.
We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are ...available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech
78
, 227 (1998); M. Minale, Rheol. Acta
47
, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess “
ab initio
” the robustness and limitations of such theoretical models, our simulations are also key to discuss --in controlled situations-- some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the “transparency” transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.
Graphical abstract
By using direct numerical simulations (DNS) at unprecedented resolution, we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at ...large scale leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By seeding the flow with millions of inertial particles, we quantify—for the first time—the effects of those coherent vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively show that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from the entangled interaction of the vertical structures with the turbulent background. Finally, we present the first-ever measurement of the relative importance between Stokes drag, Coriolis force, and centripetal force along the trajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusion properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis.
We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following ...the trajectories of up to 120 million particles with Stokes numbers, St, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: (i) the root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value at quite small Stokes numbers; (ii) at a given St the normalized acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers; (iii) the tails of the probability density function of the normalized acceleration $a/a_{\rm rms}$ decrease with St. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small St, and filtering induced by the particle response time, that takes over at larger St.
Results from direct numerical simulations (DNS) of particle relative dispersion in three-dimensional homogeneous and isotropic turbulence at Reynolds number
$\def \xmlpi #1{}\def \mathsfbi ...#1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_{\lambda } \sim 300$
are presented. We study point-like passive tracers and heavy particles, at Stokes number
$\mathit{St}=0.6,1$
and 5. Particles are emitted from localised sources, in bunches of thousands, periodically in time, allowing an unprecedented statistical accuracy to be reached, with a total number of events for two-point observables of the order of
${10^{11}}$
. The right tail of the probability density function (PDF) for tracers develops a clear deviation from Richardson’s self-similar prediction, pointing to the intermittent nature of the dispersion process. In our numerical experiment, such deviations are manifest once the probability to measure an event becomes of the order of – or rarer than – one part over one million, hence the crucial importance of a large dataset. The role of finite-Reynolds-number effects and the related fluctuations when pair separations cross the boundary between viscous and inertial range scales are discussed. An asymptotic prediction based on the multifractal theory for inertial range intermittency and valid for large Reynolds numbers is found to agree with the data better than the Richardson theory. The agreement is improved when considering heavy particles, whose inertia filters out viscous scale fluctuations. By using the exit-time statistics we also show that events associated with pairs experiencing unusually slow inertial range separations have a non-self-similar PDF.
Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and ...A. Ajdari,
Phys. Rev. Lett.
, 2009,
103
, 036001, we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity) are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of the flow and strictly zero elsewhere. The compacton coexistence with regions of zero fluidity ("non-flowing vacuum") is shown to be stabilized by the presence of mechanical noise, which ultimately shapes up the equilibrium distribution of the fluidity field, the latter acting as an order parameter for the flow-noflow transitions occurring in the material.
Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems.
We perform direct numerical simulations of an unstably stratified turbulent channel flow to address the effects of buoyancy on the boundary layer dynamics and mean field quantities. We systematically ...span a range of parameters in the space of friction Reynolds number (
$\mathit{Re}_{{\it\tau}}$
) and Rayleigh number (
$\mathit{Ra}$
). Our focus is on deviations from the logarithmic law of the wall due to buoyant motion. The effects of convection in the relevant ranges are discussed, providing measurements of mean profiles of velocity, temperature and Reynolds stresses as well as of the friction coefficient. A phenomenological model is proposed and shown to capture the observed deviations of the velocity profile in the log-law region from the non-convective case.
A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified as vT =(Csδ)2(|S|—|〈S〉|): the ...magnitude of the mean shear |〈S〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|; CS is the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Reτ = 395 and Reτ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.
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