Liquid Atomization and Sprays for Particle Coating and ...maeresearch.ucsd.edu/lasheras/papers/Pfpres.pdf•INTRODUCTION • Liquid Jet Breakup and Atomization • Motivation • Dissertation

Juan C. Lasheras and Alberto Aliseda

University of California, San DiegoDepartment of Mechanical and Aerospace

EngineeringWittaker Institute for Bio-Medical Engineering

La Jolla CA 92093-0411

[email protected]

Liquid Atomization and Sprays for Particle Liquid Atomization and Sprays for Particle Coating and EncapsulationCoating and Encapsulation

•INTRODUCTIONINTRODUCTION

• Liquid Jet Breakup and Atomization

• Motivation

• Dissertation Objectives•EXPERIMENTAL OBSERVATIONS AND RESULTSEXPERIMENTAL OBSERVATIONS AND RESULTS

• Experimental Setup and Techniques

• High-Speed Video Observations

• Droplet-Size Measurements

•INITIAL BREAKUP MECHANISMSINITIAL BREAKUP MECHANISMS

• Mechanisms of Breakup of Liquid Drops in High-Speed Gas Streams

• A Phenomenological Model for the Initial Breakup of Coaxial Liquid-Gas Jets based on the Rayleigh-Taylor Instability

• Discussion and Comparison of the Model with the Experiments

•SECONDARY BREAKUP MECHANISMSSECONDARY BREAKUP MECHANISMS

• Turbulent Breakup and Droplet-Droplet Collisions

• Droplet Acceleration – The ‘Convective Shuffling’ Effect

OUTLINEOUTLINE

coating in a continuous fluid bed:

Top Spray Bottom Spray

Particle Coating and EncapsulationParticle Coating and Encapsulation

Batch fluid bed coating

Top Spray

Batch fluid bed coatingBottom Spray(Wurster Coating)

Batch fluid bed coatingTangential Spray


Wurster Air Fluidization Wurster Air Fluidization Coating ProcessCoating Process

Spouted BedSpouted Bed


mailto:[email protected]

Pan CoatingPan Coating

Drying Gas Outlet

Drying Gas Inlet

Vector Pans Need Side Inlet

Tablet bed

Baffle

Process principles

Al Berchielli. Pfizer, Inc.Groton/New London Laboratories

Process principles

Spray

Droplet impact (collision )

with the particle

Spray/Air flow InteractionDroplet evaporationHeat transfer

Characteristics of the spray

Drop size distributionDrop velocity distributionDrop volume fraction

Loading of particlesOrientation of the particlesParticle/spay interaction timeCycling time

Particles Air Flow

Coat Drying, Re-crystallization , etc.

Spray

Droplet impact (collision )

with the particle

Spray/Air flow InteractionDroplet evaporationHeat transfer

Characteristics of the spray

Drop size distributionDrop velocity distributionDrop volume fraction

Loading of particlesOrientation of the particlesParticle/spay interaction timeCycling time

Particles Air Flow

Coat Drying, Re-crystallization , etc.

LIQUID ATOMIZATIONLIQUID ATOMIZATION

• atomization consists of the disintegration of a liquid mass into a multitude of small droplets

• in general, the disruption of a liquid mass to form smaller fragments occurs when the stabilizing influences of surface tension and viscosity are overcome by distorting forces

• PRESSURE ATOMIZATION

• AIR-ASSISTED ATOMIZATION

LIQUID JET BREAKUP LIQUID JET BREAKUP PRESSURE ATOMIZATIONPRESSURE ATOMIZATION

• Rayleigh-Plateau capillary breakup ⇒

a cylindrical liquid column is unstable when its length exceeds its perimeter and when this condition occurs, two drops will form which have less surface energy than the original

columnDdrop ~ Djet

• pressure atomization ⇒

Ddrop << Djet

Vjet ⇑

LIQUID JET BREAKUPLIQUID JET BREAKUPGAS-ASSISTED or AIRBLAST GAS-ASSISTED or AIRBLAST

ATOMIZATIONATOMIZATION

• the breakup and atomization of a liquid jet injected into a high-speed gas stream is fundamentally different from that which occurs for the same jet discharging into a stagnant gas

