Mechanisms of Atomization - University of Notre Damemjm/atomization.pdf · Mechanisms of...

http://www.nd.edu/~mjm [email protected]

Mechanisms of Atomizationin

Fluid-Fluid Channel Flows

Mark J. McCready

Department of Chemical Engineering


Acknowledgements

• DOE, Basic Energy Sciences• NASA, Microgravity Program• CoWorkers

– Chia Chang, David Leighton– Ben Woods, Mike King, Massimo Sangalli– Bill Kuru, Xiaohong Wang , Don Uphold


Outline• Importance of atomization processes• Basestate for stratified atomization

– Sheared layer flow with waves– Some characteristics of waves and

questions

• Linear stability for these flows– Some results and limitations

• Atomization Mechanisms


Importance of atomization

– In annular flow, the entrained fraction canbe 20-40% of the liquid (Fore and Dukler,1995; Asali et al., 1985).

– Current (mostly) empirical correlations areinadequate.

• What is known about atomization

– Atomization occurs from solitary and rollwaves (Woodmansee and Hanratty, 1968;Whalley,Hewitt & Terry, 1979).


Importance of atomizationSpecific applications

• Gas-liquid contacting

• (novel process improvements(mixing/contacting) with ~$0 capital costs)

• “Optimal” gas-liquid mass transfer process willinvolve some atomization,and some specialoverall fluid geometry

• Phase change process affected by liquid onthe wall

• Pressure drop, transport rates in annular flow


Starting geometry of interest

liquid

gas

Two-fluid stratified flow


Wave regime map


Wavetracings

across thetransition


Background wave field


Onset of Solitary waves


Solitary waves well above onset


Wave spectra across the transition


Spectra as a function of distance

10-6

10-5

10-4

10-3

10-2

wave spectrum (cm2-s)

0.12 3 4 5 6 7

12 3 4 5 6 7

102 3 4 5 6 7

100frequency (1/s)

40

30

20

10

0

-10

growt

h rat

e (1/

s)

RL = 300RG = 9975

µL = 5 cP

linear growth k-ε model

wave spectrum @ 1.2 m 3.8 m 6 m

Data of Bruno andMcCready, 1988


Wave transition as gas increases


Wave transition as gas increases (more)


Solitary waves in gas-liquid flow


Solitary Wave Scaling

6

0.001

2

4

6

0.01

2

4

6

0.1

mea

n pe

riod

0.012 3 4 5 6 7

0.12 3 4 5 6 7

1(R-Rcritical)/Rcritical

µ = 15 cP

µ = 20 cP power law exponent= 1.35 power law exponent=1.5


Gas-liquid flow interfacial stability problemturbulence model: k-ε

Solve the base state with either a smooth or roughinterface (try to match data).

thenSolve the differential stability problem the best we can

ρ1

∂ki•

∂t • + ui• ∂k •

∂xi• = ∂

∂xi• µ1 +

µ t•

σ ke

∂k •

∂xi• + µ t

• 2sij• ∂ui

•

∂x j• – ρ1ε• – 2µ1

∂ k •

∂xi•

2

ρ1

∂ui•

∂t • + u j• ∂ui

•

∂x j• = –

∂ p•

∂xi• + ρ1g

•sin θ + ∂∂x j

• µ1 + µ t• 2sij

•

Liquid-phase: 0 ≤ y• ≤ d1

ρ1

∂ε•

∂t • + ui• ∂ε•

∂xi• = ∂

∂xi• µ1 +

µ t•

σ ε

∂ε•

∂xi• + c1 f1µ t

• ε•

k • 2sij• ∂ui

•

∂x j•

+ 2µ1µ t

• ∂2ui•

∂x j•∂xl

•

2

– ρ1c1 f1ε• 2

k •


Stability equations continuedas-phase: d1 ≤ y• ≤ d1 + d2

ρ2

∂ui•

∂t • + u j• ∂ui

•

∂x j• = –

∂ p•

∂xi• + ρ2g

•sin θ + ∂∂x j

• µ2 + µ t• 2sij

•

ρ2

∂k •

∂t • + ui• ∂k •

∂xi• = ∂

∂xi• µ2 +

µ t•

σ ke

∂k •

∂xi• + µ t

• 2sij• ∂ui

•

∂x j• – ρ2ε• – 2µ2

∂ k •

∂xi•

2

ρ2

∂ε•

∂t • + ui• ∂ε•

∂xi• = ∂

∂xi• µ2 +

µ t•

σ ε

∂ε•

∂xi• + c1 f1µ t

• ε•

k • 2sij• ∂ui

•

∂x j•

+ 2µ2µ t

• ∂2ui•

∂x j•∂xl

•

2

– ρ2c1 f1ε• 2

k •


Stability equations continued

µkub,k' ''

mk+ Γ b,kφk

'' ''– 2α 2 Γ b,kφk

' '+ α 4Γ b,kφk = iαR

rkmk

ub,k – c φk''

– α 2φk – ub,k'' φk

µkkb,k' '

+ µkub,k''

mk+Γ b,k kk

''– α 2kk + Γ b,k

' kk+ 2µb,kub,k

'

mkφk

''+ α 2φk +

kb,k'

kb,k

kb,k'

2kb,kk k – kk

'

= iαRrkmk

ub,k – c kk – kb,k' φk

µkεb,k' '

mk+ Γ b,kΓ b,k εk

'' – α 2εk + Γ b,k' εk +2c1 f1

µb,kub,k'

mkφk

''+ α 2φk + rkRc2 f2

εb,k

kb,k

εb,k

kb,kk k – 2εk

+

ub,k'' 2

mkc1 f1

εb,k

kb,kµk + εk –

mkµb,k

kb,kk k +

2mk

rkRµk + 2µb,kφk

'''

= iαRrkmk

ub,k – c εk – εb,k' φk

µk = cµ fµrkR

kb,k

εb,k2kk –

kb,k

εb,kεk

k=1 (liquid-phase) 0 ≤ y ≤ 1

k=2 (gas-phase) 1 ≤ y ≤ n2 + 1


Stability Equations cont.

