Grain size modeling of a Ni-base superalloy using cellular automata algorithm

Nickel-base superalloys are used in highly demanding applications such as energy and aerospace industries. These alloys present good corrosion resistance, weldability and mechanical stability at high temperatures. Numerical methods are commonly used to predict the mechanical and microstructural behavior of heat resistant alloys. The aim of the present work was to model recrystallized grain size evolution under isothermal conditions using the cellular automata (CA) technique. The CA model was applied to simulate hot compression of Inconel 718 nickel-base alloy at 980 °C and 1020 °C. A finite element analysis was conducted to acquire input parameters to the model such as strain and strain rate. Hardening and recovery coefficients were calculated in order to represent the competitive effects during deformation. The influence of local changes of initial grain with fully and partial recrystallized microstructures were simulated by CA and compared with isothermal hot compression results. The model was able to comprehensively predict necklace type microstructures. The average grain size was generally in good agreement with the experimental data.     

Diffuse interface method for fluid flow and heat transfer in cellular solids

This work presents a contribution on the numerical modelling capabilities for the simulation of fluid flow and heat transfer in cellular solids – in particular we focus on open cell aluminium foams. Rather than applying one of the classical academical or commercial numerical finite volume (FV), finite difference (FD) or finite element (FE) interface tracking methods, we base our models on an interface capturing phase field method (Nestler, 2005). A coupled diffuse interface lattice Boltzmann fluid flow solver (Ettrich, 2014) and a diffuse interface heat transfer approach (Ettrich et al., 2014) are combined in view of dealing with even more convoluted geometries, incorporating the dynamics of interfaces and complex multiphysics applications. Numerical results for the combined fluid flow and heat transfer simulations in open cell metal foams are in very good agreement with experimental data (Ettrich and Martens, 2012; Ettrich et al., 2012).     

A synchronous cellular automaton model of mass transport in porous media

In this work we present a fully synchronous coarse grained cellular automaton model for large-scale simulations at molecular level. The model is based on Margolus partitioning scheme, which was generalized as to describe quantitatively diffusion, adsorption and directed flow in porous media. Our aim is to create conceptually simple and computationally efficient framework to model the mass transport in porous materials with large representative volume. This work focuses on the fundamental aspects of the generalized Margolus cellular automaton. We exemplify the model by solving several diffusion problems, studying the monolayer adsorption, chromatography on disordered porous structures and chemical transformation in a system with phase separation. The results indicate that the model reflects the essential features of these phenomena. Absence of round-off errors, fully synchronous way of implementation, autonomous physically meaningful time scale and ease-to-handle boundary conditions make this model a promising framework for study various transport phenomena in porous structures.     

Large-scale parallel lattice Boltzmann–cellular automaton model of two-dimensional dendritic growth

An extremely scalable lattice Boltzmann (LB)–cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid–liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites.     

Modelling of the strength–porosity relationship in glass-ceramic foam scaffolds for bone repair

Foam-like glass-ceramic scaffolds based on three different glass compositions (45S5 Bioglass and two other experimental formulations, CEL2 and SCNA) were produced by sponge replication and characterized from morphological, architectural and mechanical viewpoints. The relationships between porosity and compressive or tensile strength were systematically investigated and modelled, respectively, by using the theory of cellular solids mechanics or quantized fracture mechanics. Models results are in good agreement with experimental findings, which highlights the satisfactory predictive capabilities of the presented approach. The developed models could contribute to improve the rational design of porous bioceramics with custom-made properties. Knowing the scaffold recommended strength for a specific surgical need, the application of the models allows to predict the corresponding porosity, which can be tailored by varying the fabrication parameters in a controlled way so that the device fulfils the desired mechanical requirements.     

Hidden potentialities

The search for “complexity signatures” in natural laws is a main concern for researchers working in many different fields, going from physics to biology. Very simple laws are able to produce unforeseen behaviors, and from their “simplicity” sometimes it is not possible to predict anything about the potential complexities they are able to produce when applied to random initial conditions. Here elementary cellular automata (ECA) are used to illustrate this idea. In fact, using a recently developed approach to establish a correspondence between ECA rules and logical functions that constitute their structure (logical spectra) we analyzed ECA groups represented by automata 120 and 164. The automaton governed by rule 120 generates complex patterns under certain random initial conditions, whereas the one corresponding to rule 164 is known as a simple law when it is evaluated at random initial conditions. However, slight changes in the initial conditions of both ECA produce dramatic “simplicity–complexity transitions”, as it is shown here. These examples show that complexity, even in very simple formal systems, results from a subtle interplay between the structure of the laws and the initial conditions. Moreover, they draw attention to the importance of investigating if analogous comportments hold in large-scale natural phenomena as the yet enigmatic genotype–phenotype mapping.     

Radio planning of energy-aware cellular networks

This paper introduces a joint planning and management optimization approach for cellular networks to limit energy consumption while guaranteeing QoS and minimizing operators Capex and Opex. The modeling framework shows that an effective energy-efficient operation depends on the planning decisions. Conversely, it also shows that planning with energy management operation in view yields more versatile topologies than more traditional models based only on Capex. Results for LTE networks are provided and show that savings up to 65% in energy expenses are possible with slight increases in capital investments.     

From bulk to cellular structures: A review on ceramic/graphene filler composites

A revision on ceramic/graphene composites is presented. The more representative results for a wide number of bulk composites are compared, making special emphasis on their mechanical (fracture toughness, strength) and elastic properties, along with wear and friction topics. The electrical functionality boosted by the contacted graphene network is critically assessed for conducting and dielectric ceramic matrices. Regarding thermal transport, the enhancement or depletion of thermal conductivity is reviewed for different materials and specific orientations. Furthermore, new developments on layered materials and coatings, as well as on three-dimensional cellular composites, which certainly widen the scope of applications for this remarkable group of ceramic materials, are looked over.     

Two-dimensional numerical simulations of detonation cellular structures in H2O2Ar mixtures with OpenFOAM®

In the present work, the solver rhoCentralRfFoam, developed using the finite volume framework provided by OpenFOAM^®, is employed to perform numerical simulations of two-dimensional detonations. This solver uses the central scheme of Kurganov, Noelle, and Petrova for dealing with convective terms. Also, the detailed kinetic model for hydrogen oxidation of Marinov, Westbrook, and Pitz was used for properly defining chemically induced source terms, and the semi-implicit Bulirsh Stöer (SIBS) method was employed for solving the stiff ODE system required to compute the species' rates. The present study intends to investigate the solver's capability for computing cellular structures, which develop when non-planar detonations are propagating in confined mixtures. Interactions between waves, resulting from several ignition points, are used as perturbation sources for the onset of cellular structures. Numerical simulations allowed us to identify a well-shaped cellular structure and other different structures that are not clearly defined, close to the ignition sources. However, after extending the computational domain, convergence towards a unique cellular pattern is attained. Such cellular pattern compares with most of the available data. Also, in order to improve the presentation of cellular structures and their dynamic behavior, a numerical schlieren technique is utilized for some flow variables (e.g. vorticity and density).