NASA Technical Reports Server (NTRS) by Krieger Krieger

NASA/CRm1999-209170

Bubble Flow Salvatore Case

Generation Under

Cezar

Western

July 1999

in a Continuous

Reduced

Gravity

Pais Reserve

University,

Cleveland,

Ohio

Liquid

Conditions

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NASA/CR--1999-209170

Bubble Generation in a Continuous Liquid Flow Under Reduced Gravity Conditions Salvatore Case

Cezar

Western

Prepared

National

Pais

Reserve

under

Grant

Aeronautics

Space

Administration

Glenn

Research

July 1999

Center

University,

NGT5-1168

and

Cleveland,

Ohio

Acknowledgments

I wish

to express

my thanks

and deep

Professor Simon Ostrach for given me through out this given me for all these interaction I have had to tackle numerous

I am also help with merits. crew,

thankful to Mr. John the parabolic flight My thanks also go especially Mr. John

gratitude

to my dissertation

advisors,

Professor

Yasuhiro

Kamotani

and

their patience, encouragement, guidance and unwavering support they have work. I am greatly indebted to them for the unswerving support they have years. Their numerous suggestions have made this work possible. The with them for these past years has given me the confidence necessary problems. Without their help and guidance I would not have been in this position. Thank you. B. McQuillen and Dr. Bhim Singh of NASA Glenn Research Center, for all their experiments. The physical suffering that I endured during these flights has its to Mr. Bud Vance and Mr. Mike Dobbs for their technical support. The DC-9 Yaniec and Mr. Eric Neumann were especially kind to me, and helped me at some crucial moments. Thank you.

I also wish to thank my colleagues for their patience and cooperation. Many thanks are due to Mr. A. Bhunia, Dr. J.P. Kizito, Dr. J. Masud, Dr. F.B. Weng, and Ms. L. Wang. The efforts of Mr. A. Bhunia in helping me with the theoretical analysis are highly appreciated. I thank Dr. Jehanzeb Masud for his patience in helping me edit the thesis document. Thanks are also due to Kevin Stultz, Mike Anderson and to Dr. John Kizito for their help with video image digitization. Finally,

I wish

to gratefully acknowledge the financial help I have received from the National Space Administration as a NASA Research Fellow under grant (NGT5-1168).

Aeronautics

and

Trade names or manufacturers" names are used in this report for identification only. This usage does not constitute an official endorsement, either expressed or implied, by the National Aeronautics and Space Administration.

Available NASA Center for Aerospace 7121 Standard Drive Hanover, MD 21076 Price Code: A08

Information

from National

Technical

Information

Service

5285 Port Royal Road Springfield, VA 22100 Price Code: A08

TABLE

LIST

OF TABLES

AND

OF CONTENTS

FIGURES

NOMENCLATURE

viii

CHAPTER

1 INTRODUCTION

CHAPTER

2 EXPERIMENTAL

2.1 Reduced

Gravity

2.2 Test

Sections

2.3 Test

Flow

2.4 Flow

Visualization

Aircraft

Loop

and Test

Procedure

RESULTS

Parameters Parameters

and Uncertainty

Estimates

4.1 Theoretical 4.2 Numerical

ANALYSIS

Model

Comparison

of Dimensionless

CHAPTER

5 NUMERICAL

CHAPTER

6 CONCLUSIONS

43 45

Configuration

4 THEORETICAL

4.3 Range

Configuration

3.4 Cross-flow CHAPTER

and Data Acquisition

Tasks

3.1 Non-dimensional

3.3 Co-flow

Facilities

Layout

3 EXPERIMENTAL

3.2 Experimental

2.5 Experimental CHAPTER

WORK

with Experimental Variables

PREDICTIONS

Results

83 86 88 96

REFERENCES

105 Â°..

111

LIST

Table

OF TABLES

AND

FIGURES

Paqe

Comparison numerical

of bubble

diameter

predictions

experimental

of bubble

values

with

109

size

Fi,qure #

Paqe #

Co-flow

Cross-flow

Experimental

Test

Flow

Visualization

Co-flow

Experimental

Test Loop

110

Set-up

Experimental

Set-up

Section

111 112

Assembly

Layout

113

Set-up

configuration:

DB_ with superficial O N =.1

114

Variation

of bubble

gas velocity

diameter

115

UGS, for Dp = 2.54

cm,

Co-flow configuration: Gas iniection nozzle aspect ratio effect on bubble diameter DB for the 1.27 cm and 1.9 cm test section

116

Co-flow

117

configuration:

Variation

of bubble

respect to superficial liquid velocity 1.9 and 2.54 cm test sections 9

Co-flow

configuration:

Effect

superficial liquid velocity 51 cc/s, Dp = cm 10 Co-flow

configuration:

function

of superficial

velocity

Bubble

for the Dp = 1.27

diameter

diameter.

formation

gas velocity

and Fixed

frequency

and superficial

and 1.9 cm test sections

JÂĽ

with

ULS for Dp = 1.27,

of nozzle

on bubble

diameter,

118 Qd =

as a liquid

119

Co-flow

configuration:

generation under 12

at relatively

reduced

Co-flow

of bubble liquid

120

velocity

video

frame

gas velocity

of bubble under

red-

121

conditions Single

at low superficial

reduced

Co-flow

frame

conditions Single

configuration:

generation

video

high surrounding

at high superficial

gravity

under

gravity

configuration:

formation uced

Single

gravity

configuration:

L N as a function

video liquid

frame

of bubble

122

and gas velocities

conditions Change

of bubble

neck

length

123

of UGS for the 1.27 cm test section

Co-flow configuration: Variation of void fraction with repect to UGS for DN = 0.1 and 0.2, DR = 1.9 cm

124

Cross-flow

125

meter

configuration:

as a function

Variation

of bubble

dia-

of UGS and ULs, for D e = 1.27 cm

and ON* = 0.1 17

Cross-flow

configuration:

diameter cm,

Cross-flow meter

aspect

D N = 0.1

of air injection

ratio on bubble

and

Variation

to superficial

De = 1.27,

1.9 and 2.54

Cross-flow

configuration: and nozzle

diameter,

nozzle

126

Dp = 1.27

0.2

configuration:

with respect

velocity

Effect

of bubble liquid

velocity

dia-

127

for

cm test sections Effect

diameter

of superficial

on bubble

liquid

128

size for a fixed

Qd = 44 cc/s and Dp = 1.27 cm 2O

Cross-flow

configuration:

Variation

of bubble

mation frequency with respect to superficial for De = 1.27 and 1.9 cm; for D N = .1 21

Cross-flow

configuration:

Effect

of volumetric

for-

129

gas velocity,

gas

and liquid flow rates on void fraction with respect to variation in nozzle diameter for a fixed Dp = 1.9 cm

13O

Cross-flow configuration: Comparison between experimental values of bubble diameter obtained with the cross-flow system (crf) with those obtained with the co-flow system (cof). Fixed Dp= 1.27 cm and DN"= .1, with ULS= 17.4 cm/s

131

Comparison of bubble diameter and void fraction for the co and cross-flow configurations. Fixed Qc= 68 cc/s, Dp = 1.9 cm and D N = .38 cm

132

Single

133

video

frame

flow configuration velocities 25

Single

video

at high

frame

flow configuration velocities

than

Co-flow

Comparison

of bubble

superficial

of bubble at lower

those

of bubble

formation

in figure

used

and gas

in the crossliquid

of bubble

134

and gas

in the Theoretical

diameter

predictions

in the cross-

liquid

superficial

used

configuration

numerical

generation

Model

experimental size;

135

values

with

lines represent

computed values, symbols represent experimental values, D N = .1 and .2; p = 0.0012; Rep = 1653, Wep = 1.97 and Frp = 4.07;

Ree = 4064,

Wep = 8.93,

Wep = 3.88, Frp = 31.19

and Frp -- 7.99;

Comparison

of numerical

symbols

Ree = 4579,

Wep

Ree = 2318,

= 15.13

and 136

represent

values;

and Frp = 10.28;

and experimental

experimental

values,

bubble lines

formation

represent

computed

DN = 0.1, Rep = 2667, Wep = 3.84 and Frp = 4.43; Ree = 2318, Wep = 3.88 and Frp = 7.99

D N = 0.2,

Numerical

prediction

for variation

of bubble

diameter

Rep = 1,300 Numerical

nozzle 138

prediction

for the effect

of pipe diameter

ached

137

with

respect to change in superficial gas velocity and gas injection diameter; p = 0.0012, Frp = 105.25, Wep = 0.912 and

time,

bubble

diameter;

on det.

p = 0.0012,

Dp curve

Rep = 1000, Wep = 1.1, Frp = 498; 1.5 Dp curve aee = 667, Wep = 0.32, Frp = 65.5; 2 De curve

â&#x20AC;˘ D N = 0.20,

â&#x20AC;˘ DN = 0.133, D N = 0.1,

Rep = 500, Wep = 0.136, Frp = 15.5

139

Numerical prediction for the effect of superficial liquid velocity under reduced,and normalgravity conditions; p = 0.0012, DN = 0.1, and RepUGs= 500; 0.01 g curve • Bop = .867, 1 g curve: Bop = 86.7

140

Numerical

prediction

for the effect

of gravity

level

bubble diameter; comparison between !he reduced gravity and the normal gravity environments; p = 0.0012, D N = 0.1, Rep = 750,

We e = .608;

1 g curve

• Frp = 2.8

Numerical

prediction

on detached

bubble

0.01

g Curve:

Fre = .028; ...141

for the effect diameter;

of surface

p = 0.0012,

tension Frp = 22.42, 142

Rep = 600 and DN" = 0.1 34

Numerical prediction for the effect of liquid viscosity; p = 0.0012, Frp = 62.21, Wep = 0.54 and D N = 0.1; "mu"

curve

5 "mu"

curve

" Rep = 1,000;

2 "mu"

curve

Rep = 200 and 10 "mu"

vii

• Rep = 500; curve

• Rep = 100

143

NOMENCLATURE

Symbols

Ae,

Effective

Bop

Bond

number

Drag

coefficient

CDW

Coefficient

Cic

Added

Dimensional

DB"

Non-dimensional

Flow

conduit

Gas

injection

DR*

Non-dimensional

Frp

Froude

Buoyancy

Liquid

drag force

Inertia

force

Gas

Reference

Surface

LN (En)

cross-sectional

bubble

(Weberp

mass

coefficient bubble

nozzle

of non-dim,

diameter

diameter)

diameter

flux (pcULs2Dp 2) force

neck

bubble

wall

(D B / Dp)

nozzle

[(pc-Pd)ULs 2 / pcgDe]

force

drag

expanse

diameter

gas injection

momentum

an infinite

to the flow conduit

(function

force

Bubble

through

diameter

pipe inner

tension

moving

respect

bubble

number

upon by liquid

/ Froudep)

of a bubble

of drag with

area acted

length

viii

diameter

(DN / Dp)

Greek

Reference

length

(Dp)

Rep

Reynolds

number

based

on pipe diameter

ReB

Reynolds

number

based

on bubble

Volumetric

liquid flow rate

Volumetric

gas flow rate

Reference

time

Ue_

[(ds/dt)

UGS

Superficial

UGS*

Non-dimensional

superficial

ULS

Superficial

velocity

Bubble

volume

Wep

Weber

number

Distance

ds/dt

bubble

diameter

(pcULsDe

/ I_c)

(pcUeffDB / _c)

(Dp / ULs)

- ULS] gas velocity

liquid

(pcULs2Dp

from center

gas velocity

/ _c)

bubble

center

velocity

away

to gas injection

nozzle

from the gas injection

tip nozzle

tip

Symbols Void fraction z_

Dist.

Liquid

Gas

_c, _d

bet. fronts

of detached

and previously

density density Liquid

and gas absolute

viscosities

detached

bubbles

CHAPTER

INTRODUCTION

The

development

conditions

generation

and

duration

With well

prompted

advent

flow

scope

,as well

under

of results

programs

this new knowledge

some

powerplants

separate

a gas

examples, and water

the presence due

such

design

reduced

gravity

thermal

energy

and

of gravity, to their

with manned

obtained

from

Earth,

the

development

and

different

such

long

of space, Space

become

research

indicated terrestrial

will

Station,

imperative. broaden

Ostrach

industries

the

(1988).

stand

profit

occur

often

basis.

flow

together

refrigerators,

desalination there

from

that

a liquid

being

conditions

feasible

exploration

of an International

microgravity

it is highly

where

construction

Consequently,

Situations

under

applications

dealing

near term

microgravity

exploiting

research

systems.

studies

Commercialization

flow

space

of programs

as the possible

two-phase

transport

life support

the

two-phase

oil

facilities

is a tendency densities,

in a pipe and

( Hewitt, for the

with

liquids

gas 1996 gas

pipelines, and

and

descending

nuclear

Hill,

liquid

1997).

phases

and

gases

rising. This phenomenon is not

observed

Eventhough,

have

flows

many Terra,

phenomena,

flows,

in particular

system

for

liquid bus

condenses The

performed

gravity

conditions.

to examine

understanding

prediction

of such

volume

currently for

thermal

liquid

flows

the

for

Space

flows

gas-liquid

the quite

system

used

liquid),

as the heat

of this

system

than

at a lower

the

flow

in boiling

for

observed difficult,

rate

can

and

This

the

be used

and condensation.

liquid

vapor

Subsequently,

With

the Station.

since

management

through

weight,

replace

operation

spacecraft,

is dissipated

system.

thermal

while

is its reduced liquid

use in space;

systems,

design

aboard

two-phase

possible

heat sink aboard

is heated,

an all

Earth-based

control

Station.

vapor)

of liquid

are transferred

thermal

as the primary

control

are studied

in use

to function

advantage

understanding

of two-phase

intended

(becoming

smaller

energy

lack

accurate

gas-liquid

loops,

(becoming

main

improved

design

is designed

boils

gravity

In a gas-liquid and

still

rendering

benefit

reduced

thermal

been

reduced

intractable.

the

pumped

there

thus

not downright

Besides

experiments

under

large

warms

cools

and

the radiators. it requires

a smaller amounts

the reintroduction

of of

the Shuttle-C program, any weight saving for payload transfer to orbit is of utmost importance.

Furthermore,

heat

transfer

associated

with

space-based

nuclear

powerplants, be they located in orbit, on reduced gravity extra-terrestrial soil, or aboard spacecraft, is highly dependent on two-phase flow research under reduced and microgravity conditions. Such studies can prevent emergencies associated with unanticipated loss of coolant, which can result in catastrophe. For space-based thermal management systems, an alternative to using heat pipes for transporting thermal energy is to utilize capillary pumped loops (Herold and Kolos, 1997). This device provides heat rejection at a wider range of temperatures and avoids counterflows of liquid and vapor typically found in heat pipes.

Another useful space application is transport of cryogens, such as liquid oxygen and liquid nitrogen, which vaporize to some extent as they flow through pipes or into storage tanks, thereby creating gas-liquid flows. In particular, the design of propulsion and life support systems stands to benefit from this application.

Last but not least, the study of gas-liquid flows under reduced gravity conditions can yield results which can be adapted to improving design of equipment used in both terrestrial and microgravity applications. Since gas-liquid flows in a reduced gravity environment are considered as simpler to analyze than those under normal gravity conditions, there is increased interest from NASA's Microgravity Science Program, resulting in studies which simulate reduced gravity using both drop towers and aircraft flying parabolic trajectories, such as the KC-135 and the DC-9 Reduced Gravity Aircraft.

Under normal gravity conditions, bubble generation is usually accomplished by injecting gas through an orifice into a quiescent liquid medium. Due to the buoyancy force created by the Earth's gravitational field, the bubble grows and detaches quite readily.

On the other hand, under reduced gravity conditions, the role that the buoyancy force plays upon bubble growth and consequent detachment, is significantly diminished. Thus, in a reduced gravity environment larger and more spherical bubbles can be obtained. Since the role of buoyancy is minimized, another bubble detaching force is required in order to control bubble size and frequency of generation. Hypothetically speaking, an

electrostatic, temperature or acoustic field can create the necessary conditions for bubble detachment. In view of all these possibilities, the most practical solution to the problem at hand is to use the drag force provided by liquid flowing through the two-phase flow conduit, as pointed out by Chuang and Goldschmidt (1970) and more recently by Kim et al. (1994).

Two configurations generally used for bubble dispersion in a flowing liquid are the co-flow and the cross-flow geometries. In the co-flow configuration, the dispersed phase is introduced through a nozzle in the same direction with the liquid flow; whereas in the cross-flow geometry, gas is injected perpendicular to the direction of liquid flow.

Independent of flow system configuration, under both normal and reduced gravity conditions, there exist three major flow patterns which occur with increasing gas injection rate, namely bubble, slug (Taylor bubble) and annular (Jayawardena et al., 1997). Bubble and annular flows are mostly used in space-based two-phase systems. Due to vibrations caused by slugs, which result in unwanted accelerations, determining the correct flow pattern is imperative for efficient operation of such systems.

Bubble

generation

namely

constant

and

Kuloor,

flow,

1970).

volumetric

gas

process.

flow

regime Krevelen

and

turbulent

regime.

importance,

The

from

Hoftijzer,

constant there

are three

dynamic

and

low flow

rates,

typically

whereas

industrial

dynamic

regime

bubble

1971).

In the

can

(including single

further

which

pairing)

bubble bubbles

gravity

level,

deviate

from

double

bubble

the

gas

spherical

subregime, flux,

bubble

and

double which

system

shape.

two bubbles coalescence

higher

of gas

at low gas

becomes

injection

1971 ).

occurs

can coalesce

practical

subregimes,

equal

size

and

Prince,

flow

rates,

produced.

spherical

flow

rates,

such

are

can

at the

(Van to the

of utmost

(McCann

gas

static

1 cm3/s

(Wraith,

two

bubbles

of bubble The

bubble

approximately, these

regimes

range

the

formation

rate corresponds

the

into

bubble

than

hence

covers

(Kumar

thesis,

regimes.

smaller

and

divided

subregime,

spaced

Depending

known

high gas flow

applications

in this the

turbulent

conditions,

conditions

studied

throughout

1 cm3/s to 104 cm3/s for an air-water

single

increasing

conditions,

into three

intermediate

static,

1950),

For

is the

dynamic

uniformly

flow

on the gas flux,

at very

be divided

and

remains

the

can

pressure

constant

rate

namely

occurs

injection

constant

Depending

generation,

rates

due to gas

namely nozzle

frequent,

can

in the

exit.

With

in time

forming a gas jet and thereby leading to a transition from the dynamic to the turbulent regime.

The present reduced gravity work focuses on single bubble formation and presents an experimentally observed mechanism for the onset condition of coalescence. Under reduced and microgravity conditions, a single bubble can grow larger than the pipe diameter before detachment occurs, thereby giving rise to a Taylor bubble. A Taylor bubble can also be formed by coalescence of two smaller bubbles at the gas injection nozzle interface. The inception of a Taylor bubble characterizes the transition from bubbly to slug flow, which has been extensively studied by Duckier et al. (1988), Colin et. al. (1991), Bousman et. al. (1996) and more recently by Jayawardena et.al. (1997). These investigators performed several two-phase flow experiments under reduced gravity conditions, to allow for high speed measurement of void fraction, liquid film thickness and pressure drop. They found that flow pattern occurrence is influenced by liquid and gas superficial velocities, tube diameter, liquid viscosity and surface tension.

Bubble generation by nozzle injection in a quiescent liquid has been extensively studied in the past. A compendium of pertinent literature is presented by Rabiger and Vogelpohl (1986) as well as by Tsuge (1986).

More recently, buoyancy tower

on bubble

experiments.

bubble

the

buoyancy

same force

conditions,

by buoyancy cross-flow,

lines,

the

nucleation

that

under

bubbles

the

orifices reduced

to the

under

the

gas

tends

influence

by performing gravity

of drop

conditions

injection

orifice

to increase

growth

reduced

Hence, flow

a solid

conditions.

at rate

formed

studied

with

the

diameter increasing

in water

process

process in the

grows

growth

for

normal

formation

of a by the gravity

frequency

in size.

gas

diffusion

in a quiescent

experiments that

forces

abscence

reduced

bubble

the

is dominated

moderately

and

that

under

influenced

surface

showed

that

is primarily

is increased,

bubble

detaching

observed

conditions,

performed and

They

gravity

bubble

concluded

are critical

detachment

normal

horizontal They

flux

(1996)

and

this

and the detaching

(1997)

Webbon

liquid.

of liquid,

gas

Baines site

and

momentum

bubble

flux.

gravity

bubbles

Buyevich

or a co-flow

decreases

and

investigated

submerged

proportional

in a quiescent

while

momentum

conditions,

gas

showed

and the gas

gravity

normal

from

(1995)

rate.

generation

Mori

formation

is directly

bubble

slightly

Rath

that the size of generated

gas injection

Along

and

They

diameter

and also

gas

Pamperin

using

evolution

liquid carbon bubble

from under dioxide shape

during growth, as a direct result of gas injection rate, is important for determining departure size. It was shown that growing bubbles form a neck at the bubble base before detachment occurs. As this neck pinches off, the remaining section of the bubble collapses into the nucleation cavity, directly affecting the growth rate of subsequent bubbles.

