Water droplet freezing on cold surfaces with distinct wetabilities
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ORIGINAL
Water droplet freezing on cold surfaces with distinct wetabilities Armin Bodaghkhani 1
&
Xili Duan 2
Received: 27 May 2020 / Accepted: 13 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper investigates the total freezing time of droplets on surfaces with various wettabilities with horizontal and inclined orientations. A two-dimensional Volume of Fluid (VOF) method was applied to capture the liquid-air interface, and an automatic localized grid treatment technique was applied to increase the accuracy, especially near the impact and spreading areas. The Kistler and Shikhumurzaev dynamic contact angle models were implemented to impose the dynamic contact angles on different surfaces. An enthalpy-porosity technique was used to predict the phase change of droplets after impact with the surface. The results of the nondimensional droplet diameter ratios and total freezing times for both dynamic contact angle models have been presented and verified with experimental data. The effects of both wetting properties and the surface inclination on the freezing time have been analyzed. The results indicate that a lower surface temperature, a decrease in static contact angle and a higher inclination will result in more rapid freezing of droplets. Keywords Droplet freezing . Droplet impact . Wettability . Liquid-air interface . Dynamic contact angle
Nomenclature ρ Density ! v two-dimensional velocity field xi two-dimensional space t time ! g gravitational acceleration ! t tress tensor kinematic viscosity I unit tensor μ Viscosity S source term liquid fraction vp pull velocity Amush mushy zone constant ap Volume fraction in the cell pth Phase name
* Armin Bodaghkhani [email protected] Xili Duan [email protected] 1
Faculty of Sustainable Design Engineering, University of Prince Edward Island (UPEI), Charlottetown, PEI, Canada
2
Department of Mechanical Engineering, Memorial University of Newfoundland (MUN), St. John’s, NL, Canada
Ca σ u fH θeq θdyn H λ h href c ΔH l L T θ θA θR We Re V0 D0 D=D0
Level set function Capillary number Surface tension contact line velocity Hoffman’s function equilibrium contact angle Dynamic contact angle enthalpy per unit volume thermal conductivity sensible enthalpy sensible enthalpy at a reference temperature specific heat modified latent heat equation liquid volume fraction latent heat of the phase change liquid volume fraction of a numerical cell occupied by solid and liquid Temperature Inclined surface angle Static contact Angle Advancing contact angle Receding contact angle Droplet Weber number Droplet Reynolds number Droplet initial velocity Droplet initial diameter droplet diameter ratio
Heat Mass Transfer
1 Introduction The impact of liquid or super-cooled droplets on a surface is a highly interesting physical phenomenon. Examples include the impingements of cold liquid droplets of the spray for cooling purposes [1], the interaction of atomized fuel droplets with the piston in internal combustion engine applications [2], t
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