532.516 Mathematical modeling of hydrodynamic resistance during oscillatory flow of viscoelastic fluid in a flat channel
Abdikarimov N. I. (Ургенчский государственный университет Адрес: 220100, Узбекистан, город Ургенч, улица Х. Олимжона, 14.), Navruzov K. N. (Ургенчский государственный университет Адрес: 220100, Узбекистан, город Ургенч, улица Х. Олимжона, 14.)
VISCOELASTIC FLUID, UNSTEADY FLOW, “IMPEDANCE” FUNCTION, OSCILLATORY FLOW, AMPLITUDE, PHASE
doi: 10.18698/2309-3684-2024-2-3545
The problems of oscillatory flow of an elastic-viscous fluid in a flat channel for a given harmonic oscillation of fluid flow are solved based on the generalized Maxwell model. The “impedance” function was determined, and with the help of this function the dependence of the hydrodynamic resistance on the dimensionless oscillation frequency was studied for various values of the elastic Deborah number and the concentration of the Newtonian fluid. It is shown that in the oscillatory flow of an elastic-viscous fluid, the hydrodynamic resistance decreases depending on the Deborah number. This effect makes it possible to estimate the hydrodynamic resistance for a given law of change in the longitudinal velocity averaged over the cross section of the channel, with oscillatory flow and, thereby, allows us to determine the dissipation of the energy of the medium, which is important in the regulation of hydraulic and pneumatic systems.
[1] Jons J.R., Walters T.S. Flow of elastic-viscous liquids in channels under the influence of a periodic pressure gradient. Part 1. Rheologica Acta, 1967, vol. 6, pp. 240-245.
[2] Khabakhpasheva E., Popov V., Kekalov A., and Mikhailova E. Pulsating flow of viscoelastic fluids in tubes. J. Non-Newtonian Fluid Mechanics, 1989, vol.33, iss. 3, pp. 289-304.
[3] Casanellas L., Ortin J. Laminar oscillatory flow of Maxwell and Oldroyd-B fluids. J. Non-Newtonian Fluid Mechanics, 2011, vol. 166, iss. 23-24, p. 1315-1326.
[4] Hassan A. Abu-El, El-Maghawru E.M. Unsteady axial viscoelastic pipe flows of an Oldroyd-B fluid. Rheology-New Concepts. Applications and Methods, 2013, vol. 6, pp. 91-106.
[5] Akilov Zh.A., Dzhabbarov M.S., Khuzhayorov B.Kh. Tangential shear stress under the periodic flow of a viscoelastic fluid in a cylindrical tube. Fluid Dynamics, 2021, vol. 56, no. 2, pp. 189-199.
[6] Ding Z., JianY. Electrokinetic oscillatory flow and energy microchannelis: a linear analysis. Journal of Fluid Mechanics, 2021, vol. 919, art. A20.
[7] Popov D.N. Nestacionarnye gidromekhanicheskie processy [Unsteady hydromechanical processes]. Moscow, Mashinostroenie Publ., 1982, 424 p.
[8] Astarita G., Marrucci G. Osnovy gidromekhaniki nen'yutonovskih zhidkostej [Fundamentals of hydromechanics of non-Newtonian fluids]. Moscow, Мir Pupl., 1978, 309 p.
[9] Loytsyansky L.G. Mekhanika zhidkosti i gaza [Mechanics of fluid and gas]. Moscow, Drofa [Bustard], 2003, 840 p.
[10] Kolesnichenko V.I., Sharifulin A.N. Vvedenie v mekhaniku neszhimaemoj zhidkosti [Introduction to Incompressible Fluid Mechanics]. Permian, Izdatel'stvo PNIMU [Publishing house PNIMU], 2019, 127 p.
Абдикаримов Н.И., Наврузов К.Н. Математическое моделирование гидродинамических сопротивлений при колебательном течении упруговязкой жидкости в плоском канале. Математическое моделирование и численные методы, 2024, № 2, с. 35–45.
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