Effect of Freeze Pipe Eccentricity in Artificial Ground Freezing Applications

Artificial ground freezing (AGF) is a reliable geotechnical support technique that has been widely used in numerous mining and civil applications. There are plenty of mathematical models that can be found in the literature to better understand AGF systems. However, there are only a few fully conjugate heat transfer models, which study the interaction between the freeze pipe and the ground, of typical (AGF) applications. These fully conjugate models are often computationally expensive due to multiple reasons. First, the mesh count is substantially increased throughout the freeze pipe to accurately capture the sharp temperature and velocity variations (especially near the walls). Furthermore, a small time step is often adapted to ensure the stability of the numerical algorithm. In addition, the large computational domain of the ground (several hundreds of meters) and long operational time of AGF applications (several years) result in a significant increase in the computational cost of AGF mathematical models.

In this study, we present a new computationally efficient hybrid mathematical model that couples analytical and numerical solutions to reduce the computational costs of fully conjugate AGF models. The hybrid model is based on a 1+1D space marching algorithm applied over a discretized axisymmetric 2-D domain. The mathematical model solves 1D transient energy, momentum, and continuity conservation equations within the freeze pipe and the ground in the radial direction along with transient spatial correction in the axial direction. In this hybrid model, numerous analytical solutions were obtained and embedded in the solution algorithm to reduce the computational costs associated with numerical solution of the Navier Stokes equations. In fact, numerical solutions were only used to solve the two-phase freezing problem within the ground domain because of the lack of accurate solutions of the two phase Stefan problem with heat flux boundaries.

After developing the hybrid model, its accuracy and computational efficiency were investigated. First, the hybrid model was validated against experimental data. Then the model was further verified against other 2-D fully conjugate numerical models available in the literature. The validation and verification processes confirmed the high accuracy of the hybrid model. After that, the computational cost of the hybrid model was compared with that of the numerical fully conjugate model. The results show that the computational cost of the hybrid model is much lower, as compared with the fully conjugate numerical model. Thus, we were able to develop a reliable fully conjugate AGF model that is computationally efficient, proving a potential for field application.