Arbitrary Lagrangian Eulerian Technique Research Articles

Toward three-dimensional modeling of the interaction between the air flow and a clamped–free yarn inside the main nozzle of an air jet loom

In air jet looms, the weft yarn is transported from the prewinder to the reed by means of an air flow. In this work, the motion of a yarn inside a main nozzle during the first stage of an insertion process is modeled and analyzed. In this stage, the weft yarn is clamped at one side and free at the other side. Therefore, the deformation waves of a clamped–free yarn are modeled. A three-dimensional, two-way, fluid–structure interaction simulation has been performed in which the yarn is represented as a flexible cylinder and the arbitrary Lagrangian–Eulerian technique is employed. The results of the simulation have been compared quantitatively and qualitatively with experiments. It was, however, not possible to match the initial position and stress state of the yarn in the simulations to that in the experiments. This causes large differences between the simulated and measured yarn positions and wave characteristics, especially at the beginning. The agreement between experimental and simulated wave characteristics notably improves as time progresses, but substantial differences remain. Analyzing the overall motion of the yarn inside the main nozzle shows that the mixing region, where the shocks are located, can be considered as an excitation point. In this point, the aerodynamic normal forces are high if the yarn is not located on the axis of the main nozzle. All deformation waves start from the mixing region and propagate along the yarn.

Modeling the effects of high strain rate loading on RC columns using Arbitrary Lagrangian Eulerian (ALE) technique

In recent years, many studies have been conducted by governmental and nongovernmental organizations across the world in an attempt to better understand the effect of explosive loads on buildings in order to better design against specific threats. This study is intended to contribute to increase the knowledge about how explosions affect reinforced concrete (RC) columns. In this study, a nonlinear model is developed to study the blast response of RC columns subjected to explosive loads. Numerical modeling of RC column under explosive load is presented using advanced finite element code LS DYNA. The obtained numerical model is validated with the experimental test and the results are in substantial agreement with the experimental data. ALE method for blast analysis is presented in the current research. The effects of scaled distance on the damage profile of RC columns are investigated. The results demonstrate that the level of damage increased with describing the scaled distance. Also the results shown duration for the blast loading, and hence the impulse, varies with charge masses at the specified scaled distance. Higher magnitude charge masses produced longer blast loading durations than lower magnitude charge masses. This means that at the same scaled distance, a charge mass of higher magnitude produced a higher impulse than the lower magnitude charge mass. The findings of this research represent the scaled distance is an important parameter that should be taken into account when analyzing the behavior of RC columns under explosive effects. The data collected from this research are being used to improve the knowledge of how structures will respond to a blast event, and improve finite element models for predicting the blast performance of concrete structures.

Rotational motion and lateral migration of an elliptical magnetic particle in a microchannel under a uniform magnetic field

We have numerically investigated the motion of an elliptical magnetic particle in a microfluidic channel subjected to an external uniform magnetic field. By using the direct numerical simulation method and an arbitrary Lagrangian–Eulerian technique, the involved particle–fluid-magnetic field problem can be solved in a fully coupled manner. The numerical predictions of the particle trajectory and orientation with and without a uniform magnetic field are in qualitative agreement with the existing experimental results, and numerical results have revealed the impacts of key parameters such as inlet flow velocity, magnetic field direction, and particle shape on the rotational motion and lateral migration of the elliptical particle. Meanwhile, the shape-based particle separation in a low Reynolds number flow with the aid of an applied uniform magnetic field has also been numerically demonstrated.

Mineral dissolution and wormholing from a pore-scale perspective

A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions. The approach employs a Darcy–Brinkman–Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface. The methodology compares well with the arbitrary-Lagrangian–Eulerian technique. The simulation framework is validated using an experimental microfluidic device to image the dissolution of a single calcite crystal. The evolution of the calcite crystal during the acidizing process is analysed and related to the flow conditions. Macroscopic laws for the dissolution rate are proposed by upscaling the pore-scale simulations. Finally, the emergence of wormholes during the injection of acid in a two-dimensional domain of calcite grains is discussed based on pore-scale simulations.

