Eulerian-Lagrangian Model Research Articles

Performance Analysis of Internal Ballistic Multiphase Flow of Composite Charge Structure

Different charge structures have different interior ballistic performance. Existing research is based on experimental measurements or the lumped parameter method to obtain limited ballistic characteristics, which indirectly impacts the analysis of the parameters’ distribution, requiring a complex modeling solution process. Besides this, the ignition performance of different charge structures needs to be further explored. The disadvantages of previous studies have limited the feasibility of further optimization of the composite charge structure. In this paper, we apply a two-dimensional two-phase flow method based on the Eulerian–Lagrangian model to study the performance of different composite charge structures. First, we establish the mathematical model of different particle types based on interior ballistics, which is directly related to the research foundation of subsequent ballistic performance. Next, we investigate the multi-scale reaction flow of complex charge structures by the two-phase flow method and obtain the distribution of parameters in the chamber. Finally, we conduct a study with different particle charge parameters to explore the sensitivity of ballistic characteristics to structural parameters. The results show that the tubular propellant has good ignition performance in different charge structures, and the ignition consistency can be improved by charging tubular propellant in the center of the chamber. However, more tubular propellants are ineffective at significantly improving ignition performance, and result in a decrease in combustion chamber pressure. These results may be promising for the optimization of various charge structures.

Significance of recirculating micro-bubbles in oxygenation from poly-dispersed plumes

Poly-disperse bubble plumes are simulated to explore the effect of interactions between multiple bubbles of varying sizes on the liquid flow, plume dynamics, and oxygen transfer in aeration processes. An Eulerian-Lagrangian model based on the multiphase particle-in-cell method (MPPIC) implemented in OpenFOAMTM has been extended to account for bubbly flow. Bubbles have been approximated as spherical particles whose diameters change in response to pressure and nitrogen and oxygen mass dissolution and transfer. The mass transfer model relies on a Sherwood number correlation which accounts for the individual bubble size and relative velocity and is parameterized against the liquid phase temperature. A Large Eddy Simulation (LES) approach based on a transport equation for the turbulent kinetic energy has been adopted to model the effect of the sub-grid scales (SGS) of turbulence on the liquid flow and bubble motion. The bubble injection is defined in terms of the air mass transfer and the bubble size distribution. The model has been compared against experimental measurements of the evolution in oxygen concentration in a 1m deep water tank in response to bubble plumes generated from a porous ceramic plates at two different flow rates. The interaction between milli- and micro-bubbles over a wide range of sizes has been shown to create significant differences in the aeration process. A method to correct for bubble recirculation has been proposed and allows for good agreement between measured and simulated volumetric transfer rates. The simulation has shown the important role that the interplay between bubble sizes takes in determining the oxygen transfer efficiency. Larger standard deviations from Gaussian bubble size distributions have been shown in particular to reduce recirculation from smaller bubbles thereby reducing the aeration efficiency at an equivalent flow rate. An analysis of the age distribution by bubble size plumes suggest that the largest bubble have an important role in increasing the entrainment of smaller bubbles limiting their recirculation and reducing their retention time.

Effect of Indoor Condition with Cross Ventilation on Deposition of Airborne Droplets Emitted from Human Cough

Prediction of airborne transmission in different environmental condition remains as the research challenge in the field. This has motivated the present study to obtain the direct impact of flow field to the physical nature of transmission. ANSYS Fluent 2022 R1 software is utilised in this research to numerically investigate and visualize flow pattern in a closed environment with cross ventilation and its effect to the emitted droplets deposition. The effect of different indoor parameters towards airborne transmission are investigated, which include wind velocity, air relative humidity (RH), and exposure time after emission. Simulation result revealed increasing wind velocity according to Beaufort wind scale of 1.0 to 3.9 m/s, increases transmission rate due to enhanced convection effect. Surrounding air with higher RH leads to a larger mean diameter of particles due to hygroscopic growth effect, while evaporation effect dominates in lower air RH, leading to particle shrinkage. In a light wind breeze, droplet mass of 5.15 mg deposited on receiver body within 0.5 s of transmission when RH is 40%, while only 3.29 mg droplets reached receiver in RH of 99.5%. Droplet particles settle on the floor within 1.50 s revealed 0.66 mg deposited mass in higher RH, while 0.26 mg of droplets deposited in lower RH. Deposition at transmitter body is possible due to recirculation effect of incoming wind generated between transmitter and receiver, leading to 3.7 times higher deposited mass in lower RH as compared to in higher RH. This research highlights application of Euler-Lagrange model to represent the trajectory of cough droplets influenced by indoor condition with horizontal wind, in the effort to strengthen safety and health judgement in the event of a pandemic.

