TY - GEN

T1 - Hyperbolic phase-field approach for solidification with supercooling

AU - Chen, Yuqi

AU - McDonough, James M.

AU - Tagavi, Kaveh A.

PY - 1999

Y1 - 1999

N2 - This report concerns the solidification of a 'supercooled' liquid, whose temperature is initially below the equilibrium melt temperature, Tm of the solid. A new approach, the phase-field method, will be applied for this Stefan problem with supercooling, which simulates the solidification process of a pure material into a supercooled liquid in a spherical region. The advantage of the phase-field method is that it bypasses explicitly tracking the freezing front. In this approach the solid-liquid interface is treated as diffuse, and a dynamic equation for the phase variable is introduced in addition to the equation for heat flow. Thus, there are two coupled partial differential equations for temperature and phase field. In the reported study, an implicit numerical scheme using finite-difference techniques on a uniform mesh is employed to solve both Fourier phase-field equations and non-Fourier (known as damped wave or telegraph) phase-field equations. The latter guarantees a finite speed of propagation for the solidification front. Both Fourier (parabolic) and non-Fourier (hyperbolic) Stefan problems with supercooling are satisfactorily simulated and their solutions compared in the present work.

AB - This report concerns the solidification of a 'supercooled' liquid, whose temperature is initially below the equilibrium melt temperature, Tm of the solid. A new approach, the phase-field method, will be applied for this Stefan problem with supercooling, which simulates the solidification process of a pure material into a supercooled liquid in a spherical region. The advantage of the phase-field method is that it bypasses explicitly tracking the freezing front. In this approach the solid-liquid interface is treated as diffuse, and a dynamic equation for the phase variable is introduced in addition to the equation for heat flow. Thus, there are two coupled partial differential equations for temperature and phase field. In the reported study, an implicit numerical scheme using finite-difference techniques on a uniform mesh is employed to solve both Fourier phase-field equations and non-Fourier (known as damped wave or telegraph) phase-field equations. The latter guarantees a finite speed of propagation for the solidification front. Both Fourier (parabolic) and non-Fourier (hyperbolic) Stefan problems with supercooling are satisfactorily simulated and their solutions compared in the present work.

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M3 - Conference contribution

AN - SCOPUS:0033313955

SN - 0791816567

T3 - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

SP - 175

EP - 183

BT - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

T2 - Heat Transfer Division - 1999 ((The ASME International Mechanical Engineering Congress and Exposition)

Y2 - 14 November 1999 through 19 November 1999

ER -