Arbitrary Lagrangian-Eulerian Method Research Articles

Dynamic Seismic Probabilistic Risk Assessment of Nuclear Power Plants Using Advanced Structural Methodologies

The conditional core damage probability (CCDP) of a representative nuclear power plant is estimated for a beyond design basis earthquake (BDBE) using state-of-the-art structural models within a dynamic probabilistic risk assessment (DPRA) framework. Randomness of seismic excitation and uncertainty of structural parameters are considered using a simulation-based approach. Finite element models are developed for the structure and a liquid container (hydro-accumulator), and fluid–structure interaction is considered with the arbitrary Lagrangian-Eulerian method. The CCDP is evaluated through a time-dependent event tree. Also, correlation among multiple hydro-accumulators is investigated. The results show that operator action and implementation time of mobile safety equipment are critical under BDBE in case of loss of offsite power following an earthquake. It was also found necessary to adopt a DPRA approach to determine the available time for action and core damage timing probabilistically.

On the water entry impact characteristics of high-speed vehicle with an Arbitrary Lagrangian-Eulerian method

This paper investigates the fluid-structure interaction process of high-speed vehicles during water entry using the Arbitrary Lagrangian-Eulerian method. Through mesh independence verification and comparison of numerical simulation results with experimental data and empirical formulas, the reliability and accuracy of the computational method are confirmed. The study comprehensively analyzes flow field pressure distribution, cavity evolution characteristics, and vehicle force features, evaluating the impact of water-entry angle, Froude number (Fr), and cavitator dimension. The results indicate that during water entry, the instantaneous impact forces are mainly concentrated on the wetted surface at the bottom of the vehicle and the plane at the head. The peak stress at the entry point is significantly higher than at other locations, and stress waves propagate along the vehicle body, concentrating at the hollow structure due to the structural characteristics. The change in water-entry angle does not significantly affect the decay of Fr for the vehicle, but increasing the water-entry angle leads to an earlier and larger peak stress at the mid-point monitoring location of the vehicle. In addition, the study also found that the stress level increases with the increase of the Froude number, resulting in larger high-stress areas and peak stresses. However, the cavity evolution at the same water-entry depth is essentially independent of the variation in Fr. With the increase in cavitator dimension, the water-entry load and cavity profile will also significantly increase, and vehicles with larger cavitator dimension will generate larger stress waves upon impact.

Numerical Simulation of Electromagnetic-Thermal-Fluid Coupling for the Deformation Behavior of Titanium-Aluminum Alloy under Electromagnetic Levitation.

Electromagnetic levitation (EML) is a good method for high-temperature processing of reactive materials such as titanium-aluminum (Ti-Al) alloys. In this study, the oscillation and deformation processes of Ti-48Al-2Cr alloy specimens at different high-frequency currents during the EML process were simulated using the Finite Element Method and Arbitrary Lagrangian-Eulerian (ALE) methods. The data of oscillation, stabilization time, deformation, and distribution of electromagnetic-thermal-fluid fields were finally obtained. The accuracy of the simulation results was verified by EML experiments. The results show the following: the strength and distribution of the induced magnetic field inside the molten droplet are determined by the high-frequency current; under the coupling effect of the electromagnetic field, thermal field, and fluid field, the temperature rise of electromagnetic heating is rapid, and accompanied by strong stirring, resulting in a uniform distribution of the internal temperature and a small temperature difference. Under the joint action of gravity and Lorentz force, the molten droplets are first within a damped oscillation and then tend to stabilize with time, and finally maintain the "near rhombus" shape.

