Coupled Eulerian-Lagrangian Method Research Articles

Characterization of non-steady-stage during friction stir welding

Friction stir welding (FSW) has been widely applied in joining lightweight metals such as aluminum alloys. Similar to traditional arc welding, FSW also experiences a non-steady-stage in the initial stage of welding. Regarding the characteristics of the non-steady-stage during the FSW process, there has been a lack of research by scholars in this area. In this work, the Coupled Eulerian-Lagrangian (CEL) method was employed to perform a numerical simulation of the FSW process. Combined with related experiments, it was discovered that the instability of temperature and axial force leads to the characteristic transition from tunnel defects to void defects during the non-steady-stage. Furthermore, the length of the non-steady-stage was found to be 30 mm, and its duration is influenced by the welding conditions. Tensile tests have confirmed that the welding quality of the remaining part, after removing the keyhole at the weld’s end, is reliable.

Numerical Simulation of a Submerged Floating Tunnel: Validation and Analysis

The dynamic response analysis of submerged floating tunnels (SFTs) under seismic action is a complex two-way fluid–structure coupling problem that requires expertise in structural dynamics, fluid mechanics, and advanced computational methods. The coupled Eulerian–Lagrangian (CEL) method is a promising method for solving fluid–structure interaction problems, but its application to SFTs is not well established. Therefore, it is crucial to verify the accuracy and reliability of the CEL method in fluid–structure coupling simulations. This study verified the applicability of the CEL method for simulating one-way and two-way fluid–structure coupling cylindrical flow problems, and then applied the CEL method for the analysis of a shaking table test of a model SFT. A comparison of results obtained with the CEL method with those obtained in a previous indoor model test of an SFT demonstrates the agreement between the results of the CEL method and the overall trend of the experimental results, indicating the reliability of the method for the seismic analysis of SFTs. Moreover, the analysis of the dynamic response characteristics of SFTs under seismic conditions provides data support and a technological means for the seismic design of SFTs.

Deflation analysis of an air cushion for underwater shaking tables

The deflation process of inflatable membrane structures has always been a topic worthy of in-depth research. Inflatable membrane structures are employed for waterproofing in underwater environments, and their deflation process often poses safety concerns, warranting increased attention. An air cushion, which is applied to waterproof the underwater shaking table, is researched. It is arranged between the shaking table and the cover plates and can provide waterproof protection for the driving equipment of the shaking table. This article mainly studies the complete process of deflation for the waterproof air cushion. Force analysis was conducted on the air cushion membrane at different stages of deflation, and the factors that affect force during the deflation process were determined. A simulation method that combines the CEL (Coupled Eulerian-Lagrangian) method and fluid cavity method was used to analyze the deflation process of the air cushion, taking into account the effects of different deflation speeds and initial inflation pressures on the process. Based on the analysis results of the pressure-air volume curve and the deformation of the air cushion, the deflation process can be divided into three stages: elastic shrinkage stage, extrusion deformation stage, and free deformation stage. Based on the analysis results of dynamic stability, the extrusion deformation stage is further divided into two sub-stages: the extrusion stable stage and the extrusion unstable stage. It was found that the air cushion can achieve stability during both the elastic shrinkage stage and the extrusion stable stage, leading to the proposal of an evaluation method for air cushion deflation. Finally, the instantaneous leakage process of different positions on the air cushion was analyzed, and engineering suggestions were provided based on the analysis results. The research results provide a reference for the application of underwater inflatable membrane structures.

Drilling process of indexable drill bit based on Coupled Eulerian-Lagrangian method: A simulation study

42CrMo steel has the characteristics of high strength, high wear resistance, high impact resistance, and fatigue resistance. Therefore, drilling 42CrMo steel has always been a challenging task. The indexable drill bit has the advantages of high processing efficiency and low processing cost and has been widely used in the field of aerospace hole processing. To better understand the machining mechanism of the indexable drill bit, this paper uses the Coupled Eulerian-Lagrangian method (CEL) to simulate the three-dimensional drilling model for the first time. The simulation results of the drilling force obtained by the CEL method and Lagrangian method are compared with the experimental results. It is verified that the CEL method is easy to converge and can avoid the problem of program interruption caused by mesh distortion, and the CEL simulation value is more consistent with the actual value. Secondly, the simulation results of cutting force and blade cutting edge node temperature under different process parameters are extracted. The variation of time domain cutting force, frequency domain cutting force and tool temperature with process parameters are obtained. This study provides a new method for the prediction of cutting performance and the optimization of process parameters of indexable drills.

