Linear stability analysis of ice growth under supercooled water film driven by a laminar airflow

Abstract

We propose a theoretical model for ice growth under a wind-driven supercooled water film. The thickness and surface velocity of the water layer are variable by changing the air stream velocity. For a given water supply rate, linear stability analysis is carried out to study the morphological instability of the ice-water interface. In this model, water and air boundary layers are simultaneously disturbed due to the change in ice shape, and the effect of the interaction between air and water flows on the growth condition of the ice-water interface disturbance is taken into account. It is shown that as the wind speed increases, the amplification rate of the disturbance is significantly affected by variable stresses exerted on the water-air interface by the air flow as well as restoring forces due to gravity and surface tension. We predict that an ice pattern of a centimeter-scale in wavelength appears and the wavelength decreases as the wind speed increases, and that the ice pattern moves in the direction opposite to the water flow. The effect of the air stress disturbance on the heat transfer coefficient at the water-air interface is also investigated for various wind speeds.

Solutions for Two-Dimensional Instabilities of Ice Surfaces Uniformly Wetted by Thin Films

“…A number of authors have studied the ice surface instability using a variety of models and the reader should consult Tsao & Rothmayer,11,12 Tsao, 13 Rothmayer, 14, 15 Otta, 16 Otta & Rothmayer, 17 and Ueno & Farzaneh 18,19 for details. The instability mechanism is believed by the authors to occur in situations where the ice surface is highly wetted (see Vargas et al 20 ).…”

Experimental Study of the Dynamics of Water Film on an Aluminum Substrate under Wind Shear

“…It seems that the interfacial shear stress on the water film surface, τ, becomes the key factor to determine the film thickness. It is obviously insufficient to take the skin friction force as τ, because the skin friction force refers to airflow along the surface of a smooth solid flat plate, and takes no account of the features of the water surface [17]. Since even minor surface perturbation have a considerable influence on air shear stress and also increase the interfacial friction factor, the best way to relate interfacial shear stress to airspeed and film flow rate is experimentally.…”

“…In computational fluid dynamics (CFD) simulations [12,14,15], the most common substitute was the wall friction stress in the boundary layer without liquid water, which was evaluated based on the control volume analysis of the layer near the body. To consider the fluctuations between gas and liquid phases would strengthen the shear, Du et al [16] and Karev et al [17] applied the correlation from the experimental results of the stratified flow in their computations. In regard to the surface roughness, the interval and amplitude of the interfacial waves were usually used.…”

Ice formation within a thin film flowing over a flat plate

“…Like Tsao & Rothmayer (2002), the ice modes propagate upstream. Furthermore, Ueno & Farzaneh (2011) show that the heat transfer coefficient at the air-water interface is strongly affected by disturbances to the air shear stress.…”

“…They also find ice modes that propagate upstream and suggest that, provided that the timescale for ice growth is longer than the timescale associated with the film flow, this upstream propagation can be explained by considering the imbalance in heat flux when the ice surface is perturbed by a small amount. Ueno & Farzaneh (2011) consider the Nelson et al (1995) steady-state film with the plate replaced by a large ice region. They find the undisturbed solution, which is then perturbed and the growth of free surface and ice instabilities are investigated.…”