Arbitrary Lagrangian Eulerian Research Articles

TwoPhaseInterTrackFoam: an OpenFOAM module for Arbitrary Lagrangian/Eulerian Interface Tracking with Surfactants and Subgrid-Scale Modeling

We provide an implementation of the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian (ALE) Interface-Tracking method for simulating incompressible, immiscible two-phase flows as an OpenFOAM module. In addition to interface-tracking capabilities that include tracking of two fluid phases, an implementation of a Subgrid-Scale (SGS) modeling framework for increased accuracy when simulating sharp boundary layers is enclosed. The SGS modeling framework simplifies embedding subgrid-scale profiles into the unstructured Finite Volume discretization. Our design of the SGS model library significantly simplifies adding new SGS models and applying SGS modeling to Partial Differential Equations (PDEs) in OpenFOAM. Program summaryProgram Title: twoPhaseInterTrackFoamCPC Library link to program files:https://doi.org/10.17632/6b49wb7fvd.1Developer's repository link:https://gitlab.com/interface-tracking/twophaseintertrackfoamreleaseLicensing provisions: GPLv3Programming language: C++Nature of problem: Two-phase flow problems involving surface-active agents (surfactants), variable surface tension force and very sharp boundary layers.Solution method: An OpenFOAM implementation of the Arbitrary Lagrangian / Eulerian Interface Tracking method.

Regime map of non-coalescence between two equal-sized uncharged water droplets suspended in oil: A numerical study

This paper is devoted to numerical simulation of collision and consequent separation of conductive same-sized droplets of different sizes (from 0.3 to 2 mm) under the effect of a constant voltage exceeding the threshold of the transition from coalescence to non-coalescence. The computations were based on the arbitrary Lagrangian–Eulerian method—the interface between the two phases was represented as a geometry line that moves in accordance with the calculated fluid velocity throughout the solution of the problem. Four possible modes and ranges of electric field strength values corresponding to them were identified, ranked by their negative impact on the demulsification process: rebound, separation into three or multiple drops, and electrospraying. This includes the narrow ranges of electrospraying beside the “coalescence-non-coalescence” threshold and during the “rebound-multidrops” transition. A “regime map”—a diagram of possible outcomes depending on the size of drops and the electric field strength—was formed and analyzed to summarize the results and identify the most favorable modes of demulsification processes. The map revealed an area when coalescence is substituted with only rebound when drop radius increases, i.e., when there will be no smaller drops after the interaction.

Nonlinear vibrations analysis of a fuel rod in nuclear heating reactor

Nonlinear vibrations of a single fuel rod in nuclear heating reactor with fixed-fixed ends and subjected to various excitation levels are comprehensively analyzed using explicit dynamics. The responses of empty, pellet-filled, and water-submerged rod are investigated. Pellet-cladding and pellet-pellet interactions are addressed by a penalty-based contact treatment, meanwhile the fluid-structure interactions (FSI) between the vibrating fuel rod and surrounding coolants are simulated by the Arbitrary Lagrangian-Eulerian (ALE) method, wherein the water is modeled as Eulerian elements. The results reveal that both empty and pellet-filled rods exhibit frequency hardening phenomena, where eigenfrequencies increase with vibration amplitude due to geometric nonlinearity. The damping decay resulting from fuel pellet motions is found to be positively correlated with vibration amplitude, thereby enhancing the reactor safety. For submerged rod, the frequency decreases due to added mass effects, and the overall system damping increases despite structural damping from dry friction and impacts is reduced.

Modelling and analysis of the impact of chatter and cutting forces on machined surfaces in milling

The Chatter vibrations are a critical issue in milling, affecting workpiece quality and potentially damaging machines. This study analyzes the causes of chatter and proposes preventive methods. After reviewing the existing research, the transfer function is analyzed using an orthogonal cutting model, highlighting its evolution concerning system stability. A dynamic stability map is developed to help select optimal spindle speeds and cutting depths. Experiments using an innovative chatter detection device, based on noise analysis, demonstrate real-time identification of chatter, enhancing operational stability. The second part focuses on modeling cutting forces, essential for optimizing machining conditions and mitigating vibrations. A thermo-mechanical approach is applied using the Abaqus simulator and the Arbitrary Lagrangian-Eulerian (ALE) method to study the impact of cutting conditions on mechanical stress and temperature at the tool-workpiece interface. The results show that cutting parameters significantly influence both stress distribution and thermal behavior. By combining real-time chatter detection with precise cutting force modeling, this study offers an effective way to optimize machining parameters, improving process stability and operational efficiency. This integrated approach enhances the accuracy of predictive models and contributes to better machining outcomes.

