breakage of single droplets in 2-d turbulent flowsdomino.bhrgroup.com/portals/0/meeting...

Breakage of Single Droplets

in 2-D Turbulent Flows

UM - HSMRP

Derrick I. Ko* and Richard V. Calabrese

University of Maryland

College Park, MD 20742-2111 USA

DOMINO-HSMRP Project Meetings

24 May 2017

Project Objective

• Goal: Determine conditions for break-up of large

single droplets due to short-term, high-intensity

deformation events in turbulent flows.

– Aim to correlate breakage probability to an

appropriately-defined Weber number.

– Studied two fluids as dispersed phase: oil droplets

and air bubbles.

2

Experimental Approach

• Droplets passed through 2-D channel flow with orifice

– Droplets experience deformation due to the well-defined velocity field

• Experimentally monitor breakage events to determine droplet

trajectories and locations of break-up

– High-resolution, standard frames-per-second (fps) camera with strobe

– High fps camera for visualizing breakage dynamics

• CFD simulations will inform experiment selection and data

interpretation

– Flow loop and experimental design

– Deformation rates and other flow field properties along droplet trajectories

• Combine experimental and computational results to develop

new models for predicting droplet break-up 3

Drop Break-up in Simple Flows

4

Reynolds Number

1 0.1 0.01 10 100 1000 104 0.001 105 106

Droplet

Diameter 𝑑

𝐿= 𝑓 Ca, λ

Creeping / Stokes

Flow (Re < 1)

ηKolmogorov

Lmacro

𝑑

𝐿= 𝑓 We, Vi

Inertial Subrange

Viscous Subrange

Tra

nsit

ion

Flo

w

𝑑

𝐿= 𝑓 We, Vi, Re

𝑑

𝐿= 𝑓 Ca, Re, λ

Laminar Inertial Flow

(1 < Re < 1000)

λ =𝜇𝑑𝜇𝑐

Ca =𝜇𝑐𝑈

𝜎

Re =𝜌𝑐𝑈𝐿

𝜇𝑐

We =𝜌𝑐𝑈

2𝐿

𝜎 Vi =𝜌𝑐𝜌𝑑

𝜇𝑑𝑈

𝜎

Macroscale

Not well studied

Not well studied

Grace Curves

107

Turbulent Flow

(Re > 10,000)

Experimental Apparatus

and Design

Breakage of Single Droplets in 2-D Turbulent Flows

5

Design Criteria

• 4” x ½” cross-section in open channel (8:1)

– Rectangular cross-section for easier imaging

• 36” entrance length prior to test section

– CFD used to determine the entrance length based on the inlet

configuration

• Minimum of 24” downstream of contraction

– Reattachment of wake region to limit exit effects

6

Experimental Flow Loop

7

z

x

8”

18”

18”

18”

Upstream

Section

Test

Section

Downstream

Section

Discharge

Tank

Seepex Progressive

Cavity Pump

Mass Flow Meter

(40-90 L/m)

Holding

Tank

(55L)

Test Section Detail

Channel Cross Section

Height = 1.27 cm (1/2 in.)

Width = 10.16 cm (4 in.)

Orifice Cross Section

Height = 0.32 cm (1/8 in.)

(25% open)

Width = 10.16 cm (4 in)

Continuous Phase

Properties

Density = 998 kg/m3

Viscosity = 1 cP

Maximum Re = 27,000

23” Inlet

Section

Drop injection port

Note: open channel and orifice have the same Reynolds number

Apparatus

Downstream

Section

Discharge

Tank

Test

Section

Camera

Strobe

Inlet Section

Upstream

Section

Pressure

Transmitter

Holding

Tank

• 25% Orifice leaves center 1/8” (25%) of channel

open for flow

• Injection of droplets automated by syringe

pump

• Two General Radio #1539a stroboscopes triggered

by programmable microcontroller provides

backlighting of droplets and bubbles

Test Section Details

9

10” minus

1/8” orifice

z

y

Orifice Slit

(25% open)

