Abstract
Ice accretion is considered in the impact of a supercooled water droplet on a smooth or rough solid surface, the roughness accounting for earlier icing. In this theoretical investigation, the emphasis and novelty lie in the full nonlinear interplay of the droplet motion and the growth of the ice surface being addressed for relatively small times, over a realistic range of Reynolds numbers, Froude numbers, Weber numbers, Stefan numbers and capillary under-heating parameters. The Prandtl number and the kinetic under-heating parameter are taken to be order unity. The ice accretion brings inner layers into play forcibly, affecting the outer flow. (The work includes viscous effects in an isothermal impact without phase change, as a special case, and the differences between impacts with and without freezing.) There are four main findings. First, the icing dynamically can accelerate or decelerate the spreading of the droplet whereas roughness on its own tends to decelerate spreading. The interaction between the two and the implications for successive freezings are found to be subtle. Second, a focus on the dominant physical effects reveals a multi-structure within which restricted regions of turbulence are implied. The third main finding is an essentially parabolic shape for a single droplet freezing under certain conditions. Fourth is a connection with a body of experimental and engineering works and with practical findings to the extent that the explicit predictions here for ice-accretion rates are found to agree with the experimental range.
Highlights
The high-speed impact of a two-dimensional supercooled cylindrical water droplet or small drop on a dry, possibly rough, but essentially flat, solid surface is investigated in the current paper
In addition to considering the flow, which is governed by inertial, viscous, gravitational and capillary effects, characterised by the Reynolds number, the Froude number and the Weber number, we have other parameters to account for relating to the heat transfer and temperature dependence of the material properties
The fluid mechanics of drop impact with surfaces is of importance in a variety of different fields
Summary
The high-speed impact of a two-dimensional supercooled cylindrical water droplet or small drop on a dry, possibly rough, but essentially flat, solid surface is investigated in the current paper. We have phase changes, which here are assumed to be confined to solidification of the drop, avoiding the phenomena of vaporisation and substrate melting. For example high-speed impacts with solids can cause severe erosion, whilst engineering applications include spray cooling and ink-jet printing. Ice formation during an impact or a succession of impacts can readily lead to complex phenomena due to flow interacting with heat transfer and phase changes. A range of potentially relevant features is discussed first in the introduction below and the focus is drawn to major aspects in anticipation of the work within the present paper
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