Abstract
The theory of stable dendritic growth within a forced convective flow field is tested against the enthalpy method for a single-component nickel melt. The growth rate of dendritic tips and their tip diameter are plotted as functions of the melt undercooling using the theoretical model (stability criterion and undercooling balance condition) and computer simulations. The theory and computations are in good agreement for a broad range of fluid velocities. In addition, the dendrite tip diameter decreases, and its tip velocity increases with increasing fluid velocity.
Highlights
It is well known that the growth of dendritic crystals takes place in many areas of modern science ranging from materials physics, geophysics and atmosphere physics to the chemical industry, biophysics and life science[1,2,3,4,5,6]
To determine the stable dendritic growth mode, as well as to establish the boundaries of morphologic transitions of the internal structure in solidified materials, it is necessary to independently determine the growth rate V of the dendrite tip and its diameter q depending on the melt undercooling DT
The present study compares the theory of stable dendritic growth in the presence of a forced convection with computer simulations by the enthalpy method
Summary
It is well known that the growth of dendritic crystals takes place in many areas of modern science ranging from materials physics, geophysics and atmosphere physics to the chemical industry, biophysics and life science[1,2,3,4,5,6]. To determine the stable dendritic growth mode, as well as to establish the boundaries of morphologic transitions of the internal structure in solidified materials, it is necessary to independently determine the growth rate V of the dendrite tip and its diameter q depending on the melt undercooling DT This problem can be solved using the microscopic solvability theory together with the sharp interface model, which lead to two transcendental equations for V and q as functions of DT and other physical parameters of dendritic growth. To obtain the marginal wavenumbers km entering in the solvability integral (13), the linear stability analysis should be carried out (see, among others,[14]) It leads to the marginal mode of the wavenumber km (see, for details,19,21), which is determined by the following cubic equation where. These two equations allow us to obtain V and q for a given DT
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