A Simulation Model for the Separation of Dispersed Liquid ... · Based on the Coupling of CFD and Population Balances. ... with multiphase mixture model in FLUENTTM ... phase averaged

Computational Fluid Dynamics in Chemical Reaction Engineering VJune 15th to 20th 2008, Whistler, British Columbia, Canada

Steffen Schütz, Gabriele Gorbach, Christian Winkler and Manfred Piesche

Institute of Mechanical Process Engineering IMVTUniversity of Stuttgart, Germany

A Simulation Model for the Separation of

Dispersed Liquid-Liquid Systems in Hydrocyclones

Based on the Coupling of CFD and Population Balances

Institute of Mechanical Process Engineering, University of Stuttgart, GermanyECI Conference Computational Fluid Dynamics in Chemical Reaction Engineering V, Whistler, British Columbia, Canada

Goals

Calculation of flow field

Calculation of particle tracks

(e. g. Euler-Lagrange)

Interactions between phases

(e. g. Euler-Euler)

– Breakup / coalescence

(Population balances)

CFD software (e.g. FLUENTTM)

Modelling of liquid-liquid separation with particle-particle interaction


Goals

User defined functions (UDF)

Breakup / coalescence (Population balances)

– Separation process



(e. g. Euler-Lagrange)

Interactions between phases

(e. g. Euler-Euler)

– Breakup / coalescence

(Population balances)


Modelling of liquid-liquid separation with particle-particle interaction


Goals

User defined functions (UDF)

Breakup / coalescence (Population balances)

Separation process



Modelling of liquid-liquid separation with droplet-droplet interaction in a hydrocyclone with direct impact of a non-homogeneous flow field


Basics

Population theory

Solution strategy

Results

Summary and Outlook

Outline


Basics – Separation Processes in Hydrocyclones

Continuous separators

Overflow

Underflow

Inlet

&oV

&uV

&inV


Basics – Separation Processes in Hydrocyclones

Overflow

Underflow

Inlet

Continuous separators&oV

&uV


using Euler-Lagrange model

“big” particle/droplet

“small” particle/droplet

Separation due to density difference

Phase with higher density:

Accumulation to larger radii

(here: dispersed water

droplets)

Phase with lower density:

Transport to smaller radii

(here: continuous diesel fuel)

&inV


Qin(dp ) =

f · Qo(dp ) + g · Qu(dp )

g · Qu(dp )

f · Qo(dp )

Qin(dp )

1 10 100 10000,0

0,2

0,4

0,6

0,8

1,0

Qein

Ver

teilu

ngss

umm

e Q

(dp)

[-]

Tropfengröße dp [µm]

Cum

ulat

ive

size

dis

trib

utio

n Q

3(d p

) [1

]

Qin

Droplet size dp [µm]

Basics – Separation Processes Without Particle-Particle Interaction

e. g. stable droplets at

low concentrations

f = integral droplet mass fraction overflow

g = integral droplet mass fraction underflow


Qin(dp ) ≠f · Qo(dp ) + g · Qu(dp )

g · Qu(dp )

f · Qo(dp )

Qin(dp )

1 10 100 10000,0

0,2

0,4

0,6

0,8

1,0

Qein

Ver

teilu

ngss

umm

e Q

(dp)

[-]


Cum

ulat

ive

size

dis

trib

utio

n Q

3(d p

) [1

]

Qin


Inte

ract

ion

e. g. interacting droplets

Basics – Separation Processes With Particle-Particle Interaction


Qreal (dp ) =f · Qo(dp ) + g · Qu(dp )

g · Qu(dp )

f · Qo(dp )

Qin(dp )

1 10 100 10000,0

0,2

0,4

0,6

0,8

1,0

Qein

Ver

teilu

ngss

umm

e Q

(dp)

[-]


Cum

ulat

ive

size

dis

trib

utio

n Q

3(d p

) [1

]

