.S. Midwest covaries with large-scale atmospheric circulation. Our results show that an intensification of the mean winds tends to increase the proportion of total rainfall that originates from the ocean. This analysis may help to constrain future projections of rainfall extremes in the central United States, as projected changes in humidity over the ocean are typically more robust and better understood than those over land.

ASSESSMENT OF MULTIFLUID, EULERIAN INTEGRAL THIN FILM AND DPM APPROACHES FOR THE NUMERICAL SIMULATION OF A BEARING CHAMBER

In this work several computational approaches are tested for the two-phase simulation of the ELUBSYS bearing chamber in the high-speed regime-a four-equation Eulerian multifluid model, a steady-state Eulerian integral thin film (EITF) approach, a discrete parcel method (DPM) approach, and a simplified EITF-DPM coupled approach. While computationally expensive, the multifluid model captured the global liquid dynamics in the chamber and predicted that most of the oil is in the form of a thin film that flows on the stationary walls. The much more cost-efficient EITF approach achieved accurate results for the oil thickness distribution at the counter-current region but did not account for the large amounts of oil flowing out through the top vent. The DPM approach was used to assess the dispersed phase dynamics in both one-way and two-way coupling configurations, outlining a significant influence of the latter on the gas phase dynamics. Finally, the coupled EITFDPM approach was able to overcome some of the limitations observed by its individual counterparts by predicting a continuous film throughout the chamber circumference and a higher vent outflow, while still retaining most of the expected film distribution characteristics in the bearing chamber.

Atomic surface achieved through a novel cross-scale model from macroscale to nanoscale.

Chemical mechanical polishing (CMP) is widely used to achieve an atomic surface globally, yet its cross-scale polishing mechanisms are elusive. Moreover, traditional CMP normally employs toxic and corrosive slurries, resulting in potential pollution to the environment. To overcome these challenges, a novel cross-scale model from the millimeter to nanometer scale is proposed, which was confirmed by a newly developed green CMP process. The developed CMP slurry consisted of hydrogen peroxide, sodium carbonate, sodium hydroxycellulose, and silica. Prior to CMP, fused silica was polished by a ceria slurry. After CMP, the surface roughness (Sa) was 0.126 nm, the material-removal rate was 88.3 nm min-1, and the thickness of the damaged layer was 8.8 nm. The proposed model was built by fibers, through integrating Eulerian and Lagrangian models and reactive force field-molecular dynamics. The results predicted by the model were in good agreement with those of CMP experimentally. A model for large-sized fibers revealed that a direct contact area of 11.12% was obtained for a non-woven polishing pad during the CMP experiments. Another model constructed via combining Eulerian and Lagrangian functions showed that the stress at the intersections of the fibers varied mainly from 0.1 to 0.01 MPa and was higher than the stress at other parts. An increase in viscosity led to a decrease in the areas with low stress, demonstrating that viscosity enhanced the stress and facilitated the removal of material. At the microscale and nanoscale, the stress of the abrasive surface exposed to the workpiece changed from 2.21 to 6.43 GPa. Stress at the interface contributed to the formation of bridging bonds, further promoting the removal of material. With increasing the compressive stress, the material-removal form was transformed from a single atom to molecular chains. The proposed model and developed green CMP offer new insights to understand the cross-scale polishing mechanism, as well as for designing and manufacturing novel polishing slurries, pads, and setups.

Mathematical modeling of the effect of SEN outport shape on the bubble size distribution in a wide slab caster mold

Herein, the effects of outport shapes of the submerged entry nozzle (SEN) on the size distribution of argon bubbles were studied in a wide slab caster mold by the mathematical modeling. The Eulerian–Eulerian model coupled with Multiple-Size-Group (MUSIG) approach were used to solve equations of the two phase flow and polydispersed bubbly flow in the mold, respectively. The effect of the SEN outport angle and shape on the distribution of the molten steel flow, argon gas volume fraction, and argon bubble size were investigated. The outport shapes of the SEN included large rectangular, small rectangular, square, trapezoid, and runway. Results showed that the speed of molten steel increased within the range of 260 mm from the SEN, and decreased within the range of 550 mm from the narrow face with the outport angle of SEN increased from 20° to 45°. The bubble diameter was 5.7 mm at 255 mm distance from the SEN along the mold width at different outport angles. The average speed of molten steel at the outport of SEN decreased from 0.91 to 0.72 m/s with the outport shape changed from small rectangular to runway, trapezoid, square and large rectangular. The average diameter of bubbles was approximate 5.2 mm at the outport for the five types of nozzles, and increased from 3.2 to 3.45 mm inside the mold with the outport shape changed from the runway to square, trapezoid, large rectangular and small rectangular, indicating the rate of bubble breakup was larger with the runway and square SEN casting.