• breakup ⇒ kinetic energy transfer from the gas to the liquid

⇒ gas-assisted or airblast atomization

GAS

GAS

Coaxial Atomization

• coaxial jets present a simple way to mix two fluid streams

• common arrangement in fuel-injection applications and many other technologies

MULTI-PARAMETER, TWO-PHASE FLOW PROBLEM

GAS

GAS

LIQUID

BREAKUP OF A LIQUID JET BY A HIGH-SPEED GAS STREAM

COAXIAL ATOMIZATIONCOAXIAL ATOMIZATION

COAXIAL ATOMIZER GEOMETRYCOAXIAL ATOMIZER GEOMETRY

Ul

Ug

Dg Dl

λ1

Ag/Al ∼ O(1)

Ul

Ug

Ug

Ag /Al ∼ O(100-1000)

Coaxial SpraysCoaxial SpraysNON-DIMENSIONAL NON-DIMENSIONAL

PARAMETERSPARAMETERS

Rel = UlDl/νl liquid-jet Reynolds number

Oh = µl/(ρlσDl)1/2 Ohnesorge number

We = ρg(Ug-Ul)2Dl/σ Weber number

Reg = Ug(Dg-Dl)/νg gas-jet Reynolds number

M = ρgUg2/ρlUl

2 dynamic pressure ratio

m = ρlUlAl/ρgUgAg mass flux ratio

Agl = (Dg2-Dl,o

2)/Dl2 gas-to-liquid nozzle exit area ratio

NON-DIMENSIONAL NON-DIMENSIONAL PARAMETERSPARAMETERS

liquid-jet Reynolds number Rel = UlDl/νl ratio

of inertia to viscous forces in the liquid jet,

large=turbulent, small=laminar

Air-jet Reynolds number Reg = Ug(Dg-Dl)/νg

ratio of inertia to viscous forces in the liquid

jet, large=turbulent, small=laminar

NON-DIMENSIONAL NON-DIMENSIONAL PARAMETERSPARAMETERS

Webber Number We = ρg(Ug-Ul)2Dl/σ ratio of inertia forces to surface tension

Ohnesorge number Oh = µl/(ρlσDl)1/2 ratio of viscous forces to surface tension forces

Sequence from Joseph et al., 1999, University of Minnesota

Coaxial Jet Breakup, Ug = 165 m/s, Ul = 1.7 m/s, Ag/Al = 125

1 cm

UCSD

1 mm2.5 mm

OBSERVATIONS OF THE BREAKUP OBSERVATIONS OF THE BREAKUP PROCESSPROCESS

Ph.D. Dissertation Presentation – February 15th, 2002

Gas Flow

Droplet

Wave Crest

HIGH-SPEED GAS FLOW OVER LIQUID JET HIGH-SPEED GAS FLOW OVER LIQUID JET AND DROPLET SURFACESAND DROPLET SURFACES

GEOMETRIC SIMILARITY

DROPLET BREAKUP MECHANISMS

(Pilch and Erdman)

HIGH-SPEED DROPLET BREAKUPHIGH-SPEED DROPLET BREAKUP

SHEAR BREAKUP AND CATASTROPHIC

BREAKUP

COAXIAL JET AND DROPLET BREAKUP COAXIAL JET AND DROPLET BREAKUP REGIMES IN HIGH-SPEED GAS FLOWSREGIMES IN HIGH-SPEED GAS FLOWS

COAXIAL JET BREAKUP REGIMES Lasheras and Hopfinger, Ann. Rev.

Fluid Mech. 2000

DROPLET BREAKUP REGIMES Hsiang and Faeth, Int.

J. Multiphase Flow. 1992

10

15

20

25

30

35

0 20 40 60 80

x/D g

Dro

ple

t S

MD

(µ

m)

OBSERVED SPATIAL VARIATION OF OBSERVED SPATIAL VARIATION OF THE MEAN DROPLET DIAMETERTHE MEAN DROPLET DIAMETER

• beyond the initial breakup region, the mean drop size is observed to evolve with downstream distance

• the droplet SMD first decreases, reaching a minimum value, and then subsequently increases slightly with remaining downstream distance

• secondary droplet breakup mechanisms and other effects associated with the convection of the droplets downstream are necessary to explain these observations

