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## Particles in Turbulence |

Generalized
framework for particle advection using template metaprogramming
and MPI In
recent times we have sketched a general scheme to combine C++ programming
strategies with parallel computation. Our goal is to develop a framework
capable to either interface with data or with a CFD code in order to produce
particle trajectories for the different numerical codes available on the
market. We aim at a high performance for either scientific or applied
situations.
We propose a novel diagnostic
that will allow the tracking of dispersed phase material lines through droplet
tagging. A chamber capable of creating (nearly) isotropic homogeneous flow is
densely seeded with droplets. The droplets are created from a phosphorescent
solution made out of a lanthanide chelate (Eu+3). The lifetime of the
phosphorescent signal is on the order of 1 ms, which is comparable to the Kolmogorov time scale.
A well-defined volume of the droplet cloud is tagged through a high-power laser
and tracked in time using an intensified high speed camera. The deformation and
intensity profile of the tagged volume provide insight into the dynamical
aspects of preferential concentration in turbulent flows at the smallest
scales, i. e. the Kolmogorov scales.
In the present study, we investigated the orientation and
distribution of finite-size and rigid fibres in
turbulent channel flow through fully resolved DNS. The turbulent flow is modelled by an entropy lattice-Boltzmann method and the
interaction between fibres and carrier fluid is odelled through an external boundary force (EBF) method.
Direct contact and lubrication force models for fibre-fibre,
fibre-wall interactions have been implemented as well
in this study. Simulations have been carried out in channel flow with a
friction Reynolds number of 180 and fibre lengths
between 3 and 24 viscous length units. The fibre
diameter has been kept at 2 viscous units in all cases and the total number of fibres is up to 65000. The single phase case has been shown
to give good agreement with standard simulations with pseudospectral
methods for the same Reynolds number. The simulations show that the fibres
accumulate in high-speed streaks near the wall. This preferential concentration
is caused by the interaction of the fibres with the
wall and not by inertial effects because the fibres
are almost neutrally buoyant. Since the fibres
accumulate in the high-speed streaks, they have a higher mean velocity than the
fluid flow.Longer fibres
show a more accentuated excess in mean velocity near the wall. We present a
conceptual model for this behaviour. Moreover, near the
wall, shorter fibres have a higher
fluctuation intensities in spanwise and wall-normal
directions than longer fibres. Some turbulent
statistical quantities of fibres and fluid will be
shown in order to understand the new observations.
A new algorithm
for particulate turbulent flows in the two-way coupling regime
At
increasing mass loads, small particles heavier than the surrounding fluid are
able to modify the dynamics of the turbulent suspension by their back reaction
on the carrier fluid. The
related phenomenology has been addressed in detail for turbulent anisotropic
flows by the authors using standard particle in cell methods. This approach
should be used with upmost care, given certain intrinsic difficulties related
to the description of the particle as a localized source of momentum for the
flow, associated with the Stokes drag the particle experiences in the relative
motion with respect to the carrier fluid (slip velocity). Purpose
of the present talk is discussing the main features of a new way to treat the
coupling problem currently under development in view of fast and accurate
simulations of huge number of sub-Kolmogorov particles. The idea is using in a
smart way certain properties of the unsteady Stokeslet
to inject in the computation mesh the vorticity
generated in the interaction between particles and carrier fluid. Potentially
and pitfalls of the new approach will be discussed using known elementary
solution for the fluid-particle interaction problem and presenting preliminary
results concerning the alteration of the turbulence due to coupling with the
suspended phase in comparison with careful simulations made with the standard
particle in cell method.
The
clustering properties of model gyrotactic organisms
are studied in low Re turbulent flows by means of Direct
numerical simulations (DNS). In
particular, we show that when turbulent acceleration is large enough gyrotactic organisms clusterize
in intense vorticity regions. However,
when turbulent acceleration is much smaller than gravitational acceleration,
clustering is still possible via another mechanism. We also show that crucial
parameter is the reorientation time of the microorganisms with respect to the
fluid vorticity.
