Laguerre-Voronoi Tessellations Research Articles

Transport and deposition of nanoparticles in porous media at the pore scale using an Eulerian-Lagrangian method

BackgroundNanoparticle deposition in a subsurface environment decreases the amount of material in the bulk fluid, increases surface roughness, and affects nanofluid flow. Nanoparticle transport in porous media is a complex, multiscale phenomenon. Its macroscopic behavior is determined by phenomena at the pore-scale. Hence, it is necessary and of interest to study the transport and deposition of nanoparticles in porous media using a pore-scale approach. MethodsA computational solver is developed using an Eulerian-Lagrangian approach within the OpenFOAM library. A Berea sandstone and three open-cell metal foams with porosities of 0.8, 0.85, and 0.9, constructed by Laguerre-Voronoi tessellation, were analyzed to study nanoparticle behavior in water. Significant findingsNanoparticle deposition on solid surfaces is influenced by porosity, double layer thickness (NDL), surface potential magnitude (NE1), and nanoparticle diameter. Brownian motion that has a significant impact on nanoparticle transport and deposition is also examined. For nanoparticles with 20 nm diameter, the fraction of particles deposited in foam with 0.8 porosity is about 17 % more than the foam with 0.9 porosity. This difference decreases with nanoparticle diameter. For the particles with 100 nm diameter and more, the effects of Brownian motion on nanoparticle deposition becomes negligible.

Numerical design of open-porous titanium scaffolds for Powder Bed Fusion using Laser Beam (PBF-LB)

The paper concerns the numerical design of novel three-dimensional titanium scaffolds with complex open-porous structures and desired mechanical properties for the Powder Bed Fusion using Laser Beam (PBF-LB). The 60 structures with a broad range of porosity (38–78%), strut diameters (0.70–1.15 mm), and coefficients of pore volume variation, CV(Vp), 0.35–5.35, were designed using the Laguerre-Voronoi tessellations (LVT). Their Young's moduli and Poisson's ratios were calculated using Finite Element Model (FEM) simulations.The experimental verification was performed on the representative designs additively manufactured (AM) from commercially pure titanium (CP Ti) which, after chemical polishing, were subjected to uniaxial compression tests. Scanning Electron Microscopy (SEM) observations and microtomography (μ-CT) confirmed the removal of the support structures and unmelted powder particles. PBF-LB structures after chemical polishing were in close agreement with the CAD models' dimensions having 4–12% more volume.The computational and experimental results show that elastic properties were predicted in very close agreement for the low CV(Vp), and with even 30–40% discrepancies for CV(Vp) higher than 4.0, mainly due to PBF-LB scaffold architecture drawbacks rather than CAD inaccuracy. Our research demonstrates the possibility of designing the open-porous scaffolds with pore volume diversity and tuning their elastic properties for biomedical applications.

High-resolution reconstruction-based investigation of multi-scale lamellar microstructures by coupled crystal plasticity and in-situ experiment

This study aims to establish a novel approach to better understand and predict material behavior in multi-scale lamellar microstructures. High-resolution reconstruction is built on collaborative characterization at both grain and sub-grain scale. A framework for microstructural characterization integrates, secondary electron imaging (SEI), electron backscatter diffraction (EBSD), and image recognition, to ensure that the reconstructed microstructure adequately represents the equivalent grain size, lamellar spacing, and lamellar geometric orientation. Importantly, a high-resolution reconstruction algorithm was developed combining the Laguerre-Voronoi tessellation and minimum bounding sphere (MBS), which allows the reconstructed model retain multi-scale microstructures. Finally, the mechanical properties of pearlite were investigated by combining crystal plasticity simulation with in-situ scanning electron microscopy (SEM) tensile testing based on high-resolution reconstruction. Stress-strain field analysis revealed that cross-lamellae strain bands originate from ferrite large deformation-induced shear transmission, with marked strain distribution heterogeneity within identical lamellae. This concurrently validated the excellent reliability of the novel strategy.

