Quantification of mesh induced anisotropy effects in the phase-field method

2011

Phys. Rev. E

We use a phase-field model for the growth of dendrites in dilute binary alloys under coupled thermo-solutal control to explore the dependence of the dendrite tip velocity and radius of curvature upon undercooling, Lewis number (ratio of thermal to solutal diffusivity), alloy concentration and equilibrium partition coefficient. Constructed in the quantitatively valid thin-interface limit the model uses advanced numerical techniques such as mesh adaptivity, multigrid and implicit time-stepping to solve the non-isothermal alloy solidification problem for materials parameters that are realistic for metals. From the velocity and curvature data we estimate the dendrite operating point parameter, σ*. We find that σ* is non-constant and, over a wide parameter space, displays first a local minimum followed by a local maximum as the undercooling is increased. This behaviour is contrasted with a similar type of behaviour to that predicted by simple marginal stability models to occur in the radius of curvature, on the assumption of constant σ*.

Section: Description Of the Modelmentioning

confidence: 99%

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

2011

Phys. Rev. E

“…Unlike the implementation of most phase-field models, which use spatially second order difference approximations, here we have used fourth order approximations in order to capture any bias-field effects, which are themselves proposed to be spatially fourth order [17]. The first and second differentials are calculated using a (spatially) fourth order accurate 9-point stencil, while a compact, 17-point, fourth order stencil has been used for the Laplacian terms, compact stencils being superior in their ability to reduce the mesh induced [22] anisotropy. The stencils, and the weights associated with each point therein, are illustrated graphically in Fig.…”

Section: Computational Modelmentioning

confidence: 99%

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Journal of Applied Physics

2015

The accepted view on dendritic side-branching is that side-branches grow as the result of selective amplification of thermal noise and that in the absence of such noise dendrites would grow without the development of side-arms. However, recently there has been renewed speculation about dendrites displaying deterministic side-branching [see e.g. ME Glicksman, Metall. Mater. Trans A 43 (2012) 391]. Generally, numerical models of dendritic growth, such as phase-field simulation, have tended to display behaviour which is commensurate with the former view, in that simulated dendrites do not develop side-branches unless noise is introduced into the simulation. However, here we present simulations that show that under certain conditions deterministic side-branching may occur. We use a model formulated in the thin interface limit and a range of advanced numerical techniques to minimise the numerical noise introduced into the solution, including a multigrid solver. Spontaneous side-branching seems to be favoured by high undercoolings and by intermediate values of the capillary anisotropy, with the most branched structures being obtained for an anisotropy strength of 0.03. From an analysis of the tangential thermal gradients on the solid-liquid interface, the mechanism for side-branching appears to have some similarities with the deterministic model proposed by Glicksman.

“…This allows the application of standard second order central difference stencils for the calculation of first and second differentials, while a compact 9-point scheme has been used for Laplacian terms, in order to reduce the mesh induced [15] anisotropy. To ensure sufficient mesh resolution around the interface region and to handle the multi-scale nature of the problem local mesh refinement (coarsening) is employed when the weighted sum of the gradients of φ and θ exceeds (falls below) some predefined value.…”

Section: Description Of the Modelmentioning

confidence: 99%

A Phase-Field Model for the Diffusive Melting of Isolated Dendritic Fragments

2014

Metall Mater Trans A

A thermal phase-field model constructed in the 'thin-interface' limit and incorporating a number of advanced numerical techniques as such adaptive mesh refinement, implicit time-stepping and a multigrid solver has been used to study the isolated diffusive melting of dendritic fragments. The results of the simulations are found to be fully consistent with the experimental observation of such melting in microgravity during the Isothermal Dendrite Growth Experiment. It is found that the rate at which the ratio of semi-major to semi-minor axes changes is a function of the melt Stefan number, which may help explain why both melting at (approximately) constant ratio and melting at slowly increasing ratio have been observed.