TY - JOUR

T1 - On a Scenario of Transition to Turbulence for a Polymer Fluid Flow in a Circular Pipe

AU - Semisalov, B. V.

N1 - This study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences (project no. FWNF-2022-0008).

PY - 2024/4

Y1 - 2024/4

N2 - Abstract: Equations describing nonstationary and stationary flows of an incompressible polymer fluid through a pipe are derived based on the rheological mesoscopic Pokrovskii–Vinogradov model. Their exact stationary solutions are obtained and conditions providing their existence are outlined. Numerical simulation of the stabilization of a nonstationary flow is carried out 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 the existence of stationary solutions. The obtained results enable us to describe constructively the process of destruction of laminar Poiseuille-type flows, which usually initiates the onset of turbulence. The key role in mechanics of this process is played by the size and orientation of macromolecules of the polymer fluid. The mathematical description of the process uses essentially the solutions’ singular points.

AB - Abstract: Equations describing nonstationary and stationary flows of an incompressible polymer fluid through a pipe are derived based on the rheological mesoscopic Pokrovskii–Vinogradov model. Their exact stationary solutions are obtained and conditions providing their existence are outlined. Numerical simulation of the stabilization of a nonstationary flow is carried out 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 the existence of stationary solutions. The obtained results enable us to describe constructively the process of destruction of laminar Poiseuille-type flows, which usually initiates the onset of turbulence. The key role in mechanics of this process is played by the size and orientation of macromolecules of the polymer fluid. The mathematical description of the process uses essentially the solutions’ singular points.

KW - Poiseuille-type flow

KW - exact solution

KW - laminar-turbulent transition

KW - mesoscopic model

KW - polymer fluid

KW - singular point of solution

KW - stabilization of nonstationary flow

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85191193363&origin=inward&txGid=1062e1fcc4cf34360fed58e6f4014381

UR - https://www.mendeley.com/catalogue/38d47ae9-a10c-3480-b07a-2847179e0fba/

U2 - 10.1134/S2070048224020145

DO - 10.1134/S2070048224020145

M3 - Article

VL - 16

SP - 197

EP - 207

JO - Mathematical Models and Computer Simulations

JF - Mathematical Models and Computer Simulations

SN - 2070-0482

IS - 2

ER -