Abstract
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.
Similar content being viewed by others
References
C. Fletcher, Computational Techniques for Fluid Dynamics, Springer-Verlag, Heidelberg (1988).
L. G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon Press, Oxford-New York (1966).
P. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill, London (1981).
A. M. Elizarov, N. B. Il’inskii, and A. V. Potashev, Inverse Boundary-Value Problems of Aerohydrodynamics [in Russian], Nauka, Moscow (1994).
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).
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).
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).
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).
L. G. Loitsyanskii, Laminar Boundary Layer [in Russian], Fizmatgiz, Moscow (1962).
G. Schlichting, Boundary Layer Theory, McGraw-Hill, New York (1968).
R. Eppler, Airfoil Design and Data, Springer-Verlag, Berlin (1990).
Th. Lutz, Berechnung und Optimierung Subsonisch Umstromter Profile und Rotationskorper, VDI Verlag, Dusseldorf (2000).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 6, pp. 16–26, November–December, 2009.
Rights and permissions
About this article
Cite this article
Solov’ev, S.A. Determining the shape of an axisymmetric body in a viscous incompressible flow on the basis of the pressure distribution on the body surface. J Appl Mech Tech Phy 50, 927–935 (2009). https://doi.org/10.1007/s10808-009-0126-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10808-009-0126-7