# Drag reduction of a car model by linear genetic programming control

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## Abstract

We investigate open- and closed-loop active control for aerodynamic drag reduction of a car model. Turbulent flow around a blunt-edged Ahmed body is examined at \(Re_{H}\approx 3\times 10^{5}\) based on body height. The actuation is performed with pulsed jets at all trailing edges (multiple inputs) combined with a Coanda deflection surface. The flow is monitored with 16 pressure sensors distributed at the rear side (multiple outputs). We apply a recently developed model-free control strategy building on genetic programming in Dracopoulos and Kent (Neural Comput Appl 6:214–228, 1997) and Gautier et al. (J Fluid Mech 770:424–441, 2015). The optimized control laws comprise periodic forcing, multi-frequency forcing and sensor-based feedback including also time-history information feedback and combinations thereof. Key enabler is linear genetic programming (LGP) as powerful regression technique for optimizing the multiple-input multiple-output control laws. The proposed LGP control can select the best open- or closed-loop control in an unsupervised manner. Approximately 33% base pressure recovery associated with 22% drag reduction is achieved in all considered classes of control laws. Intriguingly, the feedback actuation emulates periodic high-frequency forcing. In addition, the control identified automatically the only sensor which listens to high-frequency flow components with good signal to noise ratio. Our control strategy is, in principle, applicable to all multiple actuators and sensors experiments.

## Notes

### Acknowledgements

The authors acknowledge the great support during the experiment by J.-M. Breux, J. Laumonier, P. Braud and R. Bellanger. The thesis of RL is supported by the OpenLab Fluidics between PSA Peugeot-Citroën and Institute Pprime (Fluidics @ poitiers). We appreciate valuable stimulating discussions with: Markus Abel, Diogo Barros, Steven Brunton, Eurika Kaiser, Siniša Krajnović, Vladimir Parezanović, Rolf Radespiel, Peter Scholz, Richard Semaan, Andreas Spohn and Mattias Wahde.

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