Simulation of cooling of aboveground water pipeline with heat insulation

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Aboveground water pipelines are often more preferred in the organization of water supply systems in permafrost and low ambient temperatures conditions. If the water movement in such pipeline stops, there is a risk of cooling and subsequent freezing of the liquid. The purpose of this work is to study the dynamics of the cooling process of an aboveground water pipeline with heat insulation and to calculate the cooling time of water to the freezing temperature. To build a mathematical model of the cooling process, the method of averaging the equations of hydrodynamics and thermal conductivity is used. The model equations do not contain any assumptions about the nature of the water movement in the pipeline during the cooling process. The possibility of using the equations of the model in a quasi-stationary form is justified. The range of task parameter values at which this approximation applies is determined. The possibilities of applying different boundary conditions on the surface of the water pipeline are also considered. In the quasi-stationary approximation, a dependence on the time of the average water temperature in the pipeline was found. An explicit formula is also obtained for calculating the cooling time of water to the freezing temperature. The criteria for the applicability of the obtained formulas have been established. For a wide range of parameters, water cooling time is calculated from the specified initial temperature to the freezing temperature. Ranges of values of parameters at which increase of thickness of heat insulator layer and increase of initial water temperature lead to significant increase of water cooling time in pipeline are determined.