Symmetry Boundary Conditions Research Articles

Magnetostructural assessment of DEMO TF coils with ENEA Winding Pack configuration

The present paper deals with a multiphysics study of the DEMO Toroidal Field (TF) coils with Winding Pack (WP) layout proposed by the Italian agency ENEA. The latest WP configuration, so far designed adopting the Wind&React technique, is composed of 202 Nb3Sn rectangular conductors, with steel jacket thickness progressively increased from the plasma-facing side, arranged in 6 double layers. Each conductor is designed to carry an operative current of 73.4 kA (14.8 MAt for one TF coil) and to ensure the requirement of 12 T of magnetic peak field. The electromagnetic (EM) Lorentz forces have been preliminary evaluated with a magnetostatic 3D analysis at different instants of plasma scenario and then used to perform the 3D structural assessment of the TF coil. For both models (i.e., electromagnetic and mechanical), the WP has been represented as a homogenized material with the cyclic symmetry boundary conditions, allowing to reduce the computational effort. In the structural model, a preliminary design of outer inter-coil structures and gravity support have been included allowing them to identify critical locations in a reliable way. In addition to the EM loads at different plasma scenario instants also the cooling down has been considered as loading condition. The stress assessment on the steel Casing was performed, exploiting the stress linearization along several paths chosen in the most critical locations.

Open-Cell Nickel Alloy Foam–Natural Rubber Hybrid: Compression Energy Absorption Behavior Analysis and Experiment

This work deals with the compression energy absorption aspects of an open-cell nickel foam–natural rubber hybrid material. A comprehensive numerical analysis and elaborate experiments were the main tools used in this investigation. Open-cell nickel foam was analyzed as tetrakaidecahedron geometry. Inputs to the geometric dimensions were obtained by subjecting the nickel foam samples to x-ray micro-computed tomography (µCT) technique. A Mooney–Rivlin 2 parameter-based material model was implemented for the rubber part. Analysis was carried out using finite element-based commercial software ANSYS® with explicit dynamics as the chosen analysis scheme. During analysis, symmetry boundary conditions were applied considering each unit cell to be a mirror image of the adjacent cells. Static compression experiments were conducted on fabricated samples for validation of analysis with regard to energy absorption behavior. Scanning electron microscopy examination was carried out on hybrid samples both pre- and post-compression test for better understanding of compression mechanism. The compression energy absorption value of hybrid sample is significantly better than open-cell nickel foam and natural rubber values. The study clearly demonstrates interfacial bonds failure coupled with progressive deformation of foam cell ligaments as the main reasons for enhanced energy absorption during compression loading and presents the results quantitatively as a novel feature. In the end, the paper thoroughly compares the analysis and results in a critical way.

Behaviour of Steel-Concrete Composite (SCC) girder under impact due to rock fall

This paper presents a comprehensive numerical investigation on static and dynamic behaviour of the steel-concrete-composite (SCC) girders. Finite element model of steel concrete composite girder under quasi static loads is generated and the responses are validated with the experimental results conducted by the first author. Subsequently, the FE model is adopted to predict the dynamic behaviour of the SCC girder due to rock fall. In order to understand the significance of the studs in SCC girder and their behaviour under impact loading due to rock fall, in this regard two cases are demonstrated. First case is to understand the behaviour of SCC girders without any shear connection and, second is with full shear connection. All the numerical investigations are carried out using commercially available nonlinear explicit finite element code ABAQUS. During finite element analysis the attention has been paid to appropriately model the symmetry boundary conditions, and material behaviour for both steel and concrete. The well suited concrete damage plasticity model is adopted and input parameters are provided based on the standard laboratory tests. Present numerical model could closely predict the flexural capacities for three SCC girders having various stud spacing's. The progressive movement of plastic zone in the steel beam section has been found with the increased loading. This indicates maximum utilization of steel beam capacity as the neutral axis lies near top flange. Failure mode of the composite girder under rock fall event have also been predicted which may be helpful in the design of a protective strategy.

