On the dynamics of vortex–droplet interactions, dispersion and breakup in a coaxial swirling flow

Abstract

This paper discusses the fundamental mechanisms of vortex–droplet interactions leading to flow distortion, droplet dispersion and breakup in a complex swirling gas flow field. In particular, the way in which the location of droplet injection determines the degree of inhomogeneous dispersion and breakup modes has been elucidated in detail using high-fidelity laser diagnostics. The droplets are injected as monodispersed streams at various spatial locations such as the vortex breakdown bubble and the shear layers (inner and outer) exhibited by the swirling flow. Simultaneous time-resolved particle image velocimetry ($3500~\text{frames}~\text{s}^{-1}$) and high-speed shadowgraphy measurements are employed to delineate the two-phase interaction dynamics. These measurements have been used to evaluate the fluctuations in instantaneous circulation strength $\unicode[STIX]{x1D6E4}^{\prime }$ caused by the flow field eddies and the resultant angular dispersion in the droplet trajectories $\unicode[STIX]{x1D703}^{\prime }$. The droplet–flow interactions show two-way coupling at low momentum ratios ($MR$) and strong one-way coupling at high momentum ratios. The gas phase flow field is globally altered at low airflow rates (low $MR$) due to impact of droplets with the vortex core. The flow perturbation is found to be minimal and mainly local at high airflow rates (high $MR$). Spectral coherence analysis is carried out to understand the correlation between eddy circulation strength $\unicode[STIX]{x1D6E4}^{\prime }$ and droplet dispersion $\unicode[STIX]{x1D703}^{\prime }$. The droplet dispersion shows strong coherence with the flow in certain frequency bands. Subsequently, proper orthogonal decomposition (POD) is implemented to elucidate the governing instability mechanism and frequency signatures associated with the turbulent coherent structures. The POD results suggest dominance of the Kelvin–Helmholtz (KH) instability mode (axial and azimuthal shear). The frequency range pertaining to high coherence between dispersion and circulation shows good agreement with KH instability quantified from POD analysis. The droplets injected at the inner shear layer (ISL) and outer shear layer (OSL) show different interaction dynamics. For instance, droplet dispersion at the OSL exhibits secondary frequency (shedding mode) coupling in addition to the KH mode, whereas ISL injection couples only in a single narrow frequency band (i.e. KH mode). Further, high-speed shadow imaging ($7500~\text{frames}~\text{s}^{-1}$) is employed to visualize the breakup dynamics of the droplets. The effect of coherent structures on the droplet breakup modes is shown as a function of the Weber number ($We$) defined based on the circulation strength. The wide fluctuations caused in the instantaneous circulation strength lead to different breakup modes (bag, multimodal, shear thinning, catastrophic) even for fixed airflow rates. These fluctuations also lead to inhomogeneous spatial dispersion of the droplets in the swirling gas flow field. We are able to present the dispersion contours in terms of the Stokes number and a spatial homogeneity parameter. In essence, the dispersion inhomogeneity is found to be a strong function of the injection location, the phase relationship with the eddies and the momentum ratio ($MR$).