Arbitrary Lagrangian-Eulerian Method Research Articles

Research on the characteristics and similarity relationships of impact load reduction of a vehicle entering water

The strong, transient, and high-peak impact load caused by a vehicle entering water at high speed is the primary factor threatening its structural strength and equipment safety. One of the effective methods for water entry protection is to use head-mounted buffer components. To this end, based on the arbitrary Lagrangian-Eulerian method, a numerical model of impact load reduction of water entry was established in this study. The results showed that the impact load could be characterised by a narrow pulse width and a high peak value, which gradually stabilises in a fluctuating manner. Five typical stages in the failure process of the cushion foam and four typical stages in that of the nose cap were observed. The prediction accuracy decreased as the scaling ratio decreased. Furthermore, the buffer components increased the occurrence of an error in the prediction results of the scaling model. The primary causes are the strain-rate sensitivity of the foam and dissimilarity in the failure criteria, which lead to dissimilarities in the foam failure process after scaling. This research will be useful for the designing of water load reduction structures and scaled model experimental schemes.

Numerical study on atmospheric explosive welding based on the 2D structured arbitrary Lagrangian-Eulerian method

Smooth particle hydrodynamics (SPH) is often adopted to simulate the waveform interface, which has a crucial effect on the bonding quality in explosive welding (EXW). However, owing to the nature of the SPH method, it is difficult to evaluate the influence of the air medium and calculate detailed waveform structure. In this study, a Cu-Q235 steel EXW model containing air medium was established using a structured arbitrary Lagrangian-Eulerian (S-ALE) method. A full-size 2D model was first performed to acquire welding parameters, which were set to the initial conditions for the next oblique collision method. Subsequently, the experiment was conducted to verify the accuracy of the simulations. The results show that the S-ALE method can effectively predict the waveform and acquire the detailed process of the EXW. With the addition of an air medium, the calculated velocity and pressure of the shock wavefront were approximately 3300 m·s−1 and 15 MPa, respectively. Despite the limited effect of the gas shockwave on the overall waveform, the influence on the large-scale or thin plates cannot be ignored. Furthermore, the simulation indicates that the participation of the air during the wave formation led to the generation of the pore in the vortex zone. The proposed method could predict the waveform structure and optimize the manufacturing process of composite plates in the atmospheric EXW.

Study on structural response of water-back plate under the combined action of shock wave and bubble loads generated by cylindrical charge in deep-water environment

The structural response of the water-back plate under the combined action of shock wave and bubble loads at water depths of 1–300 m is investigated numerically using an arbitrary Lagrange–Euler method. The accuracy of the numerical model is verified by a comparison with the shallow-water experimental results and theoretical results. Specifically, the influences of the water depth and length-to-diameter ratio of the cylindrical charge on the combined damage effect of the shock wave and bubble loads are analysed. The following conclusions are drawn. As water depth increases from 1 m to 300 m, the plastic deformation energy of the water-back plate decreases, meanwhile the permanent deformation mode of a water-backed plate changes from convex to concave under the combined action of shock wave and bubble loads; when the charge has large length-to-diameter, the plastic deformation energy of radial plate under combined action of the shock wave and bubble loads is higher than that of axial plate at water depths of 1–300 m, and both difference decrease with increasing water depth; the combined damage effect of the shock wave and bubble loads can be enhanced in the radial direction by increasing the length-to-diameter ratio in deep-water environments. When the length-to-diameter ratio increases from 1:1 to 8.2:1, the plastic deformation energy of the radial plate gradually increases by 7.58 % from 10.68 to 11.49 J.

Dynamic response and vulnerability analysis of pier under near-field underwater explosion

Marine reinforced concrete constructions (suspended tunnels, undersea pipelines, and cross-sea bridges) are inherently at risk from underwater explosions due to the rising incidence of worldwide terrorism. Sea-crossing bridges are as an important land-sea connection channel, whose anti-explosion performance cannot be ignored. In this paper, the dynamic response and damage mechanism of piers of sea-crossing bridge under underwater explosion loads are studied by the arbitrary Lagrangian-Eulerian (ALE) method. Firstly, the correctness of the explosive load and reinforced concrete material models is verified by the Zamyshlyaev formula and underwater explosion test, respectively. Secondly, the finite element (FE) model of a pier under an underwater explosion load is established. Taking the residual vertical bearing capacity of the pier as the performance index, the damage evaluation method and four damage levels of the pier under explosion load are put forward. The study of different parameters such as explosive weight, explosion location, explosion height, and explosion distance shows that the damage to the pier is the most serious when the detonation point is directly below the projection of the pier cap. The residual bearing capacity of the pier falls exponentially as explosive weight increases. Different detonation heights have significant effects on the damage to the pier. Additionally, it is found using the explosion vulnerability analysis approach that the pier is very susceptible to collapse when the explosive weight is 350 kg.

