Multiscale modelling of the influence of convection on dendrite formation and freckle initiation during vacuum arc remelting

Vacuum Arc Remelting (VAR) is employed to produce homogeneous ingots with a controlled, fine, microstructure. It is applied to reactive and segregation prone alloys where convection can influence microstructure and defect formation. In this study, a microscopic solidification model was extended to incorporate both forced and natural convection. The Navier-Stokes equations were solved for liquid and mushy zones using a modified projection method. The energy conservation and solute diffusion equations were solved via a combined stochastic nucleation approach along with a finite difference solution to simulate dendritic growth. This microscopic model was coupled to a 3D transient VAR model which was developed by using a multi-physics modelling software package, PHYSICA. The multiscale model enables simulations covering the range from dendrites (in microns) to the complete process (in meters). These numerical models were used to investigate: (i) the formation of dendritic microstructures under natural and forced convections; (ii) initiation of solute channels (freckles) in directional solidification in terms of interdendritic thermosolutal convection; and (iii) the macroscopic physical dynamics in VAR and their influence on freckle formation. 2D and 3D dendritic microstructure were simulated by taking into account both solutal and thermal diffusion for both constrained and unconstrained growth using the solidification model. For unconstrained equiaxed dendritic growth, forced convection was found to enhance dendritic growth in the upstream region while retarding downstream growth. In terms of dimensionality, dendritic growth in 3D is faster than 2D and convection promotes the coarsening of perpendicular arms and side branching in 3D. For constrained columnar dendritic growth, downward interdendritic convection is stopped by primary dendritic arms in 2D; this was not the case in 3D. Consequently, 3D simulations must be used when studying thermosolutal convection during solidification, since 2D simulations lead to inappropriate results. The microscopic model was also used to study the initiation of freckles for Pb-Sn alloys, predicting solute channel formation during directional solidification at a microstructural level for the first time. These simulations show that the local remelting due to high solute concentrations and continuous upward convection of segregated liquid result in the formation of sustained open solute channels. High initial Sn compositions, low casting speeds and low temperature gradients, all promote the initiation of these solute channels and hence freckles. to study the initiation of freckles for Pb-Sn alloys, predicting solute channel formation during directional solidification at a microstructural level for the first time. These simulations show that the local remelting due to high solute concentrations and continuous upward convection of segregated liquid result in the formation of sustained open solute channels. High initial Sn compositions, low casting speeds and low temperature gradients, all promote the initiation of these solute channels and hence freckles

Crystallization and melting in geological fluid mechanics

Digitisation of this thesis was sponsored by Arcadia Fund, a charitable fund of Lisbet Rausing and Peter Baldwin

Modeling Dendritic Solidification using Lattice Boltzmann and Cellular Automaton Methods

This dissertation presents the development of numerical models based on lattice Boltzmann (LB) and cellular automaton (CA) methods for solving phase change and microstructural evolution problems. First, a new variation of the LB method is discussed for solving the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term is treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The results showed that the model can deal with phase change problems more accurately and efficiently than explicit LB models. Furthermore, a new numerical technique is introduced for simulating dendrite growth in three dimensions. The LB method is used to calculate the transport phenomena and the CA is employed to capture the solid/liquid interface. It is assumed that the dendritic growth is driven by the difference between the local actual and local equilibrium composition of the liquid in the interface. The evolution of a threedimensional (3D) dendrite is discussed. In addition, the effect of undercooling and degree of anisotropy on the kinetics of dendrite growth is studied. Moreover, effect of melt convection on dendritic solidification is investigated using 3D simulations. It is shown that convection can change the kinetics of growth by affecting the solute distribution around the dendrite. The growth features of twodimensional (2D) and 3D dendrites are compared. Furthermore, the change in growth kinetics and morphology of Al-Cu dendrites is studied by altering melt undercooling, alloy composition and inlet flow velocity. The local-type nature of LB and CA methods enables efficient scaling of the model in petaflops supercomputers, allowing the simulation of large domains in 3D. The model capabilities with large scale simulations of dendritic solidification are discussed and the parallel performance of the algorithm is assessed. Excellent strong scaling up to thousands of computing cores is obtained across the nodes of a computer cluster, along with near-perfect weak scaling. Considering the advantages offered by the presented model, it can be used as a new tool for simulating 3D dendritic solidification under convection

Numerical simulations of die casting with uncertainty quantification and optimization using neural networks

Die casting is one type of metal casting in which liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters is difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, uncertainty quantification and design optimization is proposed. This framework includes high-speed numerical simulations of solidification, micro-structure and mechanical properties prediction models along with experimental inputs for calibration and validation. In order to have a better prediction of product quality, both experimental data and stochastic variations in process parameters with numerical modeling are employed. This enhances the utility of traditional numerical simulations used in die casting. OpenCast, a novel and comprehensive computational framework to simulate solidification problems in materials processing is developed. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. Multiple case studies are presented by coupling surrogate models such as polynomial chaos expansion (PCE) and neural network with OpenCast for uncertainty quantification and optimization. The effects of stochasticity in the alloy composition, boundary and initial conditions on the product quality of die casting are analyzed using PCE. Further, a high dimensional stochastic analysis of the natural convection problem is presented to model uncertainty in the material properties and boundary conditions using neural networks. In die casting, heat extraction from molten metal is achieved by cooling lines in the die which impose nonuniform boundary temperatures on the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. Thus, a multi-objective optimization problem is solved to demonstrate a procedure for improvement of product quality and process efficiency

Solidification and Gravity VII

International audienc