Since under reduced gravity conditions, the gas momentum flux presents the sole bubble detaching mechanism, this fact necessitates the presence of another detaching force to control bubble size and frequency of generation. This force can be provided by using a co-flow or a cross-flow system. Bubble formation in the cross-flow configuration has been extensively studied by AIHayes and Winterton (1981), Kawase and Ulbrecht (1981) and Kim et al. (1994). More recently, Nahra and Kamotani (1997), showed that bubble size decreases with increasing superficial liquid velocity, while the bubble time to detachment also decreases as the liquid flow rate is increased, This observation stresses the role of liquid flow as a detaching force in the bubble formation process.

Oguz et al. performed a set of microgravity experiments in order to study the effect of a cross-flow on a bubble injected from a hole located in the flow conduit wall. This situation is of primary interest for two-phase flow studies as

they

relate

to heat

drop

tower

concluded

bus that

module under

triggered

by bubble

drag and

inertia

Furthermore, cross-flow They

transfer.

tension

and the

influence

vapor

bubble

that

has

forces

departure been

acting

asymmetrical

bubble

growth,

hydrodynamic

pressure

its practical

and reduced by Chuang

of free

of a cross-flow,

bubble

combined

gravity

as for

the

installed

fall

tests.

in a They

detachment

effect

boiling,

studied

growing

liquid

drag,

shear

lift

and the contact

significance,

studied model

force

in convective

extensively on

quasi-steady

theoretical

was

of viscous

is liquid

forces.

force,

extensively

apparatus

to a series

due to the

the

Despite

experimental

subjected

deformation

geometry,

show

The

the co-flow

by Zeng

bubble the

force,

the

pressure

bubble

generation

in a co-flowing

(1970).

et al.

(1993).

the

surface

drag

buoyancy

configuration

geometry.

and Goldschmidt

the

due

force,

to the

force.

cross-flow

His work

displays

include

unsteady

the

conditions.

which

has

Kim(1992)

is an extension

liquid

not

been

proposed under

of a model

normal

proposed

]]

Sada

et al. (1978)

the effect They

liquid

reported

rate, liquid

a decrease

in bubble

formation

they

gravity

has on bubble

Oguz

configuration.

normal

velocity

recently,

bubble

performed

et al.

via single

nozzle

By keeping observed

volumetric

(1996)

air flow

a substantial

flow

observed

in Bhunia

injection

within

rate.

This

liquid

detachment

increasing

reported

some

gas

in order to observe

in a co-flow

size with

liquid

configuration. flow rate.

preliminary

results

of air

injection

in a terrestrial

vertical

rate constant,

and increasing

the water

reduction physical

et al. (1998), a

experiments

in bubble phenomenon

for bubble

co-flow

volume

with

is also

generation

configuration

flow

increasing

experimentally

via single in

upflow

nozzle

reduced

gas

gravity

environment.

Under

microgravity

resulting

two-phase

the flow conduit work,

is presented multiple

coalescence

reduced

flow

has been

covering

addressing

With

the

state

topic

by multiple studied

nozzle

conditions,

nozzle

and

and open

bubble

injection

by several

of bubble

of knowledge

by Colin

gravity

along

investigators.

slug

flow

questions

generation the

periphery

A summary

at microgravity pertaining

and of

of this

conditions, to this subject,

et al. (1996). injection

of adjacent

along

bubbles,

the periphery

it is quite

difficult

of the flow to control

conduit,

due

the uniformity

to of

generated single

bubble

nozzle

size. A better

injection,

which

alternative

is controlled

is the experimental

bubble

method

generation

used

in the

via

present

work.

The

work

at hand

gas

injection

through

Experiments phase

The

using

were

Research

formation

air as the

in liquid

Lewis

flow within

a pipe,

the

via a single

cross-flow as the

DC-9

the

nozzle

gas

system. continuous

Reduced

Gravity

study

bubble

bubbly

injection

size and frequency

(primarily

generation

Center.

investigation

in bubble flow

and

and water

aboard

Research

current

two-phase

phase

flight

the

of bubble

in a co-flow

dispersed

we are interested

as resulting

investigation

nozzle

in parabolic

at NASA

objective

Particularly, well

a single

performed

Aircraft

main

is an experimental

system.

of generation

and transition

to slug

as flow

regimes). It was

experimentally

generated constant. of gas grew bubble

observed

bubbles The

bubble

injection in size

decreased diameter

nozzle with

frequency

diameter

increasing of formation

that with in

increasing

size,

holding

was shown to pipe pipe

all

other

to increase

diameter

diameter.

increased,

superficial

and

flow

Likewise, the

detached it was time

velocity,

conditions

by increasing

and also

hence

liquid

the ratio bubbles

shown

that

to detachment

of a forming bubble decreased, as the superficial liquid velocity was increased. Furthermore, it is observed that void fraction can be accurately controlled with single nozzle gas injection by simply varying the volumetric gas and liquid flow rates. A theoretical model was developed based on previous work, for the co-flow configuration, considering two stages for bubble generation, namely the expansion stage and the detachment stage (Ramakrishnan et al., 1969 and Kim, 1994. The present numerical work is valid in the bubbly flow regime predicts

bubble

Taylor

bubbles).

forces

such

momentum two stages Under

as flux,

valid the

overall

buoyancy,

surface

liquid

drag,

generation,

gravity

results

force

tension inertia

the

to slug

balance, acting

and

(formation

nozzle

inertia,

and

diameter

the

incorporates

the

bubble

role

flow which

bubble

the detached

conditions,

criteria

agree

neck

well

is checked

at low superficial bubble

point

exit, acts

gas at the

is computed.

buoyancy

force

but is not overlooked.

Computational detachment

up to the transition

Based

of bubble

reduced

diminished

diameter

and

length

liquid

against

velocity.

begins

with

current the

At higher

to deviate

reduced

gravity

experimental superficial

greatly

from

data.

data liquid the

and

proved

velocities,

value

The

of the

as air

injection

nozzle

diameter,

theoretical

prediction.

conditions

(such

all

based

investigated.

experimental

Effects

as Reynolds pipe

diameter)

of fluid

properties,

number, on

bubble

Weber

resulting

size

no longer

injection number bubble

matches

geometry and

size

and flow

Froude are

the

number,

numerically

CHAPTER

Experimental

2.1 Reduced

Gravity

Experiments

were

Aircraft

at the

currently

flying

reported

both

the

trajectories

DC-9

Center.

Model

Center.

microgravity trajectory.

mission

Learjet

Research

the

Other

25 and

These

Reduced

flight

the

Gravity

reduced KC-135

platforms

gravity aircraft

were

Research aircraft, based

not used

in our

weightlessness

experiments.

these

The

aboard

the Learjet Space

a parabolic

per flight

Lewis

are

Johnson

In general,

Facilities

conducted

NASA

in use

the NASA

Aircraft

Work

research The

aircraft

number

achieve

of parabolic

trajectories

executed

varies.

aircraft KC-135

can perform and

in a single

as chosen

flight

a rougher

ride than

the

DC-9

mission.

trajectory,

a maximum aircraft

However,

the KC-135,

the DC-9

aircraft.

of six trajectories can

typically

due to aircraft similar

per flight,

achieve configuration

to the Learjet

aircraft,

while to

as well provides

Usually

these

unless

grounding

of 0.02g by

reduced

parabolic gravity, true major

gravity),

the

flight

drop

perform

.17g

(lunar),

and

Without

technique

currently

produces

drop

tower

offer

up to two

due to an onboard

trajectory.

towers

physical

can

flight

exceeding

that

aircraft

is necessary

(reduced

modifying

gravity

experiment

.33g

malfunction. (Martian)

resorting the

run times

Gravity

levels

be produced

space

flight,

period

the

of reduced

by 10 to 15 seconds.

lower

gravity

levels

vary

slightly

by reducing

phenomena

a day,

can

longest

flights

than

parabolic the

flight,

gravity

It is

however

level

below

0.01g.

The

DC-9

aircraft

maneuvers landing,

per flight. is

two

approximately float

time

period

time

period,

After initiates

the

A typical

three

which performed

was

data was acquired

initially

its 2g pull-up.

The

duration,

Each

parabolic

Only

were

an average

mission

hours.

experience

of 22 seconds

aircraft

performing

flight

18 to 22 seconds.

experiments,

experiments

is capable

including

attached

available

take-off

are available environment.

to the aircraft for operational

low-gravity

trajectory

5 to 10 seconds a 10-3g to 104g

of 45

floor

the

purposes.

lasts

and for

for freeSince

the

maximum Out of this

for 15 seconds.

reaches aircraft

18,000-20,000 continues

feet

to move

above

the

at a constant

ground, air speed

of 400

mph,

while

climbing

another

7000

feet

to reach

the

apex

of its flight

trajectory. During

a typical

maneuver toward

until the

apex

when

back

trajectory,

the

a 550 to 600 nose-up

Consequently, pitched

flight

the

pushover,

which

produces

less

than

DC-9

1 percent

pitched

is reached. its

pull-up

As the aircraft

slows

nose

pitched

a 35 o to 400 nose-down

or into the

as the

trace,

reaches

flight

results

attitude

parabolic

the aircraft

up to level

aircraft

traces

parabolic

terrestrial

attitude,

trajectory.

the apex

of the

gravity

for

down. it is

The

brief

parabolic

path,

approximately

seconds. When

executed

accelerations

properly, on

the

aircraft

pull-up

and

two

pullout times

maneuvers the

Earth's

generate gravitational

accelerations.

The

modified

order

to provide

In order during were ceiling) mean

DC-9

is also

intermediate

to monitor flight

mounted

aboard within

acceleration value

capable

of 0.008g

acceleration

the quality the

DC-9,

the

of flying

of the

a standard

parabolic

ranging gravity

during

time

deviation

0.1g

accurate

trace

a reduced

from

trajectories

of.the gravity

of 0.017

to 0.75g.

environment,

accelerometers

A typical

level measured with

levels

reduced

three-axis

aircraft.

modified

existent to 0.001g

z-axis trajectory,

g, in the time

(floor

has a period

7 to

conditions.

seconds Minor

corrections,

Since two

all acceleration pilots,

similar

only

data

of zero

in all three

typical

duration

of these

the co-flow

test

directions,

were

actively

recorded

by trajectory

controlled

(nose

For the experimental when

gravity

vibrations.

for the x-axis

is presented.

experiments

section

to tail)

tests

and

reported

acceleration As a direct

was

within

consequence,

was 9 to 17 seconds.

phase

1 displays

same

Plexiglas is mounted

geometries

and the cross-flow

the dispersed

the

acquired

caused

structural

on the aircraft

generated

were

reduced

Sections

distinct

Figure

experiencing

and aircraft

acting

were

was

in this trace

tip) accelerations.

0.02g

Two

observed

levels

tip to wing

aircraft

turbulence

results

investigation,

2.2 Test

the

oscillations

atmospheric

axis (wing this

when

distilled

water

system.

with

water

which

on the

acts inlet

the

of the

in our experiments,

Dry and filtered

acted

flow.

pipe

The

test

flow

conduit.

using

phase.

air was

section

injected

consists

A tee

a Swagelock

namely

air was used

as the continuous

In this configuration,

as the two phase side

used

configurations.

the co-flow

direction

pipe

while

were

branch

fitting.

in a

fitting Air

was

injected

through

welded

on.

nozzle

This

stock.

pipe,

clearing

In other

The

the

bubble

role

conduit

box filled

of this

the video section

was

filled

box indices

the tee branch

with

water, index phase,

camera,

into

liquid was

injection

of stainless

the

transparent

of pipe diameter.

well

within

the

the surrounding and

gas

mixing

surrounded

pipe, liquid region

by a Plexiglas

water.

is to

avoid

image

curved

air medium.

enclosed

fitting.

where

of the

The

continuous

in a region

video

with distilled

viewing

to the refractive

nozzle

gas

section

respective

air-injection

The

tip had been

of various

protrudes

length,

developed.

of the

the surrounding

camera.

as the

of the

use

orifice

into a small

and

entrance

fully

in refractive and

can be drilled

is injected

in view

converging the

as a nozzle

protrusion

pipe,

difference

acts

whose

facilitates

the hydrodynamic

that

rectangular

closer

tube

which

is hydrodinamically

within

The

section

holes,

words,

ensures

steel tube,

welded

diameter

steel

flow

a stainless

space

surface

This

the

of water

than

was

introduced

caused

of the

a flat

the viewing

refractive

to that

index

the

the flow

surface

box and the test of

of air. Distilled

through

two-phase

box presents

between

because

distortion

Plexiglas water

remaining

which port

the

other

perpendicular 2, was

machined

the

hole,

Two

steel

which

tube

was

there

no need

was

enclosed

The

manner obtaining

and

complete

test

section

Apparatus,

For every to minimize surfactants

were

3. This

assembly

developed

contamination added

diameter

orifice

tip was

through

as the water

test

between

experimental

equal

the

air

the

video

injected

shown

in figure

into the form

holes was

welded

Plexiglas

inlet tube.

since

stock

was

were

bored

injected

via

on.

other

tee,

The acts

as the

For this configuration,

curved

portion

camera

of the

but

was

flow

rather

surface

amount

connector

of Plexiglas

holes

box,

air

test section,

of these

way

exposed

cross-flow

in figure

This

piece

one

a viewing

directly

the maximum

air flow tube

Flow

for

by a flat Plexiglas

shown

flow.

converging

as well

configuration

positioned,

the whole

conduit

not

co-flow

of water

Through

whose

bored

flow

was

cross-flow

orthogonally tee.

two phase

conduit

the

out of a rectangular

Plexiglas

stainless

to the direction

a tee-section. into

hand,

run,

sections was

were

primarily

of data

was

at the

batch

within

of distilled

water

surface

in the

manner

interchanging

the

test sections.

The

the Learjet

Two

Phase

(1995).

water, as much

reservoir.

series

efficient

by simply

and Neumann

bubble

to the distilled

most

and cross-flow

integrated

by McQuillen a new

the

per flight,

the co-flow

mounted

was as

used

in order

possible.

2.3 Test

The

Flow

Loop

Two-Phase

these

Flow

structures

aboard

the

introduced

Layout

are

Learjet

Apparatus standard

Model

between

consists racks

the two

of three

which

Reduced

standard

distinct

have

Gravity

ones,

was

sections.

been

designed

Aircraft.

The

custom

Two for

third

designed

of use

rack,

to fit user

needs.

All three power

racks and

were

flow

equipped

control.

with

There

electrical

was

between

the two standard

racks

The

standard

rack constitutes

first

consists

the

thermocouple this

rack.

Likewise, turbine

Learjet gas

amplifier These

flow flow

and

rate

meters

flow

electronics. are

supply

cylinder

(K-bottle),

pressure

regulators

from

two

compressed

air

devices

such

rack

assembly.

although

cylinders,

electrical

metering

plumbing

rate setting

are part of this

gas

the flow

loop

for

connection

devices and

It primarily

There

test

and

the

are mounted metering

as pressure

to the

rack.

components

in our experiments, external

connections

of data acquisition.

Flow

measurement

plumbing

additional

for the purpose

liquid

devices

and

valves.

transducers Js also

space

gas was loop

and for

supplied

assembly

and

secured rack

aboard

is wide

the aircraft

by 120 cm

The second

standard

This

rack

(with

the exception

control

systems

levels

during

were rack

consists

also

crystal

rack

of the test of the

aboard

features

display,

program

Learjet

parabolic

housing.

is designated

section

Dimension-wise,

as tri-axial flight. the

as the

assembly,

high speed

video

DC-9

system),

this

various

toggle

The

second

not

interface switches

the tri-axial

and

on the

which

is 60 cm wide,

rack

is a flat plate

system

acquisition

and

acceleration

accelerometers

second

rack.

is composed

two thumbwheels

rack

rack.

visualization

to monitor

directly

panel

acquisition

the data

accelerometers,

and

data

the flow

In our experiments,

an operator

options.

an aluminum

long by 120 cm high.

as well

mounted

within

of a liquid

used

by 60 cm

This

long

to select

by 120 cm

high.

The third,

or custom-designed

regulator,

the

collector standard three

fixtures

/ separator racks.

racks

channels

recirculation

The

occupies which

allow

are for

tank

pump,

are fixed.

complete

flow

a total space attached spacing

the

liquid This

loop

adjustment

supply

rack

tank

the back and

is mounted

assembly,

of .61m mounting

on which

which

by 1.83m points

between

the

two-phase

between

the

consists

and.is

within racks

pressure

the

fixed

of these to Unistrut

aircraft.

since

two

the

These 51

distances

between

distribute

flow

fire-proof

floor

aircraft

The

floor

flow

loop

system

displayed

main

and

air to the test

section

venting

the gas

supply

of a pressure

square-edge injecting rate.

orifice.

air through

of four

minimize

are

damage

introduced

distinct flow

sections,

test

schematic

important

to the

between

the

section of the

components

namely

the

assembly flow

and the

loop

system

flow

loop

this

gas

is are

diagram.

system

is to provide

assembly

cylinder,

exits

there

regulator,

a pressure

choked

quantities

to collect

of water

the liquid

for

the test section.

are two gas

For our experiments, of two

metered

and consequently

the air which

one

thereby

In order

mounts.

A generic

Only

are set by design.

segments

the two-phase

of this

while

consists

flow

purpose

and

is composed

in this schematic

The

recycle

weight

channel

system.

in figure

in the aircraft

plywood

system,

recirculation

presented

From

assembly

padding,

the liquid

liquid

patterns

and the Unistrut

loop

system,

hole

the

metering

gauge, air flow

orifices,

flow

legs.

a solenoid

valve

rate was

depending

Each and

controlled

on the

leg a by

desired

?-4

Each

orifice

has

turndown

ratio

pressure

range.

achieve

2.0

gas

m/sec.,

velocity,

for flow

and

Thus,

air was

when

were

the annular

in the

common

into a tee upstream

downstream

Hence, function as shown

solely

sonic

mm.

the

a manner

as to

can

range

from

25.0

m/sec,

2.0

desired

range

orifice

from

.183

for

in such

desired

orifice

and

obtained

the small

large

sized

the

small

orifice,

through

the

flow

rates. 0.05 at

and

orifice

slug

flow

is essential

is desired.

upstream

of each

since

the gas

the orifice

area.

If the absolute

velocity

bubble

large

the orifice,

orifice,

is at

least

the flow

two

the

times

of gas through

is achieved,

upstream

(1971),

the

are measured

clear

of the

by Bean

through

injection

pattern

of the orifice,

once

for

through

Air

pressure

they the

1 was

are properly

orifice

the

injected

line after

once

.691

conditions.

flow

and

the

through

observed.

Temperature

plates

pressure

patterns

orifice

namely

250

velocity

atmospheric

when

diameter,

approximately

The

sonic

Superficial

a different

the

temperature gas

mass

flow

orifice

metering

flow

than

the orifice

gas

mass

and

pressure.

rate

legs

pressure

greater

and also merge

measured

the

pressure

is choked.

flow

rate More

is a direct

becomes

accurately,

function

of the

orifice

discharge

coefficient,

of the real to ideal varies

gas sonic

as the inverse

Therefore,

the

following

the sonic

square

mass

flow

mathematical

_1" is the

the inlet

root of the inlet

stagnation

rate

of injected

sonic

flow function

of an ideal

gas sonic

flow functions,

T_s is the

inlet

stagnation

temperature,

flow

ratio

stagnation

pressure

and

temperature.

be determined

from

the

C is the

orifice

discharge

Pls

gas,

is the

(_*/_1") is the ratio inlet

a is the

throat

coefficient

and

stagnation area

pressure,

of the

mg is the

of the

square

gas

mass

rate.

Furthermore,

the

downstream

Since

sonic

pressure

it is possible

verified

with

upstream the

can

gas, the

] ,r,i]

ideal

orifice,

gas

of an ideal

expression:

real to the

edged

function

flow functions,

â&#x20AC;˘ , where

flow

may have

for the

pressure

computer

orifice

before

is set with

pressure

eliminates

upon volumetric

small

a wet test meter

upstream

acquisition

configuration

and

each

a pressure

effect

flight.

Prior

regulator.

transducer

which

changes

flow

gas flow rate.

be blocked,

temperature

via a pressure

the

were and

the

to each During recorded

gas

experiment, the

rate

the

experiment, by

the

a copper-constantan

data (T-

type)

thermocouple,

subsequently

making

superficial

velocity

calibrated

from

could flow

been

the

gas

valve

and from section

minimizes

liquid

equipped maintain

flow

test

the backflow

supply with

air

a constant and

system.

aforementioned

pressure

from

piston

the which

gas

to the 5 to

experiments.

rate

and was

flow

rates

that

this

air

test

section

10 % of the

This

it passes

stainless The

observation

liters

of distilled

loaded

air

piston, the

bubbles

supply

tank from

cylinder

in turn travels

down

tube

valve

a check

into the coprevents

system.

water.

whose

feed

through

steel

check

into the gas supply

within

to prevent

rate

Hz,

system

gas

shown

of air within

assembly.

four

pressure

also

Air

holds

flow

leg (tee),

via a single

section

accurate

(1995).

the common

of water

tank

rates

flow

air flow

have

mass

in the present

it is injected

the

flow

by Bousman

enters

there of

maneuvers water

are achieved

that

mass

The

experiments gas

acquired

of gas

to ensure

a steady mass

was

measurements.

in order

steady

data

calculation

Several

provides

reported

Once

the

measured.

set point

This

on these

to time,

Typically,

has also

The

time

configuration

desired

possible

based

be set and

assembly.

flow

respectively.

