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The production and diffusion of vorticity in duct flow

Published online by Cambridge University Press:  28 March 2006

E. Brundrett  and
W. D. Baines
E. Brundrett
Affiliation:
Department of Mechanical Engineering University of Toronto, Toronto
W. D. Baines
Affiliation:
Department of Mechanical Engineering University of Toronto, Toronto
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Abstract

Secondary flows in non-circular ducts are accompanied by a longitudinal component of vorticity. The equation of motion defining this component in a turbulent flow is composed of three terms giving the rates of production, diffusion and convection. Since the expression for production is the second derivative of Reynolds strees components, longitudinal vorticity cannot exist in laminar flow. For turbulent flow in a square duct the Reynolds stress tensor is examined in detail. Symmetry requirements alone provide relationships showing that the production is zero along all lines of symmetry. General characteristics of flow in circular pipes are sufficient to indicate where the production must be greatest. Experimental measurements verify this result and define the point density of production, diffusion and convection of vorticity. Data also indicate that the basic pattern of secondary flow is independent of Reynolds number, but that with increasing values of Reynolds number the flows penetrate the corners and approach the walls. A similar experimental investigation of a rectangular duct shows that the corner bisectors separate independent secondary flow circulation zones. Production of vorticity is again associated with the region near the bisector. However, there is some evidence that the secondary flow pattern is not so complex as inferred from the distortion of the main longitudinal flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 3 , July 1964 , pp. 375 - 394
Copyright
© 1964 Cambridge University Press

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References

Brundrett, E. 1963 The production and diffusion of vorticity in channel flow. TP 6302, Department of Mechanical Engineering, University of Toronto.
Hinze, J. O. 1959 Turbulence, An Introduction to its Mechanism and Theory. New York: McGraw-Hill Book Company Inc.
Hoagland, L. G. 1960 Fully developed turbulent flow in straight rectangular ducts.. secondary flow, its cause and effect on the primary flow. Ph.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology.
Kunz, K. S. 1957 Numerical Analysis. New York: McGraw-Hill Book Company Inc.
Leutheusser, H. J. 1963 Turbulent flow in rectangular ducts. Amer. Soc. of Civil Engs., J. of the Hydraulics Division, 89, HY 3.Google Scholar
Nikuradse, J. 1926 Untersuchugen über die Geschwindigteitsverteilung in turbulenten Strömungen. Thesis, Göttingen, 1926. V.D.I.-Forsch, 281.
Prandtl, L. 1927 Über den Reibungswiderstand strömenderluft. Ergeb. Aerodyn. Versuch., Göttingen, III series.Google Scholar
Rodet, E. 1960 Etude de l'écoulement d'un fluide dans un tunnel prismatique de section trapézoidale. Publications Scientifiques et Téchniques du Ministére de L'Air, no. 369.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Webster, C. A. G. 1962 A note on the sensitivity to yaw of a hot-wire anemometer. J. Fluid Mech. 13, 307.Google Scholar