Physics of Turbulent Dispersed Flows and Simulation Approaches · Particles settling velocity: ... Shearing and rutpure of large particles/droplets In turbulent shear flows (via diffuse

Physics of Turbulent Dispersed Flows Physics of Turbulent Dispersed Flows

and Simulation Approachesand Simulation Approaches

Centro Interdipartimentale di Fluidodinamica e Idraulica, Università di Udine

Dept. Fluid Mechanics, International Center for Mechanical Sciences, Udine

Alfredo Soldati Alfredo Soldati

Applied Mathematics In Savoie, 2012

"Multiphase phase flow in industrial and environmental engineering

.Engineers and Applied Mathematicians talk together"

June 19-21 2012, Chambery, Savoie

The simplest archetypal problem…

We focus on the problem of the one single particle in a fxed vortex and we try to quantify the tendency of a particle to escape the flow streamlines.

Motion Παρα φυσι ν (according to Nature): Motion along the tangent

Motion Κ ατα φυσι ν (against Nature): Centrifugal Motion

Department of Energy Technology, University of Udine, Italy

... What if we add vortices? The problem becomes non-trivial with …preferential segregation (Maxey M. R., 1987, Phys. Fluids, 30(7), 1915-1928.)

Light particles: τp << τf

Particle Relaxation Time:

Flow Time Scale:

Particle Stokes number:

Intermediate particles: τp ≈ τf

Heavy particles: τp >> τf

Heavy Particles

Particles settling velocity: vs = dp2g(ρp-ρf)/(18 µ)

If we add vortices settling of heavyParticles under gravity becomes non-trivial with segregation (focusing)

... And it gets more complicated if we add vortices AND Gravity.(Maxey M. R., 1987, Phys. Fluids, 30(7), 1915-1928.)

Industrial MotivationsRole of Turbulence Clear. Difficult is accurate modelling for process optimization

Energy Issues: Clean Combustion


Deposition and reentrainment Issues,Sedimentation, Depulverization

Environmental MotivationsRole of Turbulence still unclear ... Beside being Difficult to Model accurately for process prediction


Cloud Physics Issues: Rain Generation

Plancton dynamics, environmental fluxes

Q. J. R. Meteorol. Soc. (2005), 131, Spatial distribution of cloud droplets in a turbulent cloud-chamber flowA. JACZEWSKI and S. P. MALINOWSKI

Turbulence Effect on Cloud RadiationK. Matsuda, R. Onishi, R. Kurose, and S. Komori

Environmental MotivationsRole of Turbulence still unclear ... Beside being Difficult to Model accurately for process prediction


Cloud Physics Issues: Rain Generation

Plancton dynamics, environmental fluxes

PNAS (2004) 101Turbulence increases the average settling velocity of phytoplankton cellsJ. Ruiz, D. Macìas, and F. Peters

Phys. Fliuds (2007) 19Influence of added mass on anomalous high rise velocity of light particles in cellular flow field: A note on the paper by Maxey 1987 C. Marchioli, M. Fantoni, and A. Soldati

Stokes Number

Particle Stokes number: with

… and which Flow Time Scale?

Usually a scale which scales With the particles.

Toschi et al.Instantaneous position of St =1 particles slice View: Particles accumulate into Regions which are called Caustics

Number concentration of Particles(By Maurizio Picciotto)

Particles in Homogeneous Isotropic Turbulence Scale Nicely with Kolmogorov Time Scale

An Environmental Application: Floaters on a free surface ... Not at all Kolmogorov Scaling

In this experiment floaters with ρ=900 kg/m3

floaters surface and are driven by the surface turbulencee

Two-dimensional Divergence:

Red: Positive – Diverging Flow

Blue: Negative --- Converging Flow

Top view of the particles and of the surface coloured with the pseudo-divergence

An interesting Segregation Pattern throughVoronoï Tessellation (…another segregation parameter)

... But if we are interested in boundary Layers …Kolmogorov scaling seems not the right one

Better the Wall variables scaling (Shear Based)

Wall


Centerline

Channel flow is a multiscale phenomenon, particles ‘visit’ all possible regionsOf the domain and interact with ever changing scales. In addition, the strong shear which dominate the wall region gives structures a distinctly streamwise Stretched pattern.

