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Surface Heat Dissipation Dependence of Thermocapillary Convection of Moderate Prandtl Number Fluid in an Annular Pool

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Abstract

In order to understand surface heat dissipation dependence of thermocapillary convection for moderate Prandtl number fluid in a deep annular pool, a series of three-dimensional numerical simulations have been carried out by using the finite volume method. The radius ratio and the aspect ratio of an annular pool are fixed at 0.5 and 1.0, respectively. The working fluid is 0.65cSt silicone oil with Prandtl number of 6.7. Surface heat dissipation Biot (Bi) number is varied from 0 to 50. Results indicate that with the increase of Biot number, the radial temperature gradient near the inner cylindrical wall decreases, and near the outer cylindrical wall it increases, so the flow is enhanced. When 0 < Bi < 10, with the increase of Marangoni number, the axisymmetric steady flow first transits to the standing wave, and then to the azimuthal waves. The standing wave should be attributed to Marangoni-Bénard instability. However, the azimuthal waves should be corresponded to hydraulic instability, which is mainly driven by the azimuthal motion of temperature fluctuation from the sudden change of flow direction near the bottom and the inner cylindrical wall. When Bi ≥ 10, when the flow destabilizes, the axisymmetric steady flow transits directly to the azimuthal waves. With the increase of Biot number, the critical Marangoni number of the flow destabilization increases. Furthermore, the fundamental frequency and the wave number of three-dimensional oscillatory flow increase gradually with the increase of Biot number.

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Abbreviations

Bi :

Biot number

d :

Depth of annular pool, m

f :

Oscillatory frequency, Hz

F :

Dimensionless oscillatory frequency

h :

Convective heat transfer coefficient, W/(m2·K)

m :

Wave number

Ma :

Marangoni number

p :

Pressure, Pa

P :

Dimensionless pressure

Pr :

Prandtl number

r :

Radius, m

R :

Dimensionless radius

t :

Time, s

T :

Temperature, K

u :

Radial velocity, m/s

U :

Dimensionless radial velocity

v :

Azimuthal velocity, m/s

V :

Dimensionless azimuthal velocity

V :

Dimensionless velocity vector

w :

Axial velocity, m/s

W :

Dimensionless axial velocity

z :

Axial coordinate, m

Z :

Dimensionless axial coordinate

α :

Thermal diffusivity, m2/s

ε :

Aspect ratio

γ T :

Temperature coefficient of surface tension, N/(m·K)

λ :

Thermal conductivity, W/(m·K)

η :

Radius ratio

μ :

Dynamic viscosity, kg/(m·s)

ν :

Kinematic viscosity, m2/s

Θ :

Dimensionless temperature

ρ :

Density, kg/m3

τ :

Dimensionless time

ψ :

Dimensionless stream function

0:

Ambient

c:

Cold

h:

Hot

i:

Inner

o:

Outer

p:

Period

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 51776022) and the Fundamental Research Funds for the Central Universities (No. 2018CDXYDL0001).

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Authors and Affiliations

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

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

  2. Chongqing City Management College, Chongqing, 401331, China

    Li Zhang

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  1. Li Zhang
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  2. You-Rong Li
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Correspondence to You-Rong Li.

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This article belongs to the Topical Collection: Thirty Years of Microgravity Research - A Topical Collection Dedicated to J. C. Legros

Guest Editor: Valentina Shevtsova

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Zhang, L., Li, YR., Wu, CM. et al. Surface Heat Dissipation Dependence of Thermocapillary Convection of Moderate Prandtl Number Fluid in an Annular Pool. Microgravity Sci. Technol. 31, 527–539 (2019). https://doi.org/10.1007/s12217-019-9680-7

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