Mathematical modelling of the method for controlling selective water intake process in a stratified reservoir
Authors: Музаев Илларион Давидович , Харебов Константин Сергеевич , Музаев Нугзар Илларионович 
Published: August 2021

Разработана математическая модель способа управления селективным водозаборным процессом, когда вода забирается из водоема с вертикальной непрерывной температурной стратификацией. Предлагаемый способ обеспечивает снабжение холодной водой систем технического водоснабжения ТЭС, АЭС, предприятий. Составленная математическая модель представляет стационарную краевую задачу гидродинамики мало сжимаемой жидкости. Сжимаемость обусловлена вертикальной температурной стратификацией. В результате решения поставленной краевой задачи определены проекции вектора скорости, вычислена линия тока, приходящая к верхней кромке донного водозаборного окна. По мере увеличения скорости водозабора через вспомогательное окно упомянутая линия тока опускается вертикально вниз и температура забираемой через нижнее окно воды уменьшается. Составляющие вектора скорости движения воды в водоеме вычислены строгими аналитическими методами математической физики. Линии тока рассчитаны методами конечных разностей Рунге - Кутты.

The purpose of this study is to develop a mathematical model of a method for controlling selective water intake process, when water is taken from a reservoir with continuous vertical temperature stratification. The methodology for solving the problem implies that water is taken from the reservoir through a window, which is adjacent to the bottom of reservoir. The water intake process is controlled by varying the rate of water intake through an auxiliary window located above the main bottom window. As the speed of water intake through the auxiliary window increases, the thickness of the active layer of water entering the opening of the bottom window decreases. The average temperature of water taken through the bottom window is shown to decrease. The stationary boundary value problem for hydrodynamics of a slightly compressible fluid is chosen as a mathematical model. In the immediate vicinity of the vertical pressure head of the reservoir, the velocity field was calculated using the theory of the boundary layer. Further, a nonlinear boundary value problem was posed that simulates the position of the streamline coming to the upper edge of the lower water intake window. The boundary value problem is solved by the Runge - Kutta finite-difference method. A set of formulas for calculating the velocity field of fluid flow was then obtained. Originality/value: 1. A new original method for controlling selective water intake in a reservoir with continuous vertical temperature stratification has been developed and theoretically justified. The method allows taking water exclusively from the deep-cold layers of the reservoir. 2. The value of the method leads to a technical solution - the installation of an additional upper water intake window above the bottom intake one. This allows controlling the temperature of water used in technical water supply systems of thermal power stations, nuclear power plants and enterprises. 3. An adequate mathematical model for the proposed method was developed and solved. Based on this model, a set of calculation formulas that allow controlling the temperature of the extracted water is obtained.