Phase-field simulation of convective effects on dendritic growth in two dimensions

Convective effects on dendritic growth and pattern formation are investigated in two dimensions using a direct numerical simulation approach. A recently developed phase-field model that incorporates melt convection phenomenologically is used to explore the dendrite tip operating state and sidebranching in a forced flow.; The full multigrid SIMPLE method is used to solve the conservation equations of flow. To fully resolve the diffuse interface region and the interactions of dendritic growth with flow, both the phase-field and flow equations are solved on a highly refined grid space where up to 2.1 million control volumes are used. A multiple time-step algorithm is developed that uses a large time step for the flow field calculations while reserving a fine time step for the phase-field progression.; The operating state (velocity and shape) of a dendrite tip in a forced flow is studied as a function of flow velocity, growth direction relative to the flow and anisotropy strength. For the upstream tip in a forced flow, the present results are found to be in quantitative agreement with the predictions of the Oseen-Ivantsov transport theory if a tip radius based on a parabolic fit is used. Furthermore, using this parabolic tip radius the ratio of the selection parameters without and with flow is shown to be in reasonable agreement with linearized solvability theory.; Dendritic sidebranching in a forced flow is also studied to quantify the effect of flow on the dynamics of sidebranching. Convection is found to effectively enhance the interfacial instability on the upstream side of a dendrite. Both the amplitude and frequency of the sidebranches on the upstream side are increased with increasing flow velocity. However, when scaled by the dendrite tip radius, the amplitude as a function of distance behind the tip with flow shows only minor differences with the purely diffusive case. The numerically predicted amplitudes of the sidebranches with and without flow are found to be in good agreement with linear Wentzel-Kramers-Brillouin theory. The wavelength of the sidebranches is found to be nearly independent of the noise level and flow velocity if scaled by the dendrite tip radius.