Advertisement

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

  • Yiran Hu
  • Donghao Zuo
  • Yaning ZhangEmail author
  • Fei Xu
  • Bingxi LiEmail author
  • Shuang Liang
Article
  • 38 Downloads

Abstract

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.

Keywords

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

List of symbols

cs

Sound speed

Cp

Specific heat (J kg−1 K−1)

e

Discrete velocity

f

Density distribution function

fflu

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

Radius

S

Specific surface area (m−1)

t

Time (s)

T

Temperature (°C)

u

Velocity vector of fluid (m s−1)

Greek symbols

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

Porosity

τ

Dimensionless relaxation time

ω

Mass coefficient

Ω

Collision term

Subscripts

b

Boundary

f

Fluid

l

Liquid phase

m

Freezing

s

Solid phase

0

Initial state

i

Lattice velocity direction

eq

Equilibrium state

ref

Reference

liq

Liquidus

pm

Porous medium

sol

Solidus

Notes

Acknowledgements

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).

References

  1. 1.
    Ingham DB, Pop I. Transport phenomena in porous media III. Amsterdam: Elsevier; 2005.Google Scholar
  2. 2.
    Peter V. Emerging topics in heat and mass transfer in porous media: from bioengineering and microelectronics to nanotechnology. Berlin: Springer; 2008.Google Scholar
  3. 3.
    Li S, Xu F. Numerical simulation of seepage and heat transfer in saturated soils based on lattice boltzmann method. J Therm Sci Technol. 2015;14(6):445–55.Google Scholar
  4. 4.
    Wang M, Wang J, Pan N, Chen S. Mesoscopic predictions of the effective thermal conductivity for microscale random porous media. Phys Rev E. 2007;75(3):036702.CrossRefGoogle Scholar
  5. 5.
    Song W, Zhang Y, Li B, Fan X. A lattice Boltzmann model for heat and mass transfer phenomena with phase transformations in unsaturated soil during freezing process. Int J Heat Mass Transf. 2016;94:29–38.CrossRefGoogle Scholar
  6. 6.
    Hong K, Gao Y, Ullah A, Xu F, Xiong Q, Lorenzini G. Multi-scale CFD modeling of gas-solid bubbling fluidization accounting for sub-grid information. Adv Powder Technol. 2018;29(3):488–98.CrossRefGoogle Scholar
  7. 7.
    Xiong Q, Yang Y, Xu F, Pan Y, Zhang J, Hong K, Lorenzini G, Wang S. Overview of computational fluid dynamics simulation of reactor-scale biomass pyrolysis. ACS Sustain Chem Eng. 2017;5(4):2783–98.CrossRefGoogle Scholar
  8. 8.
    Xiong Q, Aramideh S, Passalacqua A, Kong S. Characterizing effects of the shape of screw conveyors in gas–solid fluidized beds using advanced numerical models. J Heat Transf. 2015;137(6):061008.CrossRefGoogle Scholar
  9. 9.
    Xiong Q, Xu F, Ramirez E, Pannala S, Daw CS. Modeling the impact of bubbling bed hydrodynamics on tar yield and its fluctuations during biomass fast pyrolysis. Fuel. 2016;164:11–7.CrossRefGoogle Scholar
  10. 10.
    Uriel F, Hasslacher B, Yves P. Lattice-gas automata for the Navier–Stokes equation. Phys Rev Lett. 1986;56(14):1505–8.CrossRefGoogle Scholar
  11. 11.
    Kang QJ, Lichtner PC, Zhang DX. Lattice Boltzmann pore-scale model for multicomponent reactive transport in porous media. J Geophys Res Solid Earth. 2006; 111(B5).CrossRefGoogle Scholar
  12. 12.
    Xiong Q, Kong SC. High-resolution particle-scale simulation of biomass pyrolysis. ACS Sustain Chem Eng. 2016;4(10):5456–61.CrossRefGoogle Scholar
  13. 13.
    Xu F, Zhang Y, Jin G, Li B, Kim YS, Xie G, Fu Z. Three phase heat and mass transfer model for unsaturated soil freezing process: part 1—model development. Open Phys. 2018;16(1):75–83.CrossRefGoogle Scholar
  14. 14.
    Zhang Y, Xu F, Li B, Kim Y, Zhao W, Xie G, Fu Z. Three phase heat and mass transfer model for unsaturated soil freezing process: part 2—model validation. Open Phys. 2018;16(1):84–92.CrossRefGoogle Scholar
  15. 15.
    Huber C, Bachmann O, Manga M. Homogenization processes in silicic magma chambers by stirring and mushification (latent heat buffering). Earth Planet Sci Lett. 2009;283(1–4):38–47.CrossRefGoogle Scholar
  16. 16.
    Huang RZ, Wu HY, Cheng P. A new lattice Boltzmann model for solid-liquid phase change. Int J Heat Mass Transf. 2013;59:295–301.CrossRefGoogle Scholar
  17. 17.
    Li D, Ren QL, Tong ZX, He YL. Lattice Boltzmann models for axisymmetric solid-liquid phase change. Int J Heat Mass Transf. 2017;112:795–804.CrossRefGoogle Scholar
  18. 18.
    Lin Q, Wang SG, Ma ZJ, Wang JH, Zhang TF. Lattice Boltzmann simulation of flow and heat transfer evolution inside encapsulated phase change materials due to natural convection melting. Chem Eng Sci. 2018;189:154–64.CrossRefGoogle Scholar
  19. 19.
    Chakraborty S, Chatterjee D. An enthalpy-based hybrid lattice-Boltzmann method for modelling solid-liquid phase transition in the presence of convective transport. J Fluid Mech. 2007;592:155–75.CrossRefGoogle Scholar
  20. 20.
    Huber C, Parmigiani A, Chopard B, Manga M, Bachmann O. Lattice Boltzmann model for melting with natural convection. Int J Heat Fluid Flow. 2008;29(5):1469–80.CrossRefGoogle Scholar
  21. 21.
    Jany P, Bejan A. Scaling theory of melting with natural convection in an enclosure. Int J Heat Mass Transf. 1988;31(6):1221–35.CrossRefGoogle Scholar
  22. 22.
    Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E. 1993;47(3):1815–9.CrossRefGoogle Scholar
  23. 23.
    Shan X, Chen H. Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Phys Rev E. 1994;49(4):2941–8.CrossRefGoogle Scholar
  24. 24.
    Shan X, Doolen G. Multicomponent lattice-Boltzmann model with interparticle interaction. J Stat Phys. 1995;81(1–2):379–93.CrossRefGoogle Scholar
  25. 25.
    Shan X, Doolen G. Diffusion in a multicomponent lattice Boltzmann equation model. Phys Rev E. 1996;54(4):3614–20.CrossRefGoogle Scholar
  26. 26.
    Gross EP, Krook M. Model for collision processes in gases: small-amplitude oscillations of charged two-component systems. Phys Rev. 1956;102(102):593–604.CrossRefGoogle Scholar
  27. 27.
    He XY, Luo LS. Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys Rev E. 1997;56(6):6811–7.CrossRefGoogle Scholar
  28. 28.
    Luo LS. Unified theory of lattice boltzmann models for nonideal gases. Phys Rev Lett. 1998;81(8):1618–21.CrossRefGoogle Scholar
  29. 29.
    Guo Z, Zheng C, Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys Rev E. 2002;65(4):046308.CrossRefGoogle Scholar
  30. 30.
    Solomon A. Some remarks on the Stefan problem. Math Comput. 1966;20(95):347–60.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.School of Energy Science and EngineeringHarbin Institute of Technology (HIT)HarbinChina

Personalised recommendations