We first review experimental and numerical facts on the
preferential alignments of vorticity with the eigenframe of the deformation. We then propose a stochastic
model for the velocity gradient tensor able to reproduce realistic alignments,
in particular in a Lagrangian fashion. We finally
underline limitations of the model to give a realistic picture of pressure
effects. A new local-in-space approximation of the pressure Hessian is shown to
perform well against DNS.
The dispersion of groups of correlated particles in
turbulent flows is of much interest, both because of its relationship with
higher order moments of the concentration field and because it allows
connections to be made between the statistical and structural descriptions of
turbulence. Information on the geometry of a 3-D flow can be obtained by
following four particles, a tetrad. In recent years experimental techniques1 2
and numerical simulations 3 4 5 of tetrads have provided much insight into the
nature of turbulence. Here, a simple Lagrangian
stochastic model (LSM) for tetrads is compared with a direct numerical
simulation (DNS) of turbulence. The model is an extension of Thomson’s model6 for particle
pairs. It is constructed to satisfy the well-mixed condition and has as an
input the constant of proportionality in the second order Lagrangian
velocity structure function, C0. By varying C0, it is possible to make the
particles’ motion more (large C0) or less (small C0) diffusive than in real
turbulence and thereby assess the relative importance of ballistic versus diffusive
motion in real turbulent flows. Furthermore, results will also be presented for
a diffusion equation with a separation-dependent eddy diffusivity:
K(r) / r4/3 where r is the separation between any two particles. This is the
limiting case of the LSM in the limit C0 ! 1 and is an
extension of Richardson’s model7 for particle pairs to tetrads. DNS of tetrads show that they tend to
form more elongated shapes than is the case for tetrads formed from four uncorrelated particles.
The results of both the LSM (for values of C0 typical of real turbulence) and
Richardson’s diffusion model agree well with the DNS results. This indicates
that in the LSM no significant variation of the shape statistics with C0 is
expected. The absence of intermittency effects in the two models, and the good
agreement with DNS, suggests that intermittency does not play an important role
in determining the shape statistics of tetrads in real turbulence. Moreover,
the results also suggest that the tendency to form elongated shapes is a
kinematic effect, rather than a specific dynamical effect, for any flow field in
which the dispersion is reasonably well approximated by a diffusivity of the
form K(r). Indeed, it will be shown that in a generalised Richardson diffusion model, in which the
diffusivity is proportional to rm, the ‘degree of
elongation’ varies with m: for m > 4/3 the tetrads
tend to form more elongated shapes than in real turbulence while the reverse is
true for m < 4/3. Results on Lagrangian four-point
velocitydifference statistics will also be discussed.
Lorenzo Del Castello
and Laurens van BokhovenThe
influence of the Earth background rotation on oceanic and
atmospheric currents, as well as the effects of a rapid rotation on the flow
inside industrial machineries like mixers, turbines, and compressors, are
typical examples of fluid flows affected by rotation. Rotating turbulence has
often been studied by means of numerical simulations and analytical models, but
the experimental data available is scarce and purely of Eulerian
nature. In the present study experiments on continuously forced turbulence
subjected to different background rotation rates have been performed.
Quantitative information on the flow field is obtained by means of stereoscopic
Particle Image Velocimetry (allowing to obtain the
three velocity components in a 2D plane; Eulerian
approach) and 3D Particle Tracking Velocimetry
(providing the 3D velocity field in a certain volume of the flow domain; Lagrangian approach). The background rotation is confirmed
to induce 2-dimensionalisation of the velocity field. We will illustrate this
in the talk with the behaviour of the Lagrangian velocity PDFs with increasing rotation rates and
by the presence of the large scales which are dominated by stable
counter-rotating vertical tubes of vorticity. Direct
effects of the background rotation are also the suppression of
high-acceleration events parallel to the (vertical) rotation axis, the
enhancement of high-acceleration events for the horizontal acceleration, and
the strong amplification of the Lagrangian
auto-correlation of the acceleration component perpendicular to both the
rotation vector W and local velocity vector u. The Lagrangian
auto-correlation of the acceleration component in the plane set up by W and u
is only mildly and indirectly enhanced.