St

Observation –

In Channel flow (like in pipe flow) particles accumulate at the wall at different rates depending on their inertia (forces:drag and inertia).

Phenomenology of particle dispersion in Boundary Layers

Microscale phenomena induce Macroscale Effects

St = 25

St = 5

St = 1

St= 0.2

Accumulation at the wall is turbulence induced and non uniform.This phenomenon will persist from a qualitative viewpoint even in presence of gravity, until particle weight will dominate (large particles). N

um

be

r

Co

nc

en

tr

at

io

n


Qualitative explanation of the instantaneous transfer processes.Deposition and Entrainment are controlled by turbulence Structures localized in time and space

Red: high Streamwise vel.

Blue: lowStreamwise vel.

Purple Particles: Going To the wall

Blue Particles: Going away off the wall


In our view, before predicting deposition we should predict preferential segregation

Regular distribution Random distribution Clustered Distribution

Σp = (σ-σp)/λ, with λ = average n. particles per cell; σ = standard deviation


So we can measure particle segregation, as a function of the wall distance and as a function of particle inertia


Different times III, IV and V seems stable

particle (st=25) tend to have maximum Segregation Around z+= 10

But particles of different size segregate In different ways (at z+=10)

Here also the comparison of the DeviationFrom Poisson with the correlation dimension(Grassberger P, Procaccia I. Measuring the strangeness ofstrange attractors. Physica D. 1983; 9: 189-194.

Larger particles Will deposit due also to their inertia, coming directly from Far Away

If particles are influenced (but not dominated) by inertia, the Deposition Occurs in two steps: First Segregation into a space region and then deposition to the wall. It is found that deposition has a maximum for those particles for which segregation has a maximum

Kd

+

�

Kd+ =

J

C=

1

Ad

�dN(t)

dtN(t)V


Probability Density Function of droplet acceleration due to Turbulent fluctuations AND inertia (PDF is normalized by gravity)

Does this have an effect on Rain Generation?

The probability of having droplets with acceleration larger than gravity is large (one droplet over one thousand)

+g-g

Z. Warhaft and L. Collins (DNS of HIT)

…Collision rates and collision efficiency (coalescence) are related Toturbulence particle interactions. Clustering at small scales is

related to strong fluid accelerations.


Statistics of Acceleration for fluid particles and inertial particles are different because of inertial effects and gravitational effects. We start from an experimental work of Gerashchenko et al., 2008 JFM 617, 255-281 Data obtained with a camera moving with the flow

1. How does the presence of shear affect the Lagrangian acceleration statistics of inertial particle motion?2. What is the effect of gravity on particle acceleration statistics in wall-bounded turbulent flow?

Particle acceleration in a turbulent boundary layer:

• High speed Lagrangian tracking technique • St = τp/τh = 0.035, 0.07, 0.47• Reτ = 470, 830

OBS: With increasing St number the acceleration variance is increasing and the pdf tails become more skewed

From the experiment it is evident that large tails Exist and that they depend on particle size

… what is the specific role of shear and gravity?

DNS Experiments

Reτ 300 470 and 830

St 1 = τp uτ2/n 0.80 0.80

St 2 = τp uτ2/n 1.60 1.60

St 3 = τp uτ2/n 10.76 10.76


Z+

Hom. Iso.

Bound.Layer

Benchmark the Shear Turbulence Experiment in Cornell (Lavezzo et al., J.Fluid Mech. 2010)

Pdf of particle streamwise acceleration at Varying distance from the wall.

Symbols: ExperimentLines: DNS

St= 0.80

St= 10.76

St= 1.60


1. Pdf’s are narrower for larger Particles2. Pdf’s become more skewed for larger particles3. Pdf’s become more skewed approaching the walls

Causes will be SHEAR AND GRAVITY


Gravity is crucial even for small particles.Without gravity particles cannot decorrelate from the fluid

Enough to undergo strong Acceleration/deceleration

St (Inertia) without Gravity = All the same with the fluid

St (inertia) with Gravity = Strong Differences

So, it is the gravity! The shear alone could not make us believe that they were inertial particles.

