Coupled Eulerian-Lagrangian Method Research Articles

Modified CEL method for determination of defect formation mechanism in underwater stationary shoulder FSW based on softened pressure-overclosure contact relationship

The Coupled Eulerian-Lagrangian (CEL) method was employed to simulate underwater friction stir welding with a stationary shoulder tool (USSFSW). The governing equations in the CEL method were formulated for FSW based on the immersed boundary method. A new softened pressure-overclosure model was introduced to define contact pressure within the overclosure zone, and an initial nodal clearance control method was implemented to prevent the penetration of Eulerian elements into the Lagrangian domain. For modeling the mechanical and thermal interactions between surfaces, the VUINTERACTION subroutine was utilized. The study focused on the defect formation mechanisms during USSFSW, highlighting the roles of material flow velocity and nodal forces. Simulation results demonstrated close alignment with experimental data, revealing three flow paths that developed during the process, merging in the empty area behind the pin and generating upward material flow. Notably, the maximum flow velocity at the boundary of the third and fourth quadrants ranged from 0.189 to 0.495 m/s, while the overall maximum material flow velocity varied from 0.193 to 0.502 m/s. The nodal force was found to vary between 180 and 600 N; notably, when this force dropped below 200 N, the driving force for material flow decreased, resulting in the inability to fill the cavity behind the tool. Conversely, increasing the nodal force enhanced both backward flow (BF) and horizontal flow (HF), promoting higher material extrusion into the cavity. ​Ultimately, when the flow velocity fell below approximately 0.25 mm/s and the nodal force dropped below about 200 N, cavity defects in USSFSW became inevitable.

Analysis of damage characteristics of reinforced concrete slabs under explosive impact and research on CFRP reinforcement

To study the damage characteristics and damage model of reinforced concrete slabs under explosive impact, the failure modes of reinforced concrete slabs under near-field and contact explosion were first studied through on-site experiments. A coupled model was established based on the Coupled Eulerian-Lagrangian (CEL) method using AUTODYN finite element software. The reliability of the model was verified by comparing the numerical simulation results with experimental results. Based on this, a fully coupled model of Carbon Fiber Reinforced Polymer (CFRP) reinforcement for reinforced concrete slabs under contact explosion was established, and the influence of different CFRP thicknesses and reinforcement methods on the blast resistance performance of reinforced concrete slabs was discussed. The research results indicate that under the action of near-field explosions, the front face of reinforced concrete slabs mainly experiences slight peeling damage, and the central area of the back face forms seismic collapse and peeling damage, with damage cracks diverging from the center to the surrounding areas; Under the action of contact explosion, the front face of the reinforced concrete slab produces blast pits, the back face forms a seismic collapse zone, and peeling damage occurs; The CFRP reinforcement layer can improve the blast resistance performance of reinforced concrete slabs; There is an optimal thickness when using CFRP to enhance the blast resistance of reinforced concrete slabs.

Optimization of high-precision Bekker test plate structure for rarefied soils–example of deep-sea subsoils

The Bekker apparatus is an important tool for measuring soil bearing capacity; however, it is not entirely suitable for deep-sea sediments, and the size of the loading plate can affect the accuracy of the Bekker bearing parameters. This paper employs the Coupled Eulerian-Lagrangian (CEL) method to explore how different conditions impact Bekker bearing parameters. As the size of the loading plate gradually increases, the soil compression mechanism and load path reach a relatively stable state, leading to the stabilization of Bekker bearing parameters. The study proposes a range of plate sizes for deep-sea soils with varying strengths, noting that the physical mechanisms of low-strength soils are relatively simple, making them more consistent with the ideal conditions described by Bekker’s theory. Furthermore, an analysis of the relationship between Bekker bearing parameters and penetration depth reveals that the parameters corresponding to different strength soils vary almost parallel with depth. This is attributed to the same settlement path, where the distribution of loads and the geometrical shapes of the supporting structures remain unchanged, resulting in a similar trend in the variation of Bekker parameters. The research findings provide a theoretical basis for analyzing the bearing capacity characteristics of soft deep-sea soils.

Simulation of the effect of multi-particle temperature on Al6061 coating porosity based on Coupled Eulerian-Lagrangian (CEL) method

Cold spray is a solid-state deposition technology widely used in additive manufacturing. The particles temperature is mostly used to adjust the porosity of the coating. This article uses Pyhon script to model the multi-particle model; then the multi-particle model is nested in the CEL deposition model to simulate the actual cold spray multi-particle deposition process; The CEL method has the characteristics of high accuracy and robustness and was selected as the simulation method for the multi-particle deposition model. The porosity of the coating is expressed by studying the value of the EVF void area in the Euler domain. Multiple groups of samples were taken on the coating surface to calculate the porosity of each group, and the average value was finally taken as the porosity of the entire coating. Numerical results show that increasing the particle temperature can effectively reduce the porosity of the coating. The average porosity of the coating under the particles temperature conditions are 600 K: 5.08 %; 650 K: 4.02 %; 700 K: 3.58 %; deposition completed the inside of the coating appears to be compacted. The substrate temperature will affect the combination of the coating and the substrate. It is recommended that the temperature difference between the particles and the substrate should not be too large. The CEL method simulates the process of cold spray multi-particle deposition, which is an effective method to observe and predict the porosity of the coating, which is also unachievable by the SPH and ALE methods.

