Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-20T04:23:43.125Z Has data issue: false hasContentIssue false
  • English
  • Français

A series-expansion study of the Navier–Stokes equations with applications to three-dimensional separation patterns

Published online by Cambridge University Press:  21 April 2006

A. E. Perry  and
M. S. Chong
A. E. Perry
Affiliation:
Mechanical Engineering Department, University of Melbourne, Parkville, Victoria 3052, Australia
M. S. Chong
Affiliation:
Mechanical Engineering Department, University of Melbourne, Parkville, Victoria 3052, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

An algorithm has been developed which enables local Taylor-series-expansion solutions of the Navier-Stokes and continuity equations to be generated to arbitrary order. Much of the necessary algebra for generating these solutions can be done on a computer. Various properties of the algorithm are investigated and checked by making comparisons with known solutions of the equations of motion. A method of synthesizing nonlinear viscous-flow patterns with certain required properties is developed and applied to the construction of a number of two- and three-dimensional flow-separation patterns. These patterns are asymptotically exact solutions of the equations of motion close to the origin of the expansion. The region where the truncated series solution satisfies the full equations of motion to within a specified accuracy can be found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 207 - 223
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bippes, H. & Turk, M. 1983 Oil flow patterns of separated flow on a hemisphere cylinder at incidence. DFVLR Rep. No. IB 222–83 A 07, Göttingen, West Germany.
Dallmann, U. 1983 Topological structures of three-dimensional flow separation. DFVLR Rep. No. IB 221–82 A 07, Göttingen, West Germany.
Fairlie, B. D. 1980 Flow separation on bodies of revolution at incidence. In Proc. 7th Austr. Hydr. and Fluid Mech. Conf., Brisbane, pp. 338–341.
Hornung, H. G. 1983 The vortex skeleton model for three-dimensional steady flows. Aerodynamics of vortical type flows in three dimensions. AGARD Conf. Proc. No. 342.Google Scholar
Hornung, H. G. & Perry, A. E. 1984 Some aspects of three-dimensional separation. Part 1. Streamsurface bifurcations. Z. Flugwiss. Weltraumforschung 8, 77–87.Google Scholar
Lighthill, M. J. 1963 Attachment and separation in three-dimensional flow. In Laminar Boundary Layers (ed. L. Rosenhead), pp. 72–82. Oxford University Press.
Oswatitsch, K. 1958 Die Ablösungsbedingung von Grenzschichten. In Grenzschichtforschung (ed. H. Goertler), pp. 357–367. Springer.
Perry, A. E. 1984a A study of degenerate and non-degenerate critical points in three-dimensional flow fields. Forschungsbericht DFVLR-FB 84–36, Göttingen, West Germany.
Perry, A. E. 1984b A series expansion study of the Navier—Stokes equations. Forschungsbericht DFVLR-FB 84–34, Göttingen, West Germany.
Perry, A. E. & Chong, M. S. 1986 A series expansion study of the Navier—Stokes equations with applications to three-dimensional separation patterns—A detailed treatment. Rep. FM-17. Mech. Engng Dept, University of Melbourne.
Perry, A. E., Chong, M. S. & Hornung, H. G. 1985 Local solutions of the Navier—Stokes equations for separated flows. 3rd Symp. on Numerical and Physical Aspects of Aerodynamic Flows, California State University, Long Beach, California.
Perry, A. E. & Fairlie, B. D. 1974 Critical points in flow patterns. Adv. Geophys. B 18, 299–315.Google Scholar
Perry, A. E. & Hornung, H. G. 1984 Some aspects of three-dimensional separation. Part II. Vortex skeletons. Z. Flugwiss. Weltraumforschung 8, 155–160.Google Scholar
Tobak, M. & Peake, D. J. 1982 Topology of three-dimensional separated flows. Ann. Rev. Fluid Mech. 14, 61–85.Google Scholar