High-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation

This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing arbitrary mesh into tetrahedrons and integrating flux function in a local coordinate system at the cell interface to ensure geometric conservation law. The scheme incorporates a compact reconstruction with third-order accuracy for updating both cell-averaged conservative flow variables and their gradients. HWENO-type nonlinear reconstruction and gradient compression factors are adopted to improve the accuracy and robustness of the scheme. A multi-stage multi-derivative (MSMD) time-stepping method is also implemented to achieve high-order time accuracy with fewer middle stages. The scheme is used to study problems involving moving boundaries. The numerical experiments demonstrate the effectiveness of the scheme in capturing the accurate solutions of both low-speed smooth flow and highly compressible ones with strong shock waves.

Pinch-off dynamics of an electrohydrodynamic tip streaming jet transforming into the microdroplet

The drop-on-demand electrohydrodynamic (EHD) printing is promising for manufacturing high-resolution dot arrays. Such dot fabrication is commonly achieved through two printing modes (jet/droplet mode), i.e., continuous jet directly flying to or broken jet induced droplet depositing in the substrate. The droplet mode commonly has a higher printing frequency than the jet mode, indicating the droplet mode's advantage in drop-on-demand EHD printing. However, most research on EHD printing focuses on the jet mode, which causes the mechanism of droplet production through jet pinch-off remains unclear. This study employs an arbitrary Lagrangian–Eulerian method capable of getting a sharp interface to reveal the pinch-off mechanism. First, the development of a tip streaming from a meniscus to the pinch-off is analyzed. It is found that the high pressure at the neck is the main reason for the pinch-off of the jet into the droplet. Second, the EHD phase diagram in the parameter space of We–Cae is plotted, where We is the Weber number and Cae is the electric capillary number. Finally, the important influences of the charge relaxation on the EHD tip streaming jet's breakup behavior and the generated droplets' properties are revealed. Evolutions of the droplet's properties, including radius, velocity, and charge, with varying charge relaxation parameters are offered. These properties of the droplet show their relationships with extreme values as a function of the charge relaxation parameter. This work can serve as the theoretical basis for tuning the EHD printing manufacturing performance.

A fluid-structure interaction simulation on the impact of transcatheter micro ventricular assist devices on aortic valves

Background and ObjectiveThe implantation of ventricular assist devices (VADs) has become an important treatment option for patients with heart failure. Aortic valve insufficiency is a common complication caused by VADs implantation. Currently, there is very little quantitative research on the effects of transcatheter micro VADs or the intervention pumps on the aortic valves. MethodsIn this study, the multi-component arbitrary Lagrange-Eulerian method is used to perform fluid-structure interaction simulations of the aortic valve model with and without intervention pumps. The effects of intervention pumps implantation on the opening area of the aortic valves, the stress distribution, and the flow characteristics are quantitatively analyzed. Statistical results are consistent with clinical guidelines and experiments. ResultsThe implantation of intervention pumps leads to the valve insufficiency and causes weak valve regurgitation. In the short-term treatment, the valve regurgitation is within a controllable range. The distribution and variation of stress on the leaflets are also affected by intervention pumps. The whirling flow in the flow direction affects the closing speed of the aortic valves and optimizes the stress distribution of the valves. In the models with whirling flow, the effects of intervention pumps implantation on valve motion and stress distribution differ from those without whirling flow. However, the valve insufficiency and valve regurgitation caused by intervention pumps still exist in the models with whirling flow. Conventional artificial bioprosthetic valves have limited effectiveness in treating the valve diseases caused by intervention pumps implantation. ConclusionsThis study quantitatively investigates the impact of intervention pumps on the aortic valves, and investigates the effect of blood rotation on the valve behavior, which is a gap in previous research. We suggest that in the short-term treatment, the implantation of intervention pumps has limited impact on aortic valves, caution should be exercised against valve regurgitation issues caused by intervention pumps.

