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Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
HHeavy particles eavy particles in in turbulent turbulent flowsflows
Massimo Massimo CenciniCencini CNR-ISC Roma
INFM-SMC Università “La Sapienza” Roma
Massimo.Cencini@ roma1 . infn. itMassimo.Cencini@ roma1 . infn. it
In collaboration w ith
J. Bec, L. Biferale, G. Boffetta, A. Celani, A. Lanotte, S. J. Bec, L. Biferale, G. Boffetta, A. Celani, A. Lanotte, S. MusacchioMusacchio , F. Toschi, F. Toschi
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
OutlineOutline
Motivation and recall of basic equationsMotivation and recall of basic equations (very short) Details of numerical experimentsDetails of numerical experiments
Single particle propertiesSingle particle properties
Acceleration statistics
Lagrangian intermittency and vortex trapping
Conclusions and perspectivesConclusions and perspectives
J. Bec, L. Biferale, G. Boffetta, A. Celani, MC, A. Lanotte,S.Musacchio & F. Toschi, nlin.CD/050812 JFM under consideration
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
MotivatioMotivationsnsRain drops in clouds Rain drops in clouds (G. Falkovich et
al. Nature 141, 151 (2002)) clustering enhanced collision rate
Formation of planetesimals in theFormation of planetesimals in thesolar system solar system (J. Cuzzi et al. Astroph. J. 546, 496(2001) A. Bracco et al. Phys. Fluids 11, 2280 (2002))
Optimization of combustion processes inOptimization of combustion processes indiesel engines diesel engines (T.Elperin et al. nlin.CD/0305017)
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Equations of motion & assumptionsEquations of motion & assumptionsDissipative range physicsHeavy particlesParticle Re <<1Very dilute suspensions: no dynamical role of collisions
!<<a
fp!! >>
1vRea
<<= !aa
!=
=
),([1)(
)()(
tXudt
tdV
tVdt
tdX
s" Stokes number
!"
"#
f
p
s
a2
9
2=
Response timeStokes Time
!"
"s
St =
(Maxey & Riley Phys. Fluids 26, 883 (1983))(Maxey & Riley Phys. Fluids 26, 883 (1983))
u(x,t) u(x,t) is a turbulent and is a turbulent and incompressibleincompressible fluid velocity fieldfluid velocity field
Dynamics & Statistics as a function of StDynamics & Statistics as a function of St & Re & Re??
)](tV
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Details of DNSDetails of DNS
Main aim:Generate a database of heavy particlestrajectories to systematically study theirdynamics and statistics vs St and Re
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Simulation organizationSimulation organizationInitial particles configuration Heavy particles with 15 St ([0.1,3]) and passive tracers are homogeneously
injected as couples in a stabilized homogeneous and isotropic turbulent flow Particles having different St starts from coincident locations The initial velocity of heavy particles is set equal to the local fluid velocity
Recorded information Fast: for a subset of trajectories the full history X,V,u each 0.1 Slow: X,V,u for all particles together with the eulerian field each 10 Some particles are advanced together with their tangent space dynamics
in order to compute the full Lyapunov exponent spectrum
Notes The data set is dividend in Transient (~2-3TL)+ Bulk (~3-6TL) Eulerian field forced by fixing the energy content of the low-k shells
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
DNS summaryDNS summary
Resolution 1283, 2563, 5123
Pseudo spectral codeNormal viscosityCode fully parallelized MPI+FFTWPlatforms: SGI Altix 3700, IBM
SP4Runs over 7 - 30 days 1TB
900 +2100
(15+1)/(32+1)
7.5Millions
500.000
120Millions
5123
15+1(15+1)/(32+1)Stokes/Lyap
70GB400GBDisk usage
600+1200756 +1744Traject. Length
250.0002MillionsSlow 10
32.000250.000Fast 0.1
4Millions32MillionsTot #particles
12832563N3
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Plan of our investigationPlan of our investigation Single particle properties: Single particle properties: (this talk)(this talk)
Acceleration statistics Velocity statistics Conditional statistics
Two particles properties:Two particles properties: Relative dispersion Lyapunov exponents
Clustering and collision rates: Clustering and collision rates: (see Bec talk)(see Bec talk) Small scales clustering (fractal dimensions) Large scales clustering (in the inertial range) Collision rates (ghost collisions)
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
AccelerationAcceleration
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
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Acceleration statisticsAcceleration statisticsAt increasing St: strong dep let ion ofboth rm s acc. and pdf tails. Note thesharp fall off of the f latness.
