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Machine-learning-based feedback control for drag reduction in a turbulent channel flow

Published online by Cambridge University Press:  12 October 2020

Jonghwan Park  and
Haecheon Choi Open the ORCID record for Haecheon Choi [Opens in a new window]
Jonghwan Park
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul08826, Korea
Haecheon Choi*
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul08826, Korea Institute of Advanced Machines and Design, Seoul National University, Seoul08826, Korea
*
†Email address for correspondence: choi@snu.ac.kr
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Abstract

One of the successful feedback controls for skin-friction drag reduction designed by Choi et al. (J. Fluid Mech., vol. 262, 1994, pp. 75–110), called ‘opposition control’, has a limitation in application because the sensors need to be placed slightly away from the wall, i.e. at $y^+ = 10$, and measure the instantaneous wall-normal velocity. In the present study we train convolutional neural networks using the database of uncontrolled turbulent channel flow at $Re_{\tau } = 178$ to extract the spatial distributions of the wall shear stresses and pressure that closely represent the wall-normal velocity at $y^+ = 10$. The correlations between the predicted wall-normal velocities at $y^+ = 10$ from the wall-variable distributions and true ones are very high, and they are 0.92, 0.96 and 0.96 for the streamwise and spanwise wall shear stresses and pressure, respectively. We perform feedback controls of turbulent channel flow with instantaneous blowing and suction determined by the trained convolutional neural networks from the measured wall-variable distributions. The predicted wall-normal velocities during the controls have higher energy at small to intermediate scales than the true ones, which degrades the control performance in skin-friction drag reduction. By applying a low-pass filter to the predicted wall-normal velocities to remove those scales, we reduce skin-friction drag by up to 18 % whose amount is comparable to that by opposition control. The convolutional neural networks trained at $Re_{\tau } = 178$ are also applied to a higher Reynolds number flow ($Re_{\tau } = 578$), and provide a successful skin-friction drag reduction of 15 %.

