Two coordinate systems description of viscous flow past a circular cylinder

F.P.H. van Beckum

doi:10.1007/3-540-08004-X_303

Two coordinate systems description of viscous flow past a circular cylinder

F.P.H. van Beckum

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.

This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.

Original language	English
Title of host publication	Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede
Editors	Adriaan I. van de Vooren, Pieter J. Zandbergen
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	101-106
ISBN (Electronic)	978-3-540-37548-7
ISBN (Print)	978-3-540-08004-6
DOIs	https://doi.org/10.1007/3-540-08004-X_303
Publication status	Published - 1976
Event	5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976 - Twente University, Enschede, Netherlands Duration: 28 Jun 1976 → 2 Jul 1976 Conference number: 5

Publication series

Name	Lecture Notes in Physics
Publisher	Springer
Volume	59
ISSN (Print)	0075-8450
ISSN (Electronic)	1616-6361

Conference

Conference	5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976
Abbreviated title	NMFD
Country/Territory	Netherlands
City	Enschede
Period	28/06/76 → 2/07/76

Keywords

Convection term
Polar system
Vorticity equation
Vorticity distribution
Polar grid

Access to Document

10.1007/3-540-08004-X_303

VanBeckum1976twoFinal published version, 312 KB

Cite this

van Beckum, F. P. H. (1976). Two coordinate systems description of viscous flow past a circular cylinder. In A. I. van de Vooren, & P. J. Zandbergen (Eds.), Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede (pp. 101-106). (Lecture Notes in Physics; Vol. 59). Springer. https://doi.org/10.1007/3-540-08004-X_303

van Beckum, F.P.H. / Two coordinate systems description of viscous flow past a circular cylinder. Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede. editor / Adriaan I. van de Vooren ; Pieter J. Zandbergen. Berlin, Heidelberg : Springer, 1976. pp. 101-106 (Lecture Notes in Physics).

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abstract = "Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.",

keywords = "Convection term, Polar system, Vorticity equation, Vorticity distribution, Polar grid",

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van Beckum, FPH 1976, Two coordinate systems description of viscous flow past a circular cylinder. in AI van de Vooren & PJ Zandbergen (eds), Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede. Lecture Notes in Physics, vol. 59, Springer, Berlin, Heidelberg, pp. 101-106, 5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976, Enschede, Netherlands, 28/06/76. https://doi.org/10.1007/3-540-08004-X_303

Two coordinate systems description of viscous flow past a circular cylinder. / van Beckum, F.P.H.
Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede. ed. / Adriaan I. van de Vooren; Pieter J. Zandbergen. Berlin, Heidelberg: Springer, 1976. p. 101-106 (Lecture Notes in Physics; Vol. 59).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.

AB - Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.

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BT - Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede

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van Beckum FPH. Two coordinate systems description of viscous flow past a circular cylinder. In van de Vooren AI, Zandbergen PJ, editors, Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede. Berlin, Heidelberg: Springer. 1976. p. 101-106. (Lecture Notes in Physics). doi: 10.1007/3-540-08004-X_303