Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T06:01:08.340Z Has data issue: false hasContentIssue false
  • English
  • Français

On laminar flow in curved semicircular ducts

Published online by Cambridge University Press:  19 April 2006

Jacob H. Masliyah
Jacob H. Masliyah
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

Calculations of the flow field under laminar conditions in a helical semicircular duct have been made by numerically solving the Navier–Stokes equations. With the flat wall of the duct being the outer wall, the solution of the momentum equations for Dean numbers below 105 gave, for the secondary flow, twin counter-rotating vortices of Taylor–Goertler type. However, above a Dean number of Dn = 105, two solutions were possible. One solution was similar to that obtained for Dn < 105. The other solution revealed four vortices for the secondary flow. For Dn > 105, convergence to either flow pattern depended on the initial guess used in the numerical solution. Flow visualization confirmed the possibility of the presence of both types of secondary flow patterns.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 3 , 14 August 1980 , pp. 469 - 479
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akiyama, M. 1979 Laminar convection in curved rectangular channels. M.Sc. thesis, University of Alberta.
Austin, L. R. & Seader, J. D. 1973 Fully developed viscous flow in coiled circular pipes. A.I.Ch.E. J. 19, 85–94.Google Scholar
Benjamin, T. B. 1978a Bifurcation phenomena in steady flows of a viscous fluid. I. Theory. Proc. Roy. Soc. A 359, 1–26.Google Scholar
Benjamin, T. B. 1978b Bifurcation phenomena in steady flows of a viscous fluid. II. Experiments. Proc. Roy. Soc. A 359, 27–43.Google Scholar
Cheng, K. C. & Akiyama, M. 1970 Laminar forced convection heat transfer in curved rectangular channels. Int. J. Heat Mass Transfer 13, 471–490.Google Scholar
Cheng, K. C., Lin, R.-C. & Ou, J.-W. 1976 Fully developed laminar flow in curved rectangular channels. Trans. A.S.M.E. I, J. Fluids Engng 98, 41–48.Google Scholar
Cheng, K. C., Nakayama, J. & Akiyama, M. 1977 Effect of finite and infinite aspect ratios on flow patterns in curved rectangular channels. Proc. Int. Symp. on Flow Visualization, Tokyo, Japan.
Collins, W. M. & Dennis, S. C. R. 1975 The steady motion of a viscous fluid in curved tube. Quart. J. Mech. Appl. Math. 28, 133–156.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1976a Viscous eddies near a 90° and a 45° corner in flow through a curved tube of triangular cross-section. J. Fluid Mech. 76, 417–432.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1976b Steady flow in a curved tube of triangular cross section. Proc. Roy. Soc. A 352, 189–211.Google Scholar
Dean, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. 5 (7), 673–695.Google Scholar
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
Itö, H. 1969 Laminar flow in curved pipes. Z. angew. Math. Mech. 11, 653–663.Google Scholar
Joseph, B., Smith, E. P. & Adler, R. J. 1975 Numerical treatment of laminar flow in helically coiled tubes of square cross section. A.I.Ch.E. J. 21, 965–974.Google Scholar
Masliyah, J. H. & Nandakumar, K. 1977 Fluid flow and heat transfer in internally finned helical coils. Can. J. Chem. Engng 55, 27–36.Google Scholar
Masliyah, J. H. & Nandakumar, K. 1979 Fully developed viscous flow and heat transfer in curved semi-circular sectors. A.I.Ch.E. J. 25, 478–487.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.Google Scholar
McConalogue, D. J. & Srivastava, R. S. 1968 Motion of a fluid in a curved tube. Proc. Roy. Soc. A 307, 37–53.Google Scholar
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn, p. 503. McGraw-Hill.
Smith, F. T. 1976 Steady motion within a curved pipe. Proc. Roy. Soc. A 347, 345–370.Google Scholar
Van Dyke, M. 1978 Extended Stokes series: Laminar flow through a loosely coiled pipe. J. Fluid Mech. 86, 129–145.Google Scholar
Wilkes, M. V. 1966 A Short Introduction to Numerical Analysis, p. 74. Cambridge University Press.