Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Φ = 0 − 0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Kármán constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Φ = 0.2 , the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Φ and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.

We study the two main phenomenologies associated with the transport of inertial particles in turbulent flows, turbophoresis and small-scale clustering. Turbophoresis describes the turbulence-induced wall accumulation of particles dispersed in wall turbulence, while small-scale clustering is a form of local segregation that affects the particle distribution in the presence of fine-scale turbulence. Despite the fact that the two aspects are usually addressed separately, this paper shows that they occur simultaneously in wall-bounded flows, where they represent different aspects of the same process. We study these phenomena by post-processing data from a direct numerical simulation of turbulent channel flow with different populations of inertial particles. It is shown that artificial domain truncation can easily alter the mean particle concentration profile, unless the domain is large enough to exclude possible correlation of the turbulence and the near-wall particle aggregates. The data show a strong link between accumulation level and clustering intensity in the near-wall region. At statistical steady state, most accumulating particles aggregate in strongly directional and almost filamentary structures, as found by considering suitable two-point observables able to extract clustering intensity and anisotropy. The analysis provides quantitative indications of the wall-segregation process as a function of the particle inertia. It is shown that, although the most wall-accumulating particles are too heavy to segregate in homogeneous turbulence, they exhibit the most intense local small-scale clustering near the wall as measured by the singularity exponent of the particle pair correlation function

The Cahn–Hilliard model is increasingly often being used in combination with the incompressible Navier–Stokes equation to describe unsteady binary fluids in a variety of applications ranging from turbulent two-phase flows to microfluidics. The thickness of the interface between the two bulk fluids and the mobility are the main parameters of the model. For real fluids they are usually too small to be directly used in numerical simulations. Several authors proposed criteria for the proper choice of interface thickness and mobility in order to reach the so-called ‘sharp-interface limit’. In this paper the problem is approached by a formal asymptotic expansion of the governing equations. It is shown that the mobility is an effective parameter to be chosen proportional to the square of the interface thickness. The theoretical results are confirmed by numerical simulations for two prototypal flows, namely capillary waves riding the interface and droplets coalescence. The numerical analysis of two different physical problems confirms the theoretical findings and establishes an optimal relationship between the effective parameters of the model.

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.Many multi-scale processes-including nutrient foraging of plankton, gas/dust accretion disks in astrophysics and spray evaporation and combustion in engines [1-4]-involve the interaction between small particles and tracers transported in a turbulent flow. Here we focus on the case of droplet condensation in turbulent warm (i.e. ice-free) clouds. Clouds are a leading source of uncertainty in climate modeling [5] due to the difficulty of accurately parameterizing the macro-scale effects of microscale physical processes, such as the effect of droplet size distribution on precipitation rates and cloud albedos.The role of turbulence in cloud microphysics presents a range of open questions [6][7][8], particularly as a possible solution for the "bottleneck" problem of rain formation. All cloud droplet populations evolve through a sequence of steps: (1) nucleation/activation of cloud condensation nuclei, (2) droplet growth by condensation and (3) growth to raindrop size by collision and coalescence. The passage from (2) to (3) presents a bottleneck because collisional growth is only triggered when the droplet population acquires a sufficiently broad size distribution, but condensational growth is inversely proportional to droplet radius which intrinsically tends to narrow the size distribution. Nonetheless, warm clouds are routinely observed to precipitate within ∼20 minutes of formation. Understanding the mechanisms that break the condensational bottleneck is a longstanding and still unresolved problem in atmospheric physics.Turbulence has often been invoked as a key process in this context since it can enhance collision rates via inertial clustering [9, 10] and the so called "sling effect" [11]. Turbulence also induces fluctuations in the supersaturation field that can potentially broaden droplet spectra in the condensational stage [8]. Early studies using analytical models [12, 13] and direct numerical simulations (DNS) [14] generally showed too little broadening as compared with observations [15]. Later work attempting to simulate large-scale turbulence in an O(100 m) cloud [16][17][18] showed a dramatic broadening of the droplet size spectrum but only with ad-hoc assumptions about the small-scale supersaturation fluctuations. Lanotte at al.[19] modelled both small-and large-scale effects on the droplet size distribution with simulations of a cloud of 70 cm and pointed out the importance the Taylor Reynolds number, Re λ , the non dimensional parameter mea...

The inhomogeneity of turbulence in wall bounded flows induces the phenomenology called turbophoresis whereby inertial particles of suitable mass accumulate at the solid wall. Particles injected near the axis of a fully turbulent pipe flow, after an initial spreading phase, undergo a segregation process which eventually leads to a pseudoequilibrium distribution sufficiently downstream. Wall densities up to thousand times the reference value can be easily achieved. The process is discussed here by analyzing the direct numerical simulation ͑DNS͒ data of a spatially developing particle laden pipe flow under the assumption of dilute suspension. Development phase and asymptotic state are addressed in quantitative terms. A Shannon-like entropy is introduced to quantify the level of spreading/segregation achieved by the particle distributions along the pipe. This allows to define on a physically sound basis the length of the developing region and to summarize in a single indicator the accumulation level as a function of the particle response time. By conditional statistics, it is unequivocally shown that particles approach the wall dragged by relatively fast yet comparatively rare events where highly accumulating particles follow the fluid in-rush toward the wall. On the contrary, the outward particle flux takes place in the form of much more frequent and gentle motions away from the wall. The analysis of DNS data and a simple argument highlight the role of the elongated clusters of particles at the wall as essential features responsible for the eventual asymptotic equilibrium.

Shear thickening appears as an increase of the viscosity of a dense suspension with the shear rate, sometimes sudden and violent at high volume fraction. Its origin for noncolloidal suspension with non-negligible inertial effects is still debated. Here we consider a simple shear flow and demonstrate that fluid inertia causes a strong microstructure anisotropy that results in the formation of a shadow region with no relative flux of particles. We show that shear thickening at finite inertia can be explained as an increase of the effective volume fraction when considering the dynamically excluded volume due to these shadow regions.

Particulate flows have mainly been studied under the simplifying assumption of a one-way coupling regime where the disperse phase does not modify the carrier fluid. A more complete view of multiphase flows can be gained calling into play two-way coupling effects, i.e. by accounting for the inter-phase momentum exchange, which is certainly relevant at increasing mass loading. In this paper we present a new methodology rigorously designed to capture the inter-phase momentum exchange for particles smaller than the smallest hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. The momentum coupling mechanism exploits the unsteady Stokes flow around a small rigid sphere, where the transient disturbance produced by each particle is evaluated in a closed form. The particles are described as lumped point masses, which would lead to the appearance of singularities. A rigorous regularization procedure is conceived to extract the physically relevant interactions between the particles and the fluid which avoids any 'ad hoc' assumption. The approach is suited for high-efficiency implementation on massively parallel machines since the transient disturbance produced by the particles is strongly localized in space. We will show that hundreds of thousands of particles can be handled at an affordable computational cost, as demonstrated by a preliminary application to a particle-laden turbulent shear flow.

The macroscopic behavior of dense suspensions of neutrally-buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum limit in which its dynamics is well described by an effective suspension viscosity. This deviation is caused by the formation of a particle layer close to the wall with significant slip velocity. By assuming two distinct transport mechanisms in the near-wall layer and the turbulence in the bulk, we define an effective wall location such that the flow in the bulk can still be accurately described by an effective suspension viscosity. We thus propose scaling laws for the mean velocity profile of the suspension flow, together with a master equation able to predict the increase in drag as function of the particle size and volume fraction.