This main

during

feed function

reduced

being.entrained

is introduced a shaft

tank

located

is to gravity into

on top

the

of the

in the center

of the feed tank

and

tank. after

was

experiments,

through

data

flow

through

meter

systems

supply it splits

flow.

valves

the liquid

flow

in parallel.

were

rate

For

manually

a liquid

flow

set point, make

Typically

the

adjusted

similar

use

rate which

activated

the

flow

rate

system. on-off

water,

existent

above

flow meter,

past

a check

it passes valve

and

cell.

of the water liquid

was within

to the gas flow

of solenoid

a turbine

readout

of distilled

air pressure

valve,

to time,

the water

properties

reference

a digital time

the

with

solenoid

provides From

range.

and also

a conductivity

system.

so as to provide

desired

liquid

as a filter,

represents

of physical

flow is metered

electrically-actuated

acquisition

uncertainty

acts

connected

these

function valves

the liquid

its path

The turbine

valves

reproducibility,

rate is a direct

After

continues

of metering

of the metering

which

of the

handles.

The liquid flow

the piston.

mesh

the test flow which

by a pair setting

a screen

the bottom

the test flow and the purge

of flow

settings

from

namely

with micrometer

the

exits

through

controlled

purpose

water

flowing

into two paths,

In the present

As a result,

system

the

was Both valves

flow was

desired

within liquid which

rate

via the

calibrated

experimental

5 to 10% and

gas

allow

of the supply

the

data

acquisition

computer

necessary shut-off

during in case

of reduced

The

a flight

the purge

reference

flow

pressure

drop

the flow

phase

mixture

made

out

path,

Under order phase screen

This

and

feature

stop

the

flow

is essential

as uncontrollable

passed entered

air

reduced

whenever

for test flow

leakage

through the and

during

loop

periods

to flush

section

a dual

any gas

bubbles

was

the

/ separator

purpose

two-phase

not

since

Likewise, trapped

utilized

since

the

resulting

tank.

This

tank

of retaining

the

mixture

a relief

via

two-

water

and valve

regulator.

conditions,

buoyancy

the

continuous

phase

is introduced

cylinders.

not taken.

assembly,

collector

gravity

mixture

experiments

were

system,

test

gas-liquid

from

in these

for our investigation.

the

has

used probes

measurement

extracted

to separate

mesh

not

used

was not required

by a pressure

flow

is usually

pressure data

cell was

via capacitance

which

of aluminum

the

actuated

start

such

test

measurements

differential

venting

trajectory.

of emergency,

conductivity

After

respectively

gravity.

void fraction

the

through

from

becomes the

a series

relatively

dispersed of concentric

weak, phase,

thus

the two-

stainless

steel

Due to the and

action

remains

during

the

mesh

which

phase relief

to it during

pull-up

of the

bottom

This

screen

mesh

holes

have

of the collector passes

valve

phase,

tension,

the

large

chamber

attached 2-g

purposes.

of surface

through into

is not

the vented

When

normal

tank. the

cabin.

when

achieved,

for safe and effective Reduced

Gravity

the

Aircraft,

lower air via

continuous

are

entrained

are used.

namely

between

tank

flight

via a recirculation

phase. water

operation

to the

vented

droplets

liquid

plate

the separated

unlike

supply

recirculation

path

flow rates

to achieve

gas phase.

DC-9

liquid

in order

of the separated

the

time,

air,

the

venting

drain

drained,

to recirculate

opened

aboard

vented

screen

a circular

is subsequently

the highest

are

are simultaneously

package

and

back to the liquid

is used

requirement

The

time

valves

An important

mesh

is being

off the for

and between

mesh

Consequently,

tank

water

conditions

pump

around

screen

drains

separator

While

From

is pumped

the

gravity.

water

to act as a water

air, especially

water

this

drilled

screen

aircraft

gravity

line. A centrifugal

collector

across

of reduced

aircraft,

is located

been

spreads

periods

DC-9

the

recovered.

within

trajectories,

the

water

Two

solenoid

recirculation

and

of an experimental

is that

all non-standard

fluid

devices

such

as the test section

separator

/ collector

maximum

working

pressure

differential,

its lower

end

cabin

During

Visualization

the

course

phenomena

to Bousman 2 cm m/s

have

the liquid

to be hydrostatically differential.

With

is approximately

27.6

supply

tested respect

tank

and the

at 1.5 times to

kPa, in case

this

the

pressure

the aircraft

loses

pressurization.

2.4 Flow

flow

tank,

assembly,

(1995),

in a reduced

gravity

video

not adequate

equipment for detailed

reduced

gravity

In light

of these

the ensuing

and

such

capturing which resolution

observation bubble

as bubbles

yet can

environment.

for

direct

for determining

flow features

or length,

resolution

standard

Acquisition

of this investigation, is essential

in diameter

adequate

and Data

move

Thus,

images

of two-phase

patterns.

or slugs

with

flow

eye

According

greater does

details.

than

not provide Furthermore,

at 30 frames flow under

two-phase

can be less than

velocities

the human

two-phase

records

flow

of the

per second either

normal

is or

conditions.

restrictions,

flow patterns.

a high-speed For performing

video

system

our experiments,

is used we

to visualize used

a high-

speed

S-VHS

video

camera

which

can record

the flow

pattern

information

pole,

a rate of 250 full images/second.

The

video

fixed

camera

to the

a specially the

flow

pole,

aircraft

loop

it.

speed

video

the video

flow

test

section

lights

and

not

system.

camera

Due

to its size,

loop

assembly.

across

were

is mounted

the aircraft

be swiveled

it is quite Therefore,

assembly

provide

affect

Strobe

in order

5. This flow visualization

patterns

bar directly

strobe do

can

system

within

cabin

around

observed

which

the

for the

from

support

co-flow

test

test section.

on a Unistrut

microseconds

located

camera

aluminum

recording

housing

The

on whether

for the

These

the video

aluminum

assembly.

mounted

on a tripod-based

while

or the cross-flow

Illumination lights

floor,

designed

depending

section

is mounted

the

lighting

to offset

difficult

is achieved above

also

to mount

arrangement

camera makes

of lower

the video

using

section

two

speed

accuracy the

resolution

is positioned use of a mirror

side of

of the

"freezing"

camera

strobe

on either

shutter

recording

maximizes

the effects

the video

the test

effective

image

action

10 high of

film.

inside

as shown mounted

the

flow

in figure in front

of the video is angled

During

camera

at 450 over

flight,

hooked

prior

up to the

section

on the same

with

the test section

to each video

respect

previously,

via an optical

box

sheet

surface

bubbles.

The

acquisition

with

of the each

and

control

system.

capability

and 4 MB of random

channels display button controls

data

acquisition.

of single unit, and

Its central

ended

input

two

thumbwheels,

several

toggle

the acquisition

in case

test

for

This

mirror

of it.

television

monitor

alignment

of the

has

unit

test

a 12-bit

for

A black

card

Three resolution

cage

button,

inputting

distinct

panel, an

desired

a flat

laminated

resolution

standard

chip

and

film

the

is a 386

An operator

"ENTER"

is performed

system

to improve

memory.

voltages. an

patterns

co-flow

system.

section

access

flow

of the

system

switches

of data.

to check

of ensuing

processing

Each

a full view

a small

cross-flow

beneath

lights.

of the mirror.

water

computer

for

in order

visualization

in case

generated

used

of trajectories,

camera,

filled

is positioned

data

set

bar as the strobe

so as to provide

to the orientation

As described

Plexiglas

Unistrut

with

cards can

MHz

can

consisting emergency flow

bus

32 of a stop

conditions,

Electrical which

power

powers

solenoid used

is supplied

the data

valves

and

acquisition the

the turbine

strobe

lights,

the high-speed

During

the experiment, records

turbine

the

flow

transducers as degrees

as absolute

test

as well

acquisition

both

measurement

Data

per

electrical

pressure

in C monitors

per square

from

source

data units;

the

channels from

absolute

inch and from

system.

several

the

flow

transducers,

in appropriate

minute,

Hz source

air and water

and the thermocouple

is recorded

gallons

concerning

gas

in these water

system

the

A 28 Vdc

the absolute

written

pounds

also

and

liquid

measurements

and

the temperature

as air and water

system

superficial

errors

video

a 110 V, 60

system,

pump.

meter,

from

the

pressure

the thermocouples

Fahrenheit.

data

flow

outputs.

In particular, section,

and control

software

meter

the aircraft

recirculation

to power

and

aboard

air

mass

flow

calculates velocities are flow

and

rates

pressure

is recorded. gas

and

in meters

per

second.

and 7.5 % for the absolute

pressure

of the

Furthermore,

and records

5 % to 10 % of the rates,

upstream

liquid

desired for

transducers.

the

flow

the rates

Uncertainty setpoint temperature

for

2.5 Experimental

For

conducting

operator motion

sickness

tasks

loop

feed

occurred

are performed

line is connected

an appropriate connected

in turn are connected

of the

aboard

solenoids

operators

the flight.

aircraft,

A third

experiences

tank, rack.

on the data

racks.

located Next,

the two-phase

region

electrical

First,

the water

on the tank

the purge

acquisition

flow entry

After

all necessary

the three

supply

to the two-phase

required.

occasions).

the

metering

are

principal

between

the liquid

on the flow

to the purge

operators

on several

are made

from

fixture

one

two

prior to and during

is installed

connections

Procedure

at least

in case

(which

apparatus

and plumbing

and Test

experiments,

is necessary

Several flow

Tasks

rack,

supply

system

line is

rack,

on the flow

which

metering

rack.

Following section separator flow

this step, exit

flange,

/ collector

metering

rack

the

two-phase

located tank.

on Next,

is connected

flow the the to the

return data

data data

line is connected

acquisition acquisition acquisition

from

system cable rack,

the test

rack,

bundle while

the

from

the

power

and

control

cables

control

cable

Once,

these

installed

is connected

rack,

section

which

the above

of the

television

monitor

of the test

liquid

removal

supply

values

differ

blockage. inspected

flow

with

the

flow

return

test

is checked

video

assembly

rack

Another

strobe

test

and

panel

to the

lights

the

two

section

are mounted,

standard

Next,

supply

flow bar,

racks.

is checked

system.

the gas

Unistrut

is data

on the two-phase

in between

to the S-VHS

operator

section

metering

line.

to the

the

rack.

and the two

respect

and

respectively

assembly

tank

we must

and the by more

In case

is flushed

contamination).

experiments, meter

rack

using

the alignment

hose

is fixed

nozzle.

of organic

wet test

the

located

mirror

section

mirror

tank

made,

joins

two-phase

connected

section

the air injection

the

test

are

bar which

visualization

the

Orientation

these

connections

via two flanges,

and

flow

to the

to the data acquisition

on an Unistrut

entry

The

connected

important

acquisition

fixed

are

the

for possible

than

five

than

percent, is in fine

filled

the small

the flow

acquisition

orifice leaks.

Since

check

data

and

through

system. the

orifice this

filtered

water

is primarily orifice

If measured

orifice

condition,

with

the

orifice

the

flow

using mass

(for

used

both

flow

rate

is checked

for

loop

is visually

Next,

the

103.40

gas

supply

kPa. Following

absolute

pressure

entered

into

the zero

cassette

has

system

The

then

the

barometric

system

pressure

control

is pressurized

is measured

local

barometric

system

software

pressure

action

is connected

in unison into

a real

between

and

with

each

pressure

compares

this

consequently

adjust

the time

with

video

of the video

the

two

recording

digital

trajectories.

to the data

stamp Strobe

system,

acquisition

strobe

lights.

system

for

on it, which lighting

but does

not

and control A fresh

every

flight.

makes

used

interfere

video Each

it possible

maximize

with

the

the real

time

stamp.

reiterate,

during

experiments. stationed in front flow

video

is inserted

distinguish

the ambient and

correct

is tested

frame

digital

the

and the

offsets.

and

freezing

this step,

computer.

with

The high-speed system,

is checked

transducer

the

measurement

video

cylinder

One in front

of the

rates.

flight operator

two

controls

of the computer

flow

metering

A third

operator

operators

rack may

the

control and be

are data

rack.

necessary acquisition

The other

of setting

required

closely

conducting

software

operator

is in charge to

for

gas check

and

is stationed and

liquid

the

liquid

3"7

recirculation

line

leaks,

would

which

The

first

and

cause

operator parameters:

rate,

acquisition

camera

recording

207

and

the two liquid

Next,

the

gravity

reduced

sets

level,

gas

flow

the

flow

loop

acquisition orifice

time.

system

size

any

setting

depending

Meanwhile,

on used,

micrometer

flow

length

the second

supply

the

gas

operator

the appropriate

the liquid

using

develop

type of liquid

by adjusting sets

not

of the experiment.

diameter,

rate

does

pressure

tank

pressure

handles

located

valves.

calibrates into the

control

Both

the position that these occurs, liquid

all

this operator

the experiment.

a problem

regulator.

liquid

trajectory,

and note

inside

data

gas velocity

operator

in the eventuality If such

the

this operator

instructions

to commence for leaks

the

supply

gravity

the

termination

rate, test section

superficial

first

appropriate

piston

the abrupt

Consequently,

kPa

that

and total experiment

sets the desired regulator.

sure

configures

following data

make

supply

loop

system. instructs

operators

the tank

are ingested second

instruments

Once

aircraft

the flow

within

inputting enters

the

would the

the

software

loop apparatus

liquid

into the liquid

operator

by controlling

the

the data acquisition

monitor

of any air bubbles

bubbles then

test

try

supply feed

system.

to adjust

appropriate

tank

the

pressure

such

cases,

coalescence in

however,

of ingested

erroneous

consideration emergency,

such

connection, control

the first

panel.

This

air bubbles

flow since

most

Data

its

validity

uncontrollable

action

can

closes

visual

and nozzle

pattern.

operator

the

injected

this

highly

push

data

distorted,

bubbles

nature

leak

caused

a panic

all solenoid

valves

case

a loose

located and

result

taken

button

would

not

questionable.

since

plumbing

on top

causes

into

the

of the flow

stop.

perform

down to

with

the

aircraft

floor.

indisposed,

operator

takes

After

completing

back

in order

This

turn

injection

test

Velcro

is removed

principal

operators metal

are

strapped

ring mounts

operators

to the rear

fixed

injured

of the aircraft

trajectories,

set of parabolas

supply

removed

through

gravity

for approximately

are

the

and the

duties.

reduced

a new

back to the liquid nozzles

of the

the necessary

a set of six

lasts

inserted

one

he or she over

procedure,

bands

In case

to commence

period

recirculated Air

experimental

adjustable

otherwise third

this

ten minutes. tank, and

from changed,

within

the

aircraft

the same

During

the separator to account

airspace.

the turn,

water

/ collector for

turns

tank.

a different

aspect

ratio

removed

and

nozzle

connected

depending

on which

After

flight,

each

acquisition desired

flow

are

stored

translate

diameter.

to either

the

integers,

have are

Software

air and water

Likewise,

co-flow

air

supply

or the cross-flow

to see whether

place

during

been

obtained.

converted driven

the

hose

test

section,

used.

are checked

has taken rates

units.

pipe

was previously

the data

system

the

engineering

the experiment

voltages

to superficial

and

are

of the

and also to check

Consequently,

calculations

flow rate values

any malfunction

this from

performed

gas and liquid

data,

which

voltages

in order

velocities.

CHAPTER EXPERIMENTAL

3.1 Non-dimensional

In general,

under

dependent

gravitational

RESULTS

and DISCUSSION

Parameters

for a two-phase

environments,

flow

system

isothermal

fluid

properties,

in both

conditions flow

normal

, the

geometry,

and

bubble flow

reduced

gravity

diameter

conditions

DE} is and

the

acceleration.

Mathematically,

this functional

relation

can be expressed

as:

De = f (_, _o, _ pc, p_,Bp, D_, ULs,Q_,g),

where

(_ is the surface

tension

respectively

the

phase

while

t_d and Pd and the dynamic

(gas)

phase;

injection volumetric

dynamic

of the continuous

Dp is the two-phase

nozzle

diameter,

gas flow

the operational

(absolute)

rate

viscosity

conduit

ULS is the

environment.

and

viscosity

flow

and g is the

(liquid)

(pipe)

diameter; liquid

Pc and Pc are

density

and density

superficial

gravitational

the

phase;

of the

of the dispersed D N is the

velocity,

acceleration

liquid

gas

Qd is the

depending

note

that counting

DB, there

are 11 independent

3 independent

dimensions,

namely:

Consequently,

by applying

the Buckingham-Pi

manipulation

keeping

non-dimensional

the

relevant

parameters,

D B" = D8 / Dp; we use

diameter bubbly

and hence

physics

[L]: length theorem,

in mind,

in function

(f) and

and [t]: time. after

we obtain

some

algebraic

eight

[(11)-(3)]

namely:

DB *= f* (Rep,

where

[M]: mass,

terms

Wep, Frp, DN.

Qd. P-. P')

Dp as the reference

a relevant

physical

length

dimension

since

it is the pipe

in the problem

(for the

flow regime);

Qd* = Qd/Qc

= [QJ/[ULs(_4)Dp2],

whereQc

is the volumetric

liquid

flow

rate;

furthermore: D N" = D N /Dp

: gas injection

Rep = pcULsDp/p.c

: Reynolds

Wep = pcULs2Dp/(_

: Weber

Frm = pcULs 2 / (Pc-Pd)gDp

nozzle

aspect

number number

: Froude

ratio;

= (Inertia = (Inertia

number

force force

= (Inertia

/ Viscous

/ Surface force

force) Tension

/ Buoyancy

force) force);

P* = Pd/Pc

: density

ratio

P-* = P-d / P.c: dynamic

Since

Furthermore,

(0.01g

and a given

on the bubble

conditions,

in a reduced gas phase we obtain

of bubble

- 0.02g,

the buoyancy during

up to 340 for the present

Consequently,

process

conditions

acting

force

and air

relation

(f*).

approaches becomes

In parallel,

under

g is the terrestrial is still small

compared

to other

process

(the Froude

number

set of experiments).

environment,

for a two-phase

formation

force

on the bubble. where

phase

number

the buoyancy

its generation

gravity

the following

the functional

the Froude

(f*) since

forces

as the continuous

(_') from

environment, from

to other

acceleration),

acting

water

we can remove

be removed

gravity

gravitational

getting

we are using

phase

compared

reduced

ratio.

in a microgravity

and can

negligible

forces

viscosity

in our experiments

as the dispersed

infinity

and

using

flow system,

dimensionless

a given

under

functional

in a continuous

liquid flow:

DB* = f* (Ree, Wep,

DN', Qd*, P*)

liquid

phase

isothermal relation

for the

It is important

to understand

in the present

problem

complete

physical

phenomena. involved

are global

picture

In order

in bubble

dimensional

which

to obtain

formation

parameters

and attaching

that the non-dimensional

forces

within

Parameters

Experiments

conducted

cross-flow cm,

1.9

injection

geometry, cm and nozzle

2.54

diameter

the bubble

a liquid flowing

be obtained

from

using

both

different

sets

in an air-water to pipe

through local

of the physics a pipe,

balance

non-

of detaching

of detachment.

Estimates

co-flow of pipe

system.

configuration diameter,

Two

(DN") are

diameter

the

generation

at the time

the

considered

do not render

understanding

and Uncertainty

for three cm,

and they

accurate

on the bubble

3.2 Experimental

are

describes a more

should

acting

parameters

and namely

1.27

ratios

of air

different used,

the

namely

0.1

and

0.2.

Volumetric

gas and liquid flow

10 to 200 cc/s, considers number

depending

non-dimensional (Rep),

pipe

Weber

rates

(Qd and Qc, respectively)

on pipe diameter. parametric number

The

ranges (Wep)

and

are varied

present.experimental based pipe

on Froude

pipe

from work

Reynolds

number

(Frp).

Thus,

as parametric

ranges

we consider

Rep = 1600-8500,

Wep

= 2-75

and

executed

for

Frp = 2-340.