Pore-scale fluid flow and conjugate heat transfer study in high porosity Voronoi metal foams using multi-relaxation-time regularized lattice Boltzmann (MRT-RLB) method

This study aims to investigate pore-scale flow and conjugate heat transfer in high-porosity open-cell metal foams. Five representative elementary volume (REV) samples with different values of porosity (0.80, 0.85, and 0.90) and pore density (10, 20, and 30 PPI) are generated using the Laguerre-Voronoi tessellation (LVT) algorithm. To perform direct numerical simulations, a decoupled lattice Boltzmann solver is developed utilizing multi-relaxation-time (MRT) model for flow and regularized lattice Boltzmann (RLB) model for advection-diffusion. As a novelty, this solver is able to simulate advection-diffusion in the non-Darcy regime. To consider thermal conduction in REV samples more prominently, a constant high temperature is assigned to the solid ligaments on the inlet plane. The flow results show that the transition from the Darcy to the non-Darcy regime occurs at lower Reynolds numbers in foams with lower porosity, whereas the pore density does not affect the transition point significantly. According to the heat transfer results, metal foams cool down rapidly at high flow velocities while the temperature rise in the fluid is minimal. Also, increasing pore density from 10 PPI to 30 PPI and decreasing porosity from 0.90 to 0.80 increase the h-ReK slope in the non-Darcy regime by 190% and 17.5%, respectively.

PRESSURE GRADIENT COMPUTATION FOR FOAMS WITH DIFFERENT GEOMETRIC PROPERTIES: BASED ON ANN AND SVR MACHINE LEARNING MODEL AND TRAINED BY CFD SIMULATIONS

In this research work, a combination of computational fluid dynamics (CFD) simulation and artificial intelligence (AI) methods are conducted to study the effects of geometric properties of aluminum foams on airflow and to compute and predict pressure gradients in foams with such varied geometric parameters as porosity (65-90%) and pore diameter (200-2000 μm). The 3D foam structures are created by the Laguerre-Voronoi tessellations method. Based on the CFD results, pressure gradient for 114 different foams can be calculated in terms of inlet flow velocity (in the range 0.1-8 m/s). Foam pressure gradient is found to increase with increasing inlet flow velocity but with decreasing pore diameter and porosity. Comparisons reveal that the results obtained in the present study for pressure gradient are consistent with the data reported in the literature. It is, therefore, concluded that CFD simulation is a useful tool for pressure gradient estimation in a variety of foam types. Unique simulations are, however, needed each time foam structural properties change, which entails significant increases in the associated computation costs. This drawback may, nonetheless, be at least partially addressed by taking advantage of soft computing methods such as machine learning (ML). Artificial neural network (ANN) and support vector regression (SVR) as subsets of AI are designed (models with input variables inlet velocity and the foam structural parameters: porosity, pore diameter, and strut diameter) and trained using CFD results to predict pressure gradients in a large number of foams. When applied to new foam samples, the ML models exhibit an acceptable performance in predicting pressure gradients. Using such provisions, the method can be effectively used for predicting pressure gradient in various porous media at minimum computation costs.

Elastic Properties of Open Cell Metallic Foams-Modeling of Pore Size Variation Effect.

Elastic properties of open-cell metallic foams are investigated in correlation with relative density and pore size variation. A variety of foam architectures, with open porosity above 70% (relative density below 0.30) and various pore size distributions, were modeled using Laguerre–Voronoi tessellations (LVT). The coefficient of pore volume variation, CV(V), was introduced to quantify the uniformity of designed structures and ranged between 0.5 to 2.1. Elastic behavior of the modeled foams to uniaxial compression along three orthogonal directions was analyzed using the finite element (FE) method. It is shown that Young’s modulus and Poisson’s ratio of open-cell metals is not solely a function of relative density (porosity) but the pore size variation as well. For similar porosity (approx. 74–98%), Young’s modulus and Poisson’s ratio may be reduced by approx. 25–30% and 10–25%, respectively, when CV(V) increases from 0.5 to 2.1. Furthermore, the incorporation of a relationship between Young’s modulus and the coefficient of pore volume variation to the Gibson–Ashby model is proposed.

Pore-scale direct numerical simulation of fluid dynamics, conduction and convection heat transfer in open-cell Voronoi porous foams

The pore-scale analysis includes the pore network simulation and direct numerical simulation, which the latter is more accurate and provides more details about the problem. This study presents a pore-scale direct numerical simulation of flow and convection-conduction heat transfer in open-cell metal foams with a complex structure. First, using the Laguerre–Voronoi tessellations (LVT) algorithm, three foam samples with various porosities (76.6%, 84.4%, and 93.8%) and a constant pore density of 20 pores per inch (PPI) are generated. Next, the open-source library of OpenFOAM is employed to perform heat transfer and flow analysis in Darcy and non-Darcy regimes. Results were verified through comparison with available experimental and numerical data. The effects of foams' porosity, solid material, and Reynolds number on flow characteristics and heat transfer are investigated. Results are presented in terms of the permeability, Forchheimer coefficient, the volumetric and average heat transfer coefficient, and temperature and velocity distribution. By decreasing porosity, the flow complexity increases with subsequent increments in heat transfer and pressure drop. Also, the conductive heat transfer through the foam plays a vital role in the total heat transfer rate. These pore-scale outcomes could be used in macro-scale thermo-fluid models to perform more accurate simulations with less computational costs.