Qin


Inte

ract

ion



Meyer: PhD Thesis (2001) University of Hannover


1 10 100 10000,0

0,2

0,4

0,6

0,8

1,0

Qein Qreal

Ver

teilu

ngss

umm

e Q

(dp)

[-]


g · Qu(dp )

f · Qo(dp )

Qin(dp )

Cum

ulat

ive

size

dis

trib

utio

n Q

3(d p

) [1

]


Inte

ract

ionBreakup

CoalescenceQreal (dp ) =f · Qo(dp ) + g · Qu(dp )



Qin

Meyer: PhD Thesis (2001) University of Hannover


Shift of droplet size distribution

with time and position is described

by population balances

Droplet mass as characteristic

particle property

Balancing of number density

distribution Fi [1/m³] of each

droplet size class i

Population Theory

Hulburt, H. M., Katz, S.Chemical Engineering Science 19 (1964), 555-574


( ) ( )

( ) ( ) ( ) ( )

ii i

i i i i

Fv F

t

B F B F D F D F+ − + −

∂ ρ+ ∇ ⋅ ρ

∂

= − + −

r

6447448 6447448





particle property




Population Theory

Birth Terms B(Fi)Droplet Coalescence

Death Terms D(Fi)Droplet Breakup

Hulburt, H. M., Katz, S.Chemical Engineering Science 19 (1964), 555-574


m

m*>m

Population Theory

Generation by breakup

( ) ( )

( ) ( ) ( ) ( )

ii i

i i i i

Fv F

t

B F B F D F D F+ − + −

∂ ρ+ ∇ ⋅ ρ

∂

= − + −

r





particle property





m

m*<m

m*>m

Generation by coalescence


Population Theory





particle property




( ) ( )

( ) ( ) ( ) ( )

ii i

i i i i

Fv F

t

B F B F D F D F+ − + −

∂ ρ+ ∇ ⋅ ρ

∂

= − + −

r


m

m*>m

Reduction by coalescence

Population Theory





particle property




( ) ( )

( ) ( ) ( ) ( )

ii i

i i i i

Fv F

t

B F B F D F D F+ − + −

∂ ρ+ ∇ ⋅ ρ

∂

= − + −

r


m

m*>m

m*<m

Reduction by breakup

Population Theory






particle property




( ) ( )

( ) ( ) ( ) ( )

ii i

i i i i

Fv F

t

B F B F D F D F+ − + −

∂ ρ+ ∇ ⋅ ρ

∂

= − + −

r


m

m*>m

m*<m


Population Theory






particle property




( ) ( ) ( ) ( )ii i i i

Fv F B F D F

t± ±∂ ρ

+ ∇ ⋅ ρ = ± ±∂

r

Description by interaction kinetics


Population Theory

( )( ) ( )( ) ( )( ) ( )( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( )

i i i i

m

coll i i0

m mmax

coll i i0

mmax

br im

br i

B F m, t B F m, t D F m, t D F m, t

1 m m*,m * g m m*,m * F m m*, t F m*, t dm *2

m,m * g m,m * F m, t F m*, t dm *

m * m,m * g m * F m*, t dm *

g m F m, t

+ − + −

−

− + − =

+ λ − − −

− λ

+ υ β

−

∫

∫

∫

Generation by coalescence





Kinetic approach of Coulaloglou/TavlaridesChemical Engineering Science 32 (1977), 1289-1297

Strongly empirical

Influence of turbulence on droplet breakup is not considered

Kinetic approach of Lehr (PhD Thesis (2001) University of Hannover, Germany)

Definition of critical velocity (only dependent of disperse phase)