In this work we perform a study of the aggregation-fragmentation
dynamics in synthetic turbulence. We are interested in the effect of the
density of the advected particles on the process. The
advection is modeled using a Lagrangian description
which incorporates particle inertia, and considers the approximation of
spherical particles displaced by the action of forces which include the Stokes
drag and an added mass term. Particles of different densities follow distinct
trajectories when carried by the flow field. The two distinct well known cases
of preferential concentration are bubbles and aerosols, which have particle
density lower and higher than the fluid density, respectively. These two
particle types segregate in distinct regions of the flow, with high vorticity in the case of bubbles, and low vorticity in the case of aerosols. In our study we are
particularly interested in the sizes of formed aggregates which result from the
dynamics of collision and break-out of particles during their advection. The
collision rate depends on the fractal size of the segregation region, while the
fragmentation rate on the other hand depends on the shear forces that the
particle experiences in that region. We systematically study the dependence of
aggregation and fragmentation on the flow-particle density ratio in both cases
of light and heavy particles, and we investigate the influence of the flow
properties on the final size distribution of aggregates. Additionally, we
consider the aggregation-fragmentation process of two types of primary
particles with slightly distinct densities. We obtain the collision rates for
particles in such a mixture, and characterise how the
size distribution of the aggregates and the aggregate composition depend on the
fragmentation rate and on the densities of the primary particles. This part of
the study is motivated by the formation and the break up
of marine aggregates, which consist of organic and inorganic components having
different densities. Depending on their environment their composition can be
very different, and their dynamics is an essential part in biological cycles in
the ocean.
An important aspect in
numerical simulations of particle laden turbulent flows is the interpolation of
the flow field needed for the computation of the Lagrangian
particle trajectories. This study focuses on estimating the interpolation error
and compares it with the discretisation error of the
flow field. In this way one can balance the errors in order to achieve an
optimal result. As a spin-off of the theoretical analysis a practical method is
proposed which enables direct estimation of the interpolation error from the
energy spectrum. The same is done for the discretisation
error. The theory is verified by DNS simulations using a spectral code. Here
fluid particle trajectories are computed using several interpolation methods.
It is shown that B-spline interpolation has the best accuracy compared with the
computational overhead. The accuracy of the interpolation method has direct
consequences for the acceleration spectrum of the fluid particle and is also
important for the correct calculation of the hydrodynamic forces on neutrally
buoyant particles.
Turbulence-induced
coagulation of droplets is an important effect in the growth of raindrops. The
effects of turbulence on the coagulation process are not yet fully understood.
We are preparing an experiment, which we describe in this presentation. In the
proposed experiment we insert fluorescent droplets with a typical diameter of
20 microns into a speaker-driven turbulence chamber. The droplets are excited
with a UV laser. The fluorescent light emitted by the particles is captured
with four intensified cameras. 3D particle tracking is used to gather droplet
trajectories. We also investigate the development in time of the droplet size
spectrum with phase-Doppler anemometry. With this experiment we will study the
coagulation of droplets in turbulence.
Next to Rayleigh-Benard convection, Taylor-Couette
flow is the paradigmatic flow in closed systems. This holds in particular for
turbulent flows in closed systems. In the last years we have build a facility with which we can reach a Reynolds number
of 2e6 and which allows for independent inner and outer cylinder rotation. This
is enough to achieve the so-called ultimate regime of turbulence in which the
boundary layers become unstable. We will report on latest measurements with
this facility and on accompanying numerical simulations.
Inertial-particle
dispersion and diffusion We
analytically investigate the dynamics of inertial particles in incompressible
flows in the limit of small but finite inertia, focusing on two specific
instances. First, we study the concentration of particles continuously emitted
from a point source with a given exit velocity distribution. The anisotropy of
the latter turns out to be a necessary factor for the presence of a correction
(with respect to the corresponding tracer case) at order square root of the
Stokes number. Secondly, by means of a multiple-scale expansion, we analyse the particle effective diffusivity, and in
particular its dependence on Brownian diffusivity, gravity effects and
particle-to-fluid density ratio. In both cases, we obtain forced
advection--diffusion equations for auxiliary quantities in the physical space,
thus simplifying the problem from the full phase space to a system which can
easily be solved numerically.