… and now to Modelling. We need to save on CPU Time/space What is filtering? Try with the Caspian Sea

Non Filtered

Filtered

...but if particles are larger than the filter scale?

Large is the price to compute this High Frequency part of the Spectrum!

Τp<<ΤpΤp>>


Significant underestimation of wall

concentration for large particles

LES is tested on the prediction of particle concentration.Unfortunately it does not maintain expectations…. Of course, the test is hard… it is the time integral of the deposition flux


St=1

St=5

St=25

... and the reason for wrong underestimated deposition is wrong estimate of local segregation ...

Influence of the Stokes number on local particle segregation

Z=H (channel centerline)Z<0.15H (near-wall region)

LES predicts LESS segregation for larger particles and MORE segregation for smaller particles. These results in bounded flow confirm

previous results by Simonin in HIT

LES

DNS LES

DNS

LES

DNS

LES

DNS


... Sources of errors in A-Priori TestsThese errors are bound to be affected by Inertia!

Blue (DNS);

Light Blue Filter);

White (Coarser Filter)

It seems that modelling has to fix two sourcesOf errors: The filtered flow field and the wrong position of the particle.


Filtering DNS to obtain the ideal LES

Filtered Coarsening 4

Filtered Coarsening 8

... Can we fix the Error? Perhaps find a subgrid scale model ...


We compute the Fluid Velocity seen by Particles in DNS andDNS-Filtered Fields.

Then We make the Difference.

We compute this Difference along Particle traj. In DNSFields.

... and before finding a model we should aim for theWork this model should do ... Therefore compute the error


... and before finding a model we should aim for theWork this model should do ... Therefore compute the error

... And the error has a shape which changes with space and inertia


Thankful to …


Coworkers: Cristian Marchioli, Maurizio Picciotto, Coworkers: Cristian Marchioli, Maurizio Picciotto, Andrea Giusti, Valentina Lavezzo, Marina Andrea Giusti, Valentina Lavezzo, Marina Campolo, Stella Dearing, Dafne MolinCampolo, Stella Dearing, Dafne Molin

Funding from: Ministry of Research, Ministry of Funding from: Ministry of Research, Ministry of Production, Regional AuthorityProduction, Regional Authority

Other Interests



Stable / Unstable stratificationWith Temperature dependent Physical Properties

stable stratification

Neutrally-buoyant

IGW (Internal gravity waves)

unstable stratification

Thermal plumes and large scale convection

Shearing and rutpure of large particles/droplets Shearing and rutpure of large particles/droplets In turbulent shear flows (via diffuse interface In turbulent shear flows (via diffuse interface models – Cahn Hilliard)models – Cahn Hilliard)

Re = 150, Ch = 0.025, Pe = 2000, Ca=8.25, 256x128x129, ∆ t = 10-5

Shearing and rutpure of large particles/droplets Shearing and rutpure of large particles/droplets In turbulent shear flows (via diffuse interface In turbulent shear flows (via diffuse interface models – Cahn Hilliard)models – Cahn Hilliard)

Re = 150, Ch = 0.025, Pe = 2000, Ca=8.25, 256x128x129, ∆ t = 10-5

the simplest light particle rising

( ) ( ) gVvuvuD

Cdt

vdm

pFppp

p

D

p

p

ρρρπ −+−−=42

1 2

FG

FDFP

Force balance

• FP Gravity

• FG Buoyancy

• FD Drag

•Stokes Regime(, Rep<1)

•Steady State( )µ

ρρ18

2 gDv FppStokes

p

−

=

Notions on the influence of inertia on the motion of a) particles heavier than the fluid and b) particles lighter than the fluid:

Inertial Particles segregate in

low vorticity, high strain regions

Particles Settling under gravity Bubbles Rising under gravity

Bubbles segregate in high vorticity, low strain regions

a. Inertia will drive particles out of the vortices increasing settling; b. Lack of inertia drive bubbles at the center of vortices, trapping them.

(Maxey, PoF 1986, Wang and Maxey, JFM 1993, Provenzale, AnnuRev 1999)

... a simple model

Object is to study the behavior of particle only slightly lighter than the surrounding fluid in a Taylor-Green Cellular Flow.

