Abstract
The active control of flow past an elliptical cylinder using the deep reinforcement learning (DRL) method is conducted. The axis ratio of the elliptical cylinder Γ varies from 1.2 to 2.0, and four angles of attack α = 0°, 15°, 30°, and 45° are taken into consideration for a fixed Reynolds number Re = 100. The mass flow rates of two synthetic jets imposed on different positions of the cylinder θ1 and θ2 are trained to control the flow. The optimal jet placement that achieves the highest drag reduction is determined for each case. For a low axis ratio ellipse, i.e., Γ = 1.2, the controlled results at α = 0° are similar to those for a circular cylinder with control jets applied at θ1 = 90° and θ2 = 270°. It is found that either applying the jets asymmetrically or increasing the angle of attack can achieve a higher drag reduction rate, which, however, is accompanied by increased fluctuation. The control jets elongate the vortex shedding, and reduce the pressure drop. Meanwhile, the flow topology is modified at a high angle of attack. For an ellipse with a relatively higher axis ratio, i.e., Γ ⩾ 1.6, the drag reduction is achieved for all the angles of attack studied. The larger the angle of attack is, the higher the drag reduction ratio is. The increased fluctuation in the drag coefficient under control is encountered, regardless of the position of the control jets. The control jets modify the flow topology by inducing an external vortex near the wall, causing the drag reduction. The results suggest that the DRL can learn an active control strategy for the present configuration.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
YAO, Y., XU, C., and HUANG, W. Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall. Applied Mathematics and Mechanics (English Edition), 39(9), 1267–1276 (2018) https://doi.org/10.1007/s10483-018-2364-7
LOU, B., YE, S., WANG, G., and HUANG, Z. Numerical and experimental research of flow control on an NACA 0012 airfoil by local vibration. Applied Mathematics and Mechanics (English Edition), 40(1), 1–12 (2019) https://doi.org/10.1007/s10483-019-2404-8
LI, Q., PAN, M., ZHOU, Q., and DONG, Y. Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability. Applied Mathematics and Mechanics (English Edition), 40(7), 1041–1052 (2019) https://doi.org/10.1007/s10483-019-2500-8
CHOI, H., JEON, W. P., and KIM, J. Control of flow over a bluff body. Annual Review of Fluid Mechanics, 40, 113–139 (2008)
BEARMAN, P. W. and HARVEY, J. K. Control of circular cylinder flow by the use of dimples, AIAA Journal, 31(10), 1753–1756 (1993)
BEARMAN, P. W. and OWEN, J. C. Reduction of bluff-body drag and suppression of vortex shedding by the introduction of wavy separation lines. Journal of Fluids and Structures, 12(1), 123–130 (1998)
SCHULMEISTER, J. C., DAHL, J. M., WEYMOUTH, G. D., and TRIANTAFYLLOU, M. S. Flow control with rotating cylinders. Journal of Fluid Mechanics, 825, 743–763 (2017)
BEARMAN, P. W. Investigation of the flow behind a two-dimensional model with a blunt trailing edge and fitted with splitter plates. Journal of Fluid Mechanics, 21(2), 241–255 (1965)
TOKUMARU, P. J. and DIMOTAKIS, P. E. Rotary oscillation control of a cylinder wake. Journal of Fluid Mechanics, 224, 77–90 (1991)
SHILES, D. and LEONARD, A. Investigation of a drag reduction on a circular cylinder in rotary oscillation. Journal of Fluid Mechanics, 431, 297–322 (2001)
LU, L., QIN, J. M., TENG, B., and LI, Y. C. Numerical investigations of lift suppression by feedback rotary oscillation of circular cylinder at low Reynolds number. Physics of Fluids, 23(3), 033601 (2011)
SHUKLA, R. K. and ARAKERI, J. H. Minimum power consumption for drag reduction on a circular cylinder by tangential surface motion. Journal of Fluid Mechanics, 715, 597–641 (2013)
HWANG, Y., KIM, J., and CHOI, H. Stabilization of absolute instability in spanwise wavy two-dimensional wakes. Journal of Fluid Mechanics, 727, 346–378 (2013)
GUERCIO, G. D., COSSU, C., and PUJALS, G. Stabilizing effect of optimally amplified streaks in parallel wakes. Journal of Fluid Mechanics, 739, 37–56 (2014)
TAMMISOLA, O. Optimal wavy surface to suppress vortex shedding using second-order sensitivity to shape changes. European Journal of Mechanics-B/Fluids, 62, 139–148 (2017)
MAO, X. and WANG, B. Spanwise localized control for drag reduction in flow passing a cylinder. Journal of Fluid Mechanics, 915, A112 (2021)
GAD-EL-HAK and MOHAMED. Flow Control: Passive, Active, and Reactive Flow Management, Cambridge University Press, Cambridge (2000)
BRUNTON, S. L., NOACK, B. R., and KOUMOUTSAKOS, P. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 52(1), 477–508 (2020)
RABAULT, J., KUCHTA, M., JENSEN, A., REGLADE, U., and CERARDI, N. Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics, 865, 281–302 (2019)
RABAULT, J. and KUHNLE, A. Accelerating deep reinforcement learning strategies of flow control through a multi-environment approach. Physics of Fluids, 31 (9), 94–105 (2019)
