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DES of turbulent flow over wall-mounted obstacles using wall functions


An adaptive wall function is employed in Detached-Eddy Simulation (DES), a hybrid Reynolds-averaged Navier-Stokes (RANS) — Large Eddy Simulation (LES) model, of turbulent flow past two wall-mounted cubic obstacles in tandem at a Reynolds number Re = 22,000 based on the bulk velocity and the obstacle height. Numerical results are compared with previously published DES solutions obtained on wall integration grids and the experimental measurements of Martinuzzi and Havel (2000). The result shows that wallfunction approach in DES allows reasonable reproduction of coherent vortical structures massively separated from the wall-mounted obstacles to be achieved on wall function grids which require just the half of grid nodes of wall resolving grids. The numerical solutions computed by wall function computations reveal energetic unsteady flow fields with complex coherent vortical structures separated from obstacle edges, whose accuracy is better than those obtained by the unsteady RANS computations on the wall integration grid. Wall function solutions appear to be comparable to the wall-resolving DES solutions in most regions except at the junction of obstacle and the bottom wall where the flow is dominated by the horseshoe vortex with intense unsteadiness. The result confirms that DES with wall function approximation can reasonably resolves geometry-induced unsteady three-dimensional turbulent motions.

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  1. Fröhlich, J. and von Terzi, D. (2008). “Hybrid LES/RANS methods for the simulation of turbulent flows.” Progress in Aerospace Science, Vol. 44, No. 5, pp. 349–337.

  2. Goncalves, E. and Houdeville, R. (2001). “Reassessment of the wall functions approach for RANS computation.” Aerosp. Sci. Technol. Vol. 5, No. 1, pp. 1–14.

  3. Hassan, Y. A. and Barsamian, H. R. (2001). “New-wall modeling for complex flows using the large eddy simulation technique in curvilinear coordinates.” Int. J. Heat Mass Transfer, Vol. 44, No. 21, pp. 4009–4026.

  4. Kalitzin G., Medic, G., Iaccarino, G., and Durbin, P. (2005). “Near-wall behavior of RANS turbulence models and implications for wall functions.” J. Comput. Physics, Vol. 204, No. 1, pp. 265–291.

  5. Keating, A., Prisco, G.D., and Piomelli, U. (2006). “Interface conditions for hybrid RANS/LES calculations.” Int. J. Heat Fluid Flow, Vol. 27, No. 5, pp. 777–788.

  6. Martinuzzi, R. and Havel, B. (2000). “Turbulent flow around two interfering surface mounted cubic obstacles in tandem arrangement.” ASME J. Fluids Eng., Vol. 122, No. 1, pp. 24–31.

  7. Nicoud, F., Baggett, J. S., Moin, P. and Cabot, W. (2001). “Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation.” Physics of Fluids, Vol. 13, No. 10, pp. 2968–2984.

  8. Paik, J., Sotiropoulos F., and Sale, M. J. (2005). “Numerical simulation of swirling flow in a complex hydro-turbine draft tube using unsteady statistical turbulence models.” J. Hydraul. Engrg. ASCE, Vol. 131, No. 6, pp. 441–456.

  9. Paik, J., Sotiropoulos, F. and Porté-Agel, F. (2009). “Detached eddy simulation of flow around two wall-mounted cubes in tandem.” Int. J. Heat Fluid Flow, Vol. 30, No. 2, pp. 286–305.

  10. Piomelli, U. (2008). “Wall-layer models for large-eddy simulations.” Progress in Aerospace Sciences, Vol. 44, No. 6, pp. 437–446.

  11. Piomelli, U. and Balaras, E. (2002). “Wall-layer models for large-eddy simulations.” Annu. Rev. Fluid Mech. Vol. 34, pp. 349–374.

  12. Porté-Agel, F., Meneveau C., and Parlange M. B. (2000). “A scaledependent dynamic model for large-eddy simulation: A application to a neutral atmospheric boundary layer.” J. Fluid Mech., Vol. 415, No. 1, pp. 261–84.

  13. Roni, P., Beechie, T. J., Bilby, R. E., Leonetti, F. E., Pollock, M. M., and Pess, G. R. (2002). “A review of stream restoration techniques and a hierarchical strategy for prioritizing restoration in pacific northwest watersheds.” North Amer. J. Fish. Management, Vol. 22, No. 1, pp. 1–20.

  14. Shields Jr., F. D., Copeland, R. R., Klingeman, P. C., Doyle, M. W., and Simon, A. (2003). “Design for stream restoration.” J. Hydraul. Engrg., ASCE, Vol. 129, No. 8, pp. 575–584.

  15. Shur, M. L., Spalart, P. R., Strelets, M. K., and Traven, A. K. (2008). “A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities.” Int. J. Heat Fluid Flow, Vol. 29, No. 6, pp. 1638–1649.

  16. Smith, D. L. and Brannon, E. L., and Odeh, M. (2005). “Response of juvenile rainbow trout to turbulence produced by prismatoidal shapes.” Trans. Amer. Fish. Society, Vol. 134, No. 3, pp. 741–753.

  17. Spalart, P. R., Jou, W. H., Strelets, M., and Allmaras, S. R. (1997). Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach, Advances in DNS/LES, Liu, C. and Liu, Z. (eds.), Greyden Press, Columbus, OH.

  18. Spalart, P. R., Deck, S., Shur, M., Squires, K., Strelets, M., and Travin, A. (2006). “A new version of detached-eddy simulation, resistant to ambiguous grid densities.” Theor. Comput. Fluid Dyn., Vol. 20, No. 3, pp. 181–195.

  19. Spalart, P. R. (2009). “Detached-eddy simulation.” Annu. Rev. Fluid Mech., Vol. 41, pp. 181–292.

  20. Tang, H. S., Jones, S. C., and Sotiropoulos, F. (2003). “An overset-grid method for 3D unsteady incompressible flows.” J. Comput. Phys., Vol. 191, No. 2, pp. 567–600.

  21. Temmerman, L., Leschziner, M. A., Mellen, C. P., and Fröhlich, J. (2003). “Investigation of wall-function approximations and subgridscale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions.” Int. J. Heat Fluid Flow, Vol. 24, No. 2, pp. 157–180.

  22. Temmerman, L., Hadžiabdic, M., Leschziner, M. A., and Hanjalic, L. (2005). “A hybrid two-layer URANS-LES approach for large eddy simulation at high Reynolds numbers.” Int. J. Heat Fluid Flow, Vol. 26, No. 2, pp. 173–190.

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Correspondence to Joongcheol Paik.

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Paik, J., Sotiropoulos, F. DES of turbulent flow over wall-mounted obstacles using wall functions. KSCE J Civ Eng 16, 189–196 (2012).

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  • coherent structures
  • in-stream structures
  • turbulent flow
  • detached-eddy simulation
  • wall functions