Effect of press depth on defect formation in friction-rolling additive manufacturing

Friction-rolling additive manufacturing (FRAM) is a solid-phase additive manufacturing technology that relies on the insertion of a high-speed rotating toolhead into a previous layer to generate heat for deposit formation. Press depth is a key parameter of FRAM, and insufficient press depth may result in defects that affect the mechanical properties of the deposited material. In this study, the effect of press depth on heat generation and defect formation in materials was revealed for the first time using the Coupled Eulerian-Lagrangian method. The results showed that at a small press depth, the temperature and stress of the material on both sides of the interface are low, and the plastic deformation produced by the toolhead does not affect the interface; thus, two types of bonding defects: voids and tunnels, appear easily at the interface position. With an increase in the press depth, material flow along the travelling direction and the toolhead direction was enhanced, and the temperature, stress, and plastic deformation at the interface gradually increased, resulting in the disappearance of the defects, and the order of disappearance was related to the morphology of the toolhead. When the press depth was 1.90 mm, the materials on both sides of the bonding interface reached 70 % of the melting point, resulting in an almost defect-free interface. The simulation results were consistent with the experimental results. This study provides a better understanding of the defects formation during FRAM and provides guidance for regulating the defects in the future.

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

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.

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 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.

A novel transparent cabin used in the classroom during the coronavirus pandemic: a CFD analysis

A coronavirus family is a diverse group of many viruses. Coronavirus disease 19 (COVID-19) spreads when an infected person breathes out droplets and very small particles that contain the virus. These droplets and particles can be breathed in by other people or land on their eyes, noses, or mouths. In this paper, the airflow distribution and the movement of coronavirus particles during normal breathing and sneezing in classrooms have been studied using a CFD model developed in ANSYS® 2022R2. The objective is to find ways to control the spread of the virus that enable us to practice academic activity and deal normally with the pandemic and the spread of the disease. Experiments were done with more than one turbulence model to know which was closest to the experiments as well as to determine the best number of meshes in the classroom. The effect of turbulent dispersion on particles is resolved using a discrete random walk model for the discrete phase and the RANS model for the continuous phase in a coupled Eulerian–Lagrangian method. Furthermore, that is done in two scenarios: the first is to find the best ventilation configuration by investigating the following parameters: the effect of air change per hour, the height of the air inlets and outlets, and the infected student's position. The second is to control the spread of the coronavirus in the classroom in the event of sneezing from an infected student by placing cabins and an air filter with optimal design installed at the top around each student. It was found that optimal ventilation is achieved when fresh air enters from the side walls of the classroom at a distance of 1 m from the floor and the air exits from the ceiling in the form of two rows, and the rate change of air per hour (ACH) is 4, which leads to energy savings. In addition, a novel transparent cabin is designed for the student to sit in while in the classroom, consisting of a high-efficiency particulate air filter (HEPA) that collects any contamination and recirculates it from the top of the cabin back into the classroom with different fan speeds. Through this study, this cabin with a filter was successfully able to prevent any sneeze particles inside from reaching the rest of the students in the classroom.

Ghost material in geotechnical applications of the CEL method

The Coupled-Eulerian-Lagrangian (CEL) method is an established numerical approach for the simulation of geotechnical boundary value problems involving soil–structure interaction and large deformations. A consequence of this approach is the existence of two overlapping numerical meshes, one Lagrangian and one Eulerian. The structure is usually modeled by the Lagrangian part while the soil is represented by the Eulerian part. The material within the Eulerian part of the mesh overlap may be considered a kind of ’virtual’ or ’ghost’ material, as it only exists due to the numerical approach and has no counterpart in reality. Up to now it has never been evaluated how much this ghost material influences the simulation results. In this study, two geotechnical applications of CEL are analyzed which contain ghost material in a zone of soil–structure-interaction. Each example implements several model variants by applying different material combinations and contact formulations. Additional simulations with a pure Arbitrary-Lagrangian-Eulerian (ALE) approach, in which no ghost material exists, are presented to give further insights.

