|
Article information
2020 , Volume 25, ¹ 2, p.36-49
Muzaev I.D., Kharebov K.S., Muzaev N.I.
Mathematical modelling of the selective intake process from the interior volume in a three-layer stratified reservoir
The purpose of this work is to carry out mathematical modelling of selective water intake process in a three-layer stratified reservoir, when the water is taken from the interior volume of the intermediate layer of the reservoir. In the methodology for solving the problem, the water intake from the interior volume of the intermediate layer is modelled as a finite flow rate drain of fluid trough an infinitely thin layer. The contact initial-boundary value problem of the theory of surface and internal gravitational waves in an ideal incompressible fluid is used as a mathematical model of the water intake process. As a result we obtain a system of calculation formulas for estimation of the diameter of water intake pipe and the flow rate through it. The depth mark of the end of the water intake pipe was calculated. Originality/value: 1. The boundary value problem simulating a selective water intake process from the internal volume of the intermediate layer of a three-layer stratified reservoir was formulated and solved. 2. On the basis of the obtained set of formulas, computer experiments were performed and thus the regularities of the influence of the above external input parameters on the process were established. 3. The choice of these parameters provides selective intake exclusively from the intermediate layer, where the water is cleaner than in the lower layer and colder in summer than in the upper layer.
[full text]
Keywords: stratified reservoir, selective water intake, contact initial boundary value problem, theories of surface and internal gravitational waves, Laplace integral transformation, ideal incompressible fluid
doi: 10.25743/ICT.2020.25.2.004
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
References:
[1]. Averkiev A.G., Makarov I.I., Sinotin V.I. Besplotinnye vodozabornye sooruzheniya [Damless water intake structures]. Moscow; Leningrad: Energiya; 1969: 164. (In Russ.)
[2]. Bol’shakov V.A. Spravochnik po gidravlike [Reference book on hydraulics]. Kiev: Vyshcha Shkola; 1977: 223–225. (In Russ.)
[3]. Sokolov A.S., Makarov I.I., Kravets V.I., Kravets, Filippova Z.R. Metodicheskie ukazaniya po tekhnologicheskim raschetam vodoemov-okhladiteley [Guidance on technological calculations of water coolers]. SPb.: VNIIG; 2003: 116. (In Russ.)
[4]. Craya A. Recherches theoriques sur l’ecoulement de couches superposees de fluides de densites differentes. La Houille Blanche. 1949; (1):44–55. DOI: 10.1051/lhb/1949017
[5]. Harleman D.R.F., Stozenbach K.D. Fluid mechanics of heat disposal from power generation. Annual Review of Fluid Mechanics. 1972; (4):22–31.
[6]. Muzaev I.D., Kharebov C.S., Muzaev N.I. Automation of theoretical design for selective water intake devices. Computational Technologies. 2016; 21(4):99–110. (In Russ.)
[7]. Belolipetskiy V.M., Kostyuk V.Yu., Ershov Yu.I. Matematicheskoe modelirovanie techeniy stratifitsirovannoy zhidkosti [Mathematical modelling of stratified fluid flows]. Novosibirsk: Nauka; 1991: 176.
[8]. Muzaev I.D., Muzaev N.I. Matematicheskoe modelirovanie dlya sistemy avtomatizatsii proektirovaniya (SAPR) selektivnykh vodozabornykh ustroystv [Mathematical simulation for automation of system design (CAD) for selective water-intake devices]. Matematicheskiy forum “Issledovanie po differentsial’nym uravneniyam, matematicheskomu modelirovaniyu i problemam matematicheskogo obrazovaniya”. Vladikavkaz: YuMI VNTs RAN i RSO-A; 2014: 8(2):202–211. (In Russ.)
[9]. Sretenskiy L.N. Teoriya volnovykh dvizheniy zhidkosti [Theory of wave motions of a fluid]. Moscow: Nauka; 1977: 815. (In Russ.)
[10]. Lamb G. Gidrodinamika [Hydrodynamics]. Moscow; Leningrad: Gosudarstvennoe izdatel’stvo tekhnikoteoreticheskoy literatury; 1947: 929. (In Russ.)
[11]. Koshlyakov N.S., Gliner E.B., Smirnov M.M. Uravneniya v chastnykh proizvodnykh matematicheskoy fiziki [Partial differential equation in mathematical physics]. Moscow: Vysshaya Shkola; 1970: 710. (In Russ.)
[12]. Korn G., Korn T. Mathematical handbook for scientists and engineers. McGraw-Hill Book Company; 1968: 818.
Bibliography link:
Muzaev I.D., Kharebov K.S., Muzaev N.I. Mathematical modelling of the selective intake process from the interior volume in a three-layer stratified reservoir // Computational technologies. 2020. V. 25. ¹ 2. P. 36-49
|
