During solidification of non-eutectic alloys, non-isothermal phase change causes dendritic growth of solid front with liquid phase entrapped within the dendritic network producing the mushy region. Solidification causes rejection of solute at the solid-liquid interface and within the mushy zone, causing a sharp concentration gradient to build up across the mushy region. At the same time, a temperature gradient is present as a result of externally imposed boundary conditions as well as due to evolution of latent heat, giving rise to the so-called “double-diffusive” or thermo-solutal convection. Depending on the relative density of the solute being rejected in the liquid phase during solidification process, thermal and solutal buoyancy can either aid or oppose each other. Rejection of a heavier solute leads to aiding thermo-solutal convection situation whereas the rejection of lighter solute causes the thermal and solutal buoyancy to oppose each other. If the thermal and solutal buoyancies oppose each other, flow instability arises adjacent to the mush-bulk liquid interface regions. Thus, there may be a wide variety of convection situations present in the solidifying domain for different combinations of solution concentrations and externally imposed boundary conditions. The situation becomes even more complex if the solid phase movement along with the bulk flow is involved in the process, leading to multiphase convection. Detachment of solid phase from the solid/liquid interface can be caused by remelting (solutal and/or thermal) and shearing action of a convecting liquid adjacent to the interface. Depending on the drag of the bulk flow and the density of the solid phase relative to that of the bulk liquid, these detached particles can either float or sediment. The redistribution of the rejected solute by means of diffusion (at a local scale) and thermo-solutal convection (at system level length scales) causes heterogeneous orientation of mixture constituents over the solidifying domain popularly known as macro-segregation. From the point of view of manufacturing, severe form of macro-segregation or heterogeneous species distribution is an undesirable phenomenon and hence, a thorough understanding of the species redistribution by means of diffusion and convection during solidification process is very important. Most of the earlier studies on double diffusive convection during solidification involved fixed dendrites. However, the advection of solid particles during the solidification process can generate major instability in the flow pattern while modifying the solid front growth, and hence the macro-segregation pattern considerably. With this viewpoint in mind, the overall objective of the present work is to address these wide-varieties of single phase and multi phase flow situations and their effect on solid front growth and macro-segregation during directional solidification of non-eutectic binary alloys, numerically as well as experimentally. Different configurations of directional solidification processes involving double diffusive convection have been studied for two different kinds of non-eutectic solutions. While solidification of hypoeutectic solutions leads to aiding type double diffusive convection, the solidification of hyper-eutectic solutions is characterized by opposing type double diffusive convection. Solidification of hypo-eutectic solution generally involves single phase flow, while most of the hyper-eutectic solidification involves movement of solid phase (i.e. multiphase flow). As far as the modeling part is concerned, transport phenomena during solidification with multiphase convection are not common in existing literature. This work is a first attempt to develop a solidification model with multiphase flow based entirely on macroscopic parameters. As a first step, a generalized macroscopic framework has been developed for mathematical modeling of multiphase flow during solidification of binary alloy systems. The complete set of equivalent single-domain governing equations (mass, momentum, energy and species conservation) are coupled with the phase (solid and liquid) velocities. A generalized algorithm has been developed to determine solid detachment and solid advection phenomena, based on two critical parameters, namely: critical solid fraction and critical velocity. While the first of these two parameters (critical solid fraction) represents the strength of the dendritic bond, the second (critical velocity) stands for the intensity of flow to create drag force and solutal remelting at the dendrite roots. A new approach for evaluating liquid/solid fraction by using fixed grid enthalpy updating scheme, that accounts for multiphase flow and, at the same time, handles equilibrium and non equilibrium solidification mechanisms, has been proposed. The newly developed model has been validated with existing literatures as well as with experimental observations performed in the present work. The experimental results were obtained by using PIV as well as laser scattering techniques. Side cooled as well as top cooled configurations are studied. Single phase convection is observed for the case of hypo-eutectic solution, whereas hyper-eutectic solutions involve convection with movement of solid phase. For the case of bottom cooled hyper-eutectic solution, finger-like convection leading to freckle formation is observed. For all the hyper-eutectic cases, solid phase movement is found to alter the convection pattern and final macrosegregation significantly. The numerical results are compared with experimental observations both qualitatively as well as quantitatively.

