Lagrangian Eulerian Research Articles

Computational assessment of leg response to extreme loadings using a detailed finite element model.

This study focuses on evaluating the response of the Total Human Model for Safety™ lower extremity finite element model under blast loading. Biofidelity of the lower extremity model was evaluated against experiments with impact loading equivalent to underbody blast. The model response was found to match well with the experimental data for the average impactor speeds of 7 and 9.3 m/s resulting in an overall correlation and analysis rating of 0.86 and 0.82, respectively. The model response was then used to investigate response for antipersonnel mine explosion where the numerical setup consists of a charge mass of 40 g trinitrotoluene placed at a depth of 50 mm below the heel. The explosion was modeled using Multi Material-Arbitrary Lagrangian Eulerian method. The model was subjected to the graded input in terms of variation in standoff distance and mass of explosive to investigate the sensitivity of the model. The model found sensitive to the threat definition and predicted an increase of 110% in peak fluid-structure interaction force with 20% reduction in its time to peak and 29% increase in peak calcaneus axial force with a reduction of 33% in its time to peak when explosive mass varied from 40 g to 100 g. The location of the explosive below the foot was discovered to have significant effect on the injury pattern in near-field explosion. A comparative study suggested that the model predicted similar response and damage pattern compared to experimental data.

Parameter study for oil spray cooling on endwindings of electric machines via Eulerian–Lagrangian simulation

The demand for larger power density and torque for the power traction motors used in electrified transportation puts forward a requirement for better thermal management methods. Spray cooling is a promising direct liquid cooling technique that has been proved to possess high heat removal capability in previous research. This paper investigates the heat transfer characteristics of spray cooling on endwindings of electric machines via numerical simulation through an Eulerian–Lagrangian approach. The utilized numerical models and calculated results are validated with experimentally measured data. The influence of different parameters and options involved in the simulation settings on the final results, like the stream numbers for the spray injector, the constant heat flux versus constant temperature thermal boundary condition, the influence of splashing, the effect of heat conduction in the endwindings and the Saffman lift force, only solving the energy equation for the air after its flow field reaches a steady-state, are evaluated. Parameter analyses are also conducted for operation conditions, configuration of the spray nozzles, and material properties of the coolant liquid. It is found that larger flow rate, smaller droplet size, lower spray height, more nozzle numbers, larger thermal conductivity and smaller viscosity of the coolant liquid tend to increase the overall heat transfer performance.

Effect of Ultra-Lightweight High-Ductility Cementitious Composite in Steel–Concrete–Steel (SCS) Plate to Mitigate Ship Slamming Loads

Bottom slamming loads cause considerable local damage to a ship’s body and reduce the ship’s structural performance against harsh sea waves. Although extensive studies have worked on stiffening elements to compensate for local damage due to slamming loads, few studies have concentrated on the ship’s body itself while using new generations of composite plates. Accordingly, a numerical study is conducted to determine the effect of using ultra-lightweight high-ductility cementitious composite in steel–concrete–steel (SCS) composite plate to mitigate bottom slamming loads. A large-scale model of the ship using SCS composite plates is modelled in Abaqus software, and fluid–solid (FSI) interaction is precisely modelled using the Coupled Eulerian–Lagrangian (CEL) method. The results show that using the CEL method with a large-scale 3D model precisely simulates FSI by providing a 6.5% deviation from the experimental result. Moreover, using an SCS plate when considering ultra-lightweight high-ductility cementitious composite results in a considerable reduction (around 95%) in the maximum strain of the ship body and, accordingly, reduces local damage so that, although about 22% of the strain of the outer layer is transferred to the inner part of the ship body containing only steel plate, almost 0% stress transfer is observed for the SCS-based ship’s structure.

