Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-16T18:57:55.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of turbulence in a square annular duct

Published online by Cambridge University Press:  12 February 2009

HONGYI XU
HONGYI XU*
Affiliation:
Institute for Aerospace Research, National Research Council, Ottawa, ON, Canada
*
†Email address for correspondence: hongyi.xu@nrc.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulation (DNS) is performed to investigate the fully developed turbulence in a straight square annular duct. The mean flow field and the turbulent statistics are compared with existing experiments and numerical results. The comparisons and the analysis of the DNS data led to the discovery of the turbulent boundary layers of concave and convex 90° corners, a corner flow similarity and the scaling characteristics of corner turbulence. Analysis of the mean streamwise velocity near the concave and convex 90° corners resulted in establishing the ‘law-of-the-corner’ formulations. Comparing these formulations with the ‘law-of-the-wall’ relation, both damping and enhancing mechanisms analytically represented by the van Driest damping function, and the enhancement function were revealed for the concave and convex corner turbulence. The investigation captures the distinctive turbulence-driven secondary flows for both convex and concave 90° corners, and a corner flow similarity rule is discovered, which is associated with the pattern of these secondary flows. A turbulence energy spectrum analysis provides the distinctive features of the fully developed turbulence in the wall and corner regions. The validity of the turbulence eddy viscosity concept is evaluated based on these turbulence energy spectra. The turbulence-driven secondary-flow generation mechanisms are investigated by analysing the anisotropy of the Reynolds stresses.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 621 , 25 February 2009 , pp. 23 - 57
Copyright
Copyright © Cambridge University Press 2009

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

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.CrossRefGoogle Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 53–74.CrossRefGoogle Scholar
Breuer, M. & Rodi, W. 1994 Large eddy simulation of turbulent flow through straight and curved ducts. ERCOFTAC Bulletin 22, 26–29.Google Scholar
Brundrett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375–394.CrossRefGoogle 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. Tech Rep. 1011. Aeronautical Engineering Department, Queen May Westfield College, University of London.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Demuren, A. O. & Rodi, W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189–222.CrossRefGoogle Scholar
van Driest, E. R. 1956 Turbulent flow near a wall. J. Aeronaut. Sci. 23, 1007–1011.CrossRefGoogle Scholar
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101–129.CrossRefGoogle Scholar
Gessner, F. B. & Jones, J. B. 1965 On some aspects of fully developed turbulent flow in rectangular channels. J. Fluid Mech. 23, 689.CrossRefGoogle Scholar
Hartnett, J. P., Koh, J. C. Y & McComas, S. T. 1962 A comparison of predicted and measured friction factor for turbulent flow through rectangular duct. Trans. ASMEC: J. Heat Transfer 84, 82.CrossRefGoogle Scholar
Huser, A. & Biringen, S. 1993 Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech. 257, 65–95.CrossRefGoogle Scholar
Kajishima, T. & Miyake, Y. 1992 A discussion on eddy viscosity models on the basis of the large eddy simulation of turbulent flow in a square duct. Comp. Fluids 21, 151–161.CrossRefGoogle Scholar
von, Karman Th. 1930 Mechanische Ahnlichkeit und Turbulenz. In Proc. 3rd Intl Cong. on Applied Mechanics, Stockholm.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comp. Phys. 59, 308–323.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kolmogorov, A. N. 1942 The equation of turbulent motion in an incompressible viscous fluid. Izv. Akad. Nauk S.S.S.R. Ser. Fiz. 6, 56–58.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous imcompressible fluid a high Reynolds number. J. Fluid Mech. 12, 82–85.CrossRefGoogle 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.CrossRefGoogle Scholar
Launder, B. E. & Ying, W. M. 1973 Prediction of flow and heat transfer in ducts of square cross-section. Proc. Inst. Mech. Engng 187, 455.CrossRefGoogle Scholar
Madabhushi, R. K. & Vanka, S. P. 1991 Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A 3 (11), 2734–2745.CrossRefGoogle Scholar
Niederschulte, M. A. 1989 Turbulent flow through a rectangular channel. PhD thesis, University of Illinois at Urbana-Champaign, IL, USA.Google Scholar
Nikuradse, J. 1930 Turbulente stromung in nicht-kreisformigen Rohren. Ing. Arch. 1, 306–332.CrossRefGoogle Scholar
Nishino, K. & Kasagi, N. 1989 Turbulence statistics measurement in a two-dimensional channel flow using a three-dimensional particle tracking velocimeter. In Seventh Symp. on Turbulent Shear Flows, Stanford University, Palo Alto, California.Google Scholar
Perkins, H. J. 1970 The formation of streamwise vorticity in turbulent flow. J. Fluid Mech. 44, 721.CrossRefGoogle Scholar
Prandtl, L. 1904 Motion of fluids with very little viscosity. National Advisory Committee for Aeronautics, Technical Memorandum No. 452, pp. 484–491.Google Scholar
Prandtl, L. 1926 Uber die ausgebildete turbulenz. Verh. In 2nd Intl Kong. Fur Tech. Mech., Zurich..Google Scholar
Rai, M. M. & Moin, P. 1991 Direct simulation of turbulent flow using finite difference schemes. J. Comp. Phy. 96, 15.Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct and sinuous and the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. 51–105.Google Scholar
Speziale, C. G. 1987 On nonlinear k–l and k–ϵ models of turbulence. J. Fluid Mech. 178, 459–475.CrossRefGoogle Scholar
Wang, Jiasheng 1982 Tensor Analyses and Applications. Shanghai Institute of Mechanical Engineering.Google Scholar
Warsi, Z. U. A. 1993 Fluid Dynamics: Theoretical and Computational Approaches. CRC Press.Google Scholar
Wesseling, P. 2001 Principles of Computational Fluid Dynamics. Springer.CrossRefGoogle Scholar
Xu, H. & Pollard, A. 2001 Large eddy simulation of turbulent flows in a square annular duct. Physics of Fluids 13 (11), 3321–3337.CrossRefGoogle Scholar
Xu, H., Yuan, W. & Khalid, M. 2005 Design of a high-performance unsteady Navier–Stokes solver using flexible-cycle additive-correction multi-grid technique. J. Comp. Phys. 209, 504–540.CrossRefGoogle Scholar