Journal of Hydrodynamics

, Volume 30, Issue 1, pp 23–33 | Cite as

Five-equation and robust three-equation methods for solution verification of large eddy simulation

Article

Abstract

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark (S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

Keywords

Large eddy simulation (LES) OpenFOAM periodic channel flow solution verification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgement

The authors would like offer gratitude to Idaho National Laboratory (INL) for providing HPC resources for running all the simulations.

References

  1. [1]
    Roache P. J. Verification and validation in computational science and engineering [M]. Albuquerque, New Mexico, USA: Hermosa Publishers, 1998.Google Scholar
  2. [2]
    Roache P. J. Fundamentals of verification and validation [M]. Albuquerque, New Mexico, USA: Hermosa Publishers, 2009.Google Scholar
  3. [3]
    Oberkampf W. L., Roy C. J. Verification and validation in scientific computing [M]. Cambridge, UK: Cambridge University Press, 2010.CrossRefMATHGoogle Scholar
  4. [4]
    Eça L., Hoekstra M. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies [J]. Journal of Computational Physics, 2014, 262: 104–130.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Stern F., Wilson R. V., Coleman H. W. et al. Comprehensive approach to verification and validation of CFD simulations-Part 1: Methodology and procedures [J]. Journal of Fluids Engineering, 2001, 123(4): 793–802.CrossRefGoogle Scholar
  6. [6]
    Stern F., Wilson R., Shao J. Quantitative V&V of CFD simulations and certification of CFD codes [J]. International Journal for Numerical Methods in Fluids, 2006, 50(11): 1335–1355.CrossRefMATHGoogle Scholar
  7. [7]
    Xing T., Stern F. Factors of safety for Richardson extrapolation [J]. Journal of Fluids Engineering, 2010, 132(6): 061403.CrossRefGoogle Scholar
  8. [8]
    Xing T., Stern F. Closure to "Discussion of 'Factors of Safety for Richardson Extrapolation'" (2011, ASME J. Fluids Eng., 133, p. 115501). Journal of Fluids Engineering-Transactions of ASME, 2011, 133(11): 115502.CrossRefGoogle Scholar
  9. [9]
    Meyers J., Sagaut P. Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models? [J]. Physics of Fluids, 2007, 19(4): 048105.CrossRefMATHGoogle Scholar
  10. [10]
    Geurts B. J., Frӧhlich J. A framework for predicting accuracy limitations in large-eddy simulation [J]. Physics of Fluids, 2002, 14(6): L41–L42.CrossRefGoogle Scholar
  11. [11]
    Celik I. B., Cehreli Z. N., Yavuz I. Index of resolution quality for large eddy simulations [J]. Journal of Fluids Engineering, 2005, 127(5): 949–958.CrossRefGoogle Scholar
  12. [12]
    Celik I., Klein M., Janicka J. Assessment measures for engineering LES applications [J]. Journal of Fluids Engineering, 2009, 131(3): 031102.CrossRefGoogle Scholar
  13. [13]
    Gousseau P., Blocken B., Van Heijst G. J. F. Quality assessment of Large-Eddy Simulation of wind flow around a high-rise building: Validation and solution verification [J]. Computers and Fluids, 2013, 79(Suppl. C): 120–133.CrossRefMATHGoogle Scholar
  14. [14]
    Klein M. An attempt to assess the quality of large eddy simulations in the context of implicit filtering [J]. Flow, Turbulence and Combustion, 2005, 75(1): 131–147.CrossRefMATHGoogle Scholar
  15. [15]
    Freitag M., Klein M. An improved method to assess the quality of large eddy simulations in the context of implicit filtering [J]. Journal of Turbulence, 2006, 7: N40.CrossRefGoogle Scholar
  16. [16]
    Xing T. A general framework for verification and validation of large eddy simulations [J]. Journal of Hydrodynamics, 2015, 27(2): 163–175.CrossRefGoogle Scholar
  17. [17]
    Dutta R., Xing T. Quantitative solution verification of large eddy simulation of channel flow [C]. Proceedings of the 2nd Thermal and Fluid Engineering Conference and 4th International Workshop on Heat Transfer, Las Vegas, USA, 2017.Google Scholar
  18. [18]
    Pope S. B.Turbulent flows [M]. Cambridge, UK: Cambridge University Press, 2000.CrossRefGoogle Scholar
  19. [19]
    Yoshizawa A., Horiuti K. A statistically-derived subgridscale kinetic energy model for the large-eddy simulation of turbulent flows [J]. Journal of the Physical Society of Japan, 1985, 54(8): 2834–2839.CrossRefGoogle Scholar
  20. [20]
    Dejoan A., Schiestel R. LES of unsteady turbulence via a one-equation subgrid-scale transport model [J]. International Journal of Heat and Fluid Flow, 2002, 23(4): 398–412.CrossRefGoogle Scholar
  21. [21]
    Smagorinsky J. General circulation experiments with the primitive equations: I. The basic experiment [J]. Monthly Weather Review, 1963, 91(3): 99–164.CrossRefGoogle Scholar
  22. [22]
    Germano M., Piomelli U., Moin P. et al. A dynamic subgrid-scale eddy viscosity model [J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(7): 1760–1765.CrossRefMATHGoogle Scholar
  23. [23]
    Nicoud F., Ducros F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor, flow [J]. Turbulence and Combustion, 1999, 62(3): 183–200.CrossRefMATHGoogle Scholar
  24. [24]
    Kim J., Moin P., Moser R. Turbulence statistics in fully developed channel flow at low Reynolds number [J]. Journal of Fluid Mechanics, 1987, 177: 133–166.CrossRefMATHGoogle Scholar
  25. [25]
    De Villiers E. The potential of large eddy simulation for the modelling of wall bounded flows [D]. Doctoral Thesis, London, UK: University of London, 2007.Google Scholar
  26. [26]
    Gullbrand J. Grid-independent large-eddy simulation in turbulent channel flow using three-dimensional explicit filtering [C]. Annual research briefs: Center for Turbulence Research, San Francisco, USA, 2003.Google Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, College of EngineeringUniversity of IdahoMoscowUSA

Personalised recommendations