In
this talk I describe recent analytical progress in understanding clustering and
collision processes of inertial particles suspended in smooth random flows.
Three results are summarised. First, I discuss
mechanisms leading to clustering of inertial particles in mixing flows
(preferential concentration and multiplicative amplification). I demonstrate
under which circumstances one or the other mechanism dominates, and when both
are important. Second, I summarise new results
concerning the rate-of-caustic formation for inertial particles in random
flows. Third, these results determine the distribution of collision velocities.
I describe the known properties of this distribution. I address to which extent these results
describe the dynamics of inertial particles suspended in multi-scale turbulent
flows, and conclude with a number of open questions. The talk is based on
results obtained together with my main collaborators M.
Wilkinson and K. Gustavsson.
The purpose of the presentation is
to introduce Lagrangian stochastic models for
poly-dispersed two-phase flows. The theoretical framework will be
first recalled so as to emphasize that Lagrangian
stochastic approaches are PDF models and to relate present formulations with
respect to various PDF descriptions. Some theoretical issues that may be
overlooked in current similar models will be brought
out. The potential and interest of such approaches will be illustrated by
showing how chemical effects and surface properties
can be directly and explicitly included in a complete simulation of particle
deposition.
We
study the clustering properties of inertial particles in a turbulent
viscoelastic fluid. The investigation is carried out by means of direct
numerical simulations of turbulence in the Oldroyd-B
model. The effects of polymers on the small-scale properties of homogeneous
turbulence are considered in relation with their consequences on clustering of
particles, both lighter and heavier than the carrying fluid. We show that,
depending on particle and flow parameters, polymers can either increase or
decrease clustering.
Joint work with Y. Tagawa,
J. Martinez Mercado, E. Calzavariniy,,C. Sun and D. Lohse We quantify the clustering of inertial particles in
homogeneous isotropic turbulence using three-dimensional Voronoï
analysis on data sets from numerics in the point particle
limit and one experimental data set1. The clustering behavior at different
density ratios, particle response times (i.e. Stokes numbers St) and two
Taylor-Reynolds numbers Re are investigated. The Probability Density Functions
(PDFs) of the Voronoï cell volumes of light and heavy
particles show a different behavior from that of randomly distributed
particles, implying that clustering is present. The standard deviation of the
PDF normalized by that of randomly distributed particles is used to quantify
the clustering. Light particles show maximum clustering for St around 12. The experimental dataset shows reasonable agreement
with the numerical results. These results agree well with previous investigations.
For a Lagrangian clustering analysis, we calculate
the Lagrangian temporal autocorrelation function of Voronoï volumes. We find that the clustering of light
particles lasts much longer than that of heavy or neutrally buoyant particles.
We also compare the ratio of decorrelation times of Voronoï volume (_V ) and enstrophy (_) and find that this ratio for both light and
heavy particles is greater than unity for all St. Remarkably, this means that
light and heavy particles remain clustered for much longer times than the ow structures which cause the clustering, due to inertial
effects arising from the different density ratios.
Tracking Active Particles: Dynamics
of Insect Swarms
The Resuspension
of Small Particles by a Turbulent Flow
Crossover between large scale
instabilities and small scale intermittencies in liquid drop breakupLiquid atomization is now a widely studied field of study. It has many applications in many fields: Combustion, Air/Sea Interaction, Agricultural Spraying, Spray drying/cooling/coating... In this talk, I will show, on a chosen experiment, how first models developed thanks to instability theory, while unwieldy and somewhat inaccurate are still valid to describe the large scale of the droplet field produced. In the meantime, drawn by practical considerations and to cope with discrepancies between experiments and instability models, a turbulent atomization theory, based on Kolmogorov's lognormal distribution, has been developed. While still of practical use to describe the small scales of the droplet distribution, the accuracy of this model can be improved by extending it to log-Lévy stable distribution. This can be related to some classical modelings of turbulent intermittencies which have been rooted more recently into theory thanks to a self-avoiding random vortex stretching scenario.