Comparison of Homogenous and Buongiorno’ Model with Eulerian-Lagrangian Model for Nanofluids Heat Transfer in a Microchannel

Comparison of Homogenous and Buongiorno’ Model with Eulerian-Lagrangian Model for Nanofluids Heat Transfer in a Microchannel

Modeling of radiation heat transfer in dense-bed flows of solids in indirectly heated rotary kilns

• modification and implementation of a DOM-radiation model which combines all required physical submodels to simulate heat radiation to dense beds of particles. • Full time and space resolved simulation of thermal conversion of wet moving bulk in a large-scale rotary kiln reactor. • Analytical validation of model and justification with laboratory-scale experiments. • Efficiency optimization of the numerical solver for industrial-scale and long-time simulations on parallel supercomputers. • Parameter studies for large-scale reactors to investigate conversion rate and product quality. This work presents further development and validation of the Discrete Ordinates Model for thermal radiation implemented in OpenFOAM® for application to packed beds of particles. The radiation model is an important part of a more comprehensive model for simulating the thermochemical conversion of the discrete phase (here for instance wet biomass particles). The comprehensive Eulerian-Lagrangian model is part of a three-dimensional, time-resolved simulation of the essential chemical and physical processes occurring within and in-between particles in a moving bed. For the thermal treatment of solid particles, convective and radiative heat transfer couple the energy exchange between the reactor wall, gas- and disperse phase. The original implementation of the finite volume Discrete Ordinate Model (fvDOM) present in OpenFOAM® is valid for a dilute particulate phase and neglects the effect of local opacity due to the existence of individual particles. In the present application, a dense-packed bed of the particulate phase exists in the reactor and, therefore, this direction-based radiation model is adjusted for a computational cell with arbitrary particle volume fractions. To validate the results with the present thermal radiation model, a simple test case is first presented, where a bed of particles is heated from the top of the computational domain. A second test case relates to an experimentally investigated laboratory-scale reactor. The results of the improved fvDOM are compared to the original implementation in OpenFOAM® and the more simple and computationally cheap P-1 radiation model. In the presence of a packed bed, the P-1 model largely overpredicts the radiative heat transfer while the original fvDOM underpredicts the heat flux by about 15 % for the first test case. The new improved model delivers results within 1% deviation at the expense of maximum of 10 % increase in the computational time. Large-scale parallel simulations of real setups are crucial tools to predict the efficiency of a process and improve the operational parameters. To achieve the pre-defined product quality at minimum cost, an example of the implemented radiation model in thermochemical conversion of wet biomass in a rotary drum is been given and the importance of the radiation heat transport to the bulk is highlighted.

Numerical Study and Experimental Verification of Biomass Conversion and Potassium Release in a 140 kW Entrained Flow Gasifier.