A Method for Predicting the Load Interaction between Reinforced Thermoplastic Pipe and Sandy Soil Based on Model Testing

This study aims to investigate the interaction between reinforced thermoplastic pipes (RTPs) and sandy soil. The mechanical properties of sandy soil in the South China Sea region were determined through shear tests to obtain fundamental data. Subsequently, a specialized experimental setup was designed and assembled to study the pipe–soil interaction, specifically measuring the lateral soil resistance of flexible pipes at varying burial depths. Data analysis revealed the relationship between soil resistance, lateral displacement, and initial burial depth. To simulate the mechanical behavior of the pipe–soil interaction, the coupled Eulerian–Lagrangian (CEL) method was employed for numerical simulations. The research findings indicate that the lateral soil resistance is influenced by the uplift height and accumulation width of the soil ahead of the pipe. Within a lateral displacement range of 0.5 times the pipe diameter (0.5D), the lateral soil resistance rapidly increases, resulting in a soil uplift along the circumferential direction of the pipe. This process not only enhances the load-bearing capacity of the pipe but also increases the accumulated soil resistance, consequently expanding the soil failure zone. Furthermore, the ultimate soil resistance exhibits an increasing trend with an increasing burial depth. Once the pipe reaches a certain burial depth, the uplift height of the soil reaches a critical state. To address the grid distortion caused by soil deformation, numerical simulations based on the CEL method effectively modeled the pipe–soil interaction forces under significant lateral displacements, exhibiting good agreement with the experimental results. This study provides a solution for investigating soil resistance in submarine pipelines, thereby contributing significantly to the design and performance prediction of underwater pipelines.

Assessment of predicting temperature distribution of friction stir welded AA6061 induced by pin profiles for developing sustainable industry

Nowadays, the aspects of energy and environmental pollution have been becoming a big challenge in developing sustainable industries. Using green technology is considered as priority solution for any manufacturing process. Friction stir welding (FSW) is invented as green technology applied widely in many field industries. To evaluate its applicability, this study focused on the prediction of temperature distribution of FSWed AA6061 induced by various pin profiles. Research efforts are being made to gain a better understanding of FSW process, to explore different tool configurations, and their influence on the heat generation. The numerical model was developed in Abaqus software, utilizing the coupled Eulerian Lagrangian method, the Johnson-Cook material model, and the mass scaling technique. The model’s accuracy is verified by comparing its simulated temperature values with experimental data in Stir zone (SZ) and Heat-affected zone (HAZ). The numerical results show the high correlation with the experimental study, with the deviation around 10%. It is shown that tool pin profiles with the combination of thread and flat features generated the highest temperature.

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

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

Modelling of debris flow-boulder-barrier interactions using the Coupled Eulerian Lagrangian method

The impact load of boulders transported by debris flow is crucial in designing protective structures constructed along the potential flow paths. In this study, the Coupled Eulerian-Lagrangian (CEL) method is applied to establish a three-dimensional model for analysing debris flow, boulders, and barrier interactions in various scenarios, with an Australian rivulet serving as a case study. The proposed CEL method was verified by simulating the runout and impact behaviour based on experimental granular and debris flow tests. Subsequently, a comprehensive series of numerical simulations explores the impacts of transported boulders on a rigid tooth barrier, encompassing various boulder shapes and sizes. The results indicate a direct correlation between boulder size and impact force, while the influence of boulder shape on peak impact force is minimal. Nevertheless, boulder shape affects the arrival time, as noted with increased boulder size. Although boulder dimensions remain the primary factor affecting impact force, variations in the geometry are observed to influence the overall dynamics of debris flow-boulder interactions. This study proposes a procedure for assessing barrier impact forces through simulations combining debris flow and boulder transport with the CEL method. The research presents the effectiveness of the CEL method in estimating the impact force of media transported by debris flows in intricate 3D terrains. The findings contribute significantly to the existing measures for assessing the risk of debris flows.

