Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-25T17:20:43.374Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculation of turbulence-driven secondary motion in non-circular ducts

Published online by Cambridge University Press:  20 April 2006

A. O. Demuren  and
W. Rodi
A. O. Demuren
Affiliation:
Institut für Hydromechanik, University of Karlsruhe, Karlsruhe. F.R. Germany
W. Rodi
Affiliation:
Institut für Hydromechanik, University of Karlsruhe, Karlsruhe. F.R. Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate ε of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 140 , March 1984 , pp. 189 - 222
Copyright
© 1984 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

Aly, A. A. M., Trupp, A. C. & Gerrard, A. D. 1978 Measurements and prediction of fully developed turbulent flow in an equilateral triangular duct. J. Fluid Mech. 85, 57–83.Google Scholar
Arnal, D. & Cousteix, J. 1981 Turbulent flow in unbounded streamwise corners. In Proc. 3rd Symp. on Turbulent Shear Flows, Davis, California.
Brundett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375–394.Google Scholar
Buleev, N. I. 1963 Theoretical model of the mechanism of turbulent exchange in fluid flows. AERE Transl. 957.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81–139.Google Scholar
Einstein, H. A. & Li, H. 1958 Secondary currents in straight channels. Trans. Am. Geophys. Union 39, 1085–1088.Google Scholar
Gessner, F. B. 1964 Turbulence and mean-flow characteristics of fully developed flow in rectangular channels. Ph.D. thesis, Dept. Mech. Engng, Purdue University.
Gessner, F. B. 1973 The origin of secondary flow in turbulent flow along a corner. J. Fluid Mech. 58, 1–25.Google Scholar
Gessner, F. B. 1982 Corner flow (secondary flow of the second kind). In Kline et al. (1982), pp. 182–212.
Gessner, F. B. & Emery, A. F. 1980 The numerical prediction of developing turbulent flow in rectangular ducts. In Turbulent Shear Flows 2 (ed. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, J. Whitelaw). Springer. [Also in Trans. ASME I: J. Fluids Engng 103 (1981), 445–455.]
Gessner, F. B. & Jones, J. B. 1965 On some aspects of fully developed turbulent flow in a rectangular channel. J. Fluid Mech. 23, 689–713.Google Scholar
Gosman, D. D. & Rapley, C. W. 1978 A prediction method for fully developed flow through non-circular passages. In Numerical Methods in Laminar and Turbulent Flows (ed. C. Taylor et al.). Pentech.
Hanjaliĉ, K. & Launder, B. E. 1972 A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609–638.Google Scholar
Hinze, J. O. 1973 Experimental investigation of secondary currents in the turbulent flow through a straight conduit. Appl. Sci. Res. 28, 453–465.Google Scholar
Hoagland, L. C. 1960 Fully developed turbulent flow in straight rectangular ducts - secondary flow, its cause and effect on the primary flow. PhD thesis, Dept Mech. Engng, MIT.
Kacker, S. C. 1973 Discussion of ‘prediction of flow and heat transfer in ducts of square cross-section’. Proc. Inst. Mech. Engng 187, D147–D148.Google Scholar
Klein, A. 1981 Review: turbulent developing pipe flow. Trans. ASME I: J. Fluids Engng 103, 243–249.Google Scholar
Kline, S. J., Cantwell, B. & Lilley, G. M. (eds.) 1982 Proc. 1980–81 AFORS - HTTM Stanford Conf. on Complex Turbulent Flows, Stanford University.
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flow. Comp. Meth. Appl. Mech. & Engng 3, 269–289.Google Scholar
Launder, B. E. & Ying, W. M. 1972 Secondary flows in ducts of square cross-section. J. Fluid Mech. 54, 289–295.Google Scholar
Launder, B. E. & Ying, W. M. 1973 Prediction of flow and heat transfer in ducts of square cross-section. Proc. Inst. Mech. Engrs 187, 455–461.Google Scholar
Ljuboja, M. & Rodi, W. 1980 Calculation of turbulent wall jets with an algebraic Reynolds stress model. Trans. ASME I: J. Fluid Engng 99, 347–356.Google Scholar
Lund, E. G. 1977 Mean flow and turbulence characteristics in the near corner region of a square duct. M.S. thesis, Dept Mech. Engng, University of Washington.
Melling, A. 1975 Investigation of flow in non-circular ducts and other configurations by laser Doppler anemometry. PhD thesis, University of London.
Melling, A. & Whitelaw, J. H. 1976 Turbulent flow in a rectangular duct. J. Fluid Mech. 78, 289–315.Google Scholar
Naot, D. & Rodi, W. 1982 Numerical simulations of secondary currents in channel flow. J. Hydraul. Div. ASCE 108 (HY8), 948–968.Google Scholar
Naot, D., Shavit, H. & Wolfshtein, M. 1974 Numerical calculation of Reynolds stresses in a square duct with secondary flow. Wärme- und Stoffübertragung 7, 151–161.Google Scholar
Nikuradse, J. 1930 Turbulente Strömung in nicht-kreisförmigen Rohren. Ing. Arch. 1, 306–332.Google Scholar
Patankar, S. V. & Spalding, D. B. 1972 A calculation procedure for heat, mass and momentum transfer in 3-D parabolic flows. Intl J. Heat Mass Transfer 15, 1787–1806.Google Scholar
Perkins, H. J. 1970 The formation of streamwise vorticity in turbulent flow. J. Fluid Mech. 44, 721–740.Google Scholar
Prandtl, L. 1926 Über die ausgebildete Turbulenz. Verh. 2nd Int. Kong. für Tech. Mech., Zürich. [Transl. NACA Tech. Memo 435, pp. 62–75.]
Po, J. K. 1975 Developing turbulent flow in the entrance region of a square duct. MS thesis, University of Washington.
Ramachandra, V. 1979 The numerical prediction of flow and heat transfer in rod-bundle geometries. PhD thesis, University of London.
Reece, G. J. 1976 A generalized Reynolds stress model of turbulence. PhD thesis, Imperial College, London.
Rodi, W. 1976 A new algebraic relation for calculating the Reynolds stresses. Z. angew. Math. Mech. 56, T219–T221.Google Scholar
Rodi, W. 1980 Turbulence Models and Their Application in Hydraulics. Intl Assn for Hydraul. Res., Delft, The Netherlands.
Tatchell, D. G. 1975 Convection processes in confined three-dimensional boundary layers. PhD thesis, Imperial College, London.
Tracy, H. J. 1965 Turbulent flow in a three-dimensional channel. J. Hydraul. Div. ASCE 91 (HY6), 9–35.Google Scholar