Bubble Formation in a Horizontal Channel at Subcooled Flow ... · Bubble Formation in a Horizontal...

Bubble Formation in a Horizontal Channel at Subcooled Flow Condition

by

Saman Shaban Nejad

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Mechanical and Industrial Engineering University of Toronto

© Copyright by Saman Shaban Nejad, 2013

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Bubble Formation in a Horizontal Channel at Subcooled Flow

Condition

Saman Shaban Nejad

Master of Applied Science

Mechanical and Industrial Engineering

University of Toronto

2013

Abstract

Bubble nucleation at subcooled flow boiling condition in a horizontal annular channel with a

square cross section by the use of high-speed camera is investigated. The channel represents

a scaled-down version of a single rod of CANDU reactor core. The experiments were

performed by the use of water at pressures between 1-3 atm, constant heat flux of 0.124

MW/m2, liquid bulk subcooling of 32-1

oC and mean flow velocities of 0.3-0.4 m/s. Bubble

lift-off diameters were obtained from direct high speed videography. The developed model

for the bubble lift-off diameter was obtained by analyzing the forces acting on a bubble.

Furthermore, a model for the bubble growth rate constant was suggested. The proposed

model was then compared to experimental data and it has shown a good agreement with the

experimental data. Additionally, the effects of liquid bulk subcooling, liquid pressure and

mean flow velocity on bubble lift-off diameter were investigated.

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Acknowledgments

First of all, I would like to thank my supervisor, Dr. Nasser Ashgriz, for his guidance,

continued support and trust through all phases of this research work as well as his

suggestions and contributions during the data analysis and thesis write-up. I would also like

to thank Lu Liu for his help during image analysis. Technical advice of my friend, Dr. Reza

Karami during high-speed videography and digital image processing as well as Osmond

Sargeant and Terry Zak during various stages of the experimental setup is greatly

appreciated. Finally, I wish to thank my family and friends for their great support and

continuous encouragement during this rewarding experience which made this investigation

possible.

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Table of Contents

Abstract .................................................................................................................................... 2

Acknowledgments ................................................................................................................... 3

List of Tables ........................................................................................................................... 7

List of Figures .......................................................................................................................... 8

Nomenclature ........................................................................................................................ 12

Chapter 1 Introduction........................................................................................................... 1

Introduction ..................................................................................................................... 2 1

1.1 CANDU Power Plant- Overall View .................................................................... 2

1.2 Need to Characterize the Nucleation Process ....................................................... 5

Chapter 2 Research Objectives .............................................................................................. 7

Research Objectives ........................................................................................................ 8 2

2.1 Tasks ..................................................................................................................... 8

2.2 Approach ............................................................................................................... 9

Chapter 3 Literature Review ............................................................................................... 10

Literature Review ......................................................................................................... 11 3

3.1 Reactors Operating Conditions ........................................................................... 11

3.1.1 CANDU Nuclear Fuel Rod System Parameters ..................................... 13

3.2 Boiling................................................................................................................. 13

3.2.1 Overview of Two-Phase Flow Models ................................................... 14

3.2.2 Nucleate Boiling ..................................................................................... 17

3.2.3 Wall Heat Flux ........................................................................................ 18

3.2.4 Models for Departure and Lift-off Diameters in Subcooled flow .......... 27

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3.3 Acting Forces on a Sliding Bubble ..................................................................... 37

Chapter 4 Experimental Procedure .................................................................................... 46

Experimental Procedure .............................................................................................. 47 4

4.1 Scaling Criteria and Experimental Conditions ................................................... 47

4.1.1 Scaling Subcooled Boiling Region ......................................................... 48

4.2 Water Scaled-down facility................................................................................. 54

4.3 Digital Photographic Method for Visualization .................................................. 59

4.4 Errors and Uncertainty Analysis ......................................................................... 63

Chapter 5 Results and Discussion ....................................................................................... 65

Results and Discussion .................................................................................................. 66 5

5.1 Visualization and Image Analysis ...................................................................... 66

5.1.1 Coalescence ............................................................................................ 78

5.2 Experimental Analysis ........................................................................................ 82

5.2.1 Balance of forces acting on a bubble at the departure ............................ 82

5.2.2 Balance of forces acting on a bubble at the lift-off ................................. 84

5.2.3 Comparison between the experimental and predicted results ................. 96

Chapter 6 Summary and Conclusions .............................................................................. 106

Summary and Conclusions ........................................................................................ 107 6

Bibliography ................................................................................................................ 111 7

Appendix A: Force Balance in x-direction (departure moment) .................................... 117

Appendix B: Bubble size measurement technique ........................................................... 119

B.1. 3-D Bubble Lift-off Diameter Approximation using 2-D Image ........................ 119

B.2. Bubble Lift-off Velocity...................................................................................... 120

B.3. Bubble Upstream, Downstream, and Inclination Angles at Lift-off ................... 121

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Appendix C: MatLAB code for image analysis ................................................................ 123

C.1. Procedure ............................................................................................................. 123

C.2. MatLAB Code ..................................................................................................... 124

Appendix D: Mechanical Properties of the Zirconium tubes ......................................... 142

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List of Tables

Table 3-1: Operating conditions of various nuclear reactors 12

Table 3-2: Suggested correlations for the bubble departure 31

Table 3-3: Suggested correlations for the bubble lift-off diameter 37

Table 4-1: Set points for CANDU nominal operating conditions and the modeled chamber 54

Table 5-1: Advancing and Receding contact angles of the bubble shown in the Fig. 5-1 72

Table 5-1: Data bank 90

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List of Figures

Figure 1-1: Overall diagram of a typical CANDU Power Plant [2] ......................................... 2

Figure 1-2: CANDU nuclear reactor core [5] ........................................................................... 3

Figure 1-3: Fuel Rods, Fuel Bundles, Pressure Tubes and Calandria [7] ................................. 4

Figure 3-1: Fuel rod configuration [8] .................................................................................... 12

Figure 3-2: Typical boiling curve for water at 1 atm pressure [11] ........................................ 15

Figure 3-3: Stages of Bubble Formation [16] ......................................................................... 17

Figure 3-4: Illustration of bubble protruding out of the superheated liquid layer, by Guan [17]

................................................................................................................................................. 18

Figure 3-5: Schematic representation of subcooled flow boiling, Kandlikar [19] ................. 20

Figure 3-6: Boiling curve from the Bowring [23] model ....................................................... 22

Figure 3-7: Boiling curve for the Bergles and Rohsenow [27] model .................................... 24

Figure 3-8: Force balance of a vapour bubble at a nucleation site. ........................................ 40

Figure 3-9: Schematic diagram of bubble nucleation phenomenon. ...................................... 40

Figure 4-1: The axial void fraction distribution during forced convection subcooled boiling 49

Figure 4-2: Axial profiles of the flow quality and thermodynamic equilibrium equality in the

case of a constant wall heat flux ............................................................................................. 49

Figure 4-3: Overall view of the experimental setup ............................................................... 55

Figure 4-4: Schematics of the Tank Assembly ....................................................................... 56

Figure 4-5: Tank assembly setup ............................................................................................ 56

Figure 4-6: The Schematics of the Chamber Assembly ......................................................... 59

Figure 4-7: Chamber assembly setup ...................................................................................... 59

Figure 4-8: Camera Setup ....................................................................................................... 60

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Figure 4-9: A sample bubble for image processing ................................................................ 60

Figure 4-10: A sample of the cropped image.......................................................................... 61

Figure 4-11: Binarized image of the sample bubble .............................................................. 62

Figure 4-12: Schematic of a bubble at the final stage of image processing ........................... 62

Figure 4-13: The sample bubble before filtering the noise ..................................................... 63

Figure 5-1: Consecutive images of the nucleation to lift-off process of representative bubbles

(Pressure: 1 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kW/m

2, Subcooling: 4

oC)............ 68

Figure 5-2: Growth and collapse curve for a typical bubble at Pressure: 1 atm, Mass Flux:

350 kg/m2s, Heat Flux: 124 kW/m

2, Subcooling: 4

oC ............................................................ 70

Figure 5-3: Normal and parallel displacement of the centroid of a typical bubble at Pressure:

1 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kW/m

2, Subcooling: 4

oC .............................. 71


(Pressure: 1.5 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 9oC) ....... 73

Figure 5-5: Bubble growth in superheat layer (same flow conditions as those of the Fig. 5-4)

................................................................................................................................................. 74


(Pressure: 1.0 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 9oC). ...... 75

Figure 5-7: Consecutive images of the Bouncing phenomenon in subcooled flow boiling

(Pressure: 2 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 16oC) ........ 77

Figure 5-8: Consecutive images of the Sliding phenomenon in subcooled flow boiling


Figure 5-9: Schematic of the bubble Coalescence in Pool and Flow Boiling [69] ................. 79

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Figure 5-10: Consecutive images of the Coalescence phenomenon in subcooled flow boiling

(Pressure: 2.5 atm, Mass Flux: 400 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 15oC) ..... 80

Figure 5-11: Consecutive images of the Coalescence phenomenon in subcooled flow boiling


Figure 5-12: Force balance of a vapour bubble at lift-off ....................................................... 85

Figure 5-13: Bubble lift-off diameters vs. Subcooling for all the cases at 1 atm and their

corresponding standard deviations .......................................................................................... 88

Figure 5-14: Effect of the liquid pressure on the bubble lift-off diameter (heat flux: 124

kW/m2). .................................................................................................................................. 93

Figure 5-15: Effect of the mass flux on the bubble lift-off diameter (heat flux: 124 kW/m2).

................................................................................................................................................. 94

Figure 5-16: Effect of the fluid subcooling on the bubble lift-off diameter (heat flux: 124

kW/m2, mass flux: 300 kg/m2.s). ........................................................................................... 95

Figure 5-17: Comparison of the experimental data with the predicted data at different

pressures and for different flow conditions. ........................................................................... 97

Figure 5-18: Comparison of the experimental data versus the predicted data in different

conditions (mass flux) ............................................................................................................. 98

Figure 5-19: Comparison of the experimental data versus the predicted data in different

conditions (subcooling) ........................................................................................................... 99

Figure 5-20: Prediction results of the proposed model against the first set of the experimental

lift-off diameter (average error: 21.07%).............................................................................. 102

Figure 5-21: Prediction results of the proposed model against the second set of the

experimental lift-off diameter (average error: 16.81%) ........................................................ 102

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Figure 5-22: Prediction results of the proposed model against the entire experimental lift-off

diameter (average error: 19.91%) ......................................................................................... 103

Figure 5-23: Prediction results of five model against the present lift-off diameter data ...... 105

Figure B-1: Images taken 0.25ms apart at inlet conditions of 100oC, 1.5atm, 2gpm. The

indicated bubble detached from the heater during this period .............................................. 121

Figure B-2: Bubble Contact angle lines ................................................................................ 122

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Nomenclature

1. Symbols

b

Bubble growth constant

C

Dimensionless coefficient as indicated by its subscript

Cp

Specific Heat Capacity

D

Diameter

D2O

Deuterium

Dw

Surface contact diameter

F

Force

F

Pool boiling heat transfer suppression factor

f

Bubble Frequency [s-1

or Hz]

G

Average Mass flux, [Mg/m2s]

g

Acceleration due to Gravity [9.81m/s2 ]

Gs

Dimensionless shear rate

h

Heat transfer coefficient

H

Bubble height

Hfg

Latent heat of evaporation (Ch. 3)

hfg

Latent heat of evaporation (Ch. 4)

Ja

Jakob Number

k

Thermal Conductivity [W/m2K]

l

length

M

Molecular weight of the liquid

Mass flow rate

Npch

Phase Change Number

NS

Subcooling Number

Nu

Nusselt Number

p

Pressure

Pe

Pecelt Number

Pr

Prandtl Number

pr

Critical pressure

xiii

Heat flux

r

Radius

Re

Reynolds Number

S

Suppression factor

S

Single-phase heat transfer enhancement factor

St

Stanton Number

t

Time [s]

T

Temperature [K]

u

x-component velocity [m/s]

U235

Uranium-235

ur

Relative velocity between bubble centroid and liquid flow

[m/s]

V

Volume [m3]

v

Y-component velocity [m/s]

W

Width

We

Weber Number (dimensionless)

X

Quality

x

distance or position

2. Greek Letters

Thermal Diffusivity

[m

2/s]

Friction Factor

Dynamic Viscosity [Ns/m2]

Density [kg/m3]

Surface Tension [N/m]

Contact angle [deg or rad]

Shear Stress [N/m2]

ν Kinematic Viscosity [m2/s]

∆

Difference

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3. Subscripts

a

advancing

b

bubble- bulk

b

buoyancy (for forces)

cp

contact pressure

d

contact

du

unsteady drag

e

effective

eqb

equilibrium

f

fluid

fc

forced convection

fdb

fully developed boiling

fg

fluid-gas (phase change)

g

gas (or vapour)

h

hydraulic (for diameter)

h

hydrodynamic (for

forces)

i

inclination

inl

inlet

int

intersection

l

liquid

liq

liquid

lo

lift-off

m

mean contact angle

nb

nucleate boiling

pb

partial boiling

pool

pool boiling

qs

quasi-steady

r

receding

s

surface

xv

s

surface tension (for

forces)

sat

saturation

sl

shear lift

sub

subcooling

TP

Two-Phase

w or

wall wall

x

x-direction

y

y-direction

4. Abbreviations

BWR

Boiling Water reactor

CANDU

CANada Deuterium Uranium

CHF

Critical Heat Flux

DNB

Departure from Nucleate Boiling

DOF

Degree Of Freedom

FDB

Fully Developed Boiling

ONB

Onset of Nucleate Boiling

OSV

Onset of Significant Void

PB

Partial Boiling

PHWR

Pressurized Heavy Water Reactor

PNVG

Point of Net Vapour Generation

PWR

Pressurized Water Reactor

VVER

Russian-type pressurized water cooled

reactor

1

Chapter 1 Introduction

2

Introduction 1

1.1 CANDU Power Plant- Overall View

CANDU (CANada Deuterium-Uranium) reactor is a Canadian pressurized water nuclear

reactor in which heavy water is used as a coolant. Therefore, it is classified as a Pressurized

Heavy Water Reactor or PHWR. In Ontario’s Power generation system, CANDU has a vital

role since it generates almost 50% of Ontario’s electricity (16% of Canada’s overall

electricity requirements). This Canadian designed and built reactor is efficient and relatively

low capital cost, and has been in service with high reliability and safety for over 35 years [1].

Figure 1-1: Overall diagram of a typical CANDU Power Plant [2]

Fig. 1-1 shows a CANDU power plant consisting of the following three compartments: a

control system building, a reactor building, and a building for the steam turbine and the

electrical generator. The main component in this plant is the nuclear reactor where the

required heat is generated as a result of fission reactions. The CANDU reactor is designed to

use two independent water loops in order to remove the heat from the nuclear core. The

primary loop, in which heavy water, D2O, is used as the heat transfer fluid, and contains high

pressure tubes. All the fuel bundles are placed inside these pressure tubes. The released heat

due to the nuclear fission reactions is removed by the heavy water flow, through the pressure

tubes. Heavy water at very high pressures is used to allow it to be heated to higher

temperature, and therefore more heat to be removed from the reactor core. The inlet

temperature of the heavy water is lower than the saturated temperature and therefore, the

3

flow is subcooled and single phase at the entrance to the core. Pressurized heavy water enters

the pressure tubes as a subcooled liquid at around 11MPa at ~260oC with a degree of

subcooling (or subcooling margin) of around 50oC at 24kg/s [3], [4]. Subcooled liquid is a

liquid that its temperature is below its saturation temperature and the degree of subcooling is

the difference between the subcooled liquid temperature and the saturation temperature of the

liquid at the specified pressure. The heavy water flows through the fuel channels over 37-

element bundles and by absorbing the generated heat, it eventually becomes close to

saturated mixture. The heated flow exits from the fuel channel as a low quality (~3% to 4%)

two-phase mixture and enters the end feeders with a pressure drop of around 1MPa [3]. After

exiting the core and reaching the steam generator, all of the heat from the hot heavy water is

absorbed by the light water in the secondary loop and then, the light water becomes steam

which is fed to the steam turbine in order to generate electricity.

1. Fuel Bundles; 2. Calandria; 3. Control Rods; 4. Pressurizer; 5. Steam Generator; 6. Light water

Pump; 7. Heavy water Pump; 8. Fuel Loading Machine; 9. Moderator; 10. Pressure Tube; 11. High

Pressure Steam (to Steam Turbine); 12. Water Condensate (from Condenser); 13. Reactor Containment

Building; 14. Primary Loop

Figure 1-2: CANDU nuclear reactor core [5]

Calandria is where all the pressure tubes are placed and contains another loop of heavy water

used as a moderator. The moderator, in contrary to the primary loop with heavy water, is kept

at low pressures, i.e. atmospheric pressure. Cadmium rods (28 rods in some moderators) are

submerged into the heavy water of the moderator in the Calandria. these rods absorb the

4

radiation and are control rods which serve as an emergency shutdown system in case of an

accident, by a gravitational drop.

One of the main design advantages of the CANDU reactor is the use of a horizontal core

containing many small diameter pressure tubes (about 4” ID) in which the uranium fuel

bundles are placed. These horizontal pressure tubes are typically 6 m long and can sag in the

middle after many years of service. As a result of having horizontal orientation, on-line re-

fueling of the reactor at full power can be accomplished. A refueling machine pushes in a

new fuel bundle at one end of the pressure tube and removes an old bundle at the other end of

it. In contrast, light water reactors which are more popular in other countries must be shut

down for re-fueling purposes. Each fuel rod is approximately 50 cm long and 1 cm in

diameter and is placed inside a zirconium alloy tube. Fuel rods contain natural uranium. The

heat energy is generated via a fission reaction by the fissile uranium -235 (U235

) which make

up about 0.72% of the fuel mass [6].

Figure 1-3: Fuel Rods, Fuel Bundles, Pressure Tubes and Calandria [7]

The heavy water in the primary loop serves the dual purpose of the neutron moderator from

the nuclear fission reaction and cooling the fuel rod bundles. Since the main purpose of this

work is on the heat transfer characteristics around the fuel bundles, an electric heater and

light water have been used instead of the uranium fuel rod and heavy water, respectively.

5

Therefore, no nuclear fission reaction is involved and no need of heavy water is required (the

neutron moderating properties are not required if nuclear fission reaction is not present). This

system was scaled down in terms of pressure, mass flux, heat flux, and temperature to

investigate the bubble characteristics (although the fuel rod will be 1:1 scale). The horizontal

orientation of the pressure tubes, fuel bundles and subcooled two-phase flow phenomenon

are closely related to the objectives and scope of the present project as are discussed later. It

should be noted that the only heat source for the coolant flow in the fuel channel is from the

fuel bundles. These bundles comprise of 37 (in most CANDU reactors) fuel rods, which are

the main interest for this project. This study particularly focuses on the interface between the

heat supply and the coolant.

1.2 Need to Characterize the Nucleation Process

Because of the high heat generation rate on fuel bundles in the pressure tubes, boiling

phenomenon is used to remove heat from the fuel bundles. In CANDU, heavy water flows

over the horizontal tube bundle and removes heat from the tubes. Subcooled water enters the

channel and due to high heat transfer rate, evaporation occurs and finally two-phase flow

leaves the channel. In the nuclear rod bundles, critical heat flux (CHF) limits the amount of

power which can be obtained. Consequently, understanding the heat transfer characteristic in

CANDU reactor is critical since the heat transfer from the reactor fuel rods is bounded by the

Critical Heat Flux (CHF). If CHF is reached, the coolant cannot provide sufficient cooling

for the heat removal from the heater surface, and this leads to an uncontrolled temperature

rise and eventual failure of the fuel rod cladding material. This is normally characterized

either by a sudden increase in the surface temperature or by a small temperature spikes on the

heated surface. Thus, exceeding the critical heat flux is associated with safety risks as well as

economic losses.

Water-cooled reactors should be designed with sufficient safety margins to prevent such

occurrences. The flow inside the CANDU reactor core is subcooled flow. However, since the

heater surface is usually hot, bubbles may form on the surface. These bubbles grow in size

and separate into the core flow, but they usually collapse since the core flow is subcooled.

