Thermal performances of saturated porous soil during freezing process using lattice Boltzmann method


A stochastic growth method for generating the porous soil structure is proposed, and an enthalpy-based lattice Boltzmann phase transition model is introduced. Thermal performance of phase transition in saturated porous soil during freezing is investigated. The effects of thermal diffusivity ratio of porous medium to fluid, difference in specific heat capacity between liquid and solid phase, and porosity of porous medium are investigated. The results show that higher thermal diffusivity ratio will promote the low-temperature propagation and phase interface movement while higher specific heat capacity difference and porosity will hinder the temperature propagation and phase transition from liquid to solid. The solid–liquid interface moves from 39 to 51 mm with the ratio increasing from 2 to 5; the interface position decreases from 51 to 26 mm with the difference increasing from 2000 to 26,000; the interface moves from 59 to 47 mm when the porosity increases from 0.2 to 0.8.

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c s :

Sound speed

C p :

Specific heat (J kg−1 K−1)

e :

Discrete velocity

f :

Density distribution function

f flu :

Fluid volume fraction in calculation unit

f :

Body force per unit mass

F :

Force (N)

g :

Temperature distribution function

g :

Gravitational acceleration (m s−2)

h :

Enthalpy distribution function

H :

Total enthalpy

ΔH :

Latent heat in calculation unit

L :

Latent heat of the fluid

p :

Pressure (Pa)

q :

Heat source term

R :


S :

Specific surface area (m−1)

t :

Time (s)

T :

Temperature (°C)

u :

Velocity vector of fluid (m s−1)

β :

Volume expansivity

η :

Thermal diffusivity

λ :

Thermal conductivity (W m−1 K−1)

μ :

Dynamic viscosity (N s m−2)

ν :

Kinetic viscosity

ρ :

Density (kg m−3)

ϕ :


τ :

Dimensionless relaxation time

ω :

Mass coefficient

Ω :

Collision term






Liquid phase




Solid phase


Initial state

i :

Lattice velocity direction


Equilibrium state






Porous medium




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This study is supported by Natural Science Foundation of China (Grant No. 51776049) and Special Foundation for Major Program of Civil Aviation Administration of China (Grant No. MB20140066).

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Correspondence to Yaning Zhang or Bingxi Li.

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Hu, Y., Zuo, D., Zhang, Y. et al. Thermal performances of saturated porous soil during freezing process using lattice Boltzmann method. J Therm Anal Calorim 141, 1529–1541 (2020).

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  • Stochastic growth method
  • Lattice Boltzmann method
  • Thermal diffusivity
  • Specific heat capacity
  • Porosity