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Double-deck structures of boundary layers in flows
P. 20-22.
We consider a non-stationary problem of an incompressible viscous fluid flow along surfaces with small irregularities for large Reynolds number, which have a formal asymptotic solution with a double-deck structure of the boundary layer.
Publication based on the results of:
In book
Novosibirsk : [б.и.], 2016
Gaydukov R. K., European Journal of Mechanics - B/Fluids 2017 Vol. 66 P. 102-108
We consider the problem of a viscous compressible subsonic fluid flow along a flat plate with small periodic irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of flow in the thin boundary layer (i.e., in ...
Added: July 9, 2017
Gaydukov R., Danilov V., Наноструктуры. Математическая физика и моделирование 2016 Т. 15 № 1 С. 5-102
We study the existence conditions for a double-deck structure of a boundary layer in typical problems of incompressible fluid flow along surfaces with small irregularities (periodic or localized) for large Reynolds number. We obtain characteristic scales (a power of a small parameter included in a solution) which lead to the double-deck structure, and we obtain ...
Added: September 27, 2016
Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2015 Vol. 22 No. 2 P. 161-173
A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique ...
Added: September 3, 2015
Danilov V. G., Gaydukov R. K., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 1 P. 1-18
The problem of flow of a viscous incompressible fluid in an axially symmetric pipe with small irregularities on the wall is considered. An asymptotic solution of the problem with the double-deck structure of the boundary layer and the unperturbed flow in the environment (the “core flow”) is obtained. The results of flow numerical simulation in ...
Added: September 28, 2016
Danilov V., Gaydukov R., Mathematical notes 2015 Vol. 98 No. 4 P. 561-571
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure. ...
Added: September 27, 2015
V. G. Danilov, R. K. Gaydukov, Russian Journal of Mathematical Physics 2022 Vol. 29 No. 4 P. 431-455
A problem of a nonstationary incompressible viscous fluid ow along a plate with small fast-oscillating irregularities on the surface for a large Reynolds number is considered by using rigorous methods of mathematical physics. Depending on the scales of irregularities in the problem under study, there arises a solution that describes the double-deck or triple-deck structure boundary layers on ...
Added: August 19, 2020
Gaydukov R. K., Fonareva A. V., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 334-343
The problem of viscous compressible fluid flow in an axially symmetric pipe with small periodic irregularities on the wall is considered for large Reynolds numbers. An asymptotic solution with double-deck structure of the boundary layer and unperturbed core flow is obtained. Numerical investigations of the influence of the density of the core flow on the flow behavior in ...
Added: September 2, 2019
Gaydukov R., Сибирские электронные математические известия 2024 Т. 21 № 1 С. 178-187
In this paper we study a Rayleigh-type equation on a semi-infinite cylinder with a Coulomb-type potential.
This equation arises in the double-deck boundary layer structure in the problem of flow induced by a uniformly rotating disk with small periodic irregularities on its surface for large Reynolds numbers. Using combined numerical and analytical approach, the existence of ...
Added: February 17, 2024
Gaydukov R., Danilov V., , in : Proceedings of the International Conference DAYS on DIFFRACTION 2019. : IEEE, 2019. P. 51-56.
Equations describing the double- and triple-deck structure are demonstrated for the case of compressible flows along a small perturbed plate for large Reynolds numbers. Numerical and analytical investigations of the influence of the upstream flow on the behavior of the flow in the near-wall region are presented. ...
Added: November 1, 2019
Gaydukov R., European Journal of Mechanics - B/Fluids 2018 Vol. 71 P. 59-65
We consider the problem of flow of a viscous compressible subsonic fluid along a flat plate with small localized (hump-type) irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of the flow in the thin boundary ...
Added: November 20, 2017
Gaydukov R., Danilov V., В кн. : XII Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики: сборник трудов в 4 томах. Т. 2: Механика жидкости и газа.: Уфа : РИЦ БашГУ, 2019. С. 92-94.
В докладе приводится детальное описание нестационарных двухпалубных и трехпалубных структур пограничного слоя. А именно, рассматривается нестационарная задача обтекания вязкой несжимаемой жидкостью полубесконечной пластины с малыми периодическими неровностями при больших значениях числа Рейнольдса. Построено формальное асимптотическое решение, имеющее двух- или трехпалубную структуру пограничного слоя, в зависимости от масштабов неровности. Полученные уравнения для членов асимптотического решения исследованы ...
Added: November 1, 2019
Danilov V., Gaydukov R., В кн. : Волны и вихри в сложных средах: 5-ая Международная научная школа молодых ученых. : М. : МАКС Пресс, 2014. С. 154-157.
