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Involving non-equilibrium training dataset in data-driven turbulence modeling for turbomachinery

Published online by Cambridge University Press:  28 November 2024

J.L. Du Open the ORCID record for J.L. Du [Opens in a new window] ,
W.S. Liu Open the ORCID record for W.S. Liu [Opens in a new window] ,
L. Fang Open the ORCID record for L. Fang [Opens in a new window]  and
T.W. Bao
J.L. Du
Affiliation:
Laboratory of Complex Systems, Ecole Centrale de Pékin, Beihang University, Beijing, China
W.S. Liu
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing, China College of Engineering, Peking University, Beijing, China
L. Fang*
Affiliation:
Laboratory of Complex Systems, Ecole Centrale de Pékin, Beihang University, Beijing, China
T.W. Bao*
Affiliation:
BSS TurboTech, Beijing, China
*
Corresponding authors: L. Fang; Email: le.fang@buaa.edu.cn, T.W. Bao; Email: tianwei.bao@bssturbotechltd.cn
Corresponding authors: L. Fang; Email: le.fang@buaa.edu.cn, T.W. Bao; Email: tianwei.bao@bssturbotechltd.cn
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Abstract

In order to improve the performance of $k - \omega $ SST model in turbomachinery, previous studies have used the machine-learning (ML) technique to obtain turbulence models (for example, the ML-RANS EQ model). However, these models do not lead to satisfactory results in complex flows in turbomachinery. In this study, we use non-equilibrium training dataset to obtain a new turbulence model (i.e., the ML-RANS TR-NE-EQ model). Calculations in various cases of turbine cascade flows show that ML-RANS TR-NE-EQ model performs obviously better than ML-RANS EQ model as well as $k - \omega $ SST model.

Keywords

k − ω SST modelmachine learningnon-equilibrium turbulenceturbine cascade

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Type
Research Article
Information
The Aeronautical Journal , Volume 129 , Issue 1335 , May 2025 , pp. 1215 - 1236
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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References