REN, F., RABAULT, J., and TANG, H. Applying deep reinforcement learning to active flow control in weakly turbulent conditions. Physics of Fluids, 33(3), 037121 (2020)
REN, F., WANG, C., and TANG, H. Bluff body uses deep-reinforcement-learning trained active flow control to achieve hydrodynamic stealth. Physics of Fluids, 33(9), 093602 (2021)
XU, H., ZHANG, W., DENG, J., and RABAULT, J. Active flow control with rotating cylinders by an artificial neural network trained by deep reinforcement learning. Journal of Hydrodynamics, 32, 254–258 (2020)
FAN, D., YANG, L., WANG, Z., TRIANTAFYLLOU, M. S., and KARNIADAKIS, G. E. Reinforcement learning for bluff body active flow control in experiments and simulations. Proceedings of the National Academy of Sciences, 117(42), 26091–26098 (2020)
TOKAREV, M., PALKIN, E., and MULLYADZHANOV, R. Deep reinforcement learning control of cylinder flow using rotary oscillations at low Reynolds number. Energies, 13(22), 5920 (2020)
TANG, H., RABAULT, J., KUHNLE, A., WANG, Y., and WANG, T. Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning. Physics of Fluids, 32(5), 653605 (2020)
LAI, P., WANG, R., ZHANG, W., and XU, H. Parameter optimization of open-loop control of a circular cylinder by simplified reinforcement learning. Physics of Fluids, 33(10), 107110 (2021)
PARIS, R., BENEDDINE, S., and DANDOIS, J. Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics, 913, A25 (2021)
ZHENG, C., JI, T., XIE, F., ZHANG, X., ZHENG, H., and ZHENG, Y. From active learning to deep reinforcement learning: intelligent active flow control in suppressing vortex-induced vibration. Physics of Fluids, 33(6), 063607 (2021)
LI, J. and ZHANG, M. Reinforcement-learning-based control of confined cylinder wakes with stability analyses. Journal of Fluid Mechanics, 932, A44 (2022)
PAUL, I., PRAKASH, K. A., VENGADESAN, S., and PULLETIKURTHI, V. Analysis and characterisation of momentum and thermal wakes of elliptic cylinders. Journal of Fluid Mechanics, 807, 303–323 (2016)
RICHARDS, G. J. On the motion of an elliptic cylinder through a viscous fluid. Philosophical Transactions of the Royal Society of London Series A, 233, 279–301 (1934)
TANEDA, S. Visual study of unsteady separated flows around bodies. Progress in Aerospace Sciences, 17, 287–348 (1977)
VIEIRA, E., FONSECA, F. B., and MANSUR, S. S. Flow around elliptical cylinders in moderate Reynolds numbers. Proceedings of the 22nd International Congress of Mechanical Engineering, ABCM, Brazil, 4089–4100 (2013)
NAIR, M. T. and SENGUPTA, T. K. Onset of asymmetry: flow past circular and elliptic cylinders. International Journal for Numerical Methods in Fluids, 23(12), 1327–1345 (1996)
PAUL, I., PRAKASH, K. A., and VENGADESAN, S. Onset of laminar separation and vortex shedding in flow past unconfined elliptic cylinders. Physics of Fluids, 26(2), 023601 (2014)
PARK, J. K., PARK, S. O., and HYUN, J. M. Flow regimes of unsteady laminar flow past a slender elliptic cylinder at incidence. International Journal of Heat & Fluid Flow, 10(4), 311–317 (1989)
SCHÄFER, M., TUREK, S., DURST, F., KRAUSE, E., and RANNACHER, R. Benchmark computations of laminar flow around a cylinder. Flow Simulation with High-Performance Computers II, Springer, 547–566, Wiesbaden (1996)
GODA, K. A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. Journal of Computational Physics, 30(1), 76–95 (1979)
LOGG, A., MARDAL, K. A., and WELLS, G. Automated Solution of Differential Equations by the Finite Element Method: the FEniCS Book, Springer, Berlin (2012)
SCHULMAN, J., WOLSKI, F., DHARIWAL, P., RADFORD, A., and KLIMOV, O. Proximal policy optimization algorithms. arXiv Preprint, arXiv:1707.06347 (2017)
DURANTE, D., GIANNOPOULOU, O., and COLAGROSSI, A. Regimes identification of the viscous flow past an elliptic cylinder for Reynolds number up to 10 000. Communications in Nonlinear Science and Numerical Simulation, 102, 105902 (2021)
Author information
Authors and Affiliations
Corresponding author
Additional information
Citation: WANG, B. F., WANG, Q., ZHOU, Q., and LIU, Y. L. Active control of flow past an elliptic cylinder using an artificial neural network trained by deep reinforcement learning. Applied Mathematics and Mechanics (English Edition), 43(12), 1921–1934 (2022) https://doi.org/10.1007/s10483-022-2940-9
Project supported by the National Natural Science Foundation of China (Nos. 11988102, 92052201, 11972220, 12032016, 11825204, 91852202, and 11732010) and the Key Research Projects of Shanghai Science and Technology Commission of China (Nos. 19JC1412802 and 20ZR1419800)
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Wang, B., Wang, Q., Zhou, Q. et al. Active control of flow past an elliptic cylinder using an artificial neural network trained by deep reinforcement learning. Appl. Math. Mech.-Engl. Ed. 43, 1921–1934 (2022). https://doi.org/10.1007/s10483-022-2940-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-022-2940-9