A 2D elastic wall model to analyze the hyper‐viscous effects on blood flow across abdominal aortic aneurysm in COVID patients by fluid–structure interaction technique with ALE formulation

The worldwide dissemination of the coronavirus, as well as its dependencies, is being aided by detrimental urbanization. The impact of the viral infection upon an infected person is also thought to be influenced by any pre‐existing medical issues. Recent investigations have demonstrated that COVID‐19 patients have a higher degree of blood viscosity as a result of alterations in morphology in blood cells. Examining the importance of hyper‐viscosity in patients with COVID is crucial in determining the diseases of the arteries since viscosity is a key flow characteristic that affects the flow across a stenosis as well as an aneurysm. In the current study, a patient‐specific instance with an aneurysm across the abdominal aortal walls was taken into consideration. Given that abdominal aneurysms occur frequently in people, the high viscosity values are taken into account while examining the hyper‐viscous impact of fluid on its passage through the affected aorta. The current study is the initial endeavor to use the Arbitrary Lagrangian–Eulerian (ALE) Technique to study the impact of fluid–structure interaction (FSI) on the movement of fluid across an aneurysmal aortal section in conjunction with hyper‐viscous anomalous blood characteristics. The investigation backs up the different medical results that described the negative consequences of blood hyper‐viscosity. The computational findings from employing a finite element method (FEM) solver to resolve the fluid mechanical computations complemented alongside the solid mechanical principles indicate a possibility that the increased stress imposed by the hyper‐viscous propagates on the interior walls of the aneurysmal aorta may prompt the aneurysmal pouch to grow or breakdown. Also, the hyper‐viscous blood in COVID patients destroys the smooth muscle cells of the media layer endangering its normal structure and functions and leading to the development of new aneurysms.

3D Simulation of Debris Flows with the Coupled Eulerian–Lagrangian Method and an Investigation of the Runout

In landslide risk management, it is important to estimate the run-out distance of landslides (or debris flows) such that the consequences can be estimated. This research presents an innovative array of dimensionless equations that effectively estimate run-out distances, supported by both experimental data and numerical simulations. We employ the coupled Eulerian–Lagrangian (CEL) method to confront the challenges presented in large deformations during landslides. The soil is modelled using the Mohr–Coulomb model, and the failure of cohesionless soil slopes (e.g., sand slopes) is studied. The simulation results are used to study the characteristics of flows and run-out distances. We suggest a normalized run-out and introduce new scaling relationships for it under different conditions such as different plane angles and material properties. The granular flows under different scales can be compared directly with this new scaling law. The new relationships are validated by both experimental and numerical data. Our analysis reveals that the normalized run-out distance in debris flows is contingent on the initial geometry, plane angle, and material properties. An increase in debris volume and plane angle can contribute to an increase in the normalized run-out distance, while a rise in friction angles causes a decrease. In the case of landslides, the normalized run-out distance depends on material properties and the slope angle. An increase in slope angle leads to a corresponding increase in the normalized run-out distance.

Selection of the numerical formulation for modeling the effect of tool cutting edge microgeometries in machining of Ti6Al4V titanium alloy

The Finite-element method (FEM) is often used to simulate the metal machining process. Currently, several formulations are used in metal cutting simulation, such as Lagrangian (LAG), Eulerian (EUL), Arbitrary Lagrangian–Eulerian (ALE), and Coupled Eulerian–Lagrangian (CEL). The selection of the numerical formulation that better reproduces the material separation in machining to form the chip is a critical issue. This is quite important when the ratio between the uncut chip thickness and the cutting edge microgeometry, often represented by a cutting edge radius, is very low. In this study, orthogonal cutting of Ti6Al4V titanium alloy using different tool edge microgeometries is investigated using LAG and CEL approaches. In the case of LAG approach, two types of cutting models were develop: one using a sacrificial layer (hereby called LAG-SL), and another without sacrificial layer (hereby called LAG-nSL). The cutting models have included a constitutive model (both plasticity and damage) considering the effects of strain, strain rate, temperature, and state of stress, which have proved to be accurate enough to represent the mechanical behavior of the Ti6Al4V alloy in machining. Comprehensive comparisons between CEL and LAG-based cutting models and experimental results are carried out in terms of chip morphology, forces, and residual stresses. When compared to the experimental results, LAG-nSL model gives the best predictions of the maximum chip compression ratio (CCRm) with an error of 9.5%, cutting force (12.8%) and thrust force (9.3%) than the other two models. In the case of the of residual stress profiles, LAG-SL offers good predictions of the maximum compressive residual stress by a preference ratio of 75%. Although CEL yields the worst predictions of chip morphology and forces, it is preferred from the perspective of the thickness of the layer affected by residual stress.