A study on the different finite element approaches for laser cutting of aluminum alloy sheet

The effectiveness of finite element simulation techniques for laser cutting of 1.2-mm-thick aluminium sheets has been studied. Lagrangian and Arbitrary Lagrangian-Eulerian techniques were used to model and simulate laser cutting process. The reliability of finite element results were evaluated by general energy balance analysis and experimental results. Temperature and stress distribution along with heat-affected zone were predicted during the laser-induced process in line with experimental conditions under ABAQUS finite element code. Heat transfer analysis relying on thermal loading was employed to reach the best efficiency. By using field-emission scanning electron microscope, morphological, structural, and elemental changes in the cutting sections were analyzed along with the X-ray diffraction technique. Obtained stress and heat-affected zone are highly dependent on the element type as well as numerical method. Both numerical method, ALE and Lagrangian, are compared to each other in terms of power absorption, cut surface morphology, and cutting efficiency. The results show that ALE method is in good agreement with experimental data.

Assessment of damage to an underground box tunnel by a surface explosion

Recently, external terrorist activities have become one of the most influential events on tunnel structure safety because of the absence of proper mechanisms to detect these events in time to take preventive action. The present study used ANSYS/LS-DYNA software to investigate the damage behaviour of an underground box frame tunnel caused by a surface explosion of a sedan, van, small delivery truck (SDT), and container carrying 227, 454, 1814, and 4536kg, respectively, of TNT charge weight. The Arbitrary Lagrangian Eulerian (ALE) technique was used to simulate and monitor the propagation of the blast pressure waves into the soil. The validation results indicated that the pressure waves propagated into the soil as hemispherical waves, and the peak pressure values closely matched the predicted values of the technical design manual TM5-855-1, except for large distances. Therefore, an equation was derived to calculate the values of the peak pressure at large distances for each explosion case. Intensive parametric studies were conducted to evaluate the interaction between the explosive charge weight, the tunnel lining thickness and the burial depth, which has a significant effect on tunnel safety. The assessment of the damage levels using the single degree of freedom (SDOF) approach proved that the tunnel experienced little damage when the explosive charge is a sedan or van with a lining thickness of 250, 500 or 750mm at burial depths of 4, 6, or 8m. However, tunnel collapse occurred when the lining thickness was 250mm, and the tunnel was subjected to an explosion of an SDT or container at all investigated depths, as well as the case for a lining thickness of 500mm at a depth of 4m for the container explosion. The tunnel lining with a thickness of 750mm appeared to be highly resistant to the explosion of an SDT or container for all the investigated depths, and the best resistance was achieved at a depth of 8m, which should be considered by designers to ensure the safety of an underground box tunnel when subjected to an incredible surface explosion.

Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces

A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward difference formula. The ALE technique allows to maintain the mesh regularity during the time integration, which is not possible in the original evolving surface finite element method. Unconditional stability and optimal order convergence of the full discretizations is shown, for algebraically stable and stiffly accurate Runge-Kutta methods, and for backward differentiation formulae of order less than 6. Numerical experiments are included, supporting the theoretical results.

Identification and modeling of cutting forces in ball-end milling based on two different finite element models with Arbitrary Lagrangian Eulerian technique

This paper presents two different finite element (FE) models with Arbitrary Lagrangian Eulerian (ALE) technique to evaluate the effectiveness of FE modeling for estimating the cutting forces in ball-end milling. The milling forces are modeled using a unified mechanics of the cutting approach, which is based on the shear stress, friction coefficient and chip thickness ratio provided through the orthogonal cutting process. Two-dimensional (2D) FE models of the orthogonal cutting are designed for estimating the milling forces using this approach, and explicit dynamic thermo-mechanical analyses are performed to determine the orthogonal cutting data from a set of cutting and material parameters. The oblique transformation approach is used to carry the orthogonal cutting data to the milling cutter geometry. Simulations are numerically and analytically carried out for machining of 20NiCrMo5 material with a tungsten carbide tool and the estimated forces are compared to measured ones. The estimation of milling forces is accurately achieved by the unified mechanics of cutting approach with orthogonal cutting data based on the ALE technique using Eulerian-Lagrangian boundaries. Good agreements between the estimated and measured outcomes reveal an obvious knowledge of an efficient and accurate FE model for determining the ball-end milling forces.

