A Data-Driven Machine Learning Approach for Turbulent Flow Field Prediction Based on Direct Computational Fluid Dynamics Database

Document Type : Regular Article


Aerospace Engineering Department, Amirkabir University of Technology, Tehran, Iran



A novel approach is presented for predicting compressible turbulent flow fields using a neural network-based data-driven method. Accurate prediction in turbulent regions heavily relies on the resolution of available data. Traditional methods, employing image-based techniques by mapping scattered computational fluid dynamics (CFD) data onto Cartesian grids, encounter data scarcity in critical areas such as the boundary layer and wake. Recently, convolutional neural networks (CNN) have gained prominence as the most widely referenced technique in fluid dynamics, utilizing flow field images as datasets for flow field prediction. However, CNN requires datasets with a high pixel density to enhance training accuracy in crucial regions, thereby increasing the input data volume and machine training time. To address this challenge, our proposed method deviates from using flow field images and instead generates datasets directly from the flow field properties of CFD grid points. By employing this approach, several advantages are realized. Firstly, the network benefits from the favorable characteristics of unstructured grids, such as varying point spacing near the object surface and in the far field, which effectively reduces the amount of input data and consequently the machine training cost. Secondly, the construction of the training dataset eliminates the need for interpolation or extrapolation, thereby preserving the accuracy of CFD data. In this case, a simple multilayer perceptron can be trained using the proposed dataset. Various flow field properties, including static pressure, turbulent kinetic energy, and velocity components, can be predicted with high accuracy within a few seconds.


