A Stable Dendritic Growth with Forced Convection: A Test of Theory Using Enthalpy-Based Modeling Methods
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https://doi.org/10.1007/s11837-020-04292-4 Ó 2020 The Author(s)
MATERIALS RESEARCH IN REDUCED GRAVITY
A Stable Dendritic Growth with Forced Convection: A Test of Theory Using Enthalpy-Based Modeling Methods A. KAO ,1,7 L.V. TOROPOVA,2,8 I. KRASTINS,3 G. DEMANGE,4 D.V. ALEXANDROV,5 and P.K. GALENKO6 1.—Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE10 9LS, UK. 2.—Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, Ekaterinburg, Russian Federation 620000. 3.—Institute of Physics, University of Latvia, Miera iela 32, Salaspils LV-2169, Latvia. 4.—GPM, CNRS-UMR 6634, University of ´ tienne Du Rouvray, France. 5.—Laboratory of Multi-Scale Rouen Normandy, 76801 Saint E Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, Ekaterinburg, Russian Federation 620000. 6.—PhysikalischAstronomische Fakulta¨t, Friedrich-Schiller-Universita¨t-Jena, 07743 Jena, Germany. 7.—e-mail: [email protected]. 8.—e-mail: [email protected]
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.
INTRODUCTION 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 science1–6. As this takes place, the growth mechanisms of dendrites, their shape and interaction determine the characteristics of the internal microstructure of the crystallized substance7–9. These mechanisms, in turn, depend on heat and mass transfer processes complicated by hydrodynamic and convective fluid flows, the presence of dissolved impurities and various crystal growth symmetries. 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. Such a theoretical approach has been recently tested against experimental data and computations in a series of works10–13 in the absence of a fo
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