Numerical Simulation of Initial Development of Fluid Flow and Heat Transfer in Planar Flow Casting Process
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new functional materials that have excellent physical, mechanical, and magnetic properties; they have been widely used in a variety of fields for manufacturing various magnetic instruments and devices. The planar flow casting (PFC) process, schematically illustrated in Figure 1, is one of the most promising and commonly used processes for the manufacture of amorphous ribbons. In this process, the melt is ejected from a thin nozzle slit of the crucible under ejection pressure through a small crucible/roller gap onto a rotating copper single roller. The melt forms a puddle and is rapidly solidified at a very high cooling rate (usually 106 K/s). A thin amorphous ribbon is then formed, dragged out of the puddle, and shed further downstream by the relative substrate motion. Different from other variants of spin-casting processes such as the chill-block free-jet melt-spinning process and single-roll casting process,[1–4] the PFC process employs a small crucible/roller gap between the moving substrate HEPING LIU, Senior Engineer, and SHENGTAO QIU, Professor, are with Central Iron & Steel Research Institute, Haidian District, Beijing 100081, People’s Republic of China. Contact e-mail: [email protected] WENZHI CHEN and GUODONG LIU, Professors, are with the Advanced Technology & Materials Co. Ltd., Haidian District, Beijing 100081, People’s Republic of China. Manuscript submitted February 22, 2008. Article published online April 21, 2009. METALLURGICAL AND MATERIALS TRANSACTIONS B
and the nozzle to constrain the melt puddle; this enhances the stability of the process and allows for better control of the wider ribbon production. It is believed that the formation of the constrained melt puddle and the subsequent solidification of the melt in the puddle strongly affect the thickness and quality of the ribbon. However, due to the typically small size, the short solidification time, and the high-velocity rotation of the roller in a PFC process, it is rather difficult to investigate the process experimentally. Accordingly, only a small amount of information concerning the investigation of the shape and dynamical behavior of a PFC puddle by experimental testing has been reported.[5–7] Several mathematical models have been developed as effective tools for studying the formation of the puddle, flow fluid, and heat transfer in PFC. Among these models, some earlier ones are based mainly on a lubrication theory[8,9] or on boundary layer equations;[10–12] others are based on the solution of fluid flow with the free surface, coupled heat transfer, and solidification.[13–16] Belenkii et al.[12] performed a theoretical analysis of the fluid dynamics and heat transfer in the single-roller rapid solidification by solving two-dimensional (2-D) steady Navier–Stokes equations; these were continuity and heat-conduction equations with a neglecting free surface. Using the solution algorithm (SOLA) volume-of-fluid (VOF) code, Takeshita and Shingu[17] and Chen et al.[18,19] studied the transient fluid flow in the puddle with the evolution of a free boundary without VOLUM
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