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A note on the estimation of critical Mach numbers for compressible flow

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Summary

A method for estimating values of critical free stream Mach numbers is devised for flows past aerofoils. It is based on a variational formulation of the boundary value problem for compressible inviscid flow. The method is applied to two-dimensional flow past ellipses, and fairly good agreement with other estimates is obtained for thick ellipses.

Zusammenfassung

Es wird eine Methode zur Abschätzung der kritischen Anström-Mach-Zahl der freien Umströmung von Tragflügeln entwickelt. Sie beruht auf einer variationstheoretischen Formulierung des Randwertproblemes für die kompressible nicht-zähe Strömung. Die Methode wird auf die zwei-dimensionale Umströmung von Ellipsen angewandt. Die Übereinstimmung der Ergebnisse mit anderen Abschätzungen für den Fall dicker Ellipsen ist befriedigend.

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References

  1. P. E. Lush andT. M. Cherry,The Variational Method in Hydrodynamics, Quart. J. Mech. and Appl. Math.9, 6–21 (1956).

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  2. H. Rasmussen andN. Heys,Application of a Variational Method in Plane Compressible Flow Calculation, to appear in J. Inst. Maths. and Applics.

  3. C. C. L. Melnik andD. C. Ives,Subcritical Flows over Two-dimensional Airfoils by a Multistrip Method of Integral Relations, in Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dynamics, ed. M. Holt, Lect. Notes in Physics, Vol.8, Springer-Verlag, Berlin (1971).

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Authors and Affiliations

  1. Laboratory of Applied Mathematical Physics, The Technical University of Denmark, Lyngby, Denmark

    Henning Rasmussen

Authors
  1. Henning Rasmussen
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Rasmussen, H. A note on the estimation of critical Mach numbers for compressible flow. Journal of Applied Mathematics and Physics (ZAMP) 24, 777–782 (1973). https://doi.org/10.1007/BF01597082

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  • DOI: https://doi.org/10.1007/BF01597082

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