(lecture 4 of 4) - Åbo Akademi | Startsidausers.abo.fi/rzevenho/iCFD17-RZ4.pdf · Introductionto...

Introduction to Computational Fluid Dynamics 424512 E #4- rz

oktober 2017 Åbo Akademi Univ - Chemical Engineering Thermal and Flow Engineering - Biskopsgatan 8, 20500 Turku

1/68

Introduction to Computational Fluid Dynamics(iCFD) 424512.0 E, 5 sp

4. Multi-phase flow (an introduction...)(lecture 4 of 4)

Ron ZevenhovenÅbo Akademi University

Thermal and Flow Engineering Laboratorytel. 3223 ; [email protected]

See alsoÅA course 424514 (4 sp) 424521 (5 sp)

Fluid and particulate systemshttp://users.abo.fi/rzevenho/kursRZ.html#FPS



2/68

4.1 Fluid flow around objects:external flows



3/68

Fluid flow around objects In the cases of

– an object moving through a fluid– a fluid flow around an object

the velocity difference generates forces Forces acting parallel to the flow direction are drag

forces; forces acting perpendicular to the flow direction are lift forces

The flow field around an object can be divided in two parts: the boundary layer, where the viscous forces are active, and the free-stream velocity (or the stagnant surrounding fluid) P

ictu

re: h

ttp://

ww

w.w

eird

richa

rd.c

om/im

ages

/forc

es.jp

g

PTG


For a general surface area A ┴

(m2) perpendicular to the flow, the drag force is

FD = CD· A┴· ½ρvr2

(where ½ρvr2 is actually the pressure

difference between the front and the back of the object)

with drag coefficient CD

With increasing Re-numbers, boundary layer separationoccurs, and a wake region (sv: köl(vatten)) ariseswhere kinetic energy is only partlyconverted into pressure


4/68

Picture: KJ05

Flowaround a cylinder

Flow around cylinders, spheres /1 PTG



5/68

Flow around cylinders, spheres /2 For spherical particles

the drag coefficientequals

For flow at Re <0.1 around a sphere, the relation CD=24/Re

follows also from Stokes’ law

Fdrag = 3πηvrd

for a sphere with diameter d and relative velocity vr = vsphere-vflow

Picture: KJ05

5

D

32

D

D

D

10Re800 for

0.44 C

800Re2 for

Re6

11

Re

24 C

2Re0.2 for

Re16

31

Re

24 C

0.2 or 1Re forRe

24 C

Picture: http://www.school-for-champions.com/science/friction_changing_fluid.htm

PTG



6/68

Boundary layer separation examples

Pic

ture

: http

://w

ww

.aer

ospa

cew

eb.o

rg/q

uest

ion/

aero

dyna

mic

s/q0

215.

shtm

l

Pic

ture

: http

://w

ww

.str

uctu

ral.n

et/n

ews/

Med

ia_c

over

age/

med

ia_p

lant

_ser

vice

s.ht

ml

PTG



7/68

A smooth (a) and roughened (b) ball entering water at 25 °C

CRBH83



8/68

Fluid flow over a surface

CRBH83



9/68

4.2 Particle (bubble, droplet, ...) sizedistribution, shape



10/68

Particle (or droplet) size distribution

Particle size, X

Fre

que

ncy

dis

trib

i tio

nX

ndN

/dX

n=0 ,

1,2,

3 dN/dX N = numberL = lengthS = surfaceV = volumeXdN/dX=dL/dX

X2dN/dX=dS/dX

X3dN/dX=dV/dX

Particle size, X

Fre

que

ncy

dis

trib

i tio

nX

ndN

/dX

n=0 ,

1,2,

3 dN/dX N = numberL = lengthS = surfaceV = volumeXdN/dX=dL/dX

X2dN/dX=dS/dX

X3dN/dX=dV/dX

• Different distributions for number, length, surface and volume !

• Different particle size analysers givedifferent distributions: some measurelength, others measure surface, etc.



