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Analogy between laminar flows in curved pipes and orthogonally rotating pipes

Published online by Cambridge University Press:  26 April 2006

Hiroshi Ishigaki
Hiroshi Ishigaki
Affiliation:
Kakuda Research Center, National Aerospace Laboratory, Kakuda, Miyagi, Japan
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Abstract

The secondary flow of a viscous fluid, caused by the Coriolis force, through a straight pipe rotating about an axis perpendicular to the pipe axis is analogous to that of a fluid, caused by the centrifugal force, through a stationary curved pipe. The quantitative analogy between these two fully developed laminar flows will be demonstrated through similarity arguments, computational studies and the use of experimental data. Similarity considerations result in two analogous governing parameters for each flow, which include a new one for the rotating flow. When one of these analogous pairs of parameters of the two flows is large, it will be demonstrated that there are strong similarities between the two flows regarding friction factors, heat transfer rates, flow patterns and flow properties for the same values of the other pair of parameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 133 - 145
Copyright
© 1994 Cambridge University Press

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References

Akiyama, M. & Cheng, K. C. 1971 Boundary vorticity method for laminar forced convection heat transfer in curved pipes. Intl J. Heat Mass Transfer 14, 1659.Google Scholar
Austin, L. R. & Seader, J. D. 1973 Fully developed viscous flow in coiled circular pipes. AIChE J. 19, 85.Google Scholar
Barua, S. N. 1954 Secondary flow in a rotating straight pipe. Proc. R. Soc. Lond. A 227, 133.Google Scholar
Benton, G. S. & Boyer, D. 1966 Flow through a rapidly rotating conduit of arbitrary cross-section. J. Fluid Mech. 26, 69.Google Scholar
Berger, S. A., Talbot, L. & Yao, L. S. 1983 Flow in curved pipes. Ann. Rev. Fluid Mech. 15, 461.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1975 The steady motion of a viscous fluid in a curved tube. Q. J. Mech. Appl. Maths 28, 133.Google Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 4, 208.Google Scholar
Dean, W. R. 1928 The streamline motion of fluid in a curved pipe. Phil. Mag. 5, 673.Google Scholar
Dennis, S. C. R. & Ng, M. 1981 Dual solutions for steady laminar flow through a curved tube. Q. J. Mech. Appl. Maths 35, 305.Google Scholar
Humphrey, J. A. C., Iacovides, H. & Launder, B. E. 1985 Some numerical experiments on developing laminar flow in circular-sectioned bends. J. Fluid Mech. 113, 357.Google Scholar
Ishigaki, H. & Tamura, H. 1990 Fluid flow and heat transfer in orthogonally rotating pipes. In 3rd Japan—China Joint Conf. on Fluid Machinery, vol. 2, p. 267. Japan Soc. Mech. Engrs.
Ito, H. 1959 Friction factors for turbulent flow in curved pipes. Trans. ASME D: J. Basic Engng 81, 123.Google Scholar
Ito, H. 1987 Flow in curved pipes. Japan Soc. Mech. Engng Intl J. 30, 543.Google Scholar
Ito, H., Hasegawa, S. & Yano, M. 1986 Numerical calculations of laminar flow in rotating pipes. Rep. Inst. High Speed Mech., Tohoku-University 56, 75 (in Japanese).
Ito, H. & Nanbu, K. 1971 Flow in rotating straight pipes of circular cross section. Trans. ASME D: J. Basic Engng 93, 383.Google Scholar
Kheshgi, H. S. & Scriven, L. E. 1985 Viscous flow through a rotating square channel. Phys. Fluids 28, 2968.Google Scholar
Komiyama, Y., Mikami, F. & Okui, K. 1986 Laminar forced convection heat transfer in rectangular ducts rotating about an axis perpendicular to the duct axis. Trans. Japan Soc. Mech. Engng 52-B, 3761 (in Japanese).Google Scholar
Lei, U. & Hsu, C. H. 1989 Flow through rotating straight pipes. Phys. Fluids A 2, 63.Google Scholar
McConalogue, D. J. & Srivastava, R. S. 1968 Motion of fluid in a curved tube. Proc. R. Soc. Lond. A 307, 37.Google Scholar
Mori, Y. & Nakayama, W. 1967 Study on forced convective heat transfer in curved pipes (1st report, laminar region). Intl J. Heat Mass Transfer 8, 67.Google Scholar
Mori, Y. & Nakayama, W. 1968 Convective heat transfer in rotating radial circular pipes (1st report, laminar region). Intl J. Heat Mass Transfer 11, 1027.Google Scholar
Morris, W. D. 1981 Heat Transfer and Fluid Flow in Rotating Coolant Channels. Research Studies Press.
Nandakumar, K. & Masliyah, J. H. 1982 Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 119, 475.Google Scholar
Nandakumar, K. & Masliyah, J. H. 1986 Swirling flow and heat transfer in coiled and twisted pipes. In Advances in Transport Processes (ed. A. S. Mujumdar & R. A. Mashelkar), vol. 4, p. 49. J. Wiley.
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Patankar, S. V., Pratap, V. S. & Spalding, D. B. 1974 Prediction of laminar flow and heat transfer in helically coiled pipes. J. Fluid Mech. 62, 539.Google Scholar
Skiadaressis, D. & Spalding, D. B. 1977 Heat transfer in a pipe rotating around a perpendicular axis. Imperial College Heat Transfer Section Rep. HTS/77/3.
Soh, W. Y. & Berger, S. A. 1984 Laminar entrance flow in a curved pipe. J. Fluid Mech. 148, 109.Google Scholar
Soh, W. Y. & Berger, S. A. 1987 Fully developed flow in a curved pipe of arbitrary curvature ratio. Intl J. Numer. Meth. Fluids 7, 733.Google Scholar
Speziale, C. G. 1982 Numerical study of viscous flow in rotating rectangular ducts. J. Fluid Mech. 122, 251.Google Scholar
Thangam, S. & Hur, N. 1990 Laminar secondary flows in curved rectangular ducts. J. Fluid Mech. 217, 421.Google Scholar
Truesdell, L. C. & Adler, R. J. 1970 Numerical treatment of fully developed laminar flow in helically coiled tubes. AIChE J. 16, 1010.Google Scholar
Ward-Smith, A. J. 1980 Internal Fluid Flow, p. 251. Clarendon.