Recent advances in well-posed Eulerian models for polydisperse multiphase flows

The current state-of-the-art for computational modeling of polydisperse multiphase flows is reviewed and future research directions are discussed. Physics-based computational models at three distinct levels of abstraction: the microscale, mesoscale and macroscale; are discussed and compared. Special emphasis is placed on the relationship between the models at different scales and on how information from the finer scales is used to provide closures at the coarser scales. For disperse multiphase flows, it is argued that the passage from a direct-numerical simulation at the microscale to the kinetic description at the mesoscale is the crucial step for ensuring the validity of the macroscale model. In particular, the passage from the microscale to the mesoscale requires physics-based closures, while the passage from the mesoscale to the macroscale requires mathematical closures. The choices made in the physical and mathematical closures of the spatial fluxes and coupling terms will determine whether the Eulerian model is well-posed. In addition, the use of quadrature-based moment methods for polydisperse particles is presented as an efficient macroscale closure when dealing with a distribution of particle sizes. Examples of monodisperse and polydisperse multiphase flows are provided for cases where the fluid phase is compressible (high speed) and incompressible (low speed).

Numerical investigation on the effect of Al2O3-water nanofluid on direct steam generation in parabolic trough collectors

The utilization of solar energy through direct steam generation (DSG) in parabolic trough collectors is a novel approach. In addition, due to higher thermophysical properties, the effect of using nanofluid as the coolant has been the subject of some of the recent studies but the applicability of the nanofluids in DSG process has not been studied before. In this study, the flow boiling of Al2O3 nanofluid at volume fractions 1%, 1.5% and 2%, under uniform and non-uniform heat fluxes has been studied numerically. The Eulerian model was used and non-equilibrium RPI was applied as the boiling model. The validation was done for flow boiling of pure water and Al2O3 nanofluid separately, with the available data in the literature. The results showed that the vapor volume fraction at the outlet is higher under non-uniform heat flux and adding nanoparticles would increase the vapor generation in the tube. Adding nanoparticles to the pure water increased the vapor volume fraction at the outlet up to about 8.64% in respect to pure water under uniform and non-uniform heat fluxes. The average Nu was up to 544% higher under non-uniform heat flux compared to uniform heat flux. Due to the presence of stratified flow, increasing nanofluid concentration reduced the average Nu up to 21.24% and 10.24% under uniform and non-uniform heat flux, respectively.

Study on reactivity characteristic of TDA droplet group with gaseous phosgene for preparing TDI

Toluene diisocyanate stands as a pivotal chemical, predominantly synthesized through the phosgenation reaction between toluene diamine and phosgene. To address the inherent limitations of existing phosgenation methods, we pioneered a novel phosgenation reaction based on flash atomization and confirmed its feasibility with preliminary theoretical calculations. This manuscript delves deeper into the superiority of this method and refines its reaction parameters. By integrating the discrete phase model with the Eulerian model, we studied the reaction dynamics of droplet sprays, exploring the effects of spray velocity, droplet size, phosgene temperature, and particle size distribution on the reaction. Our results highlight that, with a mean droplet diameter of 70 μm and a spray velocity of 40 m/s, an impressive reaction yield of 97.4 % can be achieved. This research enriches our understanding of the gas–liquid two-phase phosgenation method, setting the stage for its future exploration and potential applications in Toluene diisocyanate and other isocyanate industry.

