Eulerian-Lagrangian Method Research Articles

Comparison of different discontinuous Galerkin methods based on various reformulations for gKdV equation: Soliton dynamics and blowup

In this work, we explore the use of several discontinuous Galerkin (DG) methods for simulating soliton dynamics in the generalized Korteweg-de Vries (gKdV) equation. The presence of high-order nonlinearity in this model can lead to the finite-time blowup phenomenon, which challenges every aspect of a numerical scheme. The considered DG schemes encompass popular methods derived from the energy and/or Hamiltonian conservations of the gKdV equation. To evaluate the performance of these DG schemes from various angles, we present a series of numerical experiments. Through comprehensive comparisons, we aim to identify the scheme that exhibits the best performance. To further enhance the accuracy and efficiency of DG methods, particularly in the context of blowup simulations, we incorporate the arbitrary Lagrangian-Eulerian method for adaptive mesh movement.

Numerical Study on Simulating the Deposition Process of Cold Spray Multi-Particle Al-6061 based on CEL Method

Cold spray is a solid-state deposition technique that improves the performance of part surfaces. Most scholars use the CEL framework to simulate the deposition of single particles on the substrate; Single particle depositions cannot fully characterize coating conditions. This article proposes to use the CEL method to simulate the deposition process of cold spray multi-particles on the Al6061 substrate. A multi-particle wrapped model is nested in a deposition model created by CEL to simulate the cold spray multi-particle deposition process. The Euler-Lagrangian method has the characteristics of high accuracy and robustness, and was selected as the method for multi-particle deposition model simulation; The CEL framework is a feasible method to simulate the actual cold spray multi-particle deposition process. The results show that the CEL framework can simulate the deposition of cold sprayed Al6061 multi-particles on the Al6061 substrate, observe the EVF Void value of the coating, and monitor the porosity of the coating after deposition. It is observed that the maximum substrate surface temperature after deposition is 528.2K and is located at the junction of particle and particle impact; By analyzing the temperature change curve of five points collected on the substrate over time, the curve appears multiple inflection points, indicating that heat transfer occurs between the particles and the substrate during the deposition process; the substrate first heats up and then cools down. During the multi-deposition process, the particles undergo plastic deformation and continuously squeeze the coating, thereby achieving interconnection between the particles and the substrate; Mechanical interlocking between particles forms a coating.

A numerical research on transient transport of high-temperature particles associated with air gouging process

The high-temperature particles produced by air gouging processes are common pollutants in cleaning workshops, which could endanger workers’ health. In this research, a two-way coupled Eulerian-Lagrangian method based on discrete phase modelling (DPM) was used to investigate the transport characteristics of high-temperature particles generated from air gouging processes. The particle group in the movement was divided into core zone and boundary zone, and the kinetic mechanism of particles in different zones was analysed. The results show particles in the boundary zone are more susceptible to the vortex entrainment effect than particles in the core zone, and some particles could be moved from the vortex diffusion zone to the vortex recirculation zone. The smaller the particle size, the better the followability to the hot airflow. The slower the temperature decay of particles, the more significant the thermophoresis effect, which could enhance the diffusion behaviour of the small particles. By analysing the average residence time of particles in the breathing zone, the influence of different factors on the average vertical diffusion height [Formula: see text] of particles is summarized, and a nonlinear regression prediction model of [Formula: see text] is established. The results can contribute to health risk assessment and industrial ventilation design.

