Skip to main content
Log in

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

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

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 the thin and “thick” boundary layers are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. D. Landau and E. M. Lifshitz, Fluid Mechanics 6 (Butterworth-Heinemann, 1987).

    MATH  Google Scholar 

  2. F. T. Smith, “Flow through Constricted or Dilated Pipes and Channels: Pt. 2,” Q. J. Mechanics Appl. Math. 29 (3), 365–376 (1976).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. F. T. Smith, “Flow Through Constricted or Dilated Pipes and Channels: Pt. 1,” Q. J. Mechanics Appl. Math. 29 (3), 343–364 (1976).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. P. Cathalifaud, J. Mauss, and J. Cousteix, “Nonlinear Aspects of High Reynolds Number Channel Flows,” Eur. J. Mech. BFluids 29, 295–304 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. V. G. Danilov and M. V. Makarova, “Asymptotic and Numerical Analysis of the Flow around a Plate with Small Periodic Irregularities,” Russ. J. Math. Phys. 2 (1), 49–56 (1994).

    MathSciNet  MATH  Google Scholar 

  6. V. G. Danilov, V. P. Maslov, and K. A. Volosov, Mathematical Modeling of Heat and Mass Transfer Processes (Kluwer Academic Publishers, 1995).

    Book  MATH  Google Scholar 

  7. V. G. Danilov and R. K. Gaydukov, “Vortexes in the Prandtl Boundary Layer Induced by Irregularities on a Plate,” Russ. J. Math. Phys. 22 (2), 161–173 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  8. F. T. Smith, “Laminar Flow over a Small Hump on a Flat Plate,” J. Fluid Mech. 57, 803–824 (1973).

    Article  ADS  MATH  Google Scholar 

  9. J. Cousteix and J. Mauss, Asymptotic Analysis and Boundary Layers (Springer, 2007).

    MATH  Google Scholar 

  10. P. J. Roache, Fundamentals of Computational Fluid Dynamics (Hermosa Pub., 1998).

    Google Scholar 

  11. J. Mauss, A. Achiq, and S. Saintlos, “Sur l’analyse conduisant á la théorie de la triple couche,” C. R. Acad. Sci. Paris Série II 315, 1611–1614 (1992).

    ADS  MATH  Google Scholar 

  12. J. Mauss, “Asymptotic Modeling for Separating Boundary Layers,” Lecture Notes in Phys. 442, 239–254 (1995).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. K. Stewartson, “Multistructured Boundary Layers on Flat Plates and Related Bodies,” Adv. Appl. Mech. 14, 145–239 (1974).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. G. Danilov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Danilov, V.G., Gaydukov, R.K. 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, 1–18 (2017). https://doi.org/10.1134/S1061920817010010

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920817010010

Navigation