Modelling the first droplet emission from an electrified liquid meniscus hanging at the nozzle tip

Electrohydrodynamic (EHD)-induced droplet emission is an efficient method for the production of micron- and submicron-sized droplets in technological applications. Existing studies propose several scaling laws to determine the size of the emitted droplet. However, they have usually focused on the tip streaming phenomena of a droplet when subjected to a uniform electric field. In most applications, a non-uniform distribution of the electric field is created owing to the nozzle-to-plate configuration. Here, we employ an arbitrary Lagrangian–Eulerian method to demonstrate the mechanism of the first droplet emission from an electrified liquid meniscus with a fixed volume hanging at the nozzle tip. The critical condition when tip streaming occurs is determined using our numerical results. A phase diagram in terms of the electric field and initial liquid volume is presented to obtain the commonly used jetting mode. The effects of the liquid volume, electric field strength and electrical conductivity of the liquid on the processes of jet formation and breakup are further investigated. We find a particularly non-monotonic dependence of the size of the emitted droplet on the electrical conductivity. These findings could be useful for generating microdroplets and improving injection frequency in EHD printing technology.

Numerical analysis of microwave-enhanced oil shale pyrolysis by rotation turntable based on the Arbitrary Lagrangian-Eulerian method

Microwave heating technology has great potential for efficient pyrolysis of oil shale. However, the inhomogeneous heating characteristics of microwave heating can lead to secondary cracking of pyrolysis products, thus reducing the overall oil yield. In order to address this issue, a rotational movement of oil shale under microwave heating has been proposed to obtain a uniform temperature distribution of the oil shale. Then, a new coupled three-dimensional electromagnetic-thermal-chemical-hydraulic model incorporating the Arbitrary Lagrangian-Eulerian (ALE) method was developed to investigate the temperature distribution and pyrolysis characteristics of oil shale under the rotational motion during microwave pyrolysis. The effects of rotational speed, rotational direction, and microwave power on the pyrolysis process of oil shale were explored through this model. The results showed that the introduction of rotational movement effectively addressed the uneven temperature distribution within the oil shale. Compared with the static condition, the rotational condition reduced the secondary reactions of oil products during microwave pyrolysis and increased the oil yield of oil shale to 50.12 %. As the rotation speed increased, the temperature distribution within the oil shale became more uniform, but the total oil yield reached its peak at a moderate speed of 180 s/r. Research on microwave power indicated that rotation increased the maximum usable power and highlighted that reducing the residence time of pyrolysis products within the oil shale was key to increasing oil yield. This study provides a novel approach and numerical simulation method for enhancing the microwave pyrolysis efficiency of oil shale, and the findings of this study are applicable to both the ex-situ and in-situ exploitation of oil shale.

Underwater implosion protection of a new concept composite structure for a deep-sea hollow ceramic sphere with CFRP shield

Carbon fiber–reinforced polymers (CFRP) and ceramics are lightweight, non-metallic materials with broad applications. However, their use in deep-sea engineering is limited owing to the potential risk of catastrophic implosions. This study introduces the concept of deep-sea ceramic-pressure-resistant hollow structures with CFRP shields for achieving a balance between safety and light weight. This research examines typical engineering cases, including the HROV Nereus and Titan accidents, and uses the Arbitrary Lagrangian–Eulerian method to investigate the fluid–structure interactions. First, the feasibility of the numerical method was verified, with the responses of the structure and flow field summarized. The advantages of ceramic hollow spheres with a CFRP shield were analyzed, leading to the development of a new implosion protection scheme with a composite structure. Furthermore, this study discusses the effects of the CFRP thickness, CFRP ratio, and trigger mode on implosion protection, with the results revealing that increasing the thickness and proportion of the CFRP shield considerably enhances the implosion suppression effect of the entire structure. These findings are valuable for designing pressure-resistant structures for practical engineering applications.

