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Dimensionality and morphology of particle and bubble clusters in turbulent flow


We conduct numerical experiments to investigate the spatial clustering of particles and bubbles in simulations of homogeneous and isotropic turbulence. On varying the Stokes parameter and the densities, striking differences in the clustering of the particles can be observed. To quantify these visual findings we use the Kaplan–Yorke dimension. This local scaling analysis shows a dimension of approximately 1.4 for the light bubble distribution, whereas the distribution of very heavy particles shows a dimension of approximately 2.6. However, clearly different parameter combinations yield the same dimensions. To overcome this degeneracy and to further develop the understanding of clustering, we perform a morphological (geometrical and topological) analysis of the particle distribution. For such an analysis, Minkowski functionals have been successfully employed in cosmology, in order to quantify the global geometry and topology of the large-scale distribution of galaxies. In the context of dispersed multiphase flow, these Minkowski functionals – being morphological order parameters – allow us to discern the filamentary structure of the light particle distribution from the wall-like distribution of heavy particles around empty interconnected tunnels. Movies are available with the online version of the paper.

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Journal of Fluid Mechanics
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Calzavarini et al. supplementary movie
Movie 2. Visualization of particle distribution in a turbulent flow field (Re = 75). Three-dimensional snapshot of neutrally buoyant particles with St = 0.6 and β=1.

 Video (6.7 MB)
6.7 MB

Calzavarini et al. supplementary movie
Movie 1. Visualization of particle distribution in a turbulent flow field (Re = 75). Three-dimensional snapshot of light particles (bubbles) with St = 0.6 and β=3. In the model system used in this numerical study, particles are characterized by two parameters: the Stokes number St (which is the ratio between the particle response time and the Kolmogorov time scale) and the parameter β which is related to the particle--fluid density ratio ( β = 3 ρ_f /(ρ_f + 2 ρ_p) ). Particles lighter than the fluid cluster in highly vortical regions, the opposite happens for heavy particles (see Movie 3), while neutrally buoyant particles remains on average homogeneously distributed (see Movie 2).

 Video (7.4 MB)
7.4 MB

Calzavarini et al. supplementary movie
Movie 3. Visualization of particle distribution in a turbulent flow field (Re = 75). Three-dimensional snapshot of heavy particles with St = 0.6 and β=0.

 Video (7.5 MB)
7.5 MB


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