11/68

Particle shape

Shape factor, “sphericity” Ψ

Ψ = 4.836 (volume)2/3

surface

= surface of sphere with same volumesurface of particle

0 ≤ ψ ≤ 1, ψ = 1 for a sphere



12/68

4.3a Multi-phase flows in practice- dilute



13/68

Aerosols Aerosol: A suspension of solid

or liquid particles in a gas. Aerosols are stable for at least a few seconds and in some casesmay last a year or more. The term ”aerosol” includes both the particles and the gas, which is usually air. Particle size rangesfrom 0.001 to over 100 µm.For example smoke is a dispersion of solid particles or droplets in air.

Sol: particles dispersed in a liquid, for example ink

Pic

ture

: http

://w

ww

.aer

osol

-soc

.org

.uk/

imag

es/S

tack

_plu

me.

jpg

Pic

ture

:http

://ka

psta

dt.o

rg/e

n/ph

otos

_of_

cape

_tow

n/pe

ople

_of_

sout

h_af

rica/

ZH00



14/68

A gas cyclone Advantages

Simple, cheap andcompact

Large capacity

DisadvantagesLarge pressure dropLow efficiency“Catch” removal problemsNo removal below ~5 mProblems above ~ 400 °C

ZH00

See also hydro-cyclones and other cyclones for liquid-solid, liquid-liquid and liquid-gas separations



15/68

Electrostatic precipitators (ESPs)4 process steps:

1. Particle charging2. Particle movement relative to the gas flow3. Particle collection at deposition surface4. Particle removal from deposition surface (often discontinuous)

Note: the electric properties of the particles to be removed should be suitable, otherwise use a filter system

Typically quite large, mainly usedat power plants for fly ashremoval from flue gas

Pic

ture

s: h

ttp://

ww

w.e

as.a

su.e

du/~

holb

ert/w

ise/

elec

tros

tatic

pre

cip.

htm

l



16/68

Baghouse filters

Inside out / outside in operation

Source: ZH00

Pic

ture

: http

://w

ww

.age

tmfg

.com

/Age

tSite

.dat

a/lin

eart

forf

ilter

kop.

jpg

Pic

ture

: http

://w

ww

.indu

stry

sear

ch.c

om.a

u/pr

oduc

ts/im

ages

/cba

g.gi

f


Sedimentation of suspensions

Dry solids concentrationDry solids concentration

Clear zoneClear zone

Feed zoneFeed zone

Thickening zoneThickening zone

FeedFeed EffluentEffluent

Sludge discharge

Dry solids concentrationDry solids concentration

Clear zoneClear zone

Feed zoneFeed zone

Thickening zoneThickening zone

FeedFeed EffluentEffluent

Sludge discharge

Batch sedimentation test

Pic

ture

: http

://w

ww

.geo

citie

s.co

m/fi

tzge

rrel

l/wor

k_im

g/th

icke

ner.

jpg

Continuous thickener

Åbo Akademi Univ - Chemical Engineering Thermal and Flow Engineering - Biskopsgatan 8, 20500 Turku

oktober 2017 RoNz 17

dilute dense



18/68

Flow of particle swarmsDrag coefficient for sphere in swarm, CD*,corrected for effect of neighbour particles

= voidage, porosity

Small particles, low Re: ƒ() = -4.7

Richardson - Zaki hindrance factor:

Re n< 0.2 4.650.2 ~ 1 4.35 Re-0.03

1 ~ 500 4.45 Re-0.01

> 500 2.39

nDDD CfCC )(*

ZH00



19/68

4.3b Multi-phase flows in practice- dense


Two-phase flow in tubes


20/68

Two phase flow:gas – liquid gas – solidliquid – liquid liquid – solid

Three phase, multi-phase flow:Gas-liquid-solid (trickled bed)or G/S or L/S with many size fractions

Patterns depend on relative velocities (”slip factor”) and densities



21/68

Fluidised beds – see section 4.5

Source: ZH00

gas bubble in a gas/solid

fluidised bed

dilute

”almost dilute”

dense



22/68

Crystallisers Solid product crystals can be

produced from gases, liquid melts or solutions

Advantages are: high product purity (crystallisation can be seen as a separation process!), and (except for liquid melts) low energy demand and low temperatures