Droplet SMD as a function of downstream distance in a coaxial jet spray

SMD=∑N i di3/N id i

2

Ul

Ug

Ug

• identify the mechanism of primary droplet formation

• develop a phenomenological model for the primary droplet size

• characterize the various secondary breakup mechanisms and effects that lead to downstream variations in the mean droplet diameter

EXPERIMENTAL SETUPEXPERIMENTAL SETUP

Air Air

Water

11.2 mm

1.0 mm

48.0

mm

95.0 mm

59.0

mm

Water

Air Air

1.0 mm

95.0 mm

11.2 mm

48.0

mm

59.0

mm

NOZZLE GEOMETRIES

Convergent Gas Nozzle Straight Channel Gas Nozzle

EXPERIMENTAL SETUP EXPERIMENTAL SETUP AND TECHNIQUESAND TECHNIQUES

Reservoir

Fan

Spray

Atomizer Rig

Traverser

x

Figure 3.4: Experimental Flow Facility

High-Speed Video

Reservoir

PDPA Receiver

PDPA Transmitter

Injector Assembly

Strobe Light

Figure 3.5: Top-View of Experimental Measurement Facility

EXPERIMENTAL CONDITIONSEXPERIMENTAL CONDITIONS

Rel = UlDl/νl

Oh = µl/(ρlσDl)1/2

We = ρg(Ug-Ul)2Dl/σ

Reg = Ug(Dg-Dl)/νg

M = ρgUg2/ρlUl

2

m = ρlUlAl/ρgUgAg

Agl = (Dg2-Dl,o

2)/Dl2

AirAir

Water

UgUg

Ul

Exhaust

Solenoid Valve

Dg

Dl

Dl,o

Dg = 11.2 mm, Dl,o = 1.3 mm,

Dl = (1.00 mm, 0.32 mm)

OBSERVATIONSOBSERVATIONS

Ul

Ug

Ug

Liquid Breakup Process

•the bulk of the liquid atomization is completed in the first few gas jet diameters, well within the gas potential cone by a catastrophic breakup process which generates a fine mist of droplets

•segments of the liquid jet surface are exposed to large perpendicular accelerations

~ 1 cm

1 mm

Joseph et al., UMN Drop Breakup

UCSD Coaxial Jet Breakup

We=437, m=0.07

EXPERIMENTAL INVESTIGATIONEXPERIMENTAL INVESTIGATION

Vary Liquid Jet Diameter ⇒ Dl = 0.32 mm, 1.00 mm

Vary Surface Tension ⇒ σwater = 0.073 N/m,

σethanol = 0.023 N/m

Vary Gas Boundary-Layer ⇒ dg - convergent and straight

channel gas nozzles

Vary Liquid Injection Orientation ⇒ parallel and transverse

DROP-SIZE MEASUREMENTSDROP-SIZE MEASUREMENTS

Droplet size is insensitive to the liquid jet diameter

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70

x/D g

Dro

ple

t S

MD

(µ

m)

Dl = 1.0 mm

Dl = 0.32 mm

Droplet SMD as a function of x/Dg, Ug = 165 m/s, m = 0.07

Droplet size is sensitive to the gas boundary-layer thickness


20

30

40

50

60

70

80

90

40 60 80 100 120 140 160 180

U g (m/s)

Dro

ple

t S

MD

(µ

m)

Straight Nozzle

Convergent Nozzle

Droplet SMD as a function of Ug at x/Dg = 15, Ul = 1.7 m/s, Dl = 1.0 mm


0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70

x/D g

Dro

ple

t SM

D (

µm)

Water

Ethanol

0

20

40

60

80

100

120

140

160

180

20 40 60 80 100 120 140

U g (m/s)D

rop

let

SM

D (

µm)

Water

Ethanol

Droplet SMD as a function of Ug and x/Dg for water and ethanol jets

Droplet size is significantly affected by surface tension


SMD Water/ SMD Ethanol as a function of x/Dg

Drop-size ratio ≈ σ water/σethanol ⇒ d ∝ σ1/2

1.40

1.50

1.60

1.70

1.80

1.90

2.00

0 5 10 15 20 25

x/D g

SM

D W

ate

r/S

MD

Eth

ano

l

DROP-SIZE MEASUREMENTSDROP-SIZE MEASUREMENTSEthanol droplet SMD as a function of x/Dg for

