Analytical Solution for the Steady‐State Temperature Field of Three‐Pipe Liquid Nitrogen Freezing Under High Seepage‐Flow Conditions

ABSTRACT The artificial ground freezing (AGF) method is frequently affected by groundwater seepage. Due to the combined effects of convective heat transfer by water flow and conductive heat transfer from the cold source, the artificial freezing curtain in a seepage field exhibits significant asymmetry. Most existing studies focus on brine freezing, whereas the ultra‐low temperature properties of liquid nitrogen make it suitable for freezing projects in high‐seepage environments. This study investigates the temperature field of three‐pipe liquid nitrogen freezing. An equivalent partitioning and segmentation method is employed to determine the shape of the freezing curtain, an analytical solution for the steady‐state temperature field of a three‐pipe liquid nitrogen freezing curtain under high seepage‐flow is derived. Through model tests and numerical simulations, the evolution of the three‐pipe liquid nitrogen freezing temperature field under varying seepage conditions is analyzed, and the validity of the formula is verified. The results indicate that the calculated freezing temperature aligns well with both experimental and numerical results, confirming the validity of the analytical solution through model testing. A high‐flow environment enhances heat transfer efficiency at the solid surface. As the flow rate increases, heat transfer efficiency improves, and the asymmetry of the freezing curtain becomes more pronounced. In multi‐pipe freezing, the “adjacent pipe effect” occurs. When adjacent freezing fronts contract to the critical threshold ( L c ), the freezing front expands more rapidly, shortening the intersection time of the freezing curtain. These findings provide valuable insights for designing liquid nitrogen artificial freezing systems in high seepage‐flow.