Seminar in SMMEE: Evolution of dendritic morphology during coarsening of mushy zone

Title      : Evolution of dendritic morphology during coarsening of mushy zone
Speaker : Dr Prodyut Chakraborty
Location : L7
Date      : 06-Nov-2012 (Tue)
Time      : 12 noon - 1pm

Abstract:-
Evolution of dendritic morphology during coarsening of mushy zone

Alloy solidification is characterized by the morphological transformation of mushy region from fully liquid to fully solid phase. The mushy region contains network of dendritic solid phase within liquid melt. During the solidification of binary alloys the solid fraction of the primary phase continuously evolves starting from a zero value. The final value of primary solid fraction can be obtained from the phase diagrams by considering equilibrium or non- equilibrium solidification process. In the mushy zone, the evolution of dendritic network of primary solid phase in the surrounding melt causes the evolution of the solid liquid interfacial area. Previously, specific surface area (S V) used to be measured by using digital imaging methods on a 2-D segment of the sample by measuring the perimeter and the surface area of the primary solid. At present days evaluation of specific surface area in 3-D can be achieved by the construction of 3-D mesh that can closely approximate the actual 3-D structure obtained by x-ray tomography. The objective of the present study is the evolution of specific surface area during coarsening of mushy zone with respect to the fraction solid, temperature gradient and cooling rate during directional solidification. Another important fact that remains to be fully understood is the effect of coalescence on the relationship between specific surface area S V and solid volume fraction f s. Typical characterization of dendritic structures involves parameterization of primary/secondary/tertiary arm spacing (d), dendrite tip radius (ρ) and specific surface area (S V), which is defined as the surface area per unit volume, where the volume is either enclosed by the surface or the volume of the entire domain under consideration. In the present work, an attempt has been made to understand coalescence as a function of solid fraction. We assume parabolic shapes to be the building blocks for dendritic growth. With this assumption, we develop a coalescence model that predicts the evolution of surface area as a function of solid volume fraction.

Macroscopic solidification of binary alloys in presence of solid advection

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 boundary conditions and initial concentration of the solution, there may be a wide variety of convection situations present in the solidifying domain. If the thermal and solutal buoyancies oppose each other, flow instability arises adjacent to the mush-bulk liquid interface regions. Most of the earlier studies on double diffusive convection during solidification involved fixed dendrites. However, situation becomes more complex if the solid phase is allowed to move, which leads 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 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. The present work aims at addressing this wide-variety 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. Non-eutectic solution of NH4Cl-H2O has been chosen as the model system. For the numerical studies, a new enthalpy update scheme is formulated, taking solid
phase motion into account. The experimental results were obtained by using PIV as well as laser scattering techniques. Top cooled as well as side 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.

All are invited.