Arbitrary Lagrangian-Eulerian Method Research Articles

Numerical Simulation of a Long-Span Steel Truss Bridge Subjected to Blast Loads

Few studies have focused on the blast load effects on steel truss bridges. To address this research gap, this paper conducts an extensive investigation on the above-deck blast loads on a long-span steel truss bridge. The nonlinear dynamic response and damage modes of reinforced concrete (RC) decks and steel members of the bridge under blast loads are numerically studied using the *Load_Blast_Enhanced (LBE) function and Multi-Material Arbitrary Lagrangian-Eulerian (MM-ALE) method in LS-DYNA to identify a cost-efficient approach with reasonable accuracy to simulate a long-span steel truss bridge subjected to blast loads. The LBE method is proved to be more conservative and cost-efficient than the MM-ALE method for simulating blast load effects on the structures. A high-fidelity finite element model of the bridge (i.e., I-35W truss bridge) in LS-DYNA based on the multi-scale modelling technique and the LBE function to simulate blast loads is developed to investigate the structural response under several blast scenarios. The effectiveness of ultra-high-performance concrete (UHPC) in protecting the steel truss members from blast load effects is also been investigated. The results provide valuable insights for bridge owners on the probable response and possible protective measures for long-span steel truss bridges against intensive blast loads.

Numerical Simulation of Free Surface Deformation and Melt Stirring in Induction Melting Using ALE and Level Set Methods.

This study investigates fixed and moving mesh methodologies for modeling liquid metal-free surface deformation during the induction melting process. The numerical method employs robust coupling of magnetic fields with the hydrodynamics of the turbulent stirring of liquid metal. Free surface tracking is implemented using the fixed mesh level set (LS) and the moving mesh arbitrary Lagrangian-Eulerian (ALE) formulation. The model's geometry and operating parameters are designed to replicate a semi-industrial induction melting furnace. Six case studies are analyzed under varying melt masses and coil power levels, with validation performed by comparing experimentally measured free surface profiles and magnetic field distributions. The melt's stirring velocity and recirculation patterns are also examined. The comparative analysis determines an improved performance of the ALE method, convergence, and computational efficiency. Experimental validation confirms that the ALE method reproduces the free surface shape more precisely, avoiding unrealistic topological changes observed in LS simulations. The ALE method faces numerical convergence difficulties for high-power and low-mass filling cases due to mesh element distortion. The proposed ALE-based simulation procedure is a potential numerical optimization tool for enhancing induction melting processes, offering scalable and robust solutions for industrial applications.

The effect of relative position on the motion and interactions of particle sedimentation under gravity in a finite-width vertical channel

Understanding the settling behaviour of particles and the interactions between fluid and particles in channelled fluids is crucial for various natural and industrial processes. The research presented in this study focuses on elucidating the sedimentation modes of dual particles within finite-width channels, employing the Arbitrary Lagrangian-Eulerian (ALE) method in conjunction with Hertz contact theory. We aim to understand how the initial relative position affects the dynamic characteristics of particle settlement. The threshold values of α = 35° and gap ratio (the distance between particles relative to their diameter) L/D = 3.5 are deemed critical. The phenomenon of particles ‘kissing’ does not manifest when the initial angle α ≤ 35°. As the α increases, the DKT (Drafting-Kissing-Tumbling) process recurs at earlier stage. In all cases where dual-particle are arranged in a vertically aligned pattern (D P1 = D P2 or DP1> DP2 ), the settling behaviour of particles will eventually achieve a steady state characterized by the DKT process when L/D ≤ 4.0. As the gap ratio (L/D) increases, the time taken for the kissing phenomenon is prolonged. Additionally, the two particles exchange positions and the larger particle taking the lead in the settling process. In scenarios where dual particles are arranged side by side, the kissing phenomenon does not occur. Instead, the trajectory of the particles deviates from the centreline and shifts towards the channel wall due to the Magnus effect when L/D ≤ 2.0. When L/D ≥ 3.0, particles settle as though they were a single particle. In cases involving multiple particles, the hindering effect of the wall becomes significant and can not be ignored, leading to the observation of Rayleigh-Taylor instability development. As a result, the overall settlement pattern tends to be ‘concave’.

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.

