Acta Mechanica

, Volume 59, Issue 3–4, pp 251–268 | Cite as

Unsteady incompressible two-dimensional and axisymmetric turbulent boundary layer flows

  • M. Kumari
Contributed Papers


The unsteady turbulent incompressible boundary-layer flow over two-dimensional and axisymmetric bodies with pressure gradient has been studied. An eddy-viscosity model has been used to model the Reynolds shear stress. The unsteadiness is due to variations in the free stream velocity with time. The nonlinear partial differential equation with three independent variables governing the flow has been solved using Keller's Box method. The results indicate that the free stram velocity distribution exerts strong influence on the boundary-layer characteristics. The point of zero skin friction is found to move upstream as time increases.


Shear Stress Fluid Dynamics Skin Friction Turbulent Boundary Layer Free Stream 
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]
    McCroskey, W. J., Philippe, J. J.: Unsteady viscous flow on oscillating airfoils. AIAA J.13, 71–79 (1975).Google Scholar
  2. [2]
    Telionis, D. P.: Calculations of time dependent boundary layers, in: Unsteady aerodynamics (Kinney, R. B., ed.)1, 155 (1975).Google Scholar
  3. [3]
    Nash, J. F., Carr, L. W., Singelton, R. E.: Unsteady turbulent boundary layers in two-dimensional, incompressible flow. AIAA J.13, 167–173 (1975).Google Scholar
  4. [4]
    Patel, V. C., Nash, J. F.: Unsteady turbulent boundary layers with flow reversal, in: Unsteady aerodynamics (Kinney, R. B., ed.)1, 191 (1975).Google Scholar
  5. [5]
    Cebeci, T.: Calculation of unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity. Proc. Roy. Soc. London,A355, 225–238 (1977).Google Scholar
  6. [6]
    Bradshaw, P.: NPL Aero. Rept.-1288, 1969.Google Scholar
  7. [7]
    Cebeci, T.: Calculation of laminar and turbulent boundary layers for two-dimensional time-dependent flows. NASA CR-2820, 1977.Google Scholar
  8. [8]
    Karlsson, S. K. F.: An unsteady turbulent boundary layer. J. Fluid Mech.,5, 622–636 (1959).Google Scholar
  9. [9]
    Telionis, D. P., Tsahalis, D. Th.: Unsteady turbulent boundary layers and separation. AIAA J.14, 468–474 (1976).Google Scholar
  10. [10]
    Patel, M. H.: An integral method for the oscillating turbulent boundary layer. The Aeronautical Quart.32, 271–298 (1981).Google Scholar
  11. [11]
    Fernholz, H. H., Vagt, J. D.: Turbulence meyasurements in an adverse pressuregradient three-dimensional boundary layer along a circular cylinder. J. Fluid Mech.,11, 233–269 (1981).Google Scholar
  12. [12]
    Kiya, M., Suzuki, Y., Arie, M., Hagino, M.: A contribution to the free-stream turbulence effect on the flow past a circular cylinder. J. Fluid Mech.115, 151–164 (1982).Google Scholar
  13. [13]
    Roshko, A.: Experiments on the flow past a circular cylinder at high Reynolds number. J. Fluid Mech.10, 345–356 (1961).Google Scholar
  14. [14]
    Cebeci, T., Mosinskis, G. J., Smith, A. M. O.: Calculation of seperation points in incompressible turbulent flows. J. Aircraft9, 618–624 (1972).Google Scholar
  15. [15]
    Fage, A.: Experiments on a sphere at a critical Reynolds numbers. ARC R M-1766 (1937).Google Scholar
  16. [16]
    Sears, W. R., Telionis, D. P.: Boundary layer separation in unsteady flow. SIAM J. Appl. Math.28, 215–235 (1975).Google Scholar
  17. [17]
    Williams, J. C.: Incompressible laminar boundary layer separation. Ann. Rev. Fluid Mech.9, 113–144 (1977).Google Scholar
  18. [18]
    McCroskey, W. J.: Some current research in unsteady fluid dynamics, Trans. ASME, J. Fluids Engng.99, 8–38 (1977).Google Scholar
  19. [19]
    Telionis, D. P.: Review-unsteady boundary layers, separated and attached. Trans. ASME, J. Fluids Engng.101, 29–43 (1979).Google Scholar
  20. [20]
    Telionis, D. P., Tsahalis, D. Th., Werle, M. J.: Numerical investigation of unsteady boundary layer separation. The Phys. Fluids16, 968–973 (1973).Google Scholar
  21. [21]
    Telionis, D. P., Tsahalis, D. Th.: The response of unsteady boundary layers separation to impulsive changes of outer flow. AIAA J.12, 614–619 (1974).Google Scholar
  22. [22]
    Williams, J. C. III, Johnson, W. D.: Semi-similar solutions of unsteady boundary layer flows including separation. AIAA J.12, 1388–1393 (1974).Google Scholar
  23. [23]
    Williams, J. C. III, Johnson, W. D.: New solutions to the unsteady laminar boundarylayer equations including the approach to separation, in: Unsteady aerodynamics (Kinney, R. B., ed.),1, 261 (1975).Google Scholar
  24. [24]
    Cebeci, T.: The laminar boundary layer on a circular cylinder started impulsively from rest. J. Comput. Phys.31, 153–172 (1979).Google Scholar
  25. [25]
    Williams, J. C. III: Flow developments in the vicinity of the sharp trailing edge on bodies impulsively set into motion. J. Fluid Mech.115, 27–37 (1982).Google Scholar
  26. [26]
    Van Dommelen, L. L., Shen, S. F.: An unsteady interactive separation process. AIAA J.21, 358–362 (1983).Google Scholar
  27. [27]
    Williams, J. C. III, Wang, T. J.: Semisimilar solutions of the unsteady compressible laminar boundary-layer equations. AIAA J.23, 228–233 (1985).Google Scholar
  28. [28]
    Cebeci, T., Bradshaw, P.: Physical and computational aspects of convective heat transfer. New York: Springer 1984.Google Scholar
  29. [29]
    Surma Devi, C. D., Nath, G.: Unsteady nonsimilar laminar boundary layer flows with heat and mass transfer. Acta Technica Csav28, 225–239 (1983).Google Scholar
  30. [30]
    Cebeci, T., Bradshaw, P.: Momentum transfer in boundary layers. Washington: McGraw-Hill-Hemisphere 1977.Google Scholar
  31. [31]
    Cebeci, T., Smith, A. M. O.: Analysis of turbulent boundary layers. New York: Academic Press 1974.Google Scholar
  32. [32]
    Chang, P. K.: Separation of flow. Oxford: Pergamon Press 1970.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • M. Kumari
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations