Advertisement

Flow, Turbulence and Combustion

, Volume 82, Issue 1, pp 93–120 | Cite as

Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

  • Elia MerzariEmail author
  • Hisashi Ninokata
Article

Abstract

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.

Keywords

Large eddy simulation Concentric channel Eccentric channel Dynamic model Boundary fitted coordinates Secondary flows 

References

  1. 1.
    Kacker, S.C.: Some aspects of fully developed turbulent flow in non-circular ducts. J. Fluid Mech. 57, 583–682 (1973)CrossRefADSGoogle Scholar
  2. 2.
    Nikitin, N.V.: Direct numerical simulation of turbulent flows in eccentric pipes. Comput. Math. Math. Phys. 46, 509–526 (2006)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Guellouz, M.S., Tavoularis, S.: The structure of turbulent flow in a rectangular channel containing a cylindrical rod—part 1: Reynolds averaged experiments. Exp. Therm. Fluid Sci. 29, 59–73 (2000)CrossRefGoogle Scholar
  4. 4.
    Gosset, A., Tavoularis, S.: Laminar flow instability in a rectangular channel with a cylindrical core. Phys. Fluids. 18, 044108-1–044108-8 (2006). doi:10.1063/1.2194968 CrossRefADSGoogle Scholar
  5. 5.
    Lumley, J.L.: Stochastic Tools in Turbulence. Academic, New York (1970)zbMATHGoogle Scholar
  6. 6.
    Zang, Y., Street, R.L., Koseff, J.R.: A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 1 (1994)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  8. 8.
    Jordan, S.A.: A large eddy simulation methodology in generalized curvilinear coordinates. J. Comput. Phys. 148, 322–340 (1999)zbMATHCrossRefGoogle Scholar
  9. 9.
    Jordan, S.A.: Dynamic subgrid-scale modeling for large-eddy simulations in complex topologies. J. Fluids Eng. 123(3), 619–627 (2001)CrossRefGoogle Scholar
  10. 10.
    Germano, M., Piomelli, U., Moin, P.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A. 3, 1760 (1991)zbMATHCrossRefADSGoogle Scholar
  11. 11.
    Lund, T.S.: On the Use of Discrete Filters for Large Eddy Simulation. Annual Research Briefs, Stanford University (1997)Google Scholar
  12. 12.
    Armenio, V., Piomelli, U.: A Lagrangian mixed subgrid-scale model in generalized coordinates. Flow Turbul. Combust. 65, 51–81 (2000)zbMATHCrossRefGoogle Scholar
  13. 13.
    Merzari, E., Ninokata, H.: Test of LES SGS models for the flow in annular channels. In: Proceedings of ICAPP 2007, Nice, France, 13–18 May 2007Google Scholar
  14. 14.
    Misawa, T.: Development of a numerical experimental method for the evaluation of the thermal–hydraulic design of fuel with high conversion ratio. Ph.D. thesis, Tokyo Institute of Technology (2004)Google Scholar
  15. 15.
    Suzuki, T., Kawamura, N.: Consistency of finite—difference scheme in direct simulation of turbulence. Trans. JSME. 60, 578 (1994) (in Japanese)Google Scholar
  16. 16.
    Kogaki, T., Kobayashi, T., Taniguchi, N.: Proper finite difference schemes for simulations of incompressible turbulent flow in generalized curvilinear coordinates. Trans. JSME. B. 65–633, 1559–1567 (1999) (in Japanese)Google Scholar
  17. 17.
    Nouri, J.M., Umur, H., Whitelaw, J.H.: Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli. J. Fluid Mech. 253, 617–664 (1993)CrossRefGoogle Scholar
  18. 18.
    Chung, S.Y., Rhee, G.H., Sung, H.: Direct numerical simulation of turbulent concentric annular pipe flow—part 1: flow field. Int. J. Heat Fluid Flow. 23, 426–440 (2002)CrossRefGoogle Scholar
  19. 19.
    Jiménez, J., Moin, P.: The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240 (1991)zbMATHCrossRefADSGoogle Scholar
  20. 20.
    Moin, P.: Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578 (1998)CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Nan-Sheng, L., Xi-Yun, L.: Large eddy simulation of turbulent concentric annular channel flows. Int. J. Numer. Methods Fluids. 45, 1317–1338 (2004)zbMATHCrossRefGoogle Scholar
  22. 22.
    Neves, J.C., Moin, P., Moser, R.D.: Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity. J. Fluid Mech. 272, 349–382 (1973)CrossRefADSGoogle Scholar
  23. 23.
    Kasagi, N., Horiuti, K., Miyake, Y., Miyauchi, T., Nagano, Y.: Establishment of the direct numerical simulation data bases of turbulent transport phenomena (1992). Available at http://www.thtlab.t.u-tokyo.ac.jp/DNS
  24. 24.
    Jonsson, V.K., Sparrow, E.M.: Experiments on turbulent-flow phenomena in eccentric annular ducts. J. Fluid Mech. 25, 65–86 (1966)CrossRefADSGoogle Scholar
  25. 25.
    Azouz, I., Shirazi, S.A.: Evaluation of several turbulence models for turbulent flow in concentric and eccentric annuli. J. Energy Resour. Technol. 120, 268–274 (1998)CrossRefGoogle Scholar
  26. 26.
    Snyder, W.T., Goldstein, G.A.: An analysis of fully developed laminar flow in an eccentric annulus. AIChE J. 11, 462–467 (1965)CrossRefGoogle Scholar
  27. 27.
    Hunt, J., Wray, A., Moin, P.: Eddies, streams and convergence zones in turbulent flows. Report CTR-S88, Center for Turbulence Research, Stanford University (1988)Google Scholar
  28. 28.
    Hooper, J.D., Rehme, K.: Large-scale structural effect in developed turbulent flows through closely-spaced rod arrays. J. Fluid Mech. 145, 305–337 (1984)CrossRefGoogle Scholar
  29. 29.
    Meyer, L., Rehme, K.: Large-scale turbulence phenomena in compound rectangular channels. Exp. Therm. Fluid Sci. 8, 286–304 (1994)CrossRefGoogle Scholar
  30. 30.
    Berkooz, G., Holmes, P., Lumley, J.L.: The proper orthogonal decomposition in the analisys of turbulent flow. Ann. Rev. Fluid Mech. 25, 539–575 (1993)CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    Lumley, J.L., Newman, G.R.: The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–179 (1977)zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Research Laboratory for Nuclear ReactorsTokyo Institute of TechnologyTokyoJapan

Personalised recommendations