Dynamic simulation of ion evaporation from a conductive meniscus, fluid-fluid model of plume and meniscus interactions

Ion evaporation from a conductive meniscus has been of significant interest in the theoretical investigation of electro-hydrodynamics and application exploration across various fields. This study focuses on developing a fluid-fluid methodology for the dynamical simulation of a conductive meniscus undergoing ion evaporation and uncovering the interaction between the plume and meniscus using the ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate as a case study. In the fluid-fluid model, we propose a simplified fluid plume model to acquire the charge distribution in free space, and validate it against a particle plume model and a full fluid plume model. The meniscus evolution is described by expanding the leaky dielectric model to account for charge conservation in the liquid as well as self-heating and inhomogeneous physical properties. The arbitrary Lagrangian–Eulerian method is used to track the sharp liquid–vacuum interface. Dynamic simulation with the simplified fluid plume model is more than 150 times faster than that with the full fluid plume model. The electrohydrodynamic process of the meniscus evolving to form a droplet is analyzed, with a detailed discussion on the space charge effect caused by evaporated ions. Results indicate that neglecting the space charge effect during conical meniscus formation leads to a singular meniscus tip. Instead, the reverse electric field induced by the space charge suppresses this singularity, assisting the conical meniscus to produce a jet. Additionally, the high-throughput ion evaporation significantly enlarges the diameter of droplet formed on the conical meniscus due to the reverse electric field of space charge.

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.

Principles of creating numerical models for studying the impact of impulse loads on underground structures

Summary. The current situation in Ukraine has led to new geotechnical challenges, the solution of which is aimed at protecting critical infrastructure facilities from the effects of explosive shock waves. Protective structures that are buried in the soil environment are built to protect critical infrastructure facilities. A necessary condition to ensure their safe operation is the assessment of the stress-strain state of the system “soil environment-shelter building”. It is important to choose an adequate phenomenological model of the behavior of the materials of the protective structure and the soil environment, which describes the work of materials under the impulse impacts. The paper analyses four methods of constructing numerical models for calculating the impact of impulse loads, namely: Lagrange mesh. Euler's mesh. Arbitrary Lagrangian-Eulerian (ALE). Smooth Particle Hydrodynamics (SPH). Each of the methods has its advantages and disadvantages. The Lagrangian mesh enables to easily track the boundary between materials of different structures, both before and after the calculation, and it does not require much computational time. However, this method is not practical in cases of significant model deformations with rapid changes in time. The Euler and Arbitrary Lagrange-Euler methods allow to model the problems with a large distortion of the model, such as an underground or underwater explosion. Their disadvantage is the size of the computational domain and the considerable labour intensity for the model setup. Smooth Particle Hydrodynamics is a meshless Lagrangian method. The advantage of this method is the ability to work with large model deformations. The disadvantage is labour intensity and calculation time. All of these methods of building a numerical model are available in the LS-Dyna software package. During the analysis of calculations in LS-Dyna, we found that it is advisable to use the Lagrange mesh to create a model of a structure made of reinforced concrete or steel due to their high stiffness. The Euler and ALE methods are preferable for soil, they enable a strong change in the geometry of the model under the influence of the blast. Different methods are combined to achieve adequate model performance and to obtain correct results that will closely match the actual behavior of structures, facilities and materials under impulse loads.

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.

Numerical study of fluid-structure interaction for enhanced heat transfer in microchannels with an oscillating elastic wall

The present numerical study explores the performance of fluid-structure interaction (FSI) in a microchannel with an oscillating elastic wall. A two-dimensional (2D) Computational Fluid Dynamics (CFD) simulation was performed to investigate the influence of the elastic wall's frequency and amplitude on fluid flow behavior, pressure drop, and heat transfer enhancement. The FSI governing equations were solved using the Arbitrary Lagrangian-Eulerian (ALE) method. The results indicated that the Nusselt number (Nu) decreases as oscillation frequency increases. In contrast, the Nu increased linearly with the oscillation amplitude. Additionally, the Prandtl number (Pr) showed an insignificant influence on the Nu number for the studied operating range. An optimal operating condition was identified for the microchannel with an oscillating wall, achieving a spatial average Nu number of 16.796 compared to 14.577 for a simple microchannel channel, representing a 15.23 %% enhancement in heat transfer. A correlation is derived for the spatial average Nu number as a function of the Reynolds number (Re), Strouhal number (St), Pr, and vibration amplitude ratio, providing a valuable tool for designing and optimizing microchannel systems with FSI. Finally, the Maxwell boundary conditions are incorporated into the simulation of a microchannel with a vibrating upper wall to evaluate the slip conditions.

The numerical analysis of complete and partial electrocoalescence in the droplet-layer system employing the sharp interface technique for multiphase-medium simulation

In this paper, the coalescence of a drop of water suspended in oil with a layer of water under the influence of a constant electric field is numerically investigated. Unlike most existing studies, the calculations are based on the application of the arbitrary Lagrangian-Eulerian method (ALEM), also called the moving mesh method, which belongs to the class of methods for modeling two-phase liquids with a sharp interface. Using this approach made it possible to avoid a false "escape" of the surface charge from the interface, which often occurs when using methods involving a diffuse interface. Despite the fact that ALEM does not allow describing topology changes by default, a numerical model was implemented in which the calculation is divided into three parts: the convergence of the drop and the layer before the moment of touch; the manual construction of the bridge at the moment of touch; the union of the drop and the layer. The developed model allowed us to obtain three possible modes of this process: complete coalescence, partial coalescence and a mode of stretching which has not practically been considered yet. The dependence of the volume of the separated secondary droplet on the size of the initial droplet and the average intensity of the applied electric field is obtained. The model showed good quantitative agreement with experimental studies. It has been shown that generally, the spots where the bridge and the neck are formed in case of partial coalescence do not coincide. A map of coalescence modes was obtained, i.e., the dependence of the transition threshold from coalescence to partial coalescence and from partial coalescence to stretching regime in a wide range of radii of initial droplets and electric field strengths. It has been shown that there is a maximum field strength at which droplets of any size merge with the layer. This map makes it possible to predict the coalescence regime in electrocoalescer. The proposed modeling technique can be used to calculate electrocoalescence modes at various values of the main parameters, which will help to optimize electrocoalescers at the design stage.

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.

Investigation on flooding dynamic response and mitigation measure of river bridge

Flood-induced failure of river bridges is intense due to frequently extreme and undesigned precipitation for global climate change. To reveal the dynamic characteristics and failure mechanism of bridges, flooding dynamic analysis is fully investigated via fluid–structure interaction simulation and Arbitrary Lagrangian-Eulerian method. Parametric analysis of different fluids and bridge configurations and pre-ballast mitigation measure are further conducted based on a simply-supported box-girder bridge. This study reveals several significant findings: the narrow channel can accelerate downstream flood velocity of the bridge piers to over double that of the upstream flow; moreover, unsubmerged piers experience vertical downward wave force surpassing buoyancy; the box girders exhibit three flood-response states, i.e., intact, slip and collapse, dependent on the hydraulic loading and bridge resistance capacity. Maximum horizontal wave force and displacement increase exponentially with the depth of water storage. Post-slip damage, bearing stress on the wave-facing side tends towards zero, while the wave-backing side presents a twofold increase. Maximum horizontal displacement (Xmax) distinguishes the failure states, such as 0 m ≤ Xmax ≤ 0.03 m (intact), 0.03 m < Xmax ≤ 1.39 m (slip), Xmax > 1.39 m (collapse), whose relation to the maximum horizontal wave force has been proposed for design reference and the inversion analysis of the bridge force. Applying a pre-ballast equivalent to 75 % of girder weight reduces Xmax by up to 91.5 %, shifting failure from collapse to slip. These insights offer crucial guidance for enhancing bridge safety amidst escalating flood risks.

Morphology and Effect of Load on Bridge Piers Impacted by Continuous Sea Ice

In order to study the collision of sea ice on bridge piers of a sea-crossing bridge, this study establishes a finite element model of the impact of sea ice on bridge piers in aqueous media based on explicit dynamics analysis software and programming software using the arbitrary Lagrangian Eulerian (ALE) method. The results show that, when the sea-ice spacing is larger than the sea-ice edge length, the increase in sea-ice spacing leads to a decrease in the collision force and a significant increase in the probability of climbing and overturning. The increase in sea-ice mass significantly increases the impact force on the bridge abutment, and the peak value increases linearly with the increase in mass, and the sea-ice climbing and overturning phenomena are obvious. Different shapes of sea ice are obtained by cutting the sea-ice field with the two-dimensional Voronoi method, and the maximum impact force increases significantly with the increase in the average area. Irregularly shaped sea ice leads to a larger impact force and triggers the accumulation climbing phenomenon, which is verified by experiments, and the experimental values are in good agreement with the simulated values. In conclusion, this study reveals the significant effects of the spacing, mass, and shape of sea ice on the impact force of bridge piers, which provides an important reference for the design of bridge structures.