Influence of turbulence on droplet breakup is considered

Population Theory

m

m*>m

m*<m


Droplet Reduction by Separation

Relative transport of droplets with respect to mean flux driven by centrifugal

forces results in droplet separation at the cyclone walls and at the underflow

“Drift flux” described by transport laws for drag force

Droplet separation as further contribution to the death term ( )iD F−

cx

ti,d

m,ti

d

md

m

i,pd

Di,rel D

ad

c181

v α∇α

ν−

ρρ−ρ

µ

ρ=

rr


Droplet Size Discretization

Non-equidistant droplet size discretization with discrete droplet size classes

Close size intervals with small droplets due to their high number concentration

Numerical correction to keep the droplet mass constant


Solution Strategy

Flow field simulation with multiphase mixture model in FLUENTTM

Discretization of droplet size distribution into n droplet size classes

Each droplet size class corresponds to a quasi continuous phase i





Solution of phase averaged mass and momentum balance of

the mixture (n + 1 phases) with Reynolds-Stress-Model

Solution of transport equation for volume phase fraction αi of each phase i

Solution Strategy

( ) ( )m im i i i iv B ( ) D ( )

t± ±∂ ρ α

+ ∇ ⋅ ρ α = ± α ± α∂

r


( ) ( )m im i i i iv B ( ) D ( )

t± ±∂ ρ α

+ ∇ ⋅ ρ α = ± α ± α∂

r

Droplet volume

Solution Strategy

( ) ( ) ( ) ( )ii i i i

Fv F B F D F

t± ±∂ ρ

+ ∇ ⋅ ρ = ± ±∂

r




Solution of phase averaged mass and momentum balance of

the mixture (n + 1 phases) with Reynolds-Stress-Model

Solution of transport equation for volume phase fraction αi of each phase i

corresponding i,p

ii V

Fα

=

Coupling condition

p,iV


Solution Strategy

Calculation of droplet interaction kinetics

and droplet separation

with user defined subroutines


Solution Strategy




Implementation into

birth and death terms

( ) ( )m im i i i iv B ( ) D ( )

t± ±∂ ρ α

+ ∇ ρ α = ± α ± α∂

r





Implementation into

birth and death terms

Coupled solution

of the flow field with

population balances in FLUENTTM

Solution Strategy

( ) ( )m im i i i iv B ( ) D ( )

t± ±∂ ρ α

+ ∇ ρ α = ± α ± α∂

r


Results – Cyclone Geometries

Conventional geometry Geometry with double cone (Smyth)Proc. 2nd Int. Conf. on Hydrocyclones (1984),

177-190, Bath, UK


Results – Cyclone Geometries

Conventional geometry Geometry with double cone (Smyth)Proc. 2nd Int. Conf. on Hydrocyclones (1984),

177-190, Bath, UK

Cyclone separators with one or two inlets


Separation of water droplets from diesel fuel

Density difference ∆ρ=170 kg/m³, interfacial tension σ=0.015 N/m

Droplet size distribution inlet:

Mean diameter d50e=300µm

Logarithmical discretization

into n=19 droplet size classes

Results – Phase Properties


A

A

m³/h1.0Vin =&

Results –Two Different Cyclone Geometries

m³/h1.0Vin =&

Reduced droplet breakup

Increased droplet coalescencedouble conegeometry


m³/h1.0Vin =&

Results –One and Two Cyclone Inlets

m³/h1.0Vin =&

Reduced droplet breakup

Increased droplet coalescence

A

A

A

A

secondinlet


Results – Phase Distribution

µm805d 19, phase =p

m³/h1.0Vin =&

A

A

phase fraction


A

A

phase fraction i i d P,i i(B D ) V m+ −− ⋅ ρ ⋅ ⋅ ∆

m³/h1.0Vin =&

µm805d 19, phase =p

Results – Phase Distribution


Summary and Outlook

Development of new method for coupled solution of population balances with

flow field

Modelling of droplet breakup and coalescence

Describing impact of droplet interactions on separation process

Good agreement between simulation and experiment


Development of new method for coupled solution of population balances with

flow field

Modelling of droplet breakup and coalescence

Describing impact of droplet interactions on separation process

Good agreement between simulation and experiment

Further activities

Direct numerical simulation (DNS) of droplet-droplet interactions for definition

of kinetics (Empirical assumptions are no longer required for the solution of

population balances)

