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Range of Validity of the Formulae Derived by Linear Aerodynamic Theory for the Prandtl Supersonic Jet Problem

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Recent Developments in Theoretical and Experimental Fluid Mechanics

Abstract

In some previous papers [1], [2] we considered the Prandtl plane jet problem for a gas expanding from a nozzle into the stationary atmosphere [3] and derived, within the framework of linear aerodynamics, some formulae the length L, the maximum cross-section diameter Dmax and the mean diameter Dm of the first wave of the jet. It was supposed that the pressure pj at the nozzle outlet was greater than the atmospheric pressure pa, (pj > pa). The same formulae are still valid in the linear theory even if pj < pa but in this case instead of a maximum cross-section diameter we have to consider a minimum diameter Dmin since this wave presents now a contraction.

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References

  1. Jacob, C. Sur l’expansion d’un jet supersonique dans l’atmosphère C.R. Acad. Sci. Paris, 280 (1975), A. 153–156

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  2. Jacob, C. Sur l’expansion d’un jet supersonique plan dans l’atmosphère Annali di Matematica pura ed applicata, (IV), vol. CVIII (1976)

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  3. Prandtl, L. Über die stationären Wellen in einem Gasstrahle Phys. Zeitschrift 5 (1904), 599–601

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  4. Oudart, A. L’étude des jets et la mécanique théorique des fluides. Publ. scient. et techn. du Ministére de l’Air, 234 (1949), Paris

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  5. Jacob, C. On some Extensions of the Prandtl Formula for the Wave Length of a Sonic Jet Expanding into the Atmosphere Symposium Transsonicum II, Göttingen, Sept. 8–13, 1975; Springer Verlag Berlin (1976) 217–226

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Authors
  1. C. Jacob
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Editors and Affiliations

  1. Institut für Reaktorbauelemente, Kernforschungszentrum Karlsruhe, D-7514, Eggenstein-Leopoldshafen, Germany

    U. Müller (Professor) (Professor)

  2. Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe (TH), Kaiserstraße 12, D-7500, Karlsruhe 1, Germany

    K. G. Roesner (Professor) & B. Schmidt (Professor) (Professor) &  (Professor)

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© 1979 Springer-Verlag Berlin Heidelberg

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Jacob, C. (1979). Range of Validity of the Formulae Derived by Linear Aerodynamic Theory for the Prandtl Supersonic Jet Problem. In: Müller, U., Roesner, K.G., Schmidt, B. (eds) Recent Developments in Theoretical and Experimental Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67220-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-67220-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-67222-4

  • Online ISBN: 978-3-642-67220-0

  • eBook Packages: Springer Book Archive

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