Flow

Injection

• Injection port consists of

Swagelok straight with rubber

septum

• Syringe with various needle

gauges (33, 30, 27, 26, 23, 21)

used to pierce septum and create

droplet directly in the channel

flow; droplet size dependent on

local flow conditions and surface

tension

Camera looks

into screen

Imaging with Pulnix Camera

• Data acquisition and investigative imaging

– Pulnix TM-1405GE camera with 1392 x 1040 pixel resolution

and frame rate of ~30 frames/second (fps)

– To compensate for low frame rate, the strobe to capture multiple

images per frame

• Strobe controlled by microcontroller provides ~1 μs duration flashes

up to 420 Hz or ~14 flashes/frame (fpf)

– Break-up details will not always be visible for each drop, but we

will be able to identify the location and mechanism of breakage

• High-speed imaging

– VRI Phantom V640 camera with 1600 x 700 pixel resolution and

frame rate of up to ~3000 fps

– Droplet trajectories more finely resolved than with Pulnix camera

10

Project Goals

• Goal: Develop predictive models for breakage

probability of oil droplets and air bubbles based

on appropriately defined Weber numbers using:

– Local flow conditions around the droplet

– Droplet trajectory upstream of the orifice

– Droplet trajectory through the orifice

11

Upstream Orifice

Local Conditions

2-D Channel Flows


12

CFD with 2-D Slit Orifice

Re = 27,000 Turbulent RANS Simulation

• 3-D full channel simulations

– Turbulent: RANS w-realizable k- model & enhanced

wall treatment

– Solution Methods: PISO, 2nd order upwind for

advection terms, 2nd order for pressure, 2nd order

implicit for time

– 30 x 30 grid resolution in orifice cross-section (1.4

million cell domain)

• The flow through a rectangular orifice is not

symmetric

– “Leans” left or right depending upon initial conditions

– Asymmetry maintained by Coanda effect (lower

pressure in higher speed recirculation region)

Flow

Gravity

Turbulent Flow Observations Asymmetric Flow when Channel Height / Orifice Height > 1.5

14

Re = ~13,000 Streamlines of

Mean Flow

El Khoury GK, Pettersen B, Andersson HI, and Barri M (2010). Asymmetries in an obstructed turbulent channel

flow. Physics of Fluids, vol. 22, pp. 095103. (Norwegian University of Science and Technology)

Escudier MP, Oliviera PJ, Poole RJ (2002). Turbulent flow through a plane sudden expansion of moderate

aspect ratio. Physics of Fluids, vol. 14, pp. 3641. (University of Liverpool)

El Khoury et al. (2010): 50% open 2-D orifice simulated with 3-D DNS

Escudier et al. (2002): 4:1 sudden expansion measured with LDA

Re = 110,000 Streamwise Velocity

x=0mm

x=+15mm

x=–15mm

Validation via Dye Pathlines Turbulent Water Flow with FD&C Red #3 Dye Injection

15

Re = 3,400

Uorf = 0.56 m/s

Re = 7,100

Uorf = 1.16 m/s Front View

Side View

Side View

Animations at 20 fps (2/3 real-time speed); Strobe at 1 fpf

12 H = 15.24cm (6 in)

Flow is

vertically

upward

15

Extent of Jet Lean and Recirculation Turbulent Water Flow with FD&C Red #3 Dye Injection

16

Re=3,400

Re=7,100

Re=7,100

Re=7,100

Injection

Injection

Injection

Injection

Jet leaning and the extent of ‘small’ recirculation region does

not appear to be dependent on Reynolds number, but upstream

conditions can change the side on which they occur.

1.3cm~1H 1.3cm~1H

H=1.27cm

= 0.5 in.