Import issues are crystal product morphology, crystal growth kinetics, inclusion of impurities (and crystal water), and process control (temperature ↔ product size distribution and quality) P

ictu

re:h

ttp://

ww

w.tv

t.cbi

.uni

-erla

ngen

.de/

deu/

fors

chun

g/kr

ista

lisat

ion/

crys

talli

satio

n.ht

m

A continuous crystalliser

Pic

ture

http

://w

ww

.mpi

-mag

debu

rg.m

pg.d

e/re

sear

ch/p

roje

cts/

1032

/103

5/10

35_1

043



23/68

Flow in packed beds

Darcy’s Law:

with permeability K

Kozeny - Carman equation:

Sv = specific surface = surface/volume

Sv = 6 /dp for a sphere with diameter dp

L

LS

pu

fluidv

22

3

)1(5

L

pKu

fluid

Source: ZH00



24/68

Voidage, porosity, tortuosity

Particles in fluid flows

porosity = voidage =

= volume of empty spacetotal volume

and

1 - = volume of particlestotal volume

Flow in packed beds, porous solids

porosity = voidage =

= volume of pore spacetotal volume

and

1 - = volume of solidtotal volume

Tortuosity=path in porous structure

shortest path



25/68

Conveying systems:mechanic, pneumatic, hydraulic

Pic

ture

3:h

ttp://

ww

w.m

acte

nn.c

om/p

nu_o

verv

iew

.htm

l

4 pneumatic conveying regimes :- Solid Dense Phase- Discontinuous Dense Phase - Continuous Dense Phase- Dilute Phase Conveyor belt P

ictu

re 2

: http

://w

ww

.pro

tect

owire

.com

/imag

es/a

pplic

atio

ns/c

onve

yor/

coal

-bal

timor

e-lg

.jpg

Pneumatic conveyor / drier

Pic

ture

1: h

ttp://

ww

w.b

atem

an.c

o.za

/pro

-eng

-pne

.htm

1

23


Pneumatic conveying: regimes

Increasing particle loading

Often dense transport is associatedwith large pressure fluctuations

oktober 2017 RoNz 26Åbo Akademi Univ - Chemical Engineering Thermal and Flow Engineering - Biskopsgatan 8, 20500 Turku



27/68

Flow of powders in/from silos

a. Mass flow b. Funnel flowc. Expanded flow d. “Pipe”e. Rathole f. Arching

ZH00

Discrete elements models (DEM) are useful here



28/68

4.4 Particles in (turbulent) flows



29/68

Stop distance, Stokes’ number

FLOW

Force balance for a Stokesianparticle that is slowed down:(e.g. external flow velocity

suddenly 0)

- mp dv/dt = 3 v dp F

integrate, with v = v0 @ t=0

v(t) = v0 exp (- 3 dp F t /mp)

= v0 exp (-t /)

with = pdp² / 18F

Stop distance, sst

= v0 = mpv0 / 3 dpF

= 0v(t)dt

Stokes’ number = stop distance .

characteristic system dimension

Particle relaxation time



30/68

Motion of a sphere in an unsteady flow /1

acceleration force = Stokes’ drag + virtual mass effect ++ Basset force (resistance to acceleration, history effect)

+ external forces

Fdtd

uud

d

uuVuuddt

udm

t

t

pf

ffp

pffppfpp

p

0

2½1

½3

Basset-Boussinesq-Oseen(”BBO”) equation

For particles smallerthan the Kolmogorovscale eddies



31/68

Motion of a sphere in an unsteady flow /2

Fuu

dt

uud

k fpfp

1

1

p

t

t

pf

pfp

p

m

Fd

td

uud

k

dt

udkukuk

dt

ud

03

211

with variables k1, k2, k3 :

Gas / solid systems :p / F ~ (1000), i.e.

k2 & k3 << k1:

with one time-scale constantp = 1/k1:

mechanical relaxation timeof the particle

T47,H75

ff

pfp3

fp

f22

pfp

f1

d2

18k

2

3k

d2

36k



32/68

Particles and turbulent eddies

SCQM96



33/68

Eulerian vs. Lagrangian particle representation

Focussing on a control volume (Euler), left, or focussing on particle trajectories (Lagrange), right

Euler-Euler (for fluid and particulate phase) and Euler-Lagrange methods are both widely used

time t1 time t2

time t1

time t2

time t3

time t4

time t4

ZH00B06



34/68

Turbulent particulate dispersions

Particles with densities different from that of the fluid tend to segregate due to centrifugal forces.

