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Matematicheskoe modelirovanie, 2023, Volume 35, Number 11, Pages 62–78
DOI: https://doi.org/10.20948/mm-2023-11-05
(Mi mm4505)
 

On a scenario of transition to turbulence for polymer fluid flow in a circular pipe

B. V. Semisalovab

a Sobolev Institute of Mathematics SB RAS
b Novosibirsk State University
References:
Abstract: Equations describing non-stationary and stationary flows of an incompressible polymer fluid through a pipe are derived on the basis of rheological mesoscopic Pokrovskii–Vinogradov model. Exact stationary solutions of them are obtained, and conditions providing their existence are outlined. Numerical simulation of stabilization of non-stationary flow is done, as well, and the restrictions on the values of parameters that ensure stabilization are computed. In a number of cases these restrictions coincide with the conditions of existence of stationary solutions. The obtained results enable one to describe constructively the process of destruction of laminar Poiseuille-type flows, which usually initiates onset of turbulence. The key role in mechanics of this process is played by the size and orientation of macromolecules of the polymer fluid. Mathematical description of the process uses essentially the solutions' singular points.
Keywords: polymer fluid, mesoscopic model, Poiseuille-type flow, exact solution, stabilization of non-stationary flow, laminar-turbulent transition, singular point of solution.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
Received: 13.01.2023
Revised: 13.01.2023
Accepted: 26.06.2023
English version:
Mathematical Models and Computer Simulations, 2024, Volume 16, Issue 2, Pages 197–207
DOI: https://doi.org/10.1134/S2070048224020145
Document Type: Article
Language: Russian
Citation: B. V. Semisalov, “On a scenario of transition to turbulence for polymer fluid flow in a circular pipe”, Matem. Mod., 35:11 (2023), 62–78; Math. Models Comput. Simul., 16:2 (2024), 197–207
Citation in format AMSBIB
\Bibitem{Sem23}
\by B.~V.~Semisalov
\paper On a scenario of transition to turbulence for polymer fluid flow in a circular pipe
\jour Matem. Mod.
\yr 2023
\vol 35
\issue 11
\pages 62--78
\mathnet{http://mi.mathnet.ru/mm4505}
\crossref{https://doi.org/10.20948/mm-2023-11-05}
\transl
\jour Math. Models Comput. Simul.
\yr 2024
\vol 16
\issue 2
\pages 197--207
\crossref{https://doi.org/10.1134/S2070048224020145}
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    Математическое моделирование
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