The characteristics of the bubbles can change by the flow parameters, such as heat flux, mass

flux, subcooling, and pressure. Changing from a single-phase subcooled flow to a two-phase

6

subcooled flow starts by the bubble formation on the heater rod. This phenomenon can

eventually lead to CHF. In spite of a great quantity of experimental and theoretical studies,

knowledge of the precise nature of CHF and subcooled boiling, i.e. bubble nucleation, is still

incomplete and the mechanisms of a boiling crisis are still not well understood. This is

mainly due to the very complex nature of the two-phase flow with heat transfer. Due to an

incomplete knowledge of boiling crisis mechanisms, experimental investigations on the

subcooled boiling have to be performed for each specific design of nuclear reactors.

Validated prediction methods for the design condition must be derived. This leads to a large

amount of subcooled boiling data banks and bubble nucleation prediction methods.

Because of the complexity of the problem, the experimental investigations on the bubble

formation have to be performed for each specific design and flow conditions. Due to the

limitation of the technical feasibility and financial expense, these experiments have often

been performed in a scaled model system. Two different modeling techniques are available:

geometric modeling and fluid modeling. In the geometric modeling, simplified flow channels,

e.g., circular tubes, instead of typical rod bundles are used. By using such simple flow

channels, it is possible to systematically study the effect of different mentioned parameters

on heat transfer and gain detailed knowledge of the nucleation process for a wide range of

test parameters. In the fluid modeling, a substitute fluid, e.g. Freon-12, is used instead of the

water. By a proper selection of a model fluid, the operating pressure, operating temperature,

and the heat power required can be reduced significantly. Using such modeling methods, a

large number of empirical correlations has been developed for the bubble formation and CHF

conditions.

7

Chapter 2 Research Objectives

8

Research Objectives 2

A better understanding of a thermal-hydraulic phenomenon taking place inside a nuclear

reactor core is necessary for its safe and efficient operation. The scope of the present study is

to obtain experimental data on the bubble formation and its characteristics in CANDU

nuclear reactor. For this purpose, a set of experiments have been performed on a horizontal

and uniformly heated channel. Bubble nucleation information is obtained and based on the

gathered data, a new analytical model for the bubble growth and departure from the heater

surface is proposed.

2.1 Tasks

The following tasks are achieved:

1. Development of scaling parameters to scale down the CANDU reactor core

conditions: In order to design a scaled down test section, a detailed analysis of the

bubble formation inside the tube bundles is performed and a set of dimensionless

numbers are developed. These dimensionless numbers are then used to design the

scaled down test section.

2. Design and construction of an experimental facility: An experimental facility to

allow for the measurement of bubble nucleation process on a horizontally oriented

heated tube was constructed. The heated tube is inside a channel having similar

dimensions as those in channels of a 37-element fuel bundle. The design is intended

to nearly duplicate a scaled down model of a CANDU reactor pressure tube together

with only one replica of 37-element fuel bundles placed inside. Also a preliminary

photographic study including image analysis was performed in order to develop

correlations that characterize bubble properties.

3. Scoping Study: Experimental investigation of the bubble formation and migration

throughout the system at various operating conditions was performed. Thermal and

physical characteristics of the rod-liquid interface were observed and data on the

bubble lift-off diameter were collected.

4. Validating and Comparison: The experimental data were compared with other

investigators’ experimental data. In addition, proposed models and correlations were

9

validated by the use of experimental data, and then compared with previous proposed

models.

2.2 Approach

A better understanding of the bubble nucleation in subcooled flow is needed and thus, is

investigated through a review of experimental visualization at several conditions. Various

two-phase flow regimes occurring at ONB-OSV region are reported and classified.

Theoretical and experimental bubble and wall heat flux models developed by others and used

in the past studies are also reviewed and related to the current experimental findings. An

appropriate wall temperature model as well as the bubble lift-off diameter approach is then

selected (chapter 3). Required experimental setup is described in chapter 4. Two-phase flow

experiments were performed and the flow is characterized using a high-speed camera. The

selected bubble lift-off and wall temperature concepts from chapter 3 are then theoretically

developed for the practical applications. Validation and sensitivity analysis are then

performed and the average errors are reported in chapter 5. The conclusion of the current

work and the recommendations for the future works are further explained in chapter 6.

10

Chapter 3 Literature Review

11

Literature Review 3

3.1 Reactors Operating Conditions

Bubble formation and CHF highly depends on the geometrical conditions as well as thermal-

hydraulic conditions. The followings are the most important parameters affecting the bubble

formation and CHF in a fuel element:

Pressure

Mass flux

Steam quality

Fuel rod diameter

Pitch to rod diameter ratio

Fuel rods configuration

Power distribution

Spacers

Table 3-1 gives an example of the operating conditions for different reactor designs [8]. This

table is just an example of each reactor group and it does not show all the operating

conditions that one design can have. For instance, operating pressure for different designs of

PWR’s can range from 15.0 to 16.0 MPa. The changes of the mass flux are more significant.

In designs of PWR, PHWR and VVER reactors, it was tried to avoid high void fraction in

sub-channels and therefore, the temperature of the coolant is always below the saturation

temperature. On the other hand, BWR’s have an average steam quality of 0.15 at the core

outlet due to high steam fractions at the core outlet [8].

12

Table 3-1: Operating conditions of various nuclear reactors [8]

PWR BWR CANDU (PHWR) VVER

Pressure, p, [MPa] 15.7 7.2 10.5 15.7

Ave. Mass flux, G,

[Mg/m2s]

4.0 3.0 5.0 4.0

Ave. Outlet steam

quality X, [-] -0.15 0.15 0.0 -0.15

Fuel rod diameter

d, [mm] 9.5 12.3 13.1 9.1

Pitch to diameter

ratio, [-] 1.3 1.3 1.15 1.4

Fuel rods

configuration

Square Square Hexagonal Hexagonal

** PWR: Pressurized Water Reactors; BWR: Boiling Water Reactors; CANDU: Canada Deuterium Uranium;

VVER: Russian-type pressurized water cooled reactor

For water-cooled reactors, there are usually two different kinds of fuel rod configurations, i.e.

square and hexagonal, as shown in Fig. 3-1:

a) Square lattice b) hexagonal lattice

Figure 3-1: Fuel rod configuration [8]

13

In forced convective channel flow, two different types of boiling crisis are considered. In the

subcooled or low steam quality region a boiling crisis occurs by the transition from nucleate

boiling to film boiling or departure from nucleation boiling (DNB). In the higher steam

quality region, mostly in annular flow, the boiling crisis originates from a depletion of the

liquid film (dryout). In the fuel assembly of PWR, PHWR and VVER reactors, the first kind

of boiling crisis (DNB) is mostly expected because of low steam quality in sub-channels. In

the fuel assembly of a BWR, attention is paid to the boiling crisis of the second kind (dryout)

[8].

3.1.1 CANDU Nuclear Fuel Rod System Parameters

Each CANDU reactor contains 380-480 horizontal channels depending on its model, and in

each of the horizontal channels a Calandria tube is placed which consists of the fuel rods,

heavy water coolant and pressure tube. These channels have a square lattice pattern at a

standard pitch of 11.25” which form an approximately circular array [9]. On the other hand,

each fuel rod is approximately 50 cm long and 1 cm diameter.

3.2 Boiling

Subcooled flow boiling is one of the main methods in many industrial applications in order to

achieve the highest possible heat transfer. Subcooled means that the bulk of the liquid, e.g.

water, is below its saturation point and the saturation temperature is exceeded only at a

heated surface. Thus, both convective (i.e. forced) and conductive heat transfer methods are

in use in this mechanism. Once the temperature of the heated surface and consequently, the

layer of subcooled liquid, which is in contact with it are high enough, bubbles form. These

steam bubbles grow and leave the heated surface once they reach their critical sizes, which

are function of the flow regime of the surrounding fluid, surface roughness and heat flux. At

this level of heat transfer, heat is not only removed by turbulent convection but also by

transient conduction and evaporation as a result of nucleating and departing bubbles. After

departing the heated surface, the bubbles condense as they release their latent heat to the

surrounding liquid. Therefore, to accurately model the wall heat flux distribution, all the

information regarding the nucleation site density, size of the departing bubbles, and the

bubble formation frequency should be taken into account. In subcooled flow boiling, the bulk

14

liquid is subcooled while vapour is generated near the heating surface due to the local

superheat. The local superheat activates the nucleation sites on the heater surface for bubble

nucleation.

There are two mechanisms of boiling that are responsible for the bubble nucleation, pool

boiling and flow boiling. The main difference between the two is that in pool boiling the

liquid is in static mode and no velocity is involved, while on the other hand, in flow boiling

there is fluid flow and therefore velocity effects are involved.

After the bubbles formation, they migrate to the subcooled flow and therefore, somewhere

downstream, the flow becomes two-phase flow. The two-phase flow behavior has been

extensively studied theoretically and experimentally since it occurs in wide industries such as

in nuclear reactors, boilers, oil wells and pipelines, etc. In spite of the large amount of

research effort in this field, there is still some level of uncertainly associated with it.

3.2.1 Overview of Two-Phase Flow Models

In the early literature, the flow boiling was considered to be the same as pool boiling. But

later it was shown there are differences between the two, in particular, the bubble formation

process and the critical heat flux. Therefore, different models for each flow patterns and tube

or annuli orientation are developed. In addition to the mechanisms which are explained

below, flow instability is also found to lead to CHF. However, here it is assumed that the

two-phase flow is stable and no discussion of this effect is provided.

Boiling is classified as pool boiling or flow boiling, depending on the presence of bulk fluid

motion. Boiling is called pool boiling in the absence of bulk fluid flow and flow boiling (or

forced convection boiling) in the presence of it. In the pool boiling, any motion of the fluid is

due to the natural convection currents and the motions of the bubbles are under the influence

of the buoyancy. In the flow boiling, the fluid is forced to move in a heated pipe or over a

surface by external means such as a pump. Therefore, flow boiling is always accompanied by

other convection effects. Pool and flow boiling are further classified as subcooled boiling or

saturated boiling, depending on the bulk liquid temperature.

Nukiyama has performed the pioneering work on the boiling by using an electrically heated

15

nichrome and platinum wires immersed in liquids [10]. He found that boiling takes different

forms, depending on the temperature difference between the liquid and the heater surface.

The four different boiling regimes which are shown below are: Single phase convection,

Two-phase nucleate boiling which is further divided into partial and fully developed sub-

regions, transition boiling, and film boiling.

Figure 3-2: Typical boiling curve for water at 1 atm pressure [11]

On the other hand, flow boiling exhibits the combined effects of convection and pool boiling.

The flow boiling is also classified as either external or internal flow boiling depending on

whether the fluid is forced to flow over a heated surface or inside a heated tube. External

flow boiling over a plate or cylinder is similar to pool boiling, but the added motion increases

both the nucleate boiling heat flux and the critical heat flux considerably. Internal flow

boiling is much more complicated in nature because there is no free surface for the vapor to

escape, and thus, both the liquid and the vapor are forced to flow together. Forced convective

nucleate boiling is very effective in achieving a high heat flux with a small temperature

difference between the heated surface and the cooling fluid; however, there is a boundary for

this effective heat transfer regime, which is referred to as the departure from nucleate boiling

(DNB). Reliable understanding of this DNB phenomenon is important for effective and safe

16

operation of nuclear systems and other thermal-hydraulic equipment [12]. In general, DNB is

a transition which causes the heat transfer regime move from nucleate boiling to film boiling

(or partial film boiling). This transition also involves the change from bubbly flow to

inverted annular flow. In spite of broad research in this field, detailed physical mechanisms

leading to DNB have not been clearly understood. The main reason for that is the difficulty

in observing the near wall region [13]. Three different flow regimes in flow boiling are as

follows:

Type 1: Bubbly flow

Bubbly flows happen at high mass flux and high subcooling. In this type of flow, individual

bubbles nucleate, sometimes slide and detach but not a large number of them coalesce. Wall

rooted bubbles are observed to coalesce with neighboring bubbles along the flow stream in

some cases [14]. Bubble sizes increase with decreased subcooling, decreased velocity and

lower pressure.

Type 2: Vapour clots

This can be seen usually at moderate subcooling, and the formed bubbles detach from the

nucleation sites. At regions close to CHF, most of the formed bubbles stay within the bubbly

layer and vapour clots form as a result of the coalescence among the bubbles. The length of

vapour clots are governed by Kelvin-Helmholtz instability. One may observe liquid film or

bubbly layer between the vapour clots and heated wall. In general, with increasing the

subcooling and flow rate, overall bubbly layer thickness and bubble size decreases.

Type 3: Slug flow

It can be observed at low mass flux and near saturation. Vapour slugs usually have a thin

liquid film along the wall. The wall temperatures fluctuate as a result of high temperatures

corresponding to the vapour slugs. In many cases the liquid film is not observed to dry out at

CHF [15] excluding the occurrence of dry-out type boiling crisis at these conditions.

In conclusion, it can be said that in these types of DNB regimes there is no sudden change in

macroscopic two-phase flow pattern as CHF is reached. For instance, transition to slug flow

17

at high heat flux was not observed to trigger DNB. Note also that due to strong non-

equilibrium conditions at CHF, conventional adiabatic or low heat flux two-phase flow

regime map cannot be used to predict DNB flow regimes [13].

3.2.2 Nucleate Boiling

The bubble formation is referred to as the nucleation. Nucleation can be divided into two

categories. The first one is called homogeneous nucleation, which can occur as a result of

perfect heated surface without any preferential nucleation sites. The other type is called the

heterogeneous nucleation and it is attributed to the imperfection in the heated tube and

presence of suspended particles in the subcooled liquid. In this type, nucleation happens on

cavities. First, the vapor trapped in these cavities receives energy from the hot surface and

starts growing. This is Stage I as shown in Fig. 3-3 and is called the waiting period. Then, the

bubbles keep increasing their volume and reach the mouths of the cavities. This is Stage II

and is called the growth period. The last stage happens when the radius of the bubbles and

the cavities are equal. This is Stage III, the departure period. After this point, the bubbles can

collapse or continue to grow and depart the surface depending on the conditions.

Figure 3-3: Stages of Bubble Formation [16]

The asymptotic growth phase starts once the bubble reaches a certain size after which the

bubble no longer grows monotonically [17]. When a bubble reaches outside of the

superheated liquid layer and into the bulk liquid flow, condensation occurs due to the

presence of the subcooled bulk liquid. Therefore, both phenomena, i.e. vapour generation in

the microlayer at the nucleation site and condensation at the top interface of the bubble,

18

happen at the same time and result in fluctuation of the bubble size. Depending on the wall

superheat, temperature of the superheated liquid layer, and the liquid subcooling, a bubble

may collapse on a nucleation site before departure as observed by Situ et al. [18]. This occurs

if the rate of condensation at the bulk liquid interface is higher than the rate of vapor

generation at the microlayer. Once bubbles grow to a certain critical size on the nucleation

site, as a result of convective flow related forces, the bubble will depart by either sliding on

the heater surface and then lift-off or detach from the heater surface without sliding.

Figure 3-4: Illustration of bubble protruding out of the superheated liquid layer, by Guan [17]

3.2.3 Wall Heat Flux

Kandlikar [19] divided the heat transfer area under the subcooled flow into three main

regions named as follows:

i) Single-phase heat transfer prior to ONB (Onset of Nucleate Boiling), in which the

wall temperature of the heater is below the local saturation temperature of the liquid

or just a few degrees more. In this region, the heat transfer coefficient, hfc, remains

constant (only if one neglects the minor changes of the liquid properties with

temperature), and the raise of the wall temperature is linear and parallel to that of the

bulk liquid. From Fig. 3-5 at location B, as Kandlikar mentioned, the wall

temperature passes the local liquid saturation temperature, but nucleation will not

occur instantly, since some amount of wall superheat is necessary to activate cavities

existing on the wall.

ii) The second region starts at location C, which is called the Onset of nucleate boiling,

or ONB. Starting from the nucleation sites, cavities become active, and therefore, the

19

nucleate boiling heat transfer increases its contribution to heat transfer and gradually

reduce the single-phase convective heat transfer. This region lasts until point H on

Fig. 3-5 and is broke down into three sub-regions. The first sub-region, which starts

from point C, is called Partial Boiling region (PB). The generated bubbles in this

region due to the exposure to the subcooled liquid flow, cannot grow and thus, they

are condensed. By increasing the bulk liquid temperature downstream of the ONB, a

thin layer of bubbles form on the heater wall and becomes populated by more bubbles

slowly. Fully Developed Boiling (FDB) starts from point E, which is a point where

convective heat transfer (single-phase heat transfer) becomes insignificant. In FDB,

wall temperature remains constant up to the point where the newly defined Significant

Void Flow (SVF) sub-region starts. In this region, the convective heat transfer

becomes significant once again due to the two-phase flow existing in SVF. This

region starts at point G, which is called Net Vapor Generation, or NVG (also called

OSV, onset of Significant Void). Upstream of this point, the vapor volumetric flow

fraction is very small. The main focus of this report is on this region and the

experimental results are mostly for late Partial Boiling Region and early Fully

Developed Region.

iii) Further downstream, point H is located where the saturation condition under

thermodynamic equilibrium is reached and the flow beyond this point is covered

under saturated flow boiling. This is the third region and will not be covered in this

report.

20

Figure 3-5: Schematic representation of subcooled flow boiling, Kandlikar [19]

Various models were developed to predict the heat flux and heat transfer rate in each region.

According to Warrier [20], developed models to predict the heat transfer rate during the

subcooled flow boiling can be divided into the following three categories:

1) Empirical correlations for the wall heat flux, which is mostly limited only to the

prediction of total wall heat flux for a specific flow situation. This group does not include

modeling of the heat transfer mechanisms involved and therefore, it is not able to give any

additional information in regards with the partitioning of wall heat flux between the liquid

and vapor phases.

2) Empirical correlations for partitioning of the wall heat flux, which are based on the

relevant heat transfer mechanisms and can provide information of each heat flux components

21

individually. As a result these correlations can be used for both the prediction of the wall heat

flux and the partitioning of the wall heat flux between the liquid and vapor phase. The main

goal of these correlations is to calculate the bulk void fraction, and therefore they mostly

focus on how the given total heat flux is partitioned and not the prediction of the total wall

heat flux itself.

3) Mechanistic models for the wall heat flux and partitioning. These models can be used

to predict both the wall heat flux partitioning and the overall wall heat transfer.

Since in this work, the wall temperatures at all nucleation sites were not precisely measured,

empirical correlations for wall heat flux were used to estimate the wall temperature.

Therefore, two commonly used methods in literature, named Liu and Winterton [21] method

and Chen [22] method, were selected and their results were compared. Results from other

researchers are also shown here.

The commonly used approach in obtaining the empirical method for the partial and fully

developed boiling regions is to combine the single-phase forced convection and saturated

pool nucleate boiling heat fluxes.

In partial nucleate boiling, which is a transition region between single-phase region and fully

developed nucleate region, Bowring [23] used a superposition method to get the partial

nucleate boiling heat flux as shown in Fig. 3-6:

eq. 3-1

where,

is the heat flux during partial boiling, is the single-phase forced convection heat

flux, and is the fully developed pool boiling heat flux.

For the fully developed region, the heat flux is given by Engelberg-Forster and Greif [24]:

eq. 3-2

22

where,

is the heat flux at the intersection of the single-phase and fully developed nucleate

boiling curves.

For the single-phase region heat flux is calculated as below:

( )

eq. 3-3

where,

is the liquid saturation temperature, is the liquid temperature, and is the single-

phase heat transfer coefficient which is obtained as below from the Colburn [25]:

eq. 3-4

where,

is the liquid Nusselt number, is the pipe hydraulic diameter, is the liquid thermal

conductivity, is the liquid Reynolds number, and is the liquid Prandtl number.

From the Figure 3-6, it is evident that at , then , where is the wall

temperature, and at , then .

Figure 3-6: Boiling curve from the Bowring [23] model

23

Rohsenow [26] likewise proposed a similar method to Bowring except for was calculated

as:

( ) ( )

eq. 3-5

where,

And also pool nucleate boiling correlation is:

√

( )

(

[ ( )]

)

eq. 3-6

where,

is an empirical constant that depends on the fluid-solid combination, m and n are empirical

constants that depend on the fluid properties, is the gas-liquid enthalpy difference, is

the liquid viscosity, and is the liquid heat capacity.

Later, Bergles and Rohsenow [27] suggested a correlation for the partial nucleate boiling heat

flux as:

√ [(

)(

)]

eq. 3-7

where,

is the heat flux computed from the fully developed boiling curve at .

