Upload
maeve-hamblen
View
220
Download
0
Tags:
Embed Size (px)
Citation preview
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
InertialInertial particles in particles in turbulenceturbulence
Massimo CenciniMassimo Cencini CNR-ISC Roma
INFM-SMC Università “La Sapienza” Roma [email protected]@roma1.infn.it
In collaboration with:
J. Bec, L. Biferale, G. Boffetta, A. Celani, A. Lanotte, S. Musacchio & F. Toschi
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Problem:Problem: Particles differ from fluid tracers their dynamics is dissipative due to inertia one has preferential concentration
GoalsGoals:: understanding physical mechanisms at work,characterization of dynamical & statistical properties
Main assumptionsMain assumptions: collisionless heavy & passive particles in
the absence of gravity
In many situations it is important to consider finite-size (inertial) particles transported by incompressible flows.
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Rain drops in cloudsRain drops in clouds (G. Falkovich et al. Nature 141, 151 (2002))
clustering enhanced collision rate
Formation of planetesimals in Formation of planetesimals in thethe
solar system solar system (J. Cuzzi et al. Astroph. J. 546, 496 (2001); A. Bracco et al. Phys. Fluids 11, 2280 (2002))
Optimization of combustion Optimization of combustion processes inprocesses in diesel enginesdiesel engines (T.Elperin et al. nlin.CD/0305017)
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Equations of motion & Equations of motion & assumptionsassumptions
Dissipative range physics
Heavy particles
Particle Re <<1
Dilute suspensions: no collisions
η<<a
fpρρ >>1vRe
a<<= νaa
Stokes number
Response time Stokes Time
(Maxey & Riley Phys. Fluids (Maxey & Riley Phys. Fluids 2626, 883 (1983)), 883 (1983)) Kolmogorov ett Kolmogorov ett
u(x,t) (incompressible) fluid velocity fieldu(x,t) (incompressible) fluid velocity field
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
PhenomenologyPhenomenology
Preferential concentration:particle trajectories detach from those of tracers due to their inertia inducing preferential concentration in peculiar flow regions. Used in flow visualizations in experiments
Dissipative dynamics:The dynamics is uniformly contracting in phase-space
with rateAs St increases spreading in velocity direction --> caustics
This is the only effect present in Kraichnan models
Note that as an effect of dissipation the fluid velocity islow-pass filtered
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Direct numerical Direct numerical simulationssimulations
After the fluid is stabilized
simulation box seeded with millions of particles and tracers injected randomly& homogeneously with
For a subset the initial positions of different Stokes particles coincide at t=0
~2000 particles at each St tangent dynamics integrated for measuring LE
Statistics is divided in transient(1-2ett) + Bulk (3ett)
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
DNS summaryDNS summary
Resolution 1283, 2563, 5123
Pseudo spectral code
Normal viscosity
Code parallelized MPI+FFTW
Platforms: SGI Altix 3700, IBM-SP4
Runs over 7 - 30 days
N3 5123 2563 1283
Tot #particles 120Millions
32Millions 4Millions
Fast 0.1 500.000 250.000 32.000
Slow 10 7.5Millions 2Millions 250.000
Stokes/Lyap (15+1)/(32+1)
(15+1)/(32+1)
15+1
Traject. Length
900 +2100 756 +1744 600+1200
Disk usage 1TB 400GB 70GB
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Particle Clustering Particle Clustering
Important in optimization of Important in optimization of reactions, reactions,
rain drops formation….rain drops formation….
Characterization of fractal aggregatesCharacterization of fractal aggregates
Re and St dependence in turbulence?Re and St dependence in turbulence?
Some studies on clustering:Some studies on clustering: Squires & Eaton Phys. Fluids 3, 1169 (1991)
Balkovsky, Falkovich & Fouxon Phys. Rev. Lett. 86, 2790 (2001)
Sigurgeirsson & Stuart Phys. Fluids 14, 1011 (2002)
Bec. Phys. Fluids 15, L81 (2003)
Keswani & Collins New J. Phys. 6, 119 (2004)
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Two kinds of clusteringTwo kinds of clusteringParticle preferential concentration is observed both
in the dissipativedissipative and in inertialinertial range
Instantaneous p. distribution in a slice of width ≈ 2.5η. St = 0.58 R = 185
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Small scales clusteringSmall scales clustering• Velocity is smooth we expect fractal distribution
• Probability that 2 particles are at a distance • correlation dimension D2
Use of a tree algorithm to measure dimensions at scales
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Correlation dimensionCorrelation dimension D2 weakly depending on Re
Maximum of clustering for
Particles preferentially concentrate in Particles preferentially concentrate in
the hyperbolic regions of the flow.the hyperbolic regions of the flow.