A consistent peridynamic formulation for arbitrary particle distributions

The Peridynamic Petrov–Galerkin (PPG) method is a meshfree particle method based on the weak form of the peridynamic momentum equation. It can be applied to arbitrary constitutive laws from the classical continuum mechanics theory. With non-linear approximation functions the rank deficiency present in many nodally integrated discretization schemes is prevented. The consistency of trial functions is not sufficient for the convergence with irregular particle distributions. In this paper the consistency of the test space is examined and possible correction techniques are presented. The resulting variationally consistent PPG method is able to pass the patch test and to restore the optimal convergence rates. A correction of the test functions that preserves the linear trial function consistency allows the use of displacement–pressure–dilation formulations and exhibits stability and robustness for 3-D in the regime of non-linear elasticity. Besides, the direct nodal coupling with Finite Elements and the application of symmetry boundary conditions are enabled.

Maximizing the accuracy of finite element simulation of elastic wave propagation in polycrystals.

Three-dimensional finite element (FE) modelling, with representation of materials at grain scale in realistic sample volumes, is capable of accurately describing elastic wave propagation and scattering within polycrystals. A broader and better future use of this FE method requires several important topics to be fully understood, and this work presents studies addressing this aim. The first topic concerns the determination of effective media parameters, namely, scattering induced attenuation and phase velocity, from measured coherent waves. This work evaluates two determination approaches, through-transmission and fitting, and it is found that these approaches are practically equivalent and can thus be used interchangeably. For the second topic of estimating modelling errors and uncertainties, this work performs thorough analytical and numerical studies to estimate those caused by both FE approximations and statistical considerations. It is demonstrated that the errors and uncertainties can be well suppressed by using a proper combination of modelling parameters. For the last topic of incorporating FE model information into theoretical models, this work presents elaborated investigations and shows that to improve agreement between the FE and theoretical models, the symmetry boundary conditions used in FE models need to be considered in the two-point correlation function, which is required by theoretical models.

Failure analysis on octagonal honeycomb sandwich panel under air blast loading

In recent days “honeycomb sandwich panels” are widely used against high intensity blast load due to the high energy absorption capability of the honeycomb structure. In this research paper determined the structural behavior of the honeycomb sandwich panel is subjected to the blast loading. Different honeycomb cores like square and octagonal structures are used to determine the minimum deflections for the top and back plates and also maximum energy absorption for the sandwich panel. The honeycomb sandwich panel is consists of the two solid plates (top plate and bottom plate) and one honeycomb core shell type structure. The blast is applied at a constant standoff distance from top plate of the sandwich panel. The sandwich panel is subjected to the blast load using the different masses of explosive charges such as 1 kg, 2 kg and 3 kg of the Trinitrotoluene (TNT) for the explosion in the air, at a constant standoff point distance from the top plate of sandwich panel. The finite element model is performed by ABAQUS software to determine the dynamic response for the sandwich panel. The quarter part of the honeycomb sandwich structure was modeled and imposed symmetry boundary conditions for the honeycomb sandwich panel to minimize the memory storage of the system and reduced the computation time of the analysis. The top and back face deflections of the square honeycomb sandwich panel have been validated with experimental results available in the literature in square honeycomb sandwich panel. There is a possibility of under estimation of the front face and back face deflections for the sandwich panel, if the honey comb structures are not considered an octagonal sandwich panels for different blast loads.

Constructal design method dealing with stiffened plates and symmetry boundaries

A new computational procedure for modelling the structural behavior of stiffened plates with symmetry boundary conditions is here presented. It uses two-dimensional finite elements as a way to decrease computational time without losing precision thanks to a relatively small number of elements applied for analyzing out-of-plane displacements (deflections) and stresses. Adding, the constructal design method was included in the procedure, together with the exhaustive search technique, with the scope to optimize the stress/strain status of stiffened plates by design changes. For the purpose, a reference plate without stiffeners was initially design and used as starting point. Part of the volume was reshaped into stiffeners: thickness was reduced maintaining unchanged weight, length and width. The main goal was to minimize strains and stresses by geometric changes. Results demonstrated that, thanks to this design procedure, it is always possible to find an adequate geometry transformation from reference plate into stiffeners, allowing significant improvements in mechanical behavior.

