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On the origin of counter-gradient transport in turbulent scalar flux: physics interpretation and adjoint data assimilation

Published online by Cambridge University Press:  19 November 2024

Sen Li Open the ORCID record for Sen Li [Opens in a new window] ,
Wenwu Zhou Open the ORCID record for Wenwu Zhou [Opens in a new window] ,
Hyung Jin Sung Open the ORCID record for Hyung Jin Sung [Opens in a new window]  and
Yingzheng Liu Open the ORCID record for Yingzheng Liu [Opens in a new window]
Sen Li
Affiliation:
Key Laboratory of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, PR China
Wenwu Zhou
Affiliation:
Key Laboratory of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, PR China
Hyung Jin Sung
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
Yingzheng Liu*
Affiliation:
Key Laboratory of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The present study offers a twofold contribution on counter-gradient transport (CGT) of turbulent scalar flux. First, by examining turbulent scalar mixing through synchronized particle image velocimetry and planar laser-induced fluorescence on an inclined jet in cross-flow, we clarify the previously unexplained phenomenon of CGT, revealing key flow structures, their spatial distribution and modelling implications. Statistical analysis identifies two distinct CGT regions: local cross-gradient transport in the windward shear layer and non-local effects near the wall after injection. These behaviours are driven by specific flow structures, namely Kelvin–Helmholtz vortices (local) and wake vortices (non-local), suggesting that scalar flux can be decomposed into a gradient-type term for gradient diffusion and a term for large-eddy stirring. Second, we propose a new approach for reconstruction of turbulent mean flow and scalar fields using continuous adjoint data assimilation (DA). By rectifying model-form errors through anisotropic correction under observational constraints, our DA model minimizes discrepancies between experimental measurements and numerical predictions. As expected, the introduced forcing term effectively identifies regions where traditional models fall short, particularly in the jet centreline and near-wall regions, thereby enhancing the accuracy of the mean scalar field. These enhancements occur not only within the observation region but also in unseen regions, underscoring present DA approach's reliability and practicality for reproducing mean flow behaviours from limited data. These findings lay a solid foundation for adjoint-based model-consistent data-driven methods, offering promising potential for accurately predicting complex flow scenarios like film cooling.

JFM classification

Mathematical Foundations: Variational methods Mixing: Turbulent mixing Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A81
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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