CoChat
Sign Up
Cited by 435Model Reduction and Neural NetworksComputational Fluid Dynamics and AerodynamicsAerospace and Aviation Technology

Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

Open access
Singh, Anand Pratap, Medida, Shivaji, Duraisamy, Karthik·2017·AIAA Journal
DOI 10.2514/1.j055595
Open this paper in CoChat — free accountOpen PDF

Abstract

A modeling paradigm is developed to augment predictive models of turbulence by effectively using limited data generated from physical experiments. The key components of the current approach involve inverse modeling to infer the spatial distribution of model discrepancies and machine learning to reconstruct discrepancy information from a large number of inverse problems into corrective model forms. The methodology is applied to turbulent flows over airfoils involving flow separation. Model augmentations are developed for the Spalart–Allmaras model using adjoint-based full-field inference on experimentally measured lift coefficient data. When these model forms are reconstructed using neural networks and embedded within a standard solver, it is shown that much improved predictions in lift can be obtained for geometries and flow conditions that were not used to train the model. The neural-network-augmented Spalart–Allmaras model also predicts surface pressures extremely well. Portability of this approach is demonstrated by confirming that predictive improvements are preserved when the augmentation is embedded in a different commercial, finite element solver. The broader vision is that, by incorporating data that can reveal the form of the innate model discrepancy, the applicability of data-driven turbulence models can be extended to more general flows.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.2514/1.j055595