Blast wave dynamics: The influence of the shape of the explosive

A numerical model is developed to analyse the influence of the shape of a high-explosive on the dynamics of the generated pressure wave. A Multi-Material Arbitrary Lagrangian Eulerian (MM-ALE) technique is used as the CONWEP approach is not adequate to model such situations. Validation and verification of the proposed numerical model is achieved based on experimental data obtained from the bibliography. The numerical model provides relevant information that cannot be obtained from the experimental results. The influence of the mass and shape of the high-explosive is studied and correlated to the dynamics of the generated blast wave through the analysis of peak pressures, time of arrival and impulse. Tests are done with constant mass hemispherical, cylindrical and flat-shaped Formex F4HV samples. A detailed analysis of the generated blast wave is done, along with a thorough comparison between incident and reflected waves. It is concluded that the dynamic effects of the reflected pressure pulses should always be considered in structural design, most relevantly when analysing closed structures where the number of reflections can be significant. The model is proved reliable, concluding that the frontal area of the high-explosive is a determinant driving parameter for the impulse generated by the blast.

Numerical investigation on effect of leaflet thickness on structural stresses developed in a bileaflet mechanical heart valve for its sustainable manufacturing

Flow induced structural stresses can cause mechanical prosthetic aortic valve to fail due to yielding. In this study, we have performed the structural analysis, especially the effect of leaflet thickness on equivalent stresses developed in a Bileaflet mechanical heart valve (BMHV) due to blood flow through it has been investigated. The leaflet thickness varies from 0.5mm to 0.7mm, by 0.1mm. A fluid-structure interaction approach based on Arbitrary Lagrangian Eulerian (ALE) technique has been employed with the aid of an user defined function (UDF). Results of the analysis show that high von Mises stresses are developed in BMHV with leaflet thickness of 0.5mm and 0.6mm, being 75% and 13% higher than allowable equivalent stress respectively. Such thinner leaflets are therefore, not sustainable to be replaced with diseased aortic valve.

Analysis of fluid-solid interaction in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane

This paper investigates numerically the problem of unsteady natural convection inside a square cavity partitioned by a flexible impermeable membrane. The finite element method with the arbitrary Lagrangian-Eulerian (ALE) technique has been used to model the interaction of the fluid and the membrane. The horizontal walls of the cavity are kept adiabatic while the vertical walls are kept isothermal at different temperatures. A uniform magnetic field is applied onto the cavity with different orientations. The cavity has been provided by two eyelets to compensate volume changes due the movement of the flexible membrane. A parametric study is carried out for the pertinent parameters, which are the Rayleigh number (105–108), Hartmann number (0–200) and the orientation of the magnetic field (0–180°). The change in the Hartmann number affects the shape of the membrane and the heat transfer in the cavity. The angle of the magnetic field orientation also significantly affects the shape of the membrane and the heat transfer in the cavity.

Coupling fluid–structure interaction with phase-field fracture

In this work, a concept for coupling fluid–structure interaction with brittle fracture in elasticity is proposed. The fluid–structure interaction problem is modeled in terms of the arbitrary Lagrangian–Eulerian technique and couples the isothermal, incompressible Navier–Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-formulated in Lagrangian coordinates to combine it with fluid–structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.

