Morphological instability of the solid-liquid interface in crystal growth under supercooled liquid film flow and natural convection airflow

Ring-like ripples on the surface of icicles are an example of morphological instability of the ice-water interface during ice growth under supercooled water film flow. The surface of icicles is typically covered with ripples of about 1 cm in wavelength, and the wavelength appears to be almost independent of external temperature, icicle radius, and volumetric water flow rate. One side of the water layer consists of the water-air surface and growing ice is the other. This is one of the more complicated moving phase boundary problems with two interfaces. A recent theoretical work [K. Ueno, Phys. Rev. E 68, (2003) 021603] to address the underlying instability that produces ripples is based on the assumption of the absence of airflow around icicles. In this paper, we extend the previous theoretical framework to include a natural convection airflow ahead of the water-air surface and consider whether the effect of natural convection airflow on the wavelength of ripples produced on an ice surface is essential or not.Comment: 19 pages, 5 figure

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. Both quantities compare favorably with experiments

Numerical and experimental verification of a theoretical model of ripple formation in ice growth under supercooled water film flow

Little is known about morphological instability of a solidification front during the crystal growth of a thin film of flowing supercooled liquid with a free surface: for example, the ring-like ripples on the surface of icicles. The length scale of the ripples is nearly 1 cm. Two theoretical models for the ripple formation mechanism have been proposed. However, these models lead to quite different results because of differences in the boundary conditions at the solid-liquid interface and liquid-air surface. The validity of the assumption used in the two models is numerically investigated and some of the theoretical predictions are compared with experiments.Comment: 30 pages, 9 figure