Impact of a tri-dimensional conical structure made of composite materials

This paper investigates the impact strength of a three-dimensional conical structure constructed from composite materials, focusing on its application in wave energy converters. Two glass fibre-reinforced polymers, unidirectional and bi-axial stitched fabrics, are analysed. The study includes an experimental low-velocity impact of plates with solid objects, simulating low-velocity impact with floating debris, and an experimental bottom wave slamming test where the structure is dropped from a height of 1.5 m onto a calm water surface equivalent to an initial velocity of 5.43 (m/s). In addition, a destructive buckling test is carried out by applying pressure to the conical to assess the buckling strength of both laminates. Furthermore, the experimental buckling pressure failure is compared with the pressure peak determined by a numerical simulation, based on the Arbitrary Lagrangian Eulerian formulation, and with a design pressure suggested by a classification society recommended practice. Results demonstrate that the biaxial stitched fabric reveals a higher impact strength on both impacts with solids and fluids and a higher buckling strength. Moreover, the peak pressure determined by the numerical simulation is slightly higher than that a conservative design approach predicted.

A boundary enforcement method for the truncated ship structure model during underwater contact explosion experiments

Conducting model experiments is an effective approach for investigating structural damage of ship cabin structures induced by underwater contact explosions. However, large-scale cabin model experiments often encounter challenges in establishing practical constraints, resulting in disparities in boundary constraints between the experimental model and the intact ship model. To overcome this, the present work proposes a novel method for enforcing boundary conditions that involves extending the boundaries of the experimental model, securing the model boundaries with clamps and the rigid wall, and simulating the underwater environment using the temporary water tank. Based on this method, an experiment of a broadside cabin of large ships subjected to underwater contact explosion was conducted, and results are reproduced through the Arbitrary Lagrange-Euler (ALE) method. Subsequently, the explosive load characteristics of the boundary enforcement model are further analyzed, followed by a discussion of the impact of boundary constraints on structural response, thereby validating the effectiveness of the boundary enforcement method.

Numerical Study of Air Cushion Effect in Notched Disk Water Entry Process Using Structured Arbitrary Lagrangian–Eulerian Method

This paper presents a novel numerical investigation into the air cushion effect and impact loads during the water entry of notched discs, utilizing the Structured Arbitrary Lagrangian–Eulerian (S-ALE) algorithm in LS-DYNA. Unlike prior studies that focused on smooth or unnotched geometries, the present study explores how varying notch parameters influence the fluid–solid coupling process during high-speed water entry. The reliability and accuracy of the computational method are validated through grid independence verification and comparisons with experimental data and empirical formulas. Systematic analysis of the effects of notch size, water entry velocity, and entry angle on the evolution of the free surface, impact loads, and structural responses uncovers several novel findings. Notably, increasing the notch diameter significantly enhances the formation and stability of the air cushion, leading to a considerable reduction in peak impact loads—a phenomenon not previously quantified. Additionally, higher water entry Froude numbers are shown to accelerate air cushion compression and formation, markedly affecting free surface morphology and force distribution. The results also reveal that varying the water entry angle alters the air cushion’s morphological characteristics, where larger angles induce a more pronounced but less stable air cushion, influencing the internal structural response differently across regions.

