# 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.

## References

- Ahmed SR, Ramm G, Faltin G (1984) Some salient features of the time averaged ground vehicle wake. Society of Automotive Engineers, SAE Inc 840300, USAGoogle Scholar
- Aubrun S, McNally J, Alvi F, Kourta A (2011) Separation flow control on a generic ground vehicle using steady microjet arrays. Exp Fluids 51(5):1177–1187CrossRefGoogle Scholar
- Bagheri S, Brandt L, Henningson DS (2009) Input–output analysis, model reduction and control of the flat-plate boundary layer. J Fluid Mech 620:263–298MathSciNetCrossRefzbMATHGoogle Scholar
- Barros D, Borée J, Noack BR, Spohn A, Ruiz T (2016) Bluff body drag manipulation using pulsed jets and Coanda effect. J Fluid Mech 805:422–459MathSciNetCrossRefGoogle Scholar
- Barros D (2015) Wake and drag manipulation of a bluff body using fluidic forcing. PhD thesis, École Nationale Supérieure de Mécanique et d’Aérotechnique, Poitiers, FranceGoogle Scholar
- Beaudoin J-F, Cadot O, Aider J-L, Wesfreid J (2006) Drag reduction of a bluff body using adaptive control methods. Phys Fluids 18(8):085107CrossRefGoogle Scholar
- Becker R, Garwon M, Gutknecht C, Bärwolff G, King R (2005) Robust control of separated shear flows in simulation and experiment. J Process Control 15(6):691–700CrossRefGoogle Scholar
- Brameier M, Banzhaf W (2007) Linear genetic programming. Springer Science & Business Media, BerlinGoogle Scholar
- Brunton SL, Noack BR (2015) Closed-loop turbulence control: progress and challenges. Appl Mech Rev 67(5):050801CrossRefGoogle Scholar
- Cattafesta L, Shelpak M (2011) Actuators for active flow control. Ann Rev Fluid Mech 43:247–272CrossRefzbMATHGoogle Scholar
- Choi H, Jeon W-P, Kim J (2008) Control of flow over a bluff body. Ann Rev Fluid Mech 40:113–139MathSciNetCrossRefzbMATHGoogle Scholar
- Choi H, Lee J, Park H (2014) Aerodynamics of heavy vehicles. Ann Rev Fluid Mech 46:441–468MathSciNetCrossRefzbMATHGoogle Scholar
- Dahan JA, Morgans AS, Lardeau S (2012) Feedback control for form-drag reduction on a bluff body with a blunt trailing edge. J Fluid Mech 704:360–387CrossRefzbMATHGoogle Scholar
- Debien A, von Krbek KAFF, Mazellier N, Duriez T, Cordier L, Noack BR, Abel MW, Kourta A (2016) Closed-loop separation control over a sharp-edge ramp using genetic programming. Exp Fluids 57(40):1–19Google Scholar
- Dracopoulos DC, Kent S (1997) Genetic programming for prediction and control. Neural Comput Appl 6:214–228CrossRefGoogle Scholar
- Duriez T, Parezanović V, Laurentie J-C, Fourment C, Delville J, Bonnet J-P, Cordier L, Noack BR, Segond M, Abel MW, Gautier N, Aider J-L, Raibaudo C, Cuvier C, Stanislas M, Brunton S (2014) Closed-loop control of experimental shear layers using machine learning (invited). In: 7th AIAA flow control conference, Atlanta, Georgia, pp 1–16Google Scholar
- Duriez T, Brunton S, Noack BR (2016) Machine learning control—taming nonlinear dynamics and turbulence. Fuid mechanics and its applications series, vol 116. Springer, New YorkGoogle Scholar
- Englar RJ (2004) Pneumatic heavy vehicle aerodynamic drag reduction, safety enhancement, and performance improvement. In: The aerodynamics of heavy vehicles: trucks, buses, and trainsGoogle Scholar
- Garwon M, King R (2005) A multivariable adaptive control strategy to regulate the separated flow behind a backward-facing step. In 16th IFAC World Congress, Prague, Czech RepublicGoogle Scholar
- Gautier N, Aider J-L, Duriez T, Noack BR, Segond M, Abel MW (2015) Closed-loop separation control using machine learning. J Fluid Mech 770:424–441CrossRefGoogle Scholar
- Gerhard J, Pastoor M, King R, Noack BR, Dillmann A, Morzynski M, Tadmor G (2003) Model-based control of vortex shedding using low-dimensional Galerkin models. AIAA Pap 4262(2003):115–173Google Scholar
- Glezer A, Amitay M, Honohan AM (2005) Aspects of low-and high-frequency actuation for aerodynamic flow control. AIAA J 43(7):1501–1511CrossRefGoogle Scholar
