Power-law generalization of Newton’s formula for shear stress in a liquid in the form of a tensor rheological relation
DOI:
https://doi.org/10.21638/spbu01.2022.213Abstract
A generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form and the corresponding rheological relation is written in tensor form. Depending on the exponent in this rheological ratio, one can come to a description of either a laminar or turbulent flow regime. In the latter case, there is a system of differential equations with the no-slip boundary condition. The proposed system of equations for turbulent fluid motion can be useful, at least, for obtaining preliminary, estimated characteristics of turbulent flow before starting numerical modeling using modern differential turbulence models. For some values of the exponent, this system can be used to describe the behavior of power-law fluids, as well as fluids with small additives of polymers in the manifestation of the Toms effect.Keywords:
power formulas, generalization of Newton’s formula, Blasius formula, stress tensor, differential equations of turbulent flow, analytical solutions
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Литература
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Published
2022-07-06
How to Cite
Pavlovsky V. А. (2022). Power-law generalization of Newton’s formula for shear stress in a liquid in the form of a tensor rheological relation. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(2), 338–345. https://doi.org/10.21638/spbu01.2022.213
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
