Skip to main content
Log in

USING TWO-PARAMETER VELOCITY PROFILES FOR THREE-DIMENSIONAL BOUNDARY LAYERS

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Approximations of the profiles of the longitudinal and transverse velocity components in the boundary layer calculated for the flows around a swept wing and a body of revolution by means of solving the full Navier–Stokes equations and using the boundary layer profiles from the self-similar one-parameter family of the Falkner–Skan–Cooke profiles and two-parameter family of profiles proposed by Gaster are compared. A significant advantage of using the approximation of the numerical profiles near three-dimensional separation by profiles from the two-parameter family is demonstrated.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

REFERENCES

  1. A. V. Boiko, S. V. Kirilovskiy, A. A. Maslov, and T. V. Poplavskaya, “Engineering Simulation of the Laminar-Turbulent Transition: Achievements and Problems (Review)," Prikl. Mekh. Tekh. Fiz. 56 (5), 30-49 (2015) [J. Appl. Mech. Tech. Phys. 56 (5), 761–777 (2015)].

    Article  ADS  CAS  Google Scholar 

  2. A. V. Boiko, S. V. Kirilovskiy, and T. V. Poplavskaya, “Asymptotic Boundary Conditions for Computing the Position of Laminar–Turbulent Transition by the \(e^N\) Method," Teplofiz. Aeromekh. 26 (2), 191–207 (2019) [Thermophys. Aeromech. 26 (2), 179–194 (2019)].

    Article  ADS  Google Scholar 

  3. A. V. Boiko, S. V. Kirilovskiy, A. A. Maslov, and T. V. Poplavskaya, “Computational Grids for Engineering Modeling of the Laminar–Turbulent Flow," Prikl. Mekh. Tekh. Fiz. 63 (6), 91–95 (2022) [J. Appl. Mech. Tech. Phys. 63 (6), 984–987 (2022)].

    Article  ADS  CAS  Google Scholar 

  4. A. V. Boiko, K. V. Demyanko, S. V. Kirilovskiy, et al., “Determination of Threshold N-Factors of the Laminar–Turbulent Transition in a Subsonic Boundary Layer on a Prolate Spheroid," Prikl. Mekh. Tekh. Fiz. 62 (6), 3–7 (2021) [J. Appl. Mech. Tech. Phys. 62 (6), 891–894 (2021)].

    Article  ADS  MathSciNet  Google Scholar 

  5. A. V. Boiko, K. V. Demyanko, S. V. Kirilovskiy, et al. “Modeling of Transonic Transitional Three-Dimensional Flows for Aerodynamic Applications," AIAA J. 59 (9), 3598–3610 (2021).

    Article  ADS  Google Scholar 

  6. M. Gaster, “A Two-Parameter Family of Laminar Boundary Layer Profiles on Swept Wings," Seattle, 2008. (Paper /AIAA; No. 2008-4335).

  7. V. M. Falkner and S. W. Skan, “Solutions of the Boundary-Layer Equations," London, Edinburgh, Dublin Philos. Mag. J. Sci. 12 (80), 865–896 (1931).

    Article  Google Scholar 

  8. D. R. Hartree, “On an Equation Occurring in Falkner and Skan’s Approximate Treatment of the Equations of the Boundary Layer," Math. Proc. Cambridge Philos. Soc. 33 (2), 223–239 (1937).

  9. K. Stewartson, “Further Solutions of the Falkner — Skan Equation," Math. Proc. Cambridge Philos. Soc. 50 (3), 454–465 (1954).

  10. P. A. Libby and T. M. Liu, “Further Solutions of the Falkner — Skan Equation," AIAA J. 5 (5), 1040–1042 (1967).

    Article  ADS  Google Scholar 

  11. J. C. Cooke, “The Boundary Layer of a Class of Infinite Yawed Cylinders," Math. Proc. Cambridge Philos. Soc. 46 (4), 645–648 (1950).

  12. S. A. Gaponov and B. V. Smorodskii, “Linear Stability of Three-Dimensional Boundary Layers," Prikl. Mekh. Tekh. Fiz. 49 (2), 3–14 (2008) [J. Appl. Mech. Tech. Phys. 49 (2), 157–166 (2008)].

    Article  ADS  MathSciNet  Google Scholar 

  13. A. V. Ivanov, D. A. Mischenko, and A. V. Boiko, “Method of the Description of the Laminar–Turbulent Transition Position on a Swept Wing in the Flow with an Enhanced Level of Free-Stream Turbulence," Prikl. Mekh. Tekh. Fiz. 61 (2), 109–116 (2020) [J. Appl. Mech. Tech. Phys. 61 (2), 250–255 (2020)].

    Article  ADS  Google Scholar 

  14. L. M. Mack, On the Stability of the Boundary Layer on a Transonic Swept Wing, Pasadena, 1979. (Paper /AIAA; No. 79-0264).

  15. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1979).

    Google Scholar 

  16. A. Surana, O. Grunberg, G. Haller, “Exact Theory of Three-Dimensional Flow Separation. Pt 1. Steady Separation," J. Fluid Mech. 564, 57–103 (2006).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Boiko.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2023, Vol. 64, No. 6, pp. 144-154. https://doi.org/10.15372/PMTF20230617.

Publisher’s Note. Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Boiko, A.V., Demidenko, N.V. USING TWO-PARAMETER VELOCITY PROFILES FOR THREE-DIMENSIONAL BOUNDARY LAYERS. J Appl Mech Tech Phy 64, 1068–1077 (2023). https://doi.org/10.1134/S0021894423060172

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894423060172

Keywords

Navigation