Fractal Study Of Soil Thermal Conductivity Outside Buried Pipe

The ground-coupled heat pump with buried pipe takes out the heat from the soil in the form of buried pipe heat exchange.It is known as one of the most promising renewable energy application technologies in the 21st century.For a certain ground-coupled heat pump system,the thermal conductivity of the soil directly affects the heat transfer efficiency of the buried pipe,and then affects the economy and energy saving of the ground-coupled heat pump system.Therefore,the main research object of this dissertation is the thermal conductivity of the soil outside the buried pipeBecause of the complexity of the soil structure,the traditional Euclidean geometry is difficult to accurately describe the inner pore distribution.Based on fractal theory,we can get the scaling relationship to quantitatively describe the pore size and pore bending.Using two physical parameters,pore size fractal dimension D_f and tortuosity fractal dimension _TD,to represent the self-similarity of soil internal structure,will be helpful to analyze the soil thermal conductivity better.Beginning with Laplace equation of saturated soil medium（two-phase）,the thermal conductivity of soil which consists of solid particles and air（or water）of saturated state was analyzed in this dissertation.Fourier law is firstly analyzed as a whole,which is divided into solid particle part and fluid part,and the variant form of Fourier law is obtained.Through the limited relevant boundary conditions,the temperature distribution field was obtained.By using the fractal theory,further the expression of soil thermal conductivity was derived.This model could predict the thermal conductivity of saturated soil.And comparing with existing experimental data in the literatures,its validity was verified.The results show that when R_min,sR_max,_s is smaller,the fractal dimension D_fs of solid particles is larger,and the dimensionless effective thermal conductivity k_e⁺is larger.In other words,the dimensionless effective thermal conductivity k_e⁺is positively correlated with the fractal dimension of solid particlesD_fs.The dimensionless effective thermal conductivity k_e⁺is negatively correlated with porosity（?）.With the increase of the ratio of thermal conductivity between solid and fluid phase k_s k_f,the dimensionless effective thermal conductivity k_e⁺increases at constant porosity,which shows that there is a positively correlation between the two.For unsaturated soil medium（three-phase）,this dissertation analyzes the soil thermal conductivity under the unsaturated state composed of solid,liquid（such as water）and gas（such as air）.The pore is the fractal phase,and the solid is the non-fractal phase.Focuses on the influence of internal structure of soil effective coefficient of thermal conductivity,considering the different pore sizes and the tortuosity of pores in the soil,the scaling relationship is given by the fractal dimension of pores and the fractal dimension of pore tortuosity in the fractal theory,and the critical diameter of reaction liquid saturation,thus establish the capillary solid-liquid-gas phase parallel model.The mathematical expression of the effective thermal conductivity of three-phase soil porous media is derived and the influence of related factors on it is analyzed.The results show that the dimensionless effective thermal conductivity of three-phase porous media increases with the increase of liquid saturation,but decreases with the increase of porosity.That is to say,the effective thermal conductivity of three-phase porous media is positively correlated with liquid saturation,and negatively correlated with porosity.Secondly,pore structure has a significant effect on the effective thermal conductivity of three-phase porous media.Under the condition of constant porosity,the dimensionless effective thermal conductivity of three-phase porous media decreases with the increase of fractal dimension of pores and tortuosity.Thermal conductivity of soil outside the buried pipe is the main research object in this dissertation.And the influencing factors of the thermal conductivity of soil under saturated and unsaturated conditions were analyzed.Due to the complexity of soil composition and structure,it is difficult to accurately determine the thermal conductivity.Based on the fractal theory and the properties of soil as porous medium,we analyzed the saturated and unsaturated thermal conductivity of soil with dimensions different from Euclidean geometry,and then established a fractal prediction model of thermal conductivity of porous media.The heat transfer mechanism of soil outside the buried pipe was analyzed according to the results.The study of soil thermal conductivity is helpful to strengthen the heat transfer of buried pipe,and also can promote the improvement of the design of buried pipe heat exchanger,which provides a foundation for the better use of ground-coupled heat pump system.