A high-order physical-constraints-preserving arbitrary Lagrangian–Eulerian discontinuous Galerkin scheme for one-dimensional compressible multi-material flows

In this paper, a high-order physical-constraints-preserving arbitrary Lagrangian–Eulerian (ALE) discontinuous Galerkin scheme is proposed for one-dimensional compressible multi-material flows. Our scheme couples a conservative equation related to the volume-fraction model with the Euler equations for describing the dynamics of fluid mixture. The mesh velocity in the ALE framework is obtained by using an adaptive mesh method that can automatically concentrate the mesh nodes near the regions with large gradient values and greatly reduce the numerical dissipation near material interfaces. Using this adaptive mesh, the resolution of solution near some special regions such as material interfaces can be improved effectively by our scheme. With the appropriate time step condition and using a bound-preserving and positivity-preserving limiter, our scheme can ensure the positivity of density and pressure and the boundness of volume-fraction, which further ensures the computational robustness and degree of confidence of simulations under large density or pressure ratios and so on. In general, our scheme can be applied to the simulations of compressible multi-material flows efficiently with the essentially non-oscillatory property and physical-constraints-preserving (bound-preserving and positivity-preserving) property, and its steps are more concise compared to some other methods such as the indirect ALE methods. Some examples are tested to demonstrate the accuracy, essentially non-oscillatory property and physical-constraints-preserving property of our scheme.

Embedded technology for enhanced modeling of Friction Stir Welding processes

Friction Stir Welding (FSW) is a solid-state joining process that has several benefits over conventional welding techniques. A major challenge is its high sensitivity to process parameters such as advancing and rotational speed. Simulations are a key tool for understanding the material flow and temperature evolution and help to find the best processing parameters for a given FSW task. This work proposes using the Embedded Domain Method (EDM) for the simulation of FSW to overcome the limitations of (purely) Lagrangian, Eulerian, or Arbitrary Lagrangian Eulerian (ALE) approaches.In the proposed approach, a CAD geometry of the rotating pin tool is embedded at runtime into the computational domain, which represents the to-be-welded workpieces. Resulting interface elements are integrated using a boundary conforming subintegration approach, and various stabilization techniques are employed to stabilize the thermo-mechanical problem and potential cut element instabilities.The predicted reaction forces and temperature evolution curves are in excellent agreement with experimental reference data and the sensitivity analysis of process parameters shows that the model can be used to make targeted adjustments of said parameters to gain greater control over the process.

Investigation of band-beam slabs subjected to close-in blast loading - Experimental and numerical study

"Band-beam slab" or "slab with a shallow beam" are widely used in contemporary multi-level building construction and are particularly common in lower levels and basements. These slabs are favoured for conserving space and reducing floor-to-floor heights. Consequently, understanding how band-beam slabs perform when exposed to close-range detonations is essential for critical infrastructure projects and has not been previously studied in the literature. With recent terrorism events where portable explosives ranging from 2 kg to 10 kg are more common, a close-in detonation can significantly affect the structural integrity of civil infrastructure. Thus, this study aims to examine the behaviour of band-beam slabs when subjected to close-in detonations. The paper presents both experimental results and validated Arbitrary Lagrange-Euler (ALE) numerical framework to study and assess the damage of the slabs under various loading conditions and slab designs. A total of six band-bean panels are subjected to close-in detonations of Composition-4 (C4) charges. Initially, validation of the numerical modelling is performed where damage in terms of spall crater sizing and crack patterns are observed. It was shown that the numerical modelling technique could predict crater sizes within 15 % of the area, and crack propagation, including patterns, was appropriately captured. Through numerical modelling parametrisations, it was shown that confinement detailing, such as the use of C-hooks, close spacing of shear reinforcement, and additional reinforcement in the beam-to-slab transition zone can drastically improve the performance of the panel in terms of spalling damage and deflections. Finally, it was shown that the spalling, global and local deformation can be minimised with appropriate detailing. Design recommendations for additional reinforcement to control and mitigate spalling, cracking and scabbing were proposed.

