A mathematical model of the planar flow melt spinning process

Gutiérrez, E.; Szekely, J.

doi:10.1007/bf02657132

Cited by 31 publications

(21 citation statements)

References 11 publications

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“…Various modeling approaches and analytical treatments have made some progress toward the general prediction of thermal conditions within the melt pool. [8][9][10][11][12][13][14][15][16][17] Since MS is often implemented to achieve rates sufficiently high to avoid nucleation altogether, resulting in an amorphous or glassy ribbon, nucleation control is of primary importance. However, nucleation kinetics are generally very sensitive to local temperature, with volumetric nucleation rates generally varying as exp(Ϫ1/T⌬T microstructural control remains problematic.…”

Section: Introductionmentioning

confidence: 99%

The role of melt pool behavior in free-jet melt spinning

Napolitano

Meco

2004

Metall Mater Trans A

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The influence of melt pool behavior on the competition between the nucleation of crystalline solidification products and glass formation is examined for an Fe-Si-B alloy. High-speed imaging of the melt pool, analysis of ribbon microstructure, and measurement of ribbon geometry and surface character all indicate upper and lower limits for melt spinning (MS) rates for which fully amorphous ribbons can be achieved. Comparison of the relevant time scales reveals that surface-controlled melt pool oscillation may be the dominant factor governing the onset of unsteady thermal conditions accompanied by varying amounts of crystalline nucleation observed near the lower limit. At high rates, the influence of these oscillations is minimal due to very short melt pool residence times. However, microstructural evidence suggests that the entrapment of gas pockets at the wheel-metal interface may play a critical role in establishing the upper rate limit. An observed transition in wheel-side surface character with an increasing MS rate supports this contention. The Role of Melt Pool Behavior in Free-Jet Melt Spinning R.E. NAPOLITANO and H. MECOThe influence of melt pool behavior on the competition between the nucleation of crystalline solidification products and glass formation is examined for an Fe-Si-B alloy. High-speed imaging of the melt pool, analysis of ribbon microstructure, and measurement of ribbon geometry and surface character all indicate upper and lower limits for melt spinning (MS) rates for which fully amorphous ribbons can be achieved. Comparison of the relevant time scales reveals that surface-controlled melt pool oscillation may be the dominant factor governing the onset of unsteady thermal conditions accompanied by varying amounts of crystalline nucleation observed near the lower limit. At high rates, the influence of these oscillations is minimal due to very short melt pool residence times. However, microstructural evidence suggests that the entrapment of gas pockets at the wheel-metal interface may play a critical role in establishing the upper rate limit. An observed transition in wheel-side surface character with an increasing MS rate supports this contention.

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Section: Introductionmentioning

confidence: 99%

The role of melt pool behavior in free-jet melt spinning

Napolitano

Meco

2004

Metall Mater Trans A

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“…[9]) is used to consider the phase transformation of the amorphous alloy. The value of the viscosity below the glass temperature (T £ T gp ) is assumed to be 1.0 PaAEs.…”

Section: ½6mentioning

confidence: 99%

“…[5][6][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][11][12] others are based on the solution of fluid flow with the free surface, coupled heat transfer, and solidification. [13][14][15][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.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Initial Development of Fluid Flow and Heat Transfer in Planar Flow Casting Process

Chen

Qiu

et al. 2009

Metall Mater Trans B

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This article describes the initial development of fluid flow and heat transfer in a planar flow casting (PFC) process for amorphous ribbon formation using a two-dimensional (2-D) model of fluid flow with free surface and surface tension, and heat transfer with phase transformation. The heat transfer in the rotating copper roller is incorporated into the model. A coupled fluidsolid (the puddle/roller surface) solution is employed for identifying the ideal interfacial heat transfer. The initial developments of puddle shape and flow and temperature distribution, including the air and the melt in the puddle zone, over time are presented. The time-dependent theoretical interfacial heat-transfer-coefficient and temperature profiles in the rotating roller are investigated. The effect of the varying roller speed, the PFC configurations (slit width and gap distance), and the roller parameters (roller radius and roller layer thickness) on the development of the melt flow and heat transfer in a PFC process are discussed. Numerical results show that a stable puddle shape can be formed within a very short period of time (on the order of milliseconds). The time evolution of the upstream meniscus is different from that of the downstream meniscus. The recirculation flows both in the surrounding air and in the melt of the puddle zone can be observed at a quasi-steady-state condition, but show different flow and thermal behaviors. The interfacial heat-transfer coefficient and temperature distribution of the rotating roller change with different cycles of the roller revolution until the heat-flux balance is reached. The varying parameters associated with the roller speed, slit width, gap distance, roller radius, and roller layer thickness affect the time evolution of the flow and thermal behavior in the puddle and the temperature distribution in the rotating roller.

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“…'3 the solidification thickness is found to be 11 sIt) = 2A( IX,t t = n( ¥ r (5) where the value of A is the root of the following tran- '" C. (T~ -T .) f3 (6) Here, the subscripts 'I" and ·s" represent the liquid metal and the solidified ribbon, respectively; T m' T" and T. represent the melting temperature, molten metal temperature. and wheel bulk temperature.…”

Section: Alloy Processingmentioning

confidence: 99%

The melt spinning of gamma titanium aluminides

Frazier

Chen

1992

JOM

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Rapid solidification shows great promise for the production of gamma titanium aluminides, and one of the most interesting rapid solidification techniques is melt spinning. In this work, melt-spun Ti-5SAI and Ti-48AI-2Cr-2Ta (atomic percent) were produced; the resulting alloys had uniform microstructure and composition. In addition, the investigation showed the utility of a model developed to describe heat transfer and fluid flow in melt spinning.

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A mathematical model of the planar flow melt spinning process

Cited by 31 publications

References 11 publications

The role of melt pool behavior in free-jet melt spinning

The role of melt pool behavior in free-jet melt spinning

Numerical Simulation of Initial Development of Fluid Flow and Heat Transfer in Planar Flow Casting Process

The melt spinning of gamma titanium aluminides

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