Main Subjects

Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J., & Devin, M. (2016). Tensorflow: Large-scale machine learning on heterogeneous distributed systems. ArXiv Preprint ArXiv:1603.04467. https://doi.org/10.48550/arXiv.1603.04467
Akbıyık, H., & Yavuz, H. (2021). Artificial neural network application for aerodynamics of an airfoil equipped with plasma actuators. Journal of Applied Fluid Mechanics, 14(4), 1165–1181. https://doi.org/10.47176/jafm.14.04.32133
Ansari, A., Mohaghegh, S., Shahnam, M., Dietiker, J. F., & Li, T. (2018). Data driven smart proxy for cfd application of big data analytics & machine learning in computational fluid dynamics, report two: Model building at the cell level. National Energy Technology Laboratory (NETL), Pittsburgh, PA, Morgantown. https://doi.org/10.2172/1431303
Bergstra, J., Bardenet, R., Bengio, Y., & Kégl, B. (2011). Algorithms for hyper-parameter optimization. Advances in Neural Information Processing Systems, 24.
Bhatnagar, S., Afshar, Y., Pan, S., Duraisamy, K., & Kaushik, S. (2019). Prediction of aerodynamic flow fields using convolutional neural networks. Computational Mechanics, 64(2), 525–545. https://doi.org/10.1007/s00466-019-01740-0
Brunton, S. L., Noack, B. R., & Koumoutsakos, P. (2020). Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 52, 477–508. https://doi.org/10.1146/ANNUREV-FLUID-010719-060214
Chollet, F. (2015). Keras: deep learning library for theano and tensorflow. URL: https://Keras.io
Dillmann, A., Heller, G., Schröder, W., Nitsche, W., Klaas, M., & Kreplin, H. P. (2010). New Results in Numerical and Experimental Fluid Mechanics VII: Contributions to the 16th STAB/DGLR Symposium Aachen, Germany (Vol. 112). Springer Science & Business Media. https://doi.org/10.1007/978-3-319-03158-3
Du, X., He, P., Technology, J. M. A. S. (2021). Rapid airfoil design optimization via neural networks-based parameterization and surrogate modeling. Aerospace Science and Technology, 113. https://doi.org/10.1016/j.ast.2021.106701
Ghoreyshi, M., Jirasek, A., & Cummings, R. M. (2013). Computational approximation of nonlinear unsteady aerodynamics using an aerodynamic model hierarchy. Aerospace Science and Technology, 28(1), 133–144. https://doi.org/10.1016/j.ast.2012.10.009
Guo, X., Li, W., Sigkdd, F. I. P. (2016). Convolutional neural networks for steady flow approximation. Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp. 481-490. https://www.osti.gov/biblio/416544
Hallock, J. N., & Holzäpfel, F. (2018). A review of recent wake vortex research for increasing airport capacity. Progress in Aerospace Sciences, 98, 27–36. http://dx.doi.org/10.1016/j.paerosci.2018.03.003
Hasegawa, K., Fukami, K., Murata, T., & Fukagata, K. (2020). CNN-LSTM based reduced order modeling of two-dimensional unsteady flows around a circular cylinder at different Reynolds numbers. Fluid Dynamics Research, 52(6), 65501. http://dx.doi.org/10.1088/1873-7005/abb91d
Jahangirian, A., & Hadidoolabi, M. (2005). Unstructured moving grids for implicit calculation of unsteady compressible viscous flows. International Journal for Numerical Methods in Fluids, 47(10–11), 1107–1113. https://doi.org/10.1002/FLD.877
Jahangirian, A. R., & Johnston, L. (1996). Automatic generation of adaptive unstructured grids for viscous flow applications. 5th International Conference on Numerical Grid Generation in CFD, No. CONF-960489, Mississippi State Univ. https://www.osti.gov/biblio/416544
Jin, X., Cheng, P., Chen, W. L., & Li, H. (2018). Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder. Physics of Fluids, 30(4). https://doi.org/10.1063/1.5024595
Jones, D. R., Schonlau, M., & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13(4), 455. https://doi.org/10.1023/A:1008306431147
Kashefi, A., & Mukerji, T. (2022). Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries. Journal of Computational Physics, 468, 111510. https://doi.org/10.1016/j.jcp.2022.111510
Kashefi, A., Rempe, D., & Guibas, L. J. (2021). A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries. Physics of Fluids, 33(2). https://doi.org/10.1063/5.0033376
Kavitha, R., & Mukesh Kumar, P. C. (2018). A comparison between MLP and SVR models in prediction of thermal properties of nano fluids. Journal of Applied Fluid Mechanics, 11(Special Issue), 7–14. https://doi.org/10.36884/jafm.11.SI.29411
Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. ArXiv Preprint ArXiv:1412.6980. https://doi.org/10.48550/arXiv.1412.6980
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017). ImageNet classification with deep convolutional neural networks. Communications of the ACM, 60(6), 84–90. https://doi.org/10.1145/3065386
Li, Y., Chang, J., Kong, C., & Wang, Z. (2020). Flow field reconstruction and prediction of the supersonic cascade channel based on a symmetry neural network under complex and variable conditions. AIP Advances, 10(6), 65116. http://dx.doi.org/10.1063/5.0008889
Marshall, J., Adcroft, A., Hill, C., Perelman, L., & Heisey, C. (1997). A finite‐volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal of Geophysical Research: Oceans, 102(C3), 5753–5766. https://doi.org/10.1029/96JC02775
McKay, M. D., Beckman, R. J., & Conover, W. J. (2000). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 42(1), 55–61. https://doi.org/10.2307/1268522
Miyanawala, T. P., & Jaiman, R. K. (2019). A hybrid data-driven deep learning technique for fluid-structure interaction. International Conference on Offshore Mechanics and Arctic Engineering, 58776, V002T08A004. https://doi.org/10.1115/OMAE2019-95870
Moureau, V., Domingo, P., & Vervisch, L. (2011). Design of a massively parallel CFD code for complex geometries. Comptes Rendus Mécanique, 339(2–3), 141–148. https://doi.org/10.1016/j.crme.2010.12.001
Nagawkar, J., & Leifsson, L. (2022). Multifidelity aerodynamic flow field prediction using random forest-based machine learning. Aerospace Science and Technology, 123, 107449. https://doi.org/10.1016/j.ast.2022.107449
Nemati, M., & Jahangirian, A. (2020). Robust aerodynamic morphing shape optimization for high-lift missions. Aerospace Science and Technology , 103, 105897. http://dx.doi.org/10.1016/j.ast.2020.105897
O’Shea, K., & Nash, R. (2015). An introduction to convolutional neural networks. ArXiv Preprint ArXiv:1511.08458. https://doi.org/10.48550/arXiv.1511.08458
Qi, C. R., Su, H., Mo, K., & Guibas, L. J. (2017). Pointnet: Deep learning on point sets for 3d classification and segmentation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 652–660. https://doi.org/10.48550/arXiv.1612.00593
Ruder, S. (2016). An overview of gradient descent optimization algorithms. ArXiv Preprint ArXiv:1609.04747. https://doi.org/10.48550/arXiv.1609.04747
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533–536. https://doi.org/10.1038/323533a0
Sekar, V., Jiang, Q., Shu, C., & Khoo, B. C. (2019). Fast flow field prediction over airfoils using deep learning approach. Physics of Fluids, 31(5). https://doi.org/10.1063/1.5094943
Thuerey, N., Weißenow, K., Prantl, L., & Hu, X. (2019). Deep learning methods for reynolds-averaged navier--stokes simulations of airfoil flows. AIAA Journal, 1–12. https://doi.org/10.2514/1.j058291
Wang, Z., Liu, X., Yu, J., Wu, H., & Lyu, H. (2023). A general deep transfer learning framework for predicting the flow field of airfoils with small data. Computers & Fluids, 251, 105738. http://dx.doi.org/10.1016/j.compfluid.2022.105738
Wu, H., Liu, X., An, W., Chen, S. (2020a). A deep learning approach for efficiently and accurately evaluating the flow field of supercritical airfoils. Chinese Journal of Aeronautics. http://dx.doi.org/10.1016/j.compfluid.2019.104393
Wu, P., Sun, J., Chang, X., Zhang, W., Arcucci, R., Guo, Y., & Pain, C. C. (2020b). Data-driven reduced order model with temporal convolutional neural network. Computer Methods in Applied Mechanics and Engineering, 360, 112766. https://doi.org/10.1016/j.cma.2019.112766
Yu, W., Zhao, F., Yang, W., & Xu, H. (2019). Integrated analysis of CFD simulation data with K-means clustering algorithm for soot formation under varied combustion conditions. Applied Thermal Engineering, 153, 299–305. https://doi.org/10.1016/j.applthermaleng.2019.03.011
Yuan, Z., Wang, Y., Qiu, Y., Bai, J., & Chen, G. (2018). Aerodynamic coefficient prediction of airfoils with convolutional neural network. Asia-Pacific International Symposium on Aerospace Technology, Springer Singapore. http://dx.doi.org/10.1007/978-981-13-3305-7_3