Experiments in Fluids

, 59:131 | Cite as

Jet mixing optimization using machine learning control

  • Zhi Wu
  • Dewei Fan
  • Yu ZhouEmail author
  • Ruiying Li
  • Bernd R. NoackEmail author
Research Article


We experimentally optimize mixing of a turbulent round jet using machine learning control (MLC) following Li et al. (Exp Fluids 58(article 103):1–20, 2017). The jet is manipulated with one unsteady minijet blowing in wall-normal direction close to the nozzle exit. The flow is monitored with two hotwire sensors. The first sensor is positioned on the centerline five jet diameters downstream of the nozzle exit, i.e. the end of the potential core, while the second is located three jet diameters downstream and displaced towards the shear-layer. The mixing performance is monitored with mean velocity at the first sensor. A reduction of this velocity correlates with increased entrainment near the potential core. MLC is employed to optimize sensor feedback, a general open-loop broadband frequency actuation and combinations of both. MLC has identified the optimal periodic forcing with small duty cycle as the best control policy employing only 400 actuation measurements, each lasting for 5 s. This learning rate is comparable if not faster than typical optimization of periodic forcing with two free parameters (frequency and duty cycle). In addition, MLC results indicate that neither new frequencies nor sensor feedback improves mixing further—contrary to many of other turbulence control experiments. The optimality of pure periodic actuation may be attributed to the simple jet flapping mechanism in the minijet plane. The performance of sensor feedback is shown to face a challenge for small duty cycles. The jet mixing results demonstrate the untapped potential of MLC in quickly learning optimal general control policies, even deciding between open- and closed-loop control.

Graphical abstract



This work is supported by a public Grant overseen by the French National Research Agency (ANR) as part of the “Investissement dAvenir” program, through the “iCODE Institute project” funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02, by the ANR Grants ’ACTIV_ROAD’ and ‘FlowCon’. The thesis of RL is supported by the OpenLab Fluidics between PSA Peugeot-Citroën and Institute Pprime (Fluidics@poitiers). The financial support of NSFC via Grant (approval no. 91752109) is acknowledged. We appreciate valuable stimulating discussions with Steven Brunton, Camila Chovet, Eurika Kaiser, Laurent Keirsbulck, Nathan Kutz, Richard Semaan and the French-German-Canadian-American pinball team: Guy Yoslan Cornejo-Maceda, Nan Deng, François Lusseyran, Robert Martinuzzi, Cedric Raibaudo and Luc Pastur.