Flow is

vertically

upward

Extent of Jet Lean and Recirculation Turbulent Water Flow

17

1.3 cm ~ 1H

RANS CFD

Re = 14,000

Uorf = 2.2 m/s

Full channel simulation

H = 1.27 cm

Experiment

Re = 37,000

Uorf = 6.0 m/s

Bubbles in water

1.24 cm ~ 1H

H = 1.27cm

Flow is

vertically

upward

Strain Rate Magnitude vs. Orifice Velocity

18

Limits for SRM Contours

Re

=7

70

0

Re

=1

00

00

Re

=1

40

00

Re Uch

(m/s)

Uorf

(m/s)

Max SRM

Contour

Limit

(1/s)

Min SRM

Contour

Limit

(1/s)

7700 0.305 1.22 1910 191

10000 0.413 1.65 2600 260

14000 0.555 2.22 3500 350

19000 0.745 2.98 4680 468

1576*Uorf 158*Uorf

Re

=1

90

00

Length Scales

ηKolmogorov = 5 – 20 µm

ηTaylor = 60 – 300 µm

Lmacro > 1000 µm

D = 200 – 1200 µm

Droplet Trajectories


19

Image Analysis

• Subtract background

• Threshold image

• Eliminate image artifacts (ex: single pixels)

• Use flood fill routine to identify droplets

– Droplets with less than 20 pixels are ignored

• Calculate

– Mean equivalent spherical diameter

– Incoming trajectory

– Trajectory through orifice

20

21

Experimental Conditions

Low Pressure Wake Region

High Pressure Wake Region

Flow

Rate

Q

[L/s]

Average

Orifice

Velocity

Uorf

[m/s]

Reynolds

Number

Re

0.39 1.22 7,700

0.53 1.65 10,000

0.72 2.22 14,000

0.96* 2.98 19,000

Phase Fluid Density

[kg/m3]

Viscosity

[cP]

Interfacial

Tension

w/ Water

[mN/m]

Continuous Water 998 1 -

Dispersed

Air 1.2 0.018 72.0

Crystal Oil

70FG 860 24 54.8

Flow Conditions Material Properties

Some images

‘flipped’ so jet

always leans in

same direction

* oil droplets only

200 < D < 1200 µm y

z 2δ = 3175 µm

Droplet Break-up Videos

22

Video Playback at 10 fps

1/100th real speed at Re = 10,000

1/140th real speed at Re = 14,000

Drop

Fluid Rech

D

(µm) Break-up Area Link ID#

Oil 14,000 700 Orifice leading edge Link 2/2

Oil 10,000 570 Orifice trailing edge, folding Link 3/5

Oil 10,000 760 Orifice trailing edge, folding Link 4/2

Air 10,000 700 Orifice trailing edge, binary Link 4/4

Oil 10,000 560 High pressure jet edge Link 6/10

Oil 14,000 675 Low pressure jet edge Link 2/4

Air 10,000 910 Close to orifice, but no break Link 6/4

Oil 14,000 633 Re-entrained into orifice Link 7/2

Oil_Re14000_Run02_Drop02.avi



Air_Re10000_Run04_Drop04.avi



Air_Re10000_Run06_Drop04.avi


Single Droplet Trajectory High-speed Imaging

23

-4 -2 0 2 4 6 8-4

-3

-2

-1

0

1

2

3

4

𝑧∗ = 𝑧 𝛿

𝑦∗=𝑦

𝛿

Experimental Droplet Trajectory Deformation Field

(Strain Rate Magnitude)

Break-up occurs in high deformation

regions in orifice and along jet edge.

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5-0.5

0

0.5

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5-0.5

0

0.5

Grouped Droplet Trajectories Diameter and Reynolds Number

• Grouped trajectories did not show significant

influence of diameter or Reynolds number on

trajectories near orifice.

Oil Droplets, 400 < D < 600 µm (17 droplets)

Oil Droplets, 600 < D < 800 µm (12 droplets)

Re=10,000, Drop Intact

Re=10,000, Drop Broken



24

-0.5 0 0.5 1 1.5 2 2.5 3-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Grouped Droplet Trajectories Lateral Migration

• Air bubbles migrate across jet in response to the

pressure differential that causes the leaning jet.