A comparative study on waveform prediction between SPH and S-ALE methods in impact welding

To explore the optimal method for simulating impact welding, we compared detailedly the smoothed particle hydrodynamics (SPH) and structured arbitrary Lagrangian-Eulerian (S-ALE) methods in predicting bonding interface. Based on the experimental results of Cu-Q235 steel atmospheric explosive welding, an in-depth analysis was presented. The results show that the SPH and S-ALE methods converged at element sizes of 2.5 and 2 μm, respectively. When the element size was further reduced to 0.5 % of the wavelength, the errors of both methods were less than 5 %. Benefiting from the gradient mesh, the efficiency of the S-ALE method was 2–4 times that of the SPH method at the same element size. With the addition of the gas medium, the S-ALE method derived the formation mechanism of the gap gas shockwave and indicated that the pressure distribution is not uniform. Furthermore, the local high pressure of the gas shockwave prevents the vortex closure during the wave formation, generating the pore. The calculated pressure and velocity of the wavefront were 20 MPa and 3500 m s−1, respectively. In conclusion, the SPH is suitable for fast previewing waveform interfaces, while the S-ALE method has the advantage of capturing fine waveform structures under various environmental conditions.

Lateral loading response of monopiles in sand considering installation effect

The effect of pile installation is a critical issue in the analysis and design of pile foundations but it is commonly ignored due to various numerical difficulties. In this paper, the installation process of an open-ended pipe pile into a sand deposit is simulated by using the zipper technique combined with the Arbitrary Lagrangian-Eulerian (ALE) method in the framework of three-dimensional (3D) finite element modeling. The subsequent lateral load response of the pile is also simulated and compared with that without consideration of the pile installation. The state dependent behavior of sand in associated with the pile installation and the subsequent lateral load is described using an advanced constitutive model. The study shows that for a relatively loose sand deposit, the sand surrounding the pile exhibits contraction and the disturbance zone takes the form of a trapezoid, whereas for a dense sand deposit, the sand near the pile will dilate and the disturbance zone takes the form of an inversed trapezoid. Furthermore, the deformation mode of the surrounding sand under the lateral load differs to some extent from that without consideration of the installation effect. Particularly, the location of the rotation point for the laterally loaded pile tends to move downwards when the pile installation process is considered.

Test and numerical analysis for water entry of elastic cabin from amphibious aircraft

Water-entry performance of amphibious aircraft is one of the main factors affecting the structural design. However, it is analyzed by rigid models in general, which is difficult to reflect the elastic characteristics of the structure. And it is difficult to obtain sufficient guidance for structural design from rigid-body analysis. In this study, water-entry model of an elastic cabin from amphibious aircraft was developed using the Arbitrary Lagrangian-Eulerian (ALE) method and validated by a designed 1:1 cabin water-entry test. Analysis under various conditions revealed the cabin's dynamic response in three steps: (1) the keel of the cabin section touches the water, (2) the bottom skin is wetted, and (3) the bottom skin is submerged. This study also compares the rigid-surface crashes and water-entry impacts of the cabin from the point of view of load and energy analysis. The results show that rigid-surface crash mainly affects bulkhead and keel, whereas water-entry energy is mainly absorbed by the skin, connectors, and stringers. Additionally, varying skin thicknesses showed a negative correlation with back surface deformation. The methodologies and conclusions presented in this study can offer valuable references for researchers in the field of water entry.

Numerical study on the damage of liquid-filled containers subjected to shaped charge jet impact

In the studies of the vulnerability of armored vehicles, the impact of high-velocity penetrators on liquid-filled container components is one of the critical concerns. The purpose of this study is to investigate the structural damage of the liquid-filled container subjected to shaped charge jet impact utilizing the Structural Arbitrary Lagrangian–Eulerian method in ANSYS/LS-DYNA. The numerical model is validated against available experimental data. The validation effort of the numerical model showed very good agreements with experiments in terms of radial shock wave and radial crater formation as a function of time. Using the validated model, the liquid pressure, the energy transfer as well as the influence of overmatch on the impact process were analyzed. The results indicate that the structural damage modes of containers under shaped charge jet impact include perforation and wall deformation. Perforation results from the penetration of the jet tip and tail, while wall deformation is caused by the high-velocity impact of the flowing liquid. In cases where the overmatch (OM) is equal to 1, the contribution of the tip to front and back wall perforation increment primarily depends on the impact velocity. In cases with OM less than 1, the “filtering effect” of the Rolled Homogeneous Armor (RHA) armor plate leads to the loss of the tail's contribution to front wall perforation.