Ul = 1.7, 15.5 m/s, Ug = 165 m/s

Droplet size is only slightly sensitive to the liquid stream velocity

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70

x/D g

Dro

ple

t S

MD

(m

)

Ul = 1.7 m/s

Ul = 15.5 m/s


0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70

x/D g

Dro

ple

t S

MD

(m

)

Lateral Injection

Parallel Injection

Atomization quality is slightly superior for transverse injection compared to parallel liquid injection

Droplet SMD as a function of x/Dg Ug = 165 m/s, m = 0.07, Dl = 0.32 mm

DROP-SIZE SCALINGDROP-SIZE SCALING

1

10

100

1000

1 10 100

We dg1/2

Dro

ple

t S

MD

(µm

)

Ethanol and Water DataD l = (0.32 mm, 1.0 mm)

U l = (1.7 - 16.6 m/s)

U g = (30 - 200 m/s)

Droplet SMD as a function of Wedg1/2 at x/Dg = 15 for

water and ethanol data

Droplet SMD collapses very well with Wedg1/2

~ 1 cm

1 mm



INITIAL JET BREAKUPINITIAL JET BREAKUP

• visual observations of the near-field breakup of large-area-ratio coaxial jets have revealed a mode of liquid jet breakup which appears to share common features with the disintegration of liquid droplets in high-speed gas streams

• waves developed at the liquid jet surface by the primary shear instability are drawn out and destabilized by a secondary instability which develops along these wave and ligament surfaces

• droplets appear in images to be ‘stripped’ from the surface and a visible mist is observed to emanate from the waves in a manner similar to the mist production which occurs in the accelerative destabilization of liquid droplets

Breakup Model

~ 1 cm

1 mm



INITIAL JET BREAKUPINITIAL JET BREAKUP

• visual observations of the near-field breakup of large-area-ratio coaxial jets have revealed a mode of liquid jet breakup which appears to share common features with the disintegration of liquid droplets in high-speed gas streams

• waves developed at the liquid jet surface by the primary shear instability are drawn out and destabilized by a secondary instability which develops along these wave and ligament surfaces

• droplets appear in images to be ‘stripped’ from the surface and a visible mist is observed to emanate from the waves in a manner similar to the mist production which occurs in the accelerative destabilization of liquid droplets

BREAKUP MODELBREAKUP MODEL

a=dV l

dt=

Fml

=F

ρ l∀ l

F=FD=CD12ρgUg−Uc

2 Ae

∀ l=bAeCD≈2

b=λ1

5

Acceleration Calculation

a=ρgUg−Uc

2

ρlb⇒

λ1

Ul

λ1

Ug

b

Ug

Uc

a=5ρgUg−Uc

2

ρ l λ1

⇒Uc=ρlU lρgUg

ρ lρg

DROPLET BREAKUP MECHANISMS

(Pilch and Erdman)


SHEAR BREAKUP AND CATASTROPHIC

BREAKUP

SMDd0

=C s ρl

ρg1

4Rel−1 /2


• boundary-layer stripping (Hsiang and Faeth)

• gas-assisted stretching and Rayleigh breakup (Liu and Reitz, Villermaux)

Rδ

~Weδ

−15 ρ l

ρg2

5


• Wave-crest stripping Kelvin-Helmholtz (Pilch and Erdman)

• Rayleigh-Taylor instability (Joseph et. al)

