Dissertation

Phase change and flow in multiphase systems
Martin Chudjak
PhD thesis advisor: doc. Mgr. Peter Guba, PhD.

Abstract: This thesis consists of three parts. In the first part, we report on laboratory experiments on Taylor bubbles in downward pipe flow and subsequent reconstruction of a three dimensional shape of bubbles. The pipe is enlightened by a laser sheet perpendicular to the vertical pipe axis. The bubble crossing the laser sheet is filmed by a high-speed camera. Our laser measurements reveal that the bubble shapes in the horizontal plane perpendicular to the pipe axis are not concave, but exhibit a depression in their centres. Unlike the velocity of asymmetric bubbles, we find that the shape of the bubbles projected onto the axial plane depends on a mean velocity of the downward flow, with asymmetric bubbles becoming more tapered at larger flow rates. We address a simple inviscid model to explain this dependence.
In the second part, we model the solidification and phase-change-driven flow in a ternary alloy cooled from a planar boundary. The liquid and solid phases are separated by a sharp interface. The model incorporates a fluid flow in the liquid region due to shrinkage/expansion during the phase change. We derive self-similar solutions for the temperature field, composition fields and the interface location, and perform an asymptotic analysis in the limit of the large Lewis numbers. In the case of binary systems, the two asymptotic regimes are known in the limit of large Lewis number. One controlled by the thermal diffusivity and one controlled by the solutal diffusivity. In the case of ternary systems studied here, we find that the presence of the second solute leads to eight asymptotic regimes. We identify the material and experimental parameters for which these regimes occur. The results indicate that a sufficient difference in the two solutal diffusivities accounts for the difference in the segregation of the two solutes in the solid phase. We find that a shrinkage upon freezing enhances the solidification rate if the system solidifies in the regime controlled by the thermal diffusivity, but it slows down the solidification rate if the system solidifies in the regime controlled by one or two solutal diffusivities. The expansion has the opposite effect on the rate of solidification in the regimes controlled by either thermal or solutal diffusivities. We also examine the onset of the marginal constitutional supercooling (MCS) in the liquid region above the solid/liquid interface. With the requirements of the MCS not to occur, we identify two novel regimes of solidification in which the system solidifies at a very slow rate. We also provide numerical results which show different effects of the segregation coefficients and the double-solutal diffusive effects on the onset of the MCS.
Finally, in the third part, we propose a one-dimensional model for solidification of supercooled liquids in a finite domain. The classical Stefan-type two-phase model of freezing is extended to account for the kinetic effects at the front separating the solid and liquid phases. A direct numerical simulation of the model reveals different stages of freezing dynamics: the initial stage dominated by the interfacial attachment kinetics, the intermediate quasi--equilibrium stage, and the late stage dominated by the finite-domain effects. Asymptotic solutions in the limit of small initial supercooling are derived and compared with numerical calculations for the full model.

References
[1] Juraj Kyselica, Peter Guba, Martin Chudjak: Recalescence dynamics and solidification of a supercooled melt in a finite domain, Int. J. Heat Mass Transfer, Vol. 159, (2020)