DOI QR코드

DOI QR Code

Reynolds stress correction by data assimilation methods with physical constraints

  • Thomas Philibert (Institut National de Recherche en Informatique et en Automatique) ;
  • Andrea Ferrero (Department of Mechanical and Aerospace Engineering, Politecnico di Torino) ;
  • Angelo Iollo (Institut National de Recherche en Informatique et en Automatique) ;
  • Francesco Larocca (Department of Mechanical and Aerospace Engineering, Politecnico di Torino)
  • 투고 : 2023.12.01
  • 심사 : 2024.01.15
  • 발행 : 2023.11.25

초록

Reynolds-averaged Navier-Stokes (RANS) models are extensively employed in industrial settings for the purpose of simulating intricate fluid flows. However, these models are subject to certain limitations. Notably, disparities persist in the Reynolds stresses when comparing the RANS model with high-fidelity data obtained from Direct Numerical Simulation (DNS) or experimental measurements. In this work we propose an approach to mitigate these discrepancies while retaining the favorable attributes of the Menter Shear Stress Transport (SST) model, such as its significantly lower computational expense compared to DNS simulations. This strategy entails incorporating an explicit algebraic model and employing a neural network to correct the turbulent characteristic time. The imposition of realizability constraints is investigated through the introduction of penalization terms. The assimilated Reynolds stress model demonstrates good predictive performance in both in-sample and out-of-sample flow configurations. This suggests that the model can effectively capture the turbulent characteristics of the flow and produce physically realistic predictions.

키워드

과제정보

The authors acknowledge funding from Italian Ministry of University and Research: PRIN research project 2022B2X937, "NextGenSProDesT Next Generation Space Propulsion Design Techniques".

