Influence of external flows on crystal growth: Numerical investigation

Abstract

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E 72, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically.For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Péclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Péclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow.At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger.For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.

Influence of external flows on pattern growth

“…Fits with this function work pretty well for both our numerical data (as is demonstrated in Fig. 1) and the results from selection theory [23], surprisingly also for the case of doublons.…”

“…Moreover, it is possible to evaluate the predictions of solvability theory [25] numerically for arbitrary Pe´clet numbers, which gives a curve of very similar appearance to the top curve in Fig. 1 [23].…”

“…Details of the numerical procedure, the system and grid sizes and convergence considerations may be found in Ref. [23]. Computed values of the selection parameter s ¼ Fig.…”

A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection

“…Due to its computational advantages over conventional discretizations of the Navier-Stokes equations, the lattice Boltzmann method (LBM) [28][29][30] has emerged as an alternative to predict fluid flow. Several attempts combining PFM and LBM have been made to effectively compute the dendritic growth of pure metals and alloys [31][32][33][34][35].…”

Phase-field Modeling and Simulations of Dendrite Growth

“…Because these simulations have high computational costs, adaptive mesh (ADM) techniques, [149][150][151] the numerically efficient Lattice Boltzmann method, [152][153][154][155][156][157] and parallel computing 158,159) have been used. However, for the dendrite growth problem with convection, 2D simulations [160][161][162][163][164][165] provide results completely different from the real 3D phenomena.…”