Models of advanced recording systems: A multi-timescale micromagnetic code for granular thin film magnetic recording systems

Micromagnetic modelling provides the ability to simulate large magnetic systems reliably without the computational cost limitation imposed by atomistic modelling. Through micromagnetic modelling it is possible to simulate systems consisting of thousands of grains over a time range of nanoseconds to years, depending upon the solver used. Here we present the creation and release of an open-source multi-timescale micromagnetic code combining three key solvers: Landau-Lifshitz-Gilbert; Landau-Lifshitz-Bloch; Kinetic Monte Carlo. This code, called MARS (Models of Advanced Recording Systems), is capable of accurately simulating the magnetisation dynamics in large and structurally complex single- and multi-layered granular systems as is shown by comparison to established atomistic simulation results. The short timescale simulations are achieved for systems far from and close to the Curie point via the implemented Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch solvers respectively. This enables read/write simulations for general perpendicular magnetic recording and also state of the art heat assisted magnetic recording (HAMR). The long timescale behaviour is simulated via the Kinetic Monte Carlo solver, enabling investigations into signal-to-noise ratio and data longevity. The combination of these solvers opens up the possibility of multi-timescale simulations within a single software package. For example the entire HAMR process from initial data writing and data read back to long term data storage is possible via a single simulation using MARS. The use of atomistic parameterisation for the material input of MARS enables highly accurate material descriptions which provide a bridge between atomistic simulation and real world experimentation. Thus MARS is capable of performing simulations for all aspects of recording media research and development. This ranges from material characterisation and optimisation to system design and implementation. The object orientated nature of MARS is structured to facilitate quick and simple development and easy implementation of user defined custom simulation types which can utilise either timescale or a combination of both timescales. Program summaryProgram title: MARSCPC Library link to program files:https://doi.org/10.17632/8mx7cndcdx.1Developer's repository link:https://bitbucket.org/EwanRannala/mars/Code Ocean capsule:https://codeocean.com/capsule/2549929Licensing provisions: MITProgramming language: C++Supplementary material: MARS testing methodology (PDF), HAMR simulation example video.Nature of problem: A combined model that enables the complete modelling of magnetic recording processes at elevated temperatures covering all time scales from writing (nanoseconds) up to long term data storage (years). The model must also accurately describe the granular nature of the recording media as grain sizes are reduced to a few nanometres.Solution method: Short timescale behaviours are captured via the Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch solvers for low and high temperature systems respectively. The long time scale behaviours are captured via a kinetic Monte Carlo solver. To enable complex models which account for mixed timescale behaviours the solvers are implemented as a single class structure which allows for dynamic solver selection. The granular structure is generated via a Laguerre-Voronoi tessellation with a custom implemented packing algorithm to produce highly realistic grain size distributions. Complex thermal dependencies of materials can be incorporated via atomistic parameterisation forming a multi-timescale model of the material.

Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre-Voronoi Tessellation.

Voronoi tessellations are shown to be statistically representative of polycrystalline microstructures, which have been widely accepted for the modeling of microstructures of metallurgic and ceramic materials. In this paper, a new implementation of the Voronoi diagram in Laguerre geometry is presented for the generation of numerical models of polycrystalline microstructures, where the size and shape of the grains can be controlled, and the 3D grain boundaries can be modeled with a specified thickness. The distribution of grain sizes in the models is fitted to a lognormal distribution, compared with the normal distribution in the Voronoi tessellation methods. Finally, statistical analyses of grain face and grain size distribution are performed with the models, and the macroscopic elastic properties of polycrystalline ceramic materials are simulated to verify the capability of the presented method.

