Introduction to Computational Fluid Dynamics 424512 E #4- rz
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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
Process and Systems EngineeringThermal and Flow Engineering Laboratory
tel. 3223 ; [email protected]
See alsoÅA course 424521 (5 sp)
Fluid and particulate systemshttp://users.abo.fi/rzevenho/kursRZ.html#FPS
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4.1 Fluid flow around objects:external flows
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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
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Introduction to Computational Fluid Dynamics 424512 E #4- rz
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
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Picture: KJ05
Flowaround a cylinder
Flow around cylinders, spheres /1
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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
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Boundary layer separation examples
Pic
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A smooth (a) and roughened (b) ball entering water at 25 °C
CRBH83
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Fluid flow over a surface
CRBH83
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4.2 Particle (bubble, droplet, ...) sizedistribution, shape
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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.
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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
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4.3a Multi-phase flows in practice- dilute
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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
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ZH00
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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
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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
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Baghouse filters
Inside out / outside in operation
Source: ZH00
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: http
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Introduction to Computational Fluid Dynamics 424512 E #4- rz
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
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: http
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Continuous thickener
Åbo Akademi Univ - Chemical Engineering Thermal and Flow Engineering - Biskopsgatan 8, 20500 Turku
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dilute dense
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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
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4.3b Multi-phase flows in practice- dense
Introduction to Computational Fluid Dynamics 424512 E #4- rz
Two-phase flow in tubes
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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
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Fluidised beds – see section 4.5
Source: ZH00
gas bubble in a gas/solid
fluidised bed
dilute
”almost dilute”
dense
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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
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A continuous crystalliser
Pic
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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
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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
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Conveying systems:mechanic, pneumatic, hydraulic
Pic
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4 pneumatic conveying regimes :- Solid Dense Phase- Discontinuous Dense Phase - Continuous Dense Phase- Dilute Phase Conveyor belt P
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Pneumatic conveyor / drier
Pic
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Pneumatic conveying: regimes
Increasing particle loading
Often dense transport is associatedwith large pressure fluctuations
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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
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4.4 Particles in (turbulent) flows
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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
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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
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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
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Particles and turbulent eddies
SCQM96
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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
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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
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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
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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
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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
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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
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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
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ε
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k
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l τ
Rei
pp
epR
/µ
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'''
ee
time ninteractio
time passing
eddyparticle
lifetime eddy
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4.5 Fluidised beds
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Fluidised beds: basics
Bubbling fluidised
bedBR98
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Fixed beds, fluidised beds, entrained beds
Gas fluidised beds’
liquid-like behaviour
KL91
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Circulating fluidised beds and spouted beds
KL91
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Pressure drop vs. velocity:
transition fixed fluidised bed
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Vertical particle concentration
(“density”) profiles for various
fluidisation regimes
KL91
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Fluidisation: effect of gas distributor type
BR98
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Behavior of bubbles just above a distributor
Porous plate
Perforated plate
Nozzle-type tuyere
Bubble cap tuyere
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Non-mechanical valves
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Geldart’s classification of particles in FB’s (derived for air, ambient conditions)
KL91
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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 pbed height H
porosity gravity g
fluid density F
dynamic viscosity F
particle diameter dp
particle density S
flow velocity uparticle 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
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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
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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
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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*
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Chart for the determination of particle terminal settling velocitythrough a fluid
KL91
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Geldart’s classification and FB reactor types
F
Fpp
p
FSF
F
F
FSFp
p
udAr
guu
gd
Ard
Re with
Re
)(
)(
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KL91
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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
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Bed height and bubble size
Bed 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
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KL91
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Emulsion-to-wall heat transfer /1
a. large particles, short contact time
b. small particles,long contact time
GAK97
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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
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Heat transfer in CFB combustion reactors
GAK97
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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
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4.6 Bubble reactors
LZ16
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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
10.10.2019 Åbo Akademi | Domkyrkotorget 3 | 20500 Åbo 63
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Bubble reactor for CO2dissolution analysis
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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
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Bubble reactor – tests at ÅA
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LZ172016-2017:Effect of mixing
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Bubble column at ÅA solvent losses duringprecipitated calcium carbonate (PCC) production
CO2 bubbles rising and dissolving in a bubble column reactor Simplified close-up of concentration profiles inside and outside a bubble
10/10/2019 Åbo Akademi University |Thermal and Flow Engineering | 20500 Turku Finland
66
Aqueous phase
Vapour phase
CO2
Vapours
Δi
Δo
db
CO2 H2O
NH3(aq)
CO2(aq)
NH3
concentration
position
Δi Δo
H2O
ZLSJ19
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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
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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
ZLSJ18 Zevenhoven, R., Legendre, D., Said, A., Järvinen, M. ”Carbon dioxide dissolution and ammonia losses in bubble columns for precipitated calcium carbonate (PCC) production” Chem. Eng. Res. and Des. 146 (2019) 379-390