The heat flux at ONB is given as:

[ ]

eq. 3-8

where,

p is in kPa, is in degree centigrade, and is in W/m2.

Bjorge et al. [28] suggested the following correlation for the prediction of the boiling curve

in subcooled flow boiling:

24

√ [ (

) ]

eq. 3-9

where,

, and

Figure 3-7: Boiling curve for the Bergles and Rohsenow [27] model

Liu and Winterton [21] suggested a model by combining the concepts proposed by

Kutateladze [29] and Chen [22]. The main advantage of their method is that they assumed

single-phase heat transfer would enhance by increasing the liquid velocity while the pool

boiling heat transfer is suppressed as a result of a lower effective wall superheat in flow

boiling compared to that in pool boiling. The overall subcooled flow boiling (qw) which is a

combination of single-phase and nucleate pool boiling heat fluxes is obtained as:

√( ) ( )

√( [ ]) ( )

eq. 3-10

where,

[ (

)] , it is called the pool boiling heat transfer suppression factor

, it is called the single-phase heat transfer enhancement factor

Prl and Rel are the Prandtl and Reynolds number based on liquid properties.

Also for the pool boiling heat transfer rate, the following is proposed by Cooper [30]:

25

( )

eq. 3-11

where,

M is the molecular weight of the liquid, q is the heat flux, and pr is the critical pressure of the

liquid.

Liu and Winterton obtained the following correlation to calculate the temperature difference

between the heater surface and bulk of the liquid. By having the bulk of liquid temperature,

one can easily calculate the wall temperature:

[ √( (

)( ))]

eq. 3-12

where,

( )

The older but still widely quoted 1966-Chen correlation [22] is another method to calculate

the wall superheat. The Chen correlation has been reported by Liu and Winterton [21] to

have the second lowest mean error in subcooled flow boiling among the commonly cited wall

superheat correlations, after their own 1990 correlation. The Chen correlation postulates that

heat transfer in convective boiling flow is a function of both nucleate and convective heat

transfer:

eq. 3-13

where,

(

)

and

where,

the F factor is set to 1.

Chen’s correlation was restated by Situ et al. [18] as:

26

( ) ( )

eq. 3-14

In order to create a numerically solvable non-linear equation in wall temperature, , the

equation was rewritten as:

( ) ( ) ( )

eq. 3-15

As was done with the surface temperature obtained from the Liu and Winterton method, the

surface temperature obtained by solving this equation for each case tested was used in order

to calculate the effective Jakob number. This was then used to obtain the expected bubble

lift-off diameter using the suggested modification of the Zeng et al. model and will be

presented later. The predictions for bubble lift-off diameter made using Liu and Winterton’s

correlation for wall superheat, along with mean experimental bubble size and the boiling

region for each case are presented in the form of a database in Table 5-1. A total of 802

bubbles across 44 cases were observed.

Also correlations for and are presented by Hsu [31], and Satu and

Matsumura [32]:

[ √

]

eq. 3-16

[

] [ ]

eq. 3-17

Furthermore, in fully developed nucleate flow boiling (FDB) region, only pressure and wall

temperature affect the heat flux and the flow velocity does not have any influence on it [33].

Thom et al. [34] have proposed a model to find the difference between the wall temperature

and the coolant temperature for a relatively clean surface:

(

)

eq. 3-18

27

where,

is the heat flux in Btu/hr.ft2, is the pressure in psi, and is in degree F.

Several correlation by many investigators have been proposed the over past fifty years in

order to predict OSV, such as correlations from Bowring [23], Thom et al. [34], Ahmad [35],

and Saha and Zuber [36]. The empirical correlations of Saha and Zuber are the most widely

used for the determination of the OSV point. They define two OSV regimes as their

conditions and correlations are presented below:

The thermally controlled regime:

eq. 3-19

where,

is the wall heat flux, is the pipe hydraulic diameter, and .

The hydrodynamically controlled regime occurs at:

eq. 3-20

where,

is the mass velocity.

3.2.4 Models for Departure and Lift-off Diameters in Subcooled flow

By obtaining appropriate correlations for the wall temperature and heat flux, proposing

models for departure and lift-off bubble diameters will be feasible. In this work, the main

focus is on the bubble lift-off diameter under varying flow conditions. The proposed model

will be then compared with the experimental data. There are many empirical and theoretical

28

correlations existing in literature for bubbles at the departure and lift-off. In spite of various

correlations for pool boiling, not many works have been done on flow boiling. It should be

noted that as Klausner et al. [37] reported, pool boiling correlations for bubble diameter do

not fit well for bubbles in flow boiling conditions.

Klausner et al. [37] were the earliest to differentiate the difference between the two types of

bubble motion. Bubble departure is used to characterize the sliding as the mechanism in

which bubble leaves the nucleation site. Bubble lift-off is used to characterize bubble

detachment from the heater surface, either from the nucleation site or after some finite sliding

distance. For this project, bubble lift-off diameter is measured as opposed to the departure

diameter. The reason is that the departure diameter is difficult to determine visually. In

addition, the departure diameter may be difficult to measure as the bubble may slide while it

is still early in the growth phase. For a horizontal surface, Klausner et al. [37] found that the

majority of bubbles will slide some distance before lift-off. In addition, Situ et al. [18]

observed that for vertical test surfaces that some bubbles tend to slide first and did not

directly lift-off. Thorncroft et al. [38] reported that bubbles tend to not lift-off in upward flow

boiling conditions. As shown by Zeng et al. [39], lift-off diameters for flow boiling is

typically smaller than that of pool boiling since the wall superheat is lower for flow boiling.

This results in a lower growth rate due to the presence of single-phase convective heat

transfer.

Basic force balance (with varying simplifying assumptions) is the most popular analytical

method used in developing bubble departure and lift-off diameter in flow boiling of a bubble

departing a nucleation site or the heated wall. It is typically found that these analytical

correlations are validated by an empirical study to compare the correlations with

experimental data. Analytical and experimental correlations from several authors are

presented in Tables 3-2 and 3-3 for departure and lift-off diameters, respectively. The work

done by most of these authors were based on a vertical flow channel and thus these

correlations cannot be directly applied on a horizontal CANDU channel since buoyancy is

not considered at lift-off. However, the procedure in developing these correlations can be

incorporated for the development of departure and lift-off diameter in the CANDU case and

the relationship between bubble size and experimental conditions can be readily seen.

29

The bubble departure phenomena in pool boiling have been studied since 1950s. A

correlation for the bubble departure diameter was obtained by Zuber [40] by assuming the

bubble growth occurs in a superheated and thin thermal layer near the surface. He found that

bubble departure and the flow regimes are similar to the formation of gas bubbles at orifices.

Cole [41] stated that the bubble departure diameter is proportional to the inverse of the

absolute pressure. Then, Cole and Rohsenow [42] modified the Cole’s correlation by

replacing the wall superheat with a critical temperature. Kocamustafaogullari and Ishii [43]

fitted 135 data points obtained from existing experimental results performed from 0.067 to

141.87 bar. They reported that the bubble departure diameter is a function of the contact

angle and pointed out that the active nucleation site density on a heated channel surface is the

key parameter in the prediction of the bubble number density.

Farajisarir [44] carried out a critical review and pointed out the limitations of existing models

and correlations regarding the bubble departure diameter. He examined forced convective

boiling flow at atmospheric pressure in a vertically oriented test section and proposed non-

dimensional models for the departure diameter and time. Zeng et al. [39] derived the bubble

departure diameter from the balanced force equations affecting the departing bubble based on

experimental data acquired under flow boiling conditions. He performed his tests on a

horizontal test section but the derived equations we done for both vertical and horizontal

orientations. He did not propose an explicit model for the bubble departure diameter.

Thorncroft et al. [45] summarized the literature that describes the forces acting on growing

bubbles and identified each force balance equation used for conditions of horizontal pool

boiling, vertical pool boiling, and flow boiling. Basu et al. [46] assumed that all of the energy

from the wall is first transferred to the superheated liquid layer and that a fraction of the

energy is then used to generate vapor and to heat bulk liquid due to forced and transient

convection. Basu suggested an empirical correlation of the bubble departure diameter. After

her, Sateesh et al. [47] determined the bubble departure diameter from the force balance

between the buoyancy force and the surface tension force. Duhar and Colin [48] suggested a

force balance model to predict the departure radius by referring to the theoretical results of

Magnaudet et al. [49]. An experimental study was also performed to measure the growth of

air bubbles injected into silicon oil by using high-speed video pictures for validation. The

30

model of Duhar for the bubble departure radius predicted his experimental data well, but the

injected gas flow rates were required.

Among the correlations reviewed above, the correlations developed for a vertical heated

surface are not suitable for predicting the bubble departure in a horizontal surface due to the

reason that the inclination of a heated surface affects the bubble’s behavior and heat transfer

near the wall. The studies of Farajisarir, Zuber, and Basu fall into this category. Furthermore,

the correlations reported by Cole, and Kocamustafaogullari were developed using existing

data from the literature, but most of the data were obtained under horizontal pool boiling

conditions. Farajisarir, and Basu examined the effect of high heat flux and high velocity

conditions. In addition to these, some correlations were developed using coolants other than

water and therefore, constant values used in these correlation might not be applicable to

water. Although the force balance equations suggested by Zeng and Thorncroft are very

useful, an explicit form of the departure diameter was not given.

31

Table 3-2: Suggested correlations for the bubble departure

Author Bubble Departure Diameter Comments

Cole and

Rosenhow

model [42]

[√

(

) ]

-

Kocamustaf

aogullari

and Ishii

model [43]

(modified

version of

Fritz)

(

) √

is in degrees. Applicable range is where, is the shear lift

coefficient, and is the bubble growth constant.

Farajisarir

[44]

(

)

Basu et al.

[50]

( ) [

]

√

( )

Cho et al.

[51]

[

(

√(

)

(

)

)

(

√(

)

(

)

)

]

Klausner et al. formulated [ ]

[

( ) ]

( )

( )

√ √

Literature review shows that extensive researches have been carried out on bubble departure

size, while there is only limited number of studies have been done on the bubble lift-off size

in convective boiling. So far, correlations and models for the bubble lift-off diameter have

not received as much attention as the correlations for the bubble departure diameter. This is

mainly due to the fact that most studies on the bubble-sliding phenomenon have focused on

enhancing heat transfer itself. As a result, it is essential that a proper model for the bubble

lift-off diameter be developed that is applicable to the conditions of CANDU. In here, some

32

of the previous models are presented.

Staub [52] considered several different forces acting on a nucleating bubble, including

surface tension, momentum change of the liquid due to the growth of the bubble, liquid

inertia force, evaporation vapor thrust force, buoyancy force, and drag force. He then

assumed that the surface tension, buoyancy, and drag forces were the dominant forces. In his

model, the force balances is applied on a layer of hemispherical bubble.

Unal [53] yielded a semi-empirical correlation to predict the bubble departure and maximum

diameters using experimental data in the literature. He assumed that a spherical or ellipsoidal

bubble grows on a very thin, partially dried liquid film formed between the bubble and the

heated surface. He used this model for an energy balance for a bubble in order to predict the

maximum bubble diameter when a spherical or ellipsoidal bubble grows on a very thin,

partially dried liquid film formed between the bubble and heated surface in subcooled boiling

flow. Unal’s correlation is the most popular, due to its widely applicable range. However, he

did not propose a model for the bubble lift-off diameter.

Klausner et al. [37] performed an investigation to find the effects of wall superheat and flow

velocity on the nucleation characteristics of cavities of different radii for flow boiling of

subcooled water near atmospheric pressure in a narrow rectangular channel by using a high-

speed camera. Their results show that higher flow rates require larger wall superheats to

activate the cavities. Furthermore, they investigated the effect of wall superheat and found

out the fact that as the wall superheat increases, smaller cavities are activated and the heat

transfer coefficient increases with increased nucleation activity. They measured the bubble

departure diameter in a horizontal rectangular channel using saturated R-113. They used a 25

x 25 mm2 transparent rectangular channel, and a 20-mm-wide nichrome strip was adhered to

the bottom surface of the channel. The mass flux, heat flux, and pressure ranged from 112 to

287 kg/m2, 11.0 to 26 kW/m2, and 132 to 213 kPa, respectively. They observed that the

overwhelming majority of bubbles left the nucleation site by sliding a finite distance along

the heated surface before lifting off the wall. The bubble departure was defined as the instant

that the bubble left the nucleation site, and the bubble lift-off was defined as the instant that

the bubble was detached from the heated surface. They analyzed the force balance in the flow

33

direction for bubbles growing at the nucleation site in order to predict their departure

diameter. They found that an asymmetrical bubble growth force (so-called unsteady drag

force) and surface tension force are important factors holding the bubble at the nucleation site

before departure.

Zeng et al. [39] proposed improved models for the bubble departure and lift-off diameters by

including the bubble inclination angle, following Klausner’s work. He carried out pool

boiling and flow boiling experiments and solved the force balances on a bubble for different

experimental conditions without proposing any explicit model for them. He studied the

forces acting on a bubble in saturated horizontal forced convection boiling. At the point of

bubble departure and bubble lift-off, several forces such as surface tension, hydrodynamic

pressure force, and contact pressure force were neglected because the bubble contact area on

the wall was approximated to be zero. The bubble departure diameter and bubble lift-off

diameter were modeled based on the simplified force balance equation. They measured the

bubble growth rate and bubble lift-off diameter for a saturated R-113 boiling flow using the

same test channel as Klausner et al.’s [37]. A total of 37 lift-off diameters were obtained for a

mean liquid velocity of 0.35–1.0 m/s, heat flux of 5.8–16.8 kW/m2, and pressure of 147–165

kPa. In a similar manner as Klausner et al. [37], they analyzed the force balance both in and

normal to the flow direction for the bubble in order to predict the departure and lift-off

diameters, respectively. The quasi-steady drag force, bubble growth force, and shear lift force

were considered for the departure diameter, but the surface tension force was neglected in a

manner different from that in Klausner et al.’s work [37]. The buoyancy and bubble growth

forces were considered for the lift-off diameter. The shear lift force was neglected based on

their observation that the bubble sliding velocity after departure was close to the local liquid

velocity. They proposed a bubble growth constant in Zuber’s bubble growth model [15]

based on their sample measurements for the bubble growth rate. The constant ranged from

1.0 to 1.73, and the constant of 1.7 gave the best prediction results for the departure and lift-

off diameters. Zeng mentioned that their bubble lift-off diameter model could be applied to a

vertical boiling flow with some modifications. For a vertical up flow, they expected that the

shear lift force would push the bubble against the wall, hampering bubble detachment, and

that the bubble detachment would be due to large fluctuations in transverse liquid velocity.

34

Thorncroft et al. [38] performed a visual study of bubble growth and departure in vertical up

flow and down flow forced convection boiling. They reported that the departure diameter

increases with increasing Jakob number and that the bubble-sliding phenomenon increases

the heat transfer rate from a heated wall to the fluid.

Chang [54] photographically studied the behavior of near-wall bubbles in subcooled flow

boiling for water in vertical, one-side heated, rectangular channel at mass fluxes of 500, 1500,

2000

under atmospheric pressure. His main focus was on the bubble coalescence

phenomenon and the structure of the near-wall bubble layer. He observed three

characteristics layers at sufficiently high heat fluxes (>60-70% CHF):

a) a superheated liquid with small bubbles attached on the heated wall,

b) a flowing bubble layer consisting of large coalesced bubbles over the superheated

liquid layer,

c) the liquid core over the flowing bubble layer, as well as the existence of a liquid sub-

layer under coalesced bubbles was identified photographically.

Prodanovic et al. [55] reported that the bubble diameters decreased with an increase in the

subcooling and mass flux, while the effect of mass flux became less pronounced as the OSV

(onset of significant void) was neared. For the heat flux effect, they concluded that the

maximum bubble diameter generally dropped with an increase in heat flux. This was

particularly evident at lower heat fluxes, while at a higher heat flux, the bubble diameter

remained roughly constant. They also measured the wall superheat at the film location, and

the experimentally measured Jakob number was used for the development of their correlation.

Furthermore, they measured the bubble maximum and lift-off diameters, and the maximum

bubble diameter time, bubble lift-off time, and bubble condensation time for a subcooled

boiling flow of water in a vertical annulus. The heater at the center had a diameter of 12.7

mm, the outer glass tube had an inner diameter of 22 mm, and the hydraulic equivalent

diameter was 9.3 mm. A total of 54 data sets were presented for pressures of 1.05, 2.0, and

3.0 bar, a bulk liquid velocity of 0.08 to 0.8 m/s, a heat flux of 0.2 to 1.2MW/m2, and a

subcooling of 10 to 30o C. They suggested five correlations for each of the five parameters

above as a function of Jakob number, non-dimensional sub-cooling, boiling number, and

35

density ratio. The coefficients and exponents of the correlations were determined based on

their data. They observed that the sliding velocity of small bubbles was about 0.8 of the bulk

liquid velocity for an isolated bubble region, and larger bubbles under a lower liquid velocity,

lower heat flux, and lower subcooling slid at higher velocities than the bulk liquid flow.

Basu [46] developed an empirical correlation for the bubble lift-off diameter using the

correlation of the bubble departure diameter from his experimental data and from the

literature. A reduction factor was introduced to quantify the actual number of bubbles lifting

off per unit area. Situ et al. [18] employed the force balance equation suggested by Zeng to

formulate the dimensionless form of a bubble lift-off diameter as a function of the Jakob

number and the Prandtl number. Their experimental setup was a BWR-scaled upward

annular channel (vertical). The working fluid was water and a high-speed digital video

camera was used in order to capture the dynamics of the bubble nucleation process. To

validate the correlation, forced-convective subcooled boiling experiments were carried out

under atmospheric pressure. The conditions of their experiments were at of inlet

temperature, pressure of 1 atmosphere, inlet velocity of 0.487-0.939 m/s, and heat flux of

60.7-206

. The results of the experimental data and proposed model agreed within the

averaged relative deviation of 35.1%. they observed both bubble departure and bubble lift-off

phenomena and reported that bubbles slid a longer distance as the subcooling was lower and

the mass flux was higher, similar to the results of Okawa et al. [56]. To predict the bubble

lift-off diameter, they set the force balance normal to the flow direction, and analyzed the

shear lift and the bubble growth forces. They adopted the shear lift force derived by Mei and

Klausner [57] and assumed that the bubble sliding velocity was half the local liquid velocity.

They also used Zuber’s bubble growth model with a bubble growth constant of 1.73 to

evaluate the bubble growth force. The effect of liquid subcooling on the bubble growth was

indirectly reflected by introducing the nucleate boiling suppression factor of Chen’s

correlation [22] to the bubble growth model. Their lift-off diameter model was validated

against their experimental data, and the average prediction error was 35.1%.

Bae [58] proposed a description of the bubble lift-off diameter derived from the force balance

equation by referring to Situ’s study. By modifying the function of the bubble growth rate, he

expressed the bubble lift-off diameter as a function of the bubble departure diameter. Bae

36

defined a fitted curve to simplify the force balance equation and used Unal’s correlation of

the bubble departure diameter to calculate the lift-off diameter. Chu [59] investigated

phenomena from bubble nucleation to lift-off for a subcooled boiling flow in a vertical

annulus channel by the use of a high-speed camera in terms of heat flux, mass flux, and

degree of subcooling. It was found that the bubble lift-off diameter decreased as the mass

flux and subcooling increased. On the other hand, the effect of the heat flux on the bubble

lift-off diameter was neither significant nor consistent, except for when the mass flux was

around 500 kg/m2s and the subcooling was 5.0-5.4

oC. In his work, the bubble lift-off

diameter and nucleation frequency showed stochastic behaviors, such as dependence on the

nucleation site and competition between them in removing the thermal energy from the

heated surface. Therefore, it was recommended that a sufficient number of nucleation sites

should be examined in order to obtain unbiased bubble characteristics. Also, the combined

parameter, (fb – Dlo), showed a clear dependence on the subcooling, mass flux, and heat flux.

Among the existing models correlation for the bubble diameters in a forced convective

boiling flow, Unal’s model agreed well with his database of the bubble lift-off diameters.