Heavy
particle concentration: a dynamical analysis
In
recent years, modeling of atmospheric flows at meso-γ
scale has emerged as an important research topic in numerical weather
prediction. Systematic progress in this field results from both continuous
improvement in the numerical methods and availability of high-performance
supercomputers. By employing sub-kilometer grid spacing for operational
forecasting, it is expected that severe weather events triggered by deep moist
convection can be explicitly resolved. Such a resolution
approaches the regime for which the convective processes
can be explicitly represented. Nevertheless, moist processes related to cloud physics still need
to be better parameterized.
Investigation of the moist processes by direct measurements of droplet-droplet
and droplet-turbulence interactions in real clouds is difficult due to the short
time and small length scales involved. Therefore, in this study we focus on the
numerical and laboratory-experimental investigation of collision-coalescence of
cloud droplets. Quantitative description of this process is of great importance
since the collision-coalescence plays important role in the development of warm
rain, that is, the transformation of small cloud droplets to rain drops. Our experimental approach is aimed at developing in the wind tunnel a turbulent flow and droplet
distribution similar to those occurring in the real cloud. Using direct numerical simulations (DNS) we
are able to realistically reproduce the conditions that take place in the wind
tunnel. Together, we hope to combine these two different tools to gain a better
quantitative understanding of turbulent collision-coalescence of cloud
droplets.
Joint work with L. Biferale,
A. Lanotte, F. Toschi We present a detailed investigation of particles
statistics in homogeneous isotropic turbulence. We use data from
a 3D direct numerical simulations at 10243 collocation points and R_ =
300 following the evolution of a huge number of passive tracers and heavy
inertial particles, with Stokes numbers in the range St 2 [0:5; 5]. In
particular, our simulation aims to investigate extreme events characterising the distribution of absolute and relative
dispersions in turbulent ows. To do that, we seeded the ow with hundred millions of
particles emitted from localized sources in time and in space (see _gure 1). Thanks to such huge statitics
we are able to assess in a quantitative way deviations from Richardson's
prediction due to _nite size and _nite
time-correlation lenghts in the particle pairs
distribution. Furthermore, we present the same kind of measures for heavy particles.
Joint work with V. N. Prakash,
Y. Tagawa, E. Calzavarini, J. Martinez Mercado, F. Toschi, and D. Lohse We report results from the first systematic
experimental investigation in the regime of very light and large particles in
turbulence. Using a traversing camera setup for two-dimensional particle
tracking, we study the Lagrangian acceleration
statistics of _3 mm diameter (D) air bubbles in water in active-grid generated
turbulence. The Reynolds number (Re_) is varied from 145 to 230, resulting in
size ratios, _ = D=_ in the range of 7.3{12.5, where _ is the Kolmogorov length
scale. Experiments reveal that gravity does not affect the mean value of the
vertical acceleration component but has a g2 offset on its variance. Once this
gravity offset is subtracted the variances of both the horizontal and
vertical acceleration components are about 5 _ 2 times larger than the one measured in the same flow for fluid
tracers, but still below the estimated upper bound derived from the added-mass
effect alone (which is 9 times the tracer value). This is a mark of the finite-sized
nature of the bubble. The present experimental acceleration variance
measurements are closely matched by numerical simulations of finite-size
bubbles1 where no gravity and just the Faxen
correction to the added-mass force has been taken into account. We compare the PDF of the normalized horizontal (x)
acceleration component along with the PDF from the DNS simulations with Faxen corrections, to further study the finite-size effects
on the bubbles. The finite-sized bubbles show a strongly reduced intermittent
shape. It is the first time that such a substantial change in intermittency at
growing size ratio is experimentally observed. The DNS appears to underestimate
its functional behavior by a factor _2-3 in the size ratio _.
Joint work with J. Martinez Mercado_y, V. N. Prakash_y,
C. Sun_y and D. Lohse_y We study the Lagrangian
velocity and acceleration statistics of light particles (micro-bubbles in
water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter db = 340 _m and Stokes number from 0.02 to 0.09 are
dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Re_)
ranging from 160 to 265. We reconstruct the bubble trajectories by employing
three-dimensional particle tracking velocimetry
(PTV). It is found that the probability density functions (PDFs) of the
micro-bubble acceleration show a highly non-Gaussian behavior with atness values in the range 23{30. The acceleration atness values show an increasing trend with Re_, consistent
with previous experiments1 and numerics2. These acceleration PDFs show a higher
intermittency compared to tracers3 and heavy particles4 in wind tunnel
experiments. In addition, the micro-bubble acceleration autocorrelation function
decorrelates slower with increasing Re_. We also
compare our results with experiments in von Karman flows and point-particle
direct numerical simulations with periodic boundary conditions.
