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Heat and mass transfer at a free surface with diabatic boundaries in a single-species system under microgravity conditions

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Abstract

In this paper, we analyzed the heat and mass transfer at a free surface under microgravity conditions. The SOURCE-II (Sounding Rocket COMPERE Experiment) experiment was performed on a suborbital flight in February 2012 from Esrange in North Sweden. It provided representative data with respect to solid, liquid, and vapor temperatures as well as the visible surface position. The objectives were to quantify the deformation of the free liquid surface and to correlate the apparent contact angle to a characteristic temperature difference between subcooled liquid and superheated wall. Furthermore, the influence of evaporation and condensation at the liquid/vapor interface and at the superheated wall must be taken into account to analyze heat and mass fluxes due to a characteristic temperature difference. In the following, we show evidently that the magnitude of the apparent contact angle depends on the exerted specific pressurizations of the vapor phase during the experiment and hence on the change in the saturation temperature at the free surface. The characteristic temperature difference is defined with respect to the wall temperature in the vicinity of the contact line and the saturation temperature. Therefore, apparent contact angle and temperature difference can be correlated and indicate a specific characteristic. Concerning the heat and mass transfer at the free liquid surface and the contact line, two different methods are presented to evaluate the net mass due to phase change within a certain time interval. In the first approach, the mass flow rate is calculated by means of the ideal gas law and its derivatives with respect to temperature and pressure. The second approach calculates the heat flux as well as the mass flux at the wall and in the region of the free liquid surface. In these cases, a specific heat transfer coefficient and a thermal boundary layer thickness are used.

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Abbreviations

SOURCE:

Sounding Rocket Compere Experiment

COMPERE:

Comportement des Ergols dans les Reservoir

A :

Area (m2)

C :

Constant

c p :

Specific heat capacity (J/kg K)

d :

Diameter (m)

H :

Height (m)

h :

Height (m)

Δhv :

Latent heat of vapor (J/kg)

M :

Mass flow rate (kg/s)

M w :

Molecular weight (kg/mol)

m :

Mass (kg)

\(\dot{m}\) :

Mass flux (kg/m2 s)

Δm :

Net mass (kg)

p :

Pressure (Pa)

Q :

Volume flow rate (m3/s)

q :

Heat flux (W/m2)

R :

Tank radius (m)

R i :

Individual gas constant (J/kg K)

r :

Radial coordinate (m)

T :

Temperature (°C)

t :

Time (s)

U :

Internal energy (J)

u :

Velocity (m/s)

V :

Volume (m3)

V′:

Liquid volume (m3)

V″:

Vapor volume (m3)

z :

Vertical coordinate (m)

α :

Heat transfer coefficient (W/m2 K)

γ :

Apparent contact angle (°)

γ s :

Static contact angle (°)

δ :

Distance (m)

Θ :

Characteristic temperature difference (K)

κ :

Thermal diffusivity (m2/s)

k :

Isentropic coefficient

λ :

Thermal conductivity (W/m K)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

σ :

Surface tension (N/m)

σ T :

Surface tension gradient (N/m K)

φ :

Azimuthal coordinate (°)

G:

Vapor (gas)

i :

Index number

L:

Liquid

m:

Mean

n :

Final number

S:

Solid

s :

Saturation

W:

Wall

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Acknowledgments

This project is funded by the space agency of the German Aerospace Center with resources of the Federal Ministry of Economics and Technology on the basis of a resolution of the German Bundestag under Grant Number 50 RL 0921. The principle investigators of the SOURCE experiment gratefully acknowledge the support by the European Space Agency (ESA) through the microgravity application program (MAP) Project AO-2004-111. The open and stimulating discussion within the COMPERE group during the preparation and evaluation of this experiment was always very helpful. We thank SSC and their subcontractors for the design, the manufacturing, and the successful flight of the SOURCE-II module. In the frame of private communication, we gratefully acknowledge the work of Stefan Herbert who computed the contact angle by means of the microregion model.

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  1. Center of applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, 28359, Bremen, Germany

    Eckart Fuhrmann & Michael E. Dreyer

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  1. Eckart Fuhrmann
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  2. Michael E. Dreyer
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Correspondence to Michael E. Dreyer.

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Fuhrmann, E., Dreyer, M.E. Heat and mass transfer at a free surface with diabatic boundaries in a single-species system under microgravity conditions. Exp Fluids 55, 1760 (2014). https://doi.org/10.1007/s00348-014-1760-2

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