Pore-scale simulation of flow in minichannels with porous fins

<p indent="0mm">Because of its high specific surface area, metal foam is expected to further enhance the flow and thermal performance of a minichannel heatsink. In this study, fully developed flow in minichannels with porous fins was studied. The porous geometry was constructed based on Laguerre-Voronoi tessellation and simulated in a pore scale, which eliminated the influence of parameter selection in a macroscale method. The influence of porosity, filling ratio, and Reynolds number on velocity field and pressure drop was analyzed. The general relationship between the Poiseuille number and filling ratio was determined, and a correlation was obtained using the study results. The results of this study were compared with those of the macroscale method, and finally, the influence of effective viscosity was discussed.

Missing information and data fidelity in digital microstructure acquisition

Measuring and modeling microstructure is crucial for establishing structure-property relations. Here the digitized format of the microstructure plays an increasingly vital role in modern material design and advanced manufacturing of functional materials. However, one basic issue facing digital acquisition of microstructures has attracted little attention, namely the loss of information in the first steps of data gathering and processing. The missing information leads to serious issues in a range of topics from reconstruction of microstructures to prediction of material properties. To bring forth and quantify these issues, we develope an analytical method and a new numerical simulation scheme using Laguerre-Voronoi tessellation and Xu-Li microstructure characterization method. We then define and quantify the missing information and its impact rigorously.

APPROPRIATE MODELS FOR SIMULATING OPEN-POROUS MATERIALS

In the present paper two representative models applied for modeling of two types of porous materials - open-cell foams and open-porosity tapes - are addressed. Algorithms presented here base on Laguerre-Voronoi tessellations (open-cell foams) and the sphere representation (open-porosity tapes) and enable creating the desired porosity and pore size distribution. The geometrical features of the models, such as: porosity, mean pore size, cell diameter distribution and number of faces per cell were compared with those obtained by 3D micro-computed tomography and good agreement was obtained.

Numerical investigation of pressure drop and heat transfer through open cell foams with 3D Laguerre-Voronoi model

This work reviews the theoretical backgrounds of pressure drop prediction for open cell foams. The pressure drop of open cell foams was investigated on aluminum foam structures of pore densities 10–50ppi and porosities 70–95%, with the commercial CFD analysis package: ANSYS Fluent, and performed over flow velocities ranging from 0.5m/s to 20m/s. The 3D foam structures were created by Laguerre-Voronoi tessellations. The numerical results for pressure drop were compared with the theoretical predictions by Inayat et al. and experimental data in the literature. The results show that the pressure drop of foams increases with increasing pore density and decreasing porosity. The numerical results are consistent with theoretical predictions and experimental data. The computed interfacial heat transfer coefficient was investigated. The Nusselt number increases with increasing Reynolds number, and increases with increasing porosity at constant pore density. The friction factor of foams was also evaluated.

Generation of 3D polycrystalline microstructures with a conditioned Laguerre-Voronoi tessellation technique

Voronoi tessellation techniques are widely accepted methods for the generation of representative models of polycrystalline microstructures of metallurgic and ceramic materials. Contrary to most of the Voronoi-based tessellation methods developed, the Laguerre Voronoi technique provides control over the size and shape of the cells, therefore allowing to simulate accurately the grain structure of a wide range of materials. This paper presents a method for the generation of numerical models of 3D polycrystalline microstructures, based on the Laguerre-Voronoi tessellation technique. An innovative approach to define the additional parameters required by the Laguerre-Voronoi formulation for the generation of realistic 3D microstructures is presented, providing the algorithm with information on the given microstructure from a set of 2D micrographs easily obtainable experimentally. The method implemented efficiently avoids degenerated cells (affecting the quality of the final structure) and finds the most representative set of input values by comparing 2D sections of the numerical model against 2D imaging of real polished surfaces. In this paper, the capability of the method developed is verified by reproducing the microstructure of polycrystalline alumina with various ranges of grain sizes, deriving from different sintering procedures.

Design of Reservoir Recognition Technique Component - Open Porosity in Non-Polarizing Electrodes

In the present study modeling of permeability of open-porosity ceramic materials used in non-polarizing electrodes is addressed. The structure of the material filling the electrode determines the infiltration of the ceramic structure by electrolyte, which influences the efficiency of the electrodes. The composition of electrode material was characterized with Scanning Electron Microscope Hitachi S3500N with EDS detector and the structure was determined with use of XRadia XCT400 tomograph . The complex geometry of porous materials has been designed using procedure based on Laguerre-Voronoi tessellations (LVT). A set of porous structures with different geometrical features has been developed using LVT algorithm. The approach used here allows to investigate the influence of geometrical features such pore size variation on the permeability of studied materials. Pressure drop characteristics of the developed structures has been analyzed using finite volume method (FVM). The results show that permeability of porous materials is strongly related with distribution of pore size. The study exhibits the utility of developed design procedure for optimization of non-polarizing electrodes performance.

