Jet mixing optimization using machine learning control
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.
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.
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