An Interface-Fitted Fictitious Domain Finite Element Method for the Simulation of Neutrally Buoyant Particles in Plane Shear Flow

In this paper, an interface-fitted fictitious domain finite element method is developed for the simulation of fluid–rigid particle interaction problems in cases of rotated particles with small displacement, where an interface-fitted mesh is employed for the discrete scheme to capture the fluid–rigid particle interface accurately, thereby improving the solution accuracy near the interface. Moreover, a linearization and decoupling process is presented to release the constraint between velocities of fluid and rigid particles in the finite element space, and to make the developed numerical method easy to be implemented. Our numerical experiments are carried out using two different moving interface-fitted meshes; one is obtained by a rotational arbitrary Lagrangian–Eulerian (ALE) mapping, and the other one through a local smoothing process among interface-cut elements. A unified velocity is defined in the entire domain based on the fictitious domain method, making it easier to develop an interface-fitted mesh generation algorithm in a fixed domain. Both show that the proposed method has a good performance in accuracy for simulating a neutrally buoyant particle in plane shear flow. This approach can be easily extended to fluid–structure interaction problems involving fluids in different states and structures in different shapes with large displacements or deformations.

An efficient fish migration modeling method integrating the random forest and Eulerian–Lagrangian–agent method for vertical slot fishways

An efficient fish migration modeling method integrating the random forest and Eulerian–Lagrangian–agent method for vertical slot fishways

Numerical Investigation of Uplift Failure Mode and Capacity Estimation for Deep Helical Anchors in Sand

The uplift capacity of helical anchors is generally taken as the control condition for design in different applications, including transmission tower foundations and offshore structures. However, it is difficult to identify the failure surface for a deep helical anchor, which may result in an incorrect assessment of uplift capability. This research proposes a new unified method to estimate the uplift capacity of deep single-helix and multi-helix anchors based on the investigation of failure mechanisms. The deep failure mode was identified by FEM analysis using a modified Mohr–Coulomb model considering the strain softening of sand, along with the coupled Eulerian–Lagrangian technique. Thereby, a simplified rupture surface is proposed, and the equations estimating the uplift capacity are presented by the limit equilibrium method. Two important factors—the lateral earth pressure coefficient and the average internal friction angle included in the equations—are discussed and determined. The comparisons with centrifugal tests verify the reasonability of the proposed method.

Eulerian–Lagrangian fluid dynamics study on the effects of inlet radial angle on the performance and flow pattern of multi-inlet cyclone separator

