Abstract
We discuss here a method for computation of gradually variable laminar flows for large Reynold number. The model consists in approximating locally the flow with self similar profiles. This approach permits a derivation of two coupled ordinary differential equations. One of them is the Falkner-Skan equation with specific boundary conditions that once solved permits to study variable flows in quite different problems or geometries. We apply the model to the problem of the Poiseuille flow, and compare it with the solution obtained by integrating directly the fluid motion equation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Prandtl, Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Vcrh. III. Intern. Math Kongr., Heidelberg, 484–491, (1904).
H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys., 56(1), 1–37, 1908.
M. Van Dyke, An Album of fluid motion, Parabolic Press, Stanford, CA, 1982.
J. Nikuradse, Laminare Reibunggsschicten an der längsangetrömten Platte, Monograph, Zentrale F. wiss Berichtswescn, Berlin, 1942.
R. H. Terrill, Phyl. Trans, Roy. Soc. London A 253, 55–100, 1960.
M.E. Goldstein, Q.J.M.A.M., 1(I), 43–69, 1948.
K. Hiemenz, Die grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eigetauchten geradcn Krciszylinder, Thesis, Göttingen (1911).
H. Görtler, Jour. Math. and Mechanics 6, 1–66, 1957
V. M. Falkner and S. W. Skan, Aero. Res.Coun. Rep. and Mem. no 1314, 1930.
D. Meksyn, New Methods in Laminar Boundary Layer Theory, Oxford UK: Pergamon Press, 1961.
L. Rosenhead, Laminar boundary layer, Oxford, UK: Oxford University press, 1963.
D.R. Hartree, Proc. Camb. Phil. Soc. 33II, 223–239, 1937.
H. Stewartson, Further solutions of the Falkner-Skan equations, Proc. Camb. Phil. Soc., 50, 454–465, 1954.
L. D. Landau and E. M. Lifshitz, Fluid Mechanics Pergamon Press New York 1987.
H. Schlichting, Boundary Layer Theory, McGraw-Hill, 1968.
M. Argentina & E. Cerda, to be published.
T. Bohr, V. Putkaradze and S. Watanabe, Phys. Rev. Lett 79, 1038–1041, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Argentina, M., Cerda, E. (2004). Falkner-Skan approximation for gradually variable flows. In: Descalzi, O., Martínez, J., Rica, S. (eds) Instabilities and Nonequilibrium Structures IX. Nonlinear Phenomena and Complex Systems, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0991-1_4
Download citation
DOI: https://doi.org/10.1007/978-94-007-0991-1_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3760-0
Online ISBN: 978-94-007-0991-1
eBook Packages: Springer Book Archive