φ1 = φ2 (3-18c)

φ1 + ub,1h = ch (3-18d)

φ1'

– φ2'

= h ub,1' – ub,2

' (3-18e)

φ1''

+ α 2φ1 + hub,1'' = m2 φ2

''+ α 2φ2 + hub,2

'' (3-18f)

φ1'''

+ Γ b,1' φ1

''+ ub,1

' Γ 1'

– 3α 2φ1 + iαR ub,1' φ1 – ub,1φ1

'– m2 φ2

'''+ Γ b,2

' φ2''

+ ub,2' Γ 2

'– 3α 2φ2

– iαr2R ub,2' φ2 – ub,2φ2

' – iαR 1 – r2 F + α 2S h = iαRc r2φ2'

– φ1' (3-18g)

k 1 = ε1 = µ1 = k 2 = ε2 = µ2 = 0 (3-18h)

Boundary conditions


How close is the base state?

10

2

4

68

100

2

4

h+

1002 3 4 5 6 7 8 9

1000ReL

µL = .92 cp

d = 2.54 cm

Figure 4.7 h+ - ReL correlation for horizontal gas-liquid channel flow. ReG = 4,000 - 15,000

Bruno (1988) Experiments Lin and Hanratty (1986)

friction factor model Laminar Basetate K- ε model


Friction velocity -- Re

0.001

2

3

4

56789

0.01

2

3

4

5

v* (m

/s)

1022 3 4 5 6

1032 3 4 5 6

1042

ReG

Differential turbulent gas laminar gas

1-D

fi/fs=1 fi/fs=5 fi/fs= from Andritsos

and Hanratty (1987) correlation

ReL=300

Figure 4.5 Friction velocity versus ReG at constant ReL.

d = 2.54 cm, µL = 1 cp, P=14.7 psia, T=298 K


Laminar growth rate scaling


Wave growth in turbulent flowsome similarity to laminar flow?

10−2

10−1

100

101

10−2

10−1

100

101

(ReG

−ReG,crit

)/ReG,crit

ω d

1/v*

Laminar flow for both phases(Kuru,1995)h*=0.4, λ=1 cm, Re

L=2844

h*=0.3, λ=1 cm, ReL=1228

h*=0.2, λ=1 cm, ReL=448


AtomizationMechanisms

(Woodmansee,Hanratty, 1969)


Mechanisms(Woodmansee,Hanratty, 1969)


Outside cylinder is rotated.

Rotating, Two-(matched density) liquid, Couette Flow, Wave Experiment

Hg Layer

Torque transducer

Outside cylinder is Plexiglas®, Inside cylinder is Aluminum painted black


Two-(matched density) liquid, rotatingCouette device

laser

camera

mirror

Couette Cell

mercury


Rotating Couette experiment


Wave map for rotating Couette flow experiment

50

40

30

20

10

0

plat

e sp

eed

(cm

/s)

0.80.60.40.20.0

h

No waves steady periodic unsteady waves solitary long wave stability boundary

stablelong waves steady 2-D waves occur in most of this range

Atomization


Atomization


Figure 3: A roll wave for m=0.0159, σ = 0.01 N/m, l = 0.66, and Up

= 84 cm/s. (“Dark” phase is more viscous and it is being atomized)vRelight = 560 Redark = 9.5


Figure 4: A sheet-like structure for m=0.0159, σ = 0.01 N/m, l =0.66, and Up = 84 cm/s. (“Dark” phase is more viscous and it is

being atomized)


Figure 5: A sheet-like structure just prior to break off form=0.0159, σ = 0.01 N/m, l = 0.66, and Up = 84 cm/s.

(“Dark” phase is more viscous and it is being atomized)


A series of frames 2 milliseconds apart showingthe breakup.


Breakup Occurs


The change in the height of the sheet d/d0 as a function of time.(almost) Linear stretching is observed.

0 1 2 3 4 5 6 7 8 9 10 11

0.2

0.4

0.6

0.8

1

1.2

Heig

ht, d

/d0

Time (ms)

Exptl Theory (1− .045 t)


Conclusions• 1. Atomization seems to be a generically

important process that is not understoodvery well.

– Making quantitative predictions is very difficult

• 2. Atomization in parallel two-layer flows willbe associated with the waves that are already present.

– Quantitative prediction of these waves is notpossible at present

• 3. Even base-state and linear stability predictions need further work

– This is at conditions much less severe thanatomization occurs.


Conclusions• 4. In the general case it is the more viscous

fluid that is atomizing from crests of largewaves

– Lift and shatter

– Stretch and break

• 5. There does not seem to be a reason thatsolitary waves (maybe not roll waves) canexist without significant atomization

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