Skip to main content

An approach to the problem of axisymmetric sonic flow around a slender body

  • Conference paper
Applied Mechanics
  • 603 Accesses

Abstract

To calculate the flow field set up by a slender body flying at sonic speed is a classical problem — a problem which, over the years, has been tried many times without receiving a definite solution. The dominating feature of the problem is of course its inherently nonhnear character: the linear acoustic approximation is unable to account for the sound-wave interaction which keeps finite the wave travelling with the body.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Oswatitsch, K., and F. Keune: The flow around bodies of revolution at Mach number one. Proc. of Conf. on High-Speed Aeronautics, Polytechnich Inst, of Brooklyn, 1955, p. 113.

    Google Scholar 

  2. Spreiteb, J. R., and Alberta Y. Alksne: Thin airfoil theory based on approximate solution of the transonic flow equation. NACA TN 3970 (1957).

    Google Scholar 

  3. Spreiteb, J. R., and Alberta Y. Alksne: Slender-body theory based on approximate solution of the transonic flow equation, NASA Rep. 2 (1959).

    Google Scholar 

  4. Cole, J. D., and W.W. Royce: An approximate theory for the pressure distribution and wave drag of bodies of revolution at Mach number one. Proc. 6th Midwestern Conf. on Fluid Mechanics, 1959, p. 254.

    Google Scholar 

  5. Evans, T.: An approximate solution for two-dimensional transonic flow past thin airfoils. Proc. Camb. Phü. Soc. 61, 573 (1965).

    Article  ADS  MATH  Google Scholar 

  6. Rubbert, P. E.: Analysis of transonic flow by means of parametric differentiation. Ph. D. dissertation, MIT (1965).

    Google Scholar 

  7. Rubbert, P. E., and M. T. Landahl: Solution of the transonic airfoil problem through parametric differentiation. AIAA J. 5, 470 (1967).

    Article  ADS  MATH  Google Scholar 

  8. Taylor, R. A., and J. B. McDevitt: Pressure distributions at transonic speeds for parabolicarc bodies of revolution having fineness ratios of 10, 12 and 14. NACA TN 4234 (1958).

    Google Scholar 

  9. McDevitt, J. B., and R. A. Taylor: Pressure distributions at transonic speeds for slender bodies having various axial locations of maximum diameter. NACA TN 4280 (1958).

    Google Scholar 

  10. Miles, J. W.: On linearized transonic flow theory for slender bodies. J. Aero. Sci. 23, 704 (1956).

    MATH  Google Scholar 

  11. Guderley, K. G., and H. Yoshihara: An axial-symmetric transonic flow pattern. Qu. AppL Math. 8, 333 (1951).

    MATH  Google Scholar 

  12. Miles, J. W.: On the sonic drag of a slender body, J. Aero. Sci. 23, 146 (1956).

    Article  MathSciNet  MATH  Google Scholar 

  13. Yoshihara, H.: On the flow over a cone-cylinder body at Mach number one. Wx\DC Tech. Rep. 52–295 (1952).

    Google Scholar 

  14. Müller, U.: Profile bei Schallanströmung im unendlich ausgedehnten Stromfeld. ZAMM 47, T 158 (1967).

    Google Scholar 

  15. Guderley, K. G., and M.C. Breiter: The development of infinity of axisymmetric flow patterns with a free stream Mach number one. Aerospace Res. Lab., US Air Force, ARL 66-0066 (1966).

    Google Scholar 

  16. Perl, W., and M. M. Klein: Theoretical investigation of transonic similarity for bodies of revolution. NACA TN 2239 (1950).

    Google Scholar 

  17. Cole, J. D., and A. F. Messiter: Expansion procedures and similarity laws for transonic flow. Z. angew. Math. Phys. 8, 1 (1957).

    MathSciNet  MATH  Google Scholar 

  18. Guderley, K. G.: Theorie SchaDnaher Strömungen. Berlin/Göttingen/Heidelberg: Springer 1957. English translation: Theory of transonic flow. Pergamon Press 1962.

    Book  Google Scholar 

  19. Hayes, W. D.: La seconde approximation pour les écoulements transsoniques non visqueux. J. de Méchanique 5, 163 (1966).

    MathSciNet  MATH  Google Scholar 

  20. Mxjller, E., und K. Matschat: Ähnlichkeitslösungen der transsonischen Gleichungen bei der Anström-Machzahl 1. Proc. llth Int. Congr. Appl. Mech. München 1964; Berlin/Heidelberg/ New York: Springer 1966, p. 1061.

    Google Scholar 

  21. Falkovich, S. V., and I. A. Chernov: Flow of a sonic gas stream past a body of revolution. PMM 28, 342 (1964).

    MathSciNet  Google Scholar 

  22. Randall, D. G.: Some results in the theory of almost axisymmetric flow at transonic speed. AIAA J. 3, 2339 (1965).

    Article  Google Scholar 

  23. Euvrard, T.: Ècoulement transsonique a grande distance d’un corps de ré volution. C.R. Acad. Sc. Paris 260 (Gr. 2), 5691 (1965).

    Google Scholar 

  24. Drougge, G.: An experimental investigation of the interference between bodies of revolution at transonic speeds with special reference to the sonic and supersonic area rules. Aero. Res. Inst, of Sweden (FFA), Rep. 83 (1959).

    MATH  Google Scholar 

  25. Berndt, S. B.: On the drag of slender bodies at sonic speed. Aero. Res. Inst, of Sweden (FFA), Rep. 70 (1956).

    Google Scholar 

  26. Randall, D. G.: A marching procedure for the determination of in viscid two-dimensional sonic flow past a blunt symmetrical body. Aero. Res. Council (Great Britain) C.P. No. 992 (1968).

    Google Scholar 

  27. Sedin, Y.: private communication (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Berndt, S.B. (1969). An approach to the problem of axisymmetric sonic flow around a slender body. In: Hetényi, M., Vincenti, W.G. (eds) Applied Mechanics. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85640-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-85640-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85642-6

  • Online ISBN: 978-3-642-85640-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics