We present and validate a numerical technique for computing dendritic growth of crystals from pure melts in the presence of forced convection. The Navier-Stokes equations are solved on a fixed Cartesian mesh and a mixed Eulerian-Lagrangian framework is used to treat the immersed phase boundary as a sharp solid-fluid interface. A conservative finite-volume discretization is employed which allows the boundary conditions to be applied exactly at the moving surface. Results are presented for a range of the growth parameters, namely crystalline anisotropy, flow Reynolds number and Prandtl number. Direct comparisons are made between the present results and those obtained with phase-field methods and excellent agreement is obtained. Values for the tip characteristics are tabulated to serve as benchmarks for computations of two-dimensional dendritic growth with convection.
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Department of Mechanical and Industrial Engineering, 4116 Seamans Center for the Engineering Arts and Science, University of Iowa, Iowa City, IA 52242-1527, USA;