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Aspect Ratio Dependence of Thermocapillary Flow Instability of Moderate-Prandtl Number Fluid in Annular Pools Heated from Inner Cylinder

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Abstract

This paper presented a set of direct numerical simulations on the thermocapillary flow instability of moderate-Prandtl number fluids in annular pools heated from inner cylinder. The emphasis is on the aspect ratio dependence of the critical Marangoni number of flow destabilization and the formation mechanism of the different flow patterns. It was found that the two-dimensional axisymmetric steady flow will bifurcate into three types of oscillatory flows, including the oscillatory concentric rings, the alternating straight spoke and the rotating wave patterns. The bifurcation process depends mainly on the aspect ratio of the annular pool when the radius ratio is fixed. With the increase of the aspect ratio, the first instability flow pattern is oscillatory concentric rings and the corresponding critical Marangoni number and the oscillatory frequency decrease first, and then increase slightly. When the flow pattern transits to the alternating straight spoke pattern at the aspect ratio of 0.415, there are an abrupt increase of the critical Marangoni number and a sudden decrease of the oscillatory frequency. Furthermore, when the rotating wave pattern appears, the critical Marangoni number decreases gradually, but the corresponding oscillatory frequency has only a slight decrease.

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Abbreviations

A :

Aspect ratio

c p :

Specific heat capacity, J/(kg∙K)

d :

Depth of annular pool, m

F :

Dimensionless frequency

m :

Ring number or wave number

Ma :

Marangoni number

p :

Pressure, Pa

P :

Dimensionless pressure

Pr :

Prandtl number

r :

Radius, m

R :

Dimensionless radius

T :

Temperature, K

u :

Radial velocity, m/s

U :

Dimensionless radial velocity

v :

Azimuthal velocity, m/s

V :

Dimensionless azimuthal velocity

w :

Axial velocity, m/s

W :

Dimensionless axial velocity

α :

Thermal diffusivity, m2/s

є :

Parameter, є  = (Ma-Macri)/Macri

Y T :

Surface tension temperature coefficient, N/(m∙K)

η :

Radius ratio

μ :

Dynamic viscosity of the fluid, kg/(m·s)

ν :

Kinematic viscosity of the fluid, m2/s

θ :

Azimuthal coordinate, rad

Θ :

Dimensionless temperature, Θ = (T-Tc)/(Th-Tc)

ρ :

Density, kg/m3

τ :

Dimensionless time

Ψ :

Dimensionless stream function

c:

Cold, centre

cri:

Critical

h:

Hot

i:

Inner

o:

Outer

s:

Stable

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 51776022) and Chongqing Basic and Frontier Research Project (No. cstc2019jcyj-msxmX0582, cstc2018jcyjAX0597).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Chongqing Industry Polytechnic College, Chongqing, 401120, China

    Dong-Ming Mo

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

    Li Zhang

  3. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, China

    Deng-Fang Ruan

  4. College of Energy and Power Engineering, Chongqing University, Chongqing, 400044, China

    You-Rong Li

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  1. Dong-Ming Mo
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Correspondence to Deng-Fang Ruan.

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Mo, DM., Zhang, L., Ruan, DF. et al. Aspect Ratio Dependence of Thermocapillary Flow Instability of Moderate-Prandtl Number Fluid in Annular Pools Heated from Inner Cylinder. Microgravity Sci. Technol. 33, 66 (2021). https://doi.org/10.1007/s12217-021-09909-0

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