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 50

  1. 5-6, 2004, pp. 407-431.
  2. [3]Younis, B., Gatski, T., and Speziale, C. G., 'Towards a rational model for the triple velocity correlations of turbulence,' Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences , Vol. 456, No. 1996, 2000, pp. 909-920.
  3. [4]Poroseva, S. and Murman, S. M., 'Velocity/Pressure-Gradient Correlations in a FORANS Approach to Turbulence Modeling,' 44th AIAA Fluid Dynamics Conference, AIAA Aviation, (AIAA 2014-2207) , Jun 2014.
  4. [5]Durbin, P. A., 'Near-wall turbulence closure modeling without damping functions,' Theoretical and Computational Fluid Dynamics , Vol. 3, No. 1, 1991, pp. 1-13.
  5. [6]Durbin, P., 'A Reynolds stress model for near-wall turbulence,' Journal of Fluid Mechanics , Vol. 249, 1993, pp. 465-498.
  6. [7]Milano, M. and Koumoutsakos, P., 'Neural network modeling for near wall turbulent flow,' Journal of Computational Physics , Vol. 182, No. 1, 2002, pp. 1-26.
  7. [8]Marusic, I., Candler, G., Interrante, V., Subbareddy, P., and Moss, A., 'Real time feature extraction for the analysis of turbulent flows,' Data Mining for Scientific and Engineering Applications , 2001, pp. 223-238.
  8. [9]Yarlanki, S., Rajendran, B., and Hamann, H., 'Estimation of turbulence closure coefficients for data centers using machine learning algorithms,' Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 2012 13th IEEE Intersociety Conference on , 2012, pp. 38-42.
  9. [10]Kato, H. and Obayashi, S., 'Data Assimilation for Turbulent Flows,' 16th AIAA Non-Deterministic Approaches Conference, AIAA SciTech, (AIAA 2014-1177) , Jan 2014.
  10. [11]Edeling, W., Cinnella, P., Dwight, R. P., and Bijl, H., 'Bayesian estimates of parameter variability in the ke turbulence model,' Journal of Computational Physics , Vol. 258, 2014, pp. 73-94.
  11. [12]Ray, J., Lefantzi, S., Arunajatesan, S., and DeChant, L. J., 'Bayesian Calibration of a RANS Model with a Complex Response Surface - A Case Study with Jet-in-Crossflow Configuration,' 45th AIAA Fluid Dynamics Conference Dallas, TX , Jun 2015.
  12. [13]Cheung, S. H., Oliver, T. A., Prudencio, E. E., Prudhomme, S., and Moser, R. D., 'Bayesian uncertainty analysis with applications to turbulence modeling,' Reliability Engineering & System Safety , Vol. 96, No. 9, 2011, pp. 1137-1149.
  13. [14]Oliver, T. A. and Moser, R. D., 'Bayesian uncertainty quantification applied to RANS turbulence models,' Journal of Physics: Conference Series , Vol. 318, No. 4, 2011, pp. 042032.
  14. [16]Dow, E. and Wang, Q., 'Uncertainty Quantification of Structural Uncertainties in RANS Simulations of Complex Flows,' 20th AIAA Computational Fluid Dynamics Conference Honolulu, Hawaii , Jun 2011.
  15. [17]Dow, E. and Wang, Q., 'Quantification of Structural Uncertainties in the kw Turbulence Model,' 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, Colorado , Apr 2011.
  16. [19]Gorle, C., Emory, M., and Iaccarino, G., 'RANS modeling of turbulent mixing for a jet in supersonic cross flow: model evaluation and uncertainty quantification,' Proceedings of the Seventh International Symposium on Turbulence, Heat and Mass Transfer (ICHMT Digital Library Online, Palermo, Italy, 2012) , 2012.
  17. [20]Emory, M., Larsson, J., and Iaccarino, G., 'Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures,' Physics of Fluids , Vol. 25, No. 11, 2013, pp. 110822.
  18. [22]Xiao, H., Wu, J.-L., Wang, J.-X., Sun, R., and Roy, C., 'Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Equations: An Open-Box, Physics-Based, Bayesian Approach,' arXiv preprint arXiv:1508.06315 , 2015. · arXiv
  19. [23]Weatheritt, J., The development of data driven approaches to further turbulence closures , Ph.D. thesis, University of Southampton, 2015.
  20. [24]Ling, J. and Templeton, J., 'Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty,' Physics of Fluids , Vol. 27, No. 8, 2015, pp. 085103.
  21. [28]Parish, E. J. and Duraisamy, K., 'A paradigm for data-driven predictive modeling using field inversion and machine learning,' J. Comput. Physics , Vol. 305, 2016, pp. 758-774.
  22. [29]Singh, A. P. and Duraisamy, K., 'Using field inversion to quantify functional errors in turbulence closures,' Physics of Fluids , Vol. 28, No. 4, 2016, pp. 045110.
  23. [30]Wang, J.-X., Wu, J.-L., and Xiao, H., 'Physics-Informed Machine Learning for Predictive Turbulence Modeling: Using Data to Improve RANS Modeled Reynolds Stresses,' arXiv preprint arXiv:1606.07987 , 2016. · arXiv
  24. [31]Celic, A. and Hirschel, E. H., 'Comparison of eddy-viscosity turbulence models in flows with adverse pressure gradient,' AIAA Journal , Vol. 44, No. 10, 2006, pp. 2156-2169.
  25. [33]Wilcox, D. C., 'Formulation of the kw turbulence model revisited,' AIAA Journal , Vol. 46, No. 11, 2008, pp. 2823-2838.
  26. [34]Rung, T., Bunge, U., Schatz, M., and Thiele, F., 'Restatement of the Spalart-Allmaras eddy-viscosity model in strain-adaptive formulation,' AIAA Journal , Vol. 47, No. 7, 2003, pp. 1396-1399.
  27. [36]Duraisamy, K., McCroskey, W. J., and Baeder, J. D., 'Analysis of wind tunnel wall interference effects on subsonic unsteady airfoil flows,' Journal of Aircraft , Vol. 44, No. 5, 2007, pp. 1683-1690.
  28. [37]Bremseth, J. and Duraisamy, K., 'Computational analysis of vertical axis wind turbine arrays,' Theoretical and Computational Fluid Dynamics , Vol. 30, No. 5, 2016, pp. 387-401.
  29. [38]Lakshminarayan, V. K. and Duraisamy, K., 'Adjoint-based estimation and control of spatial, temporal and stochastic approximation errors in unsteady flow simulations,' Computers & Fluids , Vol. 121, 2015, pp. 180-191.
  30. [39]Van Leer, B., 'Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method,' Journal of computational Physics , Vol. 32, No. 1, 1979, pp. 101-136.
  31. [40]Roe, P. L., 'Approximate Riemann solvers, parameter vectors, and difference schemes,' Journal of computational physics , Vol. 43, No. 2, 1981, pp. 357-372.
  32. [41]Pulliam, T. H. and Chaussee, D., 'A diagonal form of an implicit approximate-factorization algorithm,' Journal of Computational Physics , Vol. 39, No. 2, 1981, pp. 347-363.
  33. [42]Giles, M. B. and Pierce, N. A., 'An introduction to the adjoint approach to design,' Flow, turbulence and combustion , Vol. 65, No. 3-4, 2000, pp. 393-415.
  34. [43]Bishop, C. M., 'Training with noise is equivalent to Tikhonov regularization,' Neural computation , Vol. 7, No. 1, 1995, pp. 108-116.
  35. [45]Rumsey, C. L. and Ying, S. X., 'Prediction of high lift: review of present CFD capability,' Progress in Aerospace Sciences , Vol. 38, No. 2, 2002, pp. 145-180. d ∗ is the displacement thickness of the boundary layer and dP ds is the pressure gradient.
  36. [47]Zhang, Z. J. and Duraisamy, K., 'Machine Learning Methods for Data-Driven Turbulence Modeling,' 22nd AIAA Computational Fluid Dynamics Conference, AIAA Aviation, (AIAA 2015-2460), Dallas, TX , Jun 2015.
  37. [48]Zhang, Z., Duraisamy, K., and Gumerov, N., 'Efficient Multiscale Gaussian Process Regression using Hierarchical Clustering,' arXiv preprint arXiv:1511.02258v2 , 2016. · arXiv
  38. [49]Bishop, C. M., Pattern recognition and machine learning , Springer-Verlag New York, 1st ed., 2006.
  39. [55]Hughes, T. J. R., France, L. P., and Hulbert, G. M., 'A new finite element formulation for computational fluid dynamics.VIII. The Galerkin/least-squares method for advective-diffusive equations,' Computer Methods in Applied Mechanics and Engineering , Vol. 73, No. 2, 1989, pp. 173-189.
  40. [56]Shakib, F., Hughes, T. J. R., and Johan, Z., 'A new finite element formulation for computational fluid dynamics. X. The compressible Euler and Navier-Stokes equations,' Computer Methods in Applied Mechanics and Engineering , Vol. 89, No. 1-3, 1991, pp. 141-219.
  41. [57]Corson, D. A., Griffith, D. T., Ashwill, T., and Shakib, F., 'Investigating aeroelastic performance of multi-megawatt wind turbine rotors using CFD,' 53 rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, Hawaii , , No. 2012-1827, 2012.
  42. [58]Corson, D. A., Zamora, A., and Medida, S., 'A Comparative Assessment of Correlation-based Transition Models for Wind Power Applications,' 34 th AIAA Applied Aerodynamics Conference, Washington. D. C. , , No. 2016-3129, 2016.
  43. [60]Lyons, D. C., Peltier, L. J., Zajaczkowski, F. J., and Paterson, E. G., 'Assessment of DES Models for Separated Flow From a Hump in a Turbulent Boundary Layer,' Journal of Fluids Engineering , Vol. 131, No. 11, 2009, pp. 111203-1-111203-9.
  44. [61]Bagwell, T. G., 'CFD Simulation of Flow Tones From Grazing Flow Past a Deep Cavity,' Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, Chicago, IL , , No. 2006-15633, 2006, pp. 105-114.
  45. [62]Johnson, K. and Bittorf, K., 'Validating the Galerkin Least Square Finite Element Methods in Predicting Mixing Flows in Stirred Tank Reactors,' Proceedings of CFD 2002, The 10th Annual Conference of the CFD Society of Canada , , No. 40048419, 2002, pp. 490-496.
  46. [63]Jansen, K. E., Whiting, C. H., and Hulbert, G. M., 'A generalized-alpha method for integrating the filtered Navier-Stokes equations with a stabilized finite element method,' Computer Methods in Applied Mechanics and Engineering , Vol. 190, No. 3-4, 2000, pp. 305-319.
  47. [64]Ling, J., Jones, R., and Templeton, J., 'Machine learning strategies for systems with invariance properties,' Journal of Computational Physics , Vol. 318, 2016, pp. 22-35.
  48. [65]Dennis, Jr, J. E. and Mor´ e, J. J., 'Quasi-Newton methods, motivation and theory,' SIAM review , Vol. 19, No. 1, 1977, pp. 46-89.
  49. [67]Hascoet, L. and Pascual, V., 'The Tapenade Automatic Differentiation tool: principles, model, and specification,' ACM Transactions on Mathematical Software (TOMS) , Vol. 39, No. 3, 2013, pp. 20.
  50. [68]Naughton, J. W., Viken, S. A., and Greenblatt, D., 'Skin-Friction Measurements on the NASA Hump Model,' AIAA Journal , Vol. 44, No. 6, 2016, pp. 1255-1265.