On the oddness of percolation

Recently Mertens and Moore (2019 Phys. Rev. Lett. 123 230605) showed that site percolation ‘is odd’. By this they mean that on an M × N square lattice the number of distinct site configurations that allow for vertical percolation is odd. We report here an alternative proof, based on recursive use of geometric symmetry, for both free and periodic boundary conditions.

Studies on thermal management of Lithium-ion battery pack using water as the cooling fluid

Study of battery thermal management is critical for safe and better performance of Lithium-ion batteries, considering several recent battery failures and explosions. Lithium-ion batteries are generally used in stacks to meet the high energy requirements. Thus, the heat generated in a battery pack must be properly managed for efficient operation. A battery thermal management system (BTMS) is an ideal tool to understand the thermal health of a battery. An attempt is made here to study the influence of water as the coolant on the battery thermal management. A variable heat generation that depends on the discharge rate is assumed in the simulations. A 5C charge/discharge rate (per hour) per battery and two packs of 5 batteries each are considered for the analysis. Due to symmetry only half pack (2.5 batteries) with symmetry boundary conditions is considered in the simulations. The influence of volume flow rate, flow direction, and contact area on the battery thermal behaviour are analysed. Results indicate that a 5C charge/discharge produces maximum temperatures of 319.31 K and 316.93 K at flow rates of 0.25 × 10−6 m3/s and 1.6 × 10−6 m3/s, respectively. Whereas, the uncooled batteries with 5C charge/discharge produces a maximum temperature of 336.623 K. Therefore, the uncooled peak temperature is estimated to be reduced by 5.85% by circulating the coolant at 1.6 × 10−6 m3/s. Furthermore, by reversing the direction of water flow in one of the channels, leads to redistribution of heat and hence the temperature distribution in the battery pack is observed to be more uniform. Flow reversal also helped to reduce the peak temperatures by 2.77 K in the battery pack. All the calculations are performed using the commercial software COMSOL.

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Summary Espresso is a beverage brewed using hot, high-pressure water forced through a bed of roasted coffee. Despite being one of the most widely consumed coffee formats, it is also the most susceptible to variation. We report a novel model, complimented by experiment, that is able to isolate the contributions of several brewing variables, thereby disentangling some of the sources of variation in espresso extraction. Under the key assumption of homogeneous flow through the coffee bed, a monotonic decrease in extraction yield with increasingly coarse grind settings is predicted. However, experimental measurements show a peak in the extraction yield versus grind setting relationship, with lower extraction yields at both very coarse and fine settings. This result strongly suggests that inhomogeneous flow is operative at fine grind settings, resulting in poor reproducibility and wasted raw material. With instruction from our model, we outline a procedure to eliminate these shortcomings.

Numerical simulation of subcooled flow boiling in a manifold microchannel heat sink