d~ σ

ρla 1

2

PHENOMENOLOGICAL PHENOMENOLOGICAL BREAKUP MODELBREAKUP MODEL

Rayleigh-Taylor InstabilityInitial breakup due to the

d∝σ1/2Measurements indicate

Observations show ⊥ accelerations of liquid surfaces

We=37, m=0.12, Dl=0.32 mm, Ug=100 m/s, Ul=16.5 m/s

λRT≥2π σρ la

d∝ λRT

λRT

• Instability analysis yields for the critical Rayleigh-Taylor wavelength

• Rayleigh-Taylor waves set the scale for primary droplet formation


a=dV l

dt=

Fml

=F

ρ l∀ l

F=FD=CD12ρgUg−Uc

2 Ae

∀ l=bAeCD≈2

b=λ1

5


a=ρgUg−Uc

2

ρlb⇒

λ1

Ul

λ1

Ug

b

Ug

Uc

a=5ρgUg−Uc

2

ρ l λ1

⇒Uc=ρlU lρgUg

ρ lρg

PHENOMENOLOGICAL PHENOMENOLOGICAL RT BREAKUP MODELRT BREAKUP MODEL

λ1

λRT

d∝ λRT=2π σλ15ρgUg−Uc

2








λRT predicted = 210 µm λRT predicted = 188 µm

λRT predicted = 97 µm


λRT measured = 195 µm λRT measured = 185 µm

λRT measured = 85 µm


COMPARISON OF THE MODEL WITH THE COMPARISON OF THE MODEL WITH THE EXPERIMENTSEXPERIMENTS

SM D = 22268U g-1.3135

R 2 = 0.9702

SM D = 14858U g-1.2677

R 2 = 0.9741

0

20

40

60

80

100

120

140

40 60 80 100 120 140 160 180

U g (m/s)

Dro

ple

t S

MD

(m

)

Water Dl =0.32 mm, Ul = 5 m/s

Water Dl=0.32 mm, Ul = 16.6 m/s

Power (Water Dl=0.32 mm, Ul = 16.6 m/s)

Power (Water Dl =0.32 mm, Ul = 5 m/s)

SMD∝Ug−n

n = 1.25

λ1Reλ1

−1/2¿Ug

−1 /2 Ug−1 /2

1/2=Ug

−3 /4

Current Rayleigh-Taylor Model

SMD∝Ug−3 /4


GAS VELOCITY SCALING

Boundary-layer Stripping

Kelvin-Helmholtz Model

d∝Ug−4 /5

d∝Ug−3 /4

Faraday Instability, Görtler Instability

Power-law curve-fitted plots of droplet SMD as a function of Ug

n = 0.75

n = 0.75

SMD∝Ug−5 /4

Stretch-Assisted Sheet Stripping/Capillary Instability

n = 0.8

n = 0.75

ATOMIZATION OF A SMALL-DIAMETER LIQUID JET BY A HIGH-SPEED GAS STREAMATOMIZATION OF A SMALL-DIAMETER LIQUID JET BY A HIGH-SPEED GAS STREAM BREAKUP CONCLUSIONS BREAKUP CONCLUSIONS

• the breakup process for large Weber numbers in the present coaxial jet geometry occurs through an accelerative destabilization of the primary wave surfaces and an aerodynamic stripping process which closely resembles that which occurs in the breakup of liquid droplets by high-speed gas streams

• a phenomenological initial breakup model has been developed which proposes that the primary droplet size should scale with the critical wavelength of the Rayleigh-Taylor instability

• predictions from the RT model have been shown to compare very well with droplet-size measurements and instability wavelengths in the aerodynamic breakup of both water and ethanol jets

SMDd0

=C s ρl

ρg1

4Rel−1 /2


• boundary-layer stripping (Hsiang and Faeth)

• gas-assisted stretching and Rayleigh breakup (Liu and Reitz, Villermaux)

Rδ

~Weδ

−15 ρ l

ρg2

5


• Wave-crest stripping Kelvin-Helmholtz (Pilch and Erdman)

• Rayleigh-Taylor instability (Joseph et. al)

d~ σ

ρla 1

2

PHENOMENOLOGICAL PHENOMENOLOGICAL BREAKUP MODELBREAKUP MODEL

Rayleigh-Taylor InstabilityInitial breakup due to the

d∝σ1/2Measurements indicate

Observations show ⊥ accelerations of liquid surfaces


λRT≥2π σρ la

d∝ λRT

λRT

• Instability analysis yields for the critical Rayleigh-Taylor wavelength

• Rayleigh-Taylor waves set the scale for primary droplet formation


a=dV l

dt=

Fml

=F

ρ l∀ l

F=FD=CD12ρgUg−Uc

2 Ae

∀ l=bAeCD≈2

b=λ1

5


a=ρgUg−Uc

2

ρlb⇒

λ1

Ul

λ1

Ug

b

Ug

Uc

a=5ρgUg−Uc

2

ρ l λ1

⇒Uc=ρlU lρgUg

ρ lρg

PHENOMENOLOGICAL PHENOMENOLOGICAL RT BREAKUP MODELRT BREAKUP MODEL

λ1

λRT

21

)(52

cggRT UU

d−

=∝ρ

σλπλ









λRT predicted = 97 µm



λRT measured = 85 µm



SM D = 22268U g-1.3135

R 2 = 0.9702

SM D = 14858U g-1.2677

R 2 = 0.9741

0

20

40

60

80

100

120

140

40 60 80 100 120 140 160 180

U g (m/s)

