Reduced particle settling speed in turbulence

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, Ga. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6%-60% with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations is decreased. Analysing the fluid-particle relative motion, we find that the mean settling speed is progressively reduced while reducing the density ratio due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6%-10%. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all Ga if time is scaled by (2a)/u' (where 2a is the particle diameter and u' is the turbulence velocity root mean square).Comment: Accepted for publication in Journal of Fluid Mechanic

Continuous Growth of Droplet Size Variance due to Condensation in Turbulent Clouds

We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate proportional to the large-to-small turbulent scale separation and to the turbulence integral scales but independent of the mean turbulent dissipation. Direct numerical simulations confirm this result and produce realistically broad droplet size spectra over time intervals of 20 minutes, comparable with the time of rain formation.Comment: 5 pages, 3 figures+Supplemental material 6 pages, 5 figure

The effect of the Basset history force on particle clustering in Homogeneous and Isotropic Turbulence

We study the effect of the Basset history force on the dynamics of small particles transported in homogeneous and isotropic turbulence and show that this term, often neglected in previous numerical studies, reduces the small-scale clustering typical of inertial particles. The contribution of this force to the total particle acceleration is, on average, responsible for about 10% of the total acceleration and particularly relevant during rare strong events. At moderate density ratios, i.e. sand or metal powder in water, its presence alters the balance of forces determining the particle acceleration

Assessing passive scalar dynamics in bubble-induced turbulence using direct numerical simulations

By using direct numerical simulations (DNS) of bubbly flows with passive scalars, we show a transition in the scalar spectra from a k-5/3 to a k-3 scaling with the wavenumber k, in contrast with those of single-phase isotropic turbulence. For cases with a mean scalar gradient in the horizontal direction, the scalar spectrum decays faster than at high wavenumbers. While the k-3 scaling is well established in the bubbly flow velocity spectrum, the scalar spectrum behaviour is not fully understood. We find that the transition length scale of the scalar spectra is comparable to or below the bubble diameter and decreases with the molecular diffusivity of the scalar in the liquid. We use DNS to compute the scalar spectrum budget and show that the scalar fluctuations are produced by the mean scalar gradient at length scales above the bubble diameter, contrary to the velocity fluctuations. At length scales below the bubble diameter, the net scalar transfer scales as k-1 inducing the k-3 scaling of the scalar spectra. This finding is consistent with the hypothesis proposed by Dung et al. (J. Fluid Mech., vol. 958, 2023, p. A5) about the physical mechanism behind the k-3 scaling. We also show dependencies of the bubble suspension\u27s convective scalar diffusivity on the gas volume fraction and molecular diffusivity that differ based on the direction of the mean scalar gradient. For a mean scalar gradient in the vertical direction, we find and qualitatively explain a significant effect of the molecular diffusivity in the gas on the convective scalar diffusivity

A multiscale methodology for small-scale bubble dynamics in turbulence

We formulate in this paper a multiscale numerical framework that handles small-scale bubble dynamics in turbulence. Our framework involves bubbles with arbitrary density ratios with the carrier phase. We use a Moving Reference Frame method that follows a bubble to deal with a fast rising of bubbles present at high density ratios between the phases. We use a Proportional Integral Derivative controller to handle an additional acceleration term in the governing equations that stems from the change of a coordinate system from a fixed to a non-inertial one. Our framework accounts for the fact that the dynamics of bubbles are significantly influenced by the unsteadiness of the small-scale turbulent liquid fluctuations that modify the bubble shapes and alter their motion. In addition, we improve and speed up, with at least two orders of magnitude in computational time, the numerical framework recently proposed by Milan et al. (2020). The developed numerical framework can capture processes occurring at time scales even smaller than the Kolmogorov times. It can be applied to droplets, bubbles or particle systems in both laminar and turbulent flows, using any general DNS technique that handles two-phase flows

The lift force on deformable and freely moving bubbles in linear shear flows

This paper provides a comprehensive explanation for the lift force acting on a freely deformable bubble rising in a linear shear flow and examines how the lift force scales with the undisturbed shear rate in cases governed by different lift force mechanisms. Four distinct flow mechanisms are identified from previous studies, and the associated bubble-induced vorticity dynamics are outlined. We provide a theoretical framework to qualitatively explain the lift force acting on a bubble in terms of moments of the bubble-induced vorticity. We support our theoretical framework with three-dimensional multiphase direct numerical simulations to illustrate how the vorticity dynamics associated with the four mechanisms generate the lift force. These findings provide a comprehensive explanation for the behaviour of the lift force in a wide range of relevant governing parameters. Additionally, our simulation results show how differently the lift force scales with the shear rate, depending on the dominating lift force mechanism. These results indicate that the shear rate should, in general, be accounted for in highly viscous flows (low Galilei numbers) or at significant bubble deformations (moderate-to-high E\uf6tv\uf6s numbers) when modelling the lift force coefficient

Broadening of Cloud Droplet Size Spectra by Stochastic Condensation: Effects of Mean Updraft Velocity and CCN Activation

The authors study the condensational growth of cloud droplets in homogeneous isotropic turbulence by means of a large-eddy simulation (LES) approach. The authors investigate the role of a mean updraft velocity and of the chemical composition of the cloud condensation nuclei (CCN) on droplet growth. The results show that a mean constant updraft velocity superimposed onto a turbulent field reduces the broadening of the droplet size spectra induced by the turbulent fluctuations alone. Extending the authors\u27 previous results regarding stochastic condensation, the authors introduce a new theoretical estimation of the droplet size spectrum broadening that accounts for this updraft velocity effect. A similar reduction of the spectra broadening is observed when the droplets reach their critical size, which depends on the chemical composition of CCN. The analysis of the square of the droplet radius distribution, proportional to the droplet surface, shows that for large particles the distribution is purely Gaussian, while it becomes strongly non-Gaussian for smaller particles, with the left tail characterized by a peak around the haze activation radius. This kind of distribution can significantly affect the later stages of the droplet growth involving turbulent collisions, since the collision probability kernel depends on the droplet size, implying the need for new specific closure models to capture this effect