Abstract
Abstract When the fluid flow in the Czochralski crystal growth system involves swirling motion due to rotation effects, numerical simulation of the Czochralski flow can be performed using either the azimuthal velocity component or the angular momentum per unit mass, viz., the swirl, as the dependent variable to resolve the rotating motion. In the presence of a strong inward flow toward the axis, the Coriolis coupling in the azimuthal velocity equation can be a source of computational instability. This difficulty has been overcome by transforming the prognostic equation for the azimuthal velocity into the so-called swirl equation. In this article we show that although these two prognostic equations are mathematically identical to each other, numerical simulations based on them could yield appreciably different results under certain circumstances. This important as yet unresolved aspect of the Czochralski flow simulation is highlighted and the underlying cause of the discrepancy is addressed in the present study.
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