Dro

ple

t S

MD

(m

)

Water Dl =0.32 mm, Ul = 5 m/s

Water Dl=0.32 mm, Ul = 16.6 m/s

Power (Water Dl=0.32 mm, Ul = 16.6 m/s)

Power (Water Dl =0.32 mm, Ul = 5 m/s)

SMD∝Ug−n

n = 1.25

λ1Reλ1

−1/2¿Ug

−1 /2 Ug−1 /2

1/2=Ug

−3 /4

Current Rayleigh-Taylor Model

SMD∝Ug−3 /4


GAS VELOCITY SCALING

Boundary-layer Stripping

Kelvin-Helmholtz Model

d∝Ug−4 /5

d∝Ug−3 /4

Faraday Instability, Görtler Instability

Power-law curve-fitted plots of droplet SMD as a function of Ug

n = 0.75

n = 0.75

SMD∝Ug−5 /4

Stretch-Assisted Sheet Stripping/Capillary Instability

n = 0.8

n = 0.75

ATOMIZATION OF A SMALL-DIAMETER LIQUID JET BY A HIGH-SPEED GAS STREAMATOMIZATION OF A SMALL-DIAMETER LIQUID JET BY A HIGH-SPEED GAS STREAM INITIAL BREAKUP CONCLUSIONSINITIAL BREAKUP CONCLUSIONS

• the initial breakup process for large Weber numbers in the present coaxial jet geometry appears to occur through an accelerative destabilization of the primary wave surfaces and an aerodynamic stripping process which closely resembles that which occurs in the breakup of liquid droplets by high-speed gas streams

• a phenomenological initial breakup model has been developed which proposes that the primary droplet size should scale with the critical wavelength of the Rayleigh-Taylor instability

• predictions from the RT model have been shown to compare very well with droplet-size measurements and instability wavelengths in the aerodynamic breakup of both water and ethanol jets

10

15

20

25

30

35

0 20 40 60 80

x/D g

Dro

ple

t S

MD

(µ

m)

SECONDARY DROPLET SECONDARY DROPLET BREAKUP MECHANISMSBREAKUP MECHANISMS

∇ x⋅vn QbQc=0

coalescence effectsbreakup effectsaccelerative effects

Collision Weber Number

Collision Outcomes•stable coalescence•temporary coalescence •bouncing •drop shattering (Wecoll > 80)

TURBULENT BREAKUP AND TURBULENT BREAKUP AND DROPLET-DROPLET COLLISIONS DROPLET-DROPLET COLLISIONS

Turbulent Weber Number Wet=ρgud

2d

σ

Wecoll=ρ lU rel

2 d

σ

•breakup for Wet ≥ 1

(Georjon and Reitz)

1

10

100

1000

10000

50 70 90 110 130 150 170 190

U g (m/s)

Me

asu

red

an

d P

red

icte

d D

iam

ete

rs (

m)

SMD (Experiments)Turbulent Breakup CalculationCollisional Breakup Calculation

TURBULENT BREAKUP AND TURBULENT BREAKUP AND DROPLET-DROPLET COLLISIONS DROPLET-DROPLET COLLISIONS

dcrit≈ σρg 3

5 Wet crit3

5 ε−2

5

ud 2∝ εd

23

dcrit≈Wecoll critσ

ρ lU rel2

Turbulent Breakup

Collisional Breakup

Turbulent Breakup

Droplet SMD as a function of Ug, Ul = 1.7 m/s, Dl = 1.0 mm

• shattering collisions and satellite droplet forming collisions have been experimentally observed for Wecol > 80 (O’Rourke),

and numerically for Wecol > 92 (Georjon and Reitz)

Z12=5N1N2d122U1

2U2

21/2

U i2=

U2

11.5τi ε /U2

τ i=ρid i2/18μ

Collision Rate

DROPLET COLLISIONSDROPLET COLLISIONS

Collision rates for particles in turbulent fluids are typically calculated assuming ⇒

