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Journal ArticleDOI

Binary alloy solidification and freckle formation: Effect of shrinkage induced flow on solutal instability and macro-segregation

TL;DR: In this paper, a fixed grid-based numerical scheme involving volume averaging of conserved parameters is proposed to investigate the effect of shrinkage induced flow (SIF) on freckling phenomena during bottom-up solidification of binary alloys.
Abstract: Freckle formation during directional solidification of binary alloy is a well-researched subject area. However, the influence of shrinkage induced flow (SIF) on freckling phenomena is barely reported. The focus of this work is to investigate this effect during bottom-up solidification of binary alloys. A fixed grid-based numerical scheme involving volume averaging of conserved parameters is proposed. The solidification geometry under consideration is a two-dimensional mold cavity with a central riser allowing continuous melt flow into the cavity. Model validation is obtained against existing numerical results involving directional solidification of Al-4.1 wt. % Cu alloy. However, heavier solute (Cu) rejection in the melt during solidification renders the validation case study devoid of freckling phenomena. The postvalidation investigations involve bottom up solidification of Al-30 wt. % Mg alloy with lighter solute (Mg) rejection, leading to solutal instability and freckle formation. The effect of SIF on solutal instability, channel formation, and overall macro-segregation is investigated. The intensity of SIF hinges on both cooling condition and opening size. The penetration depth of SIF into the solidification domain gives rise to either early or late onset of solutal instability. SIF penetration depth till the melt domain adjacent to the mushy layer promotes early onset of solutal instability. However, SIF penetration into the mushy layer itself triggers redistribution of solute-rich melt inside this layer, leading to delayed onset of solutal instability. Since the macro-segregation is a direct consequence of advection of solute inside and adjacent to the mushy region, the influence of SIF is manifested by unprecedented macro-segregation pattern.
Citations
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01 Jan 2016
TL;DR: The numerical heat transfer and fluid flow is universally compatible with any devices to read and is available in the authors' digital library an online access to it is set as public so you can get it instantly.
Abstract: Thank you for reading numerical heat transfer and fluid flow. Maybe you have knowledge that, people have search numerous times for their favorite books like this numerical heat transfer and fluid flow, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some malicious virus inside their computer. numerical heat transfer and fluid flow is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the numerical heat transfer and fluid flow is universally compatible with any devices to read.

1,531 citations

Journal Article
TL;DR: In this paper, the authors investigated the transition from laminar to turbulent dynamics in buoyancy plumes due to localized buoyancy sources and found that this transition is sensitive to external perturbations.
Abstract: Abstract Plumes due to localized buoyancy sources are of wide interest owing to their prevalence in many situations. This study investigates the transition from laminar to turbulent dynamics. Several experiments have reported that this transition is sensitive to external perturbations. As such, a well-controlled set-up has been chosen for our numerical study, consisting of a localized heat source at the bottom of an enclosed cylinder whose walls are all maintained at a fixed uniform temperature, except for the localized heat source. At moderate Rayleigh numbers $\\mathit{Ra}$ , the flow consists of a steady, axisymmetric purely poloidal plume. On increasing $\\mathit{Ra}$ , the flow undergoes a supercritical Hopf bifurcation to an axisymmetric ‘puffing’ plume, where a vortex ring is periodically emitted from the localized heater. At higher $\\mathit{Ra}$ , this state becomes unstable to a sequence of symmetry-breaking bifurcations, going through a quasi-periodic ‘fluttering’ stage where the axisymmetric rings are tilted, and other states in which the sequence of tilted rings interact with each other. The sequence of symmetry-breaking bifurcations in the transition to turbulence culminates in a torus breakup event in which all the spatial and spatio-temporal symmetries of the system are broken.

