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Simulation of Nucleate Flow Boiling Heat

Transfer

in

A

Single

Hori

SIMULATION OF FLOW

BOILING HEAT TRANSFER IN A SINGLE

HORIZONTAL MICROCHANNEL

A Thesis

Submitted In Partial Fulfillment of The Requirements For

Awarding The Degree of

Master of Mechanical Engineering

In Faculty of Engineering and Technology

Submitted By Arup Mondal

Registration No. – 86506 of 2003-04

Examination Roll No. – M4 MEC 13-22

Under The Supervision of

Dr. Arunabha Chanda

Department of Mechanical Engineering

Jadavpur University

Kolkata- 700032

2013

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ii

This Thesis Is

Dedicated To My

Parents.

Your unconditional love and constant

support have led me at least this far. I

love you.

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iii

Faculty of Engineering and Technology

Department

of

Mechanical

Engineering

Jadavpur

University

Kolkata

2013

CERTIFICATE OF APPROVAL

The forgoing thesis entitled “ Simulation of Flow Boiling Heat Transfer in a Single

Horizontal Microchannel” is hereby approved as creditable study of Fluid Mechanics

and Hydraulics Engineering and presented in a manner satisfactory to warrant its

acceptance as a pre-requisite to the degree for which it has been submitted. It is

understood that by this approval, the undersigned, do not necessarily endorse or

approve any statement made, opinion expressed or conclusion drawn therein, but

approve the thesis only for the purpose for which it is submitted.

Committee of final examination for evaluation of thesis

…………………………… ………………………………

…………………………… ………………………………

Signature

of

Examiners

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iv

Faculty

of

Engineering

and

Technology

Department

of

Mechanical

Engineering

Jadavpur

University

Kolkata

2013

CERTIFICATE OF RECOMMENDATION

This is to certify that the thesis entitled, “ Simulation of Flow Boiling Heat Transfer

in a Single Horizontal Microchannel” which is being submitted by Arup Mondal in

partial fulfilment of the requirements for the award of the degree of Master of

Mechanical Engineering in Faculty of Engineering and Technology of Jadavpur

University, Kolkata-700032, during the academic year 2011-2013, is the record of the

student’s own work carried by him under the supervision of Dr Arunabha Chanda

………………………… ...…………………………

Dr. Arunabha Chanda

Thesis

Advisor

Dept. of Mechanical Engineering

Jadavpur

University

Kolkata

Dr. Sadhan Kumar Ghosh

Professor

and

Head

Dept. of Mechanical Engineering

Jadavpur

University

Kolkata

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v

DECLARATION

OF

ORIGINALITY

AND

COMPLIANCE

OF

ACADEMIC

ETHICS

I hereby declare that this thesis contains literature survey and original research work by the

undersigned candidate, as part of his Master of Mechanical Engineering studies.

All information in this document has been obtained and presented in accordance with

academic rules and ethical conduct.

I also declare that, as required by this rule and conduct, I have fully cited and referred all

material and results that are not original to this work.

Name : Arup Mondal

Examination Roll No : M4 MEC 13‐22

Thesis Title : “Simulation of Flow Boiling Heat

Transfer in a Single Horizontal Microchannel”

Signature :

Date :

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vi

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to Dr. Arunabha Chanda for

his guidance and assistance in this thesis. His prompt responses in all the technical

and non‐technical issues during the production of this work helped me a lot. His

encouragement and efforts led this report to successful completion in a timely

fashion.

I am thankful to Prof. Sadhan Kumar Ghosh, Head, Department of

Mechanical Engineering, Jadavpur University, for his constant help in different

academic and non‐ academic matters.

I am extending my gratefulness to all my classmates and co‐workers in CFD

laboratory whose aid & support, lend a hand to accomplish this work. The Library

staffs also helped me a lot by providing me a constant access to the relevant

textbooks and journals that were useful in this thesis work.

Lastly I am thankful to all who have assisted me directly or indirectly to

complete this work.

Date: Arup Mondal

Jadavpur University

Kolkata

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vii

ABSTRACT

Boiling in microchannels is a very efficient mode of heat transfer in which very high heat

and mass transfer coefficients can be achieved. Pumping power required for two-phase

flows is lesser than single-phase liquid flows to achieve a given heat removal.

Applications include heat pumps, automotive air conditioners, electronics cooling etc.

A numerical study of two-phase flow through the microchannel has been carried out in

this study. The computational fluid dynamics (CFD) model equations are solved using

commercial software ANSYS Fluent 13.0 to understand the hydrodynamic and thermal

behavior of the two-phase flow through microchannel. The computational model has

been validated against available literature (Liu, Lee and Garimella, 2005). Water is used

as working fluid which enters the microchannel in liquid state.

The aim of this study is to understand the effects of different fluid inlet velocity & fluid

inlet temperature on the Onset of Nucleate Boiling in a microchannel. Also at various

Reynolds no. the effect on “volume fraction of vapor”, “static temperature along the

wall” and “heat transfer coefficient” at the heated wall is investigated.

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viii

CONTENTS

Abstract

vii

Contents viii

List of Figures x

List of Tables xi

1. INTRODUCTION (1‐5)

1.1. Microchannel & Its Use 1

1.2.

Application of

Computational

Fluid

Dynamics

(CFD)

3

1.3. Objectives of The Present Work 4

1.4. Outline of The Report 4

2. LITERATURE REVIEW (6‐35)

2.1. Experimental Study of Fluid Flow and Heat Transfer

in Microchannels 6

2.2.

Theoretical, Numerical

and

Other

Studies

Related

to

Fluid Flow and Heat Transfer In Microchannels 27