Generalised similarity solutions for 3-D laminar compressible boundary layer flows on swept profiled cylinders

  • V. Saljnikov
  • Z. Boričić
  • D. Nikodijević
Part of the Acta Mechanica book series (ACTA MECH.SUPP., volume 4)


The method of generalised similarity allows us to derive solutions for the laminar steady, compressible three-dimensional boundary layer equations for flows over swept wings. The model configuration is that of an infinitely long swept profiled cylinder in an ideal gas flow whose dynamic viscosity is a linear function of temperature. A universal mathematical model is derived by successively introducing three transformations: Stewartson’s, Saljnikov’s Generalized Similarity [2] and Loitsianskii’s Group of Parameters [7]. It can be integrated numerically by the finite difference iterative method — Tridiagonal Algorithm (TDA) — with an arbitrary choice of pressure distribution, Pr and Ma numbers, as well as of the angle of sweep and the temperature boundary condition. In the article, however, an interesting practical problem of transonic swept wing with air flowing around it is considered for two cases of: a) isothermal and b) adiabatic wall. The obtained results are presented graphically and analysed.


Boundary Layer Adiabatic Wall Boundary Layer Problem Isothermal Wall Compressibility Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Gersten, K.: Die Bedeutung der Prandtlschen Grenzschichttheorie nach 85 Jahren. Z. Flugwiss. Weltraumforsch. 13, 209–218 (1989).MATHGoogle Scholar
  2. [2]
    Saljnikov, V. N.: A contribution to universal solutions of the boundary layer theory. Teor. i prim. Meh. 4, 139–163 (1978).MathSciNetGoogle Scholar
  3. [3]
    Schneider, W.: Über die Bedeutung analytischer Methoden für die Strömungs-Mechanik im Zeitalter des Computers. Vortrag am Festkolloquium, 60jähriges Jubiläum von Prof. Zierep, Karlsruhe 1989.Google Scholar
  4. [4]
    Saljnikov, V. N., Dallmann, U.: Verallgemeinerte Ähnlichkeitslösungen für 3-D lamin. stat. kompress. Grenzschichtströmungen an schiebenden profilierten Zylindern. DLR-FB 34 (1989).Google Scholar
  5. [5]
    Saljnikov, V. N., Boricié, Z., Nikodijevié, D.: Lösungen verallgemeinerter Ähnlichkeit für 3-D lamin. kompress. Flügelgrenzschichten. ZAMM 70, T462 - T465 (1990).Google Scholar
  6. [6]
    Görtler, H.: A new series for the calculation of steady laminar boundary layer flows. J. Math. Mech. 6, 1–66 (1957).MATHMathSciNetGoogle Scholar
  7. [7]
    Loitsianski, L. G.: Die universellen Gleichungen und die parametrigen Näherungen in der Theorie der laminaren Grenzschicht (in Russian). PMM 29, 70–87 (1965).Google Scholar
  8. [8]
    Reshotko, E., Beckwith, I.: Compressible laminar boundary layer over a yawed infinite cylinder with heat transfer and arbitrary Prandtl number. NASA Report 1379 (1958).Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • V. Saljnikov
    • 1
  • Z. Boričić
    • 2
  • D. Nikodijević
    • 3
  1. 1.BelgradeYugoslavia
  2. 2.NišYugoslavia
  3. 3.NišYugoslavia

Personalised recommendations