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Friction factors in the theory of bifurcating Poiseuille flow through annular ducts

Published online by Cambridge University Press:  29 March 2006

D. D. Joseph  and
T. S. Chen
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis
T. S. Chen
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Missouri – Rolla, Rolla
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Abstract

The objective of this paper is to show how to formulate a bifurcation theory for pipe flows in terms of the friction factor. We compute the slope of the friction factor vs. Reynolds number curve and the frequency change for the time-periodic solution which bifurcates from Poiseuille flow through annular ducts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 1 , 21 October 1974 , pp. 189 - 207
Copyright
© 1974 Cambridge University Press

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References

Busse, F. 1969 Bounds on the transport of mass and momentum by turbulent flow between parallel plates Z. angew. Math. Phys. 20, 1.Google Scholar
Busse, F. 1970 Bounds for turbulent shear flow J. Fluid Mech. 41, 219.Google Scholar
Chen, T. S. & Joseph, D. D. 1973 Subcritical bifurcation of plane Poiseuille flow J. Fluid Mech. 58, 337.Google Scholar
Hopf, E. 1942 Abzweigung einer periodischen Lösung von einer Stationären Lösung eines Differentialsystems Ber. Math.-Phys., Klasse Sächischen Akad. Wissenschaften, Leipzig, 94, 1–22.Google Scholar
Howard, L. N. 1963 Heat transport in turbulent convection J. Fluid Mech. 17, 405.Google Scholar
Howard, L. N. 1971 Bounds on flow quantities Ann. Rev. Fluid Mech. 4, 473.Google Scholar
Joseph, D. D. 1974 Response curves for plane Poiseuille flow Adv. in Appl. Mech. 14, 241.Google Scholar
Joseph, D. D. & Sattinger, D. H. 1972 Bifurcating time periodic solutions and their stability Arch. Rat. Mech. Anal. 45, 79.Google Scholar
Mott, J. E. & Joseph, D. D. 1968 Stability of parallel flow between concentric cylinders Phys. Fluids, 11, 2065.Google Scholar
Thomas, T. Y. 1942 Qualitative analysis of the flow of fluids in pipes Am. J. Math. 64, 754.Google Scholar
Walker, J. E., Whan, G. A. & Rothfus, R. R. 1957 Fluid friction in noncircular ducts A.I.Ch.E. J. 3, 484.Google Scholar
Wazzan, A. R., Okamura, T. T. & Smith, A. M. D. 1967 Stability of laminar boundary layers at separation Phys. Fluids, 10, 2540.Google Scholar