Manipulating microfluidic freezing phenomena of electrolytes using electromagnetic stimuli

We investigate the transients of freezing of a flowing electrolyte between cold microfluidic domain walls. We explore the novel effect of morphing the solidification characteristics of the flow system using externally applied electric and magnetic fields. The spatiotemporal evolution of solid–liquid (S–L) interface is simulated using arbitrary Lagrangian–Eulerian approach. We show that the solidification rate is highly influenced by advection effects, and for increasingly high liquid flow rates, solidification stops way before the event of channel closure. Due to electro-magneto-hydrodynamic interactions, a substantial decrease in channel closing time is observed with imposed fields. However, a considerably large electric field may lead to a significant increase in Joule heating, which marginally increases the channel closing time. The magnetic field is observed to produce smoother, curved frozen layers. The electric field tends to enhance the solidification rates more uniformly along the channel length, resulting in much flatter S–L front, hence trapping lesser liquid at channel closure. The results reveal that freezing kinetics in microfluidic devices can be morphed by using electric and magnetic fields, governed by the electric field number (En) and Hartmann number (Ha). The findings may be crucial for phase-change based microfluidic-systems, micro-castings, flow freezing valves, and diodes.

Treatment of inelastic material models within a dynamic ALE formulation for structures subjected to moving loads

AbstractThis article showcases the development of a dynamic Arbitrary Lagrangian Eulerian (ALE) formulation to account for inelastic material models within a finite element framework. Such a formulation is commonly utilized in research domains like fluid mechanics, fluid‐structure interaction, quasi static remeshing techniques, and quasi static load movement. The work at hand describes the application of the ALE formulation to efficiently analyse structures subjected to moving loads in the field of transient inelastic solid mechanics. In particular, structures such as pavements, gantry crane girders etc., which are subjected to moving loads, can be numerically simulated, and their transient response in the relevant region around the load can be obtained without relying on moving loads. The focus of this article is to facilitate the treatment of history variables stemming from inelastic material models. Of particular interest is the advection procedure required to transport the history variables through the mesh, as the material appears to flow through it. The mathematical framework necessary to treat this advection process is described in detail, considering a nonlinear viscoelastic material model on a neo‐Hookean base at finite deformations. Then, four methods for numerically achieving the advection are implemented within a transient finite element ALE formulation. These methods are compared against each other, and additionally with the conventional Lagrangian method for validation. The results demonstrate satisfactory agreement with conventional simulation methods, while offering a significant improvement in terms of computation speed. With the work at hand, the dynamic response of inelastic materials subjected to moving loads can be numerically simulated in a computationally efficient manner.

Finite element analysis of sliding wear on the borided AISI 316L stainless steel

This work implements a 3D finite element to analyze wear in borided AISI 316 L stainless steel. The 3D model was validated through sliding wear test under a ball-on-flat configuration, following the ASTM G133 standard procedures. ABAQUS software was used with an Arbitrary Lagrangian-Eulerian (ALE) remeshing technique alongside the UMESHMOTION subroutine to apply an elemental level Archard’s equation. The artificial roughening of the worn surfaces due to discretization in finite element sizes was controlled by relating the maximum increment time on each wear step to the element size and the stroke. The study also described the evolution of the stress field and the behavior of the contact area. The maximum stress was estimated after the first indentation, decreasing as the contact area increased, reaching a minimum at the last wear step. The results revealed a good correlation between the experimental and modeled data, with a maximum error of 8.34% in the contact stress and a maximum error of 22% in the wear depth.

Experimental and numerical investigation on normal strength and high strength RC arches subjected to underwater explosions

As a common structure in engineering, reinforced concrete (RC) arch may be subjected to explosion load in its life cycle. However, there are few studies on the blast resistance of RC arch against underwater explosion. A normal strength reinforced concrete (NSRC) arch and a high strength reinforced concrete (HSRC) arch were designed, and two sets of underwater explosion tests were carried out. Multi-media coupling models of the two RC arches subjected to underwater explosions were established based on the Arbitrary-Lagrangian-Eulerian (ALE) algorithm. The propagation characteristics of shock wave, the acceleration response and damage evolution of the arches were experimentally and numerically investigated. The reliability of the numerical method was verified by comparing the numerical results with the test results. Employing the verified numerical method, the effects of standoff distance and explosive weight on the dynamic response and damage distribution of the NSRC and HSRC arches were further studied. Based on extensive numerical simulations, the prediction formulas for the peak displacement of the given NSRC and HSRC arches due to specific underwater explosions were proposed. The results show that the arch vault and both sides of hance are the most vulnerable to failure when suffering the explosions centrally above the arch. The blast resistance of the HSRC arch is much stronger than that of NSRC arch. The failure modes of RC arches can be summarized as: arch vault cracking, global bending failure, combination of global bending failure and local damage, combination of global bending failure and penetration failure.