Bardina, J., Huang, P. and Coakley, T. Turbulence modeling validation, 28th Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, June 1997.Google Scholar
Launder, B.E. and Sharma, B.I. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Lett. Heat Mass Transfer, 1974, 1, (2), pp 131–137.Google Scholar
Wilcox, D.C. Reassessment of the scale-determining equation for advanced turbulence models, AIAA J., 1988, 26, (11), pp 1299–1310.Google Scholar
Menter, F.R. Zonal two equation k-w turbulence models for aerodynamic flows, 23rd Fluid Dynamics, Plasmadynamics and Lasers Conference, American Institute of Aeronautics and Astronautics, 1993.CrossRefGoogle Scholar
Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J., 1994, 32, (8), pp 1598–1605.Google Scholar
Chipongo, K., Khiadani, M. and Sookhak Lari, K. Comparison and verification of turbulence Reynolds-averaged Navier–Stokes closures to model spatially varied flows, Sci. Rep., 2020, 10, (1), p 19059.Google ScholarPubMed
Fang, L., Zhao, H.K., Lu, L.P., Liu, Y.W. and Yan, H. Quantitative description of non-equilibrium turbulent phenomena in compressors, Aerospace Sci. Technol., 2017, 71, pp 78–89.Google Scholar
Wilcox, D.C. Turbulence Modeling for CFD, 3rd ed, DCW Industries, 2006, La Canada, CA.Google Scholar
Spalart, P.R. Philosophies and fallacies in turbulence modeling, Prog. Aerospace Sci., 2015, 74, pp 1–15.Google Scholar
Park, J. and Choi, H. Toward neural-network-based large eddy simulation: Application to turbulent channel flow, J. Fluid Mech., 2021, 914, p A16.Google Scholar
Kurz, M., Offenhäuser, P. and Beck, A. Deep reinforcement learning for turbulence modeling in large eddy simulations, Int. J. Heat Fluid Flow, 2023, 99, pp 109094.Google Scholar
Pope, S.B. A more general effective-viscosity hypothesis, J. Fluid Mech., 1975, 72, (02), p 331.CrossRefGoogle Scholar
Ling, J., Kurzawski, A. and Templeton, J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance, J. Fluid Mech., 2016, 807, pp 155–166.Google Scholar
Zhang, X.L., Xiao, H., Luo, X.D. and He, G.W. Ensemble kalman method for learning turbulence models from indirect observation data, J. Fluid Mech., 2022, 949, p A26.Google Scholar
Mandler, H. and Weigand, B. A realizable and scale-consistent data-driven non-linear eddy viscosity modeling framework for arbitrary regression algorithms, Int. J. Heat Fluid Flow, 2022, 97, p 109018.Google Scholar
Weatheritt, J. and Sandberg, R. A novel evolutionary algorithm applied to algebraic modifications of the RANS stress–strain relationship, J. Comput. Phys., 2016, 325, pp 22–37.CrossRefGoogle Scholar
Zhao, Y.M., Akolekar, H.D., Weatheritt, J., Michelassi, V. and Sandberg, R.D. RANS turbulence model development using CFD-driven machine learning, J. Comput. Phys., 2020, 411, p 109413.Google Scholar
Lav, C., Banko, A.J., Waschkowski, F., Zhao, Y.M., Elkins, C.J., Eaton, J.K. and Sandberg, R.D. A coupled framework for symbolic turbulence models from deep-learning, Int. J. Heat Fluid Flow, 2023, 101, p 109140.Google Scholar
Wu, J.L., Xiao, H. and Paterson, E. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework, Phys. Rev. Fluids, 2018, 3, (7), p 074602.Google Scholar
Brener, B.P., Cruz, M.A., Macedo, M.S.S. and Thompson, R.L. A highly accurate strategy for data-driven turbulence modeling, Comput. Appl. Math., 2024, 43, (1), p 59.CrossRefGoogle Scholar
Parish, E.J. and Duraisamy, K. A paradigm for data-driven predictive modeling using field inversion and machine learning, J. Comput. Phys., 2016, 305, pp 758–774.Google Scholar
Ferrero, A., Iollo, A. and Larocca, F. Field inversion for data-augmented rans modelling in turbomachinery flows, Comput. Fluids, 2020, 201, p 104474.Google Scholar
Yan, C.Y., Li, H.R., Zhang, Y.F. and Chen, H.X. Data-driven turbulence modeling in separated flows considering physical mechanism analysis, Int. J. Heat Fluid Flow, 2022, 96, p 109004.Google Scholar
Duraisamy, K., Zhang, Z.J. and Singh, A.P. New approaches in turbulence and transition modeling using data-driven techniques, 53rd AIAA Aerospace Sciences Meeting, 2015, p 1284.Google Scholar
Yan, C.Y., Zhang, Y. and Chen, H. Data augmented turbulence modeling for three-dimensional separation flows, Phys. Fluids, 2022, 34, (7), p 075101.CrossRefGoogle Scholar
Zhu, L.Y., Zhang, W.W., Kou, J.Q. and Liu, Y.L. Machine learning methods for turbulence modeling in subsonic flows around airfoils, Phys. Fluids, 2019, 31, (1), p 015105.CrossRefGoogle Scholar