• low energy dissipation

• particles are small compared with the smallest turbulent eddies

• particles follow the fluid motion completely

CURRENT STUDY

• vigorous turbulence

• dp > η

• Particle and fluid velocities do not coincide

(Abrahamson)

• coaxial jet PDPA measurements

• 28 distinct collision events analyzed involving 7 droplet size classes

• maximum collision Weber numbers and collision rates calculated

• results compared with experimentally observed droplet shattering limits

EXPERIMENTAL ANALYSIS



Maximum Collisional Weber Number vs. Dowstream Distance,

Ug = 165 m/s, Ul = 1.7 m/s, Ag/Al = 125

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25x/Dg

Col

lisio

n W

eber

Num

ber

10 - 10 micron

15 - 15 micron

20 - 20 micron

30 - 30 micron

40 - 40 micron

50 - 50 micron

Collision Rate vs. Dowstream Distance,

Ug = 165 m/s, Ul = 1.7 m/s, Ag/Al = 125

0

5

10

15

20

25

30

35

40

45

4 6 8 10 12 14 16

x/Dg

Col

lisio

n R

ate

(#/c

c/s)

10 - 10 micron

15 - 15 micron

20 - 20 micron

30 - 30 micron

40 - 40 micron

50 - 50 micron

60 - 60 micron

•collisions leading to droplet breakup are possible based on maximum Wecoll values

•although collision rates are low in these dilute systems, their overall effect may be strong enough to explain experimental observations


n i

dv i

dxv i

dnidx

=0

RELATIVE ACCELERATION EFFECTSRELATIVE ACCELERATION EFFECTS

Mean centerline droplet velocity decays• for given initial distributions

of droplet size and droplet velocities, ni(x) may be calculated, provided that information of vi(x) exists

• ni(x) ⇒ SMD(x)

v i

dv i

dx=

34CD i

ρ g

ρ l

v i−Ug x 2

d i

CDi=24 /Rei1Rei

2 /3/6

-25

-15

-5

5

15

25

35

0 10 20 30 40 50 60

x/D g

Ud -

Ug

(m

/s)

5

10

15

20

25

30

Dro

ple

t S

MD

(m

)Ud>50 - Ugas

SMD15

20

25

30

35

0 20 40 60 80x/D g

Dro

ple

t S

MD

(M

ea

su

red

an

d

Ca

lcu

late

d f

rom

Ac

ce

lera

tio

n)

SMD Calculations

SMD experimental

RELATIVE ACCELERATION EFFECTSRELATIVE ACCELERATION EFFECTSDroplet SMD as a function of x/Dg

Ug = 165 m/s, Ul = 1.7 m/s, Dl = 1.0 mm

• the minimum SMD occurs at the same location where the slip velocity between the gas and the largest droplets is a maximum

• calculated droplet SMD evolution due to relative acceleration effects compared with measured SMD evolution

ATOMIZATION OF A SMALL-DIAMETER LIQUID JET BY A HIGH-SPEED GAS STREAMATOMIZATION OF A SMALL-DIAMETER LIQUID JET BY A HIGH-SPEED GAS STREAM SECONDARY BREAKUP CONCLUSIONSSECONDARY BREAKUP CONCLUSIONS

• an analysis of several secondary breakup mechanisms has been carried out to determine the dominant mechanisms which affect the downstream evolution of the drop-size distribution in coaxial-jet sprays

• the creation of a polydisperse size distribution in the initial breakup process leads to a convective shuffling effect wherein the relative acceleration of different drop size classes leads to a downstream variation in the mean drop size

• the current experimental results support the theory that droplet-droplet collisions leading to shattering or fragmentation are the most plausible explanation for the observed reduction in the mean droplet size in the region which follows the initial breakup process

COAXIAL ATOMIZATION AND THE PDECOAXIAL ATOMIZATION AND THE PDE

2

3

4

5

6

7

8

9

140 160 180 200 220 240

Atomizer Air Velocity (m/s)

∆P

(psi

)

15

17

19

21

23

25

SMD

(µm

)

∆ P

SMD

0

5

10

15

20

25

30

140 160 180 200 220 240

Atomizing Air Velocity (m/s)

SMD

(µm

)Exp. Water Data

Water Predicted

JP-10 Predicted

σJP-10 < σwater

• coaxial atomizer pressure drop requirements are lower than the air pressure drop available at altitude and sufficient for optimum droplet atomization