Application of the Constrained Formulation to the Nonlinear Sloshing Problem Based on the Arbitrary Lagrangian–Eulerian Method

Abstract This study deals with an application of constrained formulation to a nonlinear sloshing problem based on the arbitrary Lagrangian–Eulerian finite element method (ALE). The ALE method incorporates a discretized form of equations of motion with mesh updating algorithms in order to prevent a problem of mesh distortion. This paper focuses on an analytical aspect of such treatments as constrained systems in the formulation of the ALE method. Since the mesh updating algorithms give algebraic relations for nodal coordinates, this study treats these relations as constraints. Then, we introduce formulation for constrained systems based on the method of Lagrange multipliers. As a result of this formulation, equations of motion are given by differential algebraic equations (DAEs) consisting of differential equations for time evolution of physical quantities and algebraic equations (constraints). The present method can be classified into a kind of augmented formulation. Moreover, we present a size-reduction technique used in the Newton–Raphson method in order to remove a part of the redundant degrees-of-freedom in the iterative procedures, because the resulting set of DAEs involves a larger number of unknowns than the minimal number of degrees-of-freedom due to the introduction of the constrained formulation. The derived reduced system still holds the physically essential part of equations of motion for the sloshing problem. Even though it is not reduced to the minimal degrees-of-freedom, it does not involve algebraically complicated and inefficient procedures in computation. In addition, this study presents a method to introduce damping effects defined in the modal space into the FEM models. The proposed approach is validated by comparisons with experimental data in the time domain analysis.

A Method-of-Lines Framework for Energy Stable Arbitrary Lagrangian–Eulerian Methods

A Method-of-Lines Framework for Energy Stable Arbitrary Lagrangian–Eulerian Methods

Experimental research and finite element analysis on blast resistance of RRACFST columns

In order to research the dynamic response of rectangular recycled aggregate concrete-filled steel tubular (RRACFST) columns under blast loads, three contact blast experiments were carried out on three column models, and their different failure modes, dynamic strain rates and acceleration rates were determined. The numerical model was established using the arbitrary Lagrangian-Eulerian method and the fluid–solid coupling algorithm available in the explicit nonlinear finite element software LS-DYNA™, and the reliability and validity of the numerical model were verified by the experimental results. On this basis, the numerical model was used to analyze the parameters, as well as the effects of the replacement rate of recycled aggregate, column height, steel tube thickness and steel strength on the contact explosion resistance of RRACFST columns. Also, the advantages and disadvantages of overall refinement and local refinement are compared. The study results show that the RRACFST columns had basically no overall response to the action of contact blast loads, producing only a small explosion crater in the detonation area, without breaking the steel tube, and with no recycled aggregate concrete (RAC) overflows. The steel tube thickness was the decisive factor affecting the blast resistance performance of the RRACFST columns. In addition, for the numerical simulation of contact explosion, the local refinement was better than the overall refinement.

Numerical simulation of flow past an 8:1 oscillating rectangular cylinder at Re = 22 000

To investigate the influence of structure’s oscillatory motion on flow, the present study employs the arbitrary Lagrangian–Eulerian method in k–ω shear stress transport (SST) turbulence model to simulate the flow past an oscillating rectangular cylinder at Re= 22 000. The cylinder undergoes reciprocating sinusoidal motion at a specified frequency f e, and the frequency ratio fr (defined as the ratio of cylinder oscillation frequency f e to the stationary cylinder vortex shedding frequency f 0), ranges from 0 to 4. The results demonstrate that, in the synchronization region (0.8 ⩽ fr⩽ 1.2), the drag coefficient shows the most notable variation and reaches its maxima at fr= 1.1 and the root mean square (r.m.s.) of the lift coefficient is proportional to the square of fr (, R 2 = 0.99). Moreover, the present study compares the similarities and differences of vortex shedding morphology between stationary and oscillating cylinders. With the increase of fr, the wake vortex gradually transforms from a single-row arrangement on the wake centerline to a parallel double-row arrangement, with the main vortex modes in the wake region observed as ‘2S’, ‘P + S’, ‘2P’ and ‘C’. Furthermore, spectral analysis, including amplitude spectrum analysis and wavelet analysis, in addition to probability density function statistical methods, are employed to comprehensively understand the velocity characteristics of the wake region. The results indicate that the oscillation of the cylinder reduces the correlation of the wake velocity. Those are beneficial in understanding the interaction between turbulence and structural fluid-induced motion.