  1. Becker R, King R, Petz R, Nitsche W (2007) Adaptive closed-loop control on a high-lift configuration using extremum seeking. AIAA J 45(6):1382–92CrossRefGoogle Scholar
  2. Bourgeois JA, Martinuzzi RJ, Noack BR (2013) Generalised phase average with applications to sensor-based flow estimation of the wall-mounted square cylinder wake. J Fluid Mech 736:316–350CrossRefzbMATHGoogle Scholar
  3. Brackston RD, Wynn A, Morrison JF (2016) Extremum seeking to control the amplitude and frequency of a pulsed jet for bluff body drag reduction. Exp Fluids 57(10):article 159 (1–14) Google Scholar
  4. Bradbury LJS, Khadem AH (1975) The distortion of a jet by tabs. J Fluid Mech 70(04):801–813CrossRefGoogle Scholar
  5. Brameier M, Banzhaf W (2007) Linear genetic programming. Springer, BerlinzbMATHGoogle Scholar
  6. Brunton SL, Noack BR (2015) Closed-loop turbulence control: progress and challenges. Appl Mech Rev 67(5):050,801:01–48Google Scholar
  7. Choi H, Jeon WP, Kim J (2008) Control of flow over a bluff body. Ann Rev Fluid Mech 40:113–139MathSciNetCrossRefzbMATHGoogle Scholar
  8. Chovet C, Keirsbulck L, Noack BR, Lippert M, Foucaut JM (2017) Machine learning control for experimental shear flows targeting the reduction of a recirculation bubble. In: The 20th World Congress of the International Federation of Automatic Control (IFAC). Toulouse, France, pp 1–4Google Scholar
  9. Coats C (1997) Coherent structures in combustion. Prog Energy Combust Sci 22:427–509CrossRefGoogle Scholar
  10. Collis SS, D JR, Seifert A, Theofilis V (2004) Issues in active flow control: theory, control, simulation, and experiment. Prog Aerosp Sci 40:237–289Google Scholar
  11. Davis MR (1982) Variable control of jet decay. AIAA J 20(5):606–609CrossRefGoogle Scholar
  12. Dracopoulos DC, Kent S (1997) Genetic programming for prediction and control. Neural Comput Appl 6:214–228CrossRefGoogle Scholar
  13. Duriez T, Brunton SL, Noack BR (2016) Machine learning control—taming nonlinear dynamics and turbulence. Fluid mechanics and its applications. Springer, BerlinzbMATHGoogle Scholar
  14. Fan DW, Wu Z, Yang H, Li JD, Zhou Y (2017) Modified extremum-seeking closed-loop system for jet mixing enhancement. AIAA J 55(11):3891–3902CrossRefGoogle Scholar
  15. Freund JB, Moin P (2000) Jet mixing enhancement by high-amplitude fluidic actuation. AIAA J 38(10):1863–1870CrossRefGoogle Scholar
  16. Garnaud X, Lesshafft L, Schmid PJ, Huerre P (2013) The preferred mode of incompressible jets: linear frequency response analysis. J Fluid Mech 716:189–202MathSciNetCrossRefzbMATHGoogle Scholar
  17. Gutmark E, Grinstein F (1999) Flow control with noncircular jets. Ann Rev Fluid Mech 31(1):239–272CrossRefGoogle Scholar
  18. Henderson B (2010) Fifty years of fluidic injection for jet noise reduction. Int J Aeroacoust 9(1–2):91–122CrossRefGoogle Scholar
  19. Hilgers A, Boersma BJ (2001) Optimization of turbulent jet mixing. Fluid Dyn Res 29:345–368CrossRefGoogle Scholar
  20. Ho CM, Gutmark E (1987) Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet. J Fluid Mech 179:383–405CrossRefGoogle Scholar
  21. Hussain F, Husain HS (1989) Elliptic jets. Part 1. Characteristics of unexcited and excited jets. J Fluid Mech 208:257–320CrossRefGoogle Scholar
  22. Inoue O (1992) Double-frequency forcing on spatially growing mixing layers. J Fluid Mech 234:553–581CrossRefzbMATHGoogle Scholar
  23. Johari H, Pacheco-Tougas M, Hermanson J (1999) Penetration and mixing of fully modulated turbulent jets in crossflow. AIAA J 37(7):842–850CrossRefGoogle Scholar
  24. Kaiser E, Li R, Noack BR (2017) On the control landscape topology. The 20th World Congress of the International Federation of Automatic Control (IFAC). Toulouse, France, pp 1–4Google Scholar
  25. Koumoutsakos P, Freund J, Parekh D (2001) Evolution strategies for automatic optimization of jet mixing. AIAA J 39(5):967–969CrossRefGoogle Scholar
  26. Lee C, Kim J, Babcock D, Goodman R (1997) Application of neural networks to turbulence control for drag reduction. Phys Fluids 9(6):1740–1747CrossRefGoogle Scholar
  27. Li R, Noack BR, Cordier L, Borée J, Harambat F (2017) Drag reduction of a car model by linear genetic programming control. Exp Fluids 58(article 103):1–20Google Scholar
  28. Mardia KV, Kent JT, Bibby JM (1979) Multivariate analysis. Probability and mathematical statistics. Academic Press, CambridgezbMATHGoogle Scholar
