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Effect of Surface Evaporation on Steady Thermocapillary Convection in an Annular Pool

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Abstract

In order to understand the effect of surface evaporation on thermocapillary convection in an annular pool, a series of numerical simulation on thermocapillary convection of the fluids with Prandtl number from 0.01 to 50 in the pure vapor environment were carried out. The results show that thermocapillary convection is always coupled with the evaporation process on the free surface. With the increase of evaporation Biot number, the surface temperature decreases, and the evaporation mass flux near the hot wall increases obviously. However, near the cold wall, the evaporation mass flux increases first, and then decreases. When Marangoni number is small, the total evaporation mass rate at free surface increases with the increase of evaporation Biot number; when Marangoni number is larger, it increases first and then approaches a constant value. The aspect ratio of the annular pool has a positive influence on the thermocapillary convection strength and the total evaporation mass rate. With the increase of Prandtl number, the surface temperature rises gradually and the evaporative mass flux increases, and the thermocapillary convection cell moves gradually toward the outer wall and the free surface. This effect decreases with the increase of evaporation Biot number When evaporation Biot number is smaller, the total evaporation mass rate increases with the Prandtl number; when Biot number is larger, Prandtl number has little impact on the total evaporation mass rate.

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Abbreviations

Bi :

evaporation Biot number

c p :

specific heat capacity, kJ/(kg ⋅K)

d :

depth, m

h fg :

latent heat of vaporization, kJ/kg

j :

evaporation mass flux, kg/(m 2⋅s)

J :

nondimensional evaporation mass flux

Ja :

Jacob number

J m :

total evaporation mass rate, kg/s

M :

molar mass, g/mol

Ma :

Marangoni number

p :

pressure, Pa

P :

nondimensional pressure

Pr :

Prandtl number

r :

radius, m

R :

dimensionless radius; universal gas constant

t :

time, s

T :

temperature, K

u :

radial velocity, m/s

U :

nondimensional radial velocity

V :

nondimensional velocity vector

w :

axial velocity, m/s

W :

Nondimensional axial velocity

z :

axial coordinate, m

Z :

nondimensional axial coordinate

Greek symbols :

ᅟ

α :

accommodation coefficient; thermal diffusivity, m 2/s

ε :

aspect ratio

γ T :

temperature coefficient of surface tension, N/(m ⋅K)

η :

radius ratio

μ :

dynamic viscosity, kg/(m ⋅s)

ν :

kinematic viscosity, m 2/s

Θ:

dimensionless temperature

ρ :

density, kg/m 3

τ :

dimensionless time

ψ :

dimensionless stream function

Subscripts :

ᅟ

h:

high

i:

inner

max:

maximum

o:

outer

s:

saturation

v:

vapor

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Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant No. 11532015).

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Authors and Affiliations

  1. Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing, 400044, China

    Li Zhang, You-Rong Li & Chun-Mei Wu

  2. Chongqing Nanfang Translators College of SISU, Chongqing, 401120, China

    Li Zhang

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  1. Li Zhang
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Correspondence to You-Rong Li.

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Zhang, L., Li, YR. & Wu, CM. Effect of Surface Evaporation on Steady Thermocapillary Convection in an Annular Pool. Microgravity Sci. Technol. 28, 499–509 (2016). https://doi.org/10.1007/s12217-016-9510-0

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  • DOI: https://doi.org/10.1007/s12217-016-9510-0

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