In order each

to ensure

acquired

operation,

the the

longer

data

nozzle

erroneous

fact

software

the

difficulty

gravity,

reduces

bubble

2.0 © and

packages.

average

of the bubble's

the

an image

the number

the

bubble minor

of the detached

feature

to arrange

conditions. considered

the

operating

data

points

from

5.1 © image bubble

diameter and major bubble

pipe

Since

inner

present test

take

points

are

investigation.

flow

loop

during

experiment

acquisition is not

and

than

points.

the flight

is obtained

data

test In such

wall

to be taken

data

change

conduit.

these

the

of acquired

detached

co-flow

have

nozzle

the experimental

in the

are

air injection

on the

is obtained

OPTIMAS

Since

conditions,

not

certain

diameter

all flow

First,

normal

trajectories

the

within

impinge

due

which

THIN

would

are

during

concentric

under

dive

was taken

they

Experimental using

not

bubble

of reduced

twice,

care

in nature,

Furthermore, periods

great

than

two

Sometimes,

was

forming

to detach

repeatability,

point.

eventhough

section, cases,

data

and

perfectly by taking

video

processing spherical

for

a geometric

axis. is captured

incorporated

within

by the freezing THIN

2.0 ©. Next,

action using

of a

feature

displayed

spatial

calibration

reference

The

detached

these

of bubble

length,

geometric

Bubble

by OPTIMAS

usually

error

diameter

the desired

setpoint

desired

setpoint

3.2 Co-Flow

namely,

in this

inner

for each

investigation

of bubble

for both

errors

water

Explorer>,

respect

the

to a chosen

diameter.

of the three nozzle

is the

consecutively

is first

arithmetic

diameter

flow

measurement

pressure

is within

in measurement

and air mass

temperature

for the absolute

calculated. average

+5%

of the

are +5 to +10%

rates, and

+3 to +5%

of the

+3 to +_7.5% of the

measurement.

Configuration

diameter

in figure

Rep = 1930,

and Rep = 4700, 2.54

(pipe)

with

of the gas-injection

Uncertainty

for the

of bubble

is displayed

is achieved

diameter

in acquisition

value.

desired

Variation

reported

<Measurement

values.

Experimental mean

bubble

in the vicinity

diameter three

diameter

the flow conduit

averaged

bubbles

5.1 ÂŠ, namely

Wep

cm I.D. pipe with

6. Wep

(DB)

Data

with respect for

three

to volumetric

different

Rep

= 2.0, Frp = 2.3; Rep = 2870,

= 11.7,

Frp = 13.5.

an air injection

This

nozzle

data diameter

gas flow rate values Wep

= 4.5,

is obtained to pipe

are

(Q_)

shown, Frp = 5.1

by using diameter

the ratio

(DN')

of 0.1,

11.3

cm/s

In this The

bubble

There

bars error

diameter

we can clearly

detached

bubble that

have

value.

(fixed

velocity

of the

through

the

plays

process

DN).

the

detaching

flow surrounding

bubble

from

7.6

cm/s

diameter

size

we observe

note

values.

is + 5 % of the

figure

6 we

have

that

the

effects detaching

curves

velocity

the

(ds/dt

relative

ULs term Qd,

effects

gas

surface

tension

the liquid

velocity

of the

velocity

term,

plays

the surface

giving are

rise caused

is we

is the flowing

ds/dt role

tension

liquid

force

liquid

a detaching

rate.

force

ds/dt

the

flow

drag

- ULS), where

as the superficial

increase,

is increased,

volumetric

estimate

ULs is the

For a given hence

liquid

term,

in this

in this plot.

a constant

to properly

and

while

the bubble.

for

velocity

are fixed,

bubble

(Uts)

bubble

which

presented

In order

formation.

forces

These

which

center

role

momentum

bubble.

presenting

in acquiring

in size,

relative

attaching

bubble

trends

bubble

of bubble

when

In all plots

the three

the

pipe.

velocity

error.

decreases

to consider

liquid

see that as the superficial

across

constant

shown

considered

this experimental

note

superficial

to 18.5 cm/s.

are

are two important

First,

held

error

experimental

consider

the

and consequently

plot,

mean

by varying

term in the

and the gas

velocity

increases,

a .smaller

generated

primarily

the

liquid

Furthermore,

volumetric

note

that

gas flow rate

fact

is substantiated

over

the bubble

formation

plot

the surface

tension

and

momentum Qd,

given

force

therefore

upon the

the

increase

Figure gas

bubble

detaching

7 shows

obtained and the

to flow

conduit

Corresponding

the

1.9 cm

I.D. pipe

(ULs) constant.

forces

which

to be smaller along

that ds/dt

with

gas

increasing

at detachment with Qd,

has

effects

momentum

force

since

the

the bubble

attaching

ds/dt

effects

overcome

bubble

does

gas flow rate.

diameter

to change

I.D. flow

a given the

that the

diameter

in this

with

Subsequently, increases

preside

shown

indicates

at a constant

non-dimensional

increasing

are dealing

force

Recall

of bubble

respect

However,

to volumetric

(Qd) with

by using 1.27

gas

the variation

diameter

the bubble

this plot

of the

since

detaching

increasing.

therefore

important

diameter.

rate is increased.

is also

effects

rate

is constant injection

in size with respect

flow

nozzle

force

expect

ds/dt

velocity

any one of the curves

Along

one would

velocity

liquid

process.

is a bubble

center

superficial

with

the

which

gas flow

increases

by considering

nozzle

the volumetric

diameter

(Qd), holding

This

liquid

bubble

as a function

in aspect (DN') from

conduit

of gas

0.1 to 0.2.

at a constant

superficial

flow parameters

ratio

of volumetric

liquid

injection

This

data

ULs of 18 cm/s

velocity

are Rep = 3420,

of 45 cm/s. Wep

= 8.4,

Frp = 17.4

for the

1.9 cm

pipe and

Rep = 5740,

Wep

= 35.6,

Frp = 164.2

for

the 1o27 cm pipe.

It is shown,

that for a given

increasing note

nozzle

that

changing

for the

the

1.9

diameter

acts

On the

other of

decreases nearly

are closely

the

bubble

diameter

for the

1.27

increase

to 0.2, while

increase

the

magnitude

of the gas the bubble

for

balanced.

the

1.27

can

the

diameter

increases

gas velocity. increases

pipe

with

However,

drastically

increases

minimally

deduce

diminishes.

stresses

Since nozzle,

that the attaching use

nozzle

force,

while

surface

tension

the formed

bubble

force).

The

Weber

of 8.

I.D. case,

However,

the

momentum

that

injection

tension

is on the order

pipe

gas

surface

gas injection

(Wep)

the

force.

Qd (fixed

this signifies This

momentum

a constant

DN Â° effect

constant

to the

on pipe diameter

therefore

the

pipe,

case

hand,

36,

of superficial

I.D.

in size based

at a set value

pipe

to attach

number

stays

0.1

the value

increases

order

the bubble

(if at all).

decreasing force

1.9

D N from

with this change

For

diameter

pipe diameter,

we have

a Wep

on the

the

surface

tension

effect

since

the

bubble

diameter

and the detaching

of a modified

(Wep)m

forces

based

the

(ds/dt

smaller

- ULS) relative

than

neglected

Figure

the Wep value,

with respect

8 presents

increasing rate. section

data

liquid

For

from

11 to 27 cm/s,

cm/s

and

injection

1.9 cm

for

increased

the

from nozzle

It is shown

that

1.27

diameter

bubble

nozzle

diameter,

the

a means

stressing

conditions. surface

superficial

tension

detaching

Along force

the

tests

equal

any and

gas the

with flow

using

the 2.54

not be

liquid

the

with

gas

flow

test

1.9

cm test

velocity

section

superficial

from

liquid using

to 15

is increased

ULs is increased

8 to 15

velocity a ratio

of air

to 0.1.

increasing pipe

effectiveness

bubble

one of the three gas

(Ds)

at a set Qd equal

rate,

a forming

the

can

diameter

are performed

decreases

of volumetric

case

of volumetric

cm test section

section,

All these

diameter

value

rate of 51 cc/s,

cm test section,

test

forces

bubble

is taken

to pipe diameter

injection

plot,

8 to 14 cm/s.

values

microgravity

figure

the

in this

forces.

for a given

section,

for the 2.54

at fixed

velocity

of (Wep)m attaching

dimensional

gas flow

test

velocity,

velocity

in this

value

that bubble

to 61 cc/s and the 1.27

cc/s.

The

detaching

variation

at a set volumetric

the

showing

presented

a set Qd equal

term.

to bubble

the

superficial

The

velocity

superficial diameter

and

surrounding

under

curves

momentum

liquid

force

liquid

reduced

presented are

gas

and in this

constant.

What

changes

liquid

velocity.

increased, Note

Therefore,

the bubble

that

the

asymptotic, ds/dt

is the bubble

and

values

effects

curves

bottom

from

the

curve 2.54

the

and

note

pipe

I.D. case

Additional change figure

which injection

9. Experimental

superficial

detach

ULs is

This

and

the

have while

and that

higher. their

diameter ULs value), change

center

curve

because

similar

slowly, This

if not, could

respective

become

mean

that

attaching

and

increases

across

fact which

can be explained

bubble than

volumetric

gas

(figure

6),

between

flow

higher

the

center and

the

(Qd = 51 cc/s

displays

bubble

three

I.D. case

rates

I.D. case the

the

diameter

the 1.9 cm pipe

the 1.27 cm pipe

explained

quite

other.

bubble

primarily

previously

volumetric

data, of gas

curve

curve,

with

the

each

Qd effect.

respectively)

increase

by increasing

is prone

to decay

to top (for a given

and 61 cc/s 15 cc/s.

seems

increasing

that

bottom

the top

caused

bubble

of ULS = 40 cm/s

both

increasing

between

the

counterbalance

In parallel,

diameter

ULs are

detaching

since

effect

size decreases.

bubble

with

detaching

size

a Qd equal is shown

gas flow rate.

displays nozzle data

the important diameter

presented

role played

on bubble

in this figure

b.y flowing

detachment is obtained

liquid is shown

for a fixed

and in pipe

diameter

of 1.9 cm

and

a volumetric

gas flow

rate

of 51 cm3/s

(cc/s).

Two

sets

of gas

injection

nozzle

diameter

ratios,

namely

D N

0.1 and

0.2,

are

has upon

the

used.

We note

the constraining

detached

bubble

diameter

and a given

and

the

gas

effect

diameter

volumetric

momentum

increase

in size up to the value

is most

the

superficial

generated values

liquid

bubbles

counterbalance increases

with

the

of bubble

velocity,

is shown

DN* = 0.1,

ULS -

formation

For a given

both the surface

However,

is that,

becomes

velocity,

attaching

in figure

plot

comparable

gas injection

A graph

fixed.

velocity.

at low

nozzle

tension

superficial

hence

the

force liquid

bubble

can

of the pipe diameter.

velocity

liquid

pipe wall

of ULs are diminished,

in this

become

of superficial

are

effects

interesting

conduit

gas flow rate,

force

the

detaching

the flow

at low superficial

velocity,

What

which

large

nozzle

the

than

It is noted detaching surface

that effects

tension

diameter,

cm/s)

the

at such

high

of ULs must force

which

diameter.

frequency 10. Data

of nozzle

(higher

in size.

the bubble

effects

18 and 24 cm/s,

independent

(fa) as a function

is presented

as well

of superficial

for the 1.9 cm test

as for the

gas

section

1.27 cm test section

at DN Â°

= 0.1 and bubble rate.

ULs = 45 cm/s.

frequency

of formation

As Qd is increased,

at which

the

become

bubble

to the

1.27

cm pipe

stays

or less

From

the

volume

I.D. case constant

a fixed

the

detachment

formation is

can

increasing

with mass

bubble of

high

flow

7, the

liquid

rate,

flow

the

With

effect

frequency

rate

liquid

bubble

the

bubble

the

bubble

formation

velocity.

increasing

This

ULS , the

by the superficial

increases.

is decreasing

with

velocities.

bubble

displayed

If we refer

in figure

superficial

bubble

frequency

conservation.

gas

flow

appears

if V B , namely

conservation.

gas

the

in the value

trend

superficial

that

increasing

formation

the formation

volumetric

gas

a given

decrement

as shown

see

due to the detaching

hence

liquid

that

at such

volumetric

to increase

be explained

note

in size

increases.

velocity,

conditions

Qd = fBVB we

size decreases

Bubble

by mass

velocity,

volumetric

eventually

be explained

also

a steady

of bubble

frequency

can

superficial

can

note

liquid

increasing

trend

with

is shown

time

increasing

superficial

with

increases,

then

frequency

liquid

is constant,

Furthermore,

bubble

rate

expression

formation

again

however,

The

gas flow

increases

frequency

asymptotic.

volumetric

the

Note that for constant

In parallel,

with

increasing

velocity.

and

experimentally

subsequent observed

detachment to

under interesting

reduced

gravity

phenomenon.

Unlike

bubble

gives

generation

rise to relatively

force,

larger

under

small

and more

uniform

reduced

gravity

Figure

11 shows

bubble

reduced

gravity

conditions

0.2).

departure of

the

over

liquid,

the surface

rim of the air injection

elongation

volumetric

gas flow

rates,

(ULs

displayed

= 16 cm/s, in figure

in this photograph.

before

a spherical

Similarly,

slug

due to the

spherical

(ULs

rather

surrounding

dominates

bubbles

generation

that

ellipsoid

from

gravity

conditions,

bubbles

action

which of the

are obtained

usually buoyancy

in the present

experiments.

It is observed

forming

sized

normal

at high 35 cm/s,

surrounding Qd = 20 cc/s,

detachment, than

which tension

the

assuming

geometry

bubble

acts

force

bubble

which

tends

velocity

under

Dp = 1.27

cm,

becomes

elongated

spherical

can be attributed

D N" =

geometry.

This

to the detaching

effect

detaching to attach

force the

and

bubble

nozzle.

bubble which

before gives

detachment

appearance

also

rise to a detached

Qd = 95 CC/S, Dp = 2.54

12. The

liquid

cm,

of acorn-shaped

occurs

bubble

high

resembling

D N" = 0.1).

slugs

This

is worth

fact noting

a is

On the

other

assumes (ULs

hand,

a somewhat

= 11 cm/s,

forming

bubble

Figure

volumetric

also

Frp

presents

gas flow

rate

= 164.2;

neck

can

liquid

forming, cm,

neck

velocities,

the

as depicted

DN Â° = 0.1).

length

elongation

cm test

= 16.7,

see

Y is the bubble

respect

relative

that

being the

bubble

in figure

In this

case,

the

diameter

a function

to the

length

also

to superficial

section

looking

(En)

liquid

velocity

= 5.3,

and Rep = 5740,

Wep=

35.6

at the

photographs

intractable an elongation

distance

the

properly

length

nozzle

and DB is the detached

bubble

diameter.

gas

increases,

equal and

rates,

to the air injection

liquid

resulting

flow

rates

in an elongated

are

and in

define

given

injection

liquid

Frp

presented

gas

gas and

(ULs).

Wep

it is quite

from

at Ree = 2210,

we can define

approximately

volumetric

length

Frp = 77.2

that for low volumetric

is small,

elongation

1.27

Instead

of the forming

However,

a short

(Qd) with

Wep

length.

Y - .5D B , where

length

and

while

Dp = 1.27

a DN Â° = 0.1.

It is observed

shape

graph

for the

for

11-13,

bubble

center

displays

Rep = 3937,

figures

spherical

gas

nozzle.

is presented

= 24.3;

superficial

Qd = 10 cc/s,

the air injection

Data

at low

as En = tip to the

the elongation

nozzle

diameter.

increased, neck

region.

the At

these

flow

conditions,

value

of the air injection

Furthermore,

gas

manifests

itself

spherical

geometry

flow

volumetric

15, for

occupied

section

of the

Consequently, phase slug

flow ( Taylor

exceeds

(s) with

rate

(Qd/Qc)

values

by the

gas

two-phase

bubble

2/3, indicates

is increased

regime of

and

the

from

with respect

develops.

bubbles

This

which

neck

for

ratio various

of e. Void phase

flow

region

the

to the

phenomenon

have

(greater

void

flow

formation

is defined

volume

of fluid this

A is the distance of

fraction

the

distorted

than

3 times

flow

rate

within

Therefore of Taylor

any

regime

value

bubbles.

as the

ratio

within

a given

relationship

section

can

the front

detached

any given

is displayed

between

previously

is Srnax. = 2/3, for the bubbly ) regime.

gas

conditions,

Mathematically,

where front

of volumetric

fraction

to total

conduit.

the

the maximum conduit,

jet

elongated

as [_ = (2/3)DB3/Dp2z&],

detached

considerably

diameter).

averaged

volume

liquid flow rate

appearance

fraction flow

deviates

diameter.

and a greatly

void

length

a bubbly

the

nozzle

liquid

be written

nozzle

rate,

the gas injection

figure

elongation

as the volumetric

volumetric

Variation

the

bubble. of the two-

and Srnax. = 1, for the

of the 'void fraction

which

Data

is presented

3.9,

at two different

Frp = 8.0 and

geometries, that

the

namely

void

It is also

straight

line,

geometry, plot

gas

and

namely

relationship velocity Along

suggesting

liquid

void fraction, is a sole shape

the

time

namely

void

fraction

If we

A reason

compressibility

we can write

in which

of the volumetric

and

the

for

data why

we obtain

experimental effects.

flow

Instead,

volumetric

mathematical

UB is the bubble the distance

since

(UGs+ULs),

relationship

for the

liquid flow

rates

and is not in any

geometry,

in other

words

nozzle

diameter.

does

that

the void fraction

should

states

the

covers

a modified

ratio

of the ON).

given

flow

indeed

injection

this

bubble

If UB is written

This

(Dp,

z_ = UBt, where

flow

or less along

of solely

previously

this moving

gas and

to the flow gas

the

gas

a function

diameters

is a function

consider

DB 3 = (Qdt)/('rJ6).

nozzle

It is observed

is more

is not

Wep

for two different

volumetric

scatter

fraction

Rep = 2318,

Dp = 1.9 cm. the

data

of pipe and

s = Qd/(Qc+Qd).

the experimental

combination

void

and Qd = (/rJ4)Dp2UGs,

function

diameter

scatter.

the

lines

or form

theory

that

rates.

t is the

= (/rJ4)Dp2ULs

pipe

flow

the same

namely

Frp = 31.2,

increasing

that the given

a function that

with

for the void fraction,

and

= 15.1,

Wep

increases

apparent

suggests

conditions,

DN* = 0.1 and DN* = 0.2, for

fraction

(Qd/Qc).

the

Rep = 4579,

flow

fall on a straight not

measurement

occur

may error

the flow

On the

other

line with none be "the and

error

conduit hand,

if minimal

presence induced

of a by

Consequently,

transition

from

bubbly

using

a single

nozzle

liquid

and gas flow

as effective flow

detached

bubble rise

reduced

gravity

manner

the

moving

rear

end

While

the

subsequent

at the

away

from

expansion,

During

this

the another

control

manner, volumetric

is therefore

coalescence

of bubble

liquid

flow

nozzle

tip can

merge,

injection

nozzle

exit.

observed

that

by flattening

the gas

injection

nozzle

expansion

and

the

process,

rate,

thereby From

immediately

deforms

expands

size.

bubble

the nozzle

air

the

regime

of the two-phase

to the volumetric at the

flow

void fraction

uniformity

bubble

varying

the periphery

ability

rate relative

detached

end

the

in a precise

by simply

along

lacks

of the

hence

of monitoring

injection

and

be controlled

system

and hence

end

towards

rear

can

coalescence

shape.

moves

nozzle

a forming

rear

fraction

manner

experiments,

of the

bubble

flow,

This

gas flow and

void

injection

bubbles

further

quasi-spherical

the

however,

to bubble

detachment,

the

rates.

generated

volumetric

giving

gas

which

At a high

that to slug

as multiple

conduit,

adjacent

note

our after

out,

in this

tip. Subsequently, bubble

the

resumes

rear

its

end

of the

flattening

and

tip.

detached bubble

bubble is formed

undergoes at the

nozzle

tip.

It is

experimentally

observed

forming

can catch

when

bubble the

results

later

that

diameter

a fixed

rate,

depends

generation present

reduced

gas

Qd* = Qd/Qc)-

normal gravity

the

flux.

by a critical

injection

occurs

3.3 Cross-Flow

volumetric

gas

under

coalescence

Figure

critical

This

nozzle

rates

two

size

bubble)

liquid velocity,

can be described

Qd'cr_ic,_ (where

can

in slug (Taylor

superficial

of these

a larger

bubble

gas flow

of the detached

merger

forms

a coalesced

characterized condition,

The

and

or can result

high

up with the rear

is expanding.

in coalescence

observed

For

that at relatively

bubble, distinct

bubble.

smaller

but

diameter,

the

of coalescence

fronts it is

the

pipe

condition

form,

the

volumetric

gas

fact

shown

value

for DN Â° = 0.1 is observed

bubble

dimensionless

critical

experiment,

especially

Furthermore,

non-dimensional

conditions

of the

formation.

onset

gravity

the front

also

Sada

onset

gas

flow

rate for

a1.(1978).

of Qd'cr_c,_ at which

flow ratio

bubble In

the

onset

to be 1.35.

Configuration

presents gas flow

a graph rate

with

bubble

respect

diameter

to change

(DB)

in superficial

a function liquid

velocity.