According to Cho et al. [51] and Zeng [39], the developed model for the bubble departure

diameter depends strongly on the bubble contact angle. On the other hand, bubble lift-off

diameter depends on the buoyancy and the growth forces in a horizontal channel, while in

vertical channels, lift-off diameter is a function of the lift-off number (this dimensionless

number indicates the ratio between the shear lift and growth forces). It was, therefore,

postulated that the developed models for vertical channels are not suitable for horizontal

surfaces as it is found out that the inclination of a heated surface affects the bubble’s

behavior and heat transfer near the wall, Chu [59].

37

Table 3-3: Suggested correlations for the bubble lift-off diameter

Author Bubble Lift-off Diameter Comments

Unal [53]

√

( )

(

)

(

) ,

(

)

Applicable range for this relation is

,

Prodanovic et

al. [55]

(

)

(

)

A= 440.98, B= -0.708, C= -1.112, D=

1.747, E= 0.124

The parameters A,B,C,D,E are empirically

correlated parameters. Prodanovic et al. derived

the lift-off diameter using similar procedure as

Farajisarir [44].

Basu et al.

[50]

( ) [

]

√

( ) ,

Valid within:

Basu et al. observed a high scatter in empirical

results. of water on Zr-4 was measured to be

57o.

Situ et al.

[18] √

√

The shear lift coefficient

Bae et al.

[58] and Cho et al.

[51]

( [

(

)

]

)

√ √

Bae et al.: Cho et al.:

is an adjustable constant which Zeng et al. [39]

recommended as 1.73. Bae et al. and Cho et al.

assumed an inclination angle of zero. Bae et

al. recommends Unal's model for the departure

diameter.

3.3 Acting Forces on a Sliding Bubble

The main focus of the present study is on bubbles formation and bubble departure sizes in a

CANDU reactor. The bubble size when it detaches from the heater surface (i.e. lift-off

bubble size) can be different from the bubble departure size. The bubble departure size is the

size a bubble detaches from the nucleation site and starts to move on the surface. A bubble is

38

formed at a nucleation site, and starts to gradually grow. It is found out that once the bubble

reaches a certain diameter (size), it detaches from the nucleation site; in most of the cases, the

bubble slides for a finite distance on the heater surface and continues to grow. During this

period, vaporization happens at the inner surface of the bubble, while condensation occurs at

the outer surface if the tip of the bubble is out of the superheated layer. At some point

downstream of the nucleation site, bubbles lift-off from the surface. For bubble departure, the

force balance along the flow direction is to be considered; whereas, for the bubble lift-off

size, the force balance perpendicular to the flow direction has to be considered. While the

bubbles are attached to the heater surface and their nucleation site, they are heated by the

heater and vaporization occurs at a micro-layer under the bubbles. Obviously the heat

transfer mechanism at the wall is not the same as that in the bulk water. Also while the

bubble is attached to the heater surface and slides, it contributes to the micro-convective heat

transfer process. The departure diameter of the bubble depends on the contact angles, while

on the other hand, the lift-off diameter of the bubble is a function of different forces applied

on the bubble such as the growth force and the shear lift force. Also, the main parameter for

the evaporation heat flux and vapour generation is the bubble diameter. Once again, the main

reason for choosing the lift-off diameter rather than the departure diameter in this report is

that, it is fairly difficult to define the instant of bubble departure from the nucleation site.

In this part, a force balance analysis on a growing bubble is performed in order to predict the

bubble departure and lift-off sizes. It is postulated that the dimensionless form of the bubble

departure and lift-off diameters are functions of various non-dimensional numbers such as

Jakob, and Prandtl numbers.

According to Fig. 3-8, the forces acting on a bubble at its nucleation site are as follows (the

dynamic effects of turbulence and wave motion are ignored), Klausner et al. [37]:

x-direction:

∑

eq. 3-21

y-direction:

39

∑

eq. 3-22

where,

Fx: the force acting on bubbles at x-direction, Fsx: the surface tension force at x-

direction, Fdux: the unsteady drag force at x-direction (also called growth force because the

bubble grows asymmetrically, and the unsteady liquid flow such as the added mass force has

a dynamic effect), Fqs: the quasi-steady force in the flow direction, ρg: vapor density, Vb:

bubble volume, vgx: bubble velocity at x-direction, t: time, Fy: the force acting on bubbles

at y-direction, Fsy: the surface tension force at y-direction, Fduy: the unsteady drag force at y-

direction, Fsl: the shear-lift force, Fb: the buoyancy force (effect of liquid buoyancy and

gravity of bubbles), Fh: the hydrodynamic force, Fcp: the contact pressure force, and vgy: the

bubble velocity at y-direction.

In addition to the applied forces, it is notable that inclination angle, i.e. θi, is the angle

between the line from nucleation site to the bubble center and y-direction. Also, θa and θr are

advancing contact angle and receding contact angle, respectively. The correlations for all the

mentioned forces are provided next.

Surface tension force

The surface tension forces at x- and y-directions were given by Klausner et al. [37]:

( )

( ) ( )

eq. 3-23

where,

is the contact diameter.

and

( )

eq. 3-24

40

Figure 3-8: Force balance of a vapour bubble at a nucleation site.

Figure 3-9: Schematic diagram of bubble nucleation phenomenon.

HFdux

Fb

Fh, Fcp

Fsl

Fsx

Fsy

Fqs

Θi

ΘrΘa

Fduy

X

Y

Flow

Departure Vaporization Lift - off

CondensationHeat Flux

Sliding

41

Growth force

The unsteady drag force (growth force) is given by Chen [60] as the following for a spherical

bubble attached to a wall; the virtual added mass, Vf is:

eq. 3-25

where,

rb: bubble radius which is changing over time during the forming and growing phases.

By assuming that the growth force can be estimated as the inertial force of this added mass,

the following is obtained:

( )

(

)

eq. 3-26

where,

ρf: liquid density (kg/m3), H: the bubble height measured from the wall (m), uby: the bubble

front velocity on y-direction (m/s).

Therefore, a relation between H and uby can be written as uby = dH/dt. In this case, it was

assumed that the bubbles are spherical and as a result, H is the bubble diameter (i.e. 2rb).

Thus:

uby = dH/dt uby = 2drb/dt

eq. 3-27

From Eqs (3-26) and (3-27) the final correlation of the growth force is obtained as:

(

)

eq. 3-28

where,

: the first derivative of the bubble radius with respect to time, the second derivative of

the bubble radius with respect to time.

By the use of inclination angle, the growth force can be calculated in x- and y-directions:

Fdux=Fdu sinθi

eq. 3-29

and

42

Fduy=Fdu cosθi

eq. 3-30

One of the commonly used bubble-growth models is that of Zubers’ model [15] which also

shows the dependence of bubble’s growth on the temperature of the liquid surrounding it:

√ √

eq. 3-31

where,

is the liquid Jakob number, b is growth rate constant, and t is time.

It should be noted that the wall superheat can be used as the superheat in the Jakob number in

this case, i.e. saturated boiling. While this statement is correct, in forced convection sub-

cooled boiling, it is much more complex. At the beginning of the bubble’s growth process, its

size is small and therefore, all the liquid around it is superheated, and this makes the bubble

to grow. Bubble will continue growing till its tip reaches the subcooled water and the bubble

starts to collapse from its tip. Therefore, the wall superheat would be more than the effective

superheat surrounding the bubble (Kocamustafaogullari et al. [43]). It then can be concluded

that the bubble radius is a function of the following dimensionless numbers and time:

r = f(Jae)

( )

eq. 3-32

43

where,

( ), with being the suppression factor and equals to (by Situ et al. [18]):

where

ReTP: the two-phase Reynolds number calculated by setting vapor quality as zero, ( ).

According to the short length of the test section and its small heater power, the estimation of

the point of net vapor generation does not considerably affect the calculation of the wall

temperature.

where,

( )

Shear lift force

The shear lift force on a solid sphere at low Reynolds number was obtained by Saffman [61].

Auton [62] also derived a correlation for the shear lift force on a sphere in an inviscid shear

flow. Then, Saffman’s model was modified by Mei and Klausner to suit for a bubble, and

interpolated with Auton’s equation to derive an expression for shear lift force over wide

range of Reynolds number:

eq. 3-33

where,

ur: the relative velocity between the bubble center of mass and the liquid phase (i.e.

ur = uf − ug), and Cl: the shear lift coefficient given by Klausner et al. [37] which is:

(

)

eq. 3-34

44

where,

: a dimensionless shear rate of the oncoming flow, |

|

, Reb: the bubble

Reynolds number

.

Buoyancy force

According to Klausner et al. [37] the buoyancy force can be obtained as follow:

Fb = (ρf – ρg)gVb = (

)(ρf – ρg)g

eq. 3-35

where,

Vb: the bubble volume,

.

Quasi-steady drag force

Klausner et al. [37] modified the correlation which was obtained by Mei and Klausner [57]

by taking into account the effect of the wall:

[(

) ]

( )

eq. 3-36

where,

n = 0.65 and

[(

) ]

Contact pressure force

Klausner et al. [37] correlation for the contact pressure force is used here. It is important to

mention that this force is applied to the bubble over the contact area with the heater because

of the pressure difference inside and outside of the bubble at the reference point.

45

eq. 3-37

where,

rr: the radius of curvature of the bubble at the reference point on the surface y = 0, σ: surface

tension (N/m).

Hydrodynamic force

According to Klausner et al. [37] hydrodynamic force is calculated as follow:

eq. 3-38

where,

U is evaluated at y = rb. This force was estimated by considering an inviscid flow over a

sphere in an unbounded flow field and according to the symmetry over the majority of the

bubble surface, the contribution to hydrodynamic force is from the pressure on the of the

bubble over an area

.

46

Chapter 4 Experimental Procedure

47

Experimental Procedure 4

The flow visualization experiments were carried out to simulate the thermo-hydraulic

conditions of CANDU reactors. In this chapter, the facility and the experimental procedure

including the flow visualization are described. Also the choice of the experimental conditions

under which the films were taken will be described. Elaboration on the flow visualization

setup and image processing system for bubble analysis will be discussed.

4.1 Scaling Criteria and Experimental Conditions

Due to the difficulties of conducting the experiments in a real reactor, an electrically heated

fuel assembly was built which represents a scaled-down CANDU’s 37-element fuel rod. The

operational conditions were much lower than those of the real CANDU. The assembly needs

to correspond to the real CANDU in all other ways and therefore, dimensionless numbers

were obtained in order to maximize the similarities between the real CANDU and its

prototype. The focus is on correct development of the flow quality and the different flow

regimes that are present inside the assembly. Thus, a loop facility was built as it is explained

in Section 4.2: an assembly of only one fuel rod placed in a horizontal channel with one inlet

and one outlet on each side was built. Furthermore, to make sure that a fully developed

turbulent flow of water is established right at the entrance to the test section, another section

with similar geometry and hydraulic diameter is added just before the main chamber. The test

section is equipped with several glass sections so that visual inspection of the two-phase flow

was made possible.

Attention has to be paid in deriving the appropriate scaling criteria. Local bubble

characteristics, the flow pattern distribution and the flow development along the test section

are among the main objectives of this work. For the purpose of proper local bubble

characteristics, an analytical force balance at the moments of departure from the nucleation

site as well as the lift-off moment of the bubble was done and the main forces which result in

bubble departure or lift-off were obtained. Also, thermo-hydraulic analysis was performed to

observe the flow pattern distribution and its development along the test section. Since the

local void fraction is an important parameter, two dimensionless numbers were used to

perform the system scaling.

48

4.1.1 Scaling Subcooled Boiling Region

In a typical CANDU reactor, heavy water enters the reactor core several degrees centigrade

lower than its saturation temperature; due to this reason, the supplied heat from the heater rod

is added to the subcooled water as it flows over the rod. In literature, the flow of subcooled

fluid is divided into four regions as indicated by Fig. 4-1 [23]:

Before reaching point 1, no vapour is present in the flow and all the supplied heat is used to

increase the temperature of the subcooled flow (forced convection is cooling the heater

surface). Right at the point 1, vapour bubbles form for the first time, and from point 1 to

point 2 more bubbles are produced along the heater surface. In this region, the superheated

liquid layer has small thickness close to the wall of the heater and therefore, bubbles cannot

sufficiently grow to reach their critical sizes to be able to leave the surface. At point 2,

bubbles with sufficiently large sizes are formed and can depart from the heated wall. The

vapour volumetric fraction starts to rise rapidly. In the region between point 2 and 3,

although the vapour volumetric fraction is large, thermal equilibrium condition does not exist.

This means that part of the flowing water is still subcooled and the real vapour volumetric

fraction is larger than the volumetric fraction obtained from a heat balance. In some models,

point 2 is called the Point of Net Vapour Generation, PNVG (it is also called Onset of

Significant Void, OSV). At point 3, all of the liquid is at saturation temperature and both real

and thermal equilibrium volumetric fractions are equal.

49

Void Fraction

Channel Length

1 2 3

Figure 4-1: The axial void fraction distribution during forced convection subcooled boiling

Figure 4-2: Axial profiles of the flow quality and thermodynamic equilibrium equality in the case of a constant

wall heat flux

ONB OSV

50

After defining the four regions in a subcooled flow, it would be beneficial to see how these

properties are correlated. At the beginning of the heater cooling process by the use of

subcooled fluid, all the absorbed heat from the heater rod, is forced to increase the liquid

enthalpy up to its saturation temperature. Upon this time, no vapour is formed yet and

therefore the thermodynamic equilibrium quality, , can be defined as follow (this quality

is a function of x-coordinate which is parallel to the rod axes):

( ) ( )-

eq. 4-1

where,

hliq(x): the enthalpy of the liquid at the position x,

: the enthalpy of the liquid at saturation for a given pressure, and

hfg: the heat of evaporation.

According to Eq. (4-1), the value of is negative in the subcooled region; but as the

experiments have shown, some vapour bubbles form at the wall of the rods in the subcooled

region. As a result, part of the generated heat is consumed to form the bubbles and the rest is

used to increase the enthalpy of the liquid. Thus, the actual flow quality, ( ), is larger

than zero:

( ) ( )

eq. 4-2

where,

: the vapor mass flow rate

: the total mass flow rate

A modified version of the thermodynamic equilibrium quality, ( ), is given as:

( ) ( )-

eq. 4-3

where,

( ): the enthalpy of the two-phase mixture flow at the position x

51

By continues heating the fluid, the whole bulk of the fluid will reach the saturation point and

the flow quality, , becomes equal to the thermodynamic equilibrium quality, .

This equilibrium point is the start point of the thermodynamic equilibrium. Fig. 4-2 shows

these properties. At the first point where the bubbles form, i.e. x xd, the thermodynamic

equilibrium quality is less than zero. Onset of boiling is where is zero (also called bulk

boiling). Moreover, x = xeqb shows the area where the flow is considered as in

thermodynamic equilibrium.

Eq. (4-4), which is obtained from an energy balance of Eq. (4-3), shows the increase of the

thermodynamic equilibrium quality along the flow path:

( ) (

)

eq. 4-4

where,

: the added enthalpy to the inlet enthalpy of the flow at distance x from the inlet (It can

be calculated by using (

) and converting it to mass and heat fluxes)

Then, it can be obtained that:

eq. 4-5

where,

are heat and mass fluxes, respectively

( ) (

) (

) (

) (

) (

)

( ) (

) (

)

-

-

eq. 4-6

where,

: heat flux (assuming constant)

: fluid mass flux

l: length of a rod

Dh: the hydraulic diameter of a flow channel in the assembly

hinl: the enthalpy of the pure liquid at the inlet of the assembly

To obtain this expression, the enthalpy of the two-phase fluid at the distance x from the inlet

was calculated based on the fluid inlet enthalpy plus the added energy to the amount of the

52

existing mass at a given geometry. Then, it was rearranged to give two dimensionless

numbers which are presented below:

The phase change number:

(

) (

)

eq. 4-7

and the subcooling number:

eq. 4-8

According to the previous discussion, the actual quality is the main concern in any flow

conditions in CANDU and the modeled chamber; therefore the actual quality has to be

properly modeled rather than the thermodynamic equilibrium quality. Levy offered a profile-

fit model in which the flow quality is coupled to the thermodynamic equilibrium quality [63].

The fit ensures that:

( )

= 0 at the departure point ( ) ([ ]

)

eq. 4-9

where,

[ ] is the thermodynamic equilibrium quality at the departure point and is defined as:

[ ]

where

is the specific heat of liquid

is the saturation temperature minus local bulk fluid temperature, i.e., (Its

correlation is obtained from Levy [63]

i) the further downstream the departure point, the smaller the difference between

and :

[ ] => - →0

eq. 4-10

53

ii) the slope of ( ) at the departure point is zero:

[

]

[

] [ ]

[

]

eq. 4-11

Since,

Therefore,

[

] [ ]

According to Levy [63], the following fit fulfills the specified conditions and agrees with

experiments (Fig. 4-2):

[ ] exp ( [ ]

[ ]

)

eq. 4-12

It can be concluded that the proper scaling of the flow quality in the subcooled region can be

done if the dimensionless numbers, i.e. Npch and Ns , are matched for both CANDU and the

modeled chamber.

According to Cheng and Muller, the void fraction of a typical CANDU is zero which is

around the middle point of BWR and PWR cores. CANDU’s actual quality is less than 5%

[8]; therefore, the flow does not need to be modeled in thermal equilibrium region and

consequently, not all the dimensionless numbers, which are applicable to BWR modeling

studies, are necessary to be used in this report. Only two dimensionless numbers, i.e. the

phase change number and the subcooling number, are going to be used in order to properly

scale down the real CANDU core conditions. In the following table conditions of a typical

CANDU core and our modeled chamber are compared:

54

Table 4-1: Set points for CANDU nominal operating conditions and the modeled chamber [64]

CANDU Modeled Chamber

geometry

Length (m) 6 0.5

Diameter of rod (mm) 13.1 13.1

Dh (mm) 7.51 12.17

Number of rods 37 1

Inlet area (mm^2) - 4.146 x 102

Operating conditions

P (atm) 110 1-3

Tsat (°C) 319 100-133

ΔTsat (°C) 68 32-1

Mass flux, (kg m-2

s-1

) 5000 300-400

Heat flux, (kW m-2

) 630.5 124

4.2 Water Scaled-down facility

The experimental set up has three sub-assemblies:

(a) Tank assembly (water source)

(b) Chamber (test section)

(c) Visualization system

55

Figure 4-3: Overall view of the experimental setup

56

(a) The tank assembly includes isolated heated tank, an immersion heater, a pump and a

temperature control device. The tank is filled with filtered tab water and then, the heater raises

the water temperature to the required temperature. The rise in temperature is monitored by K-

type thermocouple which is attached to the outlet of the pump. The pump is used to circulate the

water inside the tank to achieve a uniform temperature. Thermocouple is attached to data

acquisition system to track the temperature inside the tank. After reaching desire temperature, the

outlet valve is opened allowing the water to flow into the chamber assembly through stainless

steel metal pipes.

Figure 4-4: Schematics of the Tank Assembly

Figure 4-5: Tank assembly setup

57

(b) This is the part of the assembly where nucleation happens. The assembly consists of a

combination of instruments, such as a chamber with a window and a cartridge heater. The

chamber assembly was designed so as to be able to easily monitor and vary the pressure,

temperature and the flow properties of the system. Its main aim was to create an environment

conducive for the bubble nucleation. The chamber is equipped with one window on each side

which is resistance to high pressure and temperature. Right at the inlet of the chamber, flow

meter is located to control the inlet flow. One K-type thermocouple was placed there as well in

order to record the inlet flow temperatures. This temperature is one of the control variables used

to study the bubble nucleation. To study the nucleation properly, the flow rate, the temperature

and the pressure were all recorded and their relationships to the properties of the nucleation were

analyzed. Pressure also directly affects the saturation point of water; therefore, varying the

pressure would vary the number of nucleation sites, the nucleation frequency and whether or not

the nucleation happens. The key objective of this chamber is to raise the temperature of the water

from some subcooled temperature to just under saturation at given the pressure, flow and

temperature conditions.

Another notable point is the use of zirconium tube. Heater rod is of stainless steel and in order to

have the same surface conditions and roughness as the CANDU rods, the heater was placed in a

zirconium tube, identical to that of CANDU reactors. Zirconium has unique properties such as

excellent corrosion resistance, good mechanical properties and very low thermal neutron cross

section which make it ideal cladding material for nuclear reactors. The American Society for

Testing and Materials (ASTM) offers various grades of zirconium alloys such as Zircloy-2

(Grade R60802) and Zircloy-4 (Grade R60804). The recent one is currently being used in

CANDU and its composition is Zr-1.5%Sn-0.2%Fe-0.1%Cr [65]. More details for the zirconium

tubes are presented in Appendix D.

