Solution of dendritic growth in a binary alloy by a novel point automata method

The aim of this paper is simulation of thermally induced liquid-solid dendritic growth in a binary alloy (Fe-0.6%C) steel in two dimensions by a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized phase change kinetics model that takes into account the undercooling, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The phase-change kinetics model is solved by the novel Point Automata (PA) approach. The PA method was developed and introduced [1,2] in order to circumvent the mesh anisotropy problem, associated with the classical Cellular Automata (CA) method. Dendritic structures are in the CA approach sensitive on the relative angle between the cell structure and the preferential crystal growth direction which is not physical. The CA approach used in the paper for reference comparison is established on quadratic cells and Neumann neighborhood. The PA approach is established on randomly distributed points and neighborhood configuration, similar as appears in meshless methods. Both methods provide same results in case of regular PA node arrangements and neighborhood configuration with five points. A comparison between both stochastic approaches has been made with respect to dendritic growth with different orientations of crystallographic angles. It is demonstrated that the new PA method can cope with dendritic growth of a binary alloy in any direction which is not the case with the CA method

Simulation of multiscale industrial solidification problem under influence of electromagnetic field by meshless method

Simulation and control of macrosegregation, deformation and grain size under  electromagnetic (EM) processing conditions is important in industrial solidification systems,  since it influences the quality of the casts and consequently the whole downstream processing  path. Respectively, a multiphysics and multiscale model is developed for solution of Lorentz  force, temperature, velocity, concentration, deformation and grain structure of the casts. The  mixture equations with lever rule, linearized phase diagram, and stationary thermoelastic solid  phase are assumed, together with EM induction equation for the field imposed by the low  frequency EM field or Ohm’s law and charge conservation equation for stationary EM field.  Turbulent effects are incorporated through the solution of a low-Re turbulence model. The  solidification system is treated by the mixture-continuum model, where the mushy zone is  modeled as a Darcy porous media with Kozeny-Karman permeability relation and columnar  solid phase moving with the system velocity. Explicit diffuse approximate meshless solution  procedure [1] is used for solving the EM field, and the explicit local radial basis function  collocation  method  [2]  is  used  for  solving  the  coupled  transport  phenomena  and  thermomechanics  fields.  Pressure-velocity  coupling  is  performed  by  the  fractional  step  method [3]. The point automata method with modified KGT model is used to estimate the  grain structure [4] in a post-processing mode. Thermal, mechanical, EM and grain structure  outcomes of the model are demonstrated for low frequency EM casting of round aluminium  billets. A systematic study of the complicated influences of the process parameters on the  microstructure can be investigated by the model, including intensity and frequency of the  electromagnetic field

Validation of a computational model for a coupled liquid and gas flow in micro-nozzles

The work presents verification of a numerical model for micro-jet focusing, where a coupled liquid and gas flow occurs in a gas dynamic virtual nozzle (GDVN). Nozzles of this type are used in serial femtosecond crystallography experiments to deliver samples into X-ray beam. The following performance criteria are desirable: the jet to be longer than 100 µm to avoid nozzle shadowing, the diameter as small as possible to minimize the background signal, and the jet velocity as high as possible to avoid sample’s double X-ray exposure. Previous comprehensive numerical investigation has been extended to include numerical analysis of the tip jet velocities. These simulations were then compared with the experimental data. The coupled numerical model of a 3D printed GDVN considers a laminar two-phase, Newtonian, compressible flow, which is solved based on the finite volume method discretization and interface tracking with volume of fluid (VOF). The numerical solution is calculated with OpenFOAM based compressible interFoam solver, which uses algebraic formulation of VOF. In experimental setup for model validation a 3D printed GDVN was inserted in a vacuum chamber with two windows used for illumination and visualization. Once the jet was stabilized its velocity was estimated based on a distance a droplet traveled between two consecutive illumination pulses with a known time delay. The experimental and computational study was performed for a constant liquid flow rate of 14 l/min and the gas mass flow rate in the range from 5 mg/min to 25 mg/min. The coupled numerical model reasonably predicts the jet speed and shape as a function of the gas flow

An effective integrated-RBFN Cartesian-grid discretization for the stream function-vorticity-temperature formulation in nonrectangular domains

This paper presents a new numerical collocation procedure, based on Cartesian grids and one-dimensional integrated radial-basis-function networks (1D-IRBFNs), for the simulation of natural convection defined in two-dimensional multiply-connected domains and governed by the stream function-vorticity-temperature formulation. Special emphasis is placed on the handling of vorticity values at boundary points that do not coincide with grid nodes. A suitable formula for computing vorticity boundary conditions, which is based on the approximations with respect to one coordinate direction only, is proposed. Normal derivative boundary conditions for the stream function are forced to be satisfied identically. Several test problems, including natural convection in the annulus between square and circular cylinders, are considered to investigate the accuracy of the proposed technique