A Review of CO2 Plume Dispersion Modeling for Application to Offshore Carbon Capture and Storage

The exponential increase in greenhouse gas emissions necessitates urgent measures to mitigate climate change impacts. Carbon capture and storage (CCS) has emerged as a promising solution, capturing CO2 from industrial processes and storing it underground. However, CCS implementation poses risks that demand sophisticated modeling. This review focuses on the numerical modeling of CO2 plume dispersion from reservoir leaks during offshore CCS projects, including near- and far-field modeling and the comparison between Lagrangian and Eulerian modeling in particular. Near-field modeling examines CO2 behavior in jet plume, considering depth-related changes. Far-field modeling, employing Eulerian and Lagrangian methods, evaluates dispersion in marine environments. Case studies illustrate the complexity and uniqueness of CO2 dispersion events. The Lagrangian approach emphasizes gas bubble tracking, while the Eulerian approach employs fixed grid systems for detailed hydrodynamic modeling. Both approaches contribute valuable insights, with Eulerian models excelling in site-specific complexities and Lagrangian models offering computational efficiency. A hybrid approach may offer a comprehensive understanding of CO2 dispersion.

An improved version of the piecewise parabolic method advection scheme: description and performance assessment in a bidimensional test case with stiff chemistry in toyCTM v1.0.1

Abstract. This study presents a novel method to estimate the performance of advection schemes in numerical experiments along with a semi-realistic, non-linear, stiff chemical system. This method is based on the examination of the “signature function”, an invariant of the advection equation. Apart from exposing this concept in a particular numerical test case, we show that a new numerical scheme based on a combination of the piecewise parabolic method (PPM) with the flux adjustments of Walcek outperforms both the PPM and the Walcek schemes for inert tracer advection as well as for advection of chemically active species. From a fundamental point of view, we think that our evaluation method, based on the invariance of the signature function under the effect of advection, offers a new way to evaluate objectively the performance of advection schemes in the presence of active chemistry. More immediately, we show that the new PPM + W (“piecewise parabolic method + Walcek”) advection scheme offers chemistry-transport modellers an alternative, high-performance scheme designed for Cartesian-grid Eulerian chemistry-transport models, with improved performance over the classical PPM scheme. The computational cost of PPM + W is not higher than that of PPM. With improved accuracy and controlled computational cost, this new scheme may find applications in other fields such as ocean models or atmospheric circulation models.

Numerical Simulation of Flow and Argon Bubble Distribution in a Continuous Casting Slab Mold under Different Argon Injection Modes

A three-dimensional model is established to investigate the effect of argon injection mode, argon flow rate and casting speed on the gas–liquid two-phase flow behavior inside a slab continuous casting mold. The Eulerian–Eulerian model is employed to simulate the gas–liquid flow, and the population balance model is applied to describe the bubble breakage and coalescence process in the mold. The numerical simulation results of the bubble size distribution are verified using the water model experiment. The results show that the flow field and bubble distribution are similar between the argon injection at the upper submerged entry nozzle (SEN) and tundish upper nozzle (TUN), while the number density is larger for the argon injection of TUN. The coalescence rate of bubbles and the bubble size inside the mold increase with increasing argon flow rate. When the argon flow rate exceeds 4 L/min, the flow pattern of liquid steel changes from double-roll flow to complex flow, with aggravation of the level fluctuation of the top surface near the SEN. When the casting speed increases, the bubble breakup rate increases and results in a decrease in the size of bubbles inside the mold. At a high casting speed, the flow pattern tends to form double-roll flow, and the liquid level at the narrow face of the top surface increases.

Numerical Study of Flow and Heat Transfer Characteristics for Al2O3 Nanofluid in a Double-Pipe Helical Coil Heat Exchanger.

To numerically investigate the flow and heat transfer characteristics of a water/Al2O3 nanofluid in a double-pipe helical coil heat exchanger, we simulated a two-phase Eulerian model to predict the heat transfer coefficient, Nusselt number, and pressure drop at various concentrations (i.e., volume fraction) and under diverse flow rates at the steady state. In this simulation, we used the k-epsilon turbulence model with an enhanced wall treatment method. The performance factor of the nanofluid was evaluated by accounting for the heat transfer and pressure drop characteristics. As a result, the heat transfer was enhanced by increasing the nanofluid concentration. The 1.0 vol.% nanofluid (i.e., the highest concentration) showed a heat transfer coefficient 1.43 times greater than water and a Nusselt number of 1.38 times greater than water. The pressure drop of nanofluids was greater than that of water due to the increased density and viscosity induced using nanoparticles. Based on the relationship between the Nusselt number and pressure drop, the 1.0 vol.% nanofluid was calculated to have a performance factor of 1.4 relative to water, indicating that the enhancement rate in heat transfer performance was greater than that in the pressure drop. In conclusion, the Al2O3 nanofluid shows potential as an enhanced working fluid in diverse heat transfer applications.