Interaction between underwater explosion bubbles and soil–water interface: A numerical and experimental study

To explore the interaction between underwater explosion bubbles and soil–water interface, a near soil–water interface underwater explosion model based on the arbitrary Lagrangian–Eulerian method was established in this work. The peak pressure of the shock wave, maximum bubble radius, and bubble evolution in free-field and bottom-charge underwater explosions determined from the proposed simulation were highly consistent with the experimental results, thereby validating the proposed numerical model. The effects of the explosion distance and amount of explosive charge on the bubble–soil surface interaction were evaluated. The results showed that the reflection coefficient of the soil–water interface was in the range of 1.204–1.250, suggesting that it was hardly affected by the explosion distance and amount of explosive charge. The attenuation coefficient of the saturated soil was found to be 1.058. With the decrease in the explosion distance, the period and maximum radius of the bubbles slightly increased, and soil deformation increased as the lower surface of the bubbles was closer to the soil surface. For explosion distances of 0.3 and 0.4 m, only an overall movement of the soil surface was observed. When the explosion distance was 0.2 m or lower, a powerful downward jet was generated upon the pulsation of the first bubble, resulting in craters and slender depressions in the soil. With the increase in the amount of explosive charge, the period and maximum radius of the bubbles increased, and soil deformation also increased. These findings are expected to help advance our understanding of underwater explosion dynamics.

Study on the jetting characteristics of an underwater explosion bubble collapsing near a floating body

This study explores the dynamic behavior and jet characteristics of underwater explosion (UNDEX) bubble oscillating near a rigid floating body using the arbitrary Lagrangian–Eulerian (ALE) method. Experiments on UNDEX bubble oscillating in a free field or oscillating near a rigid floating body in an explosion tank are used to validate the effectiveness of the ALE method in simulating the behaviors of high pressure bubble oscillating near a boundary in water. The numerical results are in good agreement with the experimental data. On this basis, the distribution of the field pressure and velocity of the oscillating bubble are further analyzed in detail. The evolution characteristics of the bubble jets are discussed for various values of the stand-off distance and explosion attack angle. The results reveal that a bubble produces two jet patterns for close stand-off distances (from γD=0.800 to γD=1.336) and attack angles of 0°, 45°, 75°, and 90°. The first bubble jet results in an annular splitting of the bubble, while the second jet is pointed toward the floating body. The aim of this study is to provide a reference for further understanding the jet dynamics of UNDEX bubble collapsing near a structure and the effective attack on ship sides.

An improved Arbitrary Lagrangian–Eulerian thermal-fluid model by considering powder deposition effects on melting pool during Direct Energy Deposition processes

Directed Energy Deposition (DED) has emerged notably by offering new possibilities for (re-)manufacturing parts. The multi-phase thermal-fluid models that simulate powder stream deposition are computationally too expensive. The mono-phase Arbitrary Lagrangian–Eulerian (ALE) method are limited in prediction due to exclusion of powder deposition parameters. To address this, we propose an improved 3D mono-phase thermal-fluid model that incorporates powder deposition effects and employs a Moving Thermal-Fluid (MTF) framework to accelerate simulations. Mass, energy, and momentum conservation equations are solved using the finite element method (FEM) and an implicit time integration algorithm, and the ALE method tracks the free surface during deposition. The improved ALE allows considering enthalpy and momentum related to powder deposition through the implementation of new source terms in the energy and momentum conservation equations, leading to more accurate predictions without significantly increasing computing time. Numerical investigations into powder deposition parameters, such as powder distribution, powder enthalpy, and powder momentum, are conducted to identify their impact on melting pool prediction. The in-situ and ex-situ measurements of the melting pool are also performed to check the efficiency of the proposed model. The applications highlight the importance of incorporating powder stream effects and demonstrate the proposed model’s computational efficiency compared to the classical ALE model.

