Modeling of solid phase sedimentation during directional solidification in a side cooled cavity
01 Nov 2011-International Journal of Numerical Methods for Heat & Fluid Flow (Emerald Group Publishing Limited)-Vol. 21, Iss: 8, pp 913-934
TL;DR: In this article, a numerical approach for modeling the multi-phase flow during an alloy solidification process is presented, where a fixed grid volume averaging technique has been used for solving mass, momentum, energy, and species equation while taking into account the solid phase advection and local remelting.
Abstract: Purpose – The purpose of this paper is to present a new numerical approach for modeling the multi‐phase flow during an alloy solidification process. In many solidification processes, advection of solid may have a dramatic effect on bulk convection field as well as on the solid front growth and hence on the macro‐segregation pattern. In the present work, a numerical model is developed to simulate directional solidification in presence of melt convection as well as solid advection in the form of sedimentation. A 2D cavity filled with hyper‐eutectic aqueous ammonium chloride solution (25 wt.% of ammonium chloride) being chilled from one of the side walls has been chosen as the model problem for the numerical simulation.Design/methodology/approach – A fixed grid volume averaging technique has been used for solving mass, momentum, energy, and species equation while taking into account the solid phase advection and local re‐melting. Two different criteria have been identified for the solid particles in the mush...
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TL;DR: In this paper, a modified enthalpy porosity formulation is introduced to capture melting and solidification of pure substances, which is capable of predicting all pure substances including those with large difference in phase specific heats such as water and paraffin wax.
Abstract: A modified enthalpy porosity formulation is introduced to capture melting and solidification of pure substances. When melting and solidification of pure substances are addressed by the fixed grid based volume averaging technique, it is possible to obtain two equivalent and interchangeable mathematical formulations of the energy conservation equation if the governing equation is expressed in terms of temperature as the primary dependent variable. Between these two formulations, only one form is shown to provide physically consistent numerical solutions when very large difference in specific heats for liquid and solid phases is involved. A modified enthalpy updating scheme is proposed to predict the solid/liquid fraction during melting and solidification process of pure substances having large difference in phase specific heats. The results from the proposed scheme are validated with the existing results from literature involving numerical prediction of freezing of water. The physical consistency of the simulation results obtained by solving two interchangeable forms of energy conservation equation is tested and compared considering a case study involving melting of ice. While one of the conservation forms fails to predict the melting process, the other conservation form successfully predicts physically consistent result. The proposed formulation is capable of predicting melting and solidification of all pure substances including those with large difference in phase specific heats such as water and paraffin wax.
30 citations
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TL;DR: In this paper, the first-ever demonstration of flow reversal during bottom-up solidification of water using full-field thermal and flow measurements and its direct impact on the solidifying interface is presented.
Abstract: In a wide variety of fluidic systems involving thermal and compositional gradients, local density changes lead to the onset of natural convection that influences the process itself, for example, during phase-change phenomena and magmatic flows. Accurate knowledge of the flow characteristics is essential to quantify the impact of the flow of the processes. In this work, the first-ever demonstration of flow reversal during bottom-up solidification of water using full-field thermal and flow measurements and its direct impact on the solidifying interface is presented. Based on prior optical interferometric measurements of full-field temperature distribution in water during solidification, we use the particle image velocimetry technique to quantify and reveal the changing natural convection pattern arising solely due to the density anomaly of water between 0 °C and 4 °C. The independently captured thermal and flow fields show striking similarities and clearly elucidate the plausible mechanism explaining the fo...
9 citations
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8 citations
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TL;DR: In this article, a continuum mixture model is proposed for phase change of binary alloy including the effect of thermal anisotropy, which is incorporated by an additional departure source in the conven...
Abstract: A continuum mixture model is proposed for phase change of binary alloy including the effect of thermal anisotropy. Thermal anisotropy is incorporated by an additional departure source in the conven...
1 citations
References
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TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.
Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.
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"Modeling of solid phase sedimentati..." refers methods in this paper
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TL;DR: In this article, an enthalpy formulation based fixed grid methodology is developed for the numerical solution of convection-diffusion controlled mushy region phase-change problems, where the basic feature of the proposed method lies in the representation of the latent heat of evolution, and of the flow in the solid-liquid mushy zone, by suitably chosen sources.
Abstract: An enthalpy formulation based fixed grid methodology is developed for the numerical solution of convection-diffusion controlled mushy region phase-change problems. The basic feature of the proposed method lies in the representation of the latent heat of evolution, and of the flow in the solid-liquid mushy zone, by suitably chosen sources. There is complete freedom within the methodology for the definition of such sources so that a variety of phase-change situations can be modelled. A test problem of freezing in a thermal cavity under natural convection is used to demonstrate an application of the method.
1,527 citations
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TL;DR: In this article, a set of continuum conservation equations for binary, solid-liquid phase change systems is presented. But these equations have been cast into forms amenable to clear physical interpretation and solution by conventional numerical procedures.
Abstract: Semi-empirical laws and microscopic descriptions of transport behavior have been integrated with principles of classical mixture theory to obtain a set of continuum conservation equations for binary, solid-liquid phase change systems. For a restricted, yet frequently encountered, class of phase change systems, the continuum equations have been cast into forms amenable to clear physical interpretation and solution by conventional numerical procedures.
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"Modeling of solid phase sedimentati..." refers methods in this paper
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01 Jun 1991-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, a basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented, based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly.
Abstract: A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.
459 citations
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TL;DR: Three limiting cases are identified which result in one-phase models of binary systems of binary alloy solidification and each of these models can be readily implemented in standard single phase flow numerical codes.
Abstract: The aim of this paper is to explore the range of possible one-phase models of binary alloy solidification. Starting from a general two-phase description, based on the two-fluid model, three limiting cases are identified which result in one-phase models of binary systems. Each of these models can be readily implemented in standard single phase flow numerical codes. Differences between predictions from these models are examined. In particular, the effects of the models on the predicted macro-segregation patterns are evaluated.
411 citations
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