Получено асимптотическое решение задачи о течении несжимаемой вязкой жидкости в двумерном канале с малыми неровностями на стенках при больших числах Рейнольдса, а также для случая аксиально-симметричной трубы. Показано, что пограничный слой имеет двухпалубную структуру: тонкий пристеночный пограничный слой, и «толстый» пограничный слой. Представлены результаты численного моделирования течения в пограничных слоях ...
Added: December 24, 2014
Gaydukov R., Fonareva A. V., European Journal of Mechanics - B/Fluids 2022 Vol. 94 P. 50-59
The problem of a rotating disk with slightly perturbed surface immersed in a viscous fluid is considered.
The asymptotic solutions with double-deck structure of the boundary layer are constructed for symmetric
periodic and localized types of irregularities on the disk surface for large Reynolds numbers. The paper
presents the results of numerical simulations of the flow near the ...
Added: November 14, 2021
Gaydukov R., Danilov V., Журнал вычислительной математики и математической физики 2024 № 6
Работа посвящена математическому моделированию фазового перехода лед–вода при течение жидкости внутри трубы с малым ледяным наростом на стенке при больших числах Рейнольдса. В качестве математической модели, описывающей динамику фазового перехода, используется двухпалубная модель пограничного слоя и система фазового поля. Приведены результаты численного моделирования. ...
Added: February 17, 2024
Gaydukov R., Danilov V., , in : Proceedings of the International Conference DAYS on DIFFRACTION 2018. : IEEE, 2018. P. 118-123.
Depending on the scales of periodic irregularities in the problem under study, a solution arises which describes two (“double-deck”) or three (“triple-deck”) boundary layers on the plate. Mainly, we study the equations describing the velocity oscillations in the boundary layers arising because of periodic irregularities and show their command nature. ...
Added: September 18, 2018
Fonaryova A., В кн. : Материалы Международного молодежного научного форума «ЛОМОНОСОВ-2019». : М. : МГУ, МАКС Пресс, 2019. С. 1-2.
Рассмотрена задача дозвукового течения вязкой сжимаемой жидкости (газа) в аксиально-симметричной трубе с малыми периодическими неровностями на стенке при больших значениях числа Рейнольдса и построено ее асимптотическое решение, имеющее двухпалубную структуру пограничного слоя. ...
Added: May 24, 2019
Gaydukov R. K., Borisov D. I., Mathematical notes 2016 Vol. 99 No. 5 P. 636-642
A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the ...
Added: May 18, 2016
Буров Н. А., Gaydukov R., Многофазные системы 2023 Т. 18 № 3 С. 192-195
В работе описана двухпалубная стурктура пограничного слоя в трехмерной задаче обтекания малой локализованной неровности на поверхности пластины при больших значениях числа Рейнольдса ...
Added: January 11, 2024
Gaydukov R., European Journal of Mechanics - B/Fluids 2021 Vol. 89 P. 401-410
An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow along a semi-infinite plate with small localized or periodic (fast-oscillating) irregularities on the surface whose shape depends on time. Numerical simulation of flow in the near-plate region is presented for two types of the shape change: oscillations of the ...
Added: January 4, 2021
Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2023 Vol. 30 No. 2 P. 165-175
In this paper, we construct and study a model of a phase transition in a system of two
phases (liquid and ice) and three media — water, a piece of ice, and some nonmeltable
solid substrate. Namely, the melting-crystallization process is considered in the problem
of water flow along a small ice irregularity (such as a frozen drop) ...
Added: December 14, 2022
Gaydukov R., Russian Journal of Nonlinear Dynamics 2024 Vol. 20 No. 1 P. 1-13
The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties
along a semi-infinite plate with a small localized irregularity on the surface is considered for large
Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is
constructed. The numerical simulation of the flow in the region near the surface was performed
for different ...
Added: December 26, 2023
Gaydukov R., Сибирский журнал вычислительной математики 2022 Т. 15 № 2 С. 97-109
A viscous liquid flow along a semi-infinite plate with small periodic irregularities on the surface was
considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with
induced pressure which are non-classical PDE, because they contain a limiting term. The main goal is to
construct a numerical algorithm for solving these equations with ...
Added: June 10, 2020
Fonareva A. V., Gaydukov R. K., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 224-243
A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at ...
Added: March 22, 2021
Fonaryova A., В кн. : Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского. Материалы конференции. : М. : МИЭМ НИУ ВШЭ, 2020. С. 53-55.
В работе построено формальное асимптотическое решение задачи о дозвуковом нестационарном течении вязкой сжимаемой жидкости в двумерном канале с малыми периодическими неровностями на стенках при больших значениях числа Рейнольдса. Проведено численное моделирование, демонстрирующее влияние плотности основного потока на поведение в пристеночной области. ...
Added: February 8, 2022