Simulation on underground pipe-soil heat exchange structure deformation due to frost heave

Abstract: The research background of this paper is the ground source heat pump (GSHP) technology applied in the field of agriculture energy conservation. The typical application is the GSHP used in greenhouse. However, the operating temperature of ground heat exchange pipe usually sustains below 0°C, when the GSHP runs during the winter night in cold regions. The sustaining low temperature can lead to pore water freeze and volume expansion in soil, which is called frost heave. In this paper, numerical simulation study was conducted to investigate the deformation of pipe-soil heat exchange structure due to frost heave. The numerical model, on the basis of porosity rate function, frozen soil constitutive equation, water content equation and phase change heat transfer theory, was built on the simulation platform ABAQUS and thermal-mechanical coupled subroutine compiled in Fortran. The semicircle soil computational domain and U-pipe were adopted in 2-D geometrical model. Based on the assumptions of this model, its application was restricted to: 1) The initial soil is homogeneous and saturated; 2) The difference of soils inside and outside borehole is neglected; 3) The internal and external pressure of the pipe is uniform; 4) The heat transfer takes place by conduction only; 5) The operational mode of pipe is cooling or constant temperature. This numerical model was verified by frost heave experiment, and the verification included mainly soil freezing temperature field and pipe deformation strain. The result of verification showed that the temperature of center point in the freezing area had a maximum absolute error of 0.6°C, the freezing radius had a maximum relative error of 9.1%, and the pipe strains had a maximum relative error of 16.4%. This numerical model could be applied for the study of pipe-soil structure frost heave and deformation. By means of this model, the characteristics of soil stress and pipe deformation during soil frost heave were analyzed. The results showed that elliptical deformation appeared in the pipe cross-sections under the frost heave force, which manifested as the decreasing diameter in X-axis and the increasing diameter in Y-axis. The soil stress and pipes' elliptical deformation increased with the extension of freezing area, under 1°C temperature difference between outlet and inlet pipe, the deformation of outlet pipe was greater than inlet pipe. Meanwhile, the deformation caused the pipe cross-sections' circulating area gradual decrease, and the decrease rate showed linear increase with the extension of freezing area. Moreover, the influence of different pipe cooling rate (0.1°C/h, 0.2°C/h, 0.3°C/h) were also investigated. For almost the same freezing range, the lower cooling rate of heat exchange pipe could lead to larger soil stress and pipe deformation. It can be found from the simulation, when the soil freezing diameter increased to 365 mm, the circulating area decrease rates of inlet pipe were about 3.5% in the 3 different cooling rate, and the circulating area decrease rates of outlet pipe were 4.6%, 4% and 3.8%, respectively, in cooling rate of 0.1°C/h, 0.2°C/h and 0.3°C/h. By contrast, the cooling rate showed almost no influence on the inlet pipe deformation, but an obvious influence on the outlet pipe deformation. In order to reduce the impact on the pipe cross-sections for the same heat exchange, it is reasonable to adopt a rapid cooling mode.