This paper presents a study on the influence of inlet radial angle in a multi-inlet cyclone separator using Eulerian-Lagrangian (EL) fluid dynamics approach. The investigation focuses on the behavior of air and solid particles within the cyclone. Air circulation was simulated at velocities ranging from 2 to 6 m/s, with inlet radial angles of 15°, 32°, 45°, 61°, and 72°. To model the turbulent flow, the Reynolds stress model (RSM) and renormalization group k-model (RNG) were employed, while the particle trajectories were simulated using the discrete phase model (DPM) in ANSYS Fluent. The purpose of this study was to determine how the inlet radial angle impacts various parameters: collection efficiency, pressure drop, cut-off diameter, axial velocity, and tangential velocity. The numerical data obtained from the simulations were validated and found to be consistent with the existing literature. The results revealed interesting findings. In the case of an inlet velocity of 6 m/s, the highest pressure drop of 84.5 Pa was observed for the 15° inlet radial angle, while the lowest pressure drop of 77.42 Pa was observed for the 32° inlet radial angle. It was found that the collection efficiency varied according to the radial angle of the inlet, with values of 89.00%, 91.70%, 92.50%, 94.77%, and 94.83% for 32°, 45°, 15°, 72°, and 61°, respectively. Additionally, at an inlet velocity of 2 m/s and a radial angle of 72°, 61°, 15°, 45°, and 32°, the corresponding cut-off sizes were determined to be 1.17 μm, 1.19 μm, 1.25 μm, 1.33 μm, and 1.38 μm, respectively. At an inlet velocity of 6 m/s, the peak tangential velocities were found to be approximately 1.48, 1.44, 1.44, 1.39, and 1.34 times the inlet velocity for the 15°, 72°, 61°, 45°, and 32° radial angles, respectively, within the axial location range of z = 1.5D to z = 3.4D. The peak axial velocity values for the 32°, 72°, 45°, 15°, and 61° radial angles, were reported as 0.85, 0.89, 0.92, 0.94, and 0.96 times the inlet velocity respectively.

A two‐dimensional multimaterial ALE method for compressible flows using coupled volume of fluid and level set interface reconstruction

AbstractIn this work, we present a two‐dimensional multimaterial arbitrary Lagrangian–Eulerian (ALE) method for simulating compressible flows in which a novel coupled volume of fluid and level set interface reconstruction (VOSET) method is developed for interface capturing. The VOSET method combines the merits of both the volume of fluid method and the level set method by using a geometrical iterative operation. Compared to the original VOSET method, the novel VOSET method proposed in this work further improves the accuracy and fidelity in interface reconstruction procedure, especially in under‐resolved regions. Several typical two‐dimensional numerical experiments are presented to investigate the effectiveness of the proposed VOSET method and its performance when coupling with the multimaterial ALE solver. Numerical results demonstrate its good capability in capturing material interfaces during the simulation of compressible two‐material flows.

Analysis of the tribological behavior of the high-speed and heavy-load braking interface with dynamic wear of brake pads

Using a megawatt wind turbine disc brake as a case study, this work analyzes the effects and action mechanism of dynamic wear on the braking interface of the braking pad on tribological behaviors as contact state, temperature field, and pressure distribution. The Archard wear model was incorporated into the solution of the tribological problem of the braking interface in ABAQUS using the arbitrary Lagrangian–Eulerian (ALE) technique through the UMESHMOTION subroutine. The wear interface meshes were changed without modifying other finite element analysis variables. Moreover, wear testing on the inertia braking tester validated the coupled heat-stress-wear model of the brake pad. The differences in the tribological behaviors of the braking interface with and without the dynamic wear of the braking pad were analyzed based on the simulation results of friction and wear in a braking cycle. The study revealed that the tribological behaviors of the braking interface were significantly affected by the dynamic wear of the braking pad. Specifically, the wear evolution changed the contact state, the area of stress concentration, and the temperature field distribution during the braking process. Hence, the wear properties of the brake pad were modified as a result of these tribological behaviors.

Comparative performance of nonlinear energy harvesters through strongly coupled fluid-structure-electrical interactive models

Micro power generators (MPGs) can harvest electrical power from ambient energy resources in natural environments to operate small-scale electronic devices. Such systems exploit structural vibrations due to cross-flow instabilities through fluid–structure interactions (FSI). Due to attractive features of piezoelectric transducers, we utilize them for vibration-to-electricity conversion in this work. We develop strongly coupled FSI-based computational models to handle large-amplitude structural motions in which unsteady forces exerted by fluid flows on structures, their dynamical responses, and harvested power are directly computed. Our mathematical model for incompressible flows over moving bodies relies on arbitrary Lagrangian–Eulerian (ALE) formulation. Our in-house FSI solver primarily works using radial basis interpolation technique for grid morphing. Using broad ranges of fluidic, structural, and electrical parameters, we investigate the power generation performance of two types of MPGs, working through vortex-induced vibrations of a circular cylinder and a fluttering NACA-0012 airfoil, under different excitation conditions. Optimum values of load resistance are found to maximize the harvested power. Furthermore, our findings support the linear analysis, which provides insights into the possible instabilities in the electro-mechanical system. Another salient feature of this research work is the inclusion of cubic nonlinear stiffness in the energy harvesting models.

