It is well-known that solidification front of a supercooled liquid is unstable; consequently, this instability leads to the appearance of an array of dendrites of sub-micron diameter. The shape and the velocity of the dendrite propagation are determined by the thermodynamic properties of the liquid and solid phases, including interfacial energy as well as the initial temperatures of both. Accordingly, the numerical simulation of solidification process is a rather challenging problem which requires an accurate prediction of high temperature gradients near the moving solidification front. In this study a relevant level set formulation has been developed enabling correct determination of the position and the curvature of the liquid/ solid interface. At this interface a Dirichlet boundary condition for the temperature field is imposed by applying a ghost-face method. For the purpose of updating the level set function and optimizing computing time a narrow-band around the interface is introduced. Within this band, whose width is temporally adjusted to the maximum curvature of the interface, the normal-to-interface velocity is appropriately expanded. The computational model is firstly validated along with the analytical solution of stable freezing. The tip velocity of dendritic patterns (pertinent to unstable freezing) is investigated by performing two-dimensional simulations. The computational results exhibit excellent qualitative and quantitative agreement with the marginal stability theory as well as with the available experiments in the heat-diffusion-dominated region.

a b s t r a c tTwo relevant computatio nal models, one relying on a Level-Set approach, the other one on a Volume-ofFluid tracking procedure with piecewise linear inter face reconstruction, are comparatively assessed in terms of their capability to simulate crystallizatio n of supercooled water. The models are preliminary validated by computing a one-dimensional freezing front propagation for which an analytic solution exists. Afterwards, the tip velocity of two-dimensional dendrites growing in supercooled water is determined and compared with corresponding experimental results and theoretical predictions in the range of supercooling between 1 K and 30 K. Present modeling results following closely both the underlying theory and experimen tal findings show very good mutual agreemen t.

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In this study melting of irregular ice crystals was observed in an acoustic levitator. The evolution of the particle shape is captured using a high-speed video system. Several typical phenomena have been discovered: change of the particle shape, appearance of a capillary flow of the melted liquid on the particle surface leading to liquid collection at the particle midsection (where the interface curvature is smallest), and appearance of sharp cusps at the particle tips. No such phenomena can be observed during melting of spherical particles. An approximate theoretical model is developed which accounts for the main physical phenomena associated with melting of an irregular particle. The agreement between the theoretical predictions for the melting time, for the evolution of the particle shape, and the corresponding experimental data is rather good.

A numerical study of the water entry of non-rotating and rotating rigid spheres under varying impact angles and Weber numbers is presented. The numerical algorithm uses a finite-volume discretization and the interface between the liquid and the gaseous phase is described by means of a volume-of-fluid method. An appropriate mesh translation allows the boundary condition at the surface of the moving and rotating particle to be accounted for. The simulation results are validated with experiments and found to be in very good agreement both qualitatively (evolution of cavity shape) and quantitatively (motion of particle with respect to time). An investigation of the influence of particle rotation on its water entry behavior is carried out as well as an analysis of the effect of wettability upon cavity formation. Notably, wettability of the sphere plays a role during the penetration of a free liquid surface, even at higher Weber numbers. During impact of small particles at low Weber numbers, the influence of capillary forces rises and the force emerging at the three phase contact line becomes predominant. This force is taken into account and its influence on the impact behavior is presented. It is shown that the interface penetration behavior, either water entry or escaping from water, mostly depends on the Weber number, the solid to liquid density ratio, and the particle’s wettability, while the impact angle has nearly no influence.