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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

Published online by Cambridge University Press:  18 October 2016

Julia Ling ,
Andrew Kurzawski  and
Jeremy Templeton
Julia Ling*
Affiliation:
Thermal/Fluids Science and Engineering Department, Sandia National Labs, Livermore, CA 94550, USA
Andrew Kurzawski
Affiliation:
Mechanical Engineering Department, University of Texas at Austin, Austin, TX 78712, USA
Jeremy Templeton
Affiliation:
Thermal/Fluids Science and Engineering Department, Sandia National Labs, Livermore, CA 94550, USA
*
†Email address for correspondence: [email protected]
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Abstract

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 155 - 166
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Copyright
© Cambridge University Press 2016. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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References

Banerjee, S., Kraal, R., Durst, F. & Zenger, C. H. 2007 Presentation of anisotropy properties of turbulence invariants versus eigenvalue approaches. J. Turbul. 8, 1–27.Google Scholar
Craft, T. J., Launder, B. E. & Suga, K. 1996 Development and application of a cubic eddy-viscosity model of turbulence. Intl J. Heat Fluid Flow 17, 108–115.CrossRefGoogle Scholar
Silver, D. et al. 2016 Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489.Google Scholar
Domino, S. P., Moen, C. D., Burns, S. P. & Evans, G. H.2003 SIERRA/Fuego: a multi-mechanics fire environment simulation tool. AIAA Paper 2003-149.Google Scholar
Hinton, G. et al. 2012 Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups. IEEE Signal Process. Mag. 29, 82–97.CrossRefGoogle Scholar
Gatski, T. B. & Speziale, C. G. 1993 On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254, 59–78.CrossRefGoogle Scholar
Karpathy, A., Toderici, G., Shetty, S., Leung, T., Sukthankar, R. & Li, F. F. 2014 Large-scale video classification with convolutional neural networks. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp. 1725–1732. IEEE.Google Scholar
Lecun, Y., Bengio, Y. & Hinton, G. 2015 Deep learning. Nature 521, 436–444.CrossRefGoogle ScholarPubMed
Ling, J., Jones, R. & Templeton, J. 2016a Machine learning strategies for systems with invariance properties. J. Comput. Phys. 318, 22–35.Google Scholar
Ling, J., Ruiz, A., Lacaze, G. & Oefelein, J. 2016b Uncertainty analysis and data-driven model advances for a jet-in-crossflow. In ASME Turbo Expo 2016, ASME.Google Scholar
Ling, J., Ryan, K. J., Bodart, J. & Eaton, J. K. 2016c Analysis of turbulent scalar flux models for a discrete hole film cooling flow. J. Turbomach. 138, 011006.CrossRefGoogle Scholar
Ling, J. & Templeton, J. A. 2015 Evaluation of machine learning algorithms for prediction of regions of high RANS uncertainty. Phys. Fluids 27, 085103.CrossRefGoogle Scholar
Maas, A., Hannun, A. & Ng, A. 2013 Rectifier nonlinearities improve neural network acoustic models. Proc. ICML 30, 1–6.Google Scholar
Marquillie, M., Ehrenstein, U. & Laval, J. P. 2011 Instability of streaks in wall turbulence with adverse pressure gradient. J. Fluid Mech. 681, 205–240.CrossRefGoogle Scholar
Milano, M. & Koumoutsakos, P. 2002 Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182, 1–26.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 590. Phys. Fluids 11, 943–945.Google Scholar
Parish, E. & Duraisamy, K. 2016 A paradigm for data-driven predictive modeling using field inversion and machine learning. J. Comput. Phys. 305, 758–774.Google Scholar
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107–122.Google Scholar
Pope, S. B. 1975 A more general effective-viscosity hypothesis. J. Fluid Mech. 72, 331–340.CrossRefGoogle Scholar
Ray, J., Lefantzi, S., Arunajatesan, S. & Dechant, L.2014 Bayesian calibration of a $k{-}\unicode[STIX]{x1D716}$ turbulence model for predictive jet-in-crossflow simulations. AIAA Paper 2014-2085.CrossRefGoogle Scholar
Rossi, R., Philips, D. & Iaccarino, G. 2010 A numerical study of scalar dispersion downstream of a wall-mounted cube using direct simulations and algebraic flux models. Intl J. Heat Fluid Flow 31, 805–819.CrossRefGoogle Scholar
Ruiz, A. M., Oefelein, J. C. & Lacaze, G. 2015 Flow topologies and turbulence scales in a jet-in-cross-flow. Phys. Fluids 27, 045101.CrossRefGoogle Scholar
Smith, G. F. 1965 On isotropic integrity bases. Arch. Rational Mech. Anal. 18, 282–292.CrossRefGoogle Scholar
Snoek, J., Larochelle, H. & Adams, R. P. 2012 Practical Bayesian optimization of machine learning algorithms. Adv. Neural Inform. Proc. Syst. 25, 2951–2959.Google Scholar
Tracey, B., Duraisamy, K. & Alonso, J. J.2013 Application of supervised learning to quantify uncertainties in turbulence and combustion modeling. AIAA Aerospace Sciences Meeting 2013-0259.CrossRefGoogle Scholar
Tracey, B., Duraisamy, K. & Alonso, J. J.2015 A machine learning strategy to assist turbulence model development. AIAA Aerospace Sciences Meeting 2015-1287.Google Scholar
Wallin, S. & Johansson, A. 2000 An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech. 403, 89–132.CrossRefGoogle Scholar
Zhang, Z. J. & Duraisamy, K.2015 Machine learning methods for data-driven turbulence modeling. AIAA Computational Fluid Dynamics Conf. 2015-2460.CrossRefGoogle Scholar