An arbitrary Lagrangian–Eulerian formulation for the Reynolds equation considering the JFO boundary condition

AbstractIn the realm of lubrication theory, the hydrodynamics of the fluid lubricant are commonly elucidated through the Reynolds equation. Its establishment stems from using the Eulerian description method, restricting the fluid domain to a fixed spatial configuration. However, certain scenarios necessitate coupling the Reynolds equation with solid deformation, wherein the fluid boundary undergoes alterations concurrent with the displacement or deformation of the solid. In such cases, the employment of a movable fluid domain becomes imperative. To address this requirement, this contribution introduces the arbitrary Lagrangian–Eulerian method, which effectively transforms the reference system of the Reynolds equation into a fluid domain amenable to arbitrary movement. Subsequently, the weak formulation associated with the movable fluid domain is derived and synergistically combined with a preexisting cavitation formulation. This integration facilitates an efficient solution of the Reynolds equation utilizing the finite element method while duly accounting for the mass‐conserving cavitation effects. Ultimately, a transient hydrodynamic lubrication example is presented to demonstrate the feasibility of the newly developed formulations.

Topology modification based rezoning strategies for the arbitrary Lagrangian-Eulerian method on unstructured hexahedral meshes

Topology modification based rezoning strategies for the arbitrary Lagrangian-Eulerian method on unstructured hexahedral meshes

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.

Asymmetric droplet evaporation on inclined surfaces

A computational model based on disjoining pressure is developed to study the asymmetric evaporation of droplets on an inclined substrate. In the proposed formulation, the disjoining pressure is combined with the arbitrary Lagrange-Euler method (ALE) to describe the solid-liquid interaction and investigate the contact angle hysteresis during evaporation. This model can be used to simulate the droplet evaporation modes of constant contact radius (CCR), constant contact angle (CCA) and “Stick-Slip” (mix evaporation mode), while the results are in good agreement with the experimental data. The obtained droplet shape for different inclined angles shows an asymmetric variation in contact angle at the front and rear ends, with the mean contact angle decreasing as the tilt angle increases. The evaporation flux is symmetric in the case of a horizontal substrate, however, when the substrate is tilted, the front and rear contact angles are modified, which leads to a larger evaporation flux on the rear contact line. Moreover, the asymmetric droplet morphology leads to asymmetric temperature field and vortex in the initial stage of evaporation; as evaporation proceeds, however, the flow and temperature fields within the droplet exhibit a gradual convergence towards symmetry. Moreover, when droplets evaporate on a pair of substrates with complementary tilt angles, their lifetimes exhibit a remarkable similarity. From the evaporation rate evolution, it yields that the larger the percentage of pinning time on the contact line, the faster the evaporation rate of the droplet. The evaporation rate of droplets was 14.76% higher at a tilt angle of α=0° than the case of α=45°.

Magnetic regulation on evaporation behavior of ferrofluid sessile droplets.

Active magnetic regulation is an emerging subject due to the special and programmable wettability of the sessile ferrofluid droplet. The interaction between liquid and externally applied magnetic field gives rise to controllable spreading and thus evaporation. This work reports the experimental and numerical results of the natural evaporation of a ferrofluid droplet under the effect of a nonuniform magnetic field. The evaporation process of droplets is described into two stages in terms of the geometric distortion and the appearance of the deposition pattern. The presence of the magnetic field leads to a transition of droplet drying from the disk shape with a ring to multiple peaks. A numerical model is established to simulate the evaporation process of ferrofluid droplets with the arbitrary Lagrangian-Eulerian method for tracking droplet deformation. The increasing magnetic flux could effectively enlarge the contact radius and enhance the internal flow of the ferrofluid droplet, thus promoting the evaporation process. The numerical results are verified by comparing the droplet geometry deformation with the experimental results. In both the numerical and experimental investigations, the externally applied magnetic field shortens the process of ferrofluid droplet evaporation. The design and optimization of the magnetic field play an important role in regulating ferrofluid droplet evaporation, which in turn facilitates technological advances in industries such as evaporative cooling and inkjet printing.