Incorporation of the Pore Size Variation to Modeling of the Elastic Behavior of Metallic Open-Cell Foams

Abstract In the present paper we present the approach for modeling of the elastic behavior of open-cell metallic foams concerning non-uniform pore size distribution. This approach combines design of foam structures and numerical simulations of compression tests using finite element method (FEM). In the design stage, Laguerre-Voronoi tessellations (LVT) were performed on several sets of packed spheres with defined variation of radii, bringing about a set of foam structures with porosity ranging from 74 to 98% and different pore size variation quantified by the coefficient of pore volume variation, CV(V), from 0.5 to 2.1. Each structure was numerically subjected to uni-axial compression test along three directions within the elastic region. Basing on the numerical response, the effective Young’s modulus, Eeff, was calculated for each structure. It is shown that the Eeff is not only dependent on the porosity but also on the pore size variation.

Modeling structures of open cell foams

This work proposes an original geometrical model based on randomly packed spheres using Laguerre-Voronoi tessellations to simulate geometrical and topological characteristics in the microstructure of open cell foams. The model can be used to analyze the effect of coefficient of variation on the pores distribution in real foams. The distribution of foam-cell volumes in foam structures generated in this work is dependent on the log-normal distribution of sphere volumes in corresponding randomly packed spheres. The statistical data of modeled foam structures, including distribution of the cell volume, face and edge number is very close to the characteristics of real materials. The results also show that a higher coefficient of variation in the sphere diameter would decrease the average number of faces per cell. The average number of faces varies from 13.56 to 14.43 for different coefficients of variation of sphere diameter, while the average number of faces in the Poisson-Voronoi tessellation structures is approximately 15.5. Furthermore, the porosity of foam structures, ε, decreases with the ratio of strut diameter to the average diameter of randomly packed spheres, ds/E(d), while the specific surface area of foams, SV, increases with ds/E(d).

A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

A new constructive ellipse packing algorithm is presented. It allows to respect the imposed area, shape and spatial orientation distribution (i.e. the inertia tensor) and achieve high packing densities. The packing density decreases with increasing particles aspect ratio what is in agreement with results reported in the literature. The generated packings with complex imposed area, shape and spatial orientation distributions with densities in the range of 0.74 and 0.8 are presented. The efficiency of the algorithm is demonstrated by comparison with the Optimized Dropping and Rolling method for disk packing. Moreover, the proposed packing strategy enables to generate very easily non-equiaxed polygonal structures by using Laguerre-Voronoi tessellation of the generated disk-based ellipse packing.

The influence of pore size variation on the pressure drop in open-cell foams

Abstract The paper concerns pressure drop in open-cell foam structures in correlation with variation in size of pores. The foam structures with different coefficients of variation of the pore volume CV(V) were designed using procedure based on Laguerre–Voronoi tessellations (LVT). Geometry of the generated structures was compared with the geometry of alumina foam filters used for casting. Pressure drop was calculated for structures with various pore volume distributions using the finite volume method (FVM). Validation of the LVT algorithm was performed by comparing the pressure drop obtained for modeled structures with the pressure drop of commercial alumina foam filters for aluminum casting. Two of the designed set of porous structures were printed using fast prototyping with the selective laser melting process (SLM). The pressure drop for these structures was measured experimentally and compared with the modeling results. The results show that the pressure drop is strongly related with the distribution of pore volume. Furthermore, for the investigated range of the coefficients of pore volume variation, a relationship was found between CV(V) and pressure drop.

Design of Mechanical Properties of Open-Cell Porous Materials Based on μCT Study of Commercial Foams

In the present paper numerical design of mechanical properties of open-cell porous materials is addressed. A detailed knowledge of mechanisms and parameters determining mechanical properties (i.e. Young’s Modulus, Poisson’s Ratio) of foams is essential for applications such as energy absorbers or lightweight construction materials. The foam structures were designed using procedure based on Laguerre-Voronoi tessellations (LVT) with micro-computed tomography of commercial foams used as reference. Foam morphology was studied on post-processed computed tomography images and the parameters of LVT structures were compared with commercial materials. Subsequently finite element method (FEM) calculations were performed on both types of structures to validate the LVT design algorithm. The results show that the described design procedure can be successfully used for modeling mechanical properties of open-cell foam structures.