The requirements of the project were as follows: 1.0-3.0 atm pressure, 32-1°C subcooling

temperature, low turbulence, 0.3 – 0.4 m/s inlet water velocity, 124 kW/m2 heat flux.

A custom made cartridge heater including an output power and temperature controller was

purchased from BlueWater Heaters Company. The specifications were as follows:

58

Dimensions: 0.493" OD ± .002" x 23.22" ± 2%

Voltage: 240 VAC. 1ph

Power: 2500 watts (+5%, - 10%)

Sheath: 321 stainless steel and polished

Termination: CMR termination, stainless single threaded 3/8-18 NPT fitting silver

soldered to sheath

Thermocouple: Built-in Type K ungrounded thermocouple

Others:

- 30 mm unheated at disk end, 60 mm unheated at lead end center

500 mm is heated length

- Junction centered in heated length and in center of diameter.

- 48" fiberglass insulated power and thermocouple leads.

The specifications of the zirconium tube from the manufacturer are as follows:

Outer Diameter 13.095mm ± 0.025mm

Inner Diameter 12.310mm ± 0.050mm

Length 490mm ± 0.075mm

The space between the inner wall of the tube and the electrical heater is filled with stainless steel

coating which has the same thermal conductivity as the heater metal sheet and was capable of

operating at temperature above 200oC for high thermal conductivity. The electrical heater has the

ability to generate the heat flux of up to 124kW/m2. The K-type thermocouple embedded between

the steel heating rod and the Zr-4 shell is used to measure heater temperature at the stainless steel

heater and Zr-4 shell interface and to give a first approximation to the wall temperature. The

hydraulic diameter of the chamber was therefore calculated as:

( )

( )

59

Figure 4-6: The Schematics of the Chamber Assembly

Figure 4-7: Chamber assembly setup

(c) For the visualization purposes, a high-speed CCD camera was used which is discussed in

section 4.3 in more details.

4.3 Digital Photographic Method for Visualization

A high-speed CCD camera was used to record the bubble nucleation on the heater surface at

subcooled flow conditions. Modified slider mechanism was used to allow for a 2-DOF-system.

This allowed the user to make small changes in the x- and y- directions. The lightening issue was

Chamber Inlet Dimensions (L x W) 1.09'' x 0.735''

Heater Rod Diameter 13.095mm

Hydraulic Diameter 0.4794in or 12.17mm

Inlet Area 4.146 x 102 mm

2

Length 0.5m

60

also important in the camera assembly. It should generate intense light and also the user be able

to move it. Also, the camera is adjusted to focus on an active nucleation site and for capturing

the very short bubble growth period and departure, the camera frame rate was set as high as 4000

frame per second (fps).

Figure 4-8: Camera Setup

In this study, for the best result of the flow visualization, a digital high-speed camera was used.

This was one of the main improvements of the current study over the previous ones. The

available camera has a flash-synchronized shutter speed of 1/8000 s, a total 2.74 million pixels

CCD (record pixels 128 x 512), and uses direct connection to a computer for the image recording.

After capturing the images, in order to correct the contrast and brightness of the images and also

obtaining the necessary data regarding the bubbles, image processing was performed by the use

of MatLAB and for assuring the accuracy of the result, it was checked by using Image-J software.

Figure 4-9: A sample bubble for image processing

The digital image process is performed by the use of MatLAB software. First, the appropriate

bubble images were selected as indicated by the figure above. The code allows the user to select

and crop the original image such that only the bubble in question is within the field of view.

61

Then the image was cropped in order to have the bubble as the main object in the image. A

sample of the cropped image is shown below. This cropped image undergoes a manual

thresholding process whereby the relative contrast between the bubble and the background is

adjusted. This is an important step since sufficient contrast between the edge of the bubble and

the background is required for the binarization process.

Figure 4-10: A sample of the cropped image

Before the thresholding process, the software automatically “tags” the top right and bottom left

corners of the cropped image by setting the values of the pixels of these two corners to be zero,

which for a grayscale image means they are the darkest possible colour. Once the cropped image

is selected, thresholding is performed where the image contrast is adjusted to enhance the

boundaries of the bubble for binarization purposes. A series of filters are used as a first step to

filter out noisy pixels and enhance object boundaries within the image. A Gaussian bandpass

filter was first used to filter out the noise pixels. Pixels with values greater than 125 (half way

between perfectly white and perfectly black) were replaced by white pixel to enhance the

ninarization step by removing background disturbance that may interfere with edge detection.

Please note that any bubble which is in focus was found to have edge pixel values much lower or

darker than 125 and thus, thus step would not alter the experimental data.

The method of Sobel was used to detect edges of all objects, which is identified based on the

gradient of the pixel values of the grayscale image. After completing the edge detection, the

output image would be fully binarized into black and white pixels only, with any objects (bubble

and debris/noise) outlined by white pixels as in the figure below. The MatLAB Sobel edge

detection method uses the Sobel approximation of the derivative to find he local maximum of the

pixel value transition to define edges and thus, highlights the importance of having good contrast

62

along the borders of the bubble during the threshold stage. A MatLAB bridge function is used to

bridge disconnected pixel by setting a zero valued pixel to 1 (black t white) if the pixel has two

neighboring non-zero pixel that are not connected to make sure that there is a complete trace of

the bubble boundry.

Figure 4-11: Binarized image of the sample bubble

Then, a series of steps are performed to further filter out noisy objects and to bridge disconnected

pixels at the object boundaries that may have been left out in the edge detection process. The

objects, defined as anything that is bound by an edge, is filled to white pixels.

Figure 4-12: Schematic of a bubble at the final stage of image processing

The size characteristic of every independent body is bound, and only the largest object (the

bubble of interest) is kept. Lastly, any kinks in the bubble boundaries are smoothened out to

create the image as Fig. 4-12. Using the above methods, the bubble 3-D diameter, bubble

centroid, bubble inclination, advancing, and receding angles amongst other properties are given

by the program along with the sequence of images shown above as verification of the quality of

the digital image process.

63

Figure 4-13: The sample bubble before filtering the noise

4.4 Errors and Uncertainty Analysis

There are two sources of errors in the image analysis listed as:

1) In terms of the image processing, the error that would occur is due to the thresholding

and edge detection process. Typically the maximum error one can expect may be up to 2

pixels around the circumference of the bubble (one pixel on each side). As a result, in

terms of the diameter and as an approximation, there may be a ~30-40micron error based

on the size of the each pixel (varies in every experiment).

2) The lift-off diameter is based on the Chu et al's paper. He approximates a 3-D bubble

diameter from a 2-D image. Based on sample data, there is a 0.01% to 2.94% error when

comparing a 3-D bubble diameter from a 3-D image to the 2-D approximation using the

equation he provided [59].

The uncertainties associated with the applied heat and mass fluxes were almost

and , respectively. Also the uncertainties for the pressure gauges and the thermocouples

were and , respectively.

Calibration of the flow meter was performed and its accuracy was given as . The

temperature of the fluid and the heater surface was measured by the use of four K-type

thermocouples placed on the chamber and underneath the heater surface. The pressure was also

measured at the test section by a single scale multi-purpose pressure gauge.

64

In order to have more accurate results, distilled water was used and it was passed through

purifier and demineralizer for around 24 hours before each series of tests for removing all the

impurities. The dissolved air was also removed by boiling the water in the storage tank for about

three to four hours. Once the test was started, and the steady state as well as the desire pressure

and the temperature were reached in the test section, the video recording of the bubble nucleation

was initiated and it last for about 10 seconds.

65

Chapter 5 Results and Discussion

66

Results and Discussion 5

In this chapter, characteristics of a typical vapour bubble in various subcooled boiling conditions

are discussed by using the high-speed imaging results, and the effect of the experimental

conditions such as the effect of subcooling, pressure and flow rate on the bubbles will be

investigated. Finally, simple correlations for the bubble lift-off diameter are presented and

compared with the experimental data.

5.1 Visualization and Image Analysis

In subcooled flow boiling process, bubbles nucleate in small cavities and/or pits on the surface of

the heater filled with vapour. These cavities are known as nucleation sites. Growth of bubbles is

strongly influenced by the temperature and velocity gradients. Typically, bubbles show a similar

behavior: bubbles nucleate on the cavities, grow, then slide for a short distance on the heater

surface and then detach from the surface to enter the subcooled flow region. After that, they

promptly condense. The bubbles sizes and their life-spans strongly depend on the subcooling,

surface superheat, mass flow rates and pressure. They are also a function of the cavity size and

the local surface temperature variations, as well as the surrounding bubbles (local flow

turbulence) [55].

Typical bubble behaviors from the nucleation to lift-off are shown in figures 5-1, 5-4, and 5-6 for

three different conditions. Fig. 5-1 shows the process of nucleation and bubble growth at 1atm

pressure, mass flux of 350 kg/m2s, heat flux of 124 kW/m

2 and subcooling of 4

oC. The nucleation

site is shown with a bold arrow at t = 0 ms. Once the bubble is formed, it grows and at some time

between t = 0.25 ms and t = 0.5 ms, the bubble leaves the nucleation site and therefore, departure

happens. The vertical solid line on the figure shows the nucleation site on all the pictures.

Although the bubble leaves its initial site, it still continues growing almost linearly until about t

= 2.5 ms. Note that the time intervals in the consecutive pictures are not the same. After this

point, the tip of the bubble gradually enters the subcooled region of the flow. Bubble starts to

condensate once it enters the subcooled region. The liquid surrounding a bubble is superheated

while the bubble is small. As soon as the bubble reaches a certain size, its tip enters the

subcooled region of the bulk liquid and the bubble starts to condense; thus the effective

67

superheat surrounding the bubble becomes less than the wall superheat. This effect can be seen

as the flatten top of the bubble. During the sliding time, vaporization takes place at the inner

surface of the bubble, while there may be condensation at the outer surface of the bubble. This

condition is met when the tip of the bubble is out of the superheated layer and enters the

boundaries of the subcooled bulk flow. Therefore, growth or condensation of the bubble is

governed by the overall effect of these two processes. After sliding for some distance on the

heater surface, the bubble reaches its lift-off size. At t = 7.5 ms, the bubble leaves the heater

surface and consequently, its diameter at this moment is recorded and identified as the lift-off

diameter. After the lift-off, the bubble enters the subcooled flow and therefore, shrinks. This

point is shown by the vertical dash line on the figure. The distance between the two vertical lines

(i.e. vertical dash and solid lines) shows the sliding distance of the bubble and can be used to

obtain the sliding velocity of the bubble. The rate of bubble collapse has a direct relationship

with the degree of subcooling of this region. Increasing the degree of subcooling (i.e. cooler

flow), results in a faster collapse rate for the bubble. In Fig. 5-1, the degree of subcooling is only

4oC and thus, the bubble shrinks less compared to the other condition shown in Fig. 5-4 which

has the degree of subcooling of 9oC.

Fig. 5-1 has the least pressure and degree of subcooling; subsequently it has the largest lift-off

diameter, while conditions in Fig. 5-4 provide the smallest diameter. The experimental test

section is horizontal; however, there is a small slope on the images. This slope is due to the

camera orientation with respect to the test section.

68

t= 0.0

ms

t=

0.25

ms

t= 0.5

ms

t=

0.75

ms

t= 2

ms

t= 2.5

ms

t=

3.25

ms

t= 4

ms

Nucleation

Departure

t= 4.75

ms

t= 5.25

ms

t= 5.5

ms

t= 6.0

ms

t= 6.75

ms

t= 7.0

ms

t= 7.5

ms

t= 8.0

ms

Lift-

Off

Flow direction from right to left

Figure 5-1: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1 atm, Mass

Flux: 350 kg/m2s, Heat Flux: 124 kW/m

2, Subcooling: 4

oC)

69

In Fig. 5-2 the temporal variation of the bubble volume and the equivalent spherical bubble

diameter, for the above flow conditions is shown. The bubble lifetime is divided into two parts of

growth and condensation. The condensation is further divided into two sub-parts: condensation

on the wall (while the bubble is still sliding on the heater surface) and condensation after lift-off.

As indicated by the figure, bubbles start to condense while they are still on the heater surface and

therefore, they reach their maximum size and then condensation happens. As a result, the bubble

maximum size and its lift-off size are different. This agrees with Tolubinsky and Kostanchuck

[66] and Farajisarir [44]. This is different than that of pool boiling, where the two sizes are the

same. The duration of the growth and condensation periods depend on the experimental

conditions. According to Akiyama the superheated layer thickness is small and the bubble spends

only a small fraction of its growth period in this layer (t <0.10 tm) [67]. The growth of the bubble

is more affected by micro/macro- layer evaporation, than by conduction through the superheated

layer [44]. After reaching the maximum size, evaporation from the bubble base is balanced with

condensation at the bubble top surface. After this moment, the condensation becomes dominant

while the bubble is still sliding on the heater surface and is in contact with it. The surface tension

as a result of temperature gradient across the flow is formed along the bubble interface and it is

the driving force for the bubble ejection from the wall [68]. Once the bubble detaches from the

heater surface, higher rate of condensation occurs since the bubble has lost its contact with the

heater surface and become farther from the superheated layer. It was observed that contrary to

void growth model assumptions that the OSV point coincided with bubble lift-off, ejection

occurred well before the point of OSV.

70

Figure 5-2: Growth and collapse curve for a typical bubble at Pressure: 1 atm, Mass Flux: 350 kg/m2s, Heat Flux:

124 kW/m2, Subcooling: 4

oC

The parallel and normal displacements of the bubble centroid are shown in the figure below.

These values are used to calculate the corresponding velocities. Each displacement has been

measured with respect to the bubble nucleation site. The parallel bubble velocity is defined as the

slope of the parallel displacement curve, while the normal velocity of the bubble is defined as the

slope of the normal displacement of the bubble centroid with respect to the heater surface. The

parallel velocity is constant throughout the growth and collapse process and has the same order

of magnitude of the mean flow velocity. This agrees well with Farajisarir results [44]. Please

note that the slip ratio, defined as the ratio of bubble parallel velocity to mean flow velocity,

depends only on the local conditions and not on the bubble size as reported by Akiyama and

Farajisarir. Farajisarir also found that the slip ratio ranged from 0.71-2.33 in his experiment,

while Akiyama reported values of 0.3-0.8 for the slip ratio.

0

1

2

3

4

5

6

7

8

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6 7 8 9 10 11 12

Vo

lum

e (m

m^

3)

3D

Dia

met

er (

mm

)

Time (ms)

Volume

Diamete

Growth

Region

Condensation

& Sliding

Condensation

& Lift-off

Lift-off occurs

at t = 5 ms

71

On the other hand, the bubble centroid has its maximum value of normal velocity at the region

after the lift-off. The bubble lift-off velocity is defined as the normal velocity of the bubble at the

moment of the lift-off and can be obtained by measuring the slope of the line through the points

past the dashed line. The lift-off velocity strongly depends on the subcooling condition. This is

more obvious at higher subcooling due to higher temperature gradient, as mentioned by

Farajisarir.

Figure 5-3: Normal and parallel displacement of the centroid of a typical bubble at Pressure: 1 atm, Mass Flux: 350

kg/m2s, Heat Flux: 124 kW/m

2, Subcooling: 4

oC

A sample bubble in the pressure of 1.5 atm, mass flux of 300 kg/m2s, heat flux of 124 kW/m

2, and

subcooling of 9oC is presented in Fig. 5-4. Again, nucleation takes place at t = 0 ms, but

departure happens between t = 0.5 ms and t = 0.75 ms. Due to a higher pressure inside the

chamber, and a higher degree of subcooling of the inlet flow, size of the bubble in this case, is

much smaller than the previous condition. The lift-off occurs at t = 2.75 ms, compared to t = 7.5

ms which was the lift-off moment for the conditions provided in Fig. 5-1. Sliding distance is

again reduced in this condition. All these variations are mainly due to the pressure difference in

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 1 2 3 4 5 6 7 8 9 10 11 12

Dis

pla

cem

ent

(mm

)

Time (ms)

Lp

Ln

Growth

Region

Condensation

& Lift-off

Condensation

& Sliding

72

two mentioned cases. Although they are slightly different in their mass fluxes and degrees of

subcooling, pressure plays the main role in determining the lift-off instant and diameter.

Furthermore, for better understanding of the advancing and receding contact angles (previously

shown in Fig. 3-8), the following table is presented to show these two angles at each consecutive

image of the bubble shown in Fig. 5-1:

Table 5-1: Advancing and Receding contact angles of the bubble shown in the Fig. 5-1

Time (ms) Advancing contact angle Receding contact angle Difference (θr – θa)

)t= 0.5 56 140 84

t= 0.75 58 138 80

t= 2.0 51 134 83

t= 2.5 47 134 87

t= 3.25 49 136 87

t= 4.0 45 140 95

t= 4.75 44 135 91

t= 5.25 47 141 94

t= 5.5 49 141 92

t= 6.0 51 145 94

t= 6.75 49 148 99

t= 7.0 44 138 94

t= 7.5 42 134 92

According to the table, the differences range from 80 to 99 degrees and at the moment of the lift-

off, the difference is 92 degrees. Additional investigations in this field are required for more

accurate results.

73

t= 0.0

ms

t= 0.25

ms

t= 0.5

ms

t= 0.75

ms

t= 1.0

ms

t= 1.25

ms

t= 1.5

ms

Nucleation

Departure

t= 1.75

ms

t= 2.0

ms

t= 2.25

ms

t= 2.5

ms

t= 2.75

ms

t= 3.0

ms

t= 3.5

ms

Lift-Off

Figure 5-4: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1.5 atm,

Mass Flux: 300 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 9oC)

Fig. 5-5 shows the growth of the bubble in the flow conditions of the Fig. 5-4. In this figure, a

rough estimate of the superheated layer close to the heater surface and the subcooled liquid flow

on top of that, are presented with red and blue colors, respectively. The gradient change in the

colors shows the temperature profile in a normal direction to the flow and the heater orientation.

74

In this figure, the consecutive images from Fig. 5-4 are placed in a row to visually show the

growth of the bubble in the superheated layer. The calculated heater surface temperature as well

as the water temperature is shown at the bottom and the top of the figure. In this work, only the

subcooled temperature was measured and the surface temperature was calculated using the Liu

and Winterton correlation [21]. The subcooled flow near the heater surface induces a quasi-

steady drag force on the bubble. Therefore, bubble centre line does not stay vertical to the

surface while the bubble slides and the bubble is inclined in the flow direction with some angle.

According to the figure shown below, the bubble attempts to straighten itself such that this angle,

i.e. the inclination angle, becomes zero. This occurs at the moment of lift-off, where the angle

approaches zero. One good explanation for this event is that the quasi-steady drag force becomes

negligible as a result of almost zero difference between the bubble and the surrounding liquid

velocities.

Figure 5-5: Bubble growth in superheat layer (same flow conditions as those of the Fig. 5-4)

The flow conditions of the third case which is shown in Fig. 5-6 are as follows: pressure: 1 atm,

mass flux: 300 kg/m2s, Heat Flux: 124 kW/m

2, Subcooling: 9

oC. Its main difference with the first

condition shown in Fig. 5-1 is their degrees of subcooling, i.e. 9 degrees versus 4 degrees (there

is a slight difference in their mass fluxes as well). Also, comparing this case with the second case

shows that the pressure is at 1 atm instead of 1.5 atm. Departure was seen at 0.5 ms < t < 0.75

ms, while the lift-off occurs at t = 5.5 ms. By comparing all these three cases, one can find that if

a bubble is attached to the wall for a longer time, it becomes larger. This is mainly a function of

the pressure and the degree of subcooling. To investigate how all these features affect the bubble,

we need to analyze the applied forces on a bubble, which will be discussed in more detail later.

Surface Temp.: 124 degree C

Liquid Temp.: 102 degree C

75

t= 0.0 ms

t= 0.25 ms

t= 0.5 ms

t= 0.75 ms

t= 1.25 ms

t= 1.5 ms

t= 2.0 ms

t= 2.5 ms

t= 3.0 ms

Nucleation

Departure

t= 3.5 ms

t= 4.0 ms

t= 4.5 ms

t= 4.75 ms

t= 5.0 ms

t= 5.25 ms

t= 5.5 ms

t= 5.75 ms

t= 6.0 ms

Lift-off

Figure 5-6: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1.0 atm,

Mass Flux: 300 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 9oC).