Zhang, S.M., Li, H.W., You, R.Q., Kong, T.L. and Tao, Z. A construction and training data correction method for deep learning turbulence model of Reynolds averaged Navier–Stokes equations, AIP Adv., 2022, 12, (6), p 065002.Google Scholar
Wu, J.L., Xiao, H., Sun, R. and Wang, Q.Q. Reynolds-averaged navier–stokes equations with explicit data-driven reynolds stress closure can be ill-conditioned, J. Fluid Mech., 2019, 869, pp 553–586.CrossRefGoogle Scholar
Liu, W.S., Fang, J., Rolfo, S., Moulinec, C. and Emerson, D.R. An iterative machine-learning framework for rans turbulence modeling, Int. J. Heat Fluid Flow, 2021, 90, p 108822.Google Scholar
Brener, B.P., Cruz, M.A., Thompson, R.L. and Anjos, R.P. Conditioning and accurate solutions of reynolds average navier–stokes equations with data-driven turbulence closures, J. Fluid Mech., 2021, 915, p A110.Google Scholar
Spencer, R., Przytarski, P., Adami, P., Grothe, P. and Wheeler, A.P.S. Importance of non-equilibrium modelling for compressors, J. Turbomach., 2022, pp 1–16.Google Scholar
Sun, X.X., Cao, W.B., Liu, Y.L., Zhu, L.Y. and Zhang, W.W. High Reynolds number airfoil turbulence modeling method based on machine learning technique, Comput. Fluids, 2022, 236, p 105298.Google Scholar
Abe, H., Kawamura, H. and Matsuo, Y. Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence, J. Fluids Eng., 2001, 123, (2), pp 382–393.CrossRefGoogle Scholar
Moser, R.D., Kim, J. and Mansour, N.N. Direct numerical simulation of turbulent channel flow up to ${\rm{R}}{{\rm{e}}_\tau }$ = 590, Phys. Fluids, 1999, 11, (4), pp 943–945.CrossRefGoogle Scholar
Fang, L., Bao, T.W., Xu, W.Q., Zhou, Z.D., Du, J.L. and Jin, Y.. Data driven turbulence modeling in turbomachinery — an applicability study, Comput. Fluids, 2022, 238, p 105354.Google Scholar
Duraisamy, K. Perspectives on machine learning-augmented reynolds-averaged and large eddy simulation models of turbulence, Phys. Rev. Fluids, 2021, 6, (5), p 050504.Google Scholar
Schmelzer, M., Dwight, R.P. and Cinnella, P. Discovery of algebraic reynolds-stress models using sparse symbolic regression, Flow Turbul. Combust., 2020, 104, pp 579–603.Google Scholar
Akolekar, H.D., Weatheritt, J., Hutchins, N., Sandberg, R.D., Laskowski, G. and Michelassi, V. Development and use of machine-learnt algebraic reynolds stress models for enhanced prediction of wake mixing in low-pressure turbines, J. Turbomach., 2019, 141, (4).Google Scholar
Mandler, H. and Weigand, B. On frozen-rans approaches in data-driven turbulence modeling: Practical relevance of turbulent scale consistency during closure inference and application, Int. J. Heat Fluid Flow, 2022, 97, p 109017.Google Scholar
Parneix, S., Laurence, D. and Durbin, P.A. A procedure for using dns databases, J. Fluids Eng., 1998, 120, (1), pp 40–47.Google Scholar
Weatheritt, J. and Sandberg, R.D. The development of algebraic stress models using a novel evolutionary algorithm, Int. J. Heat Fluid Flow, 2017, 68, pp 298–318.Google Scholar
Wu, C.Y. and Zhang, Y.F. Enhancing the shear-stress-transport turbulence model with symbolic regression: A generalizable and interpretable data-driven approach, Phys. Rev. Fluids, 2023, 8, (8), p 084604.Google Scholar
Liu, Y.W., Lu, L.P., Fang, L. and Gao, F. Modification of spalart–allmaras model with consideration of turbulence energy backscatter using velocity helicity, Phys. Lett. A, 2011, 375, (24), pp 2377–2381.CrossRefGoogle Scholar
Liu, Y.W., Tang, Y.M., Scillitoe, A.D. and Tucker, P.G. Modification of shear stress transport turbulence model using helicity for predicting corner separation flow in a linear compressor cascade, J. Turbomach., 2020, 142, (2), p 021004.Google Scholar
Liu, Y.W., Yan, H., Fang, L., Lu, L.P., Li, Q.S. and Shao, L. Modified k- $\omega $ model using kinematic vorticity for corner separation in compressor cascades, Sci. China Technol. Sci., 2016, 59, (5), pp 795–806.Google Scholar
Sun, W. Assessment of advanced rans turbulence models for prediction of complex flows in compressors, Chin. J. Aeronaut., 2023, 36, (9), pp 162–177.Google Scholar
Klein, T.S., Craft, T.J. and Iacovides, H. Assessment of the performance of different classes of turbulence models in a wide range of non-equilibrium flows, Int. J. Heat Fluid Flow, 2015, 51, pp 229–256.CrossRefGoogle Scholar
