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Lagrangian coherent structures in flow past a backward-facing step

Published online by Cambridge University Press:  16 August 2022

Chenyang Huang
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Marine Numerical Experimental Center, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Alistair G.L. Borthwick
School of Engineering, The University of Edinburgh, The King's Buildings, Edinburgh EH9 3FB, UK School of Engineering, Computing and Mathematics, University of Plymouth, Plymouth PL4 8AA, UK
Zhiliang Lin*
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Marine Numerical Experimental Center, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Email address for correspondence:


This paper investigates flow past a backward-facing step (BFS) in a duct at Reynolds number $Re = 5080$ based on step height, mean inflow velocity and fluid kinematic viscosity. The flow configuration matches a combustion experiment conducted by Pitz and Daily in 1983. High-resolution velocity fields are obtained in OpenFOAM by direct numerical simulation, and the flow field analysed by Lagrangian approaches. Trajectories of fluid particles in areas of interest are obtained by high-order numerical integration, and used to compute finite-time Lyapunov exponents (FTLEs) and polar rotation angles. Lagrangian coherent structures (LCSs) are extracted using geodesic theory, including hyperbolic LCSs and elliptic LCSs. We use complementary qualitative and quantitative LCS analyses to uncover the underlying flow structures. Notably, we find that a flow pathway in which fluid particles rarely diverge from adjacent particles is opened and closed by FTLE ridges determined by the periodic shedding of vortices from the BFS. Two dominant vortices with significant Lagrangian coherence, generated respectively by the separated boundary layer and shear layer, are self-sustaining and of comparable strength. Hyperbolic repelling LCSs act as transport barriers between the pathway and cores of the coherent vortices, thus playing a major part in the fluid entrainment process. Interactions between these different geometric regions partitioned by LCSs lead to intrinsic complexity in the BFS flow.

JFM Papers
© The Author(s), 2022. Published by Cambridge University Press.

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