Heavier-than-the-fluid particles are flung out of vortices and concentrate in regions that are (relatively) stagnant or do not rotate.

Particle segregation depends on time scales for particle motion compared with time scales of the turbulent fluctuations.

B92



35/68

Solid particles or droplets in turbulent gas flows

Effect of turbulence on particle trajectories and dispersion : One-way coupling

Effect of particles on turbulence (turbulence

modulation): Two-way coupling

Effects of particles on each other : Four-waycoupling

GB99



36/68

1-way, 2-way, 4-way coupling

dp = particle size (m) 2 = vol. frac. dispersed phase (i.e. solids) (-)K = Kolmogorovtime scale (s) x

12 = particle relaxation time = p (s)t

1 =Lagangianintegral time scale(s)x1, x2 = position of particles (m) PL98

Time Scales

versus

Concentration



37/68

Deterministic vs. stochastic models

Deterministic models take into account :– slip velocity = particle velocity - gas velocity,from

force balance and standard drag coefficient CD .

– interface mass / heat transport rates, using slip velocity, via Reynolds number and Sherwood / Nusselt numbers.

Stochastic models take (also) into account :– the effect of turbulent fluctuations on particle

motion

– the effect of turbulent fluctuations on interface transport



38/68

Particle size, turbulence and mass transport

Small particles relaxation time τp << characteristic time of the turbulence τt zero slip velocity relatively thick boundary layer but good diffusive mixing, “dispersion”

Large particles relaxation time τp >> characteristic time of the turbulence τt large slip velocity thin boundary layer but not good diffusive mixing

Certain particles relaxation time τp ~ characteristic time of the turbulence τt optimal for heterogeneous chemistry

H72,H75



39/68

Particle/ eddy interactions

Crossing trajectories

Interaction time < time scale for chemistry no reaction

timeparticlecentreof eddy

Particle should follow gas for

gas / solid interaction(and chemistry)

GJ96, FZ98

)τ,τmin(τ

uuτ

llnττ

ε

kC

k

lwvu

l τ

Rei

pp

epR

/µ

e

'''

ee

time ninteractio

time passing

eddyparticle

lifetime eddy



40/68

4.5 Fluidised beds



41/68

Fluidised beds: basics

Bubbling fluidised

bedBR98



42/68

Fixed beds, fluidised beds, entrained beds

Gas fluidised beds’

liquid-like behaviour

KL91



43/68

Circulating fluidised beds and spouted beds

KL91



44/68

Pressure drop vs. velocity:

transition fixed fluidised bed



45/68

Vertical particle concentration

(“density”) profiles for various

fluidisation regimes

KL91



46/68

Fluidisation: effect of gas distributor type

BR98



47/68

Behavior of bubbles just above a distributor

Porous plate

Perforated plate

Nozzle-type tuyere

Bubble cap tuyere



48/68

Non-mechanical valves



49/68

Geldart’s classification of particles in FB’s (derived for air, ambient conditions)

KL91



50/68

Minimum fluidisation velocity umf /1

gH

pFSmf

mf

fb ))(1(

Pressure drop across a fluidised bed (at minimum fluidisation conditons):

Pressure drop across a packed bed (Ergun):

pressure drop p, bed height H,

porosity ,gravity g,

fluid density F, dynamic viscosity F, particle diameter dp, particle density

S,flow velocity u,

particle sphericity

p

F

p

Fpb

d

u

d

u

H

p

2

323

2 )1(75.1

)(

)1(150

Packed bed vs. Fluidised bed

376.0pb

42.0 KL91):(source εfor estimate



51/68

Limiting cases: Remf small (“fine”), Remf large (“coarse”)

