Flow, Turbulence and Combustion

, Volume 102, Issue 1, pp 167–188 | Cite as

An Enhanced Version of Delayed Detached-Eddy Simulation Based on the \(\overline {v^{2}}-f\) Model

  • Yidao DongEmail author
  • Xiaogang Deng
  • Guangxue Wang


To overcome the scale discontinuity of the Delayed Detached-eddy simulation (DDES) based on the \(\overline {v^{2}}-f\) Reynolds-averaged Navier-Stokes (RANS) model developed by Jee and Shariff (International Journal of Heat and Fluid Flow 46(2014) 84), an improvement is proposed in the present work. For the new DDES formulation, the scale discontinuity is avoided in the transition region and the RANS mode is correctly recovered for the shielded region. However, the numerical stability of the new DDES formulation is poor, and the relaxation factor in some locations is extremely large. To improve the numerical stability, the underlying \(\overline {v^{2}}-f\) RANS model is modified. Besides, a damping function is introduced to damp the RANS region when the grid resolution is fine enough and the flow is filled with an abundance of turbulence. Numerical simulations are carried out for some typical wall-bounded flows and special attention is paid to distinguish the effect of the damping function to the resolution capability of the flowfields.


Delayed Detached-eddy simulation \(\overline {v^{2}}-f\) model Numerical stability Damping function Wall-bounded flow 



