Heavy particles in turbulent flows - CNRlagr05/pdf/cencini.pdf · M.Cencini Challenging Turbulent...

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


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


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)


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


Details of DNSDetails of DNS

Main aim:Generate a database of heavy particlestrajectories to systematically study theirdynamics and statistics vs St and Re


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


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


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)


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


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))


Two mechanismsTwo mechanisms

Preferential concentration Filtering


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


Preferential concentrationPreferential concentration

Fluid acceleration

Fluid acc. conditioned on particle positions

Heavy particle acceleration


FilteringFiltering

Fluid acceleration

Filtered fluid acc. along fluid trajectories

Heavy particle acceleration


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)


Inertia brings out of vorticesInertia brings out of vortices


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)


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


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


Acceleration correlation functionsAcceleration correlation functions


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


Transient and BulkTransient and Bulk

Transient finishes when the second moment of the coarsegrained (on a 2 volume) density reaches stationarity

256 || 512 ||

!


Signature of vortices may still beSignature of vortices may still bepresentpresent

Heavy particles in turbulent flows - CNRlagr05/pdf/cencini.pdf · M.Cencini Challenging Turbulent...

Documents

Transcript of Heavy particles in turbulent flows - CNRlagr05/pdf/cencini.pdf · M.Cencini Challenging Turbulent...