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Nonuniqueness of the solution of the problem of viscous interaction on an axisymmetric body

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Abstract

The article discusses solutions of the equations of the hypersonic boundary layer on an axisymmetric offset slender body (with a power exponent equal to 3/4), taking account of interactions with a nonviscous flow. It is shown that, in this case, the equations of the boundary layer have solutions differing from the self-similar solution corresponding to flow around a semi-infinite body. The solutions obtained are analogous to solutions for a strong interaction on a plate with slipping and triangular vanes [1–4], but are obtained over a wide range of values of the parameter of viscous interaction. An asymptotic solution is given to the problem with the approach to zero of the interaction parameter.

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Literature cited

  1. V. Ya. Neiland, “Propagation of perturbations upstream with interaction between a hypersonic flow and a boundary layer,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1970).

  2. I. G. Kozlova and V. V. Mikhailov, “Strong viscous interaction on triangular and slipping vanes,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 6 (dy1970).

  3. I. G. Kozlova and V. V. Mikhailov, “The effect of perturbations of the boundary layer on hypersonic flows with viscous interaction,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1971).

  4. V. Ya. Neiland, “The asymptotic theory of the interaction between a supersonic flow and a boundary layer,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1971).

  5. J. W. Ellinwood and H. Mirels, “Hypersonic viscous interaction theory for slender axisymmetric bodies,” AIAA paper, No. 1 (1968).

  6. V. V. Mikhailov, “Strong viscous interaction on slender three-dimensional bodies,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 5 (1969).

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Authors and Affiliations

  1. Moscow

    V. P. Provotorov

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  1. V. P. Provotorov
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–47, September–October, 1973.

The authors thank V. V. Mikhailova for discussion of the work and useful advice.

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Provotorov, V.P. Nonuniqueness of the solution of the problem of viscous interaction on an axisymmetric body. Fluid Dyn 8, 713–718 (1973). https://doi.org/10.1007/BF01023568

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  • DOI: https://doi.org/10.1007/BF01023568

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