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The upstream scale of flow development in curved circular pipes

Published online by Cambridge University Press:  20 April 2006

D. E. Olson  and
B. Snyder
D. E. Olson
Affiliation:
Pulmonary Disease Unit. Veterans Administration Medical Center/University of Michigan, Ann Arbor, Michigan 48105
B. Snyder
Affiliation:
Pulmonary Disease Unit. Veterans Administration Medical Center/University of Michigan, Ann Arbor, Michigan 48105
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Abstract

For steady airflows at moderate Dean number (100 [les ] κ [les ] 500) axial- and transversevelocity profiles were delineated by anemometry in the entry region of curved circular pipes, having curvature ratios R/a of 4.66 or 8. Uniform inlet velocity profiles were found to evolve downstream over two inviscid length scales. Axial profiles develop on the lengthscale a, the pipe radius. The upstream influence extends at least 6a into a bend. Within this region axial development is largely inviscid and apparently independent of the radius of curvature R. Secondary currents develop on the scale (aR)½. Their initial growth is consistent with a model of vorticity transport based on streamline curvature, but instead of progressing monotonically to an asymptotic value, this swirl first overshoots, then subsides approximately 2(aR)½ downstream from the inlet. Hawthorne's model of streamline twist appears to account qualitatively for this dampening.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 139 - 158
Copyright
© 1985 Cambridge University Press

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References

Agrawal Y., Talbot, L. & Gong K.1978 Laser anemometry study of flow development in curved circular pipes. J. Fluid Mech. 85, 497–518.Google Scholar
Akiyama M., Hanaoka Y., Cheng K. C., Urai, I. & Suzuki M.1983 Visual measurements of laminar flow in the entry region of a curved pipe. Proc. 3rd Intl Symp. on Flow Visualization, Ann Arbor (Ed. Wen-Jei Yang), pp. 756–760.
Dennis, S. C. R. & Ng M.1982 Dual solution of steady laminar flow through a curved tube. Q. J. Mech. Appl. Maths 35, 305–324.Google Scholar
Hawthorne W. R.1951 Secondary circulation in fluid flow Proc. R. Soc. Lond. A 206, 374–387.Google Scholar
Hawthorne W. R.1961 Flow in bent pipes. Proc. Sem. on Aeronautical Science, National Aeronautical Laboratory, Bangalore, India, pp. 307–333.
Humphrey J. A. C., Taylor, A. M. K. & Whitelaw J. H.1977 Laminar flow in a square duct of strong curvature. J. Fluid Mech. 83, 509–527.Google Scholar
Olson D. E.1971 Fluid mechanics relevant to respiration: flow within curved or elliptical tubes and bifurcating systems. Ph.D. thesis, University of London.
Olson D. E., Parker, K. H. & Snyder B.1984 A pulsed wire probe for the measurement of velocity and flow direction in slowly moving air. Trans. ASME K: J. Biomech. Engng 106, 72–78.Google Scholar
Olson, D. E. & Snyder B.1983 The growth of swirl in curved circular pipes (Letter). Phys. Fluids 26, 347–349.Google Scholar
Rowe M.1970 Measurements and computations of flow in pipe bends. J. Fluid Mech. 43, 771–783.Google Scholar
Singh M. P.1974 Entry flow in a curved pipe. J. Fluid Mech. 65, 517–539.Google Scholar
Squire, H. B. & Winter K. G.1951 The secondary flow in a cascade of airfoils in a non-uniform stream. J. Aero. Sci. 18, 271–277.Google Scholar
Taylor G. I.1929 The criterion for turbulence in curved pipes Proc. R. Soc. Lond. A 124, 243–249.Google Scholar
Yao, L.-S. & Berger S. A.1975 Entry flow in a curved pipe. J. Fluid Mech. 67, 177–196.Google Scholar