Liu, F., Lu, L.P. and Fang, L. Non-equilibrium turbulent phenomena in transitional channel flows, J. Turbul., 2018, 19, (9), pp 731–753.Google Scholar
Xiao, H., Wu, J.L., Laizet, S. and Duan, L. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations, Comput. Fluids, 2020, 200, p 104431.Google Scholar
Wang, J.X., Wu, J.L. and Xiao, H. Physics-informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on DNS data, Phys. Rev. Fluids, 2017, 2, (3), p 034603.CrossRefGoogle Scholar
Liu, W.S., Song, Z.M. and Fang, J. Nnpred: A predictor library to deploy neural networks in computational fluid dynamics software, arXiv preprint arXiv:2209.12339, September 2022.Google Scholar
Liu, W.S., Fang, J., Rolfo, S., Moulinec, C. and Emerson, D.R. On the improvement of the extrapolation capability of an iterative machine-learning based RANS framework, Comput. Fluids, 2023, 256, p 105864.CrossRefGoogle Scholar
Abadi, M., Barham, P., Chen, J.M., Chen, Z.F., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D.G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y. and Zheng, X.Q. Tensorflow: A system for large-scale machine learning, Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation, OSDI’16, USA, 2016, USENIX Association, pp 265–283. Google Scholar
Thompson, R.L., Sampaio, L.E.B., de Bragança Alves, F.A.V., Thais, L. and Mompean, G. A methodology to evaluate statistical errors in dns data of plane channel flows, Comput. Fluids, 2016, 130, pp 1–7.Google Scholar
Poroseva, S.V., Colmenares, F.J.D. and Murman, S.M. On the accuracy of rans simulations with dns data, Phys. Fluids, 2016, 28, (11), p 115102.Google ScholarPubMed
Vassilicos, J.C. Dissipation in turbulent flows, Ann. Rev. Fluid Mech., 2015, 47, (1), pp 95–114.Google Scholar
Bos, W.J.T. and Rubinstein, R. Dissipation in unsteady turbulence, Phys. Rev. Fluids, 2017, 2, (2), p 022601.Google Scholar
Li, H.R., Zhang, Y.F. and Chen, H.X. Aerodynamic prediction of iced airfoils based on modified three-equation turbulence model, AIAA J., 2020, 58, (9), pp 3863–3876.Google Scholar
Liu, F., Lu, L.P., Bos, W.J.T. and Fang, L. Assessing the nonequilibrium of decaying turbulence with reversed initial fields, Phys. Rev. Fluids, 2019, 4, (8), p 084603.Google Scholar
Fang, L. and Bos, W.J.T. An EDQNM study of the dissipation rate in isotropic non-equilibrium turbulence, J. Turbul., 2023, 24, pp 217–324.CrossRefGoogle Scholar
Shao, X., Fang, J. and Fang, L. Non-equilibrium dissipation laws in a minimal two-scale wake model, Phys. Fluids, 2023, 35, p 085105.Google Scholar
Araki, R. and Bos, W.J.T. Inertial range scaling of inhomogeneous turbulence, J. Fluid Mech., 2024, 978, p A9.Google Scholar
Ma, B., Van Doorne, C.W.H., Zhang, Z. and Nieuwstadt, F.T.M. On the spatial evolution of a wall-imposed periodic disturbance in pipe poiseuille flow at $re$ = 3000. part 1. subcritical disturbance, J. Fluid Mech., 1999, 398, pp 181–224.Google Scholar
Xu, C., Zhang, Z., den Toonder, J.M.J. and Nieuwstadt, F.T.M. Origin of high kurtosis levels in the viscous sublayer. direct numerical simulation and experiment, Phys. Fluids, 1996, 8, (7), pp 1938–1944.Google Scholar
Liu, F. Researches on the Non-Equilibrium Properties of Turbulence, PhD thesis, Beihang University, Beijing, China, 2019.Google Scholar
Hearst, R.J. and Lavoie, P. Velocity derivative skewness in fractal-generated, non-equilibrium grid turbulence, Phys. Fluids, 2015, 27, (7), p 071701.CrossRefGoogle Scholar
Hussain, A.K.M.F. and Reynolds, W.C. Measurements in fully developed turbulent channel flow, J. Fluids Eng., 1975, 97, (4), pp 568–578.Google Scholar
Pope, S.B. Turbulent Flows, Cambridge University Press, New York, 2000.Google Scholar
Zhao, H.K., Liu, Y.W., Shao, L., Fang, L. and Dong, M. Existence of positive skewness of velocity gradient in early transition, Phys. Rev. Fluids, 2021, 6, (10), p 104608.Google Scholar
Tibshirani, R. Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B (Methodolog.), 1996, 58, (1), pp 267–288.CrossRefGoogle Scholar
Zhao, H.K. Analysis of Nonequilibrium Turbulence Phenomenon and Turbulence Modeling for Compressor Internal Model Flow, PhD thesis, Beihang University, Beijing, China, 2021.Google Scholar
Tao, S.C. and Zhou, Y. Turbulent flows around side-by-side cylinders with regular and multiscale arrangements, Phys. Rev. Fluids, 2019, 4, (12), p 124602.Google Scholar