arXiv subjects

Luca Brandt

Publications and source records attributed to Luca Brandt.

At least 91 records · Page 5Linked to original sources

arXiv2017

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 $ϕ=0.5\%-10\%$. 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 $ϕ$ 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 $ϕ$ 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 $ϕ=5\%$ and $10\%$. The increase of the mean settling speed is due to the formation of particle clusters that for $ϕ=0.5\%-1\%$ 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).

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arXiv2017

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 $ϕ=0-0.2$, 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 $ϕ=0.05$ 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 $ϕ=0.1$, as a consequence of the high concentration of particles along the corner bisector. For $ϕ=0.2$ 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 $ϕ$ in dilute conditions, as observed for channel flows. However, for $ϕ=0.2$ the mean friction Reynolds number decreases below the value for $ϕ=0.1$.

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arXiv2017

Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

We present a numerical study of noncolloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an Immersed Boundary Method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ($0.1\le Φ\le 0.4$) and particle Reynolds Numbers ($0.1\le Re_p \le 10$). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $Φ$. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare their mean value with the values estimated from the homogenization theory of \cite{Chateau08}, indicating a reasonable agreement in the Stokesian regimes. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_p$. The wide spectrum of the local shear rate and its dependency on $Φ$ and $Re_p$ points to the deficiencies of the mean value of the local shear rates in estimating the rheology of these noncolloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these noncolloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $ O(Re_p)\sim 10$.

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arXiv2017

An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces

Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier-Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressure-correction approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.

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arXiv2017

Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall

We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier-Stokes (NS) equations, while the solid is a neo-Hookean material satisfying the incompressible Mooney-Rivlin law. The multiphase flow is solved with a one-continuum formulation, using a monolithic velocity field for both the fluid and solid phase, which allows the use of a fully Eulerian formulation. The simulations are carried out at Reynolds bulk $Re=2800$ and examine the effect of different elasticity and viscosity of the deformable wall. We show that the skin friction increases monotonically with the material elastic modulus. The turbulent flow in the channel is affected by the moving wall even at low values of elasticity since non-zero fluctuations of vertical velocity at the interface influence the flow dynamics. The near-wall streaks and the associated quasi-streamwise vortices are strongly reduced near a highly elastic wall while the flow becomes more correlated in the spanwise direction, similarly to what happens for flows over rough and porous walls. As a consequence, the mean velocity profile in wall units is shifted downwards when shown in logarithmic scale, and the slope of the inertial range increases in comparison to that for the flow over a rigid wall. We propose a correlation between the downward shift of the inertial range, its slope and the wall-normal velocity fluctuations at the wall, extending results for the flow over rough walls. We finally show that the interface deformation is determined by the fluid fluctuations when the viscosity of the elastic layer is low, while when this is high the deformation is limited by the solid properties.

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arXiv2017

Numerical simulations of elastic capsules with nucleus in shear flow

The shear-induced deformation of a capsule with a stiff nucleus, a model of eukaryotic cells, is studied numerically. The membrane of the cell and of its nucleus are modelled as a thin and impermeable elastic material obeying a Neo-Hookean constitutive law. The membranes are discretised by a Lagrangian mesh and their governing equations are solved in spectral space using spherical harmonics, while the fluid equations are solved on a staggered grid using a second-order finite differences scheme. The fluid-structure coupling is obtained using an immersed boundary method. The numerical approach is presented and validated for the case of a single capsule in a shear flow. The variations induced by the presence of the nucleus on the cell deformation are investigated when varying the viscosity ratio between the inner and outer fluids, the membrane elasticity and its bending stiffness. The deformation of the eukaryotic cell is smaller than that of the prokaryotic one. The reduction in deformation increases for larger values of the capillary number. The eukaryotic cell remains thicker in its middle part compared to the prokaryotic one, thus making it less flexible to pass through narrow capillaries. For a viscosity ratio of 5, the deformation of the cell is smaller than in the case of uniform viscosity. In addition, for non-zero bending stiffness of the membrane, the deformation decreases and the shape is closer to an ellipsoid. Finally, we compare the results obtained modeling the nucleus as an inner stiffer membrane with those obtained using a rigid particle.

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arXiv2017

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.