Characterization of Polymeric Membranes Under Large Deformations Using Fluid-Structure Coupling

The mechanical properties of Ogden material under biaxial deformation are obtained by using the bubble inflation technique. First, pressure inside the bubble and height at the hemispheric pole are recorded during bubble inflation experiment. Thereafter, Ogden's theory of hyperelasticity is employed to define the constitutive model of flat circular thermoplastic membranes (CTPMs) and nonlinear equilibrium equations of the inflation process are solved using finite difference method with deferred corrections. As a last step, a neuronal algorithm artificial neural network (ANN) model is employed to minimize the difference between calculated and measured parameters to determine material constants for Ogden model. This technique was successfully implemented for acrylonitrile-butadiene-styrene (ABS), at typical thermoforming temperatures, 145°C. When solving for the bubble inflation, the recorded pressure is applied uniformly on the structure. During the process inflation, the pressure is not uniform inside the bubble, thus full gas dynamic equations need to be solved to get the appropriate nonuniform pressure to be applied on the structure. In order to simulate the inflation process accurately, computational fluid dynamics in a moving fluid domain as well as fluid structure interaction (FSI) algorithms need to be performed for accurate pressure prediction and fluid structure interface coupling. Fluid structure interaction solver is then required to couple the dynamic of the inflated gas to structure motion. Recent development has been performed for the simulation of gas dynamic in a moving domain using arbitrary Lagrangian Eulerian (ALE) techniques.

Response of segmented bored transit tunnels to surface blast

Increasing threat of terrorism highlights the importance of enhancing the resilience of underground tunnels to all hazards. This paper develops, applies and compares the Arbitrary Lagrangian Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH) techniques to treat the response of buried tunnels to surface explosions. The results and outcomes of the two techniques were compared, along with results from existing test data. The comparison shows that the ALE technique is a better method for describing the tunnel response for above ground explosion with regards to modeling accuracy and computational efficiency. The ALE technique was then applied to treat the blast response of different types of segmented bored tunnels buried in dry sand. Results indicate that the most used modern ring type segmented tunnels were more flexible for in-plane response, however, they suffered permanent drifts between the rings. Hexagonal segmented tunnels responded with negligible drifts in the longitudinal direction, but the magnitudes of in-plane drifts were large and hence hazardous for the tunnel. Interlocking segmented tunnels suffered from permanent drifts in both the longitudinal and transverse directions. Multi-surface radial joints in both the hexagonal and interlocking segments affected the flexibility of the tunnel in the transverse direction. The findings offer significant new information in the behavior of segmented bored tunnels to guide their future implementation in civil engineering applications.

A numerical study of wall pressure and granular flow in a flat-bottomed silo

This paper presents a numerical study of the granular flow in the discharge of a flat-bottomed model silo. The behaviour of the stored granular material is modelled using the finite element (FE) method based on an Arbitrary Lagrangian–Eulerian (ALE) frame of reference, which has shown advantageous performance over the classical FE methods in simulating the silo filling and discharge process in a series of studies leading up to this investigation. Experimental results have been used to validate the computational model using the ALE technique. The spatial distribution and time history of the pressures acting on the vertical silo walls predicted by the FE model are found to resemble well the test results. A semi-mass flow pattern has been predicted by the numerical model, which is very consistent with the corresponding experimental observation. With the validated numerical model, the flow behaviour specifically under a flat-bottomed geometry of silos is examined. Based on the velocity distribution in the granular material, a critical velocity ratio criterion is proposed and used to identify the flow channel boundary. A further numerical study has shown that the flow behaviour in the flat-bottomed silo is closely related to the shear strength of the material, which is represented by the internal friction angle for the cohesionless sand considered in the present study.

Finite element modelling of orthogonal machining of hard to machine materials

This paper presents a detailed finite element model to predict deformation and other machining characteristics involved in high-speed orthogonal machining (cutting speed > 54 m/min) of hard-to-deform materials like Ti6Al4V. The influence of various cutting parameters like feed rate, spindle speed, and rake angle, on the output parameters like cutting force and surface finish, was analysed. The paper tries to relate the degree of surface finish with the variance of the effective plastic strain. The Johnson-Cook material model is used to describe the material constitutive behaviour, and the Johnson-Cook damage model is used to establish the damage criteria. Due to the high machining costs associated with the titanium alloy, the model is first validated using aluminium alloy (Al2024-T351), and the same model is then extended to predict the results for titanium alloy. The matrix for the design of experiments (DOE) considers a full factorial approach, with about 48 simulations, for a proper understanding on the influence of the major machining parameters. A dynamic, explicit integration scheme is used along with the arbitrary Lagrangian-Eulerian (ALE) technique to accurately predict material flow. This paper also presents a unique method to tackle the commonly encountered numerical issues involved in modelling self-contact.