Cited by

Sorted by citations

Authors
Singh, A. P., Medida, S., & Duraisamy, K.
Affiliations
  • University of Michigan (US)
  • Altair Engineering (United States) (US)
ORCID
Venue
AIAA Journal
Publisher
American Institute of Aeronautics and Astronautics (AIAA)
Published
2017-07
Volume
55
Issue
7
Pages
2215-2227
ISSN
  • 0001-1452 (ISSN-L)
  • 1533-385X
DOI
10.2514/1.j055595
OpenAlex
W2509002083
Cited by
435
References
1
Citations by year
2026: 35 · 2025: 44 · 2024: 69 · 2023: 61 · 2022: 66 · 2021: 65 · 2020: 45 · 2019: 30 · 2018: 13 · 2017: 6
FWCI
13.34
Type
journal article
Language
en
Open access
Locations
  • AIAA Journal (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Deep Blue (University of Michigan) (submittedVersion)
  • arXiv (Cornell University)
Funders
National Aeronautics and Space Administration (NNX15AN98A)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
  • Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
  • Physical Sciences › Engineering › Aerospace Engineering › Aerospace and Aviation Technology
Keywords
turbulence modeling, model mismatch, inverse modeling, Spalart-Allmaras turbulence model, flow separation, surface pressure prediction, finite element solver

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review