- Grandemange M, Gohlke M, Cadot O (2013) Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability. J Fluid Mech 722:51–84CrossRefzbMATHGoogle Scholar
- Henning L, King R (2007) Robust multivariable closed-loop control of a turbulent backward-facing step flow. J Aircraft 44(1):201–208CrossRefGoogle Scholar
- Hucho W-H (1998) Aerodynamics of road vehicles: from fluid mechanics to vehicle engineering. Society of Automotive Engineers, USAGoogle Scholar
- Joseph P, Amandolese X, Edouard C, Aider J-L (2013) Flow control using MEMS pulsed micro-jets on the Ahmed body. Exp Fluids 54(1):1–12CrossRefGoogle Scholar
- Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. The MIT Press, BostonzbMATHGoogle Scholar
- Lewalle J (1995) Tutorial on continuous wavelet analysis of experimental data. In: Mechanical Aerospace and Manufacturing Engineering Dept., Syracuse University. http://www.mame.syr.edu/faculty/lewalle/tutor/tutor.html
- Li R, Barros D, Borée J, Cadot O, Noack BR, Cordier L (2016) Feedback control of bi-modal wake dynamics. Exp Fluids 57:1–6CrossRefGoogle Scholar
- Liepmann HW, Nosenchuck DM (1982) Active control of laminar-turbulent transition. J Fluid Mech 118:201–204CrossRefGoogle Scholar
- Narayanan S, Noack BR, Banaszuk A, Khibnik AI (2002) Active separation control concept: dynamic forcing of induced separation using harmonically related frequency, 2002. United States Patent 6360763Google Scholar
- Oxlade AR, Morrison JF, Qubain A, Rigas G (2015) High-frequency forcing of a turbulent axisymmetric wake. J Fluid Mech 770:305–318CrossRefGoogle Scholar
- Parezanović V, Cordier L, Spohn A, Duriez T, Noack BR, Bonnet J-P, Segond M, Abel M, Brunton SL (2016) Frequency selection by feedback control in a turbulent shear flow. J Fluid Mech 797:247–283CrossRefGoogle Scholar
- 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
- Pfeiffer J, King R (2012) Multivariable closed-loop flow control of drag and yaw moment for a 3D bluff body. In: 6th AIAA flow control conference, Atlanta, Georgia, USA, pp 1–14Google Scholar
- Protas B (2004) Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys Fluids 16(12):4473–4488MathSciNetCrossRefzbMATHGoogle Scholar
- Roshko A (1955) On the wake and drag of bluff bodies. J Aeronaut Sci 22(2):124–132CrossRefzbMATHGoogle Scholar
- Rouméas M, Gilliéron P, Kourta A (2009) Drag reduction by flow separation control on a car after body. Int J Num Methods Fluids 60(11):1222–1240CrossRefzbMATHGoogle Scholar
- Roussopoulos K (1993) Feedback control of vortex shedding at low Reynolds numbers. J Fluid Mech 248:267–296CrossRefGoogle Scholar
- Rowley CW, Williams DR, Colonius T, Murray RM, MacMynowski DG (2006) Linear models for control of cavity flow oscillations. J Fluid Mech 547:317–330CrossRefzbMATHGoogle Scholar
- Ruiz T, Sicot C, Brizzi LE, Borée J, Gervais Y (2010) Pressure/velocity coupling induced by a near wall wake. Exp Fluids 49(1):147–165CrossRefzbMATHGoogle Scholar
- Samimy M, Debiasi M, Caraballo E, Serrani A, Yuan X, Little J, Myatt JH (2007) Feedback control of subsonic cavity flows using reduced-order models. J Fluid Mech 579:315–346MathSciNetCrossRefzbMATHGoogle Scholar
- Schmidt HJ, Woszidlo R, Nayeri CN, Paschereit CO (2015) Drag reduction on a rectangular bluff body with base flaps and fluidic oscillators. Exp Fluids 56(7):1–16CrossRefGoogle Scholar
- Seifert A, Shtendel T, Dolgopyat D (2015) From lab to full scale active flow control drag reduction: how to bridge the gap? J Wind Eng Ind Aerodyn 147:262–272CrossRefGoogle Scholar
- Wahde M (2008) Biologically inspired optimization methods: an introduction. WIT Press, AshurstGoogle Scholar
- Zhang M, Cheng L, Zhou Y (2004) Closed-loop-controlled vortex shedding and vibration of a flexibly supported square cylinder under different schemes. Phys Fluids 16(5):1439–1448CrossRefzbMATHGoogle Scholar