In this study, a Eulerian-Lagrangian model is used to study biomass gasification and release of potassium species in a 140 kW atmospheric entrained flow gasifier (EFG). Experimental measurements of water concentration and temperature inside the reactor, together with the gas composition at the gasifier outlet, are used to validate the model. For the first time, a detailed K-release model is used to predict the concentrations of gas-phase K species inside the gasifier, and the results are compared with experimental measurements from an optical port in the EFG. The prediction errors for atomic potassium (K), potassium chloride (KCl), potassium hydroxide (KOH), and total potassium are 1.4%, 9.8%, 5.5%, and 5.7%, respectively, which are within the uncertainty limits of the measurements. The numerical model is used to identify and study the main phenomena that occur in different zones of the gasifier. Five zones are identified in which drying, pyrolysis, combustion, recirculation, and gasification are active. The model was then used to study the transformation and release of different K species from biomass particles. It was found that, for the forest residue fuel that was used in the present study, the organic part of K is released at the shortest residence time, followed by the release of inorganic K at higher residence times. The release of inorganic salts starts by evaporation of KCl and continues by dissociation of K2CO3 and K2SO4, which forms gas-phase KOH. The major fraction of K is released around the combustion zone (around 0.7-1.3 m downstream of the inlet) due to the high H2O concentration and temperature. These conditions lead to rapid dissociation of K2CO3 and K2SO4, which increases the total K concentration from 336 to 510 ppm in the combustion zone. The dissociation of the inorganic salts and KOH formation continues in the gasification zone at a lower rate; hence, the total K concentration slowly increases from 510 ppm at 1.3 m to 561 ppm at the outlet.

Numerical Investigation of the Effect of Supersonic Air Temperature on the Mixing Characteristics of Liquid Fuel

The effect of supersonic air temperature on the mixing characteristics of liquid hydrocarbon fuel injected into three different supersonic airflows elevated in three steps from 373 K to 673 K was investigated numerically. Compressible Reynolds-averaged Navier–Stokes (RANS) equations were solved together with species conservation equation using ANSYS Fluent for two-phase flow simulations including fuel droplet breakup and evaporation. The turbulence model needed to close the RANS equations used the Shear Stress Transport (SST) k-ω model. The Eulerian–Lagrangian model was employed to track fuel droplets in mainstream air, and the Kelvin–Helmholtz and Rayleigh–Taylor (KH-RT) models were used to simulate the droplet breakup process. Numerical solutions were validated using experimental data. The higher the air temperature, the stronger the streamwise vortices downstream of the pylon. When the air temperature was 373 K, the liquid fuel hardly evaporated, but as the air temperature increased, and the mass fraction of the vaporized fuel and the mixing efficiency increased linearly downstream of the pylon. At air temperatures of 523 K and 673 K, the mixing efficiencies were 10% and 51% at the combustor outlet, respectively. The total pressure loss decreased slightly due to droplet evaporation as the temperature increased from 373 K to 673 K.

Numerical investigation of how gap size influences tip leakage vortex cavitation inception using a Eulerian–Lagrangian method

This paper investigates the effect of gap size on the inception of tip leakage vortex cavitation (TLVC) with a hybrid Eulerian–Lagrangian model. Good agreement is achieved between the simulation results and experimental data for velocity distributions around the TLV, bubble motion, and its size oscillations. It is found that the minimum pressure criterion is not accurate enough for the prediction of TLVC inception due to the significant effect of pressure fluctuation and increased concentration of nuclei in the TLV core region. The pressure fluctuation in the TLV core is noted to be a non-negligible factor, while the corresponding effect on nuclei dynamics in the TLV core is still unclear. To deal with this problem, the inducement of this excited turbulence is further analyzed and discussed in detail, which shows a close relationship with the TLV instability raised by the vortical interaction between TLV and tip-separation vortex/induced vortex. Our work provides an insight into the mechanism of TLVC inception through the flow characteristics in the TLV core region, which is helpful for controlling TLVC inception in engineering designs.

