Application of Machine Learning Algorithms to Predict Turbulent Viscosity
https://doi.org/10.15514/ISPRAS-2023-35(6)-13
Abstract
The article discusses machine learning algorithms for predicting turbulent viscosity using the case of flow past the backward-facing step. The training data is obtained by calculations using the OpenFOAM software package and a turbulence model. The significance of flow parameters, including velocity fluctuations, pressure and velocity gradients, strain rate tensor and their combinations and invariants are analyzed for predicting turbulent viscosity. Different machine learning algorithms are compared. It is found that the most optimal algorithm for predicting turbulent viscosity in this case is the Decision Tree Regressor. Using the chosen model, the distribution of turbulent viscosity in the computational domain is predicted for various Reynolds numbers.
Keywords
About the Authors
Daria Igorevna ROMANOVARussian Federation
Cand. Sci. (Phys.-Math.), junior researcher at the Institute of System Programming and Lomonosov Moscow State University. Research interests: computational aero and fluid mechanics, turbulent flows, slope flows, machine learning.
Andrey Sergeevich EPIKHIN
Russian Federation
Cand. Sci. (Tech.), head of the laboratory at the Institute of System Programming of the RAS. Research interests: computational fluid dynamics, turbulent and jet flows, aeroacoustics, software development.
Daria Yurevna ILINA
Russian Federation
Laboratory assistant at the Institute of System Programming of the RAS, 1st year master's degree student, Faculty of Applied Mathematics and Informatics (MIPT).
References
1. N. B. Erichson, L. Mathelin, Z. Yao, S. L. Brunton, M. W. Mahoney, and J. N. Kutz, “Shallow neural networks for fluid flow reconstruction with limited sensors,” Proceedings of the Royal Society A, vol. 476, no. 2238, p. 20200097, 2020, doi: 10.1098/rspa.2020.0097.
2. E. Haghighat, A. C. Bekar, E. Madenci, and R. Juanes, “A nonlocal physics-informed deep learning framework using the peridynamic differential operator,” Computer Methods in Applied Mechanics and Engineering, vol. 385, p. 114012, 2021, doi: 10.1016/j.cma.2021.114012.
3. S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli, “Scientific machine learning through physics–informed neural networks: Where we are and what’s next,” Journal of Scientific Computing, vol. 92, no. 3, p. 88, Jul. 2022, doi: 10.1007/s10915-022-01939-z.
4. X. Jin, S. Cai, H. Li, and G. E. Karniadakis, “NSFnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations,” Journal of Computational Physics, vol. 426, p. 109951, 2021, doi: https://doi.org/10.1016/j.jcp.2020.109951.
5. L. Lu, X. Meng, Z. Mao, and G. Karniadakis, “DeepXDE: A deep learning library for solving differential equations,” SIAM Review, vol. 63, pp. 208–228, Feb. 2021, doi: 10.1137/19M1274067.
6. J. Ling, R. Jones, and J. Templeton, “Machine learning strategies for systems with invariance properties,” Journal of Computational Physics, vol. 318, pp. 22–35, 2016, doi: 10.1016/j.jcp.2016.05.003.
7. R. McConkey, E. Yee, and F.-S. Lien, “Deep learning-based turbulence closure with improved optimal eddy viscosity prediction,” Jul. 2021.
8. Y. Frey Marioni, E. A. de Toledo Ortiz, A. Cassinelli, F. Montomoli, P. Adami, and R. Vazquez, “A machine learning approach to improve turbulence modelling from dns data using neural networks,” International Journal of Turbomachinery, Propulsion and Power, vol. 6, no. 2, 2021, doi: 10.3390/ijtpp6020017.
9. R. Fang, D. Sondak, P. Protopapas, and S. Succi, “Neural network models for the anisotropic reynolds stress tensor in turbulent channel flow,” Journal of Turbulence, vol. 21, nos. 9-10, pp. 525–543, 2020, doi: 10.1080/14685248.2019.1706742.
10. H. D. Pasinato, F. D. Gerosa, and E. A. Krumrick, “Reynolds stresses prediction using deep neural networks,” Computational Mechanics, vol. XXXVIII, pp. 905–914, 2021.
11. G. Kalitzin, G. Medic, and G. Xia, “Improvements to sst turbulence model for free shear layers, turbulent separation and stagnation point anomaly,” in 54th aiaa aerospace sciences meeting, 2016, p. 1601.
12. P. C. Rocha, H. B. Rocha, F. M. Carneiro, M. V. da Silva, and C. F. de Andrade, “A case study on the calibration of the k– sst (shear stress transport) turbulence model for small scale wind turbines designed with cambered and symmetrical airfoils,” Energy, vol. 97, pp. 144–150, 2016.
13. P. Rocha, H. Rocha, F. Carneiro, M. Silva, and A. Bueno, “K- sst (shear stress transport) turbulence model calibration: A case study on a small scale horizontal axis wind turbine,” Energy, vol. 65, Jan. 2013, doi: 10.1016/j.energy.2013.11.050.
14. D. Romanova et al., “Calibration of the k- sst turbulence model for free surface flows on mountain slopes using an experiment,” Fluids, vol. 7, no. 3, 2022, doi: 10.3390/fluids7030111.
15. K. Barkalov, I. Lebedev, M. Usova, D. Romanova, D. Ryazanov, and S. Strijhak, “Optimization of turbulence model parameters using the global search method combined with machine learning,” Mathematics, vol. 10, no. 15, 2022, doi: 10.3390/math10152708.
16. Д. И. Романова, “Калибровка k- модели турбулентности в пакете openfoam с помощью методов машинного обучения для моделирования потоков на склонах гор на основе эксперимента,” Труды Института системного программирования РАН, vol. 33, no. 4, pp. 227–240, 2021, doi: 10.15514/ispras-2021-33(4)-16.
17. R. Pitz and J. Daily, “Experimental study of combustion in a turbulent free shear layer formed at a rearward facing step,” 19th Aerospace Sciences Meeting, 1981, doi: 10.2514/6.1981-106.
18. B. Launder and D. Spalding, “The numerical computation of turbulent flows,” Comput. Methods Appl. Mech. Eng., vol. 103, pp. 456–460, Jan. 1974.
19. B. Launder, A. Morse, W. Rodi, and D. Spaldiug, “Spaldiug, the prediction of free shear flows - a comparison of the performance of six turbulence models,” Proceedings of NASA Conference on Free Shear Flows, 1972.
20. S. B. Pope, “A more general effective-viscosity hypothesis,” Journal of Fluid Mechanics, vol. 72, no. 2, pp. 331–340, 1975, doi: 10.1017/S0022112075003382.
Review
For citations:
ROMANOVA D.I., EPIKHIN A.S., ILINA D.Yu. Application of Machine Learning Algorithms to Predict Turbulent Viscosity. Proceedings of the Institute for System Programming of the RAS (Proceedings of ISP RAS). 2023;35(6):199-212. (In Russ.) https://doi.org/10.15514/ISPRAS-2023-35(6)-13