A Numerical Sensitivity Analysis of Fluid-Structure Interaction Simulations on Slamming Loads and Responses

This paper presents a parametric study on the Multi Material Arbitrary Lagrangian–Eulerian (MMALE) method for hydroelastic analysis of a non-prismatic stiffened aluminium wedge. An explicit finite element formulation with a penalty-based coupling technique is employed to evaluate the impact-induced loads and responses during free-fall water entry. Based on the penalty factor, damping factor, and number of coupling points, a sensitivity analysis is carried out. It is shown that the penalty coupling method can generate high-frequency oscillations due to the nature of the phenomenon that may affect the predicted results of slamming loads. The computed results on the stiffened and unstiffened plates of the wedge are compared with published experimental data in terms of vertical acceleration, pressure distributions, and strain responses at different locations. A reasonable agreement can be found between the numerical results and the measured values. It is found that a combination of penalty and damping can improve the simulation results and reduce numerical instabilities in hydroelastic slamming simulations.

Thermal performance of copper-distilled water nanofluid in a wavy channel

This paper carried out an experimental study to synthesize and characterize copper water based nanofluid. To do so nanoparticles were fabricated by using one-step pulsed Nd: YAG laser ablation method under ambient conditions. Copper substrate was ablated for the duration of 25 min to ensure enough volume fraction of nanoparticles inside the host fluid. Energy dispersive spectroscopy (EDS) and scanning electron microscopy were done. The morphology of the nanoparticles seems to be homogeneous. The size distribution analysis resulted in the average size of 100 nm. Also, UV–Vis spectroscopy analysis was done for four months to investigate the stability of the synthesized nanofluid. It is observed that the nanofluid is not enough stable for more than one month. On the other hand, numerical simulations were done employing Ansys Fluent software to study thermal behavior of copper nanofluid in a corrugated channel. It is observed that higher volume fraction of nanoparticles leads to the higher heat transfer rate. Also, in this study, hydrophobic wavy wall with a constant temperature was considered as a hydrodynamical approach to enhance the heat transfer rate. It is concluded that hydrophobicity contributes to the increment of Nusselt number up to 45 percent in laminar flow. Meanwhile, Discrete phase method, which attribute to the Eulerian Lagrangian approach, was simulated. Outcomes indicated that DPM method can be trusted by less than 2% error in laminar flow.

Dispersion of expectorated cough droplets with seasonal influenza in an office

We do not fully grasp viral droplet transmission processes in ventilated interior environments. The core focus of our research is to investigate the effectiveness of the protected occupied zone ventilation (POV) through computational fluid dynamics models in a simplified office setting. The large-eddy simulation technique with the Eulerian–Lagrangian model was implemented to address complicated indoor processes such as turbulence, flow–aerosol interaction, and ventilation impact. We computationally investigated the effects of desk partitions and the POV on cough droplets in an office. The ventilation approach was tested using two distinct exhaust layouts and four different ventilation rates (1.0, 1.2, 1.5, and 1.8 m/s). A comparative analysis of the ventilation flow fields, topologies, and particle directions has been studied. The findings indicate that the plane jet's ventilation rates influence the protected occupied zone ventilation performance. The ventilation rates distributed the virus droplets around the room, but compared to the up-exhaust cases, the down-exhaust cases appeared to have better shielded the healthy person. This pattern could indicate that the placement of the exhaust outlet in ventilation systems significantly influences indoor aerosol dispersion. The results also show that substantial flow streams may carry tiny particles (≤70 μm) throughout their path. Large particles (≥100 μm) could not go far in cough gas clouds. Most viral particles deposit on solid surfaces in various work sites per specific ventilation rates. Office workers need to be very cautious around these hazardous areas.

