Convolutional Neural Networks-Based For Predicting Aerodynamic Coefficient Of Airfoils At Ultra-Low Reynolds Number

Alief Kasman - Bandung Institute of Technology, Bandung, 40116, West Java, Indonesia
Arizal Zikri - Bandung Institute of Technology, Bandung, 40116, West Java, Indonesia
Fariduzzaman Fariduzzaman - National Research and Innovation Agency, South Tangerang, 15314, Banten, Indonesia
Wahyu Srigutomo - Bandung Institute of Technology, Bandung, 40116, West Java, Indonesia

Citation Format:



Many applications, including airplane design, wind turbines, and heat transmission, use symmetric or asymmetric airfoils. Engineers employ these airfoil shapes to optimize performance and efficiency. Each airfoil has a unique set of aerodynamic coefficients that must be calculated to maximize the airfoil design. Engineers utilize numerous ways to calculate coefficients, such as lift and drag. One of the methods is the prediction method, which effectively reduces time and cost. This study's training dataset is obtained from particle-based numerical computation using the Lattice Boltzmann Method (LBM). Then, Convolutional Neural Networks (CNN) are used as a prediction method to get the aerodynamic coefficients of airfoils for lift and drag based on two different Reynolds numbers. In CNN, airfoil geometry representation is essential. The Signed Distance Function (SDF) was used to convert airfoil geometry into RGB pictures. On the other hand, the SDF method cannot explain different flow conditions; in this case, it is represented by the Reynolds number (Re). Therefore, we propose a Text-based Watermarking Method (TWM) to differentiate between Re = 500 and Re = 1000. Each airfoil representation was trained and tested to generate each prediction model using a modified LeNet-5. The computation results show that using CNN with TWM on SDF to define the Reynolds numbers could predict the lift and drag coefficients with varying angles of attack. Future research can focus on generalizations to different aerodynamic aspects and practical applications in complex scenarios.


neural network; CNN, airfoil; aerodynamic coefficient; LBM

Full Text:



H. V. Phan and H. C. Park, “Insect-inspired, tailless, hover-capable flapping-wing robots: Recent progress, challenges, and future directions,” Prog. Aerosp. Sci., vol. 111, no. August, p. 100573, 2019, doi: 10.1016/j.paerosci.2019.100573.

N. T. Jafferis, E. F. Helbling, M. Karpelson, and R. J. Wood, “Untethered flight of an insect-sized flapping-wing microscale aerial vehicle,” Nature, vol. 570, no. 7762, pp. 491–495, 2019, doi: 10.1038/s41586-019-1322-0.

H. V. Phan, S. Aurecianus, T. K. L. Au, T. Kang, and H. C. Park, “Towards the Long-Endurance Flight of an Insect-Inspired, Tailless, Two-Winged, Flapping-Wing Flying Robot,” IEEE Robot. Autom. Lett., vol. 5, no. 4, pp. 5059–5066, 2020, doi: 10.1109/LRA.2020.3005127.

J. Winslow, H. Otsuka, B. Govindarajan, and I. Chopra, “Basic understanding of airfoil characteristics at low Reynolds numbers (104–105),” J. Aircr., vol. 55, no. 3, pp. 1050–1061, 2018, doi: 10.2514/1.C034415.

N. Varsha, M. D. Deshpande, and M. Sivapragasam, “Airfoil Optimisation at Ultra-Low Reynolds Number,” J. Aerosp. Sci. Technol., pp. 347–353, 2019.

J. H. García-Ortiz, A. Domínguez-Vázquez, J. J. Serrano-Aguilera, L. Parras, and C. del Pino, “A complementary numerical and experimental study of the influence of Reynolds number on theoretical models for wingtip vortices,” Comput. Fluids, vol. 180, no. xxxx, pp. 176–189, 2019, doi: 10.1016/j.compfluid.2018.12.009.

L. V. Rolandi, T. Jardin, J. Fontane, J. Gressier, and L. Joly, “Stability of the Low Reynolds Number Compressible Flow Past a NACA0012 Airfoil,” AIAA J., vol. 60, no. 2, pp. 1052–1066, 2022, doi: 10.2514/1.J060792.

T. Kouser, Y. Xiong, D. Yang, and S. Peng, “Direct Numerical Simulations on the three-dimensional wake transition of flows over NACA0012 airfoil at Re = 1000,” Int. J. Micro Air Veh., vol. 13, no. November, 2021, doi: 10.1177/17568293211055656.

D. F. Kurtulus, “Unsteady aerodynamics of a pitching NACA 0012 airfoil at low Reynolds number,” Int. J. Micro Air Veh., vol. 11, 2019, doi: 10.1177/1756829319890609.

K. Suzuki, K. Minami, and T. Inamuro, “Lift and thrust generation by a butterfly-like flapping wing-body model: Immersed boundary-lattice Boltzmann simulations,” J. Fluid Mech., vol. 767, pp. 659–695, 2015, doi: 10.1017/jfm.2015.57.

K. V. Sharma, R. Straka, and F. W. Tavares, “Current status of Lattice Boltzmann Methods applied to aerodynamic, aeroacoustic, and thermal flows,” Prog. Aerosp. Sci., vol. 115, no. March, p. 100616, 2020, doi: 10.1016/j.paerosci.2020.100616.