Corrosion deposition in deforming anodes of in-ground cathodic protection systems: A three-dimensional transient study

Cathodic protection as a complementary technique is widely considered in the industry along with the selection of suitable materials as well as efficient coating considerations. In cathodic protection (CP), anode produces a current output to protect the structure (cathode) and part of the current output is wasted by the grounding system. We developed a 3D, and time-dependent numerical model to simulate the anode corrosion (using arbitrary Lagrangian-Eulerian method), find the deposit formation (by interface tracking level set method), anode mass loss and current wasted by the grounding system. We also defined a CP efficiency as anode mass loss times the current percentage received by the structure. The CP efficiency can be utilized for anode quantity and placement pattern. The results showed when the conductivity of corrosion products (deposit) is lower than that of soil, the current output from the anode decreases over time. When the deposit conductivity is higher than that of soil, the current output from the anode increases in time, reaches a peak, then decreases. This is due to the competition among three factors: anode surface increase, medium conductivity change, and inhibition effect of the deposition layer. For the studied case, almost 54% of the current from the anode is wasted by the grounding system. To illustrate the significance of CP efficiency, this study compares three alternative anode configurations with the original design. It is observed that for a 14.5 kg anode, burying the anodes 2 m deeper enhances the mean potential distribution on the structure by 4%. Additionally, the configuration featuring the 7.7 kg anode, owing to its superior dimensional design, demonstrates improved performance compared to other configurations.

Determination of the overconsolidation ratio and undrained shear strength of cohesive soils by CPTu measurement

Estimations of the undrained shear strength (Su) and overconsolition ratio (OCR) of cohesive soil are essential for the evaluation of geology investigation. In comparison to time-consuming laboratory tests, the field piezocone penetration test (CPTu) can rapidly evaluate these parameters. However, existing studies have mainly relied on empirical correlations to estimate the undrained shear strength Su and OCR from CPTu measurements. These correlations are mainly empirical, involving fixed coefficients multiplied by CPTu measurement. Based on the coupled Eulerian-Lagrangian method, this study employed large deformation finite element modeling to summarize and extend the relationships between CPTu measurement and the estimation of undrained shear strength Su and OCR in cohesive soils. These relationships allow for predictions based on CPTu measurements without the requirement for laboratory calibration or referencing to field benchmarks. The accuracy and applicability of the proposed prediction formulas are validated through field case studies for comparative analysis.

Failure analysis of underground concrete silo under near-field soil explosion

The underground concrete silo is commonly constructed severing as vertical transport passages in mining and emergency exits for buried structures like tunnels, which, however, is possible to encounter accidental or intentional soil explosions (e.g., blasting excavation). The purpose of this study is to reveal the failure mode and mechanism of an underground concrete silo (46 m in height) subjected to a near-field soil explosion. The Coupled Lagrangian-Eulerian (CEL) method, along with two well-developed material models respectively for soil and concrete, is employed to handle the violent interactions between the exploded soil and the concrete silo. The numerical framework is first validated by simulations of a soil explosion beneath a concrete slab, where the predicted crack patterns of the concrete slab accord well with the experimental results. Subsequently, comprehensive numerical simulations are conducted to investigate the failure of the concrete silo under various soil explosion scenarios. The results indicate that the concrete silo experiences successively or simultaneously tensile spalling failure, local compression-induced tensile failure, and bending-induced tensile failure, with one or two predominating. The prevailing failure mode of the concrete silo is highly dependent on the intensity of the shock wave and the loading area. Further investigations expose that with the scaled distance increasing from 0.12 to 0.4 m/kg1/3, the dominant failure mode of the concrete silo transforms from local compression-induced tensile failure to overall bending-induced tensile failure. The critical scaled distance is 0.2 m/kg1/3. Regardless of the dominant failure mode, three-dimensional fracture planes that split the silo structure are generated. Besides, the tensile spalling failure, arising from the reflected tensile stress wave, is severe on the internal surface of the silo structure, consequently, fragments with velocities up to 12 m/s are produced, posing potential risks to humans and facilities inside the silo if any. This is the first time, to the authors’ knowledge, the failure of the prototype of a large-scale underground concrete silo arising from a large-yield and near-field soil explosion has been investigated. The finding can benefit the research community and provide a reference for the protection of the underground concrete silo as well as the facilities inside it to withstand soil explosions.