Oil Droplets, 31 droplets Air Bubbles, 12 bubbles

Average Trajectory





-0.5 0 0.5 1 1.5 2 2.5 3-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

25

High

Pressure

Region

Low

Pressure

Region

High

Pressure

Region

Low

Pressure

Region

Lateral Migration Prediction based

on Discrete Phase Model

26

-6 -4 -2 0 2 4 6 8 10

-4

-3

-2

-1

0

1

2

3

4

-6 -4 -2 0 2 4 6 8 10

-4

-3

-2

-1

0

1

2

3

4

Oil Droplets

Air Bubbles

• The lighter air bubbles

are more heavily

influenced by the

pressure differential

across the jet.

• FLUENT predicts that

the lateral migration is

greater when

Reynolds number is

lower.

Re = 19000

Re = 7700

Re = 19000

Re = 7700

D = 700 μm

D = 700 μm

Lateral Migration due to

Pressure Across Jet

Re=7700 Re=19000 ΔP = ~155 Pa ΔP = ~850 Pa

ρU2 = ~93 Pa ρU2 = ~554 Pa

ρU2

ΔP

It turns out that the

pressure across the jet

does not scale up with U2.

The stream-wise

momentum increases

relative to the lateral

force.

ΔP based on z=4δ

ΔP/ρU2 = ~1.53 ΔP/ρU2 = ~1.67

𝑦∗ = 𝑦 𝛿

Pre

ssu

re D

iffe

ren

ce

Re

lative

to

P(y

=0)

(Pa

)

27

Summary of Observations from

Droplet Paths

• Drops break on interaction with the shear layers.

• Drop paths are not strongly affected by channel

Reynolds number or droplet diameter.

• Drops tend to move toward the low pressure wake

region due to pressure differential across jet.

– Air bubbles is more strongly affected than oil droplets.

– The strength of the lateral migration depends on Reynolds

number.

28

Modeling Break-up


29

Correlate Probability of

Breakage vs Weber Number

Breakage probability can be correlated to an appropriately

defined Weber number dependent on:

• Local flow conditions can provide a potentially device-independent

criteria for break-up, but requires an intensive degree of information.

• Upstream trajectory requires the drop distribution upstream of the

orifice, but is device dependent.

• Orifice trajectory is an intermediate form that requires drop

distribution at some point in the orifice but may be useful for a wider

range of devices (e.g. multi-orifice plates). Not yet complete. 30

𝑊𝑒 =𝜌𝑑𝜌𝑐

1/3𝜌𝑐𝑈

2

𝜎/𝐷

inertial forces

interfacial forces

Levich density correction (internal pressure vs Capillary

pressure)

Local Weber Number Strain Rate Magnitude vs Time Average

31

0 5 10 15 20 250

200

400

600

800

1000

1200

1400

1600

1800

2000

Time [ms]

Magnitude o

f S

train

Rate

[

1/s

]

Run04 Drop04

-4 -2 0 2 4 6 8-4

-3

-2

-1

0

1

2

3

4

𝑧∗ = 𝑧 𝛿

𝑦∗=𝑦

𝛿

Experimental Data (High-speed Images)

Computational Data (Deformation Field)

Deformation History of Droplet

Local Weber Number Definition

32

Characteristic Strain Rate

• Shear only

• Extensional only

• Strain rate magnitude

• Shear rotated to droplet

coordinate system

• Turbulent kinetic energy

• Turbulence dissipation rate

𝑊𝑒𝑙𝑜𝑐𝑎𝑙 =𝜌𝑑𝜌𝑐

1/3𝜌𝑐𝑼

2

𝜎/𝐷 𝑡∗ =

𝑡

𝒕𝒔𝒄𝒂𝒍𝒆

Time Scale

• Particle response to

fluid motion

• Oscillation time

• Eddy time k/ε

𝑡∗

𝑊𝑒𝑙𝑜𝑐𝑎𝑙

Stable

Unstable

velocity scale

𝑈 = 𝜸 𝒕∗𝐷

Local Weber Number Peak Weber # for Different Averaging Times

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

t=t/tscale

Weber

#

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

t=t/tscale

Weber

#

𝑡∗ = 𝑡 𝑡𝑠𝑐𝑎𝑙𝑒 𝑡∗ = 𝑡 𝑡𝑠𝑐𝑎𝑙𝑒

𝑊𝑒𝑙𝑜𝑐𝑎𝑙 =𝜌𝑑𝜌𝑐

1/3𝜌𝑐𝛾

2𝐷3

𝜎 𝑡𝑠𝑐𝑎𝑙𝑒 =

𝑈𝑡𝑔

𝜌𝑑 + 𝜌𝑐 2

𝜌𝑑 − 𝜌𝑐

𝛾 is the maximum strain rate magnitude over an averaging time of tscale x t*.

