Enrico Calzavarini

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Rotation Rate of Rods in Turbulent Fluid Flow

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape.

Acceleration of heavy and light particles in turbulence: Comparison between experiments and direct numerical simulations

We compare experimental data and numerical simulations for the dynamics of inertial particles with finite density in turbulence. In the experiment, bubbles and solid particles are optically tracked in a turbulent flow of water using an Extended Laser Doppler Velocimetry technique. The probability density functions (PDF) of particle accelerations and their auto-correlation in time are computed. Numerical results are obtained from a direct numerical simulation in which a suspension of passive pointwise particles is tracked, with the same finite density and the same response time as in the experiment. We observe a good agreement for both the variance of acceleration and the autocorrelation time scale of the dynamics; small discrepancies on the shape of the acceleration PDF are observed. We discuss the effects induced by the finite size of the particles, not taken into account in the present numerical simulations.

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.

Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence

The Ra and Pr number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh–Benard turbulence, i.e., Rayleigh–Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of Rayleigh–Benard flow and therefore as model for the so-called “ultimate regime of thermal convection.” With respect to the Ra dependence of Nu and Re we confirm our earlier results [ D. Lohse and F. Toschi, “The ultimate state of thermal convection,” Phys. Rev. Lett. 90, 034502 (2003) ] which are consistent with the Kraichnan theory [ R. H. Kraichnan, “Turbulent thermal convection at arbitrary Prandtl number,” Phys. Fluids 5, 1374 (1962) ] and the Grossmann–Lohse (GL) theory [ S. Grossmann and D. Lohse, “Scaling in thermal convection: A unifying view,” J. Fluid Mech. 407, 27 (2000) ; “Thermal convection for large Prandtl number,” Phys. Rev. Lett. 86, 3316 (2001) ; “Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection,” Phys. Rev. E 66, 016305 (2002) ; “Fluctuations in turbulent Rayleigh–Benard convection: The role of plumes,” Phys. Fluids 16, 4462 (2004) ], which both predict Nu ∼ Ra1/2 and Re ∼ Ra1/2. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory Nu ∼ Pr1/2, Re ∼ Pr−1/2. For the thermal and kinetic dissipation rates we find ϵθ/(κΔ2L−2) ∼ (Re Pr)0.87 and ϵu/(ν3L−4) ∼ Re2.77, both near (but not fully consistent) the bulk dominated behavior, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. [“Comment on ultimate state of thermal convection” (private communication)].

Microbubbly drag reduction in Taylor-Couette flow in the wavy vortex regime

We investigate the effect of microbubbles on Taylor-Couette flow by means of direct numerical simulations. We employ an Eulerian-Lagrangian approach with a gas-fluid coupling based on the point-force approximation. Added mass, drag, lift and gravity are taken into account in the modelling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1 %, zero Weber number and bubble Reynolds number ≤10) induce a robust statistically steady drag reduction (up to 20 %) in the wavy vortex flow regime (Re=600-2500). The Reynolds number dependence of the normalized torque (the so-called torque reduction ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. Conf. Ser. vol. 14, 2005, p. 143). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When it is neglected, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified. Movies are available with the online version of the paper.

Evidences of Bolgiano-Obhukhov scaling in three-dimensional Rayleigh-Benard convection

We present different results from high-resolution high-statistics direct numerical simulations of a three-dimensional convective cell. We test the fundamental physical picture of the presence of both a Bolgiano-Obhukhov-like and a Kolmogorov-like regime. We find that the dimensional predictions for these two distinct regimes (characterized, respectively, by an active and passive role of the temperature field) are consistent with our analysis.

Dynamics of inertial particles in a turbulent von Kármán flow

We study the dynamics of neutrally buoyant particles with diameters varying in the range [1, 45] in Kolmogorov scale units (η) and Reynolds numbers based on Taylor scale ( Re λ ) between 590 and 1050. One component of the particle velocity is measured using an extended laser Doppler velocimetry at the centre of a von Karman flow, and acceleration is derived by differentiation. We find that the particle acceleration variance decreases with increasing diameter with scaling close to ( D /η) −2/3 , in agreement with previous observations, and with a hint for an intermittent correction as suggested by arguments based on scaling of pressure spatial increments. The characteristic time of acceleration autocorrelation increases more strongly than previously reported in other experiments, and possibly varying linearly with D /η. Further analysis shows that the probability density functions of the acceleration have smaller wings for larger particles; their flatness decreases as well, as expected from the behaviour of pressure increments in turbulence when intermittency corrections are taken into account. We contrast our measurements with previous observations in wind-tunnel turbulent flows and numerical simulations.

Quantifying Turbulence-Induced Segregation of Inertial Particles

Particles with different density from the advecting turbulent fluids cluster due to the different response of light and heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute polydisperse inertial particles evolving in turbulent flow, as obtained from direct numerical simulation of homogeneous isotropic turbulence. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale r_{seg}, quantifying the segregation degree between two particle types, is deduced.

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

Three-dimensional Voronoi 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 ) and two Taylor–Reynolds numbers ( and 180). The probability density functions (p.d.f.s) of the Voronoi 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 . Light particles show maximum clustering for 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 Voronoi volumes and their Lagrangian autocorrelations. The small Voronoi 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 Voronoi 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