On
the dynamics of non spherical particles in turbulent
flow
Resuspension of particles in an oscillating grid
turbulent flowjoint work with A. Liberzon, April 3, 2012, Turbulence Structure Laboratory,
School of Mechanical Engineering , Tel-Aviv
University, Tel-Aviv 69978, IsraelThe incipient motion condition for particulate
material exposed to a moving fluid constitutes the central problem for sediment
transport in river, coastal areas and atmospheric flows. Furthermore, it is an
important mechanism in a variety of engineering applications, such as: silicon
wafer cleaning and pneumatic conveying. Despite a significant progress in the
field of sediment transport during the past decades, description of the
mechanisms responsible for the initiation of particle motion from a surface and
re-entrainment into suspension remains a challenge. This is partially due to
the technical difficulties to quantify the forces applied on the particles and
the collection of high resolution data of particle displacement simultaneously. In this study we investigate the necessary conditions
for initial entrainment of spherical particles from smooth bed into
zero-mean-shear turbulent flow in an oscillating grid chamber. The experiments
are not designed to fully mimic the real problem of sediment transport but
rather identify key mechanisms, utilizing direct observation and quanti_cation of particle motion at the beginning, during
and after lift-off. Particle image velocimetry (PIV)
was used to determine the properties of turbulent flow and three-dimensional
particle tracking velocimetry (3D-PTV) is used to examine long duration data that synchronously
measure local flow conditions, and track the entrainment of individual test
particles through the various phases of the resuspension.
The combination of the experimental methods and different types of particles
(tracers and test particles) allow to identify the dominant scales within the
turbulence spectrum which cause resuspension and to
explore the role hydrodnamic forces (lift and drag)
play in this process. The results will provide further insight into the resuspension process of spherical particles in the transitional range of particle size Reynolds numbers 2
Turbulence modulation by
inertial particles has been studied computationally by point-particle based
simulations (PPS) and more recently by particle-resolved simulations
(PRS). The purpose of this talk is to compare results from PPS with those
from PRS, to illustrate effects of finite-particle size and issues related to
the validity and limitations of these approaches. A review of theoretical
understanding on turbulence modulation by inertial particles will also be
presented to help interpret published results and clarify relevant issues.
Abstract:
We measured the attachment rates of dispersed particles to the surface of an
air bubble that is kept stationary in a conical pipe. The experiments show
changes in attachment rates during fill-up of the bubble surface with the
particles. We discuss these results with regard to particle transport towards
the surface and to effects of the thin-film drainage process.
There
is a vast literature on how small objects undergo diffusion when subjected to
random forcing, but much less has been written about how an object rotates due
to a random torque. There is a dimensionless parameter characterising
this problem: the persistence angle \beta is the typical angle of rotation
during the correlation time of the angular velocity. When \beta is small, the
problem is simply diffusion on a sphere. But little is known about models with
finite \beta, describing smooth random motion on a sphere. I will discuss the
formulation and solution of the simplest model, which is a spherical Ornstein-Uhlenbech process. In two dimensions (circular motion) this
is exactly solvable. When \beta is large, the solution has a surprising
property, which is analogous to the phenomenon of 'superoscillations'.
In three dimensions we obtain asymptotic solutions for large \beta which
involve a solving a radial Shroedinger equation where
the angular momentum quantum number j takes non-integer values. The case where
j=(\sqrt{17}-1)/2 turns out
to be of particular significance. As well as discussing random tumbling of a
single body, I will also mention some results on the singularities of
orientation vector fields of small bodies advected in
random flows. This talk reports joint work with Alain Pumir
(ENS, Lyon) and Vlad Bezuglyy
(Open University).
Experimental
Studies of Lagrangian Acceleration and Pair
Dispersion in Thermally-Driven Turbulence [Back] |