Numerical simulation of flow around a transversely oscillating square cylinder at Re=22000

The study utilized OpenFOAM software, combined with the k-ω shear stress transport (SST) turbulence model and Arbitrary Lagrangian-Eulerian (ALE) dynamic mesh method, to investigate the influence of the oscillation amplitude on the flow dynamics around a square cylinder at Re = 2.2 × 104. It was found that various oscillation amplitudes affect the non-Gaussian characteristics of fluctuating pressure differently along the cylinder's surface: diminishing at the leading edge while intensifying at the trailing-edge corner. Concurrently, secondary recirculation bubbles near the cylinder's leading and trailing edges gradually diminish and eventually disappear with increasing oscillation amplitudes. Analysis of the amplitude spectrum of transverse velocity indicates the exclusive presence of odd-order harmonics along the central axis, while both odd and even-order harmonics are observed on either side of the central axis. Additionally, heightened oscillation amplitudes result in increased energy transfer from the cylinder to the fluid, with the energy density function predominantly exhibiting negative values and periodic variations occurring at twice the frequency of cylinder displacement or lift coefficient. As the oscillation amplitude increases, the vortex in the wake region transitions from a single-row to a double-row configuration. The research results provide important theoretical guidance for deepening the understanding of the flow characteristics around the oscillating square cylinder.

Numerical evaluation of wear parameters using meta-models

AbstractWear parameters identified by linear friction tester (LFT) experiments overestimate the wear mass loss when applied on a laboratory abrasion & skid tester 100 (LAT100) simulation. On the other hand, the identification of wear parameters directly from the LAT100 experiment can be challenging since variables such as the contact area and the slip velocity are not measured experimentally and need to be assumed. To improve the identification process, numerical calibration is used as a more suitable approach. This approach relies on meta-models as a target function for minimization. The meta-models are generated using a sample of wear parameters applied to an LAT100 finite element modeling (FEM) to calculate the corresponding wear mass.. In this model, a transport velocity is defined for the rolling simulation, and an arbitrary lagrangian–eulerian (ALE) adaptive meshing approach is adopted for the wear modeling. For the wear model, a combination of archard’s wear model and schallamach’s abrasion law is used. This model contains a pair of wear parameters to be identified. The ALE adaptive meshing technique moves the nodes independently of the material. Since the mesh topology remains the same, failure of the simulation occurs if the wear volume loss exceeds that of the element. Meta-models are created to extend wear modeling beyond this failure. Once the meta-models are created, they are used as a target function for the minimization algorithm. The minimization algorithm aims to find the optimal wear parameters by minimizing the difference between experimentally observed and numerically produced wear mass loss. The minimization algorithm inputs a set of wear parameters into the meta-models which in turn yield a prediction of the wear mass loss. The process is carried out until an optimum parameter set is identified. Such an approach has a lower accuracy if the parameters are identified directly from the experiment using assumptions regarding the contact shear stress and the sliding velocity. Nonetheless, the main advantage of parameters identified using the meta-model approach is the usability of these parameters in an LAT100 model.

An efficient moving-mesh strategy for predicting crack propagation in unidirectional composites: Application to materials reinforced with aligned CNTs

This paper presents an efficient numerical approach for reproducing the process of crack propagation inside unidirectional composites subjected to general loading conditions, with special reference to epoxy materials enhanced with embedded aligned CNTs. This approach involves a traditional FE framework improved by the Moving Mesh (MM) technique based on the Arbitrary Lagrangian-Eulerian (ALE) formulation and the Interaction Integral Method (M−integral). The MM serves as a powerful numerical tool to simulate the discrete crack advance with minimal remeshing, thus reducing the computational complexities. Instead, the M−Integral method, formulated for generally anisotropic materials, has been employed to extract the mixed-mode Stress Intensity Factors (SIFs), which are necessary to define the crack onset condition and propagation direction on the basis of the modified Maximum Hoop Stress Criterion. The proposed strategy includes the extended rule of mixtures to evaluate the homogenized elastic properties of nano-reinforced composites. The validity of the proposed methodology has been assessed through comparisons with experimental data and numerical results available in the literature.