76

The experimental results have revealed that the nucleation, departure, and liftoff steps depend on

the operating conditions. In some cases, the bubble does not depart and the nucleated bubble

grows at the nucleation site until it lifts off. In addition, a bubble may only depart from the

nucleation site and slide on the surface without lift-off. We will discuss these phenomena more

by providing some graphic examples.

In Figures 5-1 to 5-6, we had shown and discussed the normal behavior of a bubble in subcooled

liquid flow. In these cases, according to the experimental conditions, such as the inlet

temperature of the water, pressure, and mass flux, the bubble can have various sizes and

departure/ lift-off times. Furthermore, the experimental conditions influence the rate of bubble

condensation after its lift-off.

In another scenario, which is shown in Fig. 5-7, a bubble remains close to the wall after its lift-

off and in some cases bounces back and reattaches to the wall. A good explanation for that is the

existence of boundary layers close to the heated wall and velocity profile of the flow in the

chamber. This makes a lower pressure region close to the wall and forces the bubble to reattach

to the wall. In the presented case, the bubble lifts off at t= 2.0 ms after the first shown image and

then, comes back to the heater surface at t= 4.25 ms. During this time, i.e. 4.25-2.0= 2.25 ms,

during which the bubble has no contact with the heater, it shrinks due to the existence of the

subcooled liquid around it. The bubble again leaves the surface at t= 6.75 ms, and will repeat this

process for a few times before it exits the test chamber. This figure corresponds to the following

condition: inside pressure of 2 atm, mass flux of 350 kg/m2s, heat flux of 124 kW/m

2, and bulk

water temperature of 104oC, i.e. subcooling of 16

oC.

77

t= 0.0

ms

t= 1.0

ms

t= 1.5

ms

t= 2.0

ms

t= 2.5

ms

t= 3.0

ms

t= 3.5

ms

t= 4.25

ms

Lift-off

Re-

attachment

t= 4.75

ms

t= 5.0

ms

t= 5.5

ms

t= 6.0

ms

t= 6.5

ms

t= 6.75

ms

t= 7.25

ms

t= 8.0

ms

Lift-off

Figure 5-7: Consecutive images of the Bouncing phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass

Flux: 350 kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 16oC)

Fig. 5-8 shows a high subcooling case at high pressure conditions. In this case, bubbles never

reach the required lift-off size and therefore, just slide along the wall and maintain a relatively

constant size. One reason for this phenomenon can be the asymmetrical expansion of the bubble

due to the wall existence. This induces an unsteady drag force (also called the growth force) in

78

the direction normal to the wall and retards the detachment of the bubble and thus, a bubble has

difficulties to detach from the wall due to the significant effect of the growth force.

5.1.1 Coalescence

One of the main phenomena in subcooled boiling is the bubble coalescence, which plays an

essential role in forming the noticeable void fraction in a channel and causes large vapor clot

formation and sometimes, small dry area formation. The bubble coalescence occurs in two ways

[69]: 1) coalescence among the discrete bubbles located at neighboring nucleate sites; 2) growing

bubbles merge at their nucleation sites into larger flowing bubbles. Both of these were observed

in the current work. Bonjour et al. summarized the coalescence phenomena in two-phase flow

t= 0.0 ms

t= 0.5 ms

t= 1.0 ms

t= 1.5 ms

t= 2.0 ms

t= 2.5 ms

t= 3.0 ms

t= 3.5 ms

t= 4.0 ms

t= 4.5 ms

t= 5.0 ms

t= 5.5 ms

Figure 5-8: Consecutive images of the Sliding phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 300

kg/m2s, Heat Flux: 124 kW/m2, Subcooling: 26oC)

79

into three types [70]: 1) Coalescence far away from the heated wall, 2) Coalescence between

consecutive bubbles near the wall, and 3) Coalescence between adjacent bubbles near the wall.

In Bang’s work, the coalescence between adjacent bubbles mostly causes the agglomeration of

vapor remnants associated with the vaporization of interleaved liquid layer and then the

coalesced bubbles act and separate from the surface similar to the discrete bubbles. In Fig. 5-9,

Bang showed this phenomenon in more details for both pool and subcooled flow boiling:

Figure 5-9: Schematic of the bubble Coalescence in Pool and Flow Boiling [69]

80

Video recordings were made of the two-phase flow field in the channel by the use of high-speed-

camera. For more understanding of the phenomenon some sample cases are shown below:

t= 0.0 ms

t= 0.25

ms

t= 0.5 ms

t= 0.75

ms

t= 1.0 ms

t= 1.25

ms

t= 1.5 ms

t= 2.0 ms

Coalescence

Lift-off

t= 2.5 ms

t= 2.75

ms

t= 3.0 ms

t= 3.25

ms

t= 3.75

ms

t= 4.25

ms

t= 4.5 ms

Figure 5-10: Consecutive images of the Coalescence phenomenon in subcooled flow boiling (Pressure: 2.5 atm,


81

t= 0.0

ms

t= 0.5

ms

t= 1.0

ms

t= 1.25

ms

t= 1.5

ms

t= 2.0

ms

t= 2.25

ms

t= 2.5

ms

Coalescence

t=

2.75

ms

t= 3.0

ms

t=

3.25

ms

t= 3.5

ms

t=

3.75

ms

t=

4.25

ms

t= 4.5

ms

t= 5.0

ms

Lift-off

Figure 5-11: Consecutive images of the Coalescence phenomenon in subcooled flow boiling (Pressure: 2 atm,


82

As indicated by the figures above, bubbles grew on the heater surface and coalesced right before

detaching the surface. After detaching, due to the lower bulk temperature than the saturated

temperature, bubbles shrink and disappeared. The experimental data were analyzed to determine

the bubble growth rates, bubble departure diameter, bubble lift-off diameter, and bubble

departure velocities. These results will be discussed in more details in the following sections.

5.2 Experimental Analysis

5.2.1 Balance of forces acting on a bubble at the departure

A bubble will leave its nucleation site once the sum of the forces parallel to the flow direction is

equal to zero:

∑

where,

is the net force acting on a bubble along the x-direction, is the surface tension force

along the x-direction, is the unsteady drag force, and is the quasi-steady force in the

flow direction.

These forces are written as follows [39]:

[ ( )

( ) ( )] [

(

) ]

( )

where,

is the bubble radius and and are its first and second derivatives with respect to time.

The bubble radius is a function of time and the Jakob number, and thus, can be written in terms

of:

√ √

√ √

√ √

where,

b is a constant and it is suggested to be 1.73 by Zeng et al. (1993); αf is the thermal diffusivity

defined as with Cpf being the specific heat of liquid at constant pressure (J/kg.K),

83

ρf being the liquid density (kg/m3), and being the thermal conductivity (W/m.K). Ja is the

Jakob number defined as:

( )

( )

where,

ΔTsat is the wall superheat (K), hfg is the latent heat at measured at the operating pressure (kJ/kg),

Tw is the wall temperature (K), and Tsat is the saturation temperature (K). σ is the surface

tension coefficient (N/m); is the bubble contact diameter and is given as ,

by Cho et al (2011), where is the contact angle.

The advancing and receding contact angles, i.e. θa and θr, are obtained from:

and , or .

where,

is reported by Klausner as =4.5o, while Bibeau [71] , and Winterton [72] evaluated as

2.5oand 10

o, respectively. In literature, the value reported by Klausner was mostly used [37]; thus,

in this report, is assumed to be 4.5o, as well.

Rewrite the force balance as:

[ (

) ( )] [

] ( )

By defining:

(

) ( )

[ ( )] [

]

[ ( ) ( )( )]

[

]

Zeng et al. (1993) provided the following relations for the forces:

84

(1)

(2)

The contact angle and the departure diameter can be determined from the above equations. The

solution to the above equations is provided in Appendix-A.

5.2.2 Balance of forces acting on a bubble at the lift-off

At the instant of the bubble lift-off from the heater surface, the net forces normal to the flow

direction acting on the growing bubble are just balanced. The instant of the bubble lift-off was

determined as the moment that the bubble had the least contact with the heated surface. It should

be noted that in the subcooled boiling cases, the center of the bubble continuously moves away

from the nucleation site. In the pool boiling systems, a bubble departure generally means the

instant that a bubble is detached from a heated surface, and the bubble grows from the time of

nucleation to the time of departure due to the evaporation. Therefore, the total heat transfer to the

bubble can be determined based on knowing the local heat flux and the time of lift-off. On the

other hand, a departure in forced convective boiling corresponds to the instant that the bubble

leaves the nucleation site, according to Klausner et al.’s definition [37]. However, in many cases,

a bubble can slide continuously away from the nucleation site while it is actively growing due to

the evaporation heat transfer. Therefore, it is more difficult to determine the total heat transfer to

the bubble in the forced convective boiling systems.

Fig. 5-12 shows the force balance in the y-direction and at the moment of the bubble’s lift-off.

Due to the insignificant contact area between the bubble and the heater surface, the bubble

surface tension, contact pressure force and hydrodynamic force are almost zero and can be

neglected. In addition to these assumptions, the bubble inclination angle is almost zero, and

therefore, the growth force has only one component in y-direction. Thus the only forces acting on

the bubble are the growth, buoyancy and shear lift forces. The force balance in y-direction:

∑

85

Fh, Fcp = 0

Fsl

Fdu

Fsy = 0

X

Y

Fb

Fh, Fcp = 0

Fsl

Fdu

Fsy = 0

X

Y

Fb

∑

Figure 5-12: Force balance of a vapour bubble at lift-off

By Substituting the expressions of the growth force, shear lift and buoyancy forces into the

above equation:

(

)

(

) ( )

Zeng observed that for predicting the bubble lift-off diameter, the shear lift force can be omitted,

since the bubble sliding velocity at the moment of the lift-off is almost the same as the

surrounding liquid and its shape is almost spherical (having close to zero contact angle) [39].

According to these assumptions, the following correlation for the bubble lift-off diameter was

obtained:

√(

)(

( ))

eq. 5-1

The growth rate constant, b, was obtained from the Zuber’s model [15]:

√ √

eq. 5-2

86

One can see the dependence of the bubble growth on the temperature of the surrounding liquid in

that model. Various values have been offered for b for different conditions and assemblies. As an

example Zeng suggested using a value of 1.73 comparing to other values ranging from 0.24 to

3.5. In the current work different values for each pressure were tried to get the minimum error

and thus, a model for b as a function of pressure is suggested. This model was obtained by curve

fitting the experimental data. Moreover, some more experimental cases were carried out without

curve fitting in order to check the model’s prediction ability for the new data set. Generally,

bubbles have high rates of growth at the early stages of their nucleation, but this reduces in time.

This shows that b does not remain constant as the pressure changes:

√

eq. 5-3

where,

bo is found to be constant value of -0.3037, and p is the experimental pressure in atm.

As the model shows, the bubble lift-off diameter was evaluated in terms of heat flux, mass flux,

and degree of subcooling. According to the model, dependence of the bubble lift-off diameter on

the Jakob number is obvious. In this model Jae is the effective Jakob number which is:

( )

eq. 5-4

where,

( ), and is the suppression factor and equals to (by Situ et al. (2005)):

where

ReTP is the two-phase Reynolds number calculated by setting vapor quality as zero, ( ).

According to the short length of the test section and its small heater power, the estimation of the

point of net vapor generation does not considerably affect the calculation of the wall temperature.

87

where,

( )

To calculate the Jakob number, we need to either measure the heater surface temperature or

estimate it. Since in this work, the surface temperature was not measured, Liu and Winterton

method was used to estimate the surface temperature [21]:

[ √( (

)( ))]

eq. 5-5

With

( )

is the bulk liquid temperature, is the heater surface temperature, and is the water

saturated temperature. The other parameters are:

[ (

)]

( )

( )

( )

Upon analyzing the recorded images for the bubble behaviors, it was found that there are

significant differences in bubble sizes and lifetimes for bubbles in the same experimental

conditions. There are two main causes for such variations: (1) existing cavities on the surface

have different sizes, which result in various bubble sizes, and/or (2) bubbles are experiencing

varying local temporal and velocity fields. Prodanovic mentioned the later effects as the

dominant in creating scatter in experimental data [55]. In this study, bubbles whose detachment

88

diameters and initial growth rates are closest to averages for a given set of experimental

conditions are chosen. Also surface roughness plays an important role in initiating the nucleation

and bubble diameter. In this study, the average surface roughness was around 0.12 , since the

maximum roughness was around 0.6 .

In each experimental case, different values for the bubble lift-off diameter have been measured.

Therefore, in order to report one lift-off diameter for each case, an average and a standard

deviations over the entire measured lift-off diameter in each case have been calculated. In the

figure below, all the case for 1 atm along with their corresponding standard deviations are shown.

According to the figure, the maximum standard deviation was seen in Case 9 which was 0.1423

mm, while the least standard deviation was 0.0853 mm for the Case 2.

Figure 5-13: Bubble lift-off diameters vs. Subcooling for all the cases at 1 atm and their corresponding standard

deviations

Generally, experiments have revealed that bubble behavior within a given range of experimental

conditions, such as mass and heat fluxes, cannot be represented by a single model; although they

behave in a similar manner within a region bounded by the ONB and OSV [55]. One weakness

of the methods adopted by the method above is the assumption of the rigidity of the bubble from

the force balance approach, which neglects changes in surface tension forces in directions along

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35

Bu

bb

le D

iam

eter

, m

m

Subcooling, Deg. C

Mass Flux= 300 kg/s.m2



89

and normal to the flow. Kandlikar and Stumm alleviated this issue by using a control volume

approach on two halves of a bubble [73]. However, their model neglected inertial forces and thus

only accurate for low flow rate conditions.

Bubble lift-off diameter was measured from all the experimental tests. The lift-off diameter was

averaged over all the nucleation sites. In this study, it was found that our experimental conditions

covered the late stage of the partial boiling (PB) region and the early stage of the fully developed

boiling (FDB) region as well as a few cases close to the FDB- OSV border depending on the

flow and heat flux conditions. In this study, the wall superheat at the onset of nucleate boiling

(ONB) was calculated using Hsu correlation [31]. Also, the wall superheat at the FDB was

obtained by the use of Thom et al. method [34]. Saha and Zuber correlation was used in order to

determine the subcooling at the point of onset of significant void (OSV) [36]. One reason for

using an average lift-off diameter among all the nucleation sites in each experimental condition

is that the bubble data such as lift-off diameter and frequency might be different from one cavity

to another because of the differences in the microscopic structure of each cavity. Using the

proposed model for the lift-off diameter and the suggested correlation by Liu and Winterton for

calculating the wall superheat, the predicted bubble lift-off diameters were calculated and are

presented in table 5-1.

90

Table 5-2: Data bank

Label Pressure

(atm)

Mass flux

(kg/m^2.s)

Heat flux

(kW/m^2)

Local Subcooling

(deg. C)

No. of

sites

Mean lift-off

Dia (mm)

No. of

bubbles

Subcooling

Regime Jakob No.

Predicted Dia.

(mm)

Case 1 1 300 124 32 3 0.57 9 PB 30.95 0.85080086

Case 2 1 300 124 28 3 0.68 13 PB 32.78 0.934978521

Case 3 1 300 124 20 9 0.94 17 FDB 36.49 1.083776412

Case 4 1 300 124 11 4 1.5 15 FDB 39.56 1.210846785

Case 5 1 300 124 5 6 2.16 21 FDB-OSV 40.83 1.264810869

Case 6 1 350 124 28 3 0.71 12 PB 30.53 0.844914038

Case 7 1 350 124 17 4 0.93 18 FDB 36.59 1.081787668

Case 8 1 350 124 6 5 2.02 28 FDB-OSV 40.13 1.22774171

Case 9 1 350 124 4 5 2.31 24 OSV 40.53 1.241448446

Case 10 1 400 124 18 7 0.9 16 PB 36.13 1.063528267

Case 11 1 400 124 11 5 1.25 22 FDB 38.09 1.1371524

Case 12 1 400 124 9 7 1.55 31 FDB 38.75 1.16426567

Case 13 1.5 300 124 25 8 0.67 12 PB 21.42 0.733706966

Case 14 1.5 300 124 24 6 0.68 15 PB 21.78 0.750648297

Case 15 1.5 300 124 9 7 1.16 24 FDB 25.61 0.939619151

Case 16 1.5 300 124 4 6 1.79 35 FDB-OSV 26.29 0.973466614

Case 17 1.5 350 124 15 5 0.89 16 PB 24.37 0.878204133

Case 18 1.5 350 124 24 3 0.66 20 PB 21.65 0.748382913

Case 19 1.5 400 124 14 6 0.89 28 PB 24.61 0.889915732

Case 20 1.5 400 124 8 4 1.02 11 FDB 25.77 0.947708405

91

Label Pressure

(atm)

Mass flux

(kg/m^2.s)

Heat flux

(kW/m^2)

Local Subcooling

(deg. C)

No. of

sites

Mean lift-off

Dia (mm)

No. of

bubbles

Subcooling

Regime Jakob No.

Predicted Dia.

(mm)

Case 21 2 300 124 19 8 0.53 25 PB 16.7 0.573366384

Case 22 2 300 124 14 5 0.62 26 PB 17.7 0.619970516

Case 23 2 300 124 6 5 0.96 32 FDB-OSV 18.8 0.672565984

Case 24 2 300 124 2 9 1.11 41 OSV 19.09 0.686963047

Case 25 2 350 124 16 4 0.52 17 PB 16.87 0.576650616

Case 26 2 350 124 14 5 0.53 34 PB 17.28 0.596235604

Case 27 2 350 124 1 3 1.09 26 OSV 18.99 0.678289517

Case 28 2 400 124 20 6 0.49 14 PB 15.73 0.525971296

Case 29 2 400 124 14 3 0.62 33 PB 17.3 0.597516496

Case 30 2 400 124 8 7 0.84 17 PB 18.34 0.645997332

Case 31 2 400 124 1 6 1.06 21 OSV 19.02 0.67878153

Case 32 2.5 300 124 14 5 0.45 26 PB 13.34 0.494892803

Case 33 2.5 300 124 11 4 0.52 15 PB 13.84 0.519955185

Case 34 2.5 300 124 8 7 0.68 29 FDB 14.41 0.551998269

Case 35 2.5 300 124 5 4 0.9 20 FDB-OSV 12.74 0.612539887

Case 36 2.5 350 124 7 6 0.91 16 PB 14.34 0.54573634

Case 37 2.5 400 124 15 3 0.39 10 PB 12.76 0.463091916

Case 38 3 300 124 17 4 0.33 15 PB 10.69 0.414448101

Case 39 3 300 124 10 3 0.47 12 FDB 11.47 0.454121120

Case 40 3 300 124 8 7 0.57 17 FDB 11.63 0.462258710

Case 41 3 350 124 16 4 0.32 14 PB 10.54 0.404824021

Case 42 3 350 124 12 5 0.41 10 FDB 11.10 0.433719211

Case 43 3 350 124 6 5 0.59 21 FDB 11.67 0.4625945245

92

Label Pressure

(atm)

Mass flux

(kg/m^2.s)

Heat flux

(kW/m^2)

Local Subcooling

(deg. C)

No. of

sites

Mean lift-off

Dia (mm)

No. of

bubbles

Subcooling

Regime Jakob No.

Predicted Dia.

(mm)

Case 44 3 400 124 13 3 0.39 16 FDB 10.71 0.411158734

93

The experimentally determined bubble lift-off diameters are plotted versus the mass flux, the

operating pressure and the degree of subcooling. Fig. 5-14 shows the effect of the liquid

pressure on the bubble lift-off diameter. The lift-off diameter reduces by increasing the fluid

pressure at all the mass fluxes and the subcooling temperatures. The same result was

obtained by previous researchers (e.g. Tolubinsky and Kostanchuk [66]; Prodanovic [55]).

However, the present study in contrary to that of Tolubinsky’s work, shows that the bubble

lifetime and sliding time decrease with an increase in pressure (similar to Prodanovic work).

The bubble sizes are smaller at higher pressures, and bubbles collapse faster at higher

subcooling temperatures. Furthermore, Yuan et al. [74] reported that the bubble growth rate

at 0.1 MPa was about 10 times of that at 1.0 MPa in their experiments.

Figure 5-14: Effect of the liquid pressure on the bubble lift-off diameter (heat flux: 124 kW/m2).

Next, the effect of the liquid mass flux on the bubble lift-off diameter was investigated in

various conditions. The results show that the bubble lift-off diameter decreases with

increasing the mass fluxes. This is shown in Fig. 5-15. Effect of the liquid mass flux on the

bubble sizes and lifetimes is more evident in lower heat fluxes. Since in this study, the

available heat flux was relatively low, the effect of the mass flux is more pronounced. This

effect becomes less important as the OSV is neared, which is in agreement with Prodanovic’s

study [55]. It is also observed that the bubble population increases with decreasing the mass

flux, particularly at low heat fluxes where the single-phase forced convection plays an

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 1 2 3 4

Bu

bb

le D

iam

eter

, m

m

Pressure, atm

"G=300 kg/s.m2, Subcooling=8-11 deg.

C"

"G=300 kg/s.m2, Subcooling=17-24

deg. C"

G=400 kg/s.m2, Subcooling=8-9 deg. C

94

important role. Lower liquid mass flux means lower convection heat flux coefficients. This

causes less heat removal from the surface and thus, causes higher local surface temperatures

that increases the number of active nucleation sites (i.e. more bubbles can nucleate on the

surface). On the other hand, by increasing the mass flux in the chamber, the wall superheat is

lowered due to more efficient heat transfer, which results in decreasing the bubble population.

Also, the higher mass flux, which means a higher flow velocity, causes more bubbles to

separate from the wall.

Figure 5-15: Effect of the mass flux on the bubble lift-off diameter (heat flux: 124 kW/m2).

Fig. 5-16 shows the effect of the liquid subcooling on the bubble lift-off diameter. The

bubble lift-off diameter decreases by increasing the subcooling and the mass flux. Our results

are in agreement with those of Okawa et al. who reported that bubbles slid a longer distances

for lower subcooling temperatures and higher mass fluxes [56]. Generally, the bubble sizes

increase with decreasing the subcooling temperature at a fixed flow rate, heat flux and

pressure. At low subcooling temperatures, the lower temperature gradients in the liquid

surrounding a bubble lowers the condensation rates and allows the bubble to grow more

(Zeitoun and Shoukri [75]; Tolubinsky and Kostanchuk [66]; Farajisarir [44]; Kandlikar

[73]). In addition to the bubble size, lower subcooling temperature reduces the bubble

lifetimes.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

250 300 350 400 450

Bu

bb

le D

iam

eter

, m

m

Mass Flux, kg/s.m2

p=1 atm, subcooling=17-20 Deg.

C

p=1.5 atm, subcooling=24 Deg. C


C

p=2.5 atm, subcooling=14-15

Deg. C


C

95

The results also show that there are substantial variations in the bubble lift-off diameter. This

was the case even for the neighboring sites considering that the heat flux was almost the

same for all such nucleation sites, and even for cases in which the liquid subcooling between

the inlet and outlet was 3-4oC. This implies that although most of the models and correlations

assume that the bubble lift-off diameter and nucleation frequency are only a function of

external mass flow and the heat flux, bubble characteristics, such as bubble diameter and

frequency, depend on the microstructure of the nucleation cavities. Therefore, an adequate

number of nucleation sites should be considered to obtain reliable results. Also the bubble

lift-off diameter and the frequency compete with each other in removing the heat from the

heater wall which results in higher than average value for the bubble lift-off diameter and

lower the average value for the nucleation frequency, and vice versa. The heat flux for all test

cases was kept constant at 124 kW/m2.

The results have also shown that the contact angle of the bubble with the heater surface

increased with increasing flow velocities. This happens because at higher velocities, the

quasi-steady drag force increases and results in an increase in the advancing contact angle.

Figure 5-16: Effect of the fluid subcooling on the bubble lift-off diameter (heat flux: 124 kW/m2, mass flux:

300 kg/m2.s).

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35

Bu

bb

le D

iam

eter

, m

m

Subcooling, Deg. C

p=1 atm

p=1.5 atm

p=2 atm

p=2.5 atm

p=3 atm

96

5.2.3 Comparison between the experimental and predicted results

In this section, the experimentally obtained bubble lift-off diameters are compared with those

predicted by the developed model. Fig. 5-17 compares the experimental and predicted

bubble lift-off diameters at two different conditions versus the chamber pressure. The

predictions are in good agreements with the experimentally determined values. The

conditions for the data presented in this figure correspond to the conditions selected from Fig.

5-14 (only two conditions were selected).

Fig. 5-18 compares the experimental and predicted bubble lift off diameters for various mass

fluxes. Two of the conditions provided in Fig. 5-15 are selected for this comparison. The

predicted results match the experimental data with good accuracy.

In Fig. 5-19, trend in subcooling was investigated for both the experimental and predicted

bubble lift-off diameters. It is evident that they both decrease with higher subcoolings but the

values of the diameters as well as the rate of decreasing are different.

97

a) Mass flux= 300 kg/m2.s, and Subcooling= 8-11

oC

b) Mass flux= 300 kg/m2.s, Subcooling= 17-24

oC

Figure 5-17: Comparison of the experimental data with the predicted data at different pressures and for

different flow conditions.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4

Bu

bb

le D

iam

eter

, m

m

Pressure, atm

Experimental data for G=300

kg/s.m2, Subcooling=8-11 deg.

C

Predicted data for G=300


C

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

Bu

bb

le D

iam

eter

, m

m

Pressure, atm

Experimental data for G=300


C

Predicted data for G=300


C

98

a) Data for pressure= 1 atm, subcooling= 17-20oC

b) Data for pressure= 2 atm, subcooling= 16-20oC

Figure 5-18: Comparison of the experimental data versus the predicted data in different conditions (mass flux)

0

0.2

0.4

0.6

0.8

1

1.2

250 300 350 400 450

Bu

bb

le D

iam

eter

, m

m

Mass Flux, kg/s.m2

Experimental data for p=1 atm,

subcooling=17-20 Deg. C

Predicted data for p=1 atm,


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

250 300 350 400 450

Bu

bb

le D

iam

eter

, m

m

Mass Flux, kg/s.m2

Experimental data for p=2 atm,


Predicted data for p=2 atm,


99

a) Data for pressure= 1 atm, mass flux= 300 kg/m2.s

b) Data for pressure= 2.5 atm, mass flux= 300 kg/m2.s

Figure 5-19: Comparison of the experimental data versus the predicted data in different conditions (subcooling)

The general trend of the predicted and experimental data appears similar although the error

does increase as discussed above with increasing the pressure. With an increase in subcooling

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35

Bu

bb

le D

iam

eter

, m

m

Subcooling, Deg. C

Experimental data for p=1 atm

Predicted data for p=1.0 atm

0

0.2

0.4

0.6

0.8

1

0 5 10 15

Bu

bb

le D

iam

eter

, m

m

Subcooling, Deg. C

Experimental data for p=2.5 atm

Predicted data for p=2.5 atm

100

margin, the bubble lift-off diameter decreases for a constant pressure. This is likely due to the

fact that at higher subcooling, the effective wall superheat decreases due to the higher forced

convection effect with lower bulk liquid temperature. In addition, both experimental and

predicted trends show that increasing the pressure will decrease the bubble lift-off diameter

for the same subcooling.

In this work, the effect of heat flux on the bubble diameter was not investigated. To give

some idea regarding the heat flux effect, Prodanovic finding is presented [55]. He has

reported that increasing the mass flux will decrease the bubble diameter; however, when

OSV was neared, the effect of mass flux became less pronounced. He also concluded that

increasing the heat flux would decrease the maximum bubble diameter. This was observed in

low heat fluxes while in higher heat fluxes, the bubble diameter remained almost constant.

In the present study, a database for the bubble lift-off diameter was built by integrating our

experimental data. Then, the predictive capability of the proposed model was evaluated

against the database. As mentioned before, two series of experiments have been conducted in

this research work. By completion the first set, all the bubble lift-off diameters were

measured and a model by curve fitting method was proposed. Fig. 5-20 shows the errors

associated with this set. Then, the second set of experiments has been carried out in order to

compare the experimental results with the predicted bubble diameters from the proposed

model. The errors for data points of this set are also shown in Fig. 5-21. Finally, for the

purpose of error analysis over the whole work, the proposed model is compared with all the

data points and it is presented in Fig. 5-22. The proposed model provides reasonable

agreement with our experimental work by having average errors of 21.07%, 16.81% and

19.91% for each figure, respectively.

The cases in the first set of experiments are as follows:

1-6, 8-11, 13-20, 22-26, 29-37 total of 32 cases

Rest of the cases has been done for the second set of experiment.

101

The absolute error for each experiment is defined as:

| |

eq. 5-6

Also, the weighted error for a specific case based on the experimental data available is:

∑

eq. 5-7

where,

n is the number of the bubbles used to find the experimental lift off diameter, and i is the

number of the experiments (from the first to the Nth

experiment).

The weighted average error becomes:

∑(

∑

)

eq. 5-8

102

Figure 5-20: Prediction results of the proposed model against the first set of the experimental lift-off diameter

(average error: 21.07%)

Figure 5-21: Prediction results of the proposed model against the second set of the experimental lift-off

diameter (average error: 16.81%)

0.01

0.1

1

10

0.01 0.1 1 10

Pre

dic

ted

Lif

t-o

ff D

iam

eter

, m

m

Measured Lift-off Diameter, mm

0.01

0.1

1

10

0.01 0.1 1 10

Pre

dic

ted

Lif

t-o

ff D

iam

eter

, m

m


+50%

-50%

+50%

-50%

103

Figure 5-22: Prediction results of the proposed model against the entire experimental lift-off diameter (average

error: 19.91%)

There are several sources of error in our experiments. These are errors associated with the

measurement methods and apparatus, and image processing. In addition, the model has not

considered all the physical process. For instance, the shear forces are neglected and the

contact angle at the time of lift off is assumed to be zero. Although the relative velocities of

each bubble in the direction of the flow were measured, the standard deviation was high.

Therefore, the shear lift-coefficient could not be accurately determined. In addition, the

definition of the relative bubble velocity with respect to the bubble centroid may cause errors

when bubbles deform at the lift-off. Future works can include accurately characterizing the

bubble relative velocity. In the current model, b as a function of pressure was used to

provide the lowest average error of %19.91 (average weighted error of %21.53).

The present model is also compared with several commonly reported used models, as shown

in Fig. 5-23. The present model can be considered to be one of the better models for the

prediction of the bubble lift off diameter. Five models in addition to our current model are

shown in this figure. The average errors associated with Prodanovic model [55], Unal model

0.01

0.1

1

10

0.01 0.1 1 10

Pre

dic

ted

Lif

t-o

ff D

iam

eter

, m

m


+50%

-50%

104

[53], Zeng model [39], Situ model [18], and Basu model [50] are 27.8%, 44.1%, 78.2%,

53.6%, and 48.9%, respectively.

Zeng model shows the highest average error and generally overpredicts the experimental

result. This is mainly due to the use of constant value for b. He did not propose an explicit

model but the results shown are based on his proposed force balance and growth rate

constant. This model was developed for horizontal flows but does not seem to be reliable.

The second highest error was for the Situ’s model. This model was developed for vertical

chambers and the main reason for this error has come from their assumption that the bubble

sliding velocity is half of the local liquid velocity. This assumption did not coincide with

other researchers’ observations. Basu and Unal models also show high errors which is due to

the fact that their models were developed for vertical and not horizontal flows. In addition,

Unal’s model predicts the maximum bubble diameter and not the lift-off diameter. The best

result was seen in Prodanovic with only 27.8% of error which is still almost 8% higher than

our error. These comparisons clearly prove that vertical models should not be used for

horizontal flows and in order to achieve better results, more works have to be performed for

horizontal flow conditions.

105

Figure 5-23: Prediction results of five model against the present lift-off diameter data

0.01

0.1

1

10

0.01 0.1 1 10

Pre

dic

ted

Lif

t-o

ff D

iam

eter

, m

m


Current Model

Prodanovic Model

Unal Model

Zeng Model

Situ Model

Basu Model

+50%

-50%

106

Chapter 6 Summary and Conclusions

107

Summary and Conclusions 6

An experimental study is performed on the bubble nucleation on a heated zirconia rod

horizontally located in a subcooled flow channel. The project investigates two-phase

subcooled flow boiling inside a rectangular horizontal channel with heat supplied by an

electrically heated rod while vapour bubbles were created on a horizontal wall in a uniform

flow. The purpose of this investigation was to find a preliminary empirical relationship for

bubble lift-off diameter, and growth rate constant under different experimental conditions.

These experiments have been designed in order to validate the predictions, and to extend the

predictive capacity for the conditions that actually occur in practice. Image recordings were

analyzed and used to get the bubble geometrical parameters, which were needed to calculate

forces acting on the bubble. Force analysis is performed to estimate force magnitude and to

apply it to the suggested model in order to compare predicted and estimated lift-off diameters.

Agreement between these two is necessary for the model validation. A dedicated

experimental set-up has been designed so that the flow that approaches the bubble is

practically uniform. A high-speed camera has been used for filming the bubble growth and

detachment from its side view. The MatLAB image processing code was developed for data

analysis of images acquired during the experiments. Parametric studies, such as effects of

pressure, bulk liquid velocity, and inlet subcooling level were also performed. The

comparison between the current study and those of other researches shows good agreement.

Bubble growth constant before the lift-off and the bubble lift-off diameters at various flow

conditions were measured, and a bubble lift-off diameter model was developed and

correlated with experimental data. Qualitative observations were made for bubble sliding,

lift-off velocities, and contact angles at lift-off after observing significant standard deviation

in the experimental data for velocities and contact angle. Experiments were performed for

inlet water subcooling of 32oC to 1

oC, pressure of 1atm - 3atm, and flow rates of 300-400

kg/m2s at a constant heat flux of 124kW/m

2.

Based on the analysis of high-speed photography the following were concluded:

A bubble begins from an embryo and grows from its active nucleation site. After

reaching a certain size, it departs and then may slide from its original site, and finally

108

lifts-off. A sliding bubble can also coalesce with a bubble downstream and then lift-

off into the bulk flow. If heat fluxes are low, sliding bubbles may not have a chance

to coalesce before they lift-off. On the contrary, coalescence can happen before a

bubble starts to slide, due to high bubble number densities. There are also intense

interactions between bubbles and nucleation sites. A nucleation site can be activated

or deactivated by an adjacent bubble or a bubble sliding from upstream, which

occasionally happens.

The bubble lifetime was divided into two distinct regions of growth and

condensation. The growth is partitioned into two stages with growing at the

nucleation site and growing with bubble sliding on the heater surface. The

condensation region also is further subdivided into condensation with bubble sliding

on the wall and condensation after bubble ejected into the flow.

On a heating surface, bubbles serve as a heat sink with a high heat transfer coefficient

due to phase change. The temperature beneath a bubble, therefore, is expected to be

low and close to the saturation temperature. The heating surface without bubbles

covering it, is then controlled by two heat transfer mechanisms, forced convection to

the bulk flow and lateral heat conduction to the bubble-covered region. Compared to

phase change during bubble growth, the forced convection is relatively inefficient in

transferring energy. If the thermal conductivity is sufficiently high, lateral heat

conduction can be even more important than forced convection in transferring energy

from the heating surface into the bulk flow. The results predicted by the model show

that the thermal conductivity plays an important role through lateral heat conduction

inside the heater block and, therefore, has a significant impact on boiling heat transfer

performance.

At high bulk liquid subcooling most of the condensation occurred while bubbles were

sliding on the wall, though ejection was still present. At lower subcoolings, the

bubble radius, bubble growth time and condensation time increased. The density of

the nucleation sites and frequency of bubble formation were also increased with a

decrease in the subcooling.

Bubbles slide parallel to the wall with a constant velocity approximately equal to the

mean flow velocity during both the growth and condensation periods. Also, the effect

109

of flow velocity on bubble parameters was found to be negligible in the range of this

study.

Only three main forces, i.e. buoyancy force, growth force and shear lift force, are

counted for analyzing the bubble at the lift-off instant in the direction normal to the

wall. In this direction three other non-negligible forces are active: the bubble surface

tension, contact pressure force and hydrodynamic force. The latter is composed of

several contributions, related to the bubble growth and to the uniform approaching

flow.

Bubble growth rate and maximum bubble radii obtained in this study were obtained

by the use of the bubble growth model of Zuber. Lift-off bubble radius was correlated

with wall superheat (Ja), pressure and indirectly to liquid bulk subcooling:

√(

)(

( ))

The bubble growth rate constant, b, is assumed to be b = 1.73 in most applications.

The present study showed that the growth rate constant cannot be assumed as a

constant and it is a strong function of flow pressure. The constant value of b

significantly over predicted the measured bubble diameters. Although more

experiments should be performed at higher pressures to validate this model, by using

this new model, the prediction error of the bubble lift-off diameter was significantly

reduced. Therefore, a new empirical correlation for b as a function of experimental

pressure is found which better predicts the data. The new correlation for b is:

√

where . It was found that predicted diameters had an on average 19.91%

error and 21.53% weighted error using a preliminary correlation of the bubble growth

constant which assumed to vary with pressure only (comparing to the average error of

31.1% using a constant value for b at different pressures).

110

There are a few recommendations for future works, which can improve the experimental set-

up, to enable more accurate results for the model and its validation:

Simulate the bubble growth numerically by the use of different boundary conditions

matching the bubble shape observed experimentally. This simulation for different

boundary conditions will promote better understanding of the important parameters in

bubble growth. Also performing numeric modeling of the temperature field around a

bubble in the center of the test chamber, in uniform approaching flow would be

beneficial.

Perform additional experiments with higher flow velocities and different hydraulic

diameters to investigate the effect of flow and geometry on the bubble parameters.

Measure the temperature profile across the flow to obtain the local subcooling and the

thickness of the superheated layer. The temperature measurements would determine

the effect of true liquid subcooling and superheating on the bubble growth and

collapse.

Validate the physical models at various scales by using more advanced

instrumentation techniques such as x-rays, liquid crystal thermography, high speed

infrared thermography, and laser induced fluorescence.

Use more advance high-speed camera to help saving time in image analyzing as well

as capturing high-resolution images at much higher speeds.

Install Micro Motion flowmeter (ELITE Sensor CMF025) in the test pipeline to

gather and save data into LabView software.

111

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117

Appendix A: Force Balance in x-direction (departure

moment)

The force balance approach proposed by Klausner et al. [37] (and the subsequent work by

Zeng et al. [39]) has appeared most commonly in literature. The departure diameter is

important because the bubble departure frequency is expressed as a dimensionless quantity in

terms of the bubble departure diameter. Based on developments in Chapter 5, the force

balance in the x-direction of the bubble at departure is as follows:

∑

( )

( ) ( )

( ) [

[(

)

]

]

( )

( ) ( )

[

[(

)

]

] ( )

( )

[ [(

)

]

] ( )

( ) ( )

Zeng et al. [39] argues that surface tension forces may be neglected at the point of departure

because the contact diameter approaches zero at departure, that surface tension force is

generally less than that of the growth force, and that empirically measured contact diameter

118

is normally over-estimated. Thus an approximation would be to ignore the surface tension

term, which would yield:

( )

[ [(

)

]

]

119

Appendix B: Bubble size measurement technique

Upon completion the image processing, the image can be analyzed to extract experimental

data for each bubble. The following sections describe how data relevant to the bubble lift-off

diameter, the lift-off velocity, the growth, the angles of inclination, the upstream angle, and

the downstream angle were extracted from the images.

B.1. 3-D Bubble Lift-off Diameter Approximation using 2-D

Image

Image analysis of a bubble departure from the heater surface involves the conversion of the

bubble diameter found from the image analysis into an actual bubble diameter. First of all,

this process involves the conversion of a 2-D bubble image to find an approximate 3-D

bubble diameter.

The total number of pixels inside an area projected by the bubble is found by MatLAB using

the methods described before. The software outputs both a normalized 2-D diameter and an

approximated 3-D diameter (although the approximated 3-D diameter will be used as the

final data). The normalized 2-D diameter is simply reformatting the 2-D area encompassed

by the bubble to the diameter of a circle occupying the same area. This can be found by:

√

To approximate the 3-D diameter, the method developed by Chu et al. [59] will be used.