Numerical modelling of electromechanical coupling behaviors in HTS coil with implementation of H formulation in FE software

(Re)Ba2Cu3O7-x (REBCO) coated conductors (CCs) have attracted considerable concern because of their outstanding current carrying capacity in magnetic fields of high strengths. A huge electromagnetic force is generated in the superconducting coil when conducting large currents in strong magnetic field. Thus, management of stress and strain has become a key technical challenge for the stability and safety of superconducting coil during operation. To accurately predict the electro-magnetic and mechanical characteristics of superconducting coil in strong magnetic field, an electromechanical model on the basis of the H-formulation and arbitrary Lagrangian-Eulerian (ALE) method is proposed here with FE software. To verify the proposed model, the simulation outcomes of the coil during magnetization are compared with the experimental outcomes. The coupling effect of magnet at high field strengths is dependent on the position of the coil. To reduce the screening current effect, the overshoot method with plateau is found superior to the traditional overshoot method, and an increase in the stabilization time can decrease the maximum value of stress. Finally, the electromechanical behaviors of single winding coil and two-tapes co-winding coil are compared.

Study on load characteristics and structural impact response propagation law of cabin internal explosion

Aiming at the problem that the distribution of explosion load in the cabin and the propagation law of structural impact response was unclear, this paper established the numerical calculation model of explosion in a closed cabin by ALE (Arbitrary Lagrangian Eulerian) method. There was an apparent convergence of shock waves at the cabin's corners, and the pressure relief hole's area and its position significantly affected the peak of quasi-static pressure. The peak acceleration of the deck structure decreased exponentially as the distance from the location of charge increased. Peak acceleration decreased by approximately 50% for each bulkhead crossing. There was a “paper window effect” during the cabin interior explosion on the whole ship. It meant there was a limit to the value for the energy generated by the explosion to be transmitted along the frame structure. When the charge was 150 kg, it reached the limit of the energy transferred by the structure in this paper. The response of the distant structure did not change significantly with the increase in the charge quality. The research revealed the impact response propagation mechanism in the structure and provided a reference for designing protective structures.

Comparison of different discontinuous Galerkin methods based on various reformulations for gKdV equation: Soliton dynamics and blowup

In this work, we explore the use of several discontinuous Galerkin (DG) methods for simulating soliton dynamics in the generalized Korteweg-de Vries (gKdV) equation. The presence of high-order nonlinearity in this model can lead to the finite-time blowup phenomenon, which challenges every aspect of a numerical scheme. The considered DG schemes encompass popular methods derived from the energy and/or Hamiltonian conservations of the gKdV equation. To evaluate the performance of these DG schemes from various angles, we present a series of numerical experiments. Through comprehensive comparisons, we aim to identify the scheme that exhibits the best performance. To further enhance the accuracy and efficiency of DG methods, particularly in the context of blowup simulations, we incorporate the arbitrary Lagrangian-Eulerian method for adaptive mesh movement.

Corrosion deposition in deforming anodes of in-ground cathodic protection systems: A three-dimensional transient study