Breakup of thin liquid films with viscous interfaces

Thin liquid films are ubiquitous in nature and have many practical applications. From biological films to the curtain coating process, thin films are present in both large and small scales. Despite their importance, understanding the stability of these films remains a significant challenge due to the fluid–fluid interface that is free to deform, affected by interfacial tension and complex rheological behavior. Instabilities in thin films are often caused by van der Waals attractions, which can lead to the rupture of the layer. To investigate the rupture dynamics, numerical methods are commonly used, such as asymptotic derivations of the lubrication theory or interface tracking methods. In this paper, we present a computational study of the breakup dynamics of a stationary thin liquid sheet bounded by a passive gas with a viscous interface, using the arbitrary Lagrangian–Eulerian method and the Boussinesq–Scriven constitutive law to model the rheological behavior. Our results demonstrate that the stability of thin liquid films is influenced by both surface rheology and disjoining effects and that the viscous character of the interface can delay sheet breakup, leading to more stable films.

Fluid structure interaction of supersonic parachute with material failure

The material damage of parachute may occur in parachutes at high speeds, and the growth of tearing may finally lead to failure of aerospace mission. In order to study the damage mechanism of parachute, a material failure model is proposed to simulate the failure of canopy fabric. The inflation process of supersonic parachute is studied numerically based on Arbitrary Lagrange Euler (ALE) method. The ALE method with material failure can predict the transient parachute shape with damage propagation as well as the flow characteristics in the parachute inflation process, and the simulated dynamic opening load is consistent with the flight test. The damage propagation mechanism of parachute is then investigated, and the effect of parachute velocity on the damage process is discussed. The results show that the canopy tears apart by the fast flow from the initial damaged area and the damaged canopy shape leads to the asymmetric change of the flow structure. With the increase of Mach number, the canopy tearing speed increases, and the tearing directions become uncertain at high Mach numbers. The dynamic load when damage occurs increases with the Mach number, and is proportional to the dynamic pressure above the critical Mach number.

Fluid Dynamics Calculation in SF6 Circuit Breaker during Breaking as a Prerequisite for the Digital Twin Creation

The requirements to switching the capacities of SF6 circuit breakers submitted by Russian Grid companies are difficult to satisfy. The first limitation is related to material and financial costs in order to create a new requirement-satisfying switching device. The second limitation is dictated by the necessity of calculating complex physical processes in a circuit braker interrupter during fault–current making or breaking before creating a prototype. The latter task is reduced to the problem of simulating the processes of interaction between the switching arc and the SF6 gas flow. This paper deals with the solution of the problem both analytically by a special method and numerically by a numerical software package through the creation of a mathematical model of the interaction process. The switching arc is taken into account as a form of a temperature source, based on experimental data on measuring the temperature of the arc column. The key feature of the research is to use the finite element method based on a moving mesh—the Arbitrary Lagrangian Eulerian (ALE) method. Such a problem statement allows us to take the contact separation curve of the circuit breaker into account as the input data of the model. The calculations were carried out during fault-current breaking by a 110 kV SF6 dead-tank circuit breaker. The calculations of pressure and mass flow in the under-piston volume change, gas flow speed, and temperature depending on the contact separation are given. The proposed model of the switching arc was used to simulate the process of 25 kA symmetrical fault–current breaking and was compared with an experiment.

An arbitrary Lagrangian–Eulerian method for analyzing finite-amplitude viscous acoustic waves radiated from vibrational solid boundaries: An implicit method

This paper is concerned with the development of an arbitrary Lagrangian–Eulerian (ALE) method for predicting nonlinear acoustic waves radiated from large-amplitude vibrational solid boundaries immersed in viscous fluids of infinite extent. The method is formulated based on a nonlinear acoustic model characterized by velocity potential and acoustic pressure. Unsplit implementations of three perfectly matched layer (PML) techniques are presented, namely conventional PML, convolution PML, and complex frequency-shifted PML (CFS-PML), to enable bounded-domain modeling of nonlinear acoustic waves propagating in an unbounded fluid medium. The long-time stability characteristics of the three distinct PML techniques are examined through theoretical analysis and numerical verification of their ability to absorb evanescent waves. Our results reveal that the CFS-PML technique exhibits superior long-time stability performance compared to the other two techniques. The CFS-PML is also compared to two different absorbing layer techniques: the Kosloff Absorbing Layer (KAL) technique and the Acoustic Black Hole (ABH) technique. The finite element method is adopted for spatial discretization of the finite-amplitude acoustic wave model, and an implicit predictor–corrector algorithm is proposed for time advancement. Several benchmark problems, including acoustic waves produced by a vibrational piston, and transversely oscillating and pulsating cylinders, are analyzed by the proposed method. It is found that the proposed method attains a second-order rate of convergence for spatial discretization, and the convergence rate in terms of the time step size is about first-order. The application of the method to acoustic levitation problems is also demonstrated, and the nonlinear phenomenon of acoustic waves in a single-axis acoustic levitator is discussed.