Data

is presented

for three

1.27

cm test section,

Wep

= 16.7,

obtained 17.4

cm/s,

namely

Fre = 77.2

for

three

observe

that the bubble

Once

superficial

again,

this

fact

preside

over

curves

shown

in this

dealing

with

increases

increasing

along ds/dt

with

at detachment with Qd, has

the ds/dt since rate.

gas

the

bubble

attaching effects bubble

surface

Qd,

overcome does

Ree = 3937,

Frp = 164.2. velocity,

co-flow

Data

namely

ULs =

configuration,

increasing

and

a force

therefore

center upon

velocity

gas

in size

the

process. force

Along

flow

rate,

for

nozzle

which

is a bubble

one

would

gas flow ds/dt

with

rate

therefore of the

respect

forces

any

of the

one since

injection

expect

is also

effects

important

is constant

given

the bubble

the detaching

increase

considering

tension

as the volumetric

effects

the with

formation

momentum

the bubble

liquid

for

increases

liquid

the

= 35.6,

and the

velocity.

plot the

Subsequently,

Wep

obtained

is substantiated

given

DN Â° = 0.1

We e = 5.3, Frp = 24.3;

of superficial

diameter

the

using

cm/s.

data

liquid

which

smaller

values

experimental

conditions

Rep = 5740,

and 45.2

Similar,

flow

Rep = 2210,

and

distinct

31 cm/s

a constant

different

diameter.

detaching the

bubble

is increased. increasing. this

we are

plot

to be

However, Recall

indicates

gas momentum to volumetric

force

that that force

gas

flow

It is interesting

to note

volumetric

flow

each

start

gas

other.

attaching

bubble

Note that

across (fixed

hence

the

effects

increase, observation from

environment.

recall

a gas

injection

port

comparable

bubbles

by the bubble

and dominates

the detaching

size decreases

being

as the superficial

as prominent liquid

as for the co-flow

velocity

is increased,

volumetric

the surface

gas

tension

(ds/dt

- ULs) relative

the

ds/dt

term

plays

role in the process and the gas velocity

the

in size

these

be explained

at low

as Qd increases.

rise to a smaller stresses

31 cm/s,

in the

a detaching

liquid

ULS

is increased

this can

curves

that

tension

rate

for a constant

discussed,

superficial

further

are

the bubble

in size,

the surface

giving

force

presented

previously

Qd,

bubbles

that as the superficial

plays

and

overcomes

the variation

the three DN).

have

For a given

gas flux,

cm/s

flow

Again,

which

decreases

the ULs term

bubbles

by ds/dt

We note

detached

This

generated

in size.

is increased,

configuration.

while

differ

at a constant

velocity

which

the

ULs = 45.2

by the gas momentum

Moreover,

constant

for

as the volumetric

role played

liquid

rates

However

to considerably

that

increases, generated

importance

within

a flow

rate.

force

is held

velocity

term,

of bubble

the

flow

an attaching

momentum

the

role

generation.

forces bubble

are fixed, detaching

bubble. of liquid.flow conduit

for

detaching

in a reduced

gravity

Next,

the

effect

presented versus Wep

in figure

= 16.7,

increase diameter co-flow diameter

nozzle,

may

force.

flow

bubble

conditions,

and

different

bubble diameter namely

Rep = 5740,

gas

diameter

injection

is plotted

Rep

Wep

= 3937,

= 35.6,

geometries,

Frp = namely

the 1.27 cm test section.

nozzle

Since

the formed

diameter

this force bubble

we increase

acts to attach

increases

the

magnitude

the bubble

in size

for

bubble

diameter

to the

a constant

force).

that

at high superficial with

to pipe diameter. configuration,

in size,

contrary that

to the the

liquid

increasing

This fact differs

where

is similar

deduce

geometry

dimensional

at two

for two using

considerably

(DN*). Thus,

rate

the gas injection

momentum

It is observed

cm/s),

tension

nozzle

(ULs = 31 cm/s)

O N" = 0.2,

As we increase

(fixed

flow

Fre = 77.2

DN* = 0.1 and

injection

In this figure,

gas

(ULs = 45.2

of the surface

air 17.

volumetric

164.2

gas

at high

velocity, the

ratio

from

the observation

superficial

liquid

independent

of gas

observation

made

bubble

attaching

injection for

and

the

air

injection made

velocities, nozzle co-flow

detaching

tends

the

nozzle for the bubble

aspect

ratio

configuration, forces

not

counterbalance

each

detaching

forces

as the volumetric

Along

the

same

liquid

velocity

the

1.27

cm test

lines,

section

with

that

liquid

for a given

trend

hence

increasing observed diameter

18. This

the

bubble

the

seems

of ULs = 40 cm/s increasing counterbalance configuration).

graph

displayed

flow

co-flow

at a constant

that each

quite

higher. their other

the

This

1.9

and the 2.54

mean attaching

that

superficial

gas

flow

configuration, acting

increases

if not, become

similar

increasing

the

we note in size,

observe

that

asymptotic, ds/dt and

observation

and

forming that

with

a fact

also

the

bubble

with values ULs are

.detaching to

rate.

in that

Furthermore,

bubble

could

respective

by using the

at a constant

In addition,

slowly,

taken

Qd = 44 cc/s,

with

forces

in size. the

to superficial

Qd = 61 cc/s.

detaching

rate,

data

Qd = 28 cc/s

by the co-flow

configuration.

to decay and

the

respect

displays

geometry,

decreases

gas

dominate

forces

with

decreases

injection

increase

volumetric for

diameter

gas

to that

ULS we

diameter

a ON* = 0.2

the bubble

is similar

increasing bubble,

of bubble

with a DN* = 0.1 at a constant

velocity

attaching

a DN" = 0.1 at a constant

It is observed

The

the

gas flow rate is increased.

in figure

section with

instead

variation

is shown

cm test

test section

other,

the

both

effects co-flow

Additional

data

velocity

and

features

data

of 44

gas

cc/s.

liquid

trends

bubble

diameter

nozzle

diameter

injection

taken For

superficial

The

displaying

with the

two

different

velocity

observed

1.27

cm test

nozzle

as a function is shown section

from

in this plot are similar

in figure

19.

at a constant

diameters

(ULs) is varied

of superficial

(DN*

= 0.1

liquid

This

plot

gas flow

rate

and

0.2),

the

10 to 60 cm/s.

to those

displayed

by the

co-flow

configuration. Once

again,

has upon given

we note

the formed

nozzle

tension

and

the bubble

can increase

Furthermore,

the

we liquid

become liquid

attaching

nozzle

at low superficial

the

liquid

superficial

bubble

diameter.

gas

velocity,

which

volumetric

momentum

velocity

that

velocity,

large

in size.

the bubble

of surface

It is noted

tension

which

liquid rate,

fixed.

of the pipe

(higher

detaching

conduit

pipe

velocity.

both

the

However,

of ULs are diminished,

independent

becomes

comparable

are

effects

in size up to the value

the flow

gas flow

force

the detaching

observe

effects

diameter

and a given

superficial

bubbles

effect

diameter

force

superficial

the constraining

nozzle

than that effects

wall For a

surface at

low

hence

diameter. diameter,

40 cm/s) at such

the

the generated high

values

of LIEs counterbalance

increases

with

gas

injection

Variation

of bubble

flow

is displayed

rate

section,

DN* =0.1

and 24 cm/s; 32 cm/s.

liquid

a fixed

is shown

can

bubble

the

explained

size decreases velocity,

time

hence

liquid

importance

of surrounding

is worth bubble

configuration

than

a given

velocity.

This liquid

the forming

mentioning formation

at this

bubble,

pont

frequencies

(fixed

liquid

that

smaller

configuration

Qd and ULs). This

This

ULS , the

In parallel,

with

again

of flow

value

for

at similar

flow

increasing

stresses

physical

as observed in

velocity.

by the superficial

is decreasing

independent

formation

increases.

the

ULs = 18

increases

bubble

displayed

providing

test

at a set ULs =

increasing

once

gas

velocity.

the

frequency

in time, are

for the co-flow

Dp , DN) and conditions

for

liquid

With

observation flow

1.9

namely

D N" = 0.1

superficial

effect

bubble

the

of formation

conservation.

formation

for

rate,

increasing

mass

the bubble

detachment

to detach

with

flow

due to the detaching

superficial

necessary

frequency

gas

to volumetric

velocity,

of the superficial

volumetric

to increase

liquid

cm test section,

bubble

value

respect

is presented

of superficial

that the

with

(fB)

Data

as for the 1.27

at a constant

Furthermore,

20.

at two values

It is observed

frequency

in figure

as well

Qd is increased

again

formation

the

mechanism

configuration. from the

this

plot,

cross-flow

geometry

can be explained

(fixed

by the fact

that

at similar

flow

configuration

geometry

and

are smaller

conditions,

in size than

bubbles

generated

formed

using

a co-

a cross-flow

configuration.

A graph rate

of void fraction

with respect

experimental Wep

(s) averaged

to volumetric

data

is obtained

= 8.4, Frp = 17.4

(Qc = 68 cc/s),

In the

using

cross-flow that

flow

(QJQc).

less along the flow Instead,

gas

obtained

for

configuration exists

and

flow

analogous increases

liquid

be the

flow

the

rates.

configuration, given void

with

co-flow

the

given

of pipe void

scatter

sole

to the

void

the

fraction

for

not fall

gas

is not a function

Comparable

values

fraction

â&#x20AC;˘ The

of 1.9 cm.

is more

diameters

void

Frp = 31.2

volumetric

and nozzle is

= 3420,

geometry,

the

data

21. This

Rep

Wep = 15.1,

increasing

as s = [Qd /(Qc+Qd)]

fraction

conditions:

pipe diameter

the

gas flow

in figure

that the void fraction

a function that

that

of volumetric

is presented

and Rep = 4579,

line, suggesting

co-flow

should

rate,

apparent

suggests

and

the

fraction

namely

plot

flow

D N = 0.1 and 0.2 for a constant

It is also

geometry, the

(Qc = 51 cc/s)

void

a straight

volumetric

scatter

the

as a function

at the following

configuration,

observed ratio

liquid

data

(DF;, function

fraction the

fact

directly

DN).

values

cross-flow that

a data

on this

line

indicates

the

presence

compressibility

effects.

For

co-flow

both

the

obtained given

by taking flight

section speed

video

Data

flow

is presented

larger

gas

ratio,

using

obtained

the

or three

obtained detached

could

coupled

void

bubbles

times

within

inspected

with

fraction

at different

be visually

of bubble

rate,

bubbles

cm test

of a

a given

with

the

obtained

cross-flow

co-flow

bubble system

configuration

in this plot, is obtained volumetric

liquid

flow

velocity

is by using

rate

that and

high

co-flow

in figure

and

corresponding

displayed

at similar air

with

Wep of

nozzle

are slightly

configuration. void

fraction

values figure

a 1.9 cm diameter

of 68 cc/s

22.

values

injection

geometry

the co-flow

diameters with

the

is shown

the cross-flow

by using

with

DN* = 0.1 at Rep = 2210, observe

liquid

by using

between the

obtained

system,

section,

cm/s).

superficial

generated

bubbles

diameter

with the cross-flow

(ULs = 17.4

flow

by using

presented constant

values

comparison

obtained

possibly

configurations,

of _ values

which

for the 1.27

in size than

Further

error

cross-flow

two

conduit,

Fre = 24.3

volumetric aspect

the

for

between

and those

= 5.3 and

and

experimental

camera.

Comparison system

some

an average

trajectory,

of the

a 0.38

obtained

23. test cm

values

The section

gas

by data at a

injection

nozzle

diameter.

is observed well

bubbles size

that

gas

generated

relative

obtained

with

this

(fixed

Moreover,

flow

showed

note,

the

that

the

cross-flow

and

liquid

flow

conduit

geometry.

Furthermore,

that

than

in general,

those

larger

with

Dp, DN)

in view

bubble

obtained

(fixed

rates

diameters,

are slightly

geometry

that

the

closely

void

fraction

gas and

fraction

of the

is similar

to that obtained

follows

configuration.

or flow

of gas

void

geometry

This

of flow

of flow geometry

flow

21 to 70 cc/s.

configuration

the fact

are smaller

gas

from

sizes

a cross-

and/or

flow

ULs,Qd)-

of volumetric

Coalescence

stresses

system

is varied

two-phase

in the co-flow

observation

configuration.

function

obtained

with the co-flow

independent

and

the cross-flow

irrespective

conditions

rate

of volumetric

nozzle

by using

a co-flow

system,

gas flow

values

injection

to those

22,

obtained

volumetric

at similar

similar

of figure

flow

The

the

fact

Recall,

that from

of the

resulting

liquid

flow

rates

and

resulting

that

the

two-phase

flow

using

the cross-

void

fraction

our previous two-phase

discussion,

flow

is therefore

is a sole

independent

configuration.

injection

configuration,

nozzle-detached especially

bubbles

at high superficial

is. also gas

observed

velocity,

for

hence

at high

gas

flow

rates.

The

observed

for the co-flow

However,

for the cross-flow

onset

of coalescence

the fact

that

observed

(ULs

spherical gas

and

shorter =1.9

geometry, liquid neck

Taylor

bubbles Qd = 76

highly

bubbles

Qd" at which Of interest

coalescence

are already

configuration, (slugs)

cc/s,

elongated

velocities, region,

for critical

bubble

that

section.

experimentally.

at which

co-flow

by assuming

cm, DN* = 0.1).

in these

If the

value

onset

merging

is and

system.

= 25 cm/s,

display

is similar

in the previous

not observed

generated

to the

rates,

coalescence

an exact

value

system,

analogous flow

bubbles

was the

in the cross-flow

liquid

figure

occurs

for

described

geometry,

at Qd" = 1.35,

Furthermore, and

geometry,

for the co-flow

coalescing

mechanism

Strobe

neck

bubbles

in figure

illumination,

formed,

Dp = 1.9 region

an ellipsoidal

generated

as shown

are

at high

cm,

decrease

deviate At

lower

in size

gas

presented

DN" = 0.1).

and

shape.

volumetric

These

from

the

superficial

and

display

25 (ULs = 15 cm/s,

Qd = 32 cc/s,

blurred

images,

these

video

a Dp

as seen

two pictures.

volumetric

2.85

or higher,

inner

surface

gas

flow

air would of the pipe

rate jet wall

is greatly

out

of the

directly

increased, injection

opposite

so that

nozzle the nozzle.

and

Q(_" (=QJQc) impinge

In this case,

on the large

slugs,

whose

primarily The

fashion.

exceed

by coalescence

surface

of these

lengths

of these

slugs

two to three

at the injector slugs

is wave-like

is highly and

times

the

pipe diameter

are formed

site. rippled.

manifests

Furthermore, itself

in an

the overall apparently

motion random

CHAPTER THEORETICAL

4.1 Theoretical

In order gravity

4 ANALYSIS

Model

to better

understand

conditions

experimental

the physics

developed

observations

of bubble

a model

and

shed

generation

whose

some

under

purpose

light

is to

this

reduced augment

rather

complex

phenomenon.

The

present

also

model

presented

incorporates force

term.

in the

This

it describes

(ds/dt

being

is the

superficial

several

trends

which

relative

liquid

model

term

velocity

velocity).

do not match

is based

categorized

into

(ds/dt

relative

from

By having

made

our current

on a balance groups,

(1992)

model

the

liquid

inertia

point

surrounding

to the nozzle omission,

experimental

of forces namely

this

a physical

this

and

work,

within

to the

respect

by Kim

Kim's

- ULs)

with

two

done

Unlike

importance

expansion

center

of work

a1.(1997).

velocity

bubble

which

version

is of utmost

the bubble

theoretical can

Bhunia

term

since

The

is a modified

of view

liquid tip while Kim

flow ULs

shows

data.

acting

on the bubble,

detaching

or positive

forces

and

forces

facilitate

attaching

negative

bubble

forces

Second

detachment

inhibit

Law of Motion,

this

the force

components

of Equation

Buoyancy

where

Pc and

dispersed term

(g)

present force minimal

Pd are the

phase

(gas)

represents

component relative

implies,

injection

occurring.

detaching

nozzle,

Following

while

Newton's

may be written

as :

(1)

+r,+G =o

(1) are:

force

= F B = (pc - P,)FFB

of the

respectively,

while

other

from

forces

but

(2)

continuous

phase

VB is the gas

gravitational

with a reduced

is not dropped to the

name

gas

equation

densities

deals

the

from

balance

the terrestrial

investigation

from

process

F +p.+C

The

forces.

bubble

acceleration.

gravity

(liquid)

The

Eventhough

the

of motion.

its presence

the

volume.

environment,

the equation

and

the buoyancy Its effects

is accounted

for

are

in this

model. Under

reduced

microgravity

gravity

conditions

conditions, (space-based)

acceleration

due

this gravitational

to gravity

is 0.01g.

acceleration

For

reduces

further to 10"4g.The vertically

upwards

Another

detaching

momentum

present

and aids

force

model

in the bubble

which

acts

a buoyancy

detachment

force

which

acts

process.

in the direction

of gas

injection

is the gas

flux:

F_,=p_,

where

considers

Qd is the

gas

volumetric

TDN

flow

(3)

rate

and

D N is the

gas

injection

nozzle

diameter.

The

surface

towards

tension

force

the injection

F(, acts as an attaching

nozzle

along

the nozzle

F_ =_rg3 N

where

diameter. bubble

is the This

neck

snapshots

liquid formula

surface takes

before

detachment

presented

in figures

tension

force

rim and is written

11-13).

the

bubble

as:

(4)

and

Dn is the

into consideration occurs

by pulling

the

(as seen Recall

gas

injection

cylindrical

from

the

high

that we can write

nature speed

nozzle of the video

c_(1/Rl+1/R2)

= (Pg-P_),

where

of the liquid

outside

R 2 ,namely

the

neck

bubble

gas

injection

the

term

we obtain

while

of curvature

is much

nozzle

forces

pressure

the bubble,

radius

(1/R1).

pressure

Next,

Pg is the gas

the inertia

force

(1/R2)

from

formula

of the than

P_ is the

balance

cylindrical

R1 which

tip where

pressure

of curvature.

nature

with

surface the

Since of

represents

can be neglected

of the nozzle

given

bubble,

R 2 are radii

in magnitude

Consequently,

the previously

RI and

the term

in the viccinity

the

representative

greater

radius,

inside

the

respect

tension

bubble

to and

detaches,

for F_.

F_ may be written

as:

(5)

where

CMC

is the

configuration

and

located inertia this

is pushed

expanding

bubble

ds/dt

nozzle

and represents

equation

which the

at the

added

inertia

is called away bubble.

mass is the

tip. The inertia

first

inertia

can force,

which

center

term

of equation

and

see while

varies

velocity

due to bubble

the injection

As we

is an attaching

bubble

force

liquid from

coefficient

from the

away (5)

motion.

represents nozzle

depending

the

on flow

from

is called The

the the

second

inertia

nature

liquid

inertia

of this force

bubble term

of the

by the accelerating

the

origin

liquid

surface equation, can

of the

be either

"74

detaching liquid

Last

or attaching

velocity

but

which

depending

ULs with respect

not

least

is written

of the

on the relative

to ds/dt,

forces

namely

acting

magnitude the bubble

on the

bubble

wall,

CDw is the drag /kerr is the

force

acts,

respectively

coefficient

effective = +1

liquid,

written

Similar

inertia

force,

detaching

or attaching, ULs relative

developing

displayed

Through

-1

for

drag

the

U..

present

flows

smaller

velocity

force

model,

in figure at the

a liquid

acting

than

which

greater

bubble

on the

magnitude

velocity

26.

over

flow

with

conduit the

drag

than

zero

respect

- ULs.

on the center

area

of a forming

drag force

depending

DN is located

this pipe,

the

to the two-phase

bubble

as U.. = (ds/dt)

to the bubble

schematically

of diameter

is the

velocity.

(6)

respect

cross-sectional

the co-flowing

velocity

with

and Uerr is the relative

to the

center

superficial

as :

F D = "_SDCDw_p,U,_-A,_.2

where

of the

can

liquid

be either superficial

ds/dt.

consider

In this

bubble

the

co-flow

configuration

diagram,

a single

circular

center

of a circular

pipe

of diameter

of density

Pc surface

tension

nozzle Dp.

_ and dynamic

viscosity flow

Pc at a constant

rate

injected

Qc (=.25/_ULsDp2) through

volumetric

the

flow

rate

superficial

liquid

â&#x20AC;˘ A gas

of density

nozzle

in the

velocity

Pa and

direction

Qa (=.25_UGsDp2),

ULS and

volumetric

dynamic

liquid

viscosity

flow

UGS is the

where

liquid P-a is

a constant

gas

superficial

velocity.