A numerical model for the simulation of complex planar Newtonian interfaces

We present a numerical model for the simulation of complex planar interfaces at which moving solid objects can be immersed, reproducing a wide variety of experimental conditions. The mathematical model consists of the Navier-Stokes equations governing the incompressible viscous flow in the liquid subphase, the transport equation for the evolution of the surfactant concentration at the interface, and the interfacial stress balance equation. The equations are simplified by treating the problem as isothermal and the surfactant as insoluble. The bulk flow equations are discretized using a collocated finite volume method, while the interfacial flow equations are discretized using a finite area method. The Boussinesq-Scriven interface constitutive model and a variant form accounting for extensional viscosity are used to describe the extra surface stress tensor. The coupling between surfactant concentration, interfacial velocity, and bulk velocity is treated implicitly by solving the interfacial and bulk equations sequentially at each time step until a stopping criterion is satisfied. The motion of the solid is treated by an arbitrary Lagrangian-Eulerian method. The model has been implemented in the OpenFOAM framework and allows the incorporation of new interface models and solvers, making the developed new package a versatile and powerful tool in the field of computational rheology. Applications of the model include the numerical simulation of flow around objects, such as probes, immersed at a complex interface, reproducing given experimental conditions, and its use as a tool in the analysis and design of interfacial stress rheometers. Several test cases have been performed to validate the model by comparing the results obtained with analytical solutions and with numerical and experimental results available in the literature.

Dynamic response of spherical tanks subjected to the explosion of hydrogen-blended natural gas

Hydrogen is a renewable and clean energy and obtains increasing attention all around the world. Blending hydrogen into natural gas can promote hydrogen development and storage tank farms play an essential role in the storage of hydrogen-blended natural gas (HBNG). However, upon leakage from the tank, HBNG accumulates to create a vapor cloud and may explode, resulting in more severe consequences than natural gas. Furthermore, the explosion has the potential to trigger the domino effect in the spherical tank storage area, leading to multiple explosions. But little attention has been paid on this research issue. This article analyzes the dynamic response of the spherical tank exposed to HBNG explosions. The fluid–structure interaction theory is adopted to establish the whole finite element model. Meanwhile, the advanced Arbitrary Lagrangian-Eulerian (ALE) method can reduce mesh distortion and enhance computational accuracy, and the process of explosion is analyzed through the coupling of the Lagrangian mesh for the structure and the Eulerian mesh for the vapor cloud. Then, the algorithm is employed that couples shell elements with solid elements by utilizing a penalty function. Besides, the dynamic response of the spherical tank and pillar surfaces is analyzed in the trends of effective stress, displacement, velocity, and structural damage under various parameters, evaluating the energy absorbed by the spherical tank and pillar. Accordingly, the equipment damage caused by HBNG explosions considering possible damage caused by secondary explosions can be obtained. Then, the effects of the HBNG explosion chain on equipment are analyzed in tank areas. The dynamic response of structures in the explosion is closely related to the different hydrogen blended ratios, distances, and structural thickness, which significantly impact the effective stress of the spherical tank and pillar. Moreover, the damage caused by the HBNG explosion is more serious for pillars than the spherical tank, making the role of pillars crucial in supporting the spherical tank. The results obtained in this study can be used to support the design and safety operation of HBNG storage areas.

Experimental and numerical investigations on dynamic response of butt-welded plates subjected to blast load

Experimental and numerical investigations on the small-size butt-welded plates subjected to air blast loads were conducted to highlight the effect of welded joints on the blast proof structures. The inherent characteristics of welded joints, including geometry, mechanical properties and welding residual stress were evaluated and discussed in the computation of blast loading. The geometry shape was assessed through macrographic of the welded joints. The distribution of mechanical and thermal physics property was determined through basic experiments using the specimens extracted from different zones of a welded joint. Welding residual stress was calculated in a thermo-mechanical coupled model. Conventional Weapons Effects Program (CONWEP) is more economic but limited compared with Arbitrary-Lagrangian–Eulerian (ALE) method. ALE and CONWEP methods were applied to simulate the air blast load applied on the plates. Effectiveness and efficiency of the methods were discussed. The results of the two programs could both coincide well with the experiment measurements. The models under six conditions were calculated to uncouple and discuss the effect of material property distribution and welding residual stress on the dynamic response of the welded structure. Permanent deflections were considered to assess the capacity of welded structures. Welding residual stress fields and the local weak materials are advantageous to the bending deformation. The phenomenological expressions of permanent deflection across thickness under different welding conditions were established based on simulation results. The effect of aspect ratio of the welded structures was also be discussed.