Numerical simulation of the optimization for the inlet structure of the furnace in the Phosphogypsum reduction process by sulfur vapor

Amidst the backdrop of carbon peaking and the pursuit of carbon neutrality targets, the co-production of sulfuric acid and cement from phosphogypsum through sulfur reduction in a dilute phase suspended gas system has emerged as the focal point in recent research, aiming to harness the high-value potential of solid waste phosphogypsum. This paper employs a combination of numerical simulation and pilot testing to optimize the material inlet structure of the core equipment, the reduction furnace, ensuring it aligns with the requisite phosphogypsum decomposition rate in practical production settings. Utilizing the Euler-Lagrange method, the study examines gas-solid two-phase flow and chemical reactions within the reduction furnace across various inlet structures. Coupling this with the Box-Behnken Design (BBD) in Response Surface Methodology (RSM) highlighted pivotal factors influencing calcium sulfate decomposition, ranking them as B > A > AC > AB>C > BC. Ultimately, the regression equation estimation forecasts a composite of material inlet structural parameters—A (Material Inlet Height) = 2352.12 mm, B (Material Inlet Diameter) = 315.89 mm, and C (Material Inlet Angle) = 30.59°—corresponding to a 23% calcium sulfate decomposition rate, exhibiting merely a 4.62% deviation from the numerical simulation's calculated rate of 23.98% under similar conditions.

Correction: Rapid multi-material joining via flow drill screw process: experiment and FE analysis using the coupled Eulerian‒Lagrangian method

Correction: Rapid multi-material joining via flow drill screw process: experiment and FE analysis using the coupled Eulerian‒Lagrangian method

Numerical study of snow accumulation on bogies for long marshalling high-speed trains

Current numerical research on snow accumulation on bogies often simplifies train models as 1.5 cars or 3 cars, and there is less research on long marshalling trains with real bogies. In this article, based on the Euler–Lagrange method, the airflow structure and snow accumulation characteristics in the bogie area of an 8-car high-speed train (HST) are studied by numerical simulation. The results show that the airflow velocity and snow distribution concentration inside the bogie cabin vary along the flow direction. The downstream bogie cabin has a lower airflow speed, spatial snow particle concentration, and components snow accumulation. Because of the bogie cabin cover structure, the main airflow direction above the first and second bogie cabin is different, resulting in higher snow concentration and range on the windward side of the first bogie. There is a significant difference in snow accumulation characteristics between powered and nonpowered bogies. The powered bogie gearbox is directly affected by the airflow carrying snow particles, leading to severe snow accumulation on the windward side. This study provides a research foundation and engineering guidance for the snow protection strategy of HST bogies and is important for improving the comfort and safety of HSTs on snow-covered rails.

Effect of Loading Pressure on Tribological Properties for Valve Plate Pair during the Running-In Process

The friction and wear performance of the valve plate pair significantly affects the service life and reliability of axial piston pumps. Loading pressure during the running-in process is crucial to its contact characteristics, friction coefficient, running-in time, wear rate, etc. In this article, mixed lubrication modeling and analysis of the effects of loading pressure on tribological performance for valve plate pair were conducted. A finite element model was established using fractal theory and a coupled Euler-Lagrange method. Ring-on-block tests were conducted to simulate the movement and tribological properties of the valve plate pair during the running-in process. Running-in tests of the axial piston pump were carried out to detect the valve plate’s wear. Results show that the effect of increased loading pressure on the maximum contact pressure decreases gradually. The increased loading pressure can shorten the running-in time without increasing the friction coefficient. The wear mechanisms are abrasive wear and adhesive wear during the running-in process. This study provides a reference for the running-in test of axial piston pumps.