Furthermore, First

this theoretical

and foremost

the formation change

model

among

process.

of bubble

these

Therefore,

volume

is given

takes

into account

assumptions

several

is bubble

for the constant

flow

sphericity

throughout

condition,

the

to the

spherical

bubble

is taken

bubble

on the forming

Kim

(1992)

the co-flow

as the nozzle

developed configuration,

bubble

the

and the effect

is neglected

an expression

(7)

assumption,

diameter

which

rate

as :

dv. d Qd- dt - dt [6D (t)]=cÂ°nst

In addition

assumptions.

diameter

of the already

from the theoretical

for the

is given

initial

as:

added

mass

of the detached

analysis.

coefficient

used

CMc =--+3 21

where ratio

DB* is the dimensionless of bubble

(1992)

developed

account relation

the

pipe an

effect

bubble

diameter.

for

confining

of Cliff et. al. (1978),

diameter,

Likewise,

expression

of the

(8)

( 1+ 2----_x-) 1 "f 1_2 De*3(t)

this term

for

the

pipe

non-dimensionalized the

drag

wall.

co-flow

coefficient

By following

is written

as the

geometry,

Kim

CDW taking

into

the

experimental

as:

1 Cv.,

In equation through

(9),

for

literature

CD represents

infinite

correlations (Clift

= Cz_ (1 - r)'2 V

expanse.

the

For

drag

for a solid

Along sphere

summarized

by Bird

et. al. (1960).

theoretical

model

are

Consequently, sphere,

predicted

moving

diameters

experimental

results.

moving

within

is less than

a liquid

the same

that

gravity

coefficient

using are

In general, the drag

current drag

in better the

there

several

bubble,

drag

coefficient

are

available

on formulation

a quiescent

computed

the

moving

literature

through

with

a bubble

case,

spherical lines,

Results

an idealized

compared

observe bubble

drag

such

coefficient

et. al., 1978).

drag coefficient

the

(9)

infinite using

liquid

the

present

experimental coefficient

agreement coefficient of a solid

data. of

with of

a solid reduced

sphere.

bubble This

is due to internal circulation of gas inside the bubble. The circulatory fluid motion inside the forming bubble which is induced by gas injection overwhelms this internal circulation. Therefore, the bubble behaves more like a solid sphere, with respect to the drag force. A similar observation was reported by Ramakrishnan et. al. (1969) and more recently by Kim et. al. (1994). In the present model we use the following drag coefficients, respective of given flow parametric ranges:

24 CD -

ReB

for

Re B <2

18.5 Cv-v,B,.,eO.6

C D =0.44 In equation diameter,

Recall the

which

liquid

is expressed

flow,

namely

magnitudes

the liquid

velocity,

and as a reaction Likewise,

if the

500

Re B represents

that the relative

the relative than

(10),

for

Uefr can

liquid

Reynolds

between

the

be either

the bubble

velocity

front

(10) number

ReB = pcUerrDB(t)

motion

When tends

of the

to push

which

is greater

than

bubble

center

and

depending

or positive

the bubble

a drag force

based

bubble

/ Pc -

negative

of ULs and ds/dt.

experiences

-< 500

< Re B < 2000 the

velocity

2 _< ReB

theliquid

inhibits the

velocity

away

bubble

is greater from

detachment.

center

velocity,

surrounding tip and

liquid

in this

pulls

the

manner

bubble

the role

front

away

of liquid

drag

from

the

changes

gas

injection

to that

nozzle

of a detaching

force.

As a result these

of this

drag force

detaching

effective

area

role duality,

attaching

force

a bubble

has

which very

small

Zeng current bubble

in the

for

et. al. (1993)

it moves

of the

experiences

Consequently,

the

force

While

for the

investigation, is not considered.

also

the

gives

lift force

Uen < 0

from

this motion

(11)

the gas

injection

is taking

place

as discussed

of this

to the forces who

Ueff > 0

away

bubble,

consequence

as detaching compared

for

liquid flow.

wake

As a direct acts

area

detached,

due to the surrounding

(1977).

characteristics.

D_(t)

=_-

A,z =--_(DB(t)-DN)

is initiated

frontal

is:

A,#

Once

the bubble

drift flow,

forming

accounted an estimate created

Hahne

a suction

bubble. for

This

the

wake

Grigull

is induced

force

of this lift force.

a drift flow and

effect

in this model,

nozzle,

is however as shown Thus,

of the

in our

detached

In our present model, bubble formation takes place in two stages, namely the expansion stage and the detachment stage. During the expansion stage, the bubble grows radially as a result of gas injection via a single nozzle. The forming bubble remains attached to the gas injection nozzle rim. The end of the expansion stage is marked by the sum of detaching and attaching forces balancing each other, as shown in equation (1). During the expansion stage, ds/dt = .5 dDB(t)/dt and VB = (_6)DB3(t). With this in mind, the force balance equation at the end of the expansion stage is written as:

6(m

- Pd)gD_(t)+

(12.. i -2

Pd _-----_-+-2 p_CDWSDA'# 4 _N

rtDNÂ˘J +-_L-6

The

bubble

ended.

the gas

with

time the

and

-dr

phase

the detachment

to grow.

from

during

detachment

During

continues

pdD_

nozzle,

keeps

it attached

detachment the

compared

to the

-_L-6 P_C"cD_(t

commences stage,

bubble

stage volume.

increase

however

once

nozzle. the

The

increase

in bubble

volume

expansion

gas

liquid flow,

the bubble a neck

size

in neck during

the

bubble away

also

grows

which

while

has

moves

of the

size the

phase

injection

A portion

neck

the

it develops

to the adds

-2

with additional

Due to the surrounding

injection

increases

dt(t)

gas

the

remainder

is negligible

detachment

injected

when process.

Therefore,

a further

increasing

the bubble

during

detachment

the

represents

the

Furthermore, with

bubble

center

to equation

size.

center,

a velocity

ds/dt during

(1) we can

the

gas

flow

= dY/dt,

goes

toward

the bubble

volume

as Vs = (_J6)DBe 3 + Qdt , where the

located

end

the

at a distance faster

the expansion

express

entire

of this assumption,

is written

diameter

bubble

velocity

is that

As a result

stage

bubble

the

moves

assumption

bubble

than stage.

motion

expansion

Y from

the

.5dDs(t)/dt, Once

during

the

stage. nozzle

which

again,

Dae

tip,

is the

by referring

detachment

stage

as:

(pc-p,)

D;. +Q,t +

At the

end

detaches.

of the The

detachment length

(riD,

mathematically

+Qat]___]+

detachment

equal

expressed

('riD,

stage,

criterion

it is assumed

becomes

that the

the

neck

is discussed

the nozzle

bubble

neck

diameter,

pinches by Kim

1 D8 > DN

off and

a condition

(14)

the

bubble

et al. (1994).

collapses

as:

LN = Y-

(13)

)]

when which

Upon

the can

neck be

Next, the force balance equations, namely equation (12) and equation (13) as well as the detachment criterion, equation (14) are nondimensionalized with respect

to a reference

a reference

force

can be rewritten

length

LR = Dp , a reference

FR = pcULs2Dp 2. As a result,

time tR = Dp/ULs

equations

(12),

and

as:

6F_

(15) 8

We p

. (4CMc - l) + --_ U _.___E_s "2 (8CM c _ 3 + 2 9 .) Uos 96 D_

D., +_;st" Frp

"-_(

(13)

+ C.c

+__ ._ o, I .1 4 O _. D'N )

D_; + -_U_st

rc _(2C

and the detachment

. far"

+-2 CÂ°wSz_i'_-(

+ "TUos

1 , Mc - -_)U os

2C.c

-_'-

+ p

1 _;

- We--'--_=

- 2J dt Â°

(16)

criterion:

1D.

L;.= r'- g , _>_ D;

(17)

and (14)

equations

namely:

consider

non-dimensional

velocity

UGS" =

density =

15-17

ratio

bubble

p = Pd/Po Weber

stage

dimensionless pcULsDp/_c

bubble and

Number

Wep

DBe/Dp;

center

area

DN*

Froude

diameter

Y" = Y/Dp;

effective

superficial

diameter

= pcULs2Dp/a; bubble

parameters,

DB/Dp;

non-dimensional

location

non-dimensional

Ds" nozzle

non-dimensional

DBe"

non-dimensional

diameter

non-dimensional

UGs/ULs;

PcULs2/(pc-pd)gDp;

expansion

several

time Reynolds Ae_" =

gas DN/Dp;

Number the

Frp

end

tULs/Dp;

number

Rep

.25=(DB'2-DN

"2) for

Ue.'<0

and Ae." = .25_DB .2 for Ue. >0. The

Reynolds of Rep.

number Hence,

mathematical

based the

two

on bubble Reynolds

diameter numbers

coefficient ReB, which

can

CDW is a function in turn

be related

is a function

by the

following

expressions:

G,S

Re_--

drag

_U Â° D_ 2

ReB= -ddY*

for the expansion

1D_Rep

1[O I .3,+ 3 ;stlRe,

As a result

of equations

at the point

of detachment

(15) and

(16),

for the detachment

the

non-dimensional

DB" can be expressed

in functional

stage

bubble form

(18)

diameter as:

D*_ = f (p',D*v,U*_s,Ree,We

For given

values

diameter

DB째 iS first

assigned This

the term

numerical

takes

With

ordinary

the

case

method detached

equation that

the

satisfied,

in order

to determine

increment

equation

(16)

detachment

bubble

exactly

increase

(16),

Next,

the

[t'+At'],

neck

length

becomes

the

instant

when

forces

have

Y" starts equal

the

LN*

new

values

neck

order order Y"

Y'.

ON* is not are

for Y" and

expression

to increase

to the gas

bubble

considered

the

Dbe"

criterion,

of DB* and

namely

center

detachment

to obtain

commences,

same

fourth

of bubble

values

all

since

is a second a

and

method.

method

using

position

stage

to the

which

the

bubble

Bisection

Falsi

solved

At 째 is taken,

in time

the

Regula

equation,

is resolved

stage

using

the computed

of this

expansion

convergence

D8".

using

time

DB째. As

diameter

non-dimensional

the

(15)

equation

equation,

condition

to attain

(19)

)

the

differential

and

.5D B" and the

over

Dbe째 value,

bubble

with

end

equation

of iterations

limiting

.5D_*. However,

the

is preferred

recalculated the

(17) is checked

a small

arguments,

by solving

number

Runge-Kutta

namely

D_',

the obtained

non-linear

and

functional

computed

method

a fewer

value.

of these

p,Frp

faster

injection collapses

Y" = than nozzle and

detachment

occurs.

detached

Recall term

bubble

that than

Therefore,

in section

from

solution

equation

(17)

yields

the

diameter.

3.1 of Chapter

UGS (superficial

Therefore,

the

now

liquid

on, when

3, we discussed velocity)

we refer

that a more

is Qd (volumetric to UGS', this term

appropriate

gas should

flow

rate).

be thought

of as a function

of Qd, namely

4.2 Numerical

Figure

27 presents

the present from

Comparison

the

bubble different namely

gravity

theoretical

aspect

DBÂ° with ratios

This

of bubble

graph

injection

diameter

for purpose

from

obtained

of non-dimensional

gas

diameter

obtained

predictions

variation

superficial nozzle

values,

numerical

shows

with two different

ON* are presented

ULS.

Results

with

dimensionless

of gas

along

Experimental

experiments,

model.

O. 1 and 0.2

Rep for each

with

a comparison

reduced

diameter

UGs = Qd / (TrJ4)Dp 2

velocity

to pipe

corresponding of comparison.

UGS'. Two DN*,

diameter

Reynolds

number

To generate

this

plot we use

p = 0.0012,

Rep = 1653,

Wep = 8.9, and Frp = 10.3; Wep

Wep

Rep = 2318,

= 1.97

and Frp = 4.1;

Rep = 4064,

Wep = 3.9 and Frp = 8.0; Rep = 4579,

= 15.1 and Frp = 31.2.

note

other

that

flow

bubble

diameter

experimental

data.

agreement

Table

diameter

with

velocity,

namely

values

correspond

detaching considerable

pipe

gas

velocity

geometries the

same

diameter, fact

lines,

present

which

ULs = 8.5 cm/s to Wep

effects forces variation

considerably between

constant,

respect the

the ratio

conditions

as valid

detached of nozzle

constant,

by both

predictions

to all

the

theoretical

are shown

to be

data.

results.

= 1.9 to 63.4.

far outweigh

flow

numerical

to 60.5

with

by increasing

is shown

comparison

experimental

held

holding

Furthermore,

further

is increased

being

with the experimental

displays

inertia

Along

increases,

in good

when

and

in size.

diameter

bubble

superficial

conditions

grows

injection

and

as the

theoretically A wide

cm/s.

range

is presented

It is shown

surface

tension

dominate experimental

predicted

that

bubble

of superficial

liquid

in this table.

These

at high Wep,

effects

attaching and numerical

(or better forces), results.

namely

yet,

when

there

At high superficial

liquid

considerably

higher

tension

which

force

high values spherical well

than

hence

the forming

This area

employed

at high Wep,

surface

the bubble

geometry.

presently

the

gives

of Wee,

as the frontal

velocity,

tension bubble

shape

variation

starts

causes

of the bubble.

theoretical

model

the

force.

liquid inertia

Since

its sphericity, varying

Therefore,

it is the

extent

in the drag

that

from

the

coefficient

at high Wep

fails to accurately

surface

it is evident

to a great

a change

force

conditions,

predict

bubble

the

size

detachment.

From

visual

figure

27,

conditions,

observations it

of the flow

concluded

the present

theoretical

Another

parameter

closely

number

Ree

which

also

system

which

uses

a 2.54

a Rep of approximately

Figure

dimensional of the

ratio

that for both

under model

coupled

both is valid

with

depends

cm inner

the

diameter

comparison

formation

of superficial nozzle

as well

as the reduced

data and

presented microgravity

up to a maximum Wep

pipe

the

diameter.

pipe,

Wep

pipe For

of 30.

Reynolds

air-water

= 30 corresponds

7500.

presents bubble

that

field

time

of (written

gas velocity

diameter

aspect

numerical

as t = ULst/Dp)

to superficial ratios,

and

namely

liquid

experimental

non-

for various

values

velocity,

D N = 0.1

UGS â&#x20AC;˘ Note

and 0.2,

at low

values

of UGS', bubble

formation

until

an asymptotic

limit

time

remains

constant

observed

almost

this limit varies

is observed aspect longer

generating

to detach

4.3 Range

be 1.35 Since

Wep

nozzle

UGS" for onset for the the

time

increases

the

Rep = 2667,

nozzle Wep

increasing bubble

UGs"

formation

as it is empirically

diameter.

Furthermore,

as the

of UGS'; hence

injection

nozzle

the

diameter

bubble

takes

is increased.

= 3.8 Frp = 4.4,

with

a For

DN Â° = 0.1

DN Â° = 0.2.

Variables

at high

gas

tip can

exit.

rates,

a detached

thereby

resulting

In the present

reduced

gravity

of coalescence

investigation

flow

merge,

to take

1.27 cm test section

present

limit

section

= 3.9, Frp = 8.0 with

at the nozzle

at the

this

with

of UGS', however

all values

as the gas

described,

bubble

of bubbles critical

for

sharply

on test

formation

of Dimensionless

previously

forming

irrespective

this plot, we use

and Rep = 2318,

Beyond

depending

is increased,

time

decreases

is reached.

that the bubble

ratio

time

which

concentrates

place displays on

for

bubble

in coalescence experiments,

ON* = 0.1

the co-flow single

and

bubble

the

is observed configuration. generation,

numerical predictions of results under reduced and microgravity conditions which are discussed in the following chapter, display an upper limit of UGS" equal to 1.35.

In a reduced gravity environment, a single spherical bubble can grow to the size of the pipe diameter before it detaches (DB" = does

not

elliptical

detach bubble

phase

flow

bubble

However,

note the

forming

that

bubble

bubble.

prevalent liquid

whose

tension, otherwise

the

displaying

former

spherical

Consequently,

diameter

if the

This

In the

the

it forms

leads

than

the

diameter

the

to high

local

ensuing

competition

prevails

thus

inner at

grows

namely

diameter

hand

liquid

constricts liquid

can

bubble a highly

of the predict

flow

velocity

the

to the pipe

the

between

causing

the

twonon-

to 1.

surrounding

growth

In case

bubble,

the

model

up to DB" equal

bubble

a Taylor

is greater

Theoretically,

detaches,

situation

inertia.

point,

length

conduit.

dimensional

before

at this

1).

is blocked

liquid and

liquid bubble

diameter

flow

by the

area.

consequently inertia to

and

deviate

The high

surface from

its

shape.

forming

an elongated

neck

bubble region,

assumes as discussed

elongated

shape,

in Chapter

3. The

by drag

coefficient those the

frontal

theoretical

detached

conditions,

for all numerical

not take

change,

it can

as 1).

the Figure

predictions

D B equal

in the

does

size

(g B" =

numerical

experimental

be 0.95

shape

of an elongated

as used

work

bubble

in size

area

bubble

due to bubble

diameter

with

the

of a spherical

current

force of

and

obtained

to 0.94.

predictions.

present

not be used diameter

shows from

Hence,

the

are

different

from

model.

Since

theoretical

into account

bubble 27

bubble

that

the variation for accurate

prediction

approaches under

the model cut-off

in drag

the

reduced at hand

D B value

pipe gravity

agree is taken

well to

CHAPTER NUMERICAL

Since the

PREDICTIONS

FOR

REDUCED

GRAVITY

experimental

present

bubble

data

diameter,

conditions.

for

Effects

properties

of bubble

flow

and the

rate

model

is applied

to predict

bubble

generation

under

gas

In this figure,

injection

of bubble

diameter injection

non-dimensional

UNDER

CONDITIONS

are

gas

GENERATION

predictions

on the process

Variation

BUBBLE

numerical

theoretical

and

in good

reduced

geometry,

flow

agreement,

size,

in particular

and

microgravity

conditions

formation

are investigated.

DB with respect

to the superficial

nozzle

diameter

D N iS presented

bubble

diameter

D B is obtained

and

fluid

volumetric

gas

in figure

29.

as a function

dimensionless

superficial

gas

velocity

UGs

and

non-dimensional

gas

injection

nozzle

diameter

parameters

p = 0.0012,

Wep

dimensional

parameters

used

system

which

phase.

uses note

air as the

that

holding

constant

= .91, Ree = 1300 for generating dispersed

increases

and

this plot

phase

the

Frp = 105.3. correspond

and water.as

in a steady

dimensionless

manner

The

non-

to a co-flow the

with

continuous the

ratio

superficial

gas velocity

proportionality

All

the

detaching flux

conditions,

inertia

faster

of the

respect

to UGS'.

which

make

role,

hence

detached

a change on

diameter.

acting

gas

overall

force

flux.

although

with

taking

balance,

into it

of UGS'. At

significant

nozzle

gas

this figure

values

bubble

the

Og Â° with

size

as other

at the

gas momentum

injection force

the

overweighs

From

at high

drag,

microgravity

increasing

explained

on the

liquid

In parallel,

of bubble

is not

of UGS', the

in the the

flux

balance

a direct

increases,

thereby

momentum

rate.

inertia

prominent

as and

also

trend

can

such

flow

force

forces,

of gas

at high values

bubble

injection

which

indicating

reduced

the bubble

DN* iS more

gas

bubble,

under

gas

effect

impact

the

an increasing

fact

thereby

and the gas flux.

as an attaching

up the force

whereas

detaching

diameter,

significant

influencing

acts

29 shows

the effect

velocity,

buoyancy

Consequently,

of UGS', the

which

prominent more

that

act

increasing

the detaching

values

detachment;

with

figure

consideration

forces

which

reduced

rate.

nozzle

is evident

diameter

aforementioned

Furthermore,

low

and

force

effects

injection

the bubble

forces

increase

at a much

liquid

between

momentum

bubble

to superficial

point

flux

plays

diameter

has

thereby

greatly

It is further

observed

is not formed

from

a single

as it is empirically result

shows

undergoes

flow

With

takes

At this

place

34,

due

the

zero,

values numerical beyond

we start of

a value

bubble point

of Ucs*. and

The

present

experimental

this UGS° value

that

for UGS" -> 1.35 of a slug.

and the The

a single

at a much

lower

transition

from

all

plots

this

a finite unlikely

investigation results

we can safely

shown

zero.

plot

bubble

superficial bubbly

in figure

When

of UGS" = 0.001,

at any

it is highly

a slug,

gas to slug

of Ucs*.

UGs* = 0 , the

has

words

of UGs °. However,

coalescence,

0.2 to 0.3,

UGs" equal

however

range

place

before

UGS° considered, of

in other

development

to slug flow

at a value

diameter

of view,

even

to note

a value

a singularity,

the

physical

range At

presents

value

takes

cause

in DN* from

at a lower

results

observed.

bubbly

it is important start

numerical

can

or higher,

from

increase

time

figure

DN* = 0.2

bubble,

in the considered

coalescence

transition

velocity.

bubble

observed,

bubble

that for

that at DN* - 0.1, a Taylor

can

non-dimensional other

value

that a bubble

a value

consider

bubble

agreement

UGs °._

numerical

0.3.

predictions

the plots

visually diameter

zero.

will detach

good of

in these not

than

through

produce

of UGs ° which

greater

shows

however

difference

exceeds From

at very

a low

between Therefore, as valid.