Maximum of clustering seems to beMaximum of clustering seems to beconnected to preferential connected to preferential concentrationconcentration
but Counterexample: inertial p. in Kraichnan flow
(Bec talk)
Hyperbolic non-hyperbolic
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Multifractal distributionMultifractal distribution
Intermittenc
y in the mass
distribution
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Lyapunov dimensionLyapunov dimension
d D1 provides information similar to D2
can be seen as a sort of “effective” compressibility
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Inertial-range clusteringInertial-range clustering
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Characterization of clustering in the inertial Characterization of clustering in the inertial rangerange (Preliminary & Naive) (Preliminary & Naive)
From Kraichnan model ===> we do not expect fractal distribution
(Bec talk and Balkovsky, Falkovich, Fouxon 2001) Range too short to use local correlation dimension or similar
characterization
Coarse grained mass: Coarse grained mass:
St=0 ==> Poissonian
St0 ==> deviations from Poissonian. How do behave moments and PDF of the coarse grained mass?
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
PDF of the coarse-grained massPDF of the coarse-grained mass
r
s
Deviations from Poissonian are strong & depends on s, r
Is inertial range scaling inducing a scaling for
Kraichnan results suggest invariance for (bec talk)
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Collapse of CG-mass Collapse of CG-mass momentsmoments
Inertial range
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Sketchy argument for Sketchy argument for ss/r/r5/35/3
True for St<<1 (Maxey (1987) & Balkovsky, Falkovich & Fouxon (2001))
Reasonable also for St(r)<<1 (i.e. in the inertial range)
<-- Rate of volume contraction
<-- from the equation of motion
The relevant time scale for the distribution of particles is that which distinguishes their dynamics from that of tracers
can be estimated as
The argument can be made more rigorous in terms of the dynamicsdynamics of the quasilagrangian mass distributionof the quasilagrangian mass distribution and using the rate of
volume contraction. But the crucial assumption is
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Scaling of accelerationScaling of accelerationControversial result about pressure and pressure gradients(see e.g. Gotoh & Fukayama Phys. Rev. Lett. 86, 3775 (2001) and references therein)
Our data are compatible with the latter
Note that this scaling comes from assumingthat the sweeping by the large scales is the leading term
We cannot exclude that the other spectra may be observed at higher Re
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Single point acceleration Single point acceleration propertiesproperties
Some recent studies on fluid acceleration:Some recent studies on fluid acceleration: Vedula & Yeung Phys. Fluids 11, 1208 (1999)
La Porta et al. Nature 409, 1011 (2001) ; J. Fluid Mech 469, 121 (2002)
Biferale et al. Phys. Rev. Lett. 93, 064502 (2004)
Mordant et al. New J. Phys. 6, 116 (2004)
Probe of small scale intermittencyProbe of small scale intermittency
Develop Lagrangian stochastic modelsDevelop Lagrangian stochastic models
What are the effect of inertia?What are the effect of inertia?
Bec, Biferale, Boffetta, Celani, MC, Lanotte, Musacchio & Toschi
J. Fluid. Mech. 550, 349 (2006); J. Turb. 7, 36 (2006).
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Acceleration statisticsAcceleration statisticsAt increasing St: strong depletion of both rms acc. and pdf tails.
Residual dependence on Re very similar to that observed for tracers.
(Sawford et al. Phys. Fluids 15, 3478 (2003);Borgas Phyl. Trans. R. Soc. Lond A342, 379
(1993))
DNS data are in agreement with experiments by Cornell group(Ayyalasomayajula et al. Phys. Rev. Lett. Submitted)
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Two mechanismsTwo mechanisms
Preferential concentration
Filtering
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Preferential concentration & Preferential concentration & filtering filtering
Heavy particles acceleration
Fluid acc. conditioned on p. positions good at
St<<1
Filtered fluid acc. along fluid traj. good at St>1
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Preferential concentrationPreferential concentration
Fluid acceleration
Fluid acc. conditioned on particle positions
Heavy particle acceleration
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
FilteringFiltering
Fluid acceleration
Filtered fluid acc. along fluid trajectories
Heavy particle acceleration
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
Dynamical featuresDynamical featuresFrom passive tracers studies we know
that wild acceleration events comefrom trapping in strong vorticestrapping in strong vortices.
(La Porta et al 2001)
(Biferale et al 2004)
Inertia expels particles from strongvortexes ==> acceleration
depletion(a different way to see the effect of
preferential concentration)
Warwick, July 2006 M.Cencini Inertial particles in turbulent flows
ConclusionsConclusionsTwo kinds of preferential concentrations in
turbulent flows:Dissipative range: intrinsic clustering (dynamical attractor) tools borrowed from dynamical system concentration in hyperbolic regionInertial range: voids due to ejection from eddies Mass distribution recovers uniformity in a self-similar
manner (DNS at higher resolution required, experiments?) open characterization of clusters (minimum spanning
tree….??)
Preferential concentration together with the dissipative nature of the dynamics affects small scales as evidenced by the behavior of acceleration
New experiments are now available for a comparative study with DNS, preliminary comparison very promising!