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
Department of Energy Technology, University of Udine, Italy
Deposition and reentrainment Issues,Sedimentation, Depulverization
Environmental MotivationsRole of Turbulence still unclear ... Beside being Difficult to Model accurately for process prediction
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
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Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
So we can measure particle segregation, as a function of the wall distance and as a function of particle inertia
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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.
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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>>
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
... 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.
Department of Energy Technology, University of Udine, Italy
Filtering DNS to obtain the ideal LES
Filtered Coarsening 4
Filtered Coarsening 8
... Can we fix the Error? Perhaps find a subgrid scale model ...
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
... 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
Department of Energy Technology, University of Udine, Italy
Thankful to …
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
Department of Energy Technology, University of Udine, Italy
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….
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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);
Department of Energy Technology, University of Udine, Italy
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
Department of Energy Technology, University of Udine, Italy
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
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Collisions increase particle fluctioations and the overall turbulentkinetic energy of particles is increased for all the St numbers.
Department of Energy Technology, University of Udine, Italy
St = 20
St = 40
St = 10.76
St = 100
Department of Energy Technology, University of Udine, Italy
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)
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Outline
Department of Energy Technology, University of Udine, Italy
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?
Department of Energy Technology, University of Udine, Italy
A vertical bubbly two-Phase FlowBubbles modify Turbulence?
Department of Energy Technology, University of Udine, Italy
A vertical bubbly two-Phase FlowBubbles modify Turbulence?
Department of Energy Technology, University of Udine, Italy
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…
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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.
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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
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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.
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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
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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