Ground Vibration Response to Vibratory Sheet Pile Driving and Extraction

Sheet piles are extensively used as foundation structures in urban environments. However, the vibrations associated with sheet pile construction can potentially adversely affect existing buildings, as well as cause discomfort to nearby residents. This study aims to analyze ground vibration response during the driving and extraction of sheet piles. To this end, field tests of U-shaped sheet piles were conducted in Beijing silty clay, during which ground vibrations in the near-field were monitored. Subsequently, a numerical model was developed using the coupled Eulerian–Lagrangian method to simulate the pile–soil interaction characteristics and to investigate ground vibration intensity in the far-field. The research results indicate that the ground vibration response modes during the driving and extraction of sheet piles are distinctly different. Due to the entry effect, the critical depth during pile driving typically occurs in shallow soil layers, while during pile extraction, the critical depth generally corresponds to the pile’s embedded depth to overcome the soil locking effect. Ground vibrations rapidly decrease in the near-field (<6 m), while in the far-field (>6 m), the attenuation rate significantly slows down. Vibrations can be widely perceived by residents at radial distances of less than 12 m. Through a systematic assessment, it was concluded that sheet pile construction is unlikely to directly damage surrounding buildings but may inconvenience nearby residents. Additionally, a parametric analysis of the vibration source revealed that appropriately adjusting the driving frequency and amplitude can effectively reduce vibration levels.

Coupled Eulerian-Lagrangian simulation of progressive failure in shield tunnels induced by developing contact loss

Contact loss may develop between a shield tunnel and the surrounding ground due to various factors. This study evaluated the deformation and failure of shield tunnels caused by contact loss using the Coupled Eulerian-Lagrangian (CEL) method. Three-dimensional finite element models considering the behavior of segment joints were established. The CEL method for simulating contact loss and the segmental tunnel model were validated through two existing experiments. The shield tunnel structure responses, including convergent displacement of linings, dislocation between tunnel rings and joint failure process, were analyzed under typical cases of contact loss developing circumferentially and longitudinally. In addition, the impact of contact loss location was investigated. The results show that significant joint dislocation may occur at the boundary of the contact loss region. When contact loss develops to a certain level, the tunnel deformation may increase sharply, and many segment joints fail suddenly. Additionally, more joints fail when the contact loss is located at the tunnel crown than when contact loss is located at the tunnel invert and springline due to the assembled method of shield tunnel in this study in which the key segments were all positioned at the tunnel crown.

Numerical Simulation of Bird Strike with Varied L/D Ratio in Hemispherical-ended Cylinder Bird Model Using Coupled Eulerian Lagrangian Method

This research studies the numerical simulation of the finite element method for bird strike using a hemispherical-ended cylinder bird model with varying length-to-diameter (L/D) ratio, namely 1.4; 1.5; 1.6; 1.7; 1.8; 1.9; and 2.0. Birds are modelled with elastic, plastic, and hydrodynamic behaviour. The bird model uses the Coupled Eulerian-Lagrangian (CEL) method with impact speeds of 100 ms-1, 200 ms-1, and 300 ms-1. The simulation results show that the Hugoniot pressure value is around 15-36 times higher than stagnation pressure in L/D 1.4; 14-36 times in L/D 1.5; 13-30 times in L/D 1.6; 12-32 times in L/D 1.7; 12-26 times in L/D 1.8; 13-30 times in L/D 1.9; and 13-29 times in L/D 2.0. It was found that the highest Hugoniot and stagnation pressure were in L/D 1.5 and 1.8, while the lowest Hugoniot and stagnation pressure were in L/D 2.0 and 1.5, respectively. In addition, the error of the numerical results of the average Hugoniot and stagnation pressure value compared to the analytic was 2.9% and 7%, respectively.

MPM vs. CEL: Numerical modelling of penetration processes

MPM vs. CEL: Numerical modelling of penetration processes

A multigrid partition coupled Eulerian–Lagrangian method for fluid–solid interaction problems

In this paper, a multigrid partition coupled Eulerian–Lagrangian method (PCELM) is proposed to model fluid–solid interactions between fluids and moving or fixed rigid bodies. In this method, Lagrangian particles are arranged in Eulerian grids to track the interface, and the partition weighted bidirectional mapping method is used to improve the mapping accuracy between particles and grids. The multigrid domain is established to realize independent and contact calculations of the fluid and solid, which can solve for the cross-interference of multiple velocity fields in a single grid domain. Moreover, based on the contact in the particle volume domain, a more accurate fluid–solid interaction method, in which the contact properties of real grid nodes are identified by judgment and search criteria and then corrected, is proposed to overcome false contact and nonphysical penetration problems. Then, the accuracy and stability of the PCELM are verified using representative fluid–solid interactions. Finally, experiments and simulations of dam-break floods impacting the dam board are carried out. These experiments prove that the PCELM can accurately capture the free surface of dam-break floods and can provide suggestions for the installation of dam boards in hydraulic engineering.