32 citations

Journal ArticleDOI
TL;DR: In this paper , a species conservation equation considering density changes was constructed to model convective and diffusive of solutes, and the authors demonstrated that solidification shrinkage and shrinkage-flow can strongly affect the dendritic morphology and solute segregation.
Journal ArticleDOI
TL;DR: In this paper , the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments, where four different aqueous salt solutions, and different compositions thereof, were employed for experimentation.
Abstract: In this work, the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments. Four different aqueous salt solutions, and different compositions thereof, were employed for experimentation. The mixtures were solidified to analyze the effect of solute expansion coefficients on the convection currents, and the composition distribution in the bulk. The initial compositions were chosen such that all cases have the same primary solid fraction at eutectic temperature, for obtaining similar compositional changes in the bulk liquid at various stages. Similar cooling conditions were also maintained to ensure that the variation in convection strength is caused primarily by different solute expansion coefficients. A distinct observation of the free surface freezing before the bulk, termed bridging, is reported in certain cases. Further analysis revealed that the bridging could be attributed to a difference in solute convection caused by the solute expansion coefficient. Numerical simulations were performed to further ascertain the plausible initiation mechanisms for bridging. The predicted compositional and solid fraction distribution revealed lesser solute accumulation near the surface, for the lower solute expansion cases, and the resulting increase in the tendency of freezing at the top. An upper limit for the ratio of solutal to thermal Rayleigh numbers in the experimental conditions has been identified for the occurrence of bridging in high Prandtl number fluids.
Journal ArticleDOI
TL;DR: In this article , the small-time solution is used as the initial condition for the numerical integration of a problem having three moving boundaries, and the results for the case of the Al-Cu system are presented.
Abstract: The one-dimensional transient solidification of a binary alloy undergoing shrinkage is well-known as an invaluable benchmark for the testing of numerical codes that model macrosegregation. Here, recent work that considered the small-time behaviour of this problem is extended until complete solidification, thereby determining the solute profile across the entire solidified domain. The small-time solution is used as the initial condition for the numerical integration of a problem having three moving boundaries. Of particular significance is the so-called inverse segregation that is observed at the start of solidification, and the extreme segregation that is observed at the end; in the case of the example presented, which is for the often-cited Al–Cu system, the macrosegregation is found to be positive or negative, depending on whether Scheil’s equation or the lever rule is assumed at the microscale, respectively. The relevance of these results for the modelling of steady-state continuous casting processes – in particular, the phenomenon of centreline segregation – is also discussed.
References
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Journal ArticleDOI
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.

1,892 citations

01 Jan 2016
TL;DR: The numerical heat transfer and fluid flow is universally compatible with any devices to read and is available in the authors' digital library an online access to it is set as public so you can get it instantly.
Abstract: Thank you for reading numerical heat transfer and fluid flow. Maybe you have knowledge that, people have search numerous times for their favorite books like this numerical heat transfer and fluid flow, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some malicious virus inside their computer. numerical heat transfer and fluid flow is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the numerical heat transfer and fluid flow is universally compatible with any devices to read.

1,531 citations

Journal ArticleDOI
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.

896 citations

Book
31 Aug 2015
TL;DR: The 3rd edition of this popular textbook as mentioned in this paper covers current topics in all areas of casting solidification, including semi-solid and metal matrix composites solidification and molecular dynamic modeling new theories.
Abstract: The 3rd edition of this popular textbook covers current topics in all areas of casting solidification. Partial differential equations and numerical analysis are used extensively throughout the text, with numerous calculation examples, to help the reader in achieving a working knowledge of computational solidification modeling. The features of this new edition include: new chapters on semi-solid and metal matrix composites solidification a significantly extended treatment of multiscale modeling of solidification and its applications to commercial alloys a survey of new topics such as solidification of multicomponent alloys and molecular dynamic modeling new theories, including a theory on oxide bi-films in the treatment of shrinkage problems an in-depth treatment of the theoretical aspects of the solidification of the most important commercial alloys including steel, cast iron, aluminum-silicon eutectics, and superalloys updated tables of material constants

586 citations

Journal ArticleDOI
TL;DR: In this article, a newly developed continuum model has been used with a well-established control-volume-based, finite-difference scheme to investigate solidification of a binary, aqueous ammonium chloride solution in a rectangular cavity.

333 citations