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Building concentric tubes is one of biggest practical challenges in the construction of freeze-pipes of selective artificial ground freezing (S-AGF) applications for underground mines. In this study, the influence of tubes eccentricity on phase-front expansion (i.e., expansion of the frozen body) and energy consumption of S-AGF systems is analyzed. A 1 + 1D semi-conjugate model that solves two-phase transient energy conservation equation is derived based on the enthalpy method. The 1 + 1D model is first validated against experimental data and then verified with a fully conjugate model from our previous work. After that, the 1 + 1D model is extended to a field-scale of typical underground mines to examine the effect of freeze-pipe eccentricity. The results show that concentric freeze-pipes form the desired frozen ground volume 17% faster than eccentric freeze-pipes. Also, the geometrical profile of the phase-transition front of the frozen ground is found to be significantly influenced by the freeze-pipe eccentricity. Furthermore, in the passive zone, where S-AGF coolants are isolated from the ground to reduce energy consumption, freeze-pipe eccentricity can increase the coolant heat gain by 20%. This percentage can increase up to 200% if radiation heat transfer is minimized.

Solidification consists of three stages at macroscale: subcooling, freezing and cooling. Classical two-phase Stefan problems describe freezing (or melting) phenomenon initially not at the fusion temperature. Since these problems only define subcooling and freezing stages, an extension to characterize the cooling stage is required to complete solidification. However, the moving boundary in solid-liquid interface is highly nonlinear, and thus exact solution is restricted to certain domains and boundary conditions. It is therefore vital to develop approximate analytical solutions based on physically tangible assumptions, like a small Stefan number. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder. By assuming a small Stefan number, three temporal regimes and four spatial layers are considered in the asymptotic analysis. The results are compared with numerical method. Further, effects of Biot numbers are also investigated regarding interface motion and temperature profile.

Building concentric tubes is one of biggest practical challenges in the construction of freeze-pipes of artificial ground freezing (AGF) applications for deep underground mines. In this study, the influence of tubes eccentricity on phase-front expansion (i.e., expansion of the frozen body) and energy consumption of AGF systems is analyzed. A 1+1D semi-conjugate model that solves two-phase transient energy conservation equation is derived. The model is firstly validated against experimental data and then verified with a fully-conjugate model from the literature. After that, the model is extended to a field scale of typical deep underground mines to study freeze-pipe eccentricity. The results show that an eccentric freeze pipe can reduce the phase-front expansion by around 25%, as compared with a concentric one. Also, the geometrical profile of the phase-front is significantly influenced by the freeze-pipe eccentricity. Furthermore, in the passive zone, where AGF coolants are isolated from the ground to reduce energy consumption, freeze pipe eccentricity can increase the coolant heat gain by 10%. This percentage can increase up to 200% if radiation heat transfer is minimized.

Stefan problems provide one of the most fundamental frameworks to capture phase change processes. The problem in cylindrical coordinates can model outward solidification, which ensures the thermal design and operation associated with phase change materials (PCMs). However, this moving boundary problem is highly nonlinear in most circumstances. Exact solutions are restricted to certain domains and boundary conditions. It is therefore vital to develop approximate analytical solutions based on physically tangible assumptions, e.g., a small Stefan number. A great amount of work has been done in one-phase Stefan problems, where the initial state is at its fusion temperature, yet very few literature has considered two-phase problems particularly in cylindrical coordinates. This paper conducts an asymptotic analysis for a two-phase Stefan problem for outward solidification in a hollow cylinder, consisting of three temporal and four spatial scales. The results are compared with the enthalpy method that simulates a mushy region between two phases by numerical iterations, rather than a sharp interface in Stefan problems. After studying both mathematical models, the role of mushy-zone thickness in the enthalpy method is also unveiled. Moreover, a wide range of geometric ratios, thermophysical properties and Stefan numbers are selected from the literature to explore their effects on the developed model with regards to interface motion and temperature profile. It can be concluded that the asymptotic solution is capable of tracking the moving interface and evaluating the transient temperature for various geometric ratios and thermophysical properties in PCMs. The accuracy of this solution is found to be affected by Stefan number only, and the computational cost is much less compared with the enthalpy method and other numerical schemes.

In some artificial ground freezing (AGF) applications of civil or mining projects, only particular parts of the ground need to be frozen. Selective artificial ground freezing (S-AGF) is an AGF technique where a specific portion of the freeze pipe is insulated, usually by an air gap, to prevent any undesirable ground freezing. In this study, a laboratory scale experimental setup that mimics actual S-AGF systems has been established. The experimental rig is built in a fully controlled environment and equipped with advanced instrumentation. Additionally, a mathematical model coupling the flow of the coolant, air, and porous ground is developed by solving the conservation equations of mass, momentum, and energy. The mathematical model is then validated against the experimental measurements of the ground and outlet coolant temperatures. Moreover, the natural convection inside the air gap is further validated at higher Rayleigh numbers with an experimental study from the literature. The results indicate that the energy consumption of AGF plants can be significantly reduced by applying the S-AGF concept, as compared to convectional AGF systems. Also, it is found that the optimum air gap thickness, L opt , relates to the cavity height, H, and Rayleigh number, Ra H , as L opt ~ 2 HRa H - 1 / 4 .