Recently, various miniaturized electronic systems and the rapid increase in power density of microelectronic devices have created additional requirements for micro-scale heat dissipation technology. To dissipate heat in a micro-scale region efficiently, several creative cooling methods for high heat flux dissipation have been designed on the order of 1000 W/cm2. Due to its high surface-to-volume ratio, the microchannel heat sink has become the most popular one among emerging technologies and an effective tool for high heat flux thermal management. Nevertheless, in common electronic microchannel cooling systems, the traditional parallel microchannel causes a dramatic pressure loss along channel length. In this regard, the manifold microchannel heat sink cooling technology becomes promising with its high heat dissipation potential and moderate pressure drop penalty. The shortened effective flow length compared with the traditional microchannel provides a smaller pressure drop and delays the onset of the critical-heat-flux point. However, while a number of numerical and experimental studies have been conducted for the single-phase flow in the manifold microchannel, two-phase flow boiling in this kind of channel is not widely employed because of its issues with flow pattern prediction. This work develops a new solver based on open source software OpenFOAM to perform the transient process of subcooled flow boiling in the manifold microchannel heat sink. Additionally, heat transfer in the silicon substrate is considered to improve the accuracy of simulation. Similar to single-phase flow simulation for the manifold microchannel, a unit cell model extracted from the whole cooling plate is employed for the two-phase boiling flow to avoid huge computational costs. Through several reasonable assumptions, the symmetry boundary condition is applied on four lateral surfaces in the unit cell, while uniform heat flux is adopted on the bottom wall. A uniform inlet velocity boundary estimated from the total volume flow rate condition is coupled with a fixed temperature value of 7°C lower than saturation temperature. After the mesh independence test, the self-programming solver and numerical methods are validated by comparing numerical results with experimental data. It is determined that the boiling curve obtained by the empirical rate phase-change model with parameters r l= r v=100 agrees well with experimental results. Furthermore, heat transfer and pressure drop performance differences are caused by microchannel width w c and fin width w f. In comparison to sample A ( w c= w f=15 μm), decreasing w c and w f simultaneously leads to lower average wall temperature of the heated surface; the channel pressure drop between inlet and outlet surfaces rises dramatically when the widths decrease. When the total number of microchannels in the manifold microchannel cooling plate remains unchanged, increasing w c results in a decreased w f. Based on experimental results, heat sink sample C shows that the pressure loss can be considerably reduced under the premise of sacrificing a small degree of heat transfer performance, which can be attributed to the increased microchannel hydraulic diameter. The manifold microchannel heat sink with w c> w f is recommended for practical application due to lower pressure loss and average temperature variation.

3D gradient corrected SPH for fully resolved particle–fluid interactions

Fully resolved fluid–solid coupling is explored with the gradient corrected weakly compressible SPH methodology being used to simulate an incompressible Newtonian fluid as well as being used to obtain the coupling force information required to accurately represent these interactions. Gradient correction allows for the application of the Neumann boundary condition required to describe the pressure fields at solid interfaces, as well as symmetry boundary conditions for velocity (where applicable) without the use of ghost or mirrored particles. A scaling study is performed by investigating the drag on an infinitely long cylinder at different smoothed particle hydrodynamics (SPH) resolutions, with finer resolution scales showing good correlation to other studies. The drag characteristics of several particle shapes and topologies are also investigated making use of both convex and non-convex particle shapes. Clear distinction for both the fluid and solid particle responses for the various solid particle shapes are observed. Boundary effects are also explored with results showing a strong responses to changing domain geometry aspect ratios. A many particle system with two different particle shapes are simulated to investigate bulk behaviour of the different solids falling under gravity in a fluid. All results presented in this paper are obtained from full 3D simulations.

Mechanics of plastic flow past a narrow-angle wedge indenter

ABSTRACTThe indentation of a metal specimen by a narrow-angle wedge produces extreme plastic deformation, with an effect akin to cutting into the metal. Simulation of such processes is challenging, and complicated by the need to model material separation along the indentation symmetry axis. Here we use an Arbitrary Lagrangian Eulerian (ALE) framework to enforce the symmetry boundary conditions (bcs) in their original, `strong’ form, as well as conventional Lagrangian FE to impose the bcs in a complementary, `weak’ form. Taken together these two cases, representing perfectly strong and perfectly weak interfaces, produce accurate bounds on the mechanical response for indentation by wedges with semi-apical angles as small as 15 degrees, and encompass intermediate cases that would require complicated models of ductile failure. The method accurately predicts the transition from the cutting pattern to the non-cutting (radially compressive) pattern as the apical angle is increased. In combination with Lagrangian particle tracking, the simulations reveal the deformation pattern as well as strain, strain-rate, and velocity fields in narrow angle indentation at high resolution. Interestingly, the strong form predicts a thin (tens of microns), near-wall layer of intense plastic strain, which has been observed recently in indentation experiments. With the exception of this feature, the strong and weak bc solutions are quite similar. The present approach reveals insights about plastic flow past narrow obstacles in a range of related problems including cone penetration and machining, and suggests using narrow-angle indentation as a way to probe material failure.