JFM classification

Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A24
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abergel, F. & Temam, R. 1990 On some control problems in fluid mechanics. Theor. Comput. Fluid Dyn. 1, 303–325.CrossRefGoogle Scholar
Bengio, Y. 2012 Practical recommendations for gradient-based training of deep architectures. arXiv:1206.5533.CrossRefGoogle Scholar
Bewley, T. R., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179–225.CrossRefGoogle Scholar
Bewley, T. R. & Protas, B. 2004 Skin friction and pressure: the “footprints” of turbulence. Physica D 196, 28–44.CrossRefGoogle Scholar
Breiman, L. 2001 Random forests. Mach. Learn. 45, 5–32.CrossRefGoogle Scholar
Chang, Y., Collis, S. S. & Ramakrishnan, S. 2002 Viscous effects in control of near-wall turbulence. Phys. Fluids 14, 4069–4080.CrossRefGoogle Scholar
Chevalier, M., Hœpffner, J., Bewley, T. R. & Henningson, D. S. 2006 State estimation in wall-bounded flow systems. Part 2. Turbulent flows. J. Fluid Mech. 552, 167–187.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.CrossRefGoogle Scholar
Choi, H., Temam, R., Moin, P. & Kim, J. 1993 Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253, 509–543.CrossRefGoogle Scholar
Chung, Y. M. & Talha, T. 2011 Effectiveness of active flow control for turbulent skin friction drag reduction. Phys. Fluids 23, 025102.CrossRefGoogle Scholar
Glorot, X. & Bengio, Y. 2010 Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (ed. Teh, Y. & Titterington, M.), Proceedings of Machine Learning Research, vol. 9, pp. 249–256. PMLR.Google Scholar
Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A. & Bengio, Y. 2014 Generative adversarial networks. arXiv:1406.2661.Google Scholar
Güemes, A., Discetti, S. & Ianiro, A. 2019 Sensing the turbulent large-scale motions with their wall signature. Phys. Fluids 31, 125112.CrossRefGoogle Scholar
Hammond, E. P., Bewley, T. R. & Moin, P. 1998 Observed mechanisms for turbulence attenuation and enhancement in opposition-controlled wall-bounded flows. Phys. Fluids 10, 2421–2423.CrossRefGoogle Scholar
He, K., Zhang, X., Ren, S. & Sun, J. 2015 Deep residual learning for image recognition. arXiv:1512.03385.CrossRefGoogle Scholar
Hœpffner, J., Chevalier, M., Bewley, T. R. & Henningson, D. S. 2005 State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows. J. Fluid Mech. 534, 263–294.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to ${Re}_{\tau }=2003$. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Illingworth, S. J., Monty, J. P. & Marusic, I. 2018 Estimating large-scale structures in wall turbulence using linear models. J. Fluid Mech. 842, 146–162.CrossRefGoogle Scholar
Ioffe, S. & Szegedy, C. 2015 Batch normalization: accelerating deep network training by reducing internal covariate shift. arXiv:1502.03167.Google Scholar
Iwamoto, K., suzuki, Y. & Kasagi, N. 2002 Reynolds number effect on wall turbulence: toward effective feedback control. Intl J. Heat Fluid Flow 23, 678–689.CrossRefGoogle Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25, 101302.CrossRefGoogle Scholar
Kasagi, N., Suzuki, Y. & Fukagata, K. 2008 Microelectromechanical systems-based feedback control of turbulence for skin friction reduction. Annu. Rev. Fluid Mech. 41, 231–251.CrossRefGoogle Scholar
Kim, E. & Choi, H. 2017 Linear proportional-integral control for skin-friction reduction in a turbulent channel flow. J. Fluid Mech. 814, 430–451.CrossRefGoogle Scholar
Kim, J. & Lee, C. 2020 Prediction of turbulent heat transfer using convolutional neural networks. J. Fluid Mech. 882, A18.CrossRefGoogle Scholar
Kingma, D. P. & Ba, J. 2014 Adam: a method for stochastic optimization. arXiv:1412.6980.Google Scholar
Krizhevsky, A., Sutskever, I. & Hinton, G. E. 2012 ImageNet classification with deep convolutional neural networks. In Proceedings of the 25th International Conference on Neural Information Processing Systems (ed. Pereira, F., Burges, C. J. C. & Bottou, L.), pp. 1097–1105. Curran Associates Inc.Google Scholar
LeCun, Y., Bengio, Y. & Hinton, G. E. 2015 Deep learning. Nature 521, 436–444.CrossRefGoogle ScholarPubMed
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W. & Jackel, L. D. 1989 Handwritten digit recognition with a back-propagation network. In Proceedings of the 2nd International Conference on Neural Information Processing Systems (ed. Touretzky, D. S.), pp. 396–404. MIT Press.Google Scholar
Ledig, C., Theis, L., Huszár, F., Caballero, J., Cunningham, A., Acosta, A., Aitken, A., Tejani, A., Totz, J., Wang, Z., et al. 2016 Photo-realistic single image super-resolution using a generative adversarial network. arXiv:1609.04802.CrossRefGoogle Scholar