A Three-Phase Eulerian-Lagrangian Model for Activated Sludge Treatment

A Three-Phase Eulerian-Lagrangian Model for Activated Sludge Treatment

Coupled Eulerian-Lagrangian Debris Flow Model with Flexible Barrier

Natural hazards such as large debris flow events can have catastrophic effects on the environment and critical infrastructure, posing a significant threat to human life. Debris flows often exhibit high velocity, high-pressure discharges due to their bulk volume, and the capacity to transport considerable volumes of large rocks, boulders, and woody debris. Although debris flow run-out simulations are commonly performed using hydraulic modelling software, these environments are seldom capable of assessing the interaction between the debris fluid, transported material, and protective structures. In this research, large deformation numerical models are calibrated using input parameters from hydraulic modelling software. Due to the computational cost of the large deformation models involving fluid-solid-structure simulation with flexible net barriers, an equivalent stiffness method is implemented to provide comparable performance through a membrane structure. The Coupled Eulerian-Lagrangian Finite Element method is used to model the impact forces of rocky boulders on the membrane, exhibiting damage characteristics consistent with flexible ring-net protective structures. The Coupled Eulerian-Lagrangian model results highlight the performance of the simplified membrane, as shown through a benchmark simulation of debris flow with boulders.

Effect of Particle Diameter on Primary Breakup of High-Pressure Diesel Spray Atomization: A Study Based on Numerical Simulations Using the Eulerian–Lagrangian Model

The coupling of Eulerian and Lagrangian methods in the Eulerian–Lagrangian Spray Atomization (ELSA) approach is critical. This study proposes an equation for the primary breakup particle diameter D of a diesel fuel spray and adopts it as a key transition criterion for coupling. A three-dimensional diesel spray is modeled by the large-eddy simulation (LES) approach. This improved ELSA simulation was conducted using various transition criteria for particle diameter Dcr. The results show that fuel spray experiences two stages: stage I, when a liquid column appears without a dispersed phase, and stage II, when primary breakup occurs with many discrete particles. Although Dcr has little influence on the macro-spray characteristics, such as top penetration distance S and spray cone angle θ, it has significant effects on discrete particles, such as their number, average diameter, distribution and location, and spray cone area. Dcr should be determined on the basis of actual operating conditions.

Eulerian–Lagrangian modeling of deflagration to detonation transition in n-decane/oxygen/nitrogen mixtures

In this work, to promote deflagration to detonation transition (DDT), a designed hot jet in a pre-detonator is produced to initiate detonations in the main detonation tube. We perform two-dimensional simulations of the DDT process for low-volatile fuel (n-decane) mixed with nitrogen and oxygen based on the Eulerian–Lagrangian approach. The effects of fuel atomization, vaporization, and shock focusing on the flame acceleration and DDT are discussed under different nitrogen dilution ratio and droplet size conditions. The results show that the flame acceleration process can be divided into slow and fast deflagration stages. Additionally, initiation times are mainly determined by the fuel atomization and evaporation in the slow deflagration stage, which dominates the entire DDT time. Furthermore, there are different intensities of hot jets rather than stable detonation waves formed at the pre-detonator exit. Moreover, local decoupling and re-initiation events are detected near the internal wall of the U-bend, inducing the overdriven detonation decaying into stable detonation waves in the smooth tube. The results also demonstrate that the detonation pressure and velocity decrease by 13.56% and 12.55%, respectively, as the nitrogen dilution ratio increases from 0.5 to 2. In particular, as the nitrogen dilution ratio continued to increase to 2.25, the development in DDT is similar, but the jet intensity is significantly weakened. While as the droplet size increases from 10 to 40 μm, the detonation pressure and velocity decrease only by 2.69% and 1.49%, respectively.

A preliminary computational analysis towards the use of Electrically Heated Mixing Catalyst for innovative SCR after-treatment systems

This work aims at investigating the possible advantages of substituting the mixer in traditional SCR systems with an Electrically Heated Catalytic structure (EHC). First of all, EHC technology is being widely investigated in literature because it offers a concrete solution for catalyst thermal activation and film formation reduction in engine cold start conditions; however, its adoption as a mixer can also guarantee other important improvements in reducing pollutant emissions. In this work, a low-pressure injection of Ad-Blue impacts an electrically heated structure and a complete analysis of liquid droplets and film evaporation is carried out. A hybrid Eulerian-Lagrangian model has been adopted on a multi-region configuration, accounting for fluid-solid conjugate heat transfer (CHT), which plays a key role in the conversion strategy: it has been demonstrated that the heated structure can be exploited to significantly increase the exhaust gas enthalpy in the cold start, which represents an important improvement for pollutant conversion. Different heating strategies are analysed, with the objective of maximising the spray evaporation and the uniformity of the ammonia distribution downstream of the mixer. The objectives of this work are emphasizing the improvements that an electrically heated mixing catalyst can bring to the traditional SCR configuration, laying the foundation for other following studies.