• We will reproduce the numerical model of Maxey PoF (1987);

• Particle/fluid density: ρp/ρf [0.5:1.0]

• Forces Acting: Inertia; Gravity; Buoyancy; Added Mass

• many forces dominate particle motion: added mass, lift, Basset…

( )

( ) ττπν

τµπµπ d

t

duvdauva

uvdt

dm

Dt

uDmgmm

dt

vdm

tp

p

pFFFpp

p

∫ −−

−−−

−−+−=

0

2

)(

/)(66

2

1)(

Maxey and Riley, 1983

... a simple model and perhaps a nice result

Mean rise velocity, <Vy>, of light particles in (Taylor-Green) vortex flow versus particle-to-fluid density ratio, ρp/ρf (Marchioli et al., PoF, 2007 ???)

... non trivial behavior of the model

8.0=Fp ρρ 950.0=Fp ρρ 98.0=Fp ρρ

Formation of clusters

Segregation at cell boundary

Emptying clusters, limit cycles

Conclusions….


SOLOMON saith, There is no new thing upon the earth. So that as Plato had an imagination, That all knowledge was but remembrance; so Solomon giveth his sentence, That all novelty is but oblivion.

Francis Bacon, England, Natural Scientist, ‘Essays ‘(no.58)

Plato, Greece, Physicist,

Solomon, Israel and Wise man, ‘Ecclesiastes’.

Jorge Luis Borges, Argentina, Writer, ‘the Immortal’.

Collisions add a further degree of randomness to the system.What do we expect if we take collisions into account? A Different energy distribution perhaps…?

The kinetic energy associated with each particle may increase or decrease due to collisions effects. This change will have an impact also on the overall particle energy.

( )

( )687.0Re15.01Re

24

ˆ2

3

pp

D

pppp

Dp

C

guuuud

C

dt

dv

+=

+−−

= ρ

ρρ

• Tend to decorrelate particles with the coherent eddies that are responsible for their accumulation (Li et al., 2001);

• Tend to suppress small wave-lengths in the energy spectrum (Li et al., 2001);

• Increase the interaction between particles and carrier fluid (Li et al., 2001);


How can the energy be transferred? We can group collisions in two different kind: High Energy and Low Energy

Depending on the relative velocity between the colliding particles:

High energy collisions

Characterized by possible particle resuspension

Low energy collisions

Characterized by multiple collision events

Wall

Viscous sublayer

Viscous sublayerBuffer layer


How can the energy be transferred? We can group collisions in two different kind: High Energy and Low Energy

Depending on the relative velocity between the colliding particles:

Low energy collisions

Characterized by multiple collision events


Collisions increase particle fluctioations and the overall turbulentkinetic energy of particles is increased for all the St numbers.


St = 20

St = 40

St = 10.76

St = 100


How can the energy be transferred? We can group collisions in two different kind: High Energy and Low Energy and efficiency of collisions

Increasing Stokes number

For the same number concentration of particlesThe number of collisions and the relative Velocity at which they occur will change for increasing the stokes number :

This has to do with The motion of particles being less and less correlated with that of the fluid

Smaller particles

Larger particles

Physical Background: we can picture particle deposition to the wall as a multi-step process: Particles are FIRST Accumulated in the buffer Region and Then Deposited

Turbulent Particle Deposition to a wall:Physics from DNS (See also Fridlander and Johnstone, 1957)


Outline


1.1. Introduction and Literature ReviewIntroduction and Literature Review

2.2. Particle Deposition onto a SurfaceParticle Deposition onto a Surface

1.1. Acceleration Statistics for Physical InsightAcceleration Statistics for Physical Insight

2.2. Breakup and AgglomerationBreakup and Agglomeration

3.3. An outlook into Vacuity: MicrobubblesAn outlook into Vacuity: Microbubbles

4.4. LES and Modelling IssuesLES and Modelling Issues

1.1. ConclusionsConclusions

A vertical bubbly two-Phase FlowBubbles modify Turbulence?