Minimum fluidisation velocity umf /2

Dimensionless groups: Remf, Ar

0 for large Remf 0 for small Remf

2

3p

2323

)(dAr Re

Re75.1

Re)1(150

F

FSF

F

Fmfpmf

mfmf

gud

Armf

mfmf



52/68

Terminal particle (settling) velocity ut

31

342

412

21

)1(

D

F

S

ptptFDFpp C

g

duduCgVgm

gravity - lift force (buoyancy) = drag force

mass mp

gravity g volume Vp

fluid density F

dynamic viscosity F

drag coefficient cD

particle diameter dp

particle density p

terminal velocity ut

Reynolds number Re

) (

)Re15.01(Re

241000Re2

Re

242Re if ;Re

678.0

particlespherical

Cif

Cdu

tt

Dt

tDt

F

ptFt



53/68

Fluidisation Dimensionless particle size, d* and velocity, u*

Determining terminal velocity, ut :

calculate Ar = dp* Figure next page u* calculate ut

F

Fpp

p

FSF

F

F

FSFpp

ud

Arguu

gdArd

Re with Re

)(

)(

31

31

31

31

2*

2*



54/68

Chart for the determination of particle terminal settling velocitythrough a fluid

KL91



55/68

Geldart’s classification and FB reactor types

F

Fpp

p

FSF

F

F

FSFp

p

udAr

guu

gd

Ard

Re with

Re

)(

)(

31

31

31

31

2*

2

*

KL91



56/68

The Kunii-Levenspiel bubbling bed model

Gas flow = gas flow via emulsion + gas flow via bubbles

i.e., with bed area A, and superficial velocity uo :

flow (uo-umf)*A via bubbles

flow umf *A via emulsion

mfb

b

mfb

mf

bb

uu

uuδ

uu

uuδ

ε

)gd(.u

-1 :emulsion in bed of Fraction

:bubbles in bed of Fraction

0 u u u :solids of velocity Rise

u :gas emulsion of velocity rise lSuperficia

u u :phase emulsion of velocity Rise

:bubbles of velocity Rise

down s,up s,s

mf

mf

mfe

KL91



57/68

Bed height and bubble sizeBed height vs. velocity :

Bubble diameter :(Ao ~ bottomdistributor plate area)

Bubble rise velocity:(Davidson & Harrison)

21

bmf0b

2.0

8.00

4.0mf0

b

b

mf0mf

)gd(711.0)uu(u

g

)A4h()uu(54.0d

u

uu

H

HH

http

://w

ww

.cd-

adap

co.c

om/p

ress

_roo

m/d

ynam

ics/

25/im

ages

/uav

_6.jp

g

KL91



58/68

Emulsion-to-wall heat transfer /1

a. large particles, short contact time

b. small particles,long contact time

GAK97



59/68

Emulsion-to-wall heat transfer /2

radiationconductionconvectiongasconvectionparticle

radiationconductionconvection

hhfhf

hhh

/,,

/

)1(

Heat transfer coefficient, h (W/m2K) :

where ƒ = fraction of wall covered by particles

problem:particle-to-wall distance, δ ??particle/wall contact time,τ ??

wall coverage, ƒ ??

TKK

98/99

GAK97,ZKTLM99

particlepparticleparticlegasconvectionparticle ch ,,

1



60/68

Heat transfer in CFB combustion reactors

GAK97



61/68

Single particle mass transfer in a CFBC riser

Numin = 2 2

Compare with standard Ranz- Marshall equation (‘52):

Nu = 2 + 0.6 Re0.5Pr0.33

Imporant aspect consideringheat / mass transfer analogy :

inert, bed material particles areimportant from a heat transferpoint of view, not from a mass

transfer point of view.

P98



62/68

4.6 Bubble reactors

LZ16


Slag2 PCC Process- Calcium is extracted from steelmaking slag using an NH4 salt- Dissolved calcium reacts with CO2 to produce CaCO3 (PCC)

which is mass transfer (dissolution of moving CO2 bubbles) controlled

17.10.2017 Åbo Akademi | Domkyrkotorget 3 | 20500 Åbo 63


Bubble reactor for CO2dissolution analysis


64/68

Bubble movement and concentration profile. How far does the bubble rise before it is dissolved Change of diameter while rising speed and acceleration change

mass

position

LZ16


Bubble reactor – tests at ÅA


65/68

6196 6197


Bubble reactor – tests at ÅA


66/68

LZ172016-2017:Effect of mixing



67/68

Sources / further reading #4

B92 Banerjee, S. “Turbulence structures” Chem.Eng.Sci. 47(8) (1992) 1973-1817B06 A Bennett “Lagrangian fluid dynamics” Cambridge Univ. Press (2006)BR98 G L Bormand KW Ragland “Combustion engineering” McGraw-Hill (1998) Chapter 17CRBH83 Coulson, J.M., Richardson, J.F., Backhurst, J.R., Harker, J.H. “Chemical Engineering, Vol. 2 : Unit

