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Flow in curved ducts. Part 2. Rotating ducts

Published online by Cambridge University Press:  26 April 2006

P. Daskopoulos  and
A. M. Lenhoff
P. Daskopoulos
Affiliation:
Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA
A. M. Lenhoff
Affiliation:
Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA
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Abstract

When a coiled tube is rotated about the coil axis, the effects of rotation interact with centrifugal and viscous effects to complicate the flow characteristics beyond those seen in stationary curved ducts. The phenomena encountered are examined for steady, fully developed Newtonian flow in circular tubes of small curvature. The governing equations are solved using orthogonal collocation, and the results presented cover both the nature of the flow and the bifurcation structure. When rotation is in the same direction as the axial flow imposed by a pressure gradient, the flow structure remains similar to that seen in stationary ducts, i.e. with two- or four-vortex secondary flows in addition to the axial flow. There are, however, quantitative changes, which are due to the Coriolis forces resulting from rotation. The bifurcation structure also shows only quantitative changes from that for stationary ducts at all values of Taylor number examined. More complex behaviour is possible when rotation opposes the flow due to the pressure gradient. In particular, the direction of the secondary flow may be reversed at higher rotational strengths, and the mechanism of the flow reversal is explored. The flow reversal occurs smoothly at low Taylor numbers, but at higher rotational strengths a cusp appears in the primary solution branch in the vicinity of the flow reversal.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 575 - 593
Copyright
© 1990 Cambridge University Press

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References

Adler, R. J., Gorensek, M. B., Landin, M. E., Menon, M. M., Papanu, J. S. & Trost, H. F. 1981 A new method of fine particle slurry fractionation. Paper presented at ACS National Meeting, New York.
Adler, R. J., Gorensek, M. B., Menon, M. M. & Papanu, J. S. 1982 Periodic axial and secondary flow centrifugal separation. Paper presented at AIChE Annual Meeting, Los Angeles.
Barua, S. N. 1954 Secondary flow in a rotating straight pipe. Proc. R. Soc. Lond. A 227, 133–139.Google Scholar
Barua, S. N. 1963 On secondary flow in stationary curved pipes. Q. J. Mech. Appl. Maths 16, 61–77.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous fluid. I. Theory. Proc. R. Soc. Lond. A 359, 1–26.Google Scholar
Benton, G. S. & Boyer, D. 1966 Flow through a rapidly rotating conduit of arbitrary cross-section. J. Fluid Mech. 26, 69–79.Google Scholar
Daskopoulos, P. 1989 Flow in separations processes in rotating helically coiled tubes. Ph.D. thesis, University of Delaware.
Daskopoulos, P. & Lenhoff, A. M. 1989 Flow in curved ducts: bifurcation structure for stationary ducts. J. Fluid Mech. 203, 125–148 (referred to herein as I).Google Scholar
Daskopoulos, P. & Lenhoff, A. M. 1990 The Taylor—Dean problem with co-rotating cylinders. Z. Angew. Math. Phys. (in press).Google Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. (7) 4, 208–223.Google Scholar
Dean, W. R. 1928 The streamline motion of fluid in a curved pipe (second paper). Phil. Mag (7) 5, 673–695.Google Scholar
Dean, W. R. & Hurst, J. M. 1959 Note on the motion of fluid in a curved pipe. Mathematika 6, 77–85.Google Scholar
Euteneuer, G.-A. & Piesche, M. 1978 Druckabfallmessungen in stationär rotierenden, gekrümmten Kanalstrecken mit quadratischem sowie kreisförmigem Durchflußquerschnitt. Forsch. Ing.-Wes. 44, 53–56.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341–351.Google Scholar
Hocking, L. M. 1967 Boundary and shear layers in a curved rotating pipe. J. Math. Phys. Sci. 1, 123–136.Google Scholar
Itø, H. & Motai, T. 1974 Secondary flow in a rotating curved pipe. Rep. Inst. High Speed Mech. 29, 33–57.Google Scholar
Itø, H. & Nanbu, K. 1971 Flow in rotating straight pipes of circular cross section. Trans. ASME D: J. Basic Engng 93, 383–394.Google Scholar
Jones, J. R. & Walters, T. S. 1967 A note on the motion of a viscous liquid in a rotating straight pipe. Z. Angew. Math. Phys. 18, 774–781.Google Scholar
Joseph, B. & Adler, R. J. 1975 Numerical treatment of laminar flow in helically coiled tubes of square cross section. Part II. Oscillating helically coiled tubes. AIChE J. 21, 974–979.Google Scholar
Keller, H. B. 1977 Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359–255. Academic.
Keller, H. B. 1982 Continuation methods in computational fluid dynamics. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), pp. 3–255. Springer.
Kheshgi, H. S. & Scriven, L. E. 1985 Viscous flow through a rotating square channel. Phys. Fluids 28, 2968–2979.Google Scholar
Lennartz, J. W., Gorensek, M. B. & Adler, R. J. 1987 Separation of fine-particle dispersions using periodic flows in a spinning coiled tube. Part III: Batch fractionation experiments. AIChE J. 33, 506–509.Google Scholar
Ludwieg, H. 1951 Die ausgebildete Kanalströmung in einem rotierenden System. Ing. Arch. 19, 296–308.Google Scholar
Mansour, K. 1985 Laminar flow through a slowly rotating straight pipe. J. Fluid Mech. 150, 1–21.Google Scholar
Menon, M. M. 1984 Periodic centrifugal separations. M.S. thesis, Case Western Reserve University.
Miyazaki, H. 1971 Combined free and forced convective heat transfer and fluid flow in a rotating curved circular tube. Intl J. Heat Mass Transfer 14, 1295–1309.Google Scholar
Miyazaki, H. 1973 Combined free- and forced-convective heat transfer and fluid flow in rotating curved rectangular tubes. Trans. ASME C: J. Heat Transfer 95, 64–71.Google Scholar
Mori, Y. & Nakayama, W. 1968 Convective heat transfer in rotating radial circular pipes. Intl J. Heat Mass Transfer 11, 1027–1040.Google Scholar
Piesche, M. 1982 Experimente zum Strömungswiderstand in gekrümmten. rotierenden Kanälen mit quadratischem Querschnitt. Acta Mechanica 42, 145–151.Google Scholar
Piesche, M. & Felsch, K.-O. 1980 Experimental investigation of pressure loss in rotating curved rectangular channels. Arch. Mech. 32, 747–756.Google Scholar
Speziale, C. G. 1982 Numerical study of viscous flow in rotating rectangular ducts. J. Fluid Mech. 122, 251–271.Google Scholar
Van Dyke, M. 1975 Computer extension of perturbation series in fluid mechanics. SIAM J. Appl. Maths 28, 720–734.Google Scholar
Van Dyke, M. 1978 Extended Stokes series: laminar flow through a loosely coiled pipe. J. Fluid Mech. 86, 129–145.Google Scholar
Winters, K. H. 1987 A bifurcation study of laminar flow in a curved tube of rectangular cross-section. J. Fluid Mech. 180, 343–369.Google Scholar