Determining the shape of an axisymmetric body in a viscous incompressible flow on the basis of the pressure distribution on the body surface

  • S. A. Solov’evEmail author


A method is developed for determining the shape of an axisymmetric body on the basis of the pressure coefficient distribution specified along the meridional section of the body. Viscosity is taken into account within the framework of the boundary layer model. The method is based on an iterative process, which involves the solutions of the inverse problem in the plane case and of the direct problem for an axisymmetric body. A code implementing the iterative process is written, and examples of numerical results are given.

Key words

inverse boundary-value problem of aerohydrodynamics viscous incompressible fluid boundary layer axisymmetric body iterative process panel method 


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  1. 1.
    C. Fletcher, Computational Techniques for Fluid Dynamics, Springer-Verlag, Heidelberg (1988).zbMATHGoogle Scholar
  2. 2.
    L. G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon Press, Oxford-New York (1966).Google Scholar
  3. 3.
    P. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill, London (1981).Google Scholar
  4. 4.
    A. M. Elizarov, N. B. Il’inskii, and A. V. Potashev, Inverse Boundary-Value Problems of Aerohydrodynamics [in Russian], Nauka, Moscow (1994).zbMATHGoogle Scholar
  5. 5.
    O. M. Kiselev, “Construction of the body of revolution on the basis of the velocity distribution specified on the body surface,” Izv. Vyssh. Uch. Zaved., Aviats. Tekh., No. 2, 20–24 (1959).Google Scholar
  6. 6.
    I. I. Eterman, “Determination of the surface of the body of revolution on the basis of the specified pressure distribution,” Dokl. Akad. Nauk SSSR, 56, No. 4, 351–353 (1947).zbMATHGoogle Scholar
  7. 7.
    O. A. Vyachkilev, N. B. Il’inskii, G. R. Ismagilova, et al., “Inverse boundary-value problem for a cascade of airfoils located on an axisymmetric stream surface in a variable-thickness layer,” Zh. Vychisl. Mat. Mat. Fiz., 36, No. 11, 134–142 (1996).Google Scholar
  8. 8.
    N. B. Il’inskii, R. F. Mardanov, and S. A. Solov’ev, “Combined method for solving an inverse boundary-value problem of aerohydrodynamics for an axisymmetric body,” Zh. Vychisl. Mat. Mat. Fiz., 48, No. 7, 1294–1308 (2008).Google Scholar
  9. 9.
    L. G. Loitsyanskii, Laminar Boundary Layer [in Russian], Fizmatgiz, Moscow (1962).Google Scholar
  10. 10.
    G. Schlichting, Boundary Layer Theory, McGraw-Hill, New York (1968).Google Scholar
  11. 11.
    R. Eppler, Airfoil Design and Data, Springer-Verlag, Berlin (1990).Google Scholar
  12. 12.
    Th. Lutz, Berechnung und Optimierung Subsonisch Umstromter Profile und Rotationskorper, VDI Verlag, Dusseldorf (2000).Google Scholar
  13. 13.
    J. L. Hess, “On the problem of shaping an axisymmetric body to obtain low drag at large Reynolds number,” J. Ship Res., 20, 51–60 (1976).Google Scholar

Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Chebotarev Institute of Mathematics and MechanicsKazan’ State UniversityKazan’Russia

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