Advertisement

Flow, Turbulence and Combustion

, Volume 91, Issue 4, pp 849–866 | Cite as

On Near-Wall Treatment in (U)RANS-Based Closure Models

  • S. JakirlićEmail author
  • J. Jovanović
  • R. Maduta
Article

Abstract

The present work is concerned with computational evaluation of a recently formulated near-wall relationship providing the value of the dissipation rate ε of the kinetic energy of turbulence k through its exact dependence on the Taylor microscale λ: ε = 10νk/λ 2, (Jakirlić and Jovanović, J. Fluid Mech. 656:530–539, 2010). Dissipation rate determination benefits from the asymptotic behavior of the Taylor microscale resulting in its linear variation in terms of the wall distance (λ ∝ y) being valid throughout entire viscous sublayer. Accordingly, it can be applied as a unified near-wall treatment in all computational frameworks relying on a RANS-based model of turbulence (including also hybrid LES/RANS schemes) independent of modeling level—both main modeling concepts eddy-viscosity and Reynolds stress models can be employed. Presently, the feasibility of the proposed formulation was demonstrated by applying a conventional near-wall second-moment closure model based on the homogeneous dissipation rate ε h (\({\varepsilon_h =\varepsilon -0.5\partial \left( {{\nu \partial k}/ {\partial x_j }} \right)} / {\partial x_j }\); Jakirlić and Hanjalić, J. Fluid Mech. 539:139–166, 2002) and its instability-sensitive version, modeled in terms of the inverse turbulent time scale ω h (ω h  = ε h /k; Maduta and Jakirlić, 2011), to a fully-developed channel flow with both flat walls and periodic hill-shaped constrictions mounted on the bottom wall in a Reynolds number range. The latter configuration is subjected to boundary layer separation from a continuous curved wall. The influence of the near-wall resolution lowering with respect to the location of the wall-closest computational node, coarsened even up to the viscous sublayer edge situated at \(y_P^+ \approx 5\) in equilibrium flows, is analyzed. The results obtained follow closely those pertinent to the conventional near-wall integration with the wall-next node positioned at \(y_P^+ \le 0.5\).

Keywords

Computational fluid dynamics RANS Instability-sensitive URANS model Near-wall treatment Near-wall turbulence models Attached and separating flows 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Breuer, M., Manhart, M., Peller, N., Rapp, Ch.: New reference data for the hill flow test case. ERCOFTAC QNET-CFD Knowledge Base Wiki: http://www.ercoftac.org/products_and_services/wiki/; UFR_3-30 test case: http://uriah.dedi.melbourne.co.uk/w/index.php/UFR_3-30
  2. 2.
    Breuer, M., Peller, N., Rapp, CH., Manhart, M.: Flow over periodic hills – numerical and experimental study in a wide range of Reynolds numbers. Comput. Fluids 38, 433–457 (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Craft, T.J., Launder, B.E.: A Reynolds stress closure designated for complex geometries. Int. J. Heat Fluid Flow 17, 245–254 (1996)CrossRefGoogle Scholar
  4. 4.
    Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.A.: Highly resolved large-Eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Jakirlić, S., Hanjalić, K.: A new approach to modelling near-wall turbulence energy and stress dissipation. J. Fluid Mech. 539, 139–166 (2002)Google Scholar
  6. 6.
    Jakirlić, S., Jovanović, J.: On unified boundary conditions for improved prediction of near-wall turbulence. J. Fluid Mech. 656, 530–539 (2010)CrossRefzbMATHGoogle Scholar
  7. 7.
    Jovanović, J., Ye, Q.-Y., Durst, F.: Statistical interpretation of the turbulent dissipation rate in wall-bounded flows. J. Fluid Mech. 293, 321–347 (1995)CrossRefzbMATHGoogle Scholar
  8. 8.
    Launder, B.E., Spalding, D.B.: The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3(2), 269–289 (1974)CrossRefzbMATHGoogle Scholar
  9. 9.
    Le, H., Moin, P., Kim, J.: Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374 (1997)CrossRefzbMATHGoogle Scholar
  10. 10.
    Maduta, R., Jakirlić, S.: An eddy-resolving Reynolds stress transport model for unsteady flow computations. In: Fu, S., Haase, W., Peng, S.-H., Schwamborn, D. (eds.) Advances in hybrid RANS-LES modelling 4. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 117, pp. 77–89. Springer Verlag (ISBN 978-3-642-31817-7) (2011)Google Scholar
  11. 11.
    Marusic, I., Mathis, R., Hutchins, N.: Predictive model for wall-bounded turbulent flow. Science 329, 193–196 (www.sciencemag.org) (2010)Google Scholar
  12. 12.
    Menter, F.R., Egorov, Y.: The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1: theory and model description. Flow Turbul. Combust. 85, 113–138 (2010)CrossRefzbMATHGoogle Scholar
  13. 13.
    Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Reτ = 590. Phys. Fluids 11(4), 943–945 (1999)CrossRefzbMATHGoogle Scholar
  14. 14.
    Pope, S.: Turbulent flows. Cambridge University Press, ISBN 0-521-59886-9 (2000)Google Scholar
  15. 15.
    Popovac, M., Hanjalić, K.: Compound wall treatment for RANS computation of complex turbulent flows and heat transfer. Flow Turbul. Combust. 78(2), 177–202 (2007)CrossRefzbMATHGoogle Scholar
  16. 16.
    Rapp, C.H., Manhart, M.: Flow over periodic hills: an experimental study. Exp. Fluids 51, 247–269 (2011)CrossRefGoogle Scholar
  17. 17.
    Spalart, P.R.: Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307–328 (1986)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of Fluid Mechanics and Aerodynamics/Center of Smart InterfacesTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute of Fluid MechanicsFriedrich-Alexander University of Erlangen-NurembergErlangenGermany

Personalised recommendations