Operations” Pergamon Press, Oxford (1983) Chapter 3FZ98 L-S Fan, C Zhu “Principles of gas-solid flows” Cambridge Univ. Press (1998)H75 Hinze, J. O. Turbulence (2nd Ed.) New York: McGraw-Hill (1975) chapters 1,3 and 5H72 Hinze, J.O., “Turbulent fluid and particle interactions”. In: Hetsroni, G, Sideman, S., Hartnett, J.P. (eds.),

Progress in Heat and Mass Transfer - Proc. Int. Symp. on Two-Phase Systems Oxford: Pergamon Press (1972) pp. 433-452

GAK97 Grace, J.R., Avidan, A.A., Knowlton, T.M. (Eds.) "Circulating fluidised beds", Chapman & Hall, London (1997)

GB99 Gouesbet, G., Berlemont, A., “Eulerian and Lagrangian approaches for predicting the behaviour of discrete particles in turbulent flows” Progr. Energy Combust. Sci. 25 (1999) 133-159

GJ96 Graham, D.I., James, P.W. “Turbulent dispersion of particles using eddy interaction models”, Int. J. Multiphase Flow 22(1) (1996) 157-175

IGH91 Iinoya, K., Gotoh, K., Higashitani, K. “Powder technology handbook”, Marcel Dekker, New York (1991) KL91 D Kunii, O Levenspiel “Fluidization engineering” 2nd ed, Butterworth-Heinemann (1991)L00 Loth, E. “Numerical approaches for motion of dispersed particles, droplets and bubbles”, Progr. Energy

Combust. Sci. 26 (2000) 161-223LZ16 Legendre, D., Zevenhoven, R.”A numerical Euler-Lagrange method for bubble tower CO2 dissolution

modelling” Chem. Eng. Res. and Des. 111 (2016) 49-62LZ17 “Detailed experimental study on the dissolution of CO2 and air bubbles rising in water” Legendre, D.,

Zevenhoven, R., Chem. Eng. Sci. 158 (2017) 552-560M06 Michaelides, E.E. “Particles, bubbles and drops”, World Scientific (2006)P98 Palchonok, G.I. “Heat and mass transfer to a single particle in a fluidized bed” Chalmers Univ. of T., Sweden,

Ph.D.thesis (1998)PL98 Peirano, E., Leckner, B. “Fundamentals of turbulent gas-.solid flows applied to circulating fluidised bed

combustion” Progr. Energy Combust. Sci. 24 (1998) 259-296



68/68

Sources / further reading #4SCQM96 Shirolkar, J.S., Coimbra, C.F.M., Quieroz, McQuay, M. “Fundamental aspects of modelling turbulent-

particle dispersion in dilute flows” Progr. Energy Combust. Sci. 23(1996) 363-399T47 Tchen, C.-M. “Mean value and correlation problems connected with the motion of small particles suspended

in a turbulent fluid”, Delft Univ. of T., the Netherlands, Ph.D. Thesis (1947) chapter 4vD82 van Dyke, M. “An album of fluid motion”, The Parabolic Press, Stanford (CA) (1982)ZH00: Zevenhoven, R., K. Heiskanen ”Particle technology for thermal power engineers”, post-graduate course

ene-47.200, TKK, Espoo, Sept./Oct. 2000ZKLTM99 Zevenhoven, R., Kohlmann, J., Laukkanen, T., Tuominen, M., Blomster, A.-M. “Suspension-to-wall heat

transfer in CFB combustion: near-wall particle velocity and concentration measurements at low and hightemperatures” Proc. 6th Int. Conf. on CFB, Würzburg, Germany, August 1999 (J. Werther, Ed.), Frankfurt/Main (1999) 959-965

(lecture 4 of 4) - Åbo Akademi | Startsidausers.abo.fi/rzevenho/iCFD17-RZ4.pdf · Introductionto...

Documents

Transcript of (lecture 4 of 4) - Åbo Akademi | Startsidausers.abo.fi/rzevenho/iCFD17-RZ4.pdf · Introductionto...