Figure

30 presents

function phase

pipe

dimensionalized

to study

diameter

values

For of

Weber

the

respect the

D B, the

effect

plot,

velocity, the

of change flux

of liquid

parameters, number,

UGS" for

nozzle

diameter,

diameter

two-

non= D B /

DB'"

Dp on detached

(Qc) and

various

diameter

in Dp causes such

DB *Â° as a

diameter

bubble

in pipe

Qc, an increment

Froude

Wee,

this

volumetric

same

gas

bubble

to the gas injection

non-dimensional

number

non-dimensional

superficial

diameters. with

O N. In order

constant.

modified

non-dimensional

flow

bubble

the

gas

(Qd) are

a reduction

Reynolds

kept in the

number

Frp and dimensionless

nozzle

Ree,

diameter

DN*"

It is observed

that at a fixed

diameter

increases.

diameter

with

change

respect

in superficial

increase

in pipe

This

leads

fact

liquid diameter entire bubble

drag

to liquid

liquid

of UGs" the remains

stress

velocity.

Under

similar.

constant

direct

liquid effect

increasing

in pipe

bubble bubble

effect

Qd and Qc conditions,

detaching an

trend

is the

of superficial

Furthermore,

of change

is increased,

observed

diameter

bubble

Therefore,

occurs. effect

the

reduction

in the

inertia.

pipe diameter

that

in pipe

implies

diameter

as the

change

to a reduction

pipe

diameter

must

diameter

and

with range

Ues',

bubble

that over upon

an ULs.

manifested

trend

it is observed diameter

velocity

the

detached

The

maximum

figure

that

approaches

UGS" =

indicated,

theoretical

predictions

exceed

diameter level

in figure

(constant a

liquid fixed

conditions.

for the

parameters

Froude

number,

change.

However,

Frp the

Frp = 65.5;

superficial such

and

the

product

using

numerical

a fixed

p* = 0.0012, for the

1.5 Dp

for the 2 Op curve

Fre = 15.5.

and gravity

level

values liquid

and

velocity

dimensionless

number

flow

phase rate

detached

liquid

is increased, Rep, Weber

superficial.gas Rep (RepUGs*

diameter

dispersed gas

DN),

of superficial

as Reynolds

of UGS" and

g on bubble

at a constant

(constant

various

1. As

computation

Wep = 1.1, Frp = 498;

properties)

geometry

that

current

29 we use

We e = 0.32,

velocity

gas

DB'*DN * =

ensure

31. For a set of continuous

and

is computed

dimensional

figure

the

this

diameter

can be predicted

limit,

from

bubble

DB"

Therefore,

DB* =0.95

liquid

of D B" which

is 0.95.

= 0.136,

It is evident

non-dimensional

value

= 667,

Wep

30 is 0.95.

corresponds

For generating

of superficial

displayed

considering

modified

which

the

Ree

DN* = 0.1, Rep = 500,

fluids

in figure

- DN" = 0.2, Rep = 1000,

- DN* = 0.133,

DB are

at hand

at UGs* = 0.95.

effects

the

the maximum

not

for the Dp curve

The

.95, of

model to

stopped

curve

of Ues" used

a value

previously the

value

bubble

velocity all the number velocity

= pcUGsDp/_c)

and

nonWep, UGS" and

the ratio

of Wep to Frp, defined

as the Bond

number

(Bop = Wep/Frp

for

Bop

p_)gDp 2 / (_) remain

constant•

This

variation

of DB° with

Rep

g levels.

It is evident

that

figure

shows

represent

different

decreasing

trend

velocity, the fact liquid

with

increase

a phenomenon

which

that with increase drag

detached

and bubble

It is further a great

noted

deal

the other

The

.00016

gravity

superficial

that

under

the

bubble

liquid

diameter

increasing

experimentally

increases,

in DB* in the

gravity amount

based

velocity,

the

which shows

superficial

observed•

thereby

This

detaching

leading

over

liquid is due to effect

a reduction

liquid

does

(lg)

drag

not

(Bop = 0.0087),

of Rep = 500

range

Frp

liquid have

liquid velocity,

the inertia

16 for

ULs• Thus

a significant

to 5000). range

reduced

buoyancy (low

force

Frp)

which

an increase

reduction

diameter

) is in the

= •16 to

conditions, and

bubble

of Rep (500

(Frp = ULs2/gDp

and

there

to Rep = 5000.

(Bop = 87),

the entire

gravity

the superficial

velocity,

range

environment

gravity

normal

effect

conditions,

on pipe diameter

normal

Under

itself through liquid

hence

microgravity

in a normal

number

(0•C)lg).

the

values,

diameter.

to •016 for

overwhelms manifests

inertia

only by a small

Froude

is also

in superficial

of variation

hand,

decreases

liquid

in Rep and

various

= (Pc -

effect

in on

bubble

diameter.

conditions

(high

process

liquid

effect

31.

number, to note top

that

curve

condition. than

the

Frp),

there

obtained (visually

environment,

the

does

not have

the

Figure

presents

bubble

diameter.

impact

any

effect

In this figure

which

bubble

it is of utmost

interest

of gravity

level.

the

is slightly

being

in a reduced

gravity

of the

already

gravity

ON* = 0.1 and RepUGs"

= 500.

velocity

bubble

less

difference

bubble.

number

The 104g

size of the generated

Froude

gas

Froude

detachment

reduction

non-dimensional

superficial

is reduced, the

the

that

the

as shown

level

(102g)

condition,

on the

of the

explains

diameter

condition

further

also

increasing

bubble

upon

in the

variation

gravity

reduction

indicates

we use p" = 0.0012, the

dimensionless

This

role

environments

However,

gravity

Therefore,

a significant

gravity

represents

effect

force

Ree as the

microgravity

buoyancy

this figure,

buoyancy

for the

a key

gravity

considerably.

subsequently

effect

play

reduced

Therefore,

diameter

are generated.

negligible).

generating

versus

(and

at the reduced

diminished.

ULS term).

the

and

inertia

for different

number

bubbles

size

liquid

that at a fixed

in figure

infinitesimal

significantly

is a saturation

plotted

and

microgravity

the bubble

size obtained

larger

under

(via the

displayed

Bond

Bubble

that

drag

affects

It is observed

reducing

hand,

detachment

in bubble

in figure

other

liquid

velocity

detaching

difference

Frp),

of bubble

superficial The

On the

level For

Frp. has

diameter

DB" is plotted

UGS" for

values

detached

non-

dimensional

parameters

= 0.1.

The

values

corresponding

condition,

of Froude the

normal

gravity

level

order

gas flow

environment.

bubble

velocity

displayed number,

the

, with

in figure the

This

33.

bubble

Figure

33 also

under

conditions

of reduced

value

of the ratio

of superficial

surface diameter tension

tension

force

increases. force

acts

in order

for

low

that

increases

effect

change

with

superficial

liquid

velocity

gravity

and

gas velocity

observation to attach

generated

in a reduced

size

study,

formed

with

gas flow rate

range

non-

superficial

number

gas

(Wep)

of Weber

momentum

flux.

force

on bubble

microgravity.

Note

that

a fixed

to superficial

liquid

velocity,

as the

by reducing stands the bubble

tension

respect

variation

selected

in a

is increased.

of dimensionless

the

.028, gravity

increasing

of the surface

and

normal

in Weber

for

DN Â°

and

the

in bubble

parametric

2.8

as that of a bubble

De', as a function

is increased This

that

p" = .0012 are

and

as the volumetric

It is observed

the

condition

difference

respect

diameter

shows

= .608,

considered

as large

present

diameter

UGs"

twice

only slightly

complete

Frp

gravity be seen

Wep

rate, the size of a bubble

is almost

reduces

dimensional gas

It can

environment,

number

reduced

respectively.

and low volumetric gravity

as Rep = 750,

given

Weber to reason,

number, .since

to the gas injection

the the

size

bubble surface

nozzle.

The

Weber

numbers

considered

in this

graph

are

.2, .5 and

1.0,

while

other

non-dimensional

Rep = 600

Figure

34 presents

five fold

the

held

to 500,

induces

superficial

liquid

Therefore,

the generation observed

fact indicates

In this relative

constant

a higher velocity

the liquid

of smaller

that the

of bubble

are:

effect

while

liquid

gas

drag

For

= 0.0012,

O N = 0.1,

parameters:

p" = .0012,

the

viscosity All other

Reynolds

number

to 100. drag.

It stands

For the

higher

viscosity drag

flux, this

Frp = 62.2,

plot, Wep

viscous

in detaching

takes use

the

to change

is increased

Rep

to reason

the

that

This fact

explains

It is further

increasing

the

following

= .54 and DN* = 0.1.

of Rep, velocity

the bubble over

a more

center

environment. with

two

is reduced

range

bubble force.

non-dimensional

considered

than

reduces

which

respect

value.

in a more

of liquid

generating

liquid

with

acts as a detaching

bubbles

momentum

mechanism.

figure,

is always

that the role of liquid

increasing

diameter

to a given

to 200 and further

fluid

(ds/dt).

with

viscosity.

and ten fold are

1000,

viscous

the variation

liquid

parameters from

considered

and Frp = 22.4.

surrounding fold,

parameters

the

UGS'. This is diminished

bubble

detaching

non-dimensional

CHAPTER

CONCLUSIONS

The

present

data,

work

obtained

Research

which

by performing

Aircraft

section

configurations

makes

for single

It is experimentally

gas gas

variational

injector, flow

rate

conditions.

Along

superficial

liquid

geometry liquid

flow

environment.

nozzle

trends

conditions; plays

Bubble

thereby in

the

for

lines, at

showing

detaching

within

co-flow

conduit.

increasing and

gas

systems,

with

flow

nozzle

volumetric

flow

geometry increasing

rate

role which in

test

cross-flow

via a single

decreases

bubble

Gravity

cross-flow

velocity

important

and

flow

and

volumetric

forming

Reduced

co-flow

with

size

on experimental

The experimental

generation

liquid

the

DC-9

a water

increases

bubble

constant

the

of both

by bubble

diameter

is based

Center.

study

both

superficial

same

aboard

Research

displayed

velocity,

of its kind,

air injection

that

constant the

Lewis

possible

shown,

do apply.

study

experiments

at the NASA

assembly

similar

is the first

and

flow

a continuous

reduced

gravity

100

Furthermore, ratio

air

diameter,

frequency

flow

conditions. the

injection

rate

bubble

It is of interest for the From

constant

increases

pipe

directly

by increasing

diameter,

formation with

flow

showing

that

that bubble

configuration,

experimental case

for

given

nozzle

single

volumetric

gas and liquid

the pipe

gas

that

flow

increases and

flow

geometry

is increased.

conditions

injection,

kept

of a forming

for the co-flow

void

geometry

by increasing

to detachment

the bubble

flow

and

volumetric

and flow

fraction by

system

can

solely

than

geometry. be

readily

varying

the

flow rates.

it is experimentally liquid

time

is smaller

at similar

superficial

velocity

frequency

the

it is shown

the

conditions

evidence,

controlled

exit of the air injection

size

with

liquid

as the liquid flow around

to note

gas to volumetric

superficial

velocity,

manner

cross-flow

Furthermore,

varies

the bubble

liquid

decreases

diameter

flow conditions.

Likewise,

in this

bubble

diameter

of formation

superficial

constant;

that

nozzle

at constant

Bubble gas

it is observed

flow nozzle.

observed

rate

(Qd')

that

at a high

coalescence

The critical

Q,_" value

ratio

of bub.bles for onset

of volumetric occurs

at the

of coalescence

101

to occur

is 1.35

for

the

1.27

test

section,

= 0.1

at D N

for

the

co-flow

configuration.

low

superficial

detaching neck

bubble

region

injection

from

assumes

the

explain

experimentally, generation

model

is based

bubble

dynamics

one

bubble

on and

size,

and

the

volumetric

spherical

region nozzle

shape

equal

at high

diameter,

flow

and

to the

superficial

becomes

gas

while

displays

diameter

liquid

highly

rate,

a short of the

velocity

gas

and high

elongated, the

the

deviating

detaching

bubble

shape.

and

in the

the expansion

aiding

hand,

injection

enhance

a theoretical

bubble

low

is approximately

rate, this neck gas

and

on an almost

length

an ellipsoidal

order

velocity

On the other

gas flow

in value

namely

takes

whose

nozzle.

volmetric

liquid

model

stage other

are identified.

and

balance

is developed and

inhibiting

physical

is applied,

dynamic

a force

the

which

bubbly

equation, for the two

the detachment bubble

flow

phenomena

observed

concentrates

on single

regime.

This

theoretical

which

describes

the

stages

of bubble

generation,

stage.

detachment,

Two

sets

thereby

overall

of forces, controlling

102

The momentum at the gas hand, can

gas flux aids,

injection

liquid

drag

and

of the

model

predicts

performed

Effects

of co-flowing

aspect

ratio

in gravity

gravity

Therefore, than

those

being

barely

decreases

and/or enhances inhibiting

liquid

with flow the role

bubble

detachment.

role.

forces,

fact

to the

generated formed

depends

surrounding

liquid.

flow conditions

these

forces

on the relative The

theoretical with

the

impact

reduced

and

formation. size

environment

gravity

shows

liquid

velocity,

nozzle

diameter,

Furthermore, process, Overall, of generated

field

are only

that

the

theoretical bubbles,

size. slightly

difference

bubble

diameter

while

bubble flow

increasing surface

the

keeping

while

below

on bubble

conditions,

model

nozzle

that with reduction

infinitesimal

has

superficial

for

It is observed

(0.01g)

theoretical

pipe

and gas injection

of gravity

detachment

trends

forces

On the other

agreement

Reduction

constant.

in bubble

in good

are formed.

under

increasing

bubble

tension

words,

which

in a microgravity

The

geometry

In other

at detachment

properties,

bubbles

increasing

variational

from

size are investigated.

noticeable. with

and surface

experiments.

environment

bubbles

larger

increases

gravity

larger

inertia

a dual

respect

diameter

on bubble

field,

reduced

with

bubble

reduced

have

or attaching

bubble

rim detract

inertia

act as detaching

velocity

similar

nozzle

while

liquid tension model when

size

conditions viscosity plays

displays

compared

103

the

experimental

evidence.

experimental

data,

the forming

bubble

In summary, bubble

is the

both

nozzle

fraction

is shown

is independent bubbles system,

to depend

solely

the

to note

multiple

formed

bubbles

port leads

gas

injection,

to non-uniformity

flow

than

diameter).

for which

coalescence size.

with

flow

not

void

rates

and

larger

the

co-flow

considerable

It is can

than

gas

parallel,

with

injection

or slugs

in bubble

bubble

Furthermore,

bubble

bubbles

size is

(unlike

rate.

size

of gas

isothermal

bubble

gas and liquid

system

through

increases

bubble

method

sized

flowing

velocity

configuration.

cross-flow

present

uniform

gas

and flow

detached

investigate

under

diameter

on volumetric

the

liquid

bubble

difference

that the

in producing

superficial

when

shape.

liquid

configurations

volumetric

geometry

the spherical

within

with

velocities,

of flow configuration,

detached and

well

to experimentally

gas injection

Irrespective

with

from

cross-flow

diameter

10%

namely

and

while

although

importance

nozzle

increasing

obtained

(approximately

of its kind

with

of flow

are

first

gravity.

frequency),

injection

greatly

study

agree

gas and liquid

not deviate

co-flow

to decrease

predictions

at low superficial

via single

of reduced

formation

effective

does

this

for

conditions shown

especially

generation

a pipe,

Numerical

utmost

prove

its

between

alternative, adjacent

104

Results

of the present

applications propulsion, necessary Development

such

work can be used as

cryogenic for

programs

thermal

storage such

of Space (HEDS)

in a wide

management

and

long

NASA's

range

and

duration Human

of space-based

power

life

support

Exploration

generation, systems, and

the

105

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106

[12]

Hill, T.J.,

"Gas-Liquid

1997 ASME

Fluids

FEDSM97-3553 [13]

Flow

Engineering

in Oil and Gas

Division

Summer

Production",

the

Meeting,

(1997)

Jayawardena, Transition

Challenges

S., Balakotaiah, Maps

V. and Witte,

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L. C., "Flow

Two-Phase

Flows",

Pattern

AICHE

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43, 6 (1997) [14]

Kawase,

Y. and Ulbrecht,

Flowing thesis,

[15]

Kim,

Liquids Case

Kim,

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[19]

Departure

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McCann,

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[22]

[23]

Eng.,

Ph.D.

OH. (1992)

in Flowing

Ph.D thesis,

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Case

OH (1992) S., "Modelling

D.M.

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AIChE

and Zeng,

Convection

Boiling",

and Drop

J., 40, 1 (1994) L. Z., "Vapor

Int. J. Heat

and Mass

N.R.,

NASA

York

Chem.

Tech.

O. and Rath, at Submerged

Sci., E.S.,

of Bubbling

at a

26 (1971) Learjet

106814,

and Lightfoot,

H., "Influence Orifices",

N. and Vogelpohl,

Two

NASA

Phase Lewis

E.N., "Transport

3, Gulf

of Buoyancy Chem.

A., "Bubble

and Non-Newtonian Vol.

and Drops",

Flow Research

Phenomena",

(1960)

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Mechanics,

Eng.

Memo.

W.E.

Pamperin,

Newtonian

of Bubbles

OH (1995)

Stewart,

New

Formation

R. G. H., "Regimes

J. B. and Neumann,

Cleveland,

Rabiger,

"The

8 (1970)

Orifice",

R.B.,

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Formation

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in Forced

D. J. and Prince,

McQuillen,

Bird,

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R., and Kuloor,

Apparatus",

[21]

Cleveland,

Environments", Cleveland,

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and Drop

J. F., Mei, R., Bernhard,

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Y. and Ostrach,

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Univ.,

I., Kamotani,

Formation [17]

Reserve

of Bubble

Reserve

of Drops

and Microgravity

Western [16]

Western

I., "Modeling

Terrestrial

J. J., "Formation

in Terrestrial

Pub..

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Eng.

Formation

.on Bubble

Sci. 50, 19 (1995) and its Movement

Encyclopedia (1986)

of Fluid

I07

[24]

Ramakrishnan, S., Kumar, R. and Kuloor, N.R., Formation :1. Bubble Formation Under Constant Chem.

[25]

Eng.

Sada,

[28]

Van Krevelen,

D. W., Hoftijzer,

Chem.

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Prog.,

Wraith,

A.E.,

"Two

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[33]

[34]

P. J, "Bubble

Stage

Bubble

Sci.,

Formation

in Liquids",

Growth

at a Submerged

Plate

26 (1971)

Int. J. Heat and Mass

Bousman

W. S., "Studies NASA

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9 (1993)

of Two-Phase

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Report

Gas-Liquid 195434

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(1995)

McQuillen, J. B., Neumann, E. S. and Shoemaker, J. M., "Two-Phase Flow Research Using the DC-9 / KC-135 Apparatus, NASA Technical

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107175

(1996)

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W. D., "Studies

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Bousman,

W. S. and Dukler,

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[35]

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46 29 (1950)

Eng.

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M, Eng.,

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Tsuge, H., "Hydrodynamics of Bubble Formation from Submerged Orifices", Encyclopedia of Fluid Mechanics, Vol. 3, Gulf Publications,

Orifice", [29]

A., Katoh,

in Flowing

Houston [27]

24 (1969)

E., Yasunishi,

Formation [26]

Sci.,

"Studies in Bubble Flow Conditions",

Hewitt,

Tension,

Int. J. of Multiphase

G. F., "Multiphase

Conference

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Flow: 3330

The Gravity

(1996)

Flow,

Vol.

