Abstract Three-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers $\mathit{St}$) and two Taylor–Reynolds numbers (${\mathit{Re}}_{\lambda } = 75$ and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher ${\mathit{Re}}_{\lambda } $. Light particles show maximum clustering for $\mathit{St}$ around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.

Three-dimensional Lagrangian Voronoi analysis for clustering of particles and bubbles in turbulence

Modeling study on sessile water droplet during freezing with the consideration of gravity, supercooling, and volume expansion effects

We investigate the behaviour of microscopic heavy particles settling in homogeneous air turbulence. The regimes are relevant to the airborne transport of dust and droplets: the Taylor-microscale Reynolds number is . This agrees well with the present observations and previous simulations and captures the respective effects of inertia and gravity, both of which play crucial roles in the transport.

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Dynamics of small heavy particles in homogeneous turbulence: a Lagrangian experimental study

Bubbly turbulent flow in a channel is investigated using interface-resolved direct numerical simulation. An efficient coupled level-set volume-of-fluid solver based on a fast Fourier transform algorithm is implemented to enable a high resolution and fast computation at the same time. Up to 384 bubbles are seeded in the turbulent channel flow corresponding to 5.4% gas volume fraction. Bubbles are clustered in the channel center due to the downward flow direction. The bubbles induce additional pseudo-turbulence in the channel center and are also able to attenuate the energy in the boundary layer by reducing the shear production. Turbulent kinetic energy budget indicates a significant buoyancy production in the channel center. A local equilibrium between buoyancy production and dissipation is observed here besides the shear production peak in the boundary layer. Comparing the local production and dissipation indicates a coexistence of boundary layer turbulence near the wall and bubble-induced pseudo-turbulence in the channel center. The liquid phase and gas phase are coupled through the complex liquid–gas interface. Local flow topology analysis is depicted in the liquid phase around the bubbles as well as in the gas phase. The flow topology of the liquid phase and the gas phase differs from each other significantly. Local dissipation is more dominant in the liquid phase near the bubble interface, whereas local enstrophy is preferred in the gas phase. In the liquid phase, a high dissipation event is preferred close to the interface, whereas a high enstrophy event is dominant away from the interface.

Turbulence, pseudo-turbulence, and local flow topology in dispersed bubbly flow

We propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and fluid inertia forces in a homogeneous and isotropic turbulent flow. This model, that depends on the Stokes number, Reynolds number and the density ratio, reproduces the evolution of the acceleration variance as well as the relative importance and alignment of the two forces as observed from direct numerical simulations (DNS). We also report that the bubble acceleration statistics conditioned on the local kinetic energy dissipation rate are invariant with the Stokes number and the dissipation rate. Based on this observation, we propose a stochastic model for the instantaneous bubble acceleration vector accounting for the small-scale intermittency of the turbulent flows. The norm of the bubble acceleration is obtained by modelling the dissipation rate along the bubble trajectory from a log-normal stochastic process, whereas its orientation is given by two coupled random walks on a unit sphere in order to model the evolution of the joint orientation of the drag and inertia forces acting on the bubble. Furthermore, the proposed stochastic model for the bubble acceleration is used in the context of large eddy simulations (LES) of turbulent flows laden with small bubbles. To account for the turbulent motion at scales smaller than the mesh resolution, we decompose the instantaneous bubble acceleration in its resolved and residual parts. The first part is given by the drag and fluid inertia forces computed from the resolved velocity field, and the second term refers to the random contribution of small unresolved turbulent scales and is estimated with the stochastic model proposed in the paper. Comparisons with DNS and standard LES, show that the proposed model improves significantly the statistics of the bubbly phase.

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Model for the dynamics of micro-bubbles in high-Reynolds-number flows

A hybrid VoF-IBM method for the simulation of freezing liquid films and freezing drops

In this paper we study finite particle Reynolds number effects up to and the type of particle. Namely, we consider the Stokes drag law, the Schiller and Neumann relation and the Mei law. We show that an effective Stokes number, based on the mean value of the drag coefficient to account for the inertial effects involved in the drag law, gives a quasi-self-similar evolution of the variances of the bubble acceleration and of the forces exerted on the particle. This allows us to provide a satisfactory prediction of these quantities using Tchen's theory at finite particle Reynolds number. Based on these relations, we can specify the conditions under which the total inertial force (sum of the added mass and the Tchen contributions) is negligible compared with the drag force. Thus, for particles of very small dimensions, the fluid inertia force is negligible, provided the density ratio is of order 1 or larger. However, when the particle inertia becomes consequential, the threshold value of the density ratio increases significantly. Although this corresponds to the limit of the validity of the model, this draws attention to the fact that, for large Stokes numbers, the added mass and fluid inertia forces could play a more important role than is usually attributed to them.

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Fluid inertia effects on the motion of small spherical bubbles or solid spheres in turbulent flows

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Zhentong Zhang

Papers

Model for the dynamics of micro-bubbles in high-Reynolds-number flows

A hybrid VoF-IBM method for the simulation of freezing liquid films and freezing drops

Fluid inertia effects on the motion of small spherical bubbles or solid spheres in turbulent flows

Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows