Analytical solution for the steady-state temperature field of a linear three-pipe freezing system under hydrodynamic conditions

Artificial ground freezing construction under hydrodynamic conditions generally requires a longer period for the formation of a freezing curtain, bringing unique challenges in the prediction of the temperature distribution. In this study, a simple analytical formula for the steady-state temperature field in the freezing of a linear three-pipe system was derived based on the effect of multiple pipes and the principle of potential function superposition. The “partition and subsection” method was adopted to assume the freezing front shape of any single frozen steady-state temperature field in this system under hydrodynamic conditions and to further determine the temperature influence range of a single freezing pipe. To account for the effect of multiple pipes, the “superposition length ratio” was proposed to quantify the mutual effect of adjacent freezing pipes. An empirical formula for the superposition length ratio varying with different freezing pipe spacings and groundwater flow velocities was also presented. Finally, combined with a hydrothermal coupling numerical model and a linear three-pipe freezing model test under different hydrodynamic conditions, the analytical results were compared with the numerical and experimental results. The comparison results showed that the analytical model can effectively predict the steady-state temperature field of the linear three-pipe system under different hydrodynamic conditions, thus providing a theoretical basis for artificial freezing design under hydrodynamic conditions.