Advertisement

Zonal Eddy Viscosity Models Based on Machine Learning

  • R. MataiEmail author
  • P. A. Durbin
Article
First Online:

Abstract

A zonal k − ω model is constructed, with the zones created by training a decision tree algorithm. The training data are optimized, model coefficient fields. Coefficient data are binned, with each bin assigned a particular coefficient value. The zones are parameterized by training the machine learning model with a local feature set. The features are coordinate invariant flow parameters. It is shown that this model gives superior performance, compared to the base model, in the incompressible adverse pressure gradient (APG) flow test cases. The correction produced by the machine learning algorithm is self-consistent; i.e. once the solution converges, the zones remain fixed.

Keywords

Turbulence modeling Machine learning Data driven modeling Turbulence closure model k-ω model 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

This work was supported by National Science Foundation Grant No. 1507928 and NASA grant NNX15AN98A We are grateful for Prof. K. Duraisamy for providing data on optimized coefficients.

References

  1. 1.
    Wilcox, D.C.: Formulation of the kw turbulence model revisited. AIAA J. 46 (11), 2823–2838 (2008)CrossRefGoogle Scholar
  2. 2.
    Parish, E.J., Duraisamy, K.: A paradigm for data-driven predictive modeling using field inversion and machine learning. J. Comput. Phys. 305, 758–774 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Singh, A.P., Matai, R., Mishra, A., Duraisamy, K., Durbin, P.A.: Data-driven augmentation of turbulence models for adverse pressure gradient flows. In: 23rd AIAA Computational Fluid Dynamics Conference, p 3626 (2017)Google Scholar
  4. 4.
    Yarlanki, S., Rajendran, B., Hamann, H.: Estimation of turbulence closure coefficients for data centers using machine learning algorithms. In: 2012 13th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), pp 38–42. IEEE (2012)Google Scholar
  5. 5.
    Duraisamy, K., Zhang, Z.J., Singh, A.P.: New approaches in turbulence and transition modeling using data-driven techniques. In: 53Rd AIAA Aerospace Sciences Meeting, p 1284 (2015)Google Scholar
  6. 6.
    Ling, J., Templeton, J.: Evaluation of machine learning algorithms for prediction of regions of high reynolds averaged navier stokes uncertainty. Phys. Fluids 27(8), 085103 (2015)CrossRefGoogle Scholar
  7. 7.
    Tracey, B.D., Duraisamy, K., Alonso, J.J.: A machine learning strategy to assist turbulence model development. In: 53Rd AIAA Aerospace Sciences Meeting, p 1287 (2015)Google Scholar
  8. 8.
    Ling, J., Jones, R., Templeton, J.: Machine learning strategies for systems with invariance properties. J. Comput. Phys. 318, 22–35 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ling, J., Kurzawski, A., Templeton, J.: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155–166 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Wu, J.L., Wang, J.X., Xiao, H., Ling, J.: A priori assessment of prediction confidence for data-driven turbulence modeling. Flow Turbul. Combust. 99(1), 25–46 (2017)CrossRefGoogle Scholar
  11. 11.
    Wang, J.X., Wu, J.L., Xiao, H.: Physics-informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on dns data. Phys. Rev. Fluids 2(3), 034603 (2017)CrossRefGoogle Scholar
  12. 12.
    Weatheritt, J., Sandberg, R.: A novel evolutionary algorithm applied to algebraic modifications of the rans stress–strain relationship. J. Comput. Phys. 325, 22–37 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Weatheritt, J., Sandberg, R.: The development of algebraic stress models using a novel evolutionary algorithm. Int. J. Heat Fluid Flow 68, 298–318 (2017)CrossRefGoogle Scholar
  14. 14.
    Matai, R., Durbin, P.A.: LES of turbulent flow over a parametric set of bumps. Journal of Fluid Mechanics Submitted. (2019).  https://doi.org/10.1017/jfm.2019.80
  15. 15.
    Weller, H.G., Tabor, G., Jasak, H., Fureby, C.: A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12(6), 620–631 (1998)CrossRefGoogle Scholar
  16. 16.
    Driver, D.M., Seegmiller, H.L.: Features of a reattaching turbulent shear layer in divergent channelflow. AIAA J. 23(2), 163–171 (1985)CrossRefGoogle Scholar
  17. 17.
    Obi, S., Aoki, K., Masuda, S.: Experimental and computational study of turbulent separating flow in an asymmetric plane diffuser. In: Ninth Symposium on Turbulent Shear Flows, Hyoto, Japan, pp 305–1 (1993)Google Scholar
  18. 18.
    Naughton, J.W., Viken, S., Greenblatt, D.: Skin friction measurements on the nasa hump model. AIAA J. 44(6), 1255–1265 (2006)CrossRefGoogle Scholar
  19. 19.
    Greenblatt, D.: NASA Turbulence Modeling Resource. https://turbmodels.larc.nasa.gov/nasahump_grids.html (2018)

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIowa State UniversityAmesUSA

Personalised recommendations

Cite article

Buy options