Numerical Study of Tangential Traction Mechanism between Pattern Blocks of Agricultural Radial Tires and Soft Soil.

With the increasing requirements of agricultural machinery, the study of the contact relationship between the tire-soil interface and the improvement of traction efficiency has gradually become a main concern. In this study, the pattern on the agricultural tire was simplified into single-pitch pattern blocks. The pattern blocks were made of rubber material that was highly resistant to abrasion and bending. The experiment was carried out by pressing the three types of patterned block construction into the soil and the pure sliding under the soil. The simulation used the Coupled Eulerian-Lagrangian Method (CEL) to verify the experimental results. We found that the herringbone pattern block was subjected to the highest stress for the same depth of downward pressure. The horizontal force generated by the pure sliding was also the highest. The results showed that the numerically simulated and experimentally measured data exhibited similar trends and average values. In addition, the increase in the contact area between the tire and the soil reduced the compaction and sinking of the soil. The herringbone pattern structure not only had a large contact area but also produced the most significant shear force on the soil. Thus, it may generate greater traction in actual operations.

Analysis of Debris Flow Protective Barriers Using the Coupled Eulerian Lagrangian Method

Protective structures play a vital role in mitigating the risks associated with debris flows, yet assessing their performance poses crucial challenges for their real-world effectiveness. This study proposes a comprehensive procedure for evaluating the performance of protective structures exposed to impacts from media transported by large debris flow events. The method combines numerical modelling with site conditions for existing structures along the Hobart Rivulet in Tasmania, Australia. The Coupled Eulerian Lagrangian (CEL) model was validated by comparing simulation results with experimental data, demonstrating high agreement. Utilising three-dimensional modelling of debris flow–boulder interactions over the Hobart Rivulet terrain, boulder velocities were estimated for subsequent finite element analyses. Importantly, a model of interaction between boulders and I-beam posts was established, facilitating a comparative assessment of five distinct I-beam barrier systems defined as Type A to E, which are currently in use at the site. Simulation results reveal larger boulders display a slower increase in their velocities over the 3D terrain. Introducing a key metric, the failure ratio, enable a mechanism for comparative assessments of these barrier systems. Notably, the Type E barriers demonstrate superior performance due to fewer weak points within the structure. The combined CEL and FE assessments allow for multiple aspects of the interactions between debris flows, boulders, and structures to be considered, including structural failure and deformability, to enhance the understanding of debris flow risk mitigation in Tasmania.

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.

Finite element simulation of the mechanical loads during low frequency vibration-assisted drilling utilizing the CEL-method

Poor chip evacuation during drilling leads to increased heat generation in the contact zone and a decreased in borehole quality. This disadvantage can be overcome by low frequency vibration assisted drilling (LFVAD), which produces small, uniform shaped chips that allow better chip evacuation. The study presents the results of simulations of chip formation in conventional drilling (CD) and LFVAD based on the Coupled Eulerian-Lagrangian (CEL) method. The method does not require time consuming remeshing despite the high strains and strain rates that occur. In this work, a mesh refinement analysis in different spatial directions is performed in order to reduce the computational effort and preserve the accuracy of the numerical results.. A comparison with experimental data is performed for validation.

Numerical modelling of the BTA deep hole drilling process

The BTA deep hole drilling process is applied in order to produce bores with a large length to diameter ration at comparably high diameters of the bores. During drilling, first, the bore is cut by the cutting edge and shortly after that, a guide pad slides over the newly produced bore wall, burnishing the surface. These two effects condition the bore wall and alter its surface integrity depending on the process parameters. In the past, extensive destructive and non-destructive tests were conducted to obtain information on the surface integrity of the machined parts. Furthermore, a large number of in- and off-process measurements were carried out in material and cost-intensive experiments to determine values such as residual stresses or white etching layers. The presented work shows different finite element models of the BTA deep hole drilling process using continuous remeshing and, in order to reduce the calculation times, the Coupled Eulerian-Lagrangian (CEL) method as well. The results simulated based on this models comprise temperatures, process forces and surface properties that are compared to measured values from pervious works for validation. The various approaches are evaluated to determine whether they predict the bore hole surface integrity and thus support future investigations.

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.