참고문헌

  1. Balay, S., Gropp, W.D., McInnes, L.C. and Smith, B.F. (1997), Efficient Management of Parallelism in Object Oriented Numerical Software Libraries, Modern Software Tools in Scientific Computing, Birkhauser Press. 
  2. Barth, T.J. and Jespersen, D.C. (1989), "The design and application of upwind schemes on unstructured meshes", AIAA 27th Aerospace Sciences Meeting, Reno, January. https://doi.org/10.2514/6.1989-366.
  3. Broyden, C.G. (1969), "A new double-rank minimization algorithm", Notic. Am. Math. Soc., 16, 670.
  4. Ferrero, A. and D'Ambrosio, D. (2020), "A hybrid numerical flux for supersonic flows with application to rocket nozzles", Adv. Aircraft Spacecraft Sci., 7(5), 387-404. https://doi.org/10.1063/5.0026763. 
  5. Ferrero, A., Iollo, A. and Larocca, F. (2019), "RANS closure approximation by artificial neural networks", ETC 2019-13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Lausanne, Switzerland, April. 
  6. Ferrero, A., Iollo, A. and Larocca, F. (2020), "Field inversion for data-augmented RANS modelling in turbomachinery flows", Comput. Fluid., 201, 104474. https://doi.org/10.1016/j.compfluid.2020.104474. 
  7. Foures, D.P.G., Dovetta, N., Sipp, D. and Schmid, P.J. (2014), "A data-assimilation method for Reynoldsaveraged Navier-Stokes-driven mean flow reconstruction", J. Fluid Mech., 759, 404-431. https://doi.org/10.1017/jfm.2014.566. 
  8. Geuzaine, G. and Remacle, J.F. (2009), "Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities", Int. J. Numer. Meth. Eng., 79(11), 1309-1331. https://doi.org/10.1002/nme.2579 . 
  9. Greenblatt, D., Paschal, K.B., Yao, C.S., Harris, J., Schaeffler, N.W. and Washburn, A.E. (2006), "Experimental investigation of separation control Part 1: Baseline and Steady Suction", AIAA J., 44(12), 2820-2830. https://doi.org/10.2514/1.13817. 
  10. Holland, J.H. (1992), "Genetic algorithms", Scientif. Am., 267(1), 66-73.  https://doi.org/10.1038/scientificamerican0792-66
  11. Ling, J. and Templeton, J. (2015), "Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty", Phys. Fluid., 27, 085103. https://doi.org/10.1063/1.4927765. 
  12. Ling, J., Kurzawski, A. and Templeton, J. (2016), "Reynolds averaged turbulence modelling using deep neural networks with embedded invariance", J. Fluid Mech., 807, 155-166. https://doi.org/10.1017/jfm.2016.615. 
  13. Menter, F.R. (1994), "Two-equation eddy-viscosity turbulence models for engineering applications", AIAA J., 32(8), 1598-1605. https://doi.org/10.2514/3.12149. 
  14. Nelder, J.A. and Mead, R. (1965), "A simplex method for function minimization", Comput. J., 7, 308-313. https://doi.org/10.1093/comjnl/7.4.308. 
  15. Pandolfi, M. (1984), "A contribution to the numerical prediction of unsteady flows", AIAA J., 22(5), 602-610. https://doi.org/10.2514/3.48491. 
  16. Parish, J.L. and Duraisamy, K. (2016), "A paradigm for data-driven predictive modeling using field inversion and machine learning", J. Comput. Phys., 305, 758-774. https://doi.org/10.1016/j.jcp.2015.11.012. 
  17. Parneix, S., Laurence, D. and Durbin, P.A. (1998), "A procedure for using DNS databases", J. Fluid. Eng., 120(1), 40-47. https://doi.org/10.1115/1.2819658. 
  18. PETSc (2023), Portable, Extensible Toolkit for Scientific Computation. https://petsc.org/ 
  19. PETSc/TAO Users Manual (2023), Technical Report ANL-21/39-Revision 3.19, Argonne National Laboratory. 
  20. Pope, S. (1975), "A more general effective-viscosity hypothesis", J. Fluid Mech., 72(2), 331-340. https://doi.org/10.1017/S0022112075003382. 
  21. Powell, M.J.D. (1964), "An efficient method for finding the minimum of a function of several variables without calculating derivatives", Comput. J., 7, 155-162. https://doi.org/10.1093/comjnl/7.2.155. 
  22. Rumsey, C., Smith, B. and Huang, G. (2010), "Description of a website resource for turbulence modeling verification and validation", AIAA 40th Fluid Dynamics Conference and Exhibit, Chichago, USA, JuneJuly. https://doi.org/10.2514/6.2010-4742. 
  23. Rusanov, V.V. (1962), "The calculation of the interaction of nonstationary shock waves and obstacles", USSR Comput. Math. Math. Phys., 1(2), 304-320. https://doi.org/10.1016/0041-5553(62)90062-9. 
  24. Sandberg, R.D. and Michelassi, V. (2019), "The current state of high-fidelity simulations for main gas path turbomachinery components and their industrial impact", Flow Turbul. Combus., 102, 797-848. https://doi.org/10.1007/s10494-019-00013-3. 
  25. Sandberg, R.D. and Weatheritt, J. (2014), "A novel evolutionary algorithm applied to algebraic modifications of the RANS stress-strain relationship", J. Comput. Phys., 325, 73-94. https://doi.org/10.1016/j.jcp.2016.08.015. 
  26. Singh, A.P., Medida, S. and Duraisamy, K. (2017), "Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils", AIAA J., 55(7), 2215-2227. https://doi.org/10.2514/1.J055595. 
  27. Wang, J.X., Wu, J.L. and Xiao, H. (2017), "Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data", Phys. Rev. Fluid., 2, 034603. https://doi.org/10.1103/PhysRevFluids.2.034603. 
  28. Wu, J.L., Wang, J.X., Xiao, H. and Ling, J. (2017), "A priori assessment of prediction confidence for data driven turbulence modeling", Flow Turbul. Combus., 99, 25-46. https://doi.org/10.1007/s10494-017-9807-0. 
  29. Wu, J.L., Xiao, H. and Paterson, E. (2018), "Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework", Phys. Rev. Fluid., 3(7), 074602. https://doi.org/10.1103/PhysRevFluids.3.074602. 
  30. Xiao, H. and Cinnella, P. (2019), "Quantification of model uncertainty in RANS simulations: A review", Progr. Aerosp. Sci., 108, 1-31. https://doi.org/10.1016/j.paerosci.2018.10.001. 
  31. Xiao, H., Wu, J.L., Laizet, S. and Duan, L. (2020), "Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations", Comput. Fluid., 200, 104431. https://doi.org/10.1016/j.compfluid.2020.104431. 
  32. Zhao, Y., Akolekar, H.D., Weatheritt, J., Michelassi, V. and Sandberg, R.D. (2020), "RANS turbulence model development using CFD driven machine learning", J. Comput. Phys., 411, 109413. https://doi.org/10.1016/j.jcp.2020.109413.