An adjusted analytical solution for thermal design in artificial ground freezing

Artificial ground freezing is a widely used, reliable method for excavation in water-bearing ground. The questions posed in the thermal design of ground freezing projects require solving moving boundary (Stefan) problems. Approximate analytical solutions, such as the ones by St¨ ander1 and Sanger and Sayles,2 have been developed for thermal engineering design and are used by practitioners across the industry. For instance, Sanger & Sayles’ solution is widely used for the single-freeze-pipe problem, but it has proven to be of limited accuracy.3 In the present paper, an adjustment to this formula is proposed based on the re-evaluation of their empirical assumption that the ratio between the temperature penetration depth and the phase-change radius equals a constant value of 3 regardless the conditions. A sensitivity study is performed using a verified numerical model as a benchmark to study several problems with different initial and boundary conditions (initial, phase change and freeze pipe temperatures) and thermal properties of the ground (water content, thermal conductivity and heat capacity). This is done for the freezing times of 10 and 365 days, in order to consider the potential change of the ratio with the freezing time. In this way, a calibrated formula is proposed to find appropriate values of this ratio and a suitable adjustment to Sanger & Sayles’ solution is determined. Adjusting Sanger & Sayles’ solution in this manner, a significantly higher and more consistent accuracy is achieved for different boundary and initial conditions. This accuracy improvement was checked for real conditions from an engineering project, which shows that the adjustment can be useful for thermal problems in engineering design of ground freezing

Approximate analytical and numerical solutions for a two-dimensional Stefan problem

This paper proposes an approximate analytical and a numerical solution method to a two-dimensional heat conduction problem in which a liquid becomes solidified by heat transfer to a planar mold surface by using a linear perturbation method. It is assumed that the cooling rate is perturbed by a small spatially sinusoidal heat flux at the shell-mold interface. This leads to a corresponding undulation of the solidified shell thickness. Approximate analytical results are obtained for the solid/melt moving interface as a function of time and for the temperature field in the shell. The approximate analytical solution is compared with a numerical solution, and a very good agreement has been found. A limiting analytical solution in which diffusivity of the solidified shell material is assumed to be infinitely large is also obtained, and compared with the numerical predictions to establish the validity of the model and the numerical approach. It is demonstrated that solidified shell materials with higher thermal diffusivities may result in irregular growth of the shell thickness which, generally, causes cracking near the surface.King Saud Universit

Improved engineering solutions for thermal design of artificial ground freezing

La congelación artificial del terreno es un método utilizado en ingeniería civil y minera. Al congelar el terreno, su resistencia aumenta y se impermeabiliza. Cálculos térmicos con cambio de fase son necesarios para diseñar estos trabajos. Estos cálculos se pueden realizar con modelos numéricos o soluciones analíticas. En esta tesis se han investigado los parámetros que influyen en la precisión de los métodos numéricos mediante un análisis de sensibilidad y se han condensado los resultados en un código de buenas prácticas. Además, se ha utilizado un modelo numérico verificado para investigar la precisión de las soluciones analíticas. Se ha concluido que la solución más precisa para el problema de una tubería de congelación es la de Ständer. También se ha ajustado la solución analítica de Sanger & Sayles para una tubería de congelación, que presenta una mejora de precisión significativa. Finalmente, se han utilizado datos experimentales para confirmar las conclusiones.Artificial ground freezing is a method used in civil and mining engineering for ground stabilisation and groundwater cut-off. In order to design these works, thermal calculations with phase change are required, which can be performed by numerical models or analytical solutions. In this thesis, the parameters which influence the accuracy of numerical methods were investigated by means of a sensitivity analysis and the results were condensed in a code of good practice. A verified numerical model was used to investigate the accuracy of analytical solutions. It was concluded that the most accurate solution for the single freeze pipe problem is Ständer’s. Additionally, Sanger & Sayles’ solution for the single freeze pipe has been adjusted, obtaining a significant accuracy improvement. Finally, experimental data were used to confirm the conclusions