Sedimentation of finite-size spheres in quiescent and turbulent environments

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behavior of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to account for the dispersed rigid spherical particles. The solid volume fractions considered are 0.5-1%, while the solid to fluid density ratio 1.02. The particle radius is chosen to be approximately 6 Komlogorov lengthscales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reduction with respect to a single particle in quiescent fluid is about 12\% and 14\% for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated to the intermittent fast sedimentation of particle pairs in drafting-kissing-tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behavior observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulas and show that non stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.Comment: In press on Journal of Fluid Mechanic

The effect of polydispersity in a turbulent channel flow laden with finite-size particles

We study turbulent channel flows of monodisperse and polydisperse suspensions of finite-size spheres by means of Direct Numerical Simulations using an immersed boundary method to account for the dispersed phase. Suspensions with 3 different Gaussian distributions of particle radii are considered (i.e. 3 different standard deviations). The distributions are centered on the reference particle radius of the monodisperse suspension. In the most extreme case, the radius of the largest particles is 4 times that of the smaller particles. We consider two different solid volume fractions, 2% and 10%. We find that for all polydisperse cases, both fluid and particles statistics are not substantially altered with respect to those of the monodisperse case. Mean streamwise fluid and particle velocity profiles are almost perfectly overlapping. Slightly larger differences are found for particle velocity fluctuations. These increase close to the wall and decrease towards the centerline as the standard deviation of the distribution is increased. Hence, the behavior of the suspension is mostly governed by excluded volume effects regardless of particle size distribution (at least for the radii here studied). Due to turbulent mixing, particles are uniformly distributed across the channel. However, smaller particles can penetrate more into the viscous and buffer layer and velocity fluctuations are therein altered. Non trivial results are presented for particle-pair statistics.Comment: Under review in the European Journal of Mechanics/B - Fluid

Clustering and increased settling speed of oblate particles at finite Reynolds number

We study the settling of rigid oblates in quiescent fluid using interface-resolved Direct Numerical Simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle-particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio AR=1/3 and solid volume fractions $\phi=0.5\%-10\%$. The solid-to-fluid density ratio $R=1.5$ and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere with equivalent volume $Ga=60$. With this choice of parameters, an isolated oblate falls vertically with a steady wake with its broad side perpendicular to the gravity direction. At this $Ga$, the mean settling speed of spheres is a decreasing function of the volume $\phi$ and is always smaller than the terminal velocity of the isolated particle, $V_t$. On the contrary, we show here that the mean settling speed of oblate particles increases with $\phi$ in dilute conditions and is $33\%$ larger than $V_t$. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity $V_t$ between $\phi=5\%$ and $10\%$. The increase of the mean settling speed is due to the formation of particle clusters that for $\phi=0.5\%-1\%$ appear as columnar-like structures. From the pair-distribution function we observe that it is most probable to find particle-pairs almost vertically aligned. However, the pair-distribution function is non-negligible all around the reference particle indicating that there is a substantial amount of clustering at radial distances between 2 and $6c$ (with $c$ the polar radius of the oblate).Comment: Submitted to Journal of Fluid Mechanic

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

Suspensions of finite-size neutrally-buoyant spheres in turbulent duct flow

We study the turbulent square duct flow of dense suspensions of neutrally-buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $\phi=0-0.2$, using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of $5600$ is considered. We report flow features and particle statistics specific to this geometry, and compare the results to the case of two-dimensional channel flows. In particular, we observe that for $\phi=0.05$ and $0.1$, particles preferentially accumulate on the corner bisectors, close to the duct corners as also observed for laminar square duct flows of same duct-to-particle size ratios. At the highest volume fraction, particles preferentially accumulate in the core region. For channel flows, in the absence of lateral confinement particles are found instead to be uniformily distributed across the channel. We also observe that the intensity of the cross-stream secondary flows increases (with respect to the unladen case) with the volume fraction up to $\phi=0.1$, as a consequence of the high concentration of particles along the corner bisector. For $\phi=0.2$ the turbulence activity is strongly reduced and the intensity of the secondary flows reduces below that of the unladen case. The friction Reynolds number increases with $\phi$ in dilute conditions, as observed for channel flows. However, for $\phi=0.2$ the mean friction Reynolds number decreases below the value for $\phi=0.1$.Comment: Submitted to Journal of Fluid Mechanic

Rheology of confined non-Brownian suspensions

We study the rheology of confined suspensions of neutrally buoyant rigid monodisperse spheres in plane-Couette flow using Direct Numerical Simulations. We find that if the width of the channel is a (small) integer multiple of the sphere's diameter, the spheres self-organize into two-dimensional layers that slide on each other and the suspension's effective viscosity is significantly reduced. Each two-dimensional layer is found to be structurally liquid-like but their dynamics is frozen in time.Comment: Submitted to PRL. Supplemental Material added as an appendix. Includes links to youtube video

Geometrizadores proyectuales en la arquitectura argentina : Caso: Arquitecto Francisco Salamone

El presente trabajo es parte de una investigación que se centra en el análisis de obras arquitectónicas relevantes en nuestro país, desde sus aspectos compositivos-geométricos, enmarcados en el Proyecto de Investigación «Teoría de la proporción y su enseñanza: morfogeneradores geométricos en el diseño» a cargo de un equipo de docentes de las Facultades de Arquitectura y Urbanismo y de Humanidades y Ciencias de la Educación pertenecientes a la Universidad Nacional de La Plata. En particular este estudio se centra en la obra del arquitecto Francisco Salamone (1897-1957) la que se desarrolla en la provincia de Buenos Aires, donde se analizan elementos de diseño que son ordenadores proyectuales provenientes de las matemáticas. Entre los años 1936 y 1940, Francisco Salamone, realizó para la gobernación de Manuel Fresco en la provincia de Buenos Aires casi un centenar de obras, en su mayoría de estilo Art Deco, entre municipalidades, mataderos, cementerios, escuelas, plazas y equipamiento, es de suponer que debió de utilizar un método proyectual y aplicar invariantes de diseño, ya que sabemos que ha trabajado solamente él y un dibujante, una tarea ciclópea para aquella época. Esta es la conclusión a la que llegamos, luego de analizar una considerable cantidad de obras, donde se verifica que conceptos matemáticos fueron utilizados en sus proyectos.Mesa 3.Facultad de Bellas Artes (FBA