Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T06:10:09.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct

Published online by Cambridge University Press:  26 April 2006

S. Gavrilakis
S. Gavrilakis
Affiliation:
IMHEF-DME, Ecole Polytechnique Fédérale de Lausanne, Switzerland 1015
Get access Rights & Permissions [Opens in a new window]

Abstract

The mean flow and turbulent statistics obtained from the numerical simulation of the fully developed turbulent flow through a straight duct of square cross-section are reported. The Reynolds number based on the bulk velocity and hydraulic diameter is 4410. Spatial and temporal approximations of the equations of motion were derived from standard finite-difference techniques. To achieve sufficient spatial resolution 16.1 × 106 grid nodes were employed. Turbulent statistics along the wall bisectors show good agreement with plane channel data despite the influence of the sidewalls in the former flow. The mean secondary flow field consists of two counter-rotating cells symmetrically placed about the corner bisectors with their common flow towards each corner with strong evidence for the existence of a smaller and much weaker pair situated about the wall bisectors. The mean streamwise vorticity of each corner cell is found to be associated with a stronger vorticity distribution of the opposite sign having an absolute maximum on the nearest duct wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 101 - 129
Copyright
© 1992 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

Alfredsson P. H., Johansson A. V., Haritonidis, J. H. & Eckelmann H. 1988 The fluctuating wall shear stress and the velocity field in the viscous sublayer. Phys. Fluids 31, 1026–1033.Google Scholar
Bradshaw P. 1987 Turbulent secondary flows. Ann. Rev. Fluid Mech. 19, 53–74.Google Scholar
Chapman, D. R. & Kuhn G. D. 1986 The limiting behaviour of turbulence near the wall. J. Fluid Mech. 170, 265–292.Google Scholar
Cheesewright R., McGrath, G. & Petty D. G. 1990 LDA measurements of turbulent flow in a duct of square cross section at low Reynolds number. Aeronautical Engineering Dept. Rep. ER 1011. Queen May Westfield College, University of London.Google Scholar
Demuren, A. O. & Rodi W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189–222.Google Scholar
Jones O. C. 1976 An improvement in the calculation of turbulent friction in rectangular ducts. Trans. ASME J: J. Fluids Engng 98, 173–181.Google Scholar
Kim, J. & Moin P. 1985 Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Kim J., Moin, P. & Moser R. 1987 Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Knight, D. W. & Patel H. S. 1985 Boundary shear in smooth rectangular ducts. J. Hydraul. Engng ASCE 111, 29–47.Google Scholar
Kreplin, H. P. & Eckelmann H. 1979 Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22, 1233–1239.Google Scholar
Leutheusser B. E. 1963 Turbulent flow in rectangular ducts. J. Hydraul. Div., ASCE 89, 1–19.Google Scholar
Lund E. G. 1977 Mean flow and turbulence characteristics in the near corner region of a square duct. M.S. thesis, University of Washington.
Morton B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28, 277–308.Google Scholar
Nezu I., Nakagawa, H. & Tominaga A. 1985 Secondary currents in a straight channel flow and the relation to its aspect ratio. In Turbulent Shear Flows 4 (ed. L. J. S. Bradbury et al.) pp. 246–260. Springer.
Niederschulte M. A. 1989 Turbulent flow through a rectangular channel. Ph.D. thesis. University of Illinois at Urbana-Champaign.
Nishino, K. & Kasagi N. 1989 Turbulence statistics measurement in a two-dimensional channel flow using a three-dimensional particle tracking velocimeter. Seventh Symp. on Turbulent Shear Flows, Stanford University, August 21–23.
Popovich, A. T. & Hummel R. L. 1967 Experimental study of the viscous sublayer in turbulent pipe flow. AIChE J. 13, 854–860.Google Scholar
Schlichting H. 1979 Boundary-Layer Theory. McGraw-Hill.
Schumann U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–401.Google Scholar
Speziale G. C. 1986 The dissipation rate correlation and turbulent secondary flows in noncircular ducts. Trans. ASME J: J. Fluids Engng. 108, 118–120.Google Scholar
Swarztrauber P. N. 1974 A direct method for the discrete solution of separable elliptic equations. SIAM J. Numer. Anal. 11, 1136–1150.Google Scholar
Teitel, M. & Antonia R. A. 1990 The interaction region of a turbulent duct flow Phys. Fluids A 2, 808–813.Google Scholar
Townsend A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Wei, T. & Willmarth W. W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.Google Scholar
Yong C. K. 1988 Zur Wirkung von Polymer-Additiven auf die kohärente Struktur turbulenter Kanalströmungen. Doctoral dissertation, University of Essen.