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ABSTRACT
A lattice Boltzmann model is presented for simulating heat transfer with phase change in saturated soil. The model includes a quartet structure generation set for creating soil structure, double distribution functions for simulating temperature field evolution of soil particles and water, respectively, and an enthalpy-based method for tracing phase interface. The model is validated by two cases with analytical solutions. Then, we investigate the influence of porosity on freezing process in saturated sandy loam soil. The results demonstrate that porosity is the predominant factor when the location is far from the cold source; otherwise, thermal gradient is more important.
Nomenclature
| c | = | lattice speed |
| Cp | = | specific heat |
| ei | = | discrete velocity in the direction i in the lattice |
| f | = | liquid-phase fraction |
| g(r, t) | = | temperature distribution function |
| H | = | total enthalpy |
| k | = | thermal conductivity |
| L | = | characteristic length |
| La | = | latent heat of phase change |
| pc | = | initial distribution probability of solid phase |
| pi | = | growth probability in the direction i |
| r | = | lattice site |
| Sr | = | heat source term |
| Ste | = | Stefan number |
| T | = | temperature |
| t | = | time |
| Tf | = | phase change temperature |
| T0 | = | temperature of cold source |
| Ti | = | initial temperature |
| x | = | axis coordinate |
| Greek symbols | = | |
| α | = | thermal diffusivity |
| ΔH | = | the amount of heat released due to phase change |
| = | lattice space step | |
| = | lattice time step | |
| ε | = | porosity |
| ρ | = | density |
| τ | = | dimensionless relaxation time |
| ω | = | weight factor |
| Subscripts | = | |
| eff | = | effective variable |
| f | = | fluid |
| i | = | direction i in the lattice |
| l | = | liquid phase |
| ll | = | water in the liquid phase |
| ls | = | water in the solid phase |
| s | = | solid phase |
| Superscripts | = | |
| eq | = | equilibrium function |
| nm | = | growth of nth phase on the mth phase |
| * | = | dimensionless variable |
Nomenclature
| c | = | lattice speed |
| Cp | = | specific heat |
| ei | = | discrete velocity in the direction i in the lattice |
| f | = | liquid-phase fraction |
| g(r, t) | = | temperature distribution function |
| H | = | total enthalpy |
| k | = | thermal conductivity |
| L | = | characteristic length |
| La | = | latent heat of phase change |
| pc | = | initial distribution probability of solid phase |
| pi | = | growth probability in the direction i |
| r | = | lattice site |
| Sr | = | heat source term |
| Ste | = | Stefan number |
| T | = | temperature |
| t | = | time |
| Tf | = | phase change temperature |
| T0 | = | temperature of cold source |
| Ti | = | initial temperature |
| x | = | axis coordinate |
| Greek symbols | = | |
| α | = | thermal diffusivity |
| ΔH | = | the amount of heat released due to phase change |
| = | lattice space step | |
| = | lattice time step | |
| ε | = | porosity |
| ρ | = | density |
| τ | = | dimensionless relaxation time |
| ω | = | weight factor |
| Subscripts | = | |
| eff | = | effective variable |
| f | = | fluid |
| i | = | direction i in the lattice |
| l | = | liquid phase |
| ll | = | water in the liquid phase |
| ls | = | water in the solid phase |
| s | = | solid phase |
| Superscripts | = | |
| eq | = | equilibrium function |
| nm | = | growth of nth phase on the mth phase |
| * | = | dimensionless variable |