Relaxation Solution for the Transonic Flow Through a Cascade

  • T. S. Luu
  • G. Coulmy
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


The finite difference relaxation method is developped to calculate the performances of the cascade up to transonic range with occurring of shocks. The full potential equation with exact boundary conditions is solved in a conformal coordinate system constitued by the stream function and the potential function of the incompressible flow through the same cascade. The grid points on the boundary of the computational region are established after resolving the incompressible flow by the singularities method whereas the internal grid points are determined by means of the finite difference technic. The transonic potential field is computed using Jameson’s rotated upwind difference scheme in the supersonic region, and central difference scheme in the subsonic region. Thus in the supersonic regions, the disturbances are propagated from upstream to downstream; and terms provided from the truncation error acting as the artificial viscosity are introduced into the governing equation, making the occurring of the shocks automatically during the iterative process. Examples applied to cascades of compressor and turbine are also given.


Potential Flow Collocation Point Compressible Flow Transonic Flow Artificial Viscosity 
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.
    Murman E.M. and Cole J.D.: Calculation of Plane Steady Transonic Flow. AIAA Journal, vol. 9, N° 1, 1971.Google Scholar
  2. 2.
    Garabedian P.R. and Korn D.G.: Analysis of Transonic Airfoils. Communication on Pure and Applied Mathematics, vol. 24, 1971.Google Scholar
  3. 3.
    Jameson A.: Numerical Calculation of the Three-dimensional Transonic Flow over a Yawed Wing. Proc. AIAA Computational Fluid Dynamics Conference, Palm Springs Ca., 1973.Google Scholar
  4. 4.
    McDonald P.W.: The Computation of Transonic Flow Through Two-Dimensional Gas Turbine Cascades. ASME Paper, n° 71-GT-89.Google Scholar
  5. 5.
    Gopalakrisnan S. and Bozzola R.: Computation of Shocked Flows in Compressor Cascades. ASME Paper, n° 72-GT-31.Google Scholar
  6. 6.
    Luu T.S., Coulmy G. and Corniglion J.: Etude des écoulements instationnaires autour des aubes passantes par une théorie non lineaire. ATMA, 1971.Google Scholar
  7. 7.
    Luu T.S. and Coulmy G.: Calcul de lécoulement transsonique avec choc à travers une grille d’aube. ATMA, 1975.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1976

Authors and Affiliations

  • T. S. Luu
    • 1
  • G. Coulmy
    • 1
  1. 1.L.I.M.S.I.C.N.R.S.OrsayFrance

Personalised recommendations