A Hybrid Euler–Lagrange Model for the Paint Atomization Process of Air Spraying

The modeling of the paint atomization process is a barrier in computational fluid dynamics numerical simulation for the whole process of air spraying, and seriously restricts robot intelligent spray gun trajectory planning and the improvement of coating quality. Consequently, a multi-scale paint atomization model based on the hybrid Euler–Lagrange method was established in this paper, which included a large liquid micelle motion model, a particle motion model, and a turbulence flow model. The Euler method was adopted to capture the gas–liquid interface in the atomization flow field to describe the deformation and motion of large liquid micelles. The identification and transformation mechanisms of large liquid micelles and small particles were constructed by the particle motion model, and the motion of small droplets generated by paint atomization was tracked by the Lagrange method. The turbulence motion of the fluid in the process of paint atomization was described by a two-equation turbulence model. The model calculation method consisting of a finite-volume model, an adaptive hexcore mesh technique and a pressure-based coupled algorithm was established. The multi-scale atomization model was solved and model validation was carried out, which included mesh independence verification and model reliability analysis. The numerical simulation results predicted the atomization flow field parameters, paint atomization shapes, and the changing process from paint to liquid droplets, which was consistent with the experimental data. As a result, the established multi-scale atomization model in this paper is reliable for studying the paint atomization process of air spraying.

Numerical analysis of the Gas − Solid heat transfer characteristics of a lightly calcined MgO Fluidized-bed roaster

The fluidized bed roaster is a novel energy-efficient calcination device for lightly calcined magnesia production. However, the gas − solid heat transfer process in the roaster, the key which can significantly impact energy consumption and product quality, has not an in-depth study yet. In the present work, for the determination of the optimal operating parameters of the roaster, the Euler-Lagrange model of ANSYS Fluent software was employed to simulate the influence of inlet temperature and flow rate of flue gas and feed amount of magnesite on the temperature distribution, production capacity and decomposition rate. The results show that the specific energy consumption is reduced by approximately 6.45 % under the optimal operating conditions with production capacity of 5 × 104 t/a. Furthermore, the maximum production capacity reaches 5.5 × 104 t/a with 9.2 % reduction of specific energy consumption when the feed amount, flue gas flow rate and flue gas temperature are optimized as 14.5 t/h, 21,000 Nm3/h and 1660 K, respectively.

Numerical simulation of co-combustion of pulverized coal and biomass in TTF precalciner

A 3D Eulerian-Lagrangian model using MP-PIC method is developed to study the co-combustion of pulverized coal and biomass in a TTF precalciner. The results show that there are three spraying effects and five recirculation zones formed near the raw meal inlet in the precalciner. The highest temperature can reach up to 1600 K in the main combustion zone and the decomposition rate of raw meal can reach 93.9 % with no biomass input. In addition, with the increase of biomass blending ratio, the average temperature, the decomposition rate of raw meal and NOx emissions in the precalciner show a downward trend. When the biomass input is 40 %, the concentration of NO at the outlet decreased to 302 ppm. However, on the premise of ensuring that the decomposition rate of cement raw meal is not less than 85 %, the biomass blending ratio of 30 % may be the best choice.

A multi-material ALE model for investigating impact dynamics of pile-soil systems

The dynamic pile-soil interaction is one of the most important and challenging problem in geomechanics, especially when geometrical, material-related, and dynamic contact-related nonlinearities exist. Geometrical nonlinearity is a fundamental obstacle to the popular Lagrangian finite element methods (FEM) that have been utilized in other areas of geomechanics research. This paper introduces a Multi-Material Arbitrary Lagrangian-Eulerian (MM-ALE) model for predicting the pile-soil interaction and forces during lateral dynamic impact events. The study used the MM-ALE method in conjunction with an elasto-viscoplastic soil material model that included strain softening and an elasto-plastic steel material model that incorporated strain rate effects to examine pile response during lateral vehicle impacts. The model was validated using large-scale, dynamic impact test data for piles embedded in soil, thus confirming its capability to simulate the complex dynamic impact pile-soil interaction. The effects of impact velocity, embedment depth, and soil strength on impact forces, energy dissipation, and impulse response of a pile-soil system were subsequently investigated. It was determined that average impact force, Favg, and impact velocity, are proportional to one another as Favg∝v2 regardless of pile embedment depth. This relationship provides evidence for the existence of inertial or hydrodynamic drag forces in the pile-soil system during lateral impacts similar to a solid object passing through a fluid.

Analysis of SWCNT-water nanofluid flow in wavy channel under turbulent pulsating conditions: Investigation of homogeneous and discrete phase models

Improving thermal performance in heated channels has received much attention from many researchers due to its presence in various thermal systems. The present research numerically illustrated the effect of turbulent pulsating flow and SWCNT-water nanofluids in sinusoidal wavy channel on hydrothermal characteristics and entropy production. This study aims to provide a new thermal management approach for compact heat exchangers. Two various models for describing the motion of nanoparticles in a base fluid are applied. These models are Homogeneous single-phase, SPM and Lagrangian-Eulerian model (or discrete phase model), DPM. Governing equations are computationally solved utilizing the finite volume technique. This simulation covers Reynolds number, pulsation frequency, phase shift and nanoparticles concentration in the range of (4000 ≤ Re ≤ 7000), (1 ≤ f ≤ 5), (0° ≤ θ ≤ 180°) and (0% ≤ φ ≤ 3%), respectively. CFD simulations show that the pulsation frequency, f and phase shift, θ have a significant role in improving the heat transfer ratio and controlling the entropy generation through the wavy channel. Finally, it is recommended to use SWCNT/water nanofluid with a high-volume fraction (φ = 3%) as a working fluid in the considered channel due to its high heat transfer ratio and low thermal irreversibility.

An implicit Eulerian–Lagrangian model for flow-net interaction using immersed boundary method in OpenFOAM

In this paper, we propose an implicit Eulerian–Lagrangian model to resolve the fluid–structure interaction of submerged nets. The Reynolds-averaged Navier–Stokes equations are solved on an Eulerian grid using OpenFOAM and the geometry of the flexible net structures is tracked using Lagrangian points. The motion and deformation of the flexible net structures are advanced using an implicit scheme to avoid excessively small time intervals. The force acting on the net structures is calculated based on a mass–spring system. The screen model and the immersed boundary method are implemented to capture the interaction between the net structures and the surrounding fluid. We present a new drag coefficient formulation as based on a piecewise function for different net solidities to obtain a much improved drag force prediction. The numerical results are compared with a series of existing experiments showing excellent agreement and improved drag force predictions.

Compressibility and Rarefaction Effects on Particle Dynamics and Heat Transfer in Aerosol Deposition Process

The aerosol deposition (AD) method is an emerging coating technique to create a dense ceramic or metal layer on a substrate through the kinetic impaction and cumulative deposition of ultrafine solid particles under near-vacuum conditions. Prediction of the particles’ impact velocity and temperature during the AD process is crucial in enhancing the coating quality. In the present work, a two-way coupled Eulerian-Lagrangian model is developed for an AD system equipped with a converging-barrel nozzle to simulate the supersonic gas flow, particle in-flight behavior, as well as particle conditions upon impact on a flat substrate. The focus of the current study is to understand the effects of compressibility and rarefaction on particle velocity and temperature during the AD process. The effects of compressibility and rarefaction can be assessed using the Mach and Knudsen numbers. Therefore, different models for the drag coefficient and the heat transfer coefficient that take into account the Knudsen, Mach, and Reynolds number effects are implemented into the computational fluid dynamics (CFD) models. The results show that compressibility and rarefaction have significant influence on the particle temperature and velocity. As the particle size reduces, the effects of compressibility and rarefaction become more important.