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arXiv2017

Statistics of particle accumulation in spatially developing turbulent boundary layers

We present the results of a Direct Numerical Simulation of a particle-laden spatially developing turbulent boundary layer up to Reθ = 2500. Two main features differentiate the behavior of inertial particles in a zero- pressure-gradient turbulent boundary layer from the more commonly studied case of a parallel channel flow. The first is the variation along the streamwise direction of the local dimensionless parameters defining the fluid-particle in- teractions. The second is the coexistence of an irrotational free-stream and a near-wall rotational turbulent flow. As concerns the first issue, an inner and an outer Stokes number can be defined using inner and outer flow units. The inner Stokes number governs the near-wall behavior similarly to the case of channel flow. To understand the effect of a laminar-turbulent interface, we ex- amine the behavior of particles initially released in the free stream and show that they present a distinct behavior with respect to those directly injected inside the boundary layer. A region of minimum concentration occurs inside the turbulent boundary layer at about one displacement thickness from the wall. Its formation is due to the competition between two transport mecha- nisms: a relatively slow turbulent diffusion towards the buffer layer and a fast turbophoretic drift towards the wall.

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arXiv2017

Inertial migration of spherical and oblate particles in straight ducts

We study numerically the inertial migration of a single rigid sphere and an oblate spheroid in straight square and rectangular ducts. A highly accurate interface-resolved numerical algorithm is employed to analyse the entire migration dynamics of the oblate particle and compare it with that of the sphere. Similarly to the inertial focusing of spheres, the oblate particle reaches one of the four face-centred equilibrium positions, however they are vertically aligned with the axis of symmetry in the spanwise direction. In addition, the lateral trajectories of spheres and oblates collapse into an equilibrium manifold before ending at the equilibrium positions, with the equilibrium manifold tangential to lines of constant background shear for both sphere and oblate particles. The differences between the migration of the oblate and sphere are also presented, in particular the oblate may focus on the diagonal symmetry line of the duct cross-section, close to one of the corners, if its diameter is larger than a certain threshold. Moreover, we show that the final orientation and rotation of the oblate exhibit a chaotic behaviour for Reynolds numbers beyond a critical value. Finally, we document that the lateral motion of the oblate particle is less uniform than that of the spherical particle due to its evident tumbling motion throughout the migration. In a square duct, the strong tumbling motion of the oblate in the first stage of the migration results in a lower lateral velocity and consequently longer focusing length with respect to that of the spherical particle. The opposite is true in a rectangular duct where the higher lateral velocity of the oblate in the second stage of the migration, with negligible tumbling, gives rise to shorter focusing lengths. These results can help the design of microfluidic systems for bio-applications.

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arXiv2017

Turbulent channel flow of a dense binary mixture of rigid particles

We study turbulent channel flow of a binary mixture of finite-size neutrally-buoyant rigid particles by means of interface-resolved direct numerical simulations. We fix the bulk Reynolds number and total solid volume fraction, $Re_b = 5600$ and $Φ=20\%$, and vary the relative fraction of small and large particles. The binary mixture consists of particles of two different sizes, $2h/d_l=20$ and $2h/d_s=30$ where $h$ is the half channel height and $d_l$ and $d_s$ the diameter of the large and small particles. While the particulate flow statistics exhibit a significant alteration of the mean velocity profile and turbulent fluctuations with respect to the unladen flow, the differences between the mono-disperse and bi-disperse cases are small. However, we observe a clear segregation of small particles at the wall in binary mixtures, which affects the dynamics of the near wall region and thus the overall drag. This results in a higher drag in suspensions with a larger amount of large particles. As regards bi-disperse effects on the particle dynamics, a non-monotonic variation of the particle dispersion in the spanwise (homogeneous) direction is observed when increasing the percentage of small/large particles. Finally, we note that particles of the same size tend to cluster more at contact whereas the dynamics of the large particles gives highest collision kernels due to a higher approaching speed.

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arXiv2017

Effect of viscosity ratio on the self-sustained instabilities in planar immiscible jets

Previous studies have shown that intermediate surface tension has a counterintuitive destabilizing effect on 2-phase planar jets. Here, the transition process in confined 2D jets of two fluids with varying viscosity ratio is investigated using DNS. Neutral curves for persistent oscillations are found by recording the norm of the velocity residuals in DNS for over 1000 nondimensional time units, or until the signal has reached a constant level in a logarithmic scale - either a converged steady state, or a "statistically steady" oscillatory state. Oscillatory final states are found for all viscosity ratios (0.1-10). For uniform viscosity (m=1), the first bifurcation is through a surface tension-driven global instability. For low viscosity of the outer fluid, there is a mode competition between a steady asymmetric Coanda-type attachment mode and the surface tension-induced mode. At moderate surface tension, the Coanda-type attachment dominates and eventually triggers time-dependent convective bursts. At high surface tension, the surface tension-dominated mode dominates. For high viscosity of the outer fluid, persistent oscillations appear due to a strong convective instability. Finally, the m=1 jet remains unstable far from the inlet when the shear profile is nearly constant. Comparing this to a parallel Couette flow (without inflection points), we show that in both flows, a hidden interfacial mode brought out by surface tension becomes temporally and absolutely unstable in an intermediate Weber and Reynolds regime. An energy analysis of the Couette setup shows that surface tension, although dissipative, induces a velocity field near the interface which extracts energy from the flow through a viscous mechanism. This study highlights the rich dynamics of immiscible planar uniform-density jets, where several self-sustained and convective mechanisms compete depending on the exact parameters.