Oil Droplets Air Bubbles

Ut is the terminal velocity of a spherical drop.

Broken Air Bubble

Unbroken Air Bubble

Broken Oil Droplet

Unbroken Oil Droplet

Re=10000 and Re=14000 Re=10000 and Re=14000

𝑊𝑒 𝑙𝑜𝑐𝑎𝑙

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

10

20

30

40

50

60

t=t/tscale

Weber

#

Local Weber Number Removing Overlapping Data

𝑊𝑒 𝑙𝑜𝑐𝑎𝑙

𝑡∗ = 𝑡 𝑡𝑠𝑐𝑎𝑙𝑒

Combined oil and air data sets, and removed 25% of

the data to determine a potential critical Weber number.

Welocal,crit~13

Broken Oil Droplet

Unbroken Oil Droplet

Broken Air Bubble

Unbroken Air Bubble

34

Re=10000 and Re=14000

Breakage Probability vs. Weber

Number

• Coulaloglou & Tavlarides (1977) for droplets in the

inertial subrange:

• Percy & Sleicher (1987) and Galinat et al. (2005) for

“bulk” droplet break-up:

• We used the same model forms, but adjust Weber

number for macroscale droplets:

35

𝑃 = 𝐶1exp −𝐶2𝑊𝑒

𝑃 = 𝑊𝑒𝐶1exp −𝐶2𝑊𝑒

𝑊𝑒𝐶𝑇 =𝜌𝑐휀

2/3𝐷5/3

𝜎

𝑊𝑒𝑃𝑆 =(∆𝑃/𝐷𝑜)𝐷

2

𝜎

𝑊𝑒𝐺 =∆𝑃𝐷

𝜎

𝑈 = 𝛾 𝐷

Probability vs Local Weber Number

at Different Averaging Times

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weber Number

Pro

babili

ty o

f B

reak-u

p

Exponential Fit

𝑃 = 1.03exp −5.29


0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weber Number

Pro

babili

ty o

f B

reak-u

p

Exponential Fit

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weber Number

Pro

babili

ty o

f B

reak-u

p

Exponential Fit

𝑡∗ = 0 𝑡∗ = 0.04

𝑡∗ = 0.08

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weber Number

Pro

babili

ty o

f B

reak-u

p

Exponential Fit

𝑡∗ = 0.10

𝑃 = 0.958exp −2.82


𝑃 = 1.01exp −4.00


𝑃 = 0.944exp −5.54


𝛾 = 𝛾 𝑚𝑎𝑥

Upstream Weber Number

37

𝑊𝑒𝑢𝑝𝑠𝑡𝑟 =𝜌𝑑𝜌𝑐

1/3 𝜌𝑐𝑼𝒐𝒓𝒇

𝜹

2

𝐷3

𝜎

𝑦∗ =𝑦

𝛿

80%

50%

20% 𝛿 = 1.59 mm

is a complicated variable, depending on:

• Channel velocity

• Incoming trajectory of droplet

• Droplet material

• Variations due to turbulence

Can probability be predicted without depending on knowing the exact droplet

path and flow field?

𝛾

-4 -3 -2 -1 0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

y*

We

bulk

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

y*

We

bulk

Upstream Weber Number Droplet Distribution

38

𝑦∗ = 𝑦 𝛿

𝑊𝑒 𝑢

𝑝𝑠𝑡𝑟


Re = 19,000

Re = 14,000

Re = 10,000

Re = 7,700

𝑦∗ = 𝑦 𝛿

X = broken

O = unbroken

orifice opening orifice opening

Regions with less than 5 droplets will be ignored.

