Abstract
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 the near-wall region are presented.
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References
R. K. Gaydukov, “Double-Deck Structure of the Boundary Layer in the Problem of a Compressible Flow Along a Plate with Small Irregularities on the Surface,” Eur. J. of Mech. - B/Fluids 66, 102–108 (2017).
R. K. Gaydukov, “Double-Deck Structure in the Problem of a Compressible Flow Along a Plate with Small Localized Irregularities on the Surface,” Eur. J. of Mech. - B/Fluids 71, 59–65 (2018).
V. G. Danilov and R. K. Gaydukov, “Double-Deck Structure of the Boundary Layer in the Problem of Flow in an Axially Symmetric Pipe with Small Irregularities on the Wall for Large Reynolds Numbers,” Russ. J. Math. Phys. 24 (1), 1–18 (2017).
R. K. Gaydukov and V. G. Danilov, “Asymptotics of Solutions of Problems of Incompressible Fluid Flow Along Surfaces with Small Irregularities for Large Reynolds Number,” Nanostructures. Math. Phys. & Modelling 15 (1), 5–102 (2016) [in Russian].
F. T. Smith, “Flow Through Constricted or Dilated Pipes and Channels: Pt. 1,” Q. J. Mechanics Appl. Math. 29 (3), 343–364 (1976).
F. T. Smith, “Flow through Constricted or Dilated Pipes and Channels: Pt. 2,” Q. J. Mechanics Appl. Math. 29 (3), 365–376 (1976).
F. T. Smith, “Laminar flow over a small hump on a flat plate,” J. of Fluid Mech. 57, 803–824 (1973).
J. Cousteix and J. Mauss, Asymptotic Analysis and Boundary Layers (Springer, 2007).
P. Cathalifaud, J. Mauss and J. Cousteixc, “Nonlinear Aspects of High Reynolds Number Channel Flows,” Eur. J. of Mech. - B/Fluids 29, 295–304 (2010).
A. E. Malevich, V. V. Mityushev and P. M. Adler, “Couette Flow in Channels with Wavy Walls,” Acta Mech. 197, 247–283 (2007).
V. G. Danilov and R. K. Gaydukov, “Equations for Velocity Oscillations in Problems of a Fluid Flow along a Plate with Small Periodic Irregularities on the Surface for Large Reynolds Numbers,” in Proc. of the Int. Conf. DAYS on DIFFRACTION 2018, 118–123 (2018).
M. I. Vishik and L. A. Lyusternik, “Regular Degeneration and Boundary Layer for Linear Differential Equations with Small Parameter,” Uspekhi Mat. Nauk 12, 3–122 (1957).
F. Dust, Fluid Mechanics: An Introduction to the Theory of Fluid Flows (Springer, 2008).
Acknowledgments
Over the past seven years, the investigations of flows with multi-deck structures were actively supported by Professor Mikhail Karasev. We are very grateful for his various help, comments and helpful discussions.
The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE University) in 2019.
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To the memory of Mikhail Karasev
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Fonareva, A.V., Gaydukov, R.K. A Compressible Fluid Flow with Double-Deck Structure Inside an Axially Symmetric Wavy-Wall Pipe. Russ. J. Math. Phys. 26, 334–343 (2019). https://doi.org/10.1134/S1061920819030087
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DOI: https://doi.org/10.1134/S1061920819030087