  29. Maury R, Kœnig M, Cattafesta L, Jordan P, Delville J (2012) Extremum-seeking control of jet noise. Int J Aeroacoust 11(3–4):459–473CrossRefGoogle Scholar
  30. Mi J, Kalt P, Nathan G, Wong C (2007) Piv measurements of a turbulent jet issuing from round sharp-edged plate. Exp Fluids 42(4):625–637CrossRefGoogle Scholar
  31. Monkewitz P (1988) Subharmonic resonance, pairing and shredding in the mixing layer. J Fluid Mech 188:223–252CrossRefzbMATHGoogle Scholar
  32. Noack BR (2018) Closed-loop turbulence control-from human to machine learning (and retour). In: Zhou Y, Kimura M, Peng G, Lucey A, Huang L (eds) Fluid-structure-sound interactions and control. FSSIC 2017. Springer, Singapore, pp 23–32Google Scholar
  33. Parezanović V, Cordier L, Spohn A, Duriez T, Noack BR, Bonnet JP, Segond M, Abel M, Brunton SL (2016) Frequency selection by feedback control in a turbulent shear flow. J Fluid Mech 797:247–283CrossRefGoogle Scholar
  34. Paschereit CO, Wygnanski I, Fiedler HE (1995) Experimental investigation of subharmonic resonance in an axisymmetric jet. J Fluid Mech 283:365–407CrossRefGoogle Scholar
  35. Pastoor M, Henning L, Noack BR, King R, Tadmor G (2008) Feedback shear layer control for bluff body drag reduction. J Fluid Mech 608:161–196CrossRefzbMATHGoogle Scholar
  36. Rapoport D, Fono I, Cohen K, Seifert A (2003) Closed-loop vectoring control of a turbulent jet using periodic excitation. J Propul Power 19(4):646–654CrossRefGoogle Scholar
  37. Reynolds W, Parekh D, Juvet P, Lee M (2003) Bifurcating and blooming jets. Ann Rev Fluid Mech 35(1):295–315MathSciNetCrossRefzbMATHGoogle Scholar
  38. Samimy M, Kim JH, Kastner J, Adamovic I, Utkin Y (2007) Active control of high-speed and high-Reynolds-number jets using plasma actuators. J Fluid Mech 578:305–330CrossRefzbMATHGoogle Scholar
  39. Wahde M (2008) Biologically inspired optimization methods: an introduction. WIT Press, AshurszbMATHGoogle Scholar
  40. Wiltse JM, Glezer A (1993) Manipulation of free shear flows using piezoelectric actuators. J Fluid Mech 249:261–285CrossRefGoogle Scholar
  41. Wu Z, Wong CW, Wang L, Lu Z, Zhu Y, Zhou Y (2015) A rapidly settled closed-loop control for airfoil aerodynamics based on plasma actuation. Exp Fluids 56(8):article 158 (1–15) Google Scholar
  42. Wu Z, Zhou Y, Cao HL, Li WL (2016) Closed-loop enhancement of jet mixing with extremum-seeking and physics-based strategies. Exp Fluids 57:1–14CrossRefGoogle Scholar
  43. Wu Z, Wong CW, Zhou Y (2018) Dual-input/single-output extremum-seeking system for jet control. AIAA J 56(4):1463–1471CrossRefGoogle Scholar
  44. Yang H, Zhou Y (2016) Axisymmetric jet manipulated using two unsteady minijets. J Fluid Mech 808:362–396MathSciNetCrossRefzbMATHGoogle Scholar
  45. Yang H, Zhou Y, So R, Liu Y (2016) Turbulent jet manipulation using two unsteady azimuthally separated radial minijets. Proc R Soc A 472(2191):20160,417Google Scholar
  46. Zaman KBMQ, Hussain AKMF (1980) Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response. J Fluid Mech 101(3):449–491CrossRefGoogle Scholar
  47. Zaman KBMQ, Reeder MF, Samimy M (1994) Control of an axisymmetric jet using vortex generators. Phys Fluids 6(2):778–793CrossRefGoogle Scholar
  48. Zhang MM, Cheng L, Zhou Y (2004a) Closed-loop control of fluid–structure interactions on a flexibly supported cylinder. Eur J Mech B 23:189–197CrossRefzbMATHGoogle Scholar
  49. Zhang MM, Cheng L, Zhou Y (2004b) Closed-loop-controlled vortex shedding and vibration of a flexibly supported square cylinder under different schemes. Phys Fluids 16(5):1439–1448CrossRefzbMATHGoogle Scholar
  50. Zhou Y, Du C, Mi J, Wang XW (2012) Turbulent round jet control using two steady minijets. AIAA J 50(3):736–740CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Turbulence-Noise-Vibration Interaction and ControlHarbin Institute of TechnologyShenzhenPeople’s Republic of China
  2. 2.Digital Engineering Laboratory of Offshore EquipmentShenzhenPeople’s Republic of China
  3. 3.Institut PPRIME, CNRS-Université de Poitiers-ISAE-ENSMAFuturoscope ChasseneuilFrance
  4. 4.LIMSI-CNRSRue John von Neumann, Campus Universitaire d’OrsayOrsayFrance
  5. 5.Institut für Strömungsmechanik und Technische Akustik (ISTA)Technische Universität BerlinBerlinGermany

Personalised recommendations