Numerical investigation of displacement pile installation in silica sand

The penetration of deep foundations into sand is a classic geotechnical engineering problem that carries not yet fully understood aspects of the soil-pile interaction. The complexity of rigorous numerical and experimental studies of these foundations is well-stated in the literature. Extensive measurements of the properties of the soil that surrounds the pile are difficult to obtain experimentally. In this paper, the analysis of the installation of closed-ended, displacement piles in two silica sands is undertaken. Centrifuge tests from the literature on loose and dense dry sand samples are employed for validation of the numerical models, based on the Arbitrary Lagrangian-Eulerian (ALE) method. To capture the constitutive behaviour of the sand, the hypoplastic constitutive law with intergranular strain is adopted. After successful validation, an investigation on the variation of the initial conditions of the soil mass surrounding the pile during its installation is undertaken, and their influence on the tip resistance, the radial stresses, and the void ratio at the target penetration depths are identified. This paper illustrates the effect of cone apex angle on the state of sand after installation. Flat-ended piles tend to create clear zones of dilated material around the shaft.

WITHDRAWN: Effect of geo-material on dynamic response of tunnel subjected to surface explosion

Prime materials involved in a problem such as underground structures are concrete, reinforcement steel and geo-material surrounding the tunnel. Among these three materials, concrete and steel are manufactured materials and their properties can be controlled up to a certain extent. However, geomaterial is a naturally occurring material whose constitutive properties vary from region to region making it highly unpredictable. Findings from one study cannot be applied to other geotechnical problems directly, especially, in the case of tunnels subjected to surface explosion. The blast wave generated has to travel through the geo-material before it interacts with the tunnel. As the shock wave propagates radially its characteristics are most likely to get altered by the geo-material. Limited study has been carried out considering this problem. In the present study, the effect of various types of geo-material on the blast response of tunnels subjected to surface explosion is investigated. Finite element analysis has been carried out using LS-DYNA® wherein the problem has been modelled using multi-material arbitrary Lagrangian Eulerian (MM-ALE) method. Materials with fluid behavior such as air, explosive and soil are modelled using ALE formulation. Other materials including tunnel lining, reinforcing steel and rock are modelled using Lagrangian formulation. Blast loading is simulated using Jones-Wilkins-Lee (JWL) equation of state. Geo-materials considered for the comparative study are sandy loam, sandstone, and granite. Vertical displacement measured at the crown of the tunnel is used to determine the response of tunnel. Sandy loam soil being a highly compressible soil, exhibits non-linear and fluid-like behavior under high strain loading such as explosion. Tunnel undergoes extreme deformation in the case of sandy loam soil as compared rock cases. Additionally, the effect of weathering of rock on the tunnel response is investigated in the case of sandstone and granite. It was observed that weathering rock led to more displacement of tunnel crown as compared to intact rock.

Numerical Simulation of Shock Wave Damage to Medium-Range and Long-Range Targets

In order to accurately analyze the effect of a shock wave on a missile launch vehicle as a whole and on its components when the launch vehicle is at a medium or long distance from the detonation center, a simulation method based on the empirical algorithm and numerical analysis was carried out in this study. The method significantly reduced the computational cost while ensuring computational accuracy. Based on the simulation method, a finite element model for a typical missile launch vehicle was established that consisted of 2.5 million elements. Based on the structured arbitrary Lagrangian-Eulerian method and the fluid-structure coupling algorithm, it took the model only a few hours to simulate the second-level physical process. Next, a shock wave load model was built with a 2000 kg TNT equivalent detonation condition, and the degree of damage to the launch vehicle within 25–45 m from the detonation center was analyzed. The results showed that the joint action of the shock wave overpressure and the dynamic pressure was the main source of damage. Specifically, the missile launcher, the cab, and the fuel tank were the key vulnerable parts. The effective damage radius of the 2000 kg TNT equivalent detonation to the missile launch vehicle was 35 m.