Simulating multi-particle deposition based on CEL method: studing the effects of particle and substrate temperature on deposition

The subject matter of this study is to use numerical simulation methods to study the influence of the temperature of particles and substrates on the post-deposition coating during the multi-particle deposition process of cold spray. The goal is to study the temperature of Al6061 particles and the temperature of the substrate, which are factors that have a greater impact on the deposited coating, and to observe the shape of the coating and the temperature distribution of the cross-section of the substrate after deposition. The tasks to be solved are as follows: use Python scripts to model multi-particles, generate and randomly assign positions according to particle size distribution in the Euler domain, and establish a cold spray multi-particle collision model to simulate the process of cold spray deposition. The following methods were used: The influence of temperature and substrate temperature on the deposited coating was studied through a single variable method; the Coupled Eulerian Lagrangian (CEL) method was used to simulate the collision process of cold-sprayed Al6061 multi-particles. The following results were obtained: changing the temperature of Al6061 particles has a more obvious control effect on the porosity of the deposited coating; after particles of different temperatures impact the constant-temperature substrate, the high-temperature area on the surface of the substrate is mainly located at the junction of pits; after the particle temperature reaches 650K, the coating changes after deposition are no longer significant, indicating an optimal temperature range for Al6061 particle deposition; increasing the temperature of the substrate can increase the depth of particle deposition on the substrate; at the same time, it serves as a reference basis for further using the CEL method to predict the porosity of the Al6061 coating. Conclusions. The scientific novelty of the results obtained is as follows: 1) powder preheating can effectively reduce the porosity of Al6061 coating; 2) the CEL method has good robustness and is used to simulate cold spray multi-particle deposition to monitor the porosity of the coating, which cannot be achieved by the SPH and ALE methods.

Introducing an efficient capped fluidized bed and quantifying its flow and heat transfer performance

Fluid-solid particle beds have a very wide range of industrial applications but there are few publications relating to a general method to quantify solid particle bed performance for a comparative efficiency study. The conventional approach of characterizing bed efficiency involves bubble sizes, bubble frequency, byproduct quantity for bed reactors, and pressure drop for minimum fluidization. However, different solid particle beds have different states with varying flow rates, which makes the comparative study more difficult to achieve. In this work, a common approach to measure solid particle bed efficiency in terms of heat transfer is presented. The two cases considered here are 1) When work is done by the particles such as in a catalytic reactor, and 2) When work is done on the particles such as in cooling/drying of particles. In addition to the packed bed and fluidized bed, a solid particle bed called a capped fluidized bed is introduced. The Eulerian–Lagrangian method, also known as CFD-DEM simulation, is adopted for this analysis. Numerical simulations show potentially significant advantages of capped beds over packed and fluidized beds under certain fluidization states. Capped fluidized bed pressure drop is comparatively lower than that for a packed bed and similar to a fluidized bed, which allows it to operate at a wider range of flow states. Current fluidized bed performance is limited by the entrainment and possible loss of particles at high flow rates. However, the capped fluidized bed restricts the particles from leaving the bed and thus permits higher flow rate operation. Further experimental research is required to more completely characterize this type of solid particle bed.

Nonlinear dynamic morphing of conical bistable dielectric elastomer actuator

The bistable dielectric elastomer actuator (BDEA) possesses two stable positions which offers notable advantages of stable-state self-maintenance, fast response, and threshold snap-through characteristic in comparison with conventional dielectric elastomers. However, the strong nonlinearity induced by the coupling among materials, structure, and electrostatic fields greatly affect the dynamic response and gives rise to stability issues. Hence, a novel BDEA is proposed by introducing DEA film centrally connected with one mass block and linear spring, and the bistability can be adjusted by applying external voltage. A nonlinear dynamical model considering the electro-mechanical coupling effects is established using the Euler-Lagrange method, with which the snap-through procedure is theoretically analyzed and validated through the analytic method and finite element method. The influences of the electric actuation and structural parameters on the number of stable states and natural frequency are analyzed. Additionally, the supercritical pitchfork bifurcation and saddle-node bifurcation are investigated through dynamic analysis under forced vibration. Furthermore, the ranges of electrical actuation parameters can be determined for preventing the bifurcation phenomena under parametric excitations. Moreover, an active morphing strategy for achieving nonlinear dynamic morphing between steady states of BDEA using drive voltage is obtained, thereby enhancing the versatility of conical BDEA.