L. Wang et al., “Accurate computation of airfoil flow based on the lattice Boltzmann method,” Appl. Sci., vol. 9, no. 10, 2019, doi: 10.3390/app9102000.

J. A. Reyes Barraza and R. Deiterding, “Towards a generalised lattice Boltzmann method for aerodynamic simulations,” J. Comput. Sci., vol. 45, p. 101182, 2020, doi: 10.1016/j.jocs.2020.101182.

N. Pellerin, S. Leclaire, and M. Reggio, “An interpolation-based lattice Boltzmann method for non-conforming orthogonal meshes,” Comput. Math. with Appl., vol. 100, no. January, pp. 152–166, 2021, doi: 10.1016/j.camwa.2021.09.002.

D. D. Ganji and S. H. H. Kachapi, “Chapter 6 - Natural, Mixed, and Forced Convection in Nanofluid,” in Application of Nonlinear Systems in Nanomechanics and Nanofluids, D. D. Ganji and S. H. H. Kachapi, Eds., in Micro and Nano Technologies. , Oxford: William Andrew Publishing, 2015, pp. 205–269. doi:

D. Solomatine, L. M. See, and R. J. Abrahart, “Data-driven modelling: concepts, approaches and experiences,” Pract. hydroinformatics Comput. Intell. Technol. Dev. water Appl., pp. 17–30, 2008.

K. Yonekura and K. Suzuki, “Data-driven design exploration method using conditional variational autoencoder for airfoil design,” Struct. Multidiscip. Optim., vol. 64, no. 2, pp. 613–624, 2021.

X. Hui, J. Bai, H. Wang, and Y. Zhang, “Fast pressure distribution prediction of airfoils using deep learning,” Aerosp. Sci. Technol., vol. 105, p. 105949, 2020.

G. Yao, T. Lei, and J. Zhong, “A review of convolutional-neural-network-based action recognition,” Pattern Recognit. Lett., vol. 118, pp. 14–22, 2019.

L. Alzubaidi et al., “Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions,” J. big Data, vol. 8, pp. 1–74, 2021.

A. Ajit, K. Acharya, and A. Samanta, “A review of convolutional neural networks, p 1--5,” in 2020 International Conference on Emerging Trends in Information Technology and Engineering (ic-ETITE), IEEE, New York, NY. https://doi. org/10, 2020.

M. Elsaadouny, J. Barowski, and I. Rolfes, “Extracting the features of the shallowly buried objects using LeNet convolutional network,” in 2020 14th European conference on antennas and propagation (EuCAP), 2020, pp. 1–4.

Z. Yuan, Y. Wang, Y. Qiu, J. Bai, and G. Chen, “Aerodynamic coefficient prediction of airfoils with convolutional neural network,” in The Proceedings of the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018) 9th, 2019, pp. 34–46.

Y. Zhang, W. J. Sung, and D. N. Mavris, “Application of convolutional neural network to predict airfoil lift coefficient,” in 2018 AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 2018, p. 1903.

J. Viquerat and E. Hachem, “A supervised neural network for drag prediction of arbitrary 2D shapes in laminar flows at low Reynolds number,” Comput. & Fluids, vol. 210, p. 104645, 2020.

H. Chen, L. He, W. Qian, and S. Wang, “Multiple aerodynamic coefficient prediction of airfoils using a convolutional neural network,” Symmetry (Basel)., vol. 12, no. 4, p. 544, 2020.

A. A. Zikri, H. Defianti, W. Hidayat, and A. Purqon, “Geometry Representation Effectiveness in Improving Airfoil Aerodynamic Coefficient Prediction with Convolutional Neural Network,” JOIV Int. J. Informatics Vis., vol. 7, no. 3, pp. 644–650, 2023.

O. R. Bingol and A. Krishnamurthy, “NURBS-Python: An open-source object-oriented NURBS modeling framework in Python,” SoftwareX, vol. 9, pp. 85–94, 2019.

S. Albawi, T. A. Mohammed, and S. Al-Zawi, “Understanding of a convolutional neural network,” in 2017 international conference on engineering and technology (ICET), 2017, pp. 1–6.

S. Bhatnagar, Y. Afshar, S. Pan, K. Duraisamy, and S. Kaushik, “Prediction of aerodynamic flow fields using convolutional neural networks,” Comput. Mech., vol. 64, pp. 525–545, 2019.

P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,” Phys. Rev., vol. 94, no. 3, p. 511, 1954.

Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE, vol. 86, no. 11, pp. 2278–2324, 1998.

I. Goodfellow, Y. Bengio, and A. Courville, Deep learning. MIT press, 2016.

X. Glorot, A. Bordes, and Y. Bengio, “Deep sparse rectifier neural networks,” in Proceedings of the fourteenth international conference on artificial intelligence and statistics, 2011, pp. 315–323.

A. K. Dubey and V. Jain, “Comparative study of convolution neural network’s relu and leaky-relu activation functions,” in Applications of Computing, Automation and Wireless Systems in Electrical Engineering: Proceedings of MARC 2018, 2019, pp. 873–880.