Method of parametric optimization of hydraulic structures for subzero temperatures

Abstract

A method for optimizing design and geometric parameters using a "simplified" simulation of the water-cooling process is presented. This method allows solving the issues of operational manufacturability in the aspect of creating energy- and resource-saving constructions of water storage tanks. In the study to determine the size of underground and above-ground parts of the water storage tank the criterion of heat loss minimization is accepted and the mathematical model of water heat exchange with the ground under the condition of its homogeneity and stationarity of the thermal regime is compiled. The relationship between the height and the radius of the underground part at the minimum value of the heat transfer coefficient from water to the ground through the metal wall is established. Using the heat balance equation, an analytical expression is found that determines the aboveground fluid temperature for any instant of time. On the basis of the theory of differential calculus the condition of minimality of the cooling rate of water, which gives up heat through the side walls to the environment and air space under the roof of the vessel, was revealed, which made possible to optimize the size of its above-ground part. The relationship of the radius and the total volume of the water holding capacity was determined for the average values of ambient temperature and wind speed recorded in the region of the research. The developed algorithm of the method of "simplified" modeling and its representation in the form of a block diagram can be implemented at digitalization of calculation-analytical procedures for selection of structural and geometrical parameters of the vessel according to the criterion of minimum heat losses. The functions of the radius and the height of the underground and above-ground parts of the vessel from the argument of its total volume are graphically illustrated.