• at air-injection velocities greater than 220 m/s, which are realizable under typical PDE operating conditions, predicted JP-10 SMD droplet diameters are less than 10 µm (SMD values below 10 µm are currently assumed to be necessary in practice)


0. 000

0. 016

0. 032

0. 048

0. 064

0. 080

0. 096

0 2 4 6 8 10 12

r/D g

LMF

(g/c

m2 /s

) S = 0

S > S cr

0. 000

0. 004

0. 008

0. 012

0. 016

0. 020

0. 024

0. 028

0 2 4 6 8 10 12 14

r/D g

LM

F (

g/c

m2 /s

)S = 0

S > S cr0. 000

0. 002

0. 004

0. 006

0. 008

0. 010

0. 012

0 2 4 6 8 10 12 14

r/D g

LM

F (

g/c

m2/s

)

S = 0

S > S cr

x/Dg = 20

Radial LMF Distributions at Various Downstream Locations

x/Dg = 40

x/Dg = 60

• Radial liquid mass flux distributions are dramatically Radial liquid mass flux distributions are dramatically affected for supercritical swirl numbers, becoming affected for supercritical swirl numbers, becoming significantly more uniform in the radial directionsignificantly more uniform in the radial direction

SWIRL-ENHANCED ATOMIZATION SWIRL-ENHANCED ATOMIZATION AND FUEL DISPERSIONAND FUEL DISPERSION


• A high degree of A high degree of control of the liquid control of the liquid mass flux mass flux distribution is distribution is possible through possible through variation of the variation of the

swirl numberswirl number

0.000

0.008

0.016

0.024

0.032

0 2 4 6 8 10 12r/D g

LMF

(g/c

m2 /s

)

S = 0

S = 0.18

S = 0.27

S = 0.47

Radial LMF Distributions at x/Dg = 40

CONTROL OF THE RADIAL LMF DISTRIBUTIONS CONTROL OF THE RADIAL LMF DISTRIBUTIONS WITH VARYING SWIRL NUMBERWITH VARYING SWIRL NUMBER


• Supercritical gas swirl creates a radial size distribution which is nearly uniform across the spray and also reduces mean drop sizes

8

9

10

11

12

13

14

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

r/D g

d10

(µ

m)

S = 0

S = 0.47

VARIATION OF THE MEAN DROPLET VARIATION OF THE MEAN DROPLET DIAMETER FOR DIAMETER FOR SS = 0 AND = 0 AND SS > > SScrcr


PULSE DETONATION ENGINESPULSE DETONATION ENGINES SUMMARYSUMMARY

• Experimental results indicate that from the viewpoint of ‘good’ atomization quality, coaxial injection is indeed a feasible option for meeting the transient fuel-injection needs of the PDE

• Coaxial atomizer pressure drop requirements have been shown to be lower than the air pressure drop available at design Mach numbers and altitudes, and are sufficient for optimum droplet atomization; SMD < 9 µm for JP-10

• The addition of varying amounts of gas swirl has been shown to facilitate the tailoring of the radial liquid mass flux distribution and yield overall reductions in mean droplet sizes


0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100

x/D g

SM

D (

m)

Ug = 50 m/s, m =0.23,M =1.0, We =38

Ug = 80 m/s, m =0.14,M =2.6, We =100

Ug = 100 m/s, m =0.12,M =4.1, We =158

Ug = 165 m/s, m =0.07,M =11.1, We =437


DROP-SIZE SCALINGDROP-SIZE SCALING

Droplet SMD collapse with We1/2 is very good

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50We 1/2

Dro

ple

t S

MD

(m

)Dl=0.32mm, Ul=16.6, Water

Dl=1.0mm, Ul=1.7, Water

Dl=0.32mm, Ul=5.0, Water

Dl=0.32mm, Ul=5.0, Ethanol

Dl=1.0mm, Ul=1.7, Ethanol

Droplet SMD as a function of We1/2 at x/Dg = 15 for water and ethanol data

Documents

Liquid Atomization and Sprays for Particle Coating and ...maeresearch.ucsd.edu/lasheras/papers/Pfpres.pdf•INTRODUCTION • Liquid Jet Breakup and Atomization • Motivation • Dissertation