Numerical erosion prediction of aluminum induced by cavitating jet using an Eulerian–Lagrangian method

Cavitation-induced erosion in pump machinery is a significant issue that leads to material loss and increased operating costs. This study develops a numerical method based on an energy balance approach to address the risk of cavitation erosion. Compared with other published methods, three improvements are made. Firstly, it assumes that the local instantaneous pressure is the driving force behind cavity collapse, rather than the far-away ambient pressure field. Secondly, it counts erosion only at the moment that the released shock wave is strong enough to cause surface damage. Thirdly, an Eulerian–Lagrangian method is introduced to simulate multiscale cavitation, in which the volume of fluid (VOF) method and a discrete bubble model (DBM) are combined to reproduce resolvable water-vapor interfaces and unresolvable discrete bubbles, respectively. The developed numerical modeling framework is validated by predicting the erosion of pure aluminum surface caused by a cavitating jet, and it is shown that the simulated erosion region fits well against the experimental results. Additionally, appropriate model coefficients of the erosion prediction method are introduced to achieve quantitative prediction of material mass loss, and the detailed erosion behavior is discussed.

Motion characteristics and wear analysis of particles in the clearances of a twin-screw pump

The rotors of twin-screw pumps would be worn by hard particles for deep-sea oil and gas mixture transport. It led to the destruction of the seal clearance and the deterioration of pump performance. Based on the Euler–Lagrange method and dynamic grid technology, the transient numerical simulation of solid–liquid two-phase flow in a twin-screw pump was carried out and validated by experiment. The motion characteristics of particles in the tip, interlobe, flank clearance, and the causes of rotor wear were clarified. The results revealed that the severe wear at rotor tips was caused by the particles when they enter the tip clearance rather than leaving the tip clearance with the leakage jet flow. Particles passing through the flank clearance had high velocity and contributed to the wear at rotor tips. The main flow in the tooth chamber was disturbed by the interlobe and flank clearance leakage, even resulting in local high-speed reflux near the engagement. With the increase in the particle concentration and diameter, the collision frequency between particles and rotor tips increased, aggravating the risk of wear at rotor tips. The research could reveal the motion nature of particles following the liquid phase and their wear mechanism in twin-screw pumps.

Damage characteristics of ribbed cylinder in motion under near-field underwater explosion

The damage characteristics of a ribbed cylinder in the torpedo compartment shell is explored. An arbitrary Lagrange–Euler method is used to establish the fluid–structure interaction model for analyzing the ribbed cylinder’s response under near-field underwater explosion while in motion. The influence of detonation direction and standoff distance on the dynamic response of the moving ribbed cylinder is considered. The investigation reveals that the cylinder’s motion causes an uneven distribution of bubble load and secondary load, stemming from cavitation zone collapse, on the shell. This imbalance leads to a notable deflection difference between the shell’s front and rear sections, with maximum deformation concentration at the rear. In addition, in comparison to the lateral condition, static state analysis shows reduced average deflection and increased maximum deflection when the explosion point is above or below the shell, while in the sailing state, both average and maximum deflections increase. Notably, when the charge radius is between 6 and 15 times, the average damage rate in the sailing state consistently remains lower than that in the stationary state, while the maximum damage rate is higher at a specific burst distance.

