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Nudging-based data assimilation of the turbulent flow around a square cylinder

Published online by Cambridge University Press:  03 March 2022

M. Zauner ,
V. Mons Open the ORCID record for V. Mons [Opens in a new window] ,
O. Marquet Open the ORCID record for O. Marquet [Opens in a new window]  and
B. Leclaire
M. Zauner
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
V. Mons*
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
O. Marquet
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
B. Leclaire
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the estimation of the turbulent flow around a canonical square cylinder at $Re=22\,000$ based on temporally resolved but spatially sparse velocity data and solving the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Flow reconstruction from sparse data is achieved through the application of a nudging data assimilation technique. It involves the introduction of a feedback control term in the momentum equations which allows us to drive URANS predictions towards reference data, which are here extracted from a direct numerical simulation. Such a data assimilation approach induces negligible supplementary computational cost compared with that of a standard URANS simulation. The influence of the spatial resolution of the reference data on the reconstruction performances is systematically investigated. Using a spacing of the order of one cylinder length between data points, we already observe synchronisation of the low-frequency vortex shedding between the full reference flow and the one that is estimated by URANS. The present data assimilation procedure allows us to compensate for deficiencies in standard URANS calculations and leads to a significant decrease in temporal and spectral errors as computed by spectral proper orthogonal decomposition. Furthermore, high accuracy in terms of mean-flow prediction by URANS is achieved. When considering spacings between measurements that are of the order of the wavelength of the Kelvin–Helmholtz vortices, such phenomena in the shear layers at the top and bottom of the cylinder are correctly estimated, while they are not self-sustained in standard URANS. The influence of the structure of the feedback control term in the data assimilation procedure is also investigated.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Wakes/Jets: Vortex streets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 937 , 25 April 2022 , A38
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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