Cathodic protection as a complementary technique is widely considered in the industry along with the selection of suitable materials as well as efficient coating considerations. In cathodic protection (CP), anode produces a current output to protect the structure (cathode) and part of the current output is wasted by the grounding system. We developed a 3D, and time-dependent numerical model to simulate the anode corrosion (using arbitrary Lagrangian-Eulerian method), find the deposit formation (by interface tracking level set method), anode mass loss and current wasted by the grounding system. We also defined a CP efficiency as anode mass loss times the current percentage received by the structure. The CP efficiency can be utilized for anode quantity and placement pattern. The results showed when the conductivity of corrosion products (deposit) is lower than that of soil, the current output from the anode decreases over time. When the deposit conductivity is higher than that of soil, the current output from the anode increases in time, reaches a peak, then decreases. This is due to the competition among three factors: anode surface increase, medium conductivity change, and inhibition effect of the deposition layer. For the studied case, almost 54% of the current from the anode is wasted by the grounding system. To illustrate the significance of CP efficiency, this study compares three alternative anode configurations with the original design. It is observed that for a 14.5 kg anode, burying the anodes 2 m deeper enhances the mean potential distribution on the structure by 4%. Additionally, the configuration featuring the 7.7 kg anode, owing to its superior dimensional design, demonstrates improved performance compared to other configurations.

Damage characteristics of ribbed cylinder in motion under near-field underwater explosion

The damage characteristics of a ribbed cylinder in the torpedo compartment shell is explored. An arbitrary Lagrange–Euler method is used to establish the fluid–structure interaction model for analyzing the ribbed cylinder’s response under near-field underwater explosion while in motion. The influence of detonation direction and standoff distance on the dynamic response of the moving ribbed cylinder is considered. The investigation reveals that the cylinder’s motion causes an uneven distribution of bubble load and secondary load, stemming from cavitation zone collapse, on the shell. This imbalance leads to a notable deflection difference between the shell’s front and rear sections, with maximum deformation concentration at the rear. In addition, in comparison to the lateral condition, static state analysis shows reduced average deflection and increased maximum deflection when the explosion point is above or below the shell, while in the sailing state, both average and maximum deflections increase. Notably, when the charge radius is between 6 and 15 times, the average damage rate in the sailing state consistently remains lower than that in the stationary state, while the maximum damage rate is higher at a specific burst distance.

Features of numerical modeling electrical coalescence in a droplet-layer system using the arbitrary Lagrangian-Eulerian method

The electrocoalescence of a water drop at the water-oil interface was numerically analyzed using the finite element method by solving a set of equations including hydrodynamics and electrostatics. The simulation was performed using COMSOL Multiphysics software, the interface movement was implemented using an arbitrary Lagrangian-Eulerian method (also called the moving-mesh method). The influence of the initial distance from the drop to the layer, as well as the size of the entire domain on the outcome of the process was studied. The electrical coalescence and non-coalescence of a single uncharged droplet with a layer under the action of the DC field were calculated in a wide range of electric field strength. The created computer model makes it possible to calculate the voltage dependence of the detached droplet volume and charge. Also, it can help to determine features of non-coalescence, including the stretching of the droplet along the interelectrode gap and spraying.

A comparative study on the influence of typical track failures on high-speed pantograph-catenary interaction dynamics

Different track failures are proven to have different influences on train-track interactions, but their influence on pantograph-catenary interactions has not been investigated thus far. In this work, the influences of typical track failures on pantograph-catenary interaction dynamics are first investigated. A reduced train-track-pantograph-catenary interaction model is developed to study these effects. In this model, the long catenary is reduced to a small moving area around the moving pantograph, and this area is considered and modelled as the reduced catenary model based on the arbitrary Lagrangian–Eulerian method. The reduced catenary model and moving pantograph are formulated as the reduced pantograph-catenary interaction model, and it is further unidirectionally connected with the existing reduced train-track interaction model to formulate the reduced train-track-pantograph-catenary interaction model. The present reduced pantograph-catenary model is first validated by the EN50318-2018 standard, and the influences of track irregularity, track buckling, fastening failure, and track settlement on pantograph-catenary interaction dynamics are studied. The investigation results first show that the track settlement with a long wavelength has a significant influence on the pantograph-catenary interaction dynamics and can even cause contact loss with a good train-track interaction behaviour. Thus, it should be further mentioned in the maintenance of the track structure.