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Article information
2022 , Volume 27, ¹ 6, p.33-44
Muzaev I.D., Kharebov K.S., Muzaev N.I.
On an initial boundary value problem that models an effective method of water intake from a cold layer of a stratified reservoir
The purpose of the paper is to formulate and solve a contact initial boundary value problem of mathematical physics which models a selective water intake process in a two-layer stratified reservoir, provided that water is taken from it through two pipes connected to different layers and located one above another. The problem is solved analytically by the method of two-fold trigonometric Fourier series involving the integral Laplace transform and operational calculus methods for finding originals from computed images. A set of formulas for calculating the interface of layers in the process of water intake through both pipes is obtained. In addition to the geometric dimensions of the reservoir and intake pipes, the thicknesses and densities of water in the layers, they contain the flow rate (speeds) of the water taken through the lower main pipe and the upper auxiliary pipe. The upper pipe is designed to provide selective water intake through the lower pipe — so that the water intake passes exclusively from the lower bottom cold layer of the reservoir. In addition, as a result of the inclusion of the upper auxiliary pipe, the difference in average velocities in the water layers decreases sharply and thereby the interval of variation of the Richardson number sharply expands, in which the criterion condition for the stability of the flow of different density layers of water is fulfilled. The collected water is used for the needs of cooling the fuel elements of various industrial enterprises, including thermal and nuclear power plants.
[full text]
Keywords: initial boundary value problem, stratified reservoir, selective water intake process, the critical value of the speed and flow rate of the water taken, the integral Laplace transform, the image and the original of the function, the Richardson number
doi: 10.25743/ICT.2022.27.6.004
Author(s):
Muzaev Illarion Davidovich
Dr. , Professor
Position: General Scientist
Office: Geophysical Institute of Vladikavkaz Scientific Center of Russian Academy of Scienties
Address: 362002, Russia, Vladikavkaz, 93a, Markov St.
Phone Office: (8672)76-40-31
E-mail: illarion.muzaev@yandex.ru
SPIN-code: 9346-8949Kharebov Konstantin Sergeevich
PhD. , Associate Professor
Position: Leading research officer
Office: Geophysical Institute of Vladikavkaz Scientific Center of Russian Academy of Scienties
Address: 362002, Russia, Vladikavkaz, 93a, Markov St.
Phone Office: (8672)76-40-31
E-mail: kosta7x7@yandex.ru
SPIN-code: 4564-8949Muzaev Nugzar Illarionovich
Position: Junior Research Scientist
Office: Center of Geophysical Investigations of Vladikavkaz Scientific Center of the Russian Academy of Sciences and the Government of Republic of North Ossetia -Alania
Address: 362002, Russia, Vladikavkaz, 93a Markov St.,
Phone Office: (8672)76-40-31
E-mail: muzaevn@yandex.ru
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Bibliography link:
Muzaev I.D., Kharebov K.S., Muzaev N.I. On an initial boundary value problem that models an effective method of water intake from a cold layer of a stratified reservoir // Computational technologies. 2022. V. 27. ¹ 6. P. 33-44
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