Self-assembly and properties of domain walls in BiFeO3 layers grown via molecular-beam epitaxy

Bismuth ferrite layers, ∼200-nm-thick, are deposited on SrRuO3-coated DyScO3(110)o substrates in a step-flow growth regime via adsorption-controlled molecular-beam epitaxy. Structural characterization shows the films to be phase pure with substrate-limited mosaicity (0.012° x-ray diffraction ω-rocking curve widths). The film surfaces are atomically smooth (0.2 nm root-mean-square height fluctuations) and consist of 260-nm-wide [11¯1]o-oriented terraces and unit-cell-tall (0.4 nm) step edges. The combination of electrostatic and symmetry boundary conditions promotes two monoclinically distorted BiFeO3 ferroelectric variants, which self-assemble into a pattern with unprecedentedly coherent periodicity, consisting of 145 ± 2-nm-wide stripe domains separated by [001]o-oriented 71° domain walls. The walls exhibit electrical rectification and enhanced conductivity.

Electrochemical Modeling and Simulation of a Three-Electrode Lead Acid Cell

The low initial cost, ease of manufacture and relatively mature state of technology make lead-acid batteries the most popular energy storage choice for a variety of applications. Lead-acid batteries exist in different designs and configurations, each suitable for different use cases and performance targets such as cycle life, rate performance, and cost. Further performance and design improvements remain of significant salience to battery manufacturers.1–3 Electrochemical modeling can greatly complement the product development process by enabling the quick evaluation new lead-acid designs, reducing the amount of testing and validation required, and their attendant temporal and economic demands. Several continuum-level models with varying predictive capabilities have been reported in the literature. These have been used to examine the effect of various material and cell design parameters on performance.4–7 This talk describes an electrochemical modeling study for a lead-acid test cell comprising two positive electrodes engaging a single negative electrode. The one-dimensional electrochemical model employed herein is adapted from classical porous electrode models for flooded lead-acid cells. Along with the porous electrode, separator and reservoir domains of a single cell model, the test cell includes additional cathode and reservoir regions. This configuration may be observed in the terminal plates in a commercial battery layout. Classical electrochemical models,4,6 which analyze a single repeat unit in a full battery, are extended to this non-standard configuration by modeling additional porous electrode and reservoir regions. The non-standard model necessitates appropriate boundary conditions to define the coupling between electrochemical variables in different regions, since the symmetry boundary conditions typically used are no longer applicable. The modified model equations and new boundary conditions are then simulated using a finite-difference scheme for discharge and compared against experimental data for standard performance tests, namely C20, Reserve Capacity (RC) and Cold Cranking Amperage (CCA). The salient modeling and simulation differences with a standard lead-acid model are also discussed, as are the trends in predicted electrochemical variables. We expect this model to be of substantial utility in guiding the evaluation of new battery designs through the improved prediction of performance in the test cell configuration. Acknowledgements This research was supported by EXIDE Technologies. The authors also acknowledge financial support from the Department of Chemical Engineering and the Clean Energy Institute at the University of Washington. References G. J. May, A. Davidson, and B. Monahov, J. Energy Storage, 15, 145–157 (2018)J. Lannelongue, M. Cugnet, N. Guillet, and A. Kirchev, J. Power Sources, 352, 194–207 (2017).A. Jaiswal and S. C. Chalasani, J. Energy Storage, 1, 15–21 (2015).H. Gu, T. V. Nguyen, and R. E. White, J. Electrochem. Soc., 134, 2953–2960 (1987).W. B. Gu, C. Y. Wang, and B. Y. Liaw, J. Electrochem. Soc., 144, 2053–2061 (1997).M. Cugnet, S. Laruelle, S. Grugeon, B. Sahut, J. Sabatier, J.-M. Tarascon, and A. Oustaloup, J. Electrochem. Soc., 156, A974–A985 (2009).Nguyen, T. V., R. E. White, and H. Gu, J. Electrochem. Soc., 137, 2998–3004 (1990).