Non-Singular Method of Fundamental Solutions based on Laplace decomposition for 2D Stokes flow problems

In this paper, a solution of Two-Dimensional (2D) Stokes flow problem, subject to Dirichlet and fluid traction boundary conditions, is developed based on the Non-singular Method of Fundamental Solutions (NMFS). The Stokes equation is decomposed into three coupled Laplace equations for modified components of velocity, and pressure. The solution is based on the collocation of boundary conditions at the physical boundary by the fundamental solution of Laplace equation. The singularities are removed by smoothing them on disks around them. The derivatives on the boundary in the singular points are calculated through simple reference solutions. In NMFS, no artificial boundary is needed, as in the classical Method of Fundamental Solutions (MFS). Numerical examples include driven cavity flow on a square, analytically solvable solution on a circle and channel flow on a rectangle. The accuracy of the results is assessed by comparison with the MFS solution, and analytical solutions. The main advantage of the approach is its simple, boundary only meshless character of the computations, and possibility of straightforward extension of the approach to Three-Dimensional (3D) problems, moving boundary problems and inverse problems

Modelling of phase transformations in heat treatment processes

The two-domain approach and the phase-field approach, the two distinct physical models, for simulation of phase transformations in heat treatment processes are presented. Special attention is paid for linking data from a thermodynamic database to the physical models. The general procedure for linking thermodynamic data in the two-domain approach is presented. The interpolation by the radial basis functions of the thermodynamic data in the phase-field model is proposed. The physical models are applied to homogenisation of aluminum alloys. The JMatPro software for aluminium alloys is used as the thermodynamic database. The dissolution kinetics of stoichiometric and nonstoichiometric primary particles in binary and multicomponent aluminium systems is estimated. The isothermal diffusion-controlled dissolutions of the theta phase, S phase and Mg2Si phase in aluminium phase in Al-Cu, Al-Cu-Mg and Al-Mg-Si systems are computed, respectively. A comparison of the numerical results computed by the physical models are in excellent agreement. The very nice agreement between the numerical results computed by the phase-field model and previously derived the Vermolen model for the dissolution of multicomponent particles in homogenisation of aluminium alloys is demonstrated

Transient dynamics of containers partially filled with liquid

From a computational point of view, fluid behaviour under micro-gravity conditions is more complicated than under terrestrial conditions: the fluid has a tendency to undergo large topological changes, requiring an accurate and robust method for free-surface advection. Moreover, the fluid is often contained in a cavity (e.g. satellite) that itself is moving; not only because of external forces (e.g. manoeuvring thrusters on a satellite), but also under influence of the fluid motion: the dynamics of the solid-body motion and the liquid motion are coupled. In the paper a method is presented for simulating coupled liquid-solid dynamics under micro-gravity conditions (although the method also works in a terrestrial environment). The liquid dynamics is solved by discretising the Navier-Stokes equations on a Cartesian grid. Transportation of the free surface is based on the VOF-method; however, slightly adapted in order to avoid the (numerical) creation of "flotsam" and "jetsam". The solid-body motion is governed by equations for its linear and angular momentum, in which terms appear that represent the force and torque induced by the sloshing liquid. Care has to be taken in solving these equations to keep the coupling numerically stable for arbitrary liquid/solid mass ratios

Validation of a computational model for a coupled liquid and gas flow in micro-nozzles

The work presents verification of a numerical model for micro-jet focusing, where a coupled liquid and gas flow occurs in a gas dynamic virtual nozzle (GDVN). Nozzles of this type are used in serial femtosecond crystallography experiments to deliver samples into X-ray beam. The following performance criteria are desirable: the jet to be longer than 100 µm to avoid nozzle shadowing, the diameter as small as possible to minimize the background signal, and the jet velocity as high as possible to avoid sample’s double X-ray exposure. Previous comprehensive numerical investigation has been extended to include numerical analysis of the tip jet velocities. These simulations were then compared with the experimental data. The coupled numerical model of a 3D printed GDVN considers a laminar two-phase, Newtonian, compressible flow, which is solved based on the finite volume method discretization and interface tracking with volume of fluid (VOF). The numerical solution is calculated with OpenFOAM based compressible interFoam solver, which uses algebraic formulation of VOF. In experimental setup for model validation a 3D printed GDVN was inserted in a vacuum chamber with two windows used for illumination and visualization. Once the jet was stabilized its velocity was estimated based on a distance a droplet traveled between two consecutive illumination pulses with a known time delay. The experimental and computational study was performed for a constant liquid flow rate of 14 l/min and the gas mass flow rate in the range from 5 mg/min to 25 mg/min. The coupled numerical model reasonably predicts the jet speed and shape as a function of the gas flow