This work was supported by the Basic Research Foundation of National University of Defense Technology (No. ZDYYJCYJ20140101).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Spalart, P.R., Jou, W.H., Strelets, M., Allmaras, S.R.: Comments on the feas1ibility of les for wings, and on a hybrid rans/les approach. In: Proceedings of First AFOSR International Conference on DNS/LES. Greyden Press, Ruston, Louisiana (1997)Google Scholar
  2. 2.
    Quéméré, P., Sagaut, P.: Zonal multi-domain rans/les simulations of turbulent flows. Int. J. Numer. Methods Fluids 40, 903–925 (2002)CrossRefzbMATHGoogle Scholar
  3. 3.
    Menter, F.R., Kuntz, M.: Adaptation of eddy-viscosity turbulence models to unsteady separated flow behind vehicles. In: McCallen, R., Browand, F., Ross, J. (eds.) Symposium on “The Aerodynamics of Heavy Vehicles: Trucks, Buses and Trains”. Springer, Berlin (2004)Google Scholar
  4. 4.
    Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K., Travin, A.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20, 181–195 (2006)CrossRefzbMATHGoogle Scholar
  5. 5.
    Gritskevich, M.S., Garbaruk, A.V., Schütze, J., Menter, F.R.: Development of ddes and iddes formulations for the k-w shear stress transport model. Flow Turbul. Combust. 88, 431–449 (2012)CrossRefzbMATHGoogle Scholar
  6. 6.
    Nikitin, N.V., Nicoud, F., Wasistho, B., Squires, K.D., Spalart, P.R.: An approach to wall modeling in large-eddy simulations. Phys. Fluids 12, 1629–1632 (2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    Piomelli, U., Balaras, E., Pasinato, H., Squires, K.D., Spalart, P.R.: The inner-outer layer interface in large-eddy simulations with wall-layer models. Int. J. Heat Fluid Flow 24, 538–550 (2003)CrossRefGoogle Scholar
  8. 8.
    Shur, M.L., Spalart, P.R., Strelets, M.K., Travin, A.K.: An enhanced version of des with rapid transition from rans to les in separated flows. Flow Turbul. Combust 95, 709–737 (2015)CrossRefGoogle Scholar
  9. 9.
    Mockett, C., Fuchs, M., Garbaruk, A., Shur, M., Spalart, P., Strelets, M., Thiele, F., Travin, A.: Two non-zonal approaches to accelerate rans to les transition of free shear layers in des. Notes Numer. Fluid Mech. Multidiscip. Des. 130, 187–202 (2015)CrossRefGoogle Scholar
  10. 10.
    Shur, M.L., Spalart, P.R., Strelets, M.K., Travin, A.K.: A hybrid rans-les approach with delayed-des and wall-modelled les capabilities. Int. J. Heat Fluid Flow 29, 1638–1649 (2008)CrossRefGoogle Scholar
  11. 11.
    Reddy, K.R., Ryon, J.A., Durbin, P.A.: A ddes model with a smagorinsky-type eddy viscosity formulation and log-layer mismatch correction. Int. J. Heat Fluid Flow 50, 103–113 (2014)CrossRefGoogle Scholar
  12. 12.
    Yin, Z., Reddy, K.R., Durbin, P.A.: On the dynamic computation of the model constant in delayed detached eddy simulation. Phys. Fluids 27, 4–18 (2015)CrossRefGoogle Scholar
  13. 13.
    He, C., Liu, Y., Yavuzkurt, S.: A dynamic delayed detached-eddy simulation model for turbulent flows. Comput. Fluids 146, 174–189 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kim, W.W., Menon, S.: A new dynamic one-equation subgrid-scale model for large eddy simulations. AlAA 95-0356. AIAA (1995)Google Scholar
  15. 15.
    Durbin, P.A.: Near-wall turbulence closure modeling without damping functions. Theor. Comput. Fluid Dyn. 3, 1–13 (1991)zbMATHGoogle Scholar
  16. 16.
    Durbin, P.A.: A reynolds stress model for near-wall turbulence. J. Fluid Mech. 249, 465–498 (1993)CrossRefGoogle Scholar
  17. 17.
    Durbin, P.A.: Separated flow computations with the k-e-v2 model. AIAA J. 33, 659–664 (1995)CrossRefGoogle Scholar
  18. 18.
    Jee, S., Shariff, K.: Detached-eddy simulation based on the v2-f model. Int. J. Heat Fluid Flow 46, 84–101 (2014)CrossRefGoogle Scholar
  19. 19.
    D’Alessandro, V., Montelpare, S., Ricci, R.: Detached-eddy simulations of the flow over a cylinder at re = 3900 using openfoam. Comput. Fluids 136, 152–169 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Issa, R.: Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62, 40–65 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Lien, F.S., Kalitzin, G., Durbin, P.A.: Rans modelling for compressible and transitional flows. In: Proceedings of the 1998 Summer Program, Center for Turbulence Research. Stanford University (1998)Google Scholar
  22. 22.
    Chien, K.: Predictions of channel and boundary layer flows with a low-reynolds-number turbulence model. AIAA J. 20, 33–38 (1982)CrossRefzbMATHGoogle Scholar
  23. 23.
    Davidson, L., Nielsen, P.V., Sveningsson, A.: Modifications of the v2 model for computing the flow in a 3d wall jet. In: Proceedings of the International Symposium on Turbulence, Heat and Mass Transfer. Antalya (2003)Google Scholar
  24. 24.
    Sveningsson, A., Davidson, L.: Assessment of realizability constraints and boundary conditions in v2-f turbulence models. Turbul. Heat Mass Transf. 4, 585–592 (2003)Google Scholar
  25. 25.
    Kalitzin, G.: Numerical issues and freestream behavior of the v2-f model. Tech. rep., Center for Turbulence Research Annual Research Briefs, Stanford University (2004)Google Scholar
  26. 26.
    Tartinville, B., Lorrain, E., Hirsch, C.: Application of the v2-f turbulence model to turbomachinery configurations. GT2007-27708. Montreal, Canada (2007)Google Scholar
  27. 27.
    Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of fulland narrow-band velocity signals in grid-generated, isotropic’ turbulence. J. Fluid Mech. 48, 273–337 (1971)CrossRefGoogle Scholar
  28. 28.
    Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to ret = 590. Phys. Fluids 11, 943–945 (1999)CrossRefzbMATHGoogle Scholar
  29. 29.
    Lee, M., Moser, R.D.: Direct numerical simulation of turbulent channel flow up to R e τ = 5200. J. Fluid Mech. 774, 395–415 (2015)CrossRefGoogle Scholar
  30. 30.
    Mirzaei, M., Davidson, L., Sohankar, A., Innings, F.: The effect of corrugation on heat transfer and pressure drop in channel flow with different prandtl numbers. Int. J. Heat Mass Transf. 66, 164–176 (2013)CrossRefGoogle Scholar
  31. 31.
    Mirzaei, M., Sohankar, A., Davidson, L., Innings, F.: Large eddy simulation of the flow and heat transfer in a half-corrugated channel with various wave amplitudes. Int. J. Heat Mass Transf. 76, 432–446 (2014)CrossRefGoogle Scholar
  32. 32.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3, 1760–1765 (1991)CrossRefzbMATHGoogle Scholar
  33. 33.
  34. 34.
    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
  35. 35.
    Breuer, M., Peller, N., Rapp, C., 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

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of Aerospace Science and EngineeringNational University of Defense TechnologyChangshaPeople’s Republic of China
  2. 2.School of PhysicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China

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