Skip to main content
SpringerLink
Log in

On the construction and calculation of optimal nonlifting critical airfoils

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM ∞ for a given thickness ratio δ and tail angle θ t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM ∞ and δ for various θ t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM ∞ →1, δ → 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding δ and θ t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. D. Cole and L. P. Cook,Transonic Aerodynamics, North Holland, Amsterdam 1986.

    Google Scholar 

  2. D. D. Fisher,Calculation of subsonic cavities with sonic free streamlines, J. Math. Phys.,42, 14–26 (1963).

    Google Scholar 

  3. D. Gilbarg and M. Shiffman,On bodies achieving extreme values of the critical Mach number I, J. Rat. Mech. and Analysis,3, 209–230 (1954).

    Google Scholar 

  4. J. B. Helliwell and A. G. Mackie,The flow past a closed body in a high subsonic stream, J. Mech. Appl. Math.,12, 298–313 (1959).

    Google Scholar 

  5. T. R. F. Nonweiler,The sonic flow about some symmetric half-bodies, J. Fluid Mech.,4, 140–148 (1958).

    Google Scholar 

  6. D. Riabouchinsky,On steady fluid motions with free surfaces, Proc. London Math. Soc., Ser. 2,19, 206–215 (1920).

    Google Scholar 

  7. Z. Rusak,The Sonic Flow about Two-Dimensional Slender Semi-infinite Bodies, Rept. No.196, February 1991, Dept. of Math. Sci., Rensselaer Polytechnic Institute, to appear in SIAM J. on Applied Math.

  8. C. C. L. Sells,Plane subcritical flow past a lifting airfoil, Proc. Roy. Soc. A.,308, 377–401 (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept of Mathematical Sciences, Rensselaer Polytechnic Institute Troy, 12180-3590, New York, USA

    D. W. Schwendeman, M. C. A. Kropinski & J. D. Cole

Authors
  1. D. W. Schwendeman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. C. A. Kropinski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. D. Cole
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schwendeman, D.W., Kropinski, M.C.A. & Cole, J.D. On the construction and calculation of optimal nonlifting critical airfoils. Z. angew. Math. Phys. 44, 556–571 (1993). https://doi.org/10.1007/BF00953667

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00953667

Keywords

Search

Navigation