They calculated the bubble volume at lift-off based on the 2-D image using:

∑

The summation is taken from the first pixel (or bottom) to the nth

pixel which describes the

lowest and highest points the projected area of the bubble takes within the image. is the

lift-off volume, is the height of one pixel which can be taken as unity or be converted at

120

this step based on an experimental scaling factor from a reference object, and is the

cordial length of the bubble parallel to the heater surface at the kth

pixel above the heater

surface. Note that if is converted via scaling factor at this step then must also be

converted. This volume is essentially assuming that at each kth

pixel, the height of the pixel

represents the height of a cylinder of diameter and the volume of this cylinder is found

and summed from the bottom to the top of the bubble. This process is automated within the

MatLAB program after the image is binarized and filtered.

Chu et al. assumed that a bubble is circular when viewed from the top (or looking into the

heater surface) based on the experimental observations of Basu et al. [50]. As a result we can

use the following:

(

)

This formula can be used for finding the 3-D diameter using the bubble volume. Chu et al.

reported an error of 0.01% to 2.94% with an average of 1.39% when compared with bubble

diameter found from the 3-D image, which can be considered as the actual bubble diameter.

This shows that bubble diameter found using the method above from a 2-D image is a fairly

good representation of that found from a 3-D image. As a result, this approach will be used to

approximate the 3-D diameter of the bubbles taken due to the lack of 3-D imaging and image

process software.

B.2. Bubble Lift-off Velocity

Bubble instantaneous lift-off velocity will be calculated using centroid data taken from two

successive images and defined as the component of bubble velocity perpendicular to the

heater surface when it loses contact with the heater. The change in the distance of the y-

component of bubble centroid is taken over the time interval between the two images to be

the instantaneous lift-off velocity. The reference of the centroid location is the base of the

image and will cancel when velocity is calculated. The velocity vector found is perpendicular

to the base of the image and not necessarily the heater surface. Thus, if the image taken is

slightly tilted as in Fig. B-1, the absolute x-component (relative to the left of the image) of

121

bubble centroid will also be calculated to find the x-component bubble velocity at lift-off and

a vector sum of the components of each of the velocities perpendicular to the heater surface

will be found and added to find the lift-off velocity perpendicular to the heater surface.

a)

b)

B.3. Bubble Upstream, Downstream, and Inclination Angles at

Lift-off

Bubble contact angles and inclination angles are measured at the moment before lift-off or

the image in which bubble lift-off diameter is extracted. Three angles are of interest, the

inclination angle, the upstream contact angle, and the downstream contact angle as defined in

earlier sections. The inclination angle will be measured by finding the middle of the base of

the bubble or middle of the line of in which the bubble contacts the heater surface before lift-

off. The centroid data of the bubble will then be used, and a virtual line will be drawn from

the centroid to the mid-point of the heater-bubble contact line (in the 2-D image) and the

angle of this line from a line perpendicular to the heater surface will be considered the

Figure B-1: Images taken 0.25ms apart at inlet conditions of 100oC, 1.5atm, 2gpm. The indicated

bubble detached from the heater during this period

122

inclination angle. For the purposes of this experiment, since images are taken with the flow

going from right to left, a positive inclination angle will be defined if the centroid of the

bubble lies to the left of the midpoint of the heater-bubble contact, meaning that the bubble is

leaning in the direction of the flow.

The upstream and downstream contact angles are defined in a similar manner as the

inclination angle. The upstream angle will be the bubble contact angle between that of the

base on the right side of the bubble while the downstream angle will be the bubble contact

angle on its left side to be consistent with the definitions used by Klausner et al. [37]. In

order to properly estimate these two angles, the MatLAB code implements a best fit curve of

pixels at the bubble boundary from the base of the bubble to a height of the diameter of the

bubble divided by 20, although this value can be adjusted according to the needs of specific

experiments which may have varying image quality. The arc tangent of the slope of the best

fit curve yields the contact angle. Upstream and downstream contact angles will always be

positive and be less than 90o. The 2-D contact angle will be taken as the 3-D contact angle

based on the same assumption as with the 3-D bubble diameter, that the bubble is circular

when viewed from above the heater.

Fig. B-2 is an output image from the image processing phase where the contact lines have

been drawn. If the original image has a slight angle due to the positioning of the stands of the

camera, the contact angle values can be re-adjusted by finding the tilt angle using ImageJ and

adjusting the upstream, downstream angle and inclination angle values accordingly.

Figure B-2: Bubble Contact angle lines

123

Appendix C: MatLAB code for image analysis

C.1. Procedure

This code was developed by Lu Liu and the method of use of it is as follows:

1. Open Matlab

2. Open bubble.m

3. Set the current folder to that which contains the images to be analyzed

4. Ensure that bubble.m, fftshow.m, and gaussianbpf.m, and the images to be analyzed

are all part of the path

5. Run bubble.m from the Matlab console

Run in the following method, replacing any unwanted value with ~ (as is standard in

Matlab): [I2, BW4, x, y, d2D, d3D, thetaI, thetaA, thetaR, Dbase, Dmax, Daxial] =

bubble (cont, g, rot)

where:

cont – acts as a boolean switch, where 0 indicates contact angles are

not required

g – acts as a boolean switch, where bubble growth is to be measured if

g >= 1

rot - rotates the image by a set angle for growth measurements

I2 - Image data of cropped image, pre-binarization

BW4 - Binarized version of post-processed image

x -

y - height of the bubble centroid from the base of

pre-processed image

d2D - Approximated 2-D diameter based on normalization of 2-D

area

d3D - Approximated 3-D diameter based on Chu et al.

thetaI - inclination angle

thetaA - upstream or advancing contact angle

thetaR - downstream or receding contact angle

Dbase - length of the contact between bubble and heater surface

124

Dmax - Maximum diameter of the bubble

Daxial - axial (line perpendicular to the heater surface) length of the

bubble

6. In the pop up window, select the image to be analysed

7. Crop the image such that only the bubble of interest is kept

8. Adjust the contrast to 50% (width 1, centre 125)

9. Save as a .jpg image in the same folder as was the selected image. Note: the new

image's name must be unique; it cannot be a replacement of another image.

10. In the pop up window, select the newly created image

11. Console output consists of the original image name, the values that were to be

outputted, as well as five images: cropped, edge detection, filled, filtered, and angles

(inclination, upstream and downstream contact angles)

Issues that may arise due to the code:

1. The selection of the contrast ratio directly influences the perceived size of the bubble

a. for the sake of conservatism, 50% contrast is used

b. as such, all directly measured factors (angle of inclination, receding and

advancing contact angles, base diameter, axial diameter, and two-dimensional

diameter) are affected

c. therefore, selection of contrast can potentially introduce error of a magnitude

equal to the difference between measured values using the minimum and

maximum acceptable contrast ratios

2. Cropping of image directly influences the base diameter and all measured angles

a. depending on how much of the heater surface is included in the cropped

image of the bubble, these values can deviate by as much as 20% (for the base

diameter) and 50% (for the measured angles)

b. it is thus not advisable to use this code for the analysis of the base diameter,

nor for measuring the different angles. It is better to directly analyse them by

hand using ImageJ

C.2. MatLAB Code

function [I2 BW4 x y d2D d3D thetaI thetaA thetaR Dbase Dmax Daxial] =

bubble (~, ~, ~) g=1; %These operate as boolean switches cont=1; rot=0; %{ This function asks for user to input a grayscale image of a bubble to be analyzed and returns the bubble diameter (3-D approximation based on Chu et al.) and the absolute value of the height of the centroid of the bubble from the bottom of the original image.

125

[I2, BW4, x, y, d2D, d3D, thetaI, thetaA, thetaR, Dbase, Dmax, Daxial]

= bubble (cont, g, rot)

Where: cont - 0 indicates contact angles are not required g - bubble growth is to be measured if g >= 1 rot - rotates the image by a set angle for growth measurements I2 - Image data of cropped image, pre-binarization BW4 - Binarized version of post-processed image x - y - height of the bubble centroid from the base of pre-processed image d2D - Approximated 2-D diameter based on normalization of 2-D area d3D - Approximated 3-D diameter based on Chu et al. thetaI - inclination angle thetaA - upstream or advancing contact angle thetaR - downstream or receding contact angle Dbase - length of the contact between bubble and heater surface Dmax - Maximum diameter of the bubble Daxial - axial (line perpendicular to the heater surface) length of

the bubble %}

close all; if exist('0.jpg','file') ~= 0 delete('0.jpg'); end d=dir('*.jpeg'); for k=1:length(d) fname=d(k).name; [pathstr, name, ~] = fileparts(fname); movefile(fname, fullfile(pathstr, [name '.jpg'])) end

base = 0;

x = 0; y = 0; d3D = 0; BW4 = 0; d2D = 0; thetaI = 0; thetaA = 0; thetaR = 0; Dbase = 0; Dmax = 0; Daxial = 0;

[file,path] = uigetfile('.jpg'); cancel = isequal(file,0); fprintf('%s',file);

if isequal(cancel, 0)

full = fullfile(path, file);

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I = imread(full); [row,col, ~]=size(I);

oriCol = col; row = row - base; I = I (1:row, 1:col, 1:1); if g >= 1 I = imrotate(I, rot); end

imshow(I); [I2, rect] = imcrop(I); [row2, col2] = size(I2); I2(1,1) = 1; I2(row2,col2) = 1; offset = row - row2 - rect(1,2)-1; offset2 = col - col2 - rect(1,1) - 1; imshow(I2); D = dir([path, '\*.jpg']); numFile = length(D(not([D.isdir])));

imcontrast;

pause(0.5);

numFile2 = numFile;

while numFile2 == numFile D = dir([path, '\*.jpg']); numFile2 = length(D(not([D.isdir])));

pause(0.5); end

[file,~] = uigetfile('.jpg'); cancel = isequal(file,0);

if isequal(cancel, 0) full = fullfile(path, file); I2 = imread(full); ori = I2; [row, col,~] = size(I2); I2 = I2(1:row, 1:col, 1:1); [bottom, side, ~,~] = sizeof(I2); % code available from % http://www.mathworks.com/matlabcentral/fileexchange/30947-

gaussian-bandpass-filter-for-image-processing I2 = gaussianbpf(I2,60000, 1000000);

for i = 1:row for j = 1:col if I2(i,j) > 125 % this can be modified depending on the

image

127

I2(i,j) = 255; end end end imshow(I2);

BW2 = edge(I2,'sobel'); BW2 = bwmorph(BW2, 'bridge');

% Number of cleaning operations can be modified for i = 1:2 BW2 = bwmorph(BW2, 'remove'); BW2 = bwmorph(BW2, 'shrink'); BW2 = bwmorph(BW2, 'clean'); end

% filter out circles less than 5 pixels in radius; this can be % modified depending on image BW3 = BW2;

BW2 = imfill(BW2,'holes'); BW2b = BW2; se = strel('disk', 5); BW2 = imopen(BW2, se);

area = cell2mat(struct2cell(regionprops(BW2, 'Area'))); d1 = sqrt(4*area/pi); d1 = max(d1);

BW4 = ~BW2;

t = round(d1/12); if t < 1 t = 1; end se = strel('disk', t); BW4 = imclose(BW4, se); BW4 = ~BW4;

area = cell2mat(struct2cell(regionprops(BW4, 'Area'))); centroid = cell2mat(struct2cell(regionprops(BW4, 'Centroid')));

% take the largest bubble if there is more than one object d1 = sqrt(4*area/pi); index = 1; [~, col] = size(d1); for i = 1:col if d1(i) == max(d1) index = i; end end

128

d1 = max(d1); d2D = d1; % centroid output format is col, row of centroid if size(centroid) y = bottom - centroid(1,index*2) + offset; x = oriCol - (side - centroid(1,index) + offset2); end

% first is col, second is row of centroid [row, col] = size(BW4); Vol = 0; for i = 1:row count = 0; for j = 1:col if BW4(i, j) == 1 count = count +1; end

end Vol = pi/4*count^2 + Vol; end

d3D = (6/pi*Vol)^(1/3);

n = 2;

t = round(d3D/10); if t < 1 t = 2; end

if cont >= 1 [thetaI, thetaA, thetaR, BW6] = contact(BW4, centroid(1,index),

centroid(1,index*2), t); % n = 3; end

if g >= 1 [Dbase, Dmax, Daxial] = growth(BW4); end subplot(2,n,1); imshow(ori); title('Cropped Image'); subplot(2,n,2); imshow(BW3); title('Edge Detection Image'); subplot(2,n,3); imshow(BW2b); title('Filled Image'); subplot(2,n,4); imshow(BW4); title('Filtered Image');

if cont >= 1 subplot(2,n,5);

129

imshow(BW6); title('Inclination, Upstream, Downstream Contact Angles'); end if exist('0.jpg','file') ~= 0 delete('0.jpg'); end end end %fprintf('Angle of inclination: %d\nAdvancing contact angle: %d\nReceeding

contact angle: %d\n3-D diameter: %d',thetaI,thetaA,thetaR,d3D);

end

% x is col, y is row function [thetaI, thetaA, thetaR, BW4] = contact(BW4, centrX, centrY, n)

n = abs(round(n)); thetaI = 90; thetaA = 0; thetaR = 0; botX = 0; [row, col] = size(BW4); leftR = 0; leftC = 0; bool = 0; rightR = 0; rightC = 0; advanceCol = []; advanceRow = []; recedeCol = []; recedeRow = []; ai = 1; ri = 1; skip = 0; % bottom up, left to right; finds left base of nucleation site

for i = row:-1:1 for j = 1:col if BW4(i,j) == 1 && skip == 1 leftR = i; leftC = j; bool = 1; break; end if BW4(i,j) == 1 && skip < 1 skip = skip + 1; break; end end if bool == 1 break; end end skip = 0; bool = 0;

130

for i = row:-1:1 for j = col:-1:1 if BW4(i,j) == 1 && skip == 1 rightR = i; rightC = j; bool = 1; break; end if BW4(i,j) == 1 && skip < 1 skip = skip + 1; break; end end if bool == 1 break; end end

baseX = (rightC + leftC)/2; % x position baseY = (rightR + leftR)/2; % positive inclination angle when the centroid is to the left of % the base thetaI = atan((baseX - centrX)/(baseY - centrY))*180/pi; % positive inclination angle in direction of the flow or % to the left

% recede for i = leftR:-1:(leftR-n) for j = 1:col if BW4(i,j) == 1 recedeCol(ri) = j; recedeRow(ri) = i; ri = ri + 1; break; end

end end

slopeR = polyfit(recedeCol, recedeRow, 1); thetaR = atan(abs(slopeR(1)))*180/pi;

for i = rightR:-1:(rightR-n) for j = col:-1:1 if BW4(i,j) == 1 advanceCol(ai) = j; advanceRow(ai) = i; ai = ai + 1; break; end end end

131

slopeA = polyfit(advanceCol, advanceRow, 1); thetaA = atan(abs(slopeA(1)))*180/pi;

BW4 = drawLine (BW4, rightR, rightC, abs(slopeA(1)), leftR, leftC,

abs(slopeR(1)), centrX, centrY, baseX, baseY);

%imshow(BW4); %title('Inclination, Advancing, Receding Contact Angles'); end

function [BW4] = drawLine (BW4, rightR, rightC, slopeA, leftR, leftC,

slopeR, centrX, centrY, baseX, baseY)

% recede line i = leftR; j = round(leftC); [row, col] = size(BW4);

% for col going left while i < row && j > 1 && j < col && i > 1

if BW4(round(i),round(j)) == 1 BW4(round(i),round(j)) = 0; else BW4(round(i),round(j)) = 1; end j= j-1; i = i-(slopeR); end

i = leftR; j = round(leftC);

while i > 1 && i < row && j > 1 && j < col

if BW4(round(i),round(j)) == 1 BW4(round(i),round(j)) = 0; else BW4(round(i),round(j)) = 1; end j= j+1; i = i+slopeR; end % advance line i = rightR; j = round(rightC); while i > 1 && i < row && j > 1 && j < col

if BW4(round(i),round(j)) == 1 BW4(round(i),round(j)) = 0; else BW4(round(i),round(j)) = 1;

132

end j= j-1; i = i+(slopeA); end i = rightR; j = round(rightC); while i > 1 && i < row && j > 1 && j < col

if BW4(round(i),round(j)) == 1 BW4(round(i),round(j)) = 0; else BW4(round(i),round(j)) = 1; end j= j+1; i = i-slopeA; end % incline angle line % if baseX > centrX, slopeC is positive; meaning base middle is % farther from the centroid or bubble leaning toward left slopeC = (baseY - centrY)/(baseX - centrX);

i = baseY; j = round(baseX); while i > 1 && i < row && j > 1 && j < col

if BW4(round(i),round(j)) == 1 BW4(round(i),round(j)) = 0; else BW4(round(i),round(j)) = 1; end j= j-1/slopeC; i = i-1; end

i = baseY; j = round(baseX); while i > 1 && i < row && j > 1 && j < col

if BW4(round(i),round(j)) == 1 BW4(round(i),round(j)) = 0; else BW4(round(i),round(j)) = 1; end j= j+1/slopeC; i = i+1; end

end

function [Dbase, Dmax, Daxial] = growth(BW4)

Dmax = 0; Daxial = 0; leftBaseX = 0; rightBaseX = 0;

133

[row, col] = size(BW4); bool = 0; count = 0; for i = row:-1:1 for j = 1:col if BW4(i,j) == 1 && count == 1; leftBaseX = j; bool = 1; break; end if count == 0 && BW4(i,j) == 1 count = 1; break; end end if bool == 1 break; end end bool = 0; count = 0; for i = row:-1:1 for j = col:-1:1 if BW4(i,j) == 1 && count == 1; rightBaseX = j; bool = 1; break; end if count == 0 && BW4(i,j) == 1 count = 1; break; end end if bool == 1 break; end end

Dbase = rightBaseX - leftBaseX;

left = 0; prev = 0; for i = 1:row for j = 1:col if BW4(i,j) == 1 && prev == 0 left = j; prev = 1; end if BW4(i,j) == 0 && prev == 1 prev = 0; temp = j - left; if temp > Dmax Dmax = temp; end end end

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end

top = 0; prev = 0; for j = 1:col for i = 1:row if BW4(i,j) == 1 && prev == 0 top = i; prev = 1; end if BW4(i,j) == 0 && prev == 1 prev = 0; temp = i - top; if temp > Daxial Daxial = temp; end end end end

end

% coordinates are in row, col with top left corner as 1,1 function [bottom, side, width, length] = sizeof (I)

[row, col, ~] = size(I); I = I (1:row, 1:col, 1:1);

bottom = 0; side = 0; bool = 0;

for j = col:-1:1 for i = row:-1:1 if I(i,j) < 200 && bool == 0 bottom = i; side = j; bool = 1; I(i,j) = 255; end end end

left = 0; top = 0; bool = 0; for i = 1:row for j = 1:col if I(i,j) < 200 && bool == 0 left = j; top = i; bool = 1;

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I(i,j) = 255; end end end

width = side - left+1; length = bottom - top+1;

end

136

Appendix D: Mechanical Properties of the Zirconium

tubes

Composition (Weight Percent) [65]

Name Zircaloy-4

UNS Grade R60804

Tin 1.20- 1.70

Iron 0.18- 0.24

Chromium 0.07- 0.13

Nickel ---

Niobium ---

Oxygen Per P.O.

Iron + Chromium + Nickel ---

Iron + Chromium 0.28- 0.37

Properties of Zircloy-4 [65]

Density 6.55 g/cc (0.237 lbs/cu.-in.)

Coefficient of Thermal Expansion at 25oC 6 x 10

-6m/m

oC (3.3 x 10

-6 in/in-

oF)

Heat Capacity 0.285 J/g-oC (0.07 BTU/ lb-

oF)

Thermal Conductivity 21.5 Watts/m-K (149 BTU-in/hr-ft2- oF)

Melting Point 1850oC (3,362

oF)

Alpha Alpha + Beta Phase

Transformation ~810

oC

Alpha + Beta Beta Phase Transformation ~ 980oC

Hardness 89 Rb average

Modulus of Elasticity 99.3 GPa (14,402 ksi)

Poisson’s Ratio 0.37

Shear Modulus 36.2 GPa (5,249 ksi)

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Mechanical properties of Zircaloy-4 annealed 2 mm thick strip [65]

Orientation Longitudinal Transverse

Test Temperature Room Temp. 288oC Room Temp. 288

oC

Ultimate Tensile Strength

MPa 541 271 515 241

(ksi) (78.4) (39.3) (74.6) (34.9)

Tield Strength

MPa 80 152 468 170

(ksi) (55.2) (22.0) (67.8) (25.6)

Elongation, % 28 43 29 44

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