Summary and Outlook













Additional Slides


Partially structured grid – cross-section at the inlet region

Discretization – 3D


ResultsVelocity and Pressure Distribution

azim

utha

l vel

ocity

axia

l vel

ocity

radi

al v

eloc

ity

pres

sure


Daughter droplet distribution according to Chatzi

Daughter droplet distribution according to Lehr

Kinetic Approaches

( )( )

23 52 5 2 5c

32 3 3 5d 1 15 2 5c

9exp ln 2 d4

6ß m,m *d * 31 erf ln 2 d *

2

⎡ ⎤⎛ ⎞⎡ ⎤ρ⎛ ⎞⎢ ⎥⎜ ⎟− ε⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟σ⎝ ⎠⎜ ⎟⎢ ⎥⎣ ⎦⎢ ⎥⎝ ⎠⎣ ⎦=⎛ ⎞⎡ ⎤⎡ ⎤π ρ ρ⎛ ⎞⎜ ⎟+ ε⎢ ⎥⎢ ⎥⎜ ⎟⎜ ⎟σ⎝ ⎠⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦⎝ ⎠

( )( ) ( )

2

1 2 2

m *m6 2m,m * exp 18 .

m * 2 m *

⎡ ⎤⎛ ⎞−⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥β = −

⎢ ⎥π⎢ ⎥⎣ ⎦


Breakup frequency

Collision frequency

Coalescence efficiency

Kinetic Approaches –Coulaloglou and Tavlarides

( )( )

( )21 3

br 1 22 3 5 2 3d

1g d C exp C

d 1 d

⎡ ⎤σ + αε= −⎢ ⎥

+ α ρ ε⎢ ⎥⎣ ⎦

( ) ( )( ) ( )( )1 3 1 22 2 32 2 3

coll 3g d,d * C d d * d d *1ε

= + ++ α

( )( )

4c c

4 32d d *d,d * exp Cd d *1

⎡ ⎤η ρ ε ⋅⎛ ⎞λ = −⎢ ⎥⎜ ⎟+⎝ ⎠⎢ ⎥σ + α⎣ ⎦


Breakup frequency

Coalescence function

Kinetic Approaches – Lehr

9 /57 /55 / 3 19 /15c

br 3 6 /5c

2 1g (d) 0.5 d expd

⎛ ⎞⎛ ⎞ρ σ⎛ ⎞ ⎜ ⎟= ⋅ ε −⎜ ⎟ ⎜ ⎟σ ρ⎜ ⎟⎝ ⎠ ε⎝ ⎠⎝ ⎠

( ) ( )coll

21 / 3

2 maxc crit 1 / 3

(d, d*) d,d * g d,d *

(d d*) min(v , v ) exp 14

Ω = λ ⋅

⎛ ⎞⎛ ⎞απ ⎜ ⎟⎜ ⎟= + − −⎜ ⎟⎜ ⎟α⎜ ⎟⎝ ⎠⎝ ⎠


Characteristic and critical velocity

Kinetic Approaches – Lehr

( )2 / 31 / 3 2 / 3c

relative velocityturbulent fluctuation velocity

v max 2 d d * , v v *⎛ ⎞⎜ ⎟= ε + −⎜ ⎟⎜ ⎟⎝ ⎠

1424314444244443

Coalescence close to walls and in the overflow/underflow region

With high energy dissipation rate close to walls

characteristic velocity > critical velocity coalescence function only dependent on material data

critv 0.05m / s= parameter, dependent on material data


Coalescence correction term

Non-equidistant Droplet Size Discretization

Breakup correction term

coal k likl

i

m mK

m+

=

( )

br ii i

k i k kk 1

mK

m ,m m m=

=ν β ∆∑

Documents

A Simulation Model for the Separation of Dispersed Liquid ... · Based on the Coupling of CFD and Population Balances. ... with multiphase mixture model in FLUENTTM ... phase averaged