An isotropic unstructured mesh generation method based on a fluid relaxation analogy

In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three characteristic fields based on three modeling equations are computed to define the target mesh-vertex distribution, i.e. target feature-size function and density function. The modeling solutions are computed on a multi-resolution Cartesian background mesh. Second, with a target particle density and a local smoothing-length interpolated from the target field on the background mesh, a set of physically-motivated model equations is developed and solved by an adaptive-smoothing-length Smoothed Particle Hydrodynamics (SPH) method. The relaxed particle distribution conforms well with the target functions while maintaining isotropy and smoothness inherently. Third, a parallel fast Delaunay triangulation method is developed based on the observation that a set of neighboring particles generates a locally valid Voronoi diagram at the interior of the domain. The incompleteness of near domain boundaries is handled by enforcing a symmetry boundary condition. A set of two-dimensional test cases shows the feasibility of the method. Numerical results demonstrate that the proposed method produces high-quality globally optimized adaptive isotropic meshes even for high geometric complexity.

Spectral transitions for Aharonov-Bohm Laplacians on conical layers

AbstractWe consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary of the domain. We show that there exists a critical total magnetic flux depending on the aperture of the conical surface for which the system undergoes an abrupt spectral transition from infinitely many eigenvalues below the essential spectrum to an empty discrete spectrum. For the critical flux, we establish a Hardy-type inequality. In the regime with an infinite discrete spectrum, we obtain sharp spectral asymptotics with a refined estimate of the remainder and investigate the dependence of the eigenvalues on the aperture of the surface and the flux of the magnetic field.

Verificação de modelo computacional para placas com enrijecedores considerando condição de contorno de simetria

O presente artigo apresenta a modelagem computacional de placas enrijecidas submetidas a uma carga transversal uniformemente distribuída, permitindo a análise numérica de deslocamentos e tensões. O modelo computacional foi desenvolvido no software ANSYS, baseado no Método dos Elementos Finitos (MEF), empregando o elemento finito SHELL281. Este modelo foi elaborado considerando a condição de contorno de simetria, possibilitando que somente um quarto da placa enrijecida fosse simulado numericamente. As simulações com esta condição de contorno demonstraram um ganho de processamento computacional em relação às simulações da placa completa. Além disso, a sua utilização possibilitou o uso de discretizações espaciais (malhas) mais refinadas do que as usadas em modelos que consideram a placa inteira. Com o objetivo de verificar esse modelo computacional assim como avaliar sua acurácia em relação aos resultados obtidos com o modelo que considera toda a placa, análises de deflexão e de tensão foram realizadas. A verificação do modelo foi feita usando a solução independente de malha, obtida através de um teste de convergência de malha. Os resultados do modelo numérico utilizando a condição de contorno de simetria demonstraram uma boa precisão em relação ao modelo computacional da placa completa, tanto na verificação quanto em um comparativo da placa inteira em relação a seu equivalente com simetria.

Computational Modeling and Constructal Design Method Applied to the Geometric Evaluation of Stiffened Thin Steel Plates Considering Symmetry Boundary Condition

Computational Modeling and Constructal Design Method Applied to the Geometric Evaluation of Stiffened Thin Steel Plates Considering Symmetry Boundary Condition

Comparative Study of Macroscopic Rupture Criteria

Abstract In this paper, four macroscopic criteria for rupture prediction are considered for study. Analytical elasto-plastic material properties were used for simulation of tension using unit cube with symmetry boundary conditions. The commercial finite element code ABAQUS/Standard was used for simulation. The various stress-strain values obtained from simulation were post-processed for prediction of rupture using macroscopic criteria for maximum strain value of 1. Ayada, Brozzo, Oh and Rice-Tracey criteria were applied using MATLAB and the critical values of rupture were predicted. Rupture values obtained from analytical and simulated data were compared in order to perform validation. In conclusion, rupture values predicted from simulated stress-strain values have good agreement with the rupture values predicted with analytical data. Also, these four macroscopic rupture criteria were successfully applied on unit cube.