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Low-order modelling of the wake dynamics of an Ahmed body

Published online by Cambridge University Press:  01 October 2021

Bérengère Podvin Open the ORCID record for Bérengère Podvin [Opens in a new window] ,
Stéphanie Pellerin Open the ORCID record for Stéphanie Pellerin [Opens in a new window] ,
Yann Fraigneau Open the ORCID record for Yann Fraigneau [Opens in a new window] ,
Guillaume Bonnavion Open the ORCID record for Guillaume Bonnavion [Opens in a new window]  and
Olivier Cadot Open the ORCID record for Olivier Cadot [Opens in a new window]
Bérengère Podvin*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire interdisciplinaire des sciences du numérique, 91405, Orsay, France
Stéphanie Pellerin
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire interdisciplinaire des sciences du numérique, 91405, Orsay, France
Yann Fraigneau
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire interdisciplinaire des sciences du numérique, 91405, Orsay, France
Guillaume Bonnavion
Affiliation:
Institut Pprime, UPR CNRS 3346, ISAE-ENSMA, Fluides Thermique Combustion, 86961Futuroscope-Chasseneuil, France
Olivier Cadot
Affiliation:
School of Engineering, University of Liverpool, LiverpoolL69 3GH, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the large-scale signature of the random switches between two mirrored turbulent wake states of flat-backed bodies. A direct numerical simulation (DNS) of the flow around an Ahmed body at a Reynolds number ($Re$) of 10 000 is considered. Using proper orthogonal decomposition (POD), we identify the most energetic modes of the velocity field and build a low-dimensional model based on the first six fluctuating velocity modes capturing the characteristics of the flow dynamics during and between switches. In the absence of noise, the model produces random switches with characteristic time scales in agreement with the simulation and experiments. This chaotic model suggests that random switches are triggered by the increase of the vortex shedding activity. However, the addition of noise results in a better agreement in the temporal spectra of the coefficients between the model and the simulation.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Wakes/Jets: Wakes
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , R6
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Ahmed, S.R., Ramm, G. & Faitin, G. 1984 Some salient features of the time-averaged ground vehicle wake. Tech. Rep. SAE Technical Paper Series 840300. SAE International.CrossRefGoogle Scholar
Barros, D., Borée, J., Cadot, O., Spohn, A. & Noack, B.R. 2017 Forcing symmetry exchanges and flow reversals in turbulent wakes. J. Fluid Mech. 829, R1.CrossRefGoogle Scholar
Boujo, E. & Noiray, N. 2017 Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation. Proc. R. Soc. Lond. A 473, 20160894.Google ScholarPubMed
Brackston, R.D., Garci De La Cruz, J.M., Wynn, A., Rigas, G. & Morrison, J.F. 2016 Stochastic modelling and feedback control of bistability in a turbulent bluff bodywake. J. Fluid Mech. 802, 726–749.CrossRefGoogle Scholar
Cadot, O., Almarzooqi, M., Legeai, A., Parezanović, V. & Pastur, L. 2020 On three-dimensional bluff body wake symmetry breaking with free-stream turbulence and residual asymmetry. C. R. Méc 348 (6–7), 509–517.Google Scholar
Choi, H., Lee, J. & Park, H. 2014 Aerodynamics of heavy vehicles. Annu. Rev. Fluid Mech. 46, 441–468.CrossRefGoogle Scholar
Dalla Longa, L., Evstafyeva, O. & Morgans, A.S. 2019 Simulations of the bi-modal wake past three-dimensional blunt bluff bodies. J. Fluid Mech. 866, 791–809.CrossRefGoogle Scholar