Flowfield dependent variation method for one-dimensional stationary and moving boundary problems

Complex fluid problems arise during fluid-structure interactions and pose a major challenge in the development of a stable generic numerical approach. Owing to the robustness of flowfield dependent variation (FDV) method in dealing with complex flow interactions, a new numerical procedure using the FDV method coupled with arbitrary Lagrangian-Eulerian (ALE) technique is developed. The combination of FDV and ALE method is discretised using finite volume method in order to give flexibility in dealing with complicated geometries. The formulation itself yields block tridiagonal matrix for one-dimensional formulation, which can then be solved using a relatively simple block lower-upper decomposition method. One-dimensional inviscid flows for stationary and moving boundary problems are solved using the proposed method. Stability criterion for stationary boundary problems has been derived. The method is found to be conditionally stable and its stability is dependent on the FDV parameters. Several numerical tests have been conducted and the results show good agreement with exact and available numerical solutions in the literature.

A New Method to Simulate Free Surface Flows for Viscoelastic Fluid

Free surface flows arise in a variety of engineering applications. To predict the dynamic characteristics of such problems, specific numerical methods are required to accurately capture the shape of free surface. This paper proposed a new method which combined the Arbitrary Lagrangian-Eulerian (ALE) technique with the Finite Volume Method (FVM) to simulate the time-dependent viscoelastic free surface flows. Based on an open source CFD toolbox called OpenFOAM, we designed an ALE-FVM free surface simulation platform. In the meantime, the die-swell flow had been investigated with our proposed platform to make a further analysis of free surface phenomenon. The results validated the correctness and effectiveness of the proposed method for free surface simulation in both Newtonian fluid and viscoelastic fluid.

Design and Analysis of Fluid Structure Interaction in a Horizontal Micro Channel

This paper demonstrates techniques for modelling fluid-structure interactions using COMSOL Multiphysics v 4.2a, which illustrates how to solve for the flow in a continuously deforming geometry using the Arbitrary Lagrangian-Eulerian (ALE) technique and corresponding deformation, displacement analysis. The present work reports the computation of the deformation and displacement in structure along with the fluid flow in a continuously deforming geometry, for different types of structures like circular, rectangular, ellipse, which are placed inside of the flow channel as an obstacle. Fluid structure interaction between wind and sails, modelling of parachutes, fluid structure thermal calculation, stability and response of aircraft wings, the flow of blood through arteries, response of bridges and tall buildings to winds, prediction of aero elastic parameters in military aircrafts, vibration of turbine and compressor blades and the oscillation of heat exchangers can also be analysed using this method

Mesoscale simulation of the sedimentation of melting elliptical particle

In this paper, a mathematical relationship between particle melting rate and its surface heat flux is established to solve the problem of melting of elliptical particle sedimentation based on the direct numerical simulations of particle sedimentation when taking account of thermal convection within the framework of the arbitrary Lagrangian-Eulerian technique. The elliptical particle with different initial angles is released in a mesoscale channel under gravity. Compared with the isothermal elliptical particle sedimentation, the melting elliptical particle shows large differences in moving trajectories, the forces exerting on the particle and velocities, which come from the consideration of fluid convection, mass loss, and shape change. More specifically, 1) in the case of isothermal elliptical particle sedimentation, the velocity, the horizontal trajectory, and the force vary periodically. However, the amplitude recedes gradually, and finally becomes zero in the case of the melting elliptical particle, which is caused by the mass lost and shape change. 2) The equilibrium position of the major axis will finally be perpendicular to the direction of sedimentation. So, the initial angle of slope (θ) usually affects the sedimentation in the beginning, and vanishes after a period of time. 3) The downward convection induced by the cold fluid accelerates the velocity of the melting particle. The angular velocity, force and horizontal amplitude of the melting particle become smaller than those of the isothermal particle, and finally recedes to zero. In our study, the investigation of coupled heat transfer, fluid-solid system and shape change is carried out, and some new features are found out.