A numerical study of solidification and natural convection during cryogenic pipe freezing

Abstract

sections of pipeline; the pipe is cooled externally over a short length, freezing the liquid inside the pipe and forming a solid plug. The effect of natural convection on freezing in a vertical pipe containing water was investigated by modelling the process. As a first stage, the literature was reviewed and the results from previous experimental research for freezing in vertical pipes were summarised.
An analytical model was developed, assuming one-dimensional solidification and using an integral solution for the heat transfer coefficient for laminar natural convection adjacent to a heated vertical flat plate. The results obtained, assuming no decay in the water temperature during freezing, displayed good qualitative agreement with the experimental data. A method for defining the effect of convection on freezing in terms of the pipe radius and bulk temperature was proposed. A simple criterion based on the Grashof number for the temperature at which turbulent mixing becomes sufficient to halt freezing was extracted from experimental results. The formulation of a simple model of the processes which control the bulk temperature decay was undertaken and this was incorporated into the freezing model. The poor agreement with measurements of bulk temperature demonstrated the need for an improved understanding of the mixing processes.
A numerical model of pipe freezing was developed using the finite volume methodology, with the SIMPLER algorithm to predict convection, and the enthalpy method used to include solidification. A fixed (non-transforming) grid was used and the buoyancy-driven flows were assumed to be laminar. The numerical model was validated against experimental data and the dependence on numerical factors such as grid density was investigated. The development of the buoyancy-driven flows in the absence of freezing was studied and it was found that a complex mixing region forms which controls the bulk temperature inside the freezing zone. This flow development is dependent on the initial temperature and the pipe diameter, and has a negligible effect on the bulk temperature in pipes over a critical size. Plug formation was included in the model and the effects of varying the initial water temperature, the length of the pipe and the 'freezing' boundary condition were investigated. Interaction between the downwards boundary layer and the upwards core flow was noted at the plug neck, with the boundary layer becoming entrained in the core flow at the neck. The water above the neck becomes increasingly isolated from that below the neck, causing a decrease in bulk temperature and, if convection is sufficient to affect plug formation, neck migration up the plug. This agreed with experimental observations. The accuracy of the bulk temperature prediction was found to depend on the length of pipe that was modelled; this was demanding on computer resources and an open' bottom boundary condition was developed as a compromise, This allowed flow into and out of the domain and also made it possible to specify the bulk temperature. The results obtained using the different modelling approaches were analysed and the limitations of the methods discussed. Recommendations for further development were made, A series of criteria were defined (accounting for the effect of convection, turbulence and bulk temperature decay) to indicate which modelling approach to apply depending on pipe diameter and initial water temperature.

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