Both Pulnix and

Phantom data are

included.

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

y*

We

bulk

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Upstream Weber Number Breakage Probability

39

𝑦∗ = 𝑦 𝛿

𝑊𝑒 𝑢

𝑝𝑠𝑡𝑟


𝑦∗ = 𝑦 𝛿

-4 -3 -2 -1 0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

y*

We

bulk

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Regions with less than 5 droplets are ignored.

0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

y*

We

bulk

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Upstream Weber Number Contour Smoothing

𝑃 = 1 − exp (−𝐶 𝑊𝑒𝑢𝑝𝑠𝑡𝑟)

Fit exponential equation to

Probability vs We at each y*

𝑦∗ = 𝑦 𝛿

𝑊𝑒 𝑢

𝑝𝑠𝑡𝑟

𝑊𝑒𝑢𝑝𝑠𝑡𝑟 = 𝜌𝑐2𝜌𝑑

1/3𝐷3 𝜎 𝑈𝑜𝑟𝑓 𝛿 2

Pro

bab

ilit

y o

f B

reak

-up

40

orifice opening

y*

We

bulk

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

y*

We

bulk

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Upstream Weber Number Contour Smoothing

𝑦∗ = 𝑦 𝛿

𝑊𝑒 𝑢

𝑝𝑠𝑡𝑟

𝑦∗ = 𝑦 𝛿

𝑊𝑒 𝑢

𝑝𝑠𝑡𝑟

41


y*

We

bulk

-4 -3 -2 -1 0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y*

We

bulk

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Upstream Weber Number Contour Plots

42

𝑦∗ = 𝑦 𝛿

𝑊𝑒 𝑢

𝑝𝑠𝑡𝑟


𝑦∗ = 𝑦 𝛿


-3 -1 1 3 -3 -1 1 3

We 1 0.55 0.15 0.15 0.45 13 19 25 14 TOTAL DROPLETS

3 0.95 0.45 0.25 0.85 16 16 12 11 440 droplets

5 0.95 0.65 0.55 0.95 28 43 37 38

7 0.95 0.75 0.65 0.95 21 22 20 13

9 0.95 0.85 0.75 0.95 18 19 19 11

11 0.95 0.85 0.85 0.95 1 5 8 7

13 0.95 0.95 0.85 0.95 1 1 1 1

We 1 2 2 3 6 ACTUAL BREAKUP

3 15 13 4 10 314 droplets

5 27 21 29 36 0.713636 fraction

7 21 15 13 13

9 18 19 15 11

11 1 5 5 7

13 1 1 0 1

We 1 7.15 2.85 3.75 6.3 PREDICTED BREAKUP

3 15.2 7.2 3 9.35 307.9 droplets

5 26.6 27.95 20.35 36.1 0.699773 fraction

7 19.95 16.5 13 12.35

9 17.1 16.15 14.25 10.45

11 0.95 4.25 6.8 6.65

13 0.95 0.95 0.85 0.95

y*y*

Upstream Weber Number Example: Oil Droplets, Re=10000

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

y*

We

bulk

43

Summary of Key Findings

• Strain rate magnitude and shear rate scale well with

superficial channel (and orifice) velocity.

• The Weber number for break-up of macroscale droplets

should incorporate γ D as the velocity scale.

• Based on local conditions, the critical Weber number

(90% break-up) should be around 35 with a γ based on

4–8% of particle response time.

• Contour plots relating upstream Weber number,

incoming trajectory, and droplet material to probability of

break-up have been developed.

44

Future Work Orifice Weber Number

zref

• Choose a value of zref

• Determine yint, the intersection of droplet path with zref

• Calculate Weorf

• Correlate breakage probability vs Weorf and y* in a similar

fashion to the upstream analysis

2δ

𝑊𝑒𝑜𝑟𝑓 =𝜌𝑐2𝜌𝑑

1/3𝜸 𝒛𝒓𝒆𝒇, 𝒚𝒊𝒏𝒕2𝐷3

𝜎

yint

45

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