Simulation of Viscous Diffusion for Extension of the Surface Vorticity Method to Boundary Layer and Separated Flows

Abstract

A numerical method for two-dimensional incompressible viscous fluid flows is tested on the diffusion of a point vortex. It is then applied to the boundary layer to reconstruct the Blasius profile, to demonstrate flow separation, and to simulate turbulence. The significance of Thwaites' boundary layer parameter for flow separation is explained. The Kelvin-Helmholtz instability, which is responsible for two-dimensional turbulence, is represented by the motion of an array of point vortices after an initial disturbance. The formation of the Von Karman vortex street downstream of a circular cylinder is described by computer simulation, and the influence of viscous diffusion is shown. For two different cylinder Reynolds numbers the vortex shedding frequencies and oscillating lift and drag forces are evaluated.

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References

Lewis

R. I.

, ‘Surface vorticity modelling of separated flows from two-dimensional bluff bodies of arbitrary shape’, Accepted for publication to the J. Mech. Engng Sci., 1981, 23, 1–12.

Chorin

A. J.

, ‘Numerical study of slightly viscous flow’, J. Fluid Mech. 1973 57, 785–796.

Chorin

A. J.

, ‘Vortex sheet approximation of boundary layers’, J. Comp. Phys, 1978, 27, 428–442.

Rosenhead

‘The formation of vortices from a surface of discontinuity’, Proc. Roy. Soc. A 1931 134, 170–192.

Abernathy

F. H.

Kronauer

R. E.

, ‘The formation of vortex streets’, J, Fluid Mech. 1962 13, 1–20.

Gerrard

J. H.

, ‘Numerical computation of the magnitude and frequency of a lift on a circular cylinder’. Phil. Trans Roy. Soc. 1967 261, 137–162.

Clements

R. R.

, ‘An inviscid model of two-dimensional vortex shedding’, J. Fluid Mech. 1973 57, 321–326.

Kuwahara

, ‘Numerical study of flow past an inclined flat plate by an inviscid model’, J. Phys. Soc., Japan, 1973, 35, 1545–1551.

Deffenbaugh

F. D.

Marshall

F. J.

, ‘Time development of the flow about an impulsively started cylinder’, AIAA Journal 1976 14, 908–913.

10.

Blasius

, Z. Math. Phys., 1908, 56.

11.

Batchelor

G. K.

, An introduction to fluid dynamics, 1967 (Cambridge University Press).

12.

Schlichting

, Boundary layer theory, 1960 (McGraw-Hill, New York).

13.

Martensen

, ‘Die Barechnung der Druckverteilungau dicken gitterprofilen mit hilfe von Fredholmachen Integralgleichungen’, Zweiter Art. Arch. Rat. Mech. Anal., 1959, 3.

14.

Chorin

A. J.

Marsden

J. E.

, A mathematical introduction to fluid mechanics, 1979 (Springer-Verlag, Berlin).