Lee, K. H., Cortelezzi, L., Kim, J. & Speyer, J. 2001 Application of reduced-order controller to turbulent flows for drag reduction. Phys. Fluids 13, 1321–1330.CrossRefGoogle Scholar
Lee, C., Kim, J., Babcock, D. & Goodman, R. 1997 Application of neural networks to turbulence control for drag reduction. Phys. Fluids 9, 1740–1747.CrossRefGoogle Scholar
Lee, C., Kim, J. & Choi, H. 1998 Suboptimal control of turbulent channel flow for drag reduction. J. Fluid Mech. 358, 245–258.CrossRefGoogle Scholar
Lee, S. & You, D. 2019 Data-driven prediction of unsteady flow over a circular cylinder using deep learning. J. Fluid Mech. 879, 217–254.CrossRefGoogle Scholar
Lorang, L. V., Podvin, B. & Le Quéré, P. 2008 Application of compact neural network for drag reduction in a turbulent channel flow at low Reynolds numbers. Phys. Fluids 20, 045104.CrossRefGoogle Scholar
Mäteling, E., Klaas, M. & Schröder, W. 2020 Simultaneous stereo PIV and MPS3 wall-shear stress measurements in turbulent channel flow. Optics 1, 40–51.CrossRefGoogle Scholar
Milano, M. & Koumoutsakos, P. 2002 Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182, 1–26.CrossRefGoogle Scholar
Nair, V. & Hinton, G. E. 2010 Rectified linear units improve restricted Boltzmann machines. In Proceedings of the 27th International Conference on Machine Learning (ed. Fürnkranz, J. & Joachims, T.), pp. 807–814. Omnipress.Google Scholar
Oehler, S. F., Garcia-Gutiérrez, A. & Illingworth, S. J. 2018 Linear estimation of coherent structures in wall-bounded turbulence at $Re_{\tau }=2000$. J. Phys.: Conf. Ser. 1001, 012006.Google Scholar
Oehler, S. F. & Illingworth, S. J. 2018 Linear estimation and control of coherent structures in wall-bounded turbulence at $Re_{\tau }=2000$. In Proceedings of the 21st Australasian Fluid Mechanics Conference (ed. Lau, T. C. W. & Kelso, R. M.). AFMS.Google Scholar
Park, N., Yoo, J. & Choi, H. 2005 Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation. Phys. Fluids 17, 015103.CrossRefGoogle Scholar
Podvin, B. & Lumley, J. 1998 Reconstructing the flow in the wall region from wall sensors. Phys. Fluids 10, 1182–1190.CrossRefGoogle Scholar
Rebbeck, H. & Choi, K.-S. 2001 Opposition control of near-wall turbulence with a piston-type actuator. Phys. Fluids 13, 2142–2145.CrossRefGoogle Scholar
Rebbeck, H. & Choi, K.-S. 2006 A wind-tunnel experiment on real-time opposition control of turbulence. Phys. Fluids 18, 035103.CrossRefGoogle Scholar
Rumelhart, D. E., Hinton, G. E. & Williams, R. J. 1986 Learning representations by back-propagating errors. Nature 323, 533–536.CrossRefGoogle Scholar
Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., et al. 2015 ImageNet large scale visual recognition challenge. Intl J. Comput. Vis. 115, 211–252.CrossRefGoogle Scholar
Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., et al. 2016 Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489.CrossRefGoogle ScholarPubMed
Simonyan, K., Vedaldi, A. & Zisserman, A. 2013 Deep inside convolutional networks: visualising image classification models and saliency maps. arXiv:1312.6034.Google Scholar
Simonyan, K. & Zisserman, A. 2014 Very deep convolutional networks for large-scale image recognition. arXiv:1409.1556.Google Scholar
Singh, P. & Manure, A. 2019 Learn Tensorflow 2.0: Implement Machine Learning and Deep Learning Models with Python. Apress.Google Scholar
Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V. & Rabinovich, A. 2014 Going deeper with convolutions. arXiv:1409.4842.CrossRefGoogle Scholar
Tibshirani, R. 1996 Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B 58, 267–288.Google Scholar
Wang, Y.-S., Huang, W.-X. & Xu, C.-X. 2016 Active control for drag reduction in turbulent channel flow: the opposition control schemes revisited. Fluid Dyn. Res. 48, 055501.CrossRefGoogle Scholar
Yamagami, T., Suzuki, Y. & Kasagi, N. 2005 Development of feedback control system of wall turbulence using MEMS devices. In Proceedings of 6th Symposium on Smart Control of Turbulence, pp. 135–141.Google Scholar
Yoshino, T., Suzuki, Y. & Kasagi, N. 2008 Drag reduction of turbulence air channel flow with distributed micro sensors and actuators. J. Fluid Sci. Technol. 3, 137–148.CrossRefGoogle Scholar
Yun, J. & Lee, J. 2017 Prediction of near wall velocity in turbulent channel flow using wall pressure based on artificial neural network. In Proceedings of the Korean Society of Mechanical Engineers Conference, pp. 457–460. KSME.Google Scholar