Lagrangian coherent structures analysis of gas-liquid flow in a bubble column

The objective of this paper is to apply a new identifying method to investigating the gas-liquid two-phase flow behaviors in a bubble column with air injected into water. In the numerical simulations, the standard k- turbulence model is employed to describe the turbulence phenomenon occurring in the continuous fluid. The Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures (LCS) are applied to analyze the vortex structures in multiphase flow. Reasonable agreements are obtained between the numerical and experimental data. The numerical results show that the evolution of gas-liquid in the column includes initial and periodical developing stages. During the initial stage, the bubble hose is forming and extending along the vertical direction with the vortex structures formed symmetrically. During the periodical developing stage, the bubble hose starts to oscillate periodically, and the vortexes move along the bubble hose to the bottom of column alternately. Compared to the Euler-system-based identification criterion of a vortex, the FTLE field presents the boundary of a vortex without any threshold defined and the LCS represents the divergence extent of infinite neighboring particles. During the initial stage, the interfaces between the forward and backward flows are highlighted by the LCS. As for the periodical developing stage, the LCS curls near the vortex centers, providing a method of analyzing a flow field from a dynamical system perspective.