Evrard, A., Cadot, O., Herbert, V., Ricot, D., Vigneron, R. & Delery, J. 2016 Fluid force and symmetry breaking modes of a 3D bluff body with a base cavity. J. Fluids Struct. 61, 99–114.CrossRefGoogle Scholar
Fan, Y., Chao, X., Chu, S., Yang, Z. & Cadot, O. 2020 Experimental and numerical analysis of the bi-stable turbulent wake of a rectangular flat-backed bluff body. Phys. Fluids 32, 105111.CrossRefGoogle Scholar
Fares, E. 2006 Unsteady flow simulation of the Ahmed reference body using a lattice Boltzmann approach. Comput. Fluids 35 (8), 940–950 (Special issue for the Proceedings of the First International Conference for Mesoscopic Methods in Engineering and Science).CrossRefGoogle 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, 51–84.CrossRefGoogle Scholar
Grandemange, M., Gohlke, M. & Cadot, O. 2014 Turbulent wake past a three-dimensional blunt body. Part 2. Experimental sensitivity analysis. J. Fluid Mech. 752, 439–461.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer.CrossRefGoogle Scholar
Haffner, Y., Borée, J., Spohn, A. & Castelain, T. 2020 Mechanics of bluff body drag reduction during transient near-wake reversals. J. Fluid Mech. 894, A14.CrossRefGoogle Scholar
Hesse, F. & Morgans, A.-S. 2021 Simulation of wake bimodality behind squareback bluff-bodies using LES. Comput. Fluids 223, 104901.CrossRefGoogle Scholar
Howard, R.J.A. & Pourquie, M. 2002 Large eddy simulation of an Ahmed reference model. J. Turbul. 3, N12.CrossRefGoogle Scholar
Lumley, J.L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. A.M. Iaglom & V.I. Tatarski), pp. 221–227. Nauka.Google Scholar
Minguez, M., Pasquetti, R. & Serre, E. 2008 High-order large-eddy simulation of flow over the ‘Ahmed body’ car model. Phys. Fluids 20, 0951011.CrossRefGoogle Scholar
Pavia, G., Passmore, M. & Sardu, C. 2018 Evolution of the bi-stable wake of a square-back automotive shape. Exp. Fluids 59, 2742.CrossRefGoogle Scholar
Pavia, G., Passmore, M., Varney, M. & Hodgson, G. 2020 Salient three-dimensional features of the turbulent wake of a simplified square-back vehicle. J. Fluid Mech. 888, A33.CrossRefGoogle Scholar
Perry, A.K., Pavia, G. & Passmore, M. 2016 Influence of short rear end tapers on the wake of a simplified square-back vehicle: wake topology and rear drag. Exp. Fluids 57 (11), 169.CrossRefGoogle Scholar
Podvin, B., Pellerin, S., Fraigneau, Y., Evrard, A. & Cadot, O. 2020 Proper orthogonal decomposition analysis and modelling of the wake deviation behind a squareback Ahmed body. Phys. Rev. Fluids 6 (5), 064612.CrossRefGoogle Scholar
Podvin, B. & Sergent, A. 2017 Precursor for wind reversal in a square Rayleigh–Bénard cell. Phys. Rev. E 05 (1), 013112.CrossRefGoogle Scholar
Rigas, G., Morgans, A.S, Brackston, R.D. & Morrison, J.F. 2015 Diffusive dynamics and stochastic models of turbulent axisymmetric wakes. J. Fluid Mech. 778, R2.CrossRefGoogle Scholar
Rigas, G., Oxlade, A.R., Morgans, A.S. & Morrison, J.F. 2014 Low-dimensional dynamics of a turbulent axisymmetric wake. J. Fluid Mech. 755, 159.CrossRefGoogle Scholar
Soucasse, L., Podvin, B., Rivière, P. & Soufiani, A. 2020 Reduced-order modelling of radiative transfer effects on Rayleigh–Bénard convection in a cubic cell. J. Fluid Mech. 898, A2.CrossRefGoogle Scholar
Varon, E., Eulalie, Y., Edwige, S., Gilotte, P. & Aider, J.L. 2017 Chaotic dynamics of large-scale structures in a turbulent wake. Phys. Rev. Fluids 2, 034604.CrossRefGoogle Scholar
Volpe, R., Devinant, P. & Kourta, A. 2015 Experimental characterization of the unsteady natural wake of the full-scale square back Ahmed body: flow bi-stability and spectral analysis. Exp. Fluids 56 (5), 1–22.CrossRefGoogle Scholar