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A systematic experimental study on the evaporation rate of supercooled water droplets at subzero temperatures and varying relative humidity

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Abstract

Supercooled water droplets (SWD) are present in clouds at high altitude and subjected to very low temperatures and high relative humidity. These droplets exist in a metastable state. The understanding of the evaporation of SWD at these extreme conditions is of high interest to understand rain, snow, and hail generating mechanisms in clouds. This paper focuses on the experimental results of the measurements of the evaporation rates \(\beta\) of supercooled water droplets. For this purpose, single SWDs are trapped by means of optical levitation. During the evaporation process, the elastically scattered light in the forward regime is recorded and evaluated. Experiments have been performed for different relative humidities \(\phi\) at three constant ambient temperatures, namely, \({T_\infty }=268.15;~263.15;~253.15~{\text{K}}\) (\({t_\infty } = -5;\,-10;\,-20~^{\circ}{\text{C}}\)). The experimental data agrees well with direct numerical simulations (DNS) carried out with the in-house code Free Surface 3D (FS3D) and shows that the use of a simplified model is permissible for these ambient conditions.

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Abbreviations

\(Bi\) :

Biot number, \(Bi=\frac{{\alpha \,D}}{{6\,k}}\) [–]

\({B_Y}\) :

Spalding’s mass transfer number, \({B_Y}=\frac{{{Y_{1,\infty }}\,-\,{Y_{1,s}}}}{{{Y_{1,s}}\,-\,1}}\) [–]

\({c_{p{\text{,a}}}}\) :

Specific heat capacity of dry air [J/(kg K)]

\({c_{p{\text{,l}}}},~{c_{p{\text{,v}}}}\) :

Specific heat capacity of liquid water and water vapour [J/(kg K)]

\(D,~{D_0}\) :

Diameter, initial diameter for t = 0 [m]

\({D_{12,R}}\) :

Diffusion coefficient at reference temperature [m2/s]

\(f\) :

Focal length [m]

\({f_1},~{f_2}\) :

Volume fractions of liquid (1) and vapour (2) [–]

\(k\) :

Thermal conductivity [W/(m K)]

\({k_{\text{c}}}\) :

Mass transfer coefficient [m/s]

\({L_{\text{e}}}\) :

Specific latent heat of evaporation [J/kg]

\(n\) :

Real part of refractive index [–]

\(Nu\) :

Nusselt number, \(Nu=\frac{{\alpha \,D}}{k}\) [–]

\({M_1},{M_2}\) :

Molar mass of water and ambient gas [mol/kg]

\({p_\infty }\) :

Ambient pressure [Pa]

\({p_{1,s}},{p_{1,\infty }}\) :

Partial pressure of water at droplet surface and far away from droplet [Pa]

\({p_{\text{v}}}\) :

Saturation vapour pressure [Pa]

\({P_{\text{m}}}\) :

Mean laser power [W]

\(Pr\) :

Prandtl number, \(Pr=\frac{{\eta ~{c_{{p}}}}}{k}\) [–]

\(Re\) :

Reynolds number, \(Re=\frac{{\rho ~u~D}}{\eta }\) [–]

\(Sc\) :

Schmidt number, \(Sc=\frac{\eta }{{\rho \,{D_{12}}}}\) [–]

\(Sh\) :

Sherwood number, \(Sh=\frac{{{k_{\text{c}}}\,D}}{{{D_{12}}}}\) [-]

\(t\) :

Temperature [°C]

\(T\) :

Temperature [K]

\({T_{\text{w}}},{T_\infty }\) :

Wet-bulb temperature, ambient temperature [K]

\({T_{\text{R}}},~{T_{\text{s}}}\) :

Reference temperature, temperature at droplet surface [K]

\(u\) :

Approach velocity [m/s]

\(\dot V\) :

Volume flow rate at \(T=273.15~{\text{K}}\), \(p=1013.25~{\text{hPa}}\) [l/min]

\({X_{1,s}},{X_{1,\infty }}\) :

Molar fraction at droplet surface and far away from droplet [–]

\({Y_{1,s}},{Y_{1,\infty }}\) :

Mass fraction at droplet surface and far away from droplet [–]

\(\alpha\) :

Heat transfer coefficient [W/(m2 K)]

\(\beta\) :

Evaporation rate [m²/s]

\(\Delta\) :

Accuracy, range [–]

\(\eta\) :

Dynamic viscosity [kg/(m s)]

\(\Delta \theta\) :

Angular fringe distance [°]

\(\theta\) :

Scattering angle [°]

\({\theta _I}\) :

Observation angle of camera [°]

\(\lambda\) :

Laser wavelength [m]

\({\rho _{\text{R}}},{\rho _{\text{l}}}\) :

Density of gas vapour mixture and density of liquid droplet [kg/m3]

\(\tau\) :

Time [s]

\({\tau _{\text{t}}}\) :

Thermal time scale [s]

\(\phi\) :

Ambient relative humidity [%]

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Acknowledgements

This work is done within the Collaborative Research Centre Transregio SFB-TRR 75 “Droplet Dynamics under Extreme Ambient Conditions”. The authors kindly acknowledge the financial support of the German Research Foundation (DFG). The SFB-TRR 75 shares representative experimental and numerical data for interested researchers. Further download and registration information can be found on http://www.sfbtrr75.de.

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  1. Institute of Aerospace Thermodynamics, University of Stuttgart, Pfaffenwaldring 31, 70569, Stuttgart, Germany

    S. Ruberto, J. Reutzsch, N. Roth & B. Weigand

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  1. S. Ruberto
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Correspondence to S. Ruberto.

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Ruberto, S., Reutzsch, J., Roth, N. et al. A systematic experimental study on the evaporation rate of supercooled water droplets at subzero temperatures and varying relative humidity. Exp Fluids 58, 55 (2017). https://doi.org/10.1007/s00348-017-2339-5

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