Radial integral boundary element method for simulating phase change problem with mushy zone

AbstractA radial integral boundary element method (BEM) is used to simulate the phase change problem with a mushy zone in this paper. Three phases, including the solid phase, the liquid phase, and the mushy zone, are considered in the phase change problem. First, according to the continuity conditions of temperature and its gradient on the liquid-mushy interface, the mushy zone and the liquid phase in the simulation can be considered as a whole part, namely, the non-solid phase, and the change of latent heat is approximated by heat source which is dependent on temperature. Then, the precise integration BEM is used to obtain the differential equations in the solid phase zone and the non-solid phase zone, respectively. Moreover, an iterative predictor-corrector precise integration method (PIM) is needed to solve the differential equations and obtain the temperature field and the heat flux on the boundary. According to an energy balance equation and the velocity of the interface between the solid phase and the mushy zone, the front-tracking method is used to track the move of the interface. The interface between the liquid phase and the mushy zone is obtained by interpolation of the temperature field. Finally, four numerical examples are provided to assess the performance of the proposed numerical method.

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Understanding TiN Precipitation Behavior during Solidification of SWRH 92A Tire Cord Steel by Selected Thermodynamic Models

Processes ◽

10.3390/pr8010010 ◽

2019 ◽

Vol 8 (1) ◽

pp. 10

Author(s):

Lu Wang ◽

Zheng-Liang Xue ◽

Yi-Liang Chen ◽

Xue-Gong Bi

Keyword(s):

Liquid Phase ◽

Mushy Zone ◽

Manufacturing Industry ◽

Solid Phase ◽

Phase Region ◽

Tire Cord ◽

Thermodynamic Models ◽

Precipitation Behavior ◽

Phase Zone ◽

Tire Cord Steel

Tire cord steel is widely used in the tire production process of the vehicle manufacturing industry due to its excellent strength and toughness. Titanium nitride (TiN) inclusion, existing in tire rod, has a seriously detrimental effect on the fatigue and drawing performances of the tire steel. In order to control its amount and morphology, the precipitation behavior of TiN during solidification in SWRH 92A tire cord steel was analyzed by selected thermodynamic models. The calculated results showed that TiN cannot precipitate in the liquid phase region regardless of the selected models. However, the precipitation of TiN in the mushy zone would occur at the final stage during the solidification process (at solid fractions greater than 0.98) if the LRSM (Lever-rule model was applied for the N and Scheil model for Ti) or Ohnaka models (without considering the effect of carbon on secondary dendrite arm spacing (SDAS)) were adopted. For the Ohnaka model, in the case when the effect of carbon on SDAS was considered, TiN would probably precipitate in the solid phase zone rather than precipitate in the liquid phase region or mushy zone.

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The discrete unified gas kinetic scheme for solid-liquid phase change problem

International Communications in Heat and Mass Transfer ◽

10.1016/j.icheatmasstransfer.2017.12.018 ◽

2018 ◽

Vol 91 ◽

pp. 187-195 ◽

Cited By ~ 8

Author(s):

Yutao Huo ◽

Zhonghao Rao

Keyword(s):

Liquid Phase ◽

Phase Change ◽

Kinetic Scheme ◽

Unified Gas Kinetic Scheme ◽

Solid Liquid ◽

Change Problem

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Mesoscopic Models of Liquid/Solid Phase Transitions

International Journal of Modern Physics C ◽

10.1142/s0129183198001278 ◽

1998 ◽

Vol 09 (08) ◽

pp. 1405-1415 ◽

Cited By ~ 46

Author(s):

G. de Fabritiis ◽

A. Mancini ◽

D. Mansutti ◽

S. Succi

Keyword(s):

Phase Transitions ◽

Liquid Phase ◽

Mushy Zone ◽

Lattice Boltzmann ◽

Solid Phase ◽

Chaotic Motions ◽

Computational Costs ◽

Mesoscopic Models ◽

Lattice Boltzmann Models ◽

Solid Liquid

A generalization of mesoscopic Lattice-Boltzmann models aimed at describing flows with solid/liquid phase transitions is presented. It exhibits lower computational costs with respect to the numerical schemes resulting from differential models. Moreover it is suitable to describe chaotic motions in the mushy zone.

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Energy Storage With Solid/Liquid Phase Change in Presence of Natural Convection

10.1115/imece2001/aes-23643 ◽

2001 ◽

Author(s):

M. Pinelli ◽

S. Piva

Keyword(s):

Natural Convection ◽

Energy Storage ◽

Liquid Phase ◽

Phase Change ◽

Change Process ◽

Solid Phase ◽

High Energy ◽

Heat Transfer Process ◽

Phase Change Process ◽

Solid Liquid

Abstract Solid/liquid phase change process has received great attention for its capability to obtain high energy storage efficiency. In order to analyse these systems, undergoing a solid/liquid phase change, in many situations the heat transfer process can be considered conduction-dominated. However, in the past years, it has been shown that natural convection in the liquid phase can significantly influence the phase change process in terms of temperature distributions, interface displacement and energy storage. In this paper, a procedure to analyse systems undergoing liquid/solid phase change in presence of natural convection in the liquid phase based on the utilisation of a commercial computer code (FLUENT), has been developed. This procedure is applied to a cylinder cavity heated from above and filled with a Phase Change Material. It was found that when the coupling with the environment, even if small, is considered, natural convection in the liquid phase occurs. The numerical results are then compared with available experimental data. The analysis shows that the agreement between numerical and experimental results is significantly improved when the results are obtained considering the presence of circulation in the liquid phase instead of considering the process only conduction-dominated. Furthermore, some interesting features of the flow field are presented and discussed.

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Boundary integral formulation and mushy zone model for phase change problem

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/09615530110389207 ◽

2001 ◽

Vol 11 (4) ◽

pp. 371-380 ◽

Cited By ~ 2

Author(s):

S.G. Ahmed

Keyword(s):

Mushy Zone ◽

Phase Change ◽

Boundary Integral ◽

Integral Formulation ◽

Zone Model ◽

Boundary Integral Formulation ◽

Change Problem

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Solid/Liquid Phase Change in Presence of Natural Convection: A Thermal Energy Storage Case Study

Journal of Energy Resources Technology ◽

10.1115/1.1591204 ◽

2003 ◽

Vol 125 (3) ◽

pp. 190-198 ◽

Cited By ~ 21

Author(s):

M. Pinelli ◽

S. Piva

Keyword(s):

Natural Convection ◽

Energy Storage ◽

Liquid Phase ◽

Phase Change ◽

Change Process ◽

Solid Phase ◽

High Energy ◽

Heat Transfer Process ◽

Phase Change Process ◽

Solid Liquid

Solid/liquid phase change process has received great attention for its capability to obtain high energy storage efficiency. In order to analyze these systems, undergoing a solid/liquid phase change, in many situations the heat transfer process can be considered conduction-dominated. However, in the past years, it has been shown that natural convection in the liquid phase can significantly influence the phase change process in terms of temperature distributions, interface displacement and energy storage. In this paper, a procedure to analyze systems undergoing liquid/solid phase change in presence of natural convection in the liquid phase based on the utilisation of a commercial computer code (FLUENT), has been developed. This procedure is applied to the study of a cylinder cavity heated from above and filled with a phase change material. It was found that when the coupling with the environment, even if small, is considered, natural convection in the liquid phase occurs. The numerical results are then compared with available experimental data. The analysis shows that the agreement between numerical and experimental results is significantly improved when the results are obtained considering the presence of circulation in the liquid phase instead of considering the process only conduction-dominated. Furthermore, some interesting features of the flow field are presented and discussed.

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