22, No. 6 (1996)

of the Situation",

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108

[36]

Antar,

B. N., "Gas-Liquid,

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Oguz,

AIAA

Bhunia, Canadian Bhunia,

of Gas Conference

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NASA

AIAA

A., Pais, S. C., Kamotani,

Generation

[39]

27th

H. N., "Production

Environments", [38]

Two-Phase

96-2049,

S. C., Kamotani,

Co-flow

AIChE

Journal,

Bean,

Howard

ASME,

1971

Liquid

for Mechanical

Under

Normal

Flow Fluid

Bubbles

Diagnostics

Dynamics

in Low

Conference

in Reduced

Publication

3338

Gravity (1996)

Y. and Kim, I. H., "Bubble under

Reduced

Gravity

Conditions",

Engineering

Forum,

Y. and Kim,

I. H., "Bubble

and Reduced

Gravity

Toronto

Meters;

Their

Theory

(1998) Formation

Conditions",

44, 7, (1998) S., "Fluid

(1996)

and Applications,

109

Flow

Conditions

Uca

Comp_edD_

Experimental

D B"

% variation

.753

.727

.736

1.22

.965

.762

.815

.650

.336 ULS = 10.5 cm/s, Rep = 2667, Wep ........... 3.84, Frr = 4.43 .567

.572

.53O

7.92

ULS = 18 cm/s, Rep = 3420, Wet = 8.44, Frr = 17.40

.322

.503

.822

.663

ULS = 45 cm/s, Rer = 5740, Wep ......... 35.57, Frp = 164.2

.260

ULs = 8.5 cm/s, Rep = 1615, Wep 1.88, Frr = 3.88

.540

ULs = 60.5 cm/s, .230 Rep = 7684, Wep ................................. 63.7, Fry = 294.20 .320

Table

.620

.409 .459

Comparison of bubble diameter experimental numerical predictions of bubble size, D N = 0.1

values

with

110

Plexiglas

Figure

pipe

1. Experimental

Co-flow

System

Ill

Figure

2. Experimental

Cross-flow

System

112

Figure

3. Experimental

Test

Section

Assembly

113

pressure

thermocouple

transducer

probe water

regulator pressure â&#x20AC;˘

_. .......

i ........ â&#x20AC;˘

small

orifice

large

orifice

:_:__:" .......... k,,

fiow

air flow

air suppty G

cylinder

__d

......... test

section

assembly

air vent water

fill port

--_,L

piston-driven water

turbine flow

meter

separatorlcoBector tank

feedtank

_,ter _EI,_ll

_r..r..:__:_:_

111111It1_11I_ ....... _ water

Figure

4. Test Flow

Loop

........ recycle

Layout

pump

114

strobe light

s_'obe light

video camera angled mirror

test seclion assembly video recording system

rack support

data acquisitionsystem

Figure

5. Flow

Visualization

Set-up

115

,-. E

cff

2.5

{

1.5

{

| â&#x20AC;˘ UIs=7.60cm/s

e_ ,I1

â&#x20AC;˘ UIs=l 1.3cm/s

0.5

O U Is= 18.5cm/s 0

volumetric

Figure

6. Co-flow

configuration:

volumetric error value

bars

gas are

flow given

100 110

gas flow rate, QD (cc/s)

Variation rate

QD,

of bubble

diameter

for Dp = 2.54

as +_ 5 % of the mean

cm, bubble

D B with DN

= 0.1;

diameter

116

2 1.8 A

1.6 1.4 1.2

o OE ,

0.8 e_ e_

0.6 0.4

0.2 0 0

â&#x20AC;¢O Dp=1.90cm,UIs=18cm/s.Dn*=.2 Dp=l.90cm, UIs=18cm/s,Dn*=. 1 _,Dp=1.27cm,Uls=45cm/s,Dn*=.1 ,! 0 Dp=1.27cm,Uls=45cm/s,Dn*=.2 ..... , I I :

volumetric

Figure

7. Co-flow on bubble

configuration: diameter

gas flow rate, Qo (cc/s)

Gas

injection

nozzle

D B for the 1.27 and

aspect

1.9 cm test

ratio sections

effect

117

2.9 ,--_Dp=1.9cm E 0

2.5

D Dp=2.54cm

LADp=1.27cm

2.1 4.--

1.7 41,

°_

1.3 '&A

.ta e_ e_

•

0.9 0.5 5

superficial

Figure

Co-flow respect

= 15 cc/s; 61 cc/s;

liquid

configuration: to superficial Dp all test

velocity,

Variation liquid

= 1.9 cm, sections

bubble

ULS for

Qd = 51

cc/s

with

= 0.1

ULs (cmls)

velocity

and

diameter Dp

--- 1.27

= 2.54

cm,

with cm,Qd Qd

118

2.9 2.7

2.5 2.3

oDp=l.9cm,

Dn*=0.1

• Dp=1.9cm,

Dn*=0.2

2.1 1.9 1.7

1.5

e_ t,n

•

1.3 1.1

•

0.9 0.7 0.5 10

superficial

Figure

Co-flow and

configuration:

superficial

51 cc/s,

liquid

Dp = 1.9 cm

liquid

velocity,

Effect

gas

bubble

velocity

ULS (cmls)

injection

nozzle

diameter.

diameter Fixed

119

g.. 36

.g -; 29 i.-

r'!

[]

0 m

es e_ ..s es

xDp=1.90,UIs=181

[] Dp=1.90,UIs=24 ADp=1.27,U I 1

15 5

10.

Co-flow function velocity

s=45 [ [ 20

volumetric

Figure

[]

configuration: of volumetric

gas flow

rate, QD (ccls)

Bubble formation gas flow rate and

frequency superficial

for the Dp = 1.27 and 1.9 cm test sections,

(Dp values

are in cm, ULS values

are in cm/s)

as a liquid

DN =0.1;

120

Figure

11.

Co-flow

configuration:

Single

video

generation at high surrounding liquid reduced gravity conditions (ULs = 35cm/s, = 1.27cm,

DN = 0.2)

frame

bubble

velocity under Qd -- 20 cc/s, D e

121

Figure

12.

Co-flow formation gravity

configuration: Single video at high volumetric gas flow conditions

cm, D N = 0.1)

frame of bubble rate tinder reduced

(ULs = 16 cm/s, Qd = 95 cc/s, D e = 2.54

122

Figure

13.

Co-flow generation

configuration:

Single

at low volumetric

under reduced gravity conditions cc/s, Dp = 1.27cm, D_ = 0.1)

video liquid

frame and

gas

bubble

flow

(ULs = 11 cm/s,

rates

Qo = 10

123

2.2 A

.-_

1.8 X

o x

_..

1.6 X

ee-

1.4

1.2

0 L 5

]

cm/s

xUIs=31

cm/s

A UIs-45 I

cm/s I

11 13 15 17 19 21 23 25 27 29 31 33 35 volumetric

Figure

OUIs=17

gas flow

rate, QD (cc/s)

14. Co-flow configuration: Change of bubble neck length L N (elongation length, En) as a function of volumetric gas flow rate, Qd for the Dp = 1.27 cm test section

(D N = 0.1)

124

<) UIs=12cm/s,Dn*=0.1 [] UIs= 12cm/s,Dn*=0.2

0.8

â&#x20AC;¢ UIs=24cm/s,Dn*=0.1

[]

X UIs=24cm/s,Dn*=0.2

[]

<> O

0 >

$i A

0.2

0 0

0.1

0.2

0.3

volumetric

Figure

15.

Co-flow respect

0.4

0.5

0.6

0.7

0.8

0.9

gas flow rate ratio, QdQc

configuration: to Qd/Qc for Dn

Variation = 0.l

of void

fraction

and 0.2, Dp =1.9

e with

125

1.4

1.2

]

E •5

0.8

0.6

oUIs=17.4

cm/s

• UIs=31.0

cm/s

A UIs=45.2 0.4

[

volumetric

Figure

16. Cross-flow function

configuration:

20 gas flow

variation

cm/s [

rate, Qd (cc/s)

of bubble

of Qd and ULS, for Dp = 1.27cm

diameter

and DN

= 0.1

as a

126

1.4 []

E Â¢J

1.2

[]

D 1

E "0

0.8

A A

@ [] A X

0.6 d_

0.4 5

volumetric

Figure

17.

Cross-flow

configuration:

diameter aspect = 0. l and 0.2

ratio

UIs=31.0cm/s,Dn*=. 1 UIs=31.0cm/s,Dn*=.2 UIs=45.2cm/s, Dn*=. 1 UIs=45.2cm/s,Dn*=.2 i

gas flow rate, Qd (ccls)

effect

on bubble

diameter,

air

injection

nozzle

Dp = 1.27 cm, DN

127

E v

1.2

Dn*= 0.2

X Dp=1.90cm,

Dn*= 0.1

A Dp=2.54cm,

Dn*= 0.1

1.5

0.5

superficial

Figure

â&#x20AC;¢ Dp=1.27cm, 2.5

18. Cross-flow respect cc/s;

liquid velocity,

configuration: to superficial

variation liquid

Qd = 61 cc/s test

sections

ULs (cm/s)

of bubble

velocity

Dp = 1.9 cm, Qd = 28 cc/s

and

for 2.54

diameter

Dp = cm,

1.27

with cm,

Dp = 2.54

44 cm,

128

1.6 A

1.4

"-""

1.2

d' ,.: E

•

o 0

1 0

0.8

0.6

0.4

0.2

• • O Dp=1.27cm,

Dn*=0.2

• Dp=1.27cm,

Dn*= 0.1

superficial

Figure

o •

19. Cross-flow and nozzle

configuration: diameter

and Dp = 1.27 cm

liquid velocity, ULS (cmls)

effect on bubble

of superficial size for a fixed

liquid

velocity

Qd = 44 cc/s

129

kA =

25 35

_ -_ .1_

•

lO |

5 ]-

u_=T8 _/s

UIs=24cm/s

: 5

20. Cross-flow frequency

Dp=l.90cm, ADp--1.27cm,

volumetric

Figure

F_-D-p= 1.9_m

25 gas flow

configuration: with respect

30 rate,

variation to volumetric

= 1.27 and 1.9 cm; for Dr_ = •1

UIs=32cm/s 35

Oa (eels)

of bubble

formation

gas flow rate, for Dp

130

I::iQc=6_Scc/s,Dn=0.1I A _Qc=51cc_,Dn=0.2I

0.8 C O

xQc=68cc/s,

0.6

Dn=0-2

0.4 0.2

0 0

0.2

0.4

volumetric

Figure

21.

Cross-flow liquid

flow

in nozzle

0.6

gas flow rate ratio, Qd/Qc

configuration: rates diameter

0.8

on void

effect fraction

for a fixed

volumetric

gas

with

respect

to variation

Dp = 1.9 cm

and

131

1.3 A

E O

1.2

1.1

0 0

0.9 ,,Q

0.8 0.7

A UIs=17.4cm/s,

Dp=1.27cm,

cof

O UIs=17.4cm/s,

Dp=1.27cm,

crf

volumetric

Figure

22.

Comparison

with

obtained

with

the the

cm and D N = 0.1

gas flow rate, Qd (cc/s)

between

obtained

empirical

values

cross-flow co-flow

system

system (cof).

of bubble (crf) Fixed

diameter with

those

Dp = 1.27

132

2 @

1.8 A

E 119 t_

[]

1.6

0.8

[]

1.4

[] X

1.2

0.6

0 u

E t_

0.8

0.4

0 >

0.6 • [] /k X

0.4 0.2 0

_.,..,,---,.,,,,,-_ 0

volumetric

Figure

¢,) ¢u

23.

Comparison and

0.2

0 80

gas flow rate, Qd (cc/s)

of bubble

cross-flow

co-flow Db cross-flow Db cross-flow Vf co-flow Vf _

diameter

configurations. lit

1.9 cm and D N = 0.1

and void Fixed

fraction

Qo = 68

for the co cc/s,

Dp =

133

Figure

24. Single video configuration

frame of bubble generation in the cross-flow at high liquid and gas volumetric flow rates

(ULs = 25 cm/s, Qa = 76 cc/s, Dp = 1.9 cm, Ds" = 0.1)

134

Figure

25. Single

video

configuration

frame

of bubble

at lower liquid

than those used in figure Dp = 1.9 cm, DN = 0.1)

generation

in the cross-flow

and gas volumetric

23 (Ues = 15 cm/s,

flow rates

Qd = 32 cc/s,

135

U A

Figure

26. Co-flow

configuration

used

in the Theoretical

Model

136

Rep=1683,0.2 - - -

_,0.2

......

_,al

_p=1e58,a2 o

Rep=2_8,0.1

_,0.1

....

_8,0.11

_,a2 I

0.9 :5 Q8 0.7 .

====

Q6 Q5

â&#x20AC;˘

oow mw

oQw

"- Q4 Q3

0.4

0.5

0.6

0.8

0.9

nandmgas_ocity,U=

Figure

27. Comparison numerical values,

of bubble predictions

symbols

diameter

empirical

of bubble

size;

represent

empirical

lines values,

values

with

represent

computed

D N =. 1 and

.2; p"

= 0.0052; Rap = 1653, Wee = 1.97 andFrp = 4.07; Rev = 4064, Wep = 8.93, and Frp = 10.28; Rep = 2318,Wep = 3.88, and Frp = 7.99; Ree = 4579, Wep = 15.13 and Frp = 31.19

137

1.4 I ...... .

Rep=2667, 0.1 Rep=2318, 0.2

1.2

Rep--2318, 0.2 Rep--2667, 0.1 0.8 0.6

^ LI

0.4 .....

_ ........

1:3....................

[]

0.2 0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

1.2

1.3

non-dim gas velocity, U'Gs

Figure

28. Comparison of numerical and empirical bubble formation time; symbols represent empirical values, lines represent computed Frp = 4.43; 7.99

values;

DN" = 0.1,

DN" = 0.2,

ReF, = 2667,

Rep = 2318,

Wep

= 3.84

and

= 3.88

and

Frp =

138

0.95

...... _'n=0_

06. _D*n=0'31 0

0.2

"_"'' 0.4

0.6

non-dimensional

Figure

29.

Numerical with

respect

prediction to change

for

0.8

gas velocity, U'GS

variation

in superficial

injection nozzle diameter; = 0.912 and Rep = 1,300

1.2

bubble

p" = 0.0012,

gas velocity

diameter and

Frp = 105.25,

gas Wep

139

10 9 m

_r_ m_m

•" E

7 6

•_

t_ =1

......

1.5Dp

- -- 2Dp

0 0

0.2

0.4

0.6

non-dim.gas

Figure

30.

Numerical

prediction

for

0.8

velocity, U'c,s

the

effect

change

pipe

diameter

detached

bubble

diameter

= o.0012,

Frp = 498;

1.5

curve

• D N = 0.20,

Rep = 1000,

Wep

= 1.1,

Dp curve

" D N = 0.133,

Rep = 667,

Wep

= 0.32,

Frp = 65.5;

2 De curve

• D N = 0.1,

aee

= 500,

We e = 0.136,

Frp = 15.5

140

1 0.9 in

"t3

0.8

0.7

......

" ,

0.01g lg

% tm_,

t_ Â°_

-o .0 -.!

0.6 _m

0.5 0.4

d _ C

o c

0.3 0.2 0.1 0 500

1000

1500

2000

2500

3000

3500

4000

4500

5000

pipe Reynolds number, Rep

Figure

3 l. Numerical velocity

prediction under

reduced

for

the and

effect

of superficial

normal

gravity

liquid

conditions

p = 0.0012,

D N" = 0.1,

and RepUGs

= 500;

Bop = .867 (Frp = .16 to 16), 1 g curve: .00016 to .016)

0.01

g curve

Bop = 86.7

(Frp =

141

0.9 re,t,

m ,,,r_ " E

mr,,

0.8 _J s,

t'_

0.7 0.6 0,5

0.4

Â°m

0.3 C 0

e..

0.2 0,1 0

0.15

0.3

0.45

0.6

non-dim

Figure

lg .01g

......

32.

Numerical

0.75

0.9

1.05

for

the

effect

comparison

diameter;

gravity

and

0.0012,

DN Â° = 0.1, Ree = 750, Wep = .608;

normal

1 g curve

gravity

: Fre = .028

between

of gravity

bubble

Frp = 2.8;

1.35

gas velocity, U*_s

prediction

the

1.2

the

level

reduced

environments

p" -0.01

g curve:

142

0.9

O.8

0.7

'V oc

-----Wept.2

0.6

0.5

(

0.15

0.3

0.45

0.6

0.75

nan-am

Figure

33. Numerical detached

Wep=0.5

....

Wep=l.0

' i 0.9

1.05

1.2

' 1.35

gas velocity, t.l'as

prediction for the effect of surface tension on bubble diameter p = 0.0012, Frp = 22.42, Rep = 600

and

......

D N = 0.1

143

0.95 0.9 m

0.85

E _3

0.8 0.75 0.7

0.65

2mu 0.6

......

5mu lOmu

0.55 0.5 0

0.15

0.3

0.45

0.6

0.75

0.9

1.05

1.2

1.35

non-dim, gas velocity, U'GS

Figure

34. Numerical detached and

prediction bubble

DN = 0.1;"mu"

5 "mu"

curve

for the

diameter curve

• Rep = 200

effect

of liquid

p" = 0.0012, • Rep and

= 1,000; 10 "mu"

viscosity

Frp = 62.21, 2 "mu" curve

Wep

curve

• Rep

= 100

= 0.54 = 500;

REPORT

DOCUMENTATION

PAGE

Fon_Approvea OMB

),,, I Public repoaing burden gathering and maintaining collect=on of information, Davis

Highway,

Suite

1, AGENCY

for this collection of information is the data needed, and completing including suggestions for reducing 1204.

Arlington,

USE ONLY

22202-4302,

estimated to average 1 hour and reviewing the collection this burden, to Washington

and

(Leave blank')

the

Offme

2. REPORT

per response, of information. Headquarters

Management

and

including Send Services,

Budget,

DATE

'3.

the time comments Directorate

AND

Paperwork

Reduction

REPORT

TYPE AND

Project

(0704-0188).

DATES

5. FUNDING

Generation

Gravity

Conditions

in a Continuous

Liquid Flow Under

Department Cleveland,

Reserve

National

8. PERFORMING ORGANIZATION REPORT NUMBER

AND ADDRESS(ES)

University

AGENCY

Aeronautics H.

NAME(S)

E-11771

of Mechanical Engineering Ohio 44106-1749

SPONSORING/MONITORING

Glenn

Cleveland,

11.

Report

NUMBERS

WU-962-24--00--00 NGT5-1168

ORGANIZATION

Case Western

John

20503.

Cezar Pals

7. PERFORMING

Reduced

6. AUTHOR(S)

Salvatore

Washington.

COVERED

Final Contractor

SUBTITLE

Bubble

0704-0188

tor reviewing instructK)ns, searching existing data sources, regarding this burden estimate or any other aspect of this for Information Operations and Reports, 1215 Jefferson

July 1999 4_ TITLE

No.

and

Space

Research

Ohio

SUPPLEMENTARY

NAME(S)

10.

AND ADDRESS(ES)

SPONSORING/MONITORING AGENCY REPORT NUMBER

Administration

Center

at Lewis

Field

NASA

CRI1999-209170

44135-3191

NOTES

This report was submitted as a thesis in partial fulfillment of the requirements for the degree Doctor of Philosophy to the Case Western Reserve University, Cleveland, Ohio, August 1998. Project Manager, John B. McQuillen, Microgravity Science Division, NASA Glenn Research Center, organization code 6712, (216) 433-2876.

12a.

DISTRIBUTION/AVAILABILITY

Unclassified Subject This 13.

were

publication

from

the NASA

aboard

the DC-9

used: 1.27,

i.9,

Center

generation

Reduced

Gravity

for AeroSpace under reduced

Aircraft

from

10 to 200 mils.

gravity

at NASA

and 2.54 era. Two different

flow rates were varied

Information,

ratios

Glenn

(301)

conditions Research

of air injection

It was experimentally

for both co-flow

nozzle

observed

increased

and thus the time to detach void fraction

flow rates. On the other

injection based

than by using multiple

on an overall

gravity,

Predictions

of the theoretical

of fluid properties, diameter SUBJECT

hand,

deviate injection

is lar_er in a reduced TERMS

bubbles

it is observed

compare

geometry _ravity

that uniformity

to study single detachment;

or detaching

from the value

Independent

can be controlled

however,

force,

depending

well with performed of the air injection

and flow

conditions

environment

than

on generated

in the dynamic tension

on the relative

experiments. nozzle

in a normal

precise

diameter bubble

gravity

Experiments

Three

flow tube

different

0.1 and 0.2. Gas and liquid

liquid velocity,

(for either single by solely

and bubbly

the bubbles

flow

at the nozzle

at higher

size are investigated at similar

no longer

Under

tip inhibits with respect

using the theoretical flow conditions

nozzle

gas

A theoretical conditions

bubble

model,

of reduced

detachment.

Liquid

to the surrounding

velocities,

predicts

single

bubbles.

regime.

superficial'liquid

or multiple

the gas and liquid

by using

of adjacent

of the bubble

and thus the theory

nozzle

varying

more accurately

coalescence

forces

velocity

However,

environment

superficial

manner

size can be controlled

the surface

configurations.

air injection nozzle diameters. As the tube diameter was velocity was increased, the frequency of bubble formation

of the flow configuration

generation

system.

were considered:

that with increasing

gives rise to unpredictable

bubble

and cross-flow

using an air-water

to tube diameters

in a somewhat

of bubble

since this latter system

bubble

as attaching model

decreased.

transition

is employed

flux enhances

can act either

to significantly

forming

flow regime

port injection,

force balance,

the gas momentum

drag and inertia begins

and hence

621--0390.

Center,

decreased in size. The bubble diameter was shown to increase with increasing the size of the detached bubbles increased. Likewise, as the superficial liquid

volumetric

CODE

Nonstandard

generated increased, injection),

14.

Distribution:

(Max. imum 200 woras) work reports a stuoy ofbubble were

volumetric

is available

performed

diameters

DISTRIBUTION

- Unlimited

Category:

ABSTRACT The present

12b.

STATEMENT

the bubble

the experiment model.

liquid. neck length

behavior.

It is shown

Effects

that bubble

and flow geometry. 15. NUMBER OF PAGES

156 Microgravity;

Two phase flow; Bubble

16.

PRICE

CODE

A08 17.

SECURITY CLASSIFICATION OF REPORT

Unclassified NSN

7540-01-280-5500

is. SECURITYCLASSIFICATION OF THIS PAGE

Unclassified

19. SECURITY CLASSIRCATION OF ABSTRACT

20.

LIMITATION

OF ABSTRACT

Unclassified Standard

Form

Prescribed 298-102

ANSI

298 Std

(Rev. Z39-18

2-89)