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arXiv2016

Aspect ratio effect on particle transport in turbulent duct flows

The dynamics of dilute micron-sized spherical inertial particles in turbulent duct flows is studied by means of direct numerical simulations of the carrier phase turbulence with one-way coupled Lagrangian particles. The geometries are a square and a rectangular duct with width-to-height aspect ratio $AR$ of 3 operating at $Re_{τ,c}=360$ . The present study is designed to determine the effect of turbulence-driven secondary motion on the particle dynamics. Our results show that a weak cross-flow secondary motion significantly changes the cross-sectional map of the particle concentration, mean velocity and fluctuations. As the geometry of the duct is widened from $AR=1$ to 3, the secondary vortex on the horizontal wall significantly expands in the spanwise direction, and although the kinetic energy of the secondary flow increases close to the corner, it decays towards the duct centreplane in the $AR=3$ case so as the turbulent carrier phase approaches the behavior in spanwise-periodic channel flows, a fact that significantly affects the particle statistics. In the square duct the particle concentration in the viscous sublayer is maximum at the duct centreplane, whereas the maximum is found closer to the corner, at a distance of $|z/h|\approx1.25$ from the centreplane, in the $AR=3$ case. Interestingly the centreplane concentration in the rectangular duct is around 3 times lower than that in the square duct. Moreover, a second peak in the accumulation distribution is found right at the corners for both ducts. At this location the concentration increases with particle inertia. The secondary motion changes also the cross-stream map of the particle velocities significantly in comparison to the fluid flow statistics. These directly affect the particle velocity fluctuations such that multiple peaks appear near the duct walls for the particle streamwise and wall-normal velocity fluctuations.

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arXiv2016

Motion of an elastic capsule in a constricted microchannel

We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca, and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that reproduces the behavior of the three-dimensional surface area the best. We observe that, in general, area-deformation correlated quantities grow linearly with Ca, while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca. The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded (versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance.

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arXiv2016

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).

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arXiv2016

Heat transfer in laminar Couette flow laden with rigid spherical particles

We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations using a direct-forcing immersed boundary method to account for the dispersed phase. A volume of fluid approach is employed to solve the temperature field inside and outside of the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed. In addition, an average composite diffusivity can be used to predict the effective diffusivity of the suspension the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, saturating at higher volume fractions. By phase-ensemble averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated to fluid and particle velocity. We also show that the heat conduction in the solid phase reduces when increasing the particle Reynolds number and so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increase the total heat transfer.

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arXiv2016

Universal Scaling Laws for Dense Particle Suspensions in Turbulent Wall-Bounded Flows

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.

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arXiv2016

The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions

We study the effect of varying the mass and volume fraction of a suspension of rigid spheres dispersed in a turbulent channel flow. We performed several Direct Numerical Simulations using an Immersed Boundary Method for finite-size particles changing the solid to fluid density ratio, the mass fraction and the volume fraction. We find that varying the density ratio between 1 and 10 at constant volume fraction does not alter the flow statistics as much as when varying the volume fraction at constant and at constant mass fraction. Interestingly, the increase in overall drag found when varying the volume fraction is considerably higher than that obtained for increasing density ratios at same volume fraction. The main effect at density ratios of the order of 10 is a strong shear-induced migration towards the centerline of the channel. When the density ratio is further increased up to 1000 the particle dynamics decouple from that of the fluid. The solid phase behaves as a dense gas and the fluid and solid phase statistics drastically change. In this regime, the collision rate is high and dominated by the normal relative velocity among particles.

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arXiv2016

Numerical Study of the Sedimentation of Spheroidal Particles

The gravity-driven motion of rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion whereas prolate particles rotate around the vertical axis while having their broad side facing the falling direction. Instabilities of the vortices in the wake follow when farther increasing the Galileo number. We also study the drafting-kissing-tumbling associated with the settling of particle pairs. We find that the interaction time increases significantly for non-spherical particles and, more interestingly, spheroidal particles are attracted from larger lateral displacements. This has important implications for the estimation of collision kernels and can result in increasing clustering in suspensions of sedimenting spheroids.

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