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Numerical simulation of coupled heat-fluid transport in freezing soils using finite volume method

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Abstract

A solution procedure using finite volume method has been established for the coupled heat-fluid transport model of freezing soils, and details about determination of the time step interval and discretization at special nodes have been introduced. Comparison between the simulation and the freezing experiments of silica flour and Zhangye loam has been conducted, and the calculated results are in general agreement with the experimental data. The research indicates that the moisture migration in the frozen zone is insignificant, and water mainly migrates from the frozen zone to the vicinity of the moving freezing front; the moving velocity of the freezing front has a great effect on the extent of moisture accumulation to the freezing front, and high extent of accumulation occurs when the freezing front advances slowly. Finally, an apparent heat capacity model has been suggested for the temperature calculation of the soil freezing process in low water content conditions; however, when the moisture migration is significant, water redistribution during the freezing process should be considered.

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Abbreviations

C v :

Volumetric specific heat of the medium, J/(m3 K)

L :

Latent heat of the fusion of ice, 334 kJ/kg

D :

Soil water diffusivity, m2/s

K :

Hydraulic conductivity, m/s

T :

Temperature, °C

x :

Position coordinate, m

t :

Time, s

x1 ~ x3:

Independent variables of the equations

s1 ~ s10:

Coefficients of the equations

o1 ~ o2:

Coefficients of the equations

T c :

Cold end temperature, °C

t h :

Time, h

N :

The node number at the cold end of the column

N 1 :

The largest node number in the unfrozen zone

a ~ h:

Coefficients of the equations

l ~ q:

Coefficients of the equations

a′ ~ f′:

Coefficients of the equations

H, I, J:

Coefficients of the equations

C s :

Mass specific heat of the medium particles

w :

Gravimetric content of the component

g a, g b, g c :

Shape factors

\( \overline{{C_{\text{v}} }} \) :

Apparent heat capacity

α1, β1, γ1 :

Coefficients of the equations

α2, β2 :

Coefficients of the equations

ρ :

Density, kg/m3

ΔS :

Change of ice content

Δt c :

Critical time step interval, s

Δx, δx :

Grid parameters for the ith control volume

ψ :

Soil suction potential, pa

θ :

Volumetric fraction of the component

λ :

Thermal conductivity, W/m/K

i:

Ice

u:

Unfrozen water

s:

Soil skeleton

a:

Air

0:

Initial value

w:

Water

d:

Dry

i :

The ith control volume.

n:

The n face of the control volume

s:

The s face of the control volume

*:

Evaluation at last iteration step

n :

Evaluation at the nth time step

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Acknowledgments

The work is funded by the National Natural Science Foundations of China, No. 50534040 and No. 40471021.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221008, People’s Republic of China

    Yang Zhou & Guoqing Zhou

  2. School of Architecture and Civil Engineering, China University of Mining and Technology, Xuzhou, 221008, People’s Republic of China

    Yang Zhou & Guoqing Zhou

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  1. Yang Zhou
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Correspondence to Yang Zhou.

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Zhou, Y., Zhou, G. Numerical simulation of coupled heat-fluid transport in freezing soils using finite volume method. Heat Mass Transfer 46, 989–998 (2010). https://doi.org/10.1007/s00231-010-0642-2

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