Residual dependence on Re verysim ilar to that observed for tracers.
(Sawford et al. Phys. Fluids 15, 3478 (2003);Borgas Phyl. Trans. R. Soc. Lond A342, 379 (1993))
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Two mechanismsTwo mechanisms
Preferential concentration Filtering
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Preferential concentration and filteringPreferential concentration and filtering
Heavy particles acceleration
Fluid acc. conditioned on p. positions good at St<<1
Filtered fluid acc. along fluid traj. good at St>1
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Preferential concentrationPreferential concentration
Fluid acceleration
Fluid acc. conditioned on particle positions
Heavy particle acceleration
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
FilteringFiltering
Fluid acceleration
Filtered fluid acc. along fluid trajectories
Heavy particle acceleration
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Dynamical featuresDynamical features
From passive tracers studies we knowthat wild acceleration events come
from trapping in strong vorticestrapping in strong vortices.
(La Porta et al 2001)
(Biferale et al 2004)
Inertia expels particles from strongvortices leading to acceleration depletion
(this is another way to see the effect ofpreferential concentration)
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Inertia brings out of vorticesInertia brings out of vortices
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Lagrangian intermittencyLagrangian intermittency
Some recent studies on Lagrangian Intermittency of fluid tracersSome recent studies on Lagrangian Intermittency of fluid tracers Mordant et al Phys. Rev. Lett. 87, 214501 (2001), New J. Phys. 6, 116 (2004)
Biferale et al. Phys. Rev. Lett. 93 064502 (2004); nlin.CD/0501041
Characterization of small scale intermittencyCharacterization of small scale intermittency
Develop Lagrangian stochastic models valid in theDevelop Lagrangian stochastic models valid in theinertial rangeinertial range
M.Cencini Challenging Turbulent Lagrangian Dynamics
Eulerian vs Lagrangian IntermittencyEulerian vs Lagrangian IntermittencyEulerian intermittency (Multifractal Model)
Lagrangian intermittency (fluid tracers)
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Depletion of the vortex trappingDepletion of the vortex trapping
St=0 St=0 St=0.16St=0.16 St=0.37St=0.37S6 vs S2
S4 vs S2
To quantify differences in the scalingexponents we need higher resolution
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Acceleration components andAcceleration components andtype of motionstype of motions
^^
^
)( VVaa
Vaa
l
c
!=
"=
Looking at the correlation functions of thecentripetal component (which is persistent intrue spiraling motion) one can quantify the roleof vortical motion (Biferale et al 2004)
CentripetalCentripetal
LongitudinalLongitudinal
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Acceleration correlation functionsAcceleration correlation functions
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Conclusions & Conclusions & PerspectivesPerspectives Depletion of Lagrangian intermittency due to
Dynamical viewpoint: reduced vortex trapping(though vortical motion is still present andimportant)
Preferential concentration
Filtering
? Conditional statistics
? Model for heavy particle acceleration (Multifractal model?)
? Higher resolution DNS (10243) to probe larger Re & quantify…..Lagrangian scaling exponents
? Measuring small scale flow properties at particle positions (i.e.fluid …..velocity gradients) : statistical properties in terms of thelocal St
? Develop (or test the validity of existing) stochastic Lagrangian…...models
Castel Gandolfo 1-4 September 2005 M.Cencini Challenging Turbulent Lagrangian Dynamics
Transient and BulkTransient and Bulk
Transient finishes when the second moment of the coarsegrained (on a 2 volume) density reaches stationarity
256 || 512 ||
!
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