The primary focus of the present work is the development of macro-models for numerical simulation of binary alloy solidification processes, consistent with microscopic phase-change considerations, with a particular emphasis on capturing the effects of non-equilibrium species redistribution on overall macrosegregation behaviour. As a first step, a generalised macroscopic framework is developed for mathematical modelling of the process. The complete set of equivalent single-phase governing equations (mass, momentum, energy and species conservation) are solved following a pressure-based Finite Volume Method according to the SIMPLER algorithm. An algorithm is also developed for the prescription of the coupling between temperature and the melt-fraction. Based on the above unified approach of solidification modelling, a macroscopic numerical model is devised that is capable of capturing the interaction between the double-diffusive convective field and a localised fluid flow on account of solutal undercooling during non-equilibrium solidification of binary alloys. Numerical simulations are performed for the case of two-dimensional transient solidification of Pb-Sn alloys, and the simulation results are also compared with the corresponding experimental results quoted in the literature. It is observed that non-equilibrium effects on account of solutal undercooling result in an enhanced macrosegregation. Next, the model is extended to capture the effects of dendritic arm coarsening on the macroscopic transport phenomena occurring during a binary alloy solidification process. The numerical results are first tested against experimental results quoted in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom-cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation can be predicted as compared to that dictated by shrinkage-induced fluid flow alone. For an order-of-magnitude assessment of predictions from the numerical models, a systematic approach is subsequently developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. A characteristic velocity scale inside the mushy region is derived, in terms of the morphological parameters of the two-phase region. A subsequent analysis of the energy equation results in an estimation of the solid layer thickness. It is also shown from scaling principles that non-equilibrium effects result in an enhanced macro-segregation compared to the case of an equilibrium model For the sake of assessment of the scaling analysis, the predictions are validated against computational results corresponding to the simulation of a full set of governing equations, thus confirming the trends suggested by the scale analysis. In order to analytically investigate certain limiting cases of unidirectional alloy solidification, a fully analytical solution technique is established for the solution of unidirectional, conduction-dominated, alloy solidification problems. The results are tested for the problem of solidification of an ammonium chloride-water solution, and are compared with those from existing analytical models as well as with the corresponding results from a fully numerical simulation. The effects of different microscopic models on solidification behaviour are illustrated, and transients in temperature and heat flux distribution are also analysed. An excellent agreement between the present solutions and results from the computational simulation can be observed. The generalised numerical model is subsequently utilised to investigate the effects of laminar double-diffusive Rayleigh-Benard convection on directional solidification of binary fluids, when cooled and solidified from the top. A series of experiments is also performed with ammonium chloride-water solutions of hypoeutectic and hypereutectic composition, so as to facilitate comparisons with numerical predictions. While excellent agreements can be obtained for the first case, the second case results in a peculiar situation, where crystals nucleated on the inner roof of the cavity start descending through the bulk fluid, and finally settle down at the bottom of the cavity in the form of a sedimented solid layer. An eutectic solidification front subsequently progresses from the top surface vertically downwards, and eventually meets the heap of solid crystals collected on the floor of the cavity. However, comparison of experimental observations with corresponding numerical results from the present model is not possible under this situation, since the associated transport process involves a complex combination of a number of closely interconnected physical mechanisms, many of which are yet to be resolved. Subsequent to the development of the mathematical model and experimental arrangements for macroscopic transport processes during an alloy solidification process, some of the important modes of double-diffusive instability are analytically investigated, as a binary alloy of any specified initial composition is directionally solidified from the top. By employing a close-formed solution technique, the critical liquid layer heights corresponding to the onset of direct mode of instability are identified, corresponding two a binary alloy with three different initial compositions. In order to simulate turbulent transport during non-equilibrium solidification processes of binary alloys, a modified k-8 model is subsequently developed. Particular emphasis is given for appropriate modelling of turbulence parameters, so that the model merges with single-phase turbulence closure equations in the pure liquid region in a smooth manner. Laboratory experiments are performed using an ammonium chloride-water solution that is solidified by cooling from the top of a rectangular cavity. A good agreement between numerical and experimental results is observed. Finally, in order to study the effects of three-dimensionality in fluid flow on overall macrosegregation behaviour, the interaction between double-diffusive convection and non-equilibrium solidification of a binary mixture in a cubic enclosure (cooled from a side) is numerically investigated using a three-dimensional transient mathematical model. Investigations are carried out for two separate model systems, one corresponding to a typical metal-ally analogue system and other corresponding to an actual metal-alloy system. As a result of three-dimensional convective flow-patterns, a significant solute macrosegregation is observed in the transverse sections of the cavity, which cannot be captured by two-dimensional simulations.