Breakup of Aggregates

Macroscopic scale

Mesoscopic Scale

Microscopic Scale

25%

20%

15%

10%

5% 0%Solid Volume Fraction

1 m1 cm

1 μm100 μm

Laboratory scale

Breakup of Aggregates Esempi di misure sperimentali:

‟pulverization event”

Courtesy of A. Liberzon - Copyright (c) IfU, ETH Zurich http://www.ifu.ethz.ch/GWH/index_EN

Da: Institute for Chemical and Bioengineering, Prof. M. Morbidelli, Politecnico di Zurigo

Quando avviene la rottura degli aggregati?

La rottura avviene quando la dissipazione di energia nella posizione dell’aggregato supera il

valore critico per la prima volta

La rottura avviene quando la dissipazione di energia nella posizione dell’aggregato supera il

valore critico per la prima volta

Velocity gradients

Example: M.U. Bäbler, L. Biferale, A.S. Lanotte

(2011) Submitted

La grandezza chiave: Energy Dissipation Rate

errorbar = RMS

10

40

150

LO

G(

ε)

LOG(ε)

PD

F(

ε)

Analisi dei risultati:Fragmentation Rate

M.U. Bäbler, L. Biferale, A.S. Lanotte (2011) Submitted

Stima del tasso di frammentazione

Mean Exit Time

Exponential Fit

... A little Literature search on the influence of inertia on the Behavior of a floating body immersed in a vortical fluid.

First report is an oral report….

… to the best of my knowledge, the blind bard,Homer , was the first to report on this problem.

… he reported about the ten years long trip of Odysseus in his poem, the Odissy. Odysseus sailed in aboat all over the Mediterranean sea, from Troy back to Ithaca. At a certain point, he had to pass between Sicily and continental Italy, trhough a dangerous strait…


Homer investigated the problem of a body trapped into a vortex whenHe tells about the boat trip of Odysseus. Odysseus is confronted

with a Terrible dilemma: Which death to choose!

Homer knows from the ‘tales’ of the sailors about the dangerous vortices produced by the mixingstreams in the Strait. And he also knows that sailors give responsibility to two monsters

SKYLLA (or Scylla) was a monstrous sea goddess who haunted the rocks. Ships who sailed too close to her rocks would lose six men to her ravenous, darting heads.

KHARYBDIS (or Charybdis) was a sea monster whose gigantic whirlpool swirled in the straits of Messina, She was probably the goddess of the tides, with her triple drawing-expulsion.


Homer reports ion the advice Odysseus receives from an Ancient Scientist. Kirke…

Odysseus in front of Scylla and Charybdis, in Henry Fuseli's (Aarau, Art History Museum) Romance painting of Odysseus (1794-1796 ) facing the choice of monsters, giving the phrase: between Scylla and Charybdis, the meaning of the necessity of a choice between bad and bad …

KIRKE (or Circe) was a goddess pharmakeia (witch or sorceress or she-scientist) who lived with her nymph attendants (students!) on the mythical island of Aiaia. She was skilled in the magic of metamorphosis, the power of illusion, and the dark art of necromancy.

Odysseus is a proto-engineer and tries to optimizeThe apparently stiff physics … he is sent by Homer to ask advice from Kirke


And Kirke, of course with ominous and obscure words, tellsAbout the inertia necessary to escape the trapping vortex…

So, what was the advice of Kirke ? She knew that inertia (characteristic time) of the boat was small! Her advice was to change the initial conditions! First time documented (albeit orally) proof of the definition of the Particle Characteristic time.


Smaller initial velocityCharybdis Wins

Larger initial velocityNobody Wins

In this articstic rendering we can see Odysseus towards new adventures, made bold by his successes And deriding Polyphemus (William Turner, ‘Odysseus deriding Polyphemus’, National Gallery, London

Fil Rouge


1.1. Particle Clustering by Turbulence is ImportantParticle Clustering by Turbulence is Important

2.2. Influence of Scales on Clustering Influence of Scales on Clustering

3.3. Influence of Clustering on Particle Transfer in Influence of Clustering on Particle Transfer in Bounded FlowsBounded Flows

4.4. Acceleration Statistics for Physical InsightAcceleration Statistics for Physical Insight

1.1. LES and Modelling IssuesLES and Modelling Issues

1.1. ConclusionsConclusions

Documents

Physics of Turbulent Dispersed Flows and Simulation Approaches · Particles settling velocity: ... Shearing and rutpure of large particles/droplets In turbulent shear flows (via diffuse