Exploring the load characteristics and structural responses of a high-speed vehicle entering water

The process of a trans-medium vehicle crossing from air into water is referred to as water entry. It involves the interplay of air, water, and the vehicle and is a non-stationary process. In this study, we use the coupled Eulerian–Lagrangian method, along with the constitutive Johnson–Cook model and the model of cumulative damage-induced failure, to describe the dynamic plastic flow and fracture-related behavior of the vehicle shell, and use it to develop a method to numerically simulate the process of a high-speed vehicle entering water. When it contacts with water, the elasticity of the medium prompted a significant deflection and deformation in the central area of the head of the vehicle shell. As deformation approached its limit, tensile fractures occurred that caused the shell of the head to separate from the main body. Changes in its angle of water entry influenced the fracture process of the shell. The symmetric, parabolic bending deformation of the head of the vehicle shell occurred around its central axis. The time taken by different types of vehicle heads to fail varied significantly, leading to marked differences in their peak deformation. We determined the quantitative relationship between the dimensionless factor χ and the velocity of water entry, using it to estimate the ultimate water entry velocity for vehicles of different sizes but composed of the same material.

Investigation on sediment erosion in bucket region of Pelton turbine considering cavitation

In the context of constructing high-head hydro-power stations, the Pelton turbine assumes a critical role as the primary energy converter. This study employs the Eulerian–Lagrangian method to simulate the multi-phase flow occurring within the Pelton turbine bucket. Furthermore, it introduces a novel aspect by investigating and comparing the effects of cavitation on erosion within the bucket region under varying conditions of sediment-water, involving different particle sizes and concentrations. The research findings unveiled several key insights. Primarily, cavitation predominantly influences the flow characteristics of particles at the air–liquid interface, while particles with larger sizes tend to concentrate in the center of the jet. Consequently, cavitation's impact on erosion is more pronounced in the case of smaller-sized particles. Moreover, the study revealed that cavitation can either exacerbate erosion under high particle concentration conditions or mitigate it when particle concentration is low. Furthermore, the investigation highlighted variations in the degree of erosion and the affected area of the bucket based on different position angles. Particularly, at a position angle of 65°, the presence of water vapor induced by cavitation alters particle trajectories, thereby modifying the overall erosion pattern of the bucket. These findings collectively contribute to a deeper understanding of the complex interplay between cavitation and erosion within the Pelton turbine bucket.

Features of numerical modeling electrical coalescence in a droplet-layer system using the arbitrary Lagrangian-Eulerian method

The electrocoalescence of a water drop at the water-oil interface was numerically analyzed using the finite element method by solving a set of equations including hydrodynamics and electrostatics. The simulation was performed using COMSOL Multiphysics software, the interface movement was implemented using an arbitrary Lagrangian-Eulerian method (also called the moving-mesh method). The influence of the initial distance from the drop to the layer, as well as the size of the entire domain on the outcome of the process was studied. The electrical coalescence and non-coalescence of a single uncharged droplet with a layer under the action of the DC field were calculated in a wide range of electric field strength. The created computer model makes it possible to calculate the voltage dependence of the detached droplet volume and charge. Also, it can help to determine features of non-coalescence, including the stretching of the droplet along the interelectrode gap and spraying.

Investigation on mechanical behaviour of underwater launching process of bidirectional pigging robot in the subsea oil pipeline using Coupled Eulerian-Lagrangian method

Underwater launchers are typically employed for the deployment of pigging robots in subsea pipelines for the purposes of cleaning and inspection. Throughout the launching process, challenges related to vibration, damage, and other issues must be addressed and resolved. In this study, the launching process of the pigging robot is numerically simulated using Abaqus 2020. Utilising the Coupled Eulerian-Lagrangian (CEL) method, the Fluid-Structure-Interaction (FSI) model of the launching process was constructed. And the variation of parameters such as velocity, friction force and tilt angle at different inlet flow rates were analysed. The findings indicate a positive correlation between the average velocity of the pigging robot and the inlet flow rate. The factors such as friction, tilt angle, and offset distance are related to the motion process of the pigging robot. Furthermore, during the pigging robot’s traversal through narrow pipe sections, the sealing discs undergo irregular deformation, generating a reaction force on the robot and inducing vibration. In conclusion, the analysis of the impact of inlet flow velocity on the motion behaviour of the pigging robot offers a theoretical foundation and reference for the successful launch of the robot.