Evaluating the Seismic Resilience of Above-Ground Liquid Storage Tanks

Historical seismic events have repeatedly highlighted the susceptibility of above-ground liquid storage steel tanks, underscoring the critical need for their proper design to minimize potential damage due to seismic forces. A significant failure mechanism in these structures, which play essential roles in the extraction and distribution of various raw or refined materials—many of which are flammable or environmentally hazardous—is the dynamic buckling of the tank walls. This study introduces a numerical framework designed to assess the earthquake-induced hydrodynamic pressures exerted on the walls of cylindrical steel tanks. These pressures result from the inertial forces generated during seismic activity. The computational framework incorporates material and geometric nonlinearities and models the tanks using four-node shell elements with two-point integration, specifically Belytschko shell elements. The Arbitrary Lagrangian–Eulerian (ALE) method is employed to accommodate substantial structural and fluid deformations, enabling a full simulation of fluid–structure interaction through highly nonlinear algorithms. Experimental test data are utilized to validate the proposed modeling approach, particularly in replicating sloshing phenomena and identifying stress concentrations that may lead to wall buckling. The study further presents results from a parametric analysis that varies the height-to-radius and radius-to-thickness ratios of a typical anchored flat-bottomed tank, examining the seismic performance of this common storage system. These results provide insights into the relationship between tank properties and mechanical behavior under dynamic loading conditions.

A projection-based time-segmented reduced order model for fluid-structure interactions

In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian–Eulerian (ALE)-finite element method (FEM) in a monolithic frame, where spatially, each variable is separated from others in terms of their attribution (fluid/structure), category (velocity/pressure) and component (two/three dimension) while temporally, the proper orthogonal decomposition (POD) bases are constructed in some deliberately partitioned time segments tailored through extensive numerical trials. By the combination of spatial and temporal decompositions, the developed ROM approach enables prolonged simulations under prescribed accuracy thresholds. Numerical experiments are carried out to compare numerical performances of the proposed ROM with corresponding full-order model (FOM) by solving a two-dimensional FSI benchmark problem that involves a vibrating elastic beam in the fluid, where the performance of offline ROM on perturbed physical parameters in the online phase is investigated as well. Extensive numerical results demonstrate that the proposed ROM has a comparable accuracy to while much higher efficiency than the FOM. The developed ROM approach is dimension-independent and can be seamlessly extended to solve high dimensional FSI problems.

Asteroid disruption and deflection simulations for multi-modal planetary defense

Planetary defense from asteroids via deflective means alone does not offer viable solutions in terminal scenarios where there is little warning time before impact. The PI method of planetary defense enables operation in terminal interdiction modes where there is little warning time prior to impact, but can also operate in the same extended time scale interdiction modes as made possible by traditional deflection techniques, which results in a versatile, multi-modal planetary defense capability. The method is also practical and cost-effective since it relies solely on launch vehicles and penetrator materials already available today, and thus presents itself as a logical and competitive option for planetary defense. As per the PI method, we investigate the effectiveness of rubble pile asteroid disruption and deflection via hypervelocity impacts with 10:1 aspect ratio cylindrical tungsten penetrators. We present the results of an ongoing simulation campaign dedicated to investigating the PI method, using the Lawrence Livermore National Laboratory (LLNL) arbitrary Lagrangian–Eulerian (ALE) hydrodynamics code ALE3D run with the High-End Computing Capability (HECC) at NASA Ames Research Center. We model heterogeneous rubble pile asteroids with a distribution of spherical boulders of varying initial yield strengths set within a weak binder material. We find that rubble pile asteroids of this type in the 20–100 meter-class can be effectively mitigated via 20 km/s impacts with 100–1000 kg penetrators via the coupling of the penetrator kinetic energy into the bulk material of the asteroid.