Transient Source Terms Estimate in Advection-Diffusion Problems Using the Method of Fundamental Solutions and an Eulerian-Lagrangian Transformation

In this work, transient source terms in advection-diffusion problems are recovered. The solution technique proposed relies on the implicit finite difference method coupled with the method of fundamental solutions, a technique for solving partial differential equations when their fundamental solution is known. The Truncated Singular Value Decomposition was used to overcome the ill-conditioned resulting linear system. The advection-diffusion inverse problem was solved using a Eulerian–Lagrangian method. Several numerical examples were considered for testing purposes by using simulated measurements perturbed with a Gaussian random noise for different Reynolds numbers. Results show that the proposed method provides stable and accurate estimates for the source term.

Numerical Modeling for Prediction of Surface Morphology and Volumetric Defect Using Coupled Eulerian–Lagrangian Approach during Friction Stir Welding of Marine Grade Aluminum Alloy

Numerical Modeling for Prediction of Surface Morphology and Volumetric Defect Using Coupled Eulerian–Lagrangian Approach during Friction Stir Welding of Marine Grade Aluminum Alloy

Bioinspired polymeric heart valves: A combined in vitro and in silico approach

BackgroundPolymeric heart valves (PHVs) may address the limitations of mechanical and tissue valves in the treatment of valvular heart disease. In this study, a bioinspired valve was designed, assessed in silico, and validated by an in vitro model to develop a valve with optimum function for pediatric applications. MethodsA bioinspired heart valve was created computationally with leaflet curvature derived from native valve anatomies. A valve diameter of 18 mm was chosen to approach sizes suitable for younger patients. Valves of different thicknesses were fabricated via dip-coating with siloxane-based polyurethane and tested in a pulse duplicator for their hydrodynamic function. The same valves were tested computationally using an arbitrary Lagrangian–Eulerian plus immersed solid approach, in which the fluid–structure interaction between the valves and fluid passing through them was studied and compared with experimental data. ResultsComputational analysis showed that valves of 110 to 200 μm thickness had effective orifice areas (EOAs) of 1.20 to 1.30 cm2, with thinner valves exhibiting larger openings. In vitro tests demonstrated that PHVs of similar thickness had EOAs of 1.05 to 1.35 cm2 and regurgitant fractions (RFs) <7%. Valves with thinner leaflets exhibited optimal systolic performance, whereas thicker valves had lower RFs. ConclusionsBioinspired PHVs demonstrated good hydrodynamic performance that exceeded ISO 5840-2 standards. Both methods of analysis showed similar correlations between leaflet thickness and valve systolic function. Further development of this PHV may lead to enhanced durability and thus a more reliable heart valve replacement than contemporary options.

Preform geometry determination for a connecting rod forging by CEL model in Abaqus™

AbstractForging is a widely used manufacturing process, and its design and modeling are important to reducing production costs, increasing die lifespan, and improving the mechanical properties of the final product. In this study, the forging process of a connecting rod was modeled using 3D coupled Eulerian Lagrangian (CEL) analysis by FEM. The methodology adopted achieved to determine a preform geometry that reduces final flash and forging load, while ensuring complete filling of the stamp. Starting from the final geometry, the final die was designed. After the first result for an approximately 27% of flash, the material distribution was adjusted decreasing it at the regions where the flash was too large. After an iterative method was applied to determine better preform, a proposal was found that reduced forging force by approximately 42% and the percentage of flash volume by 64% in comparison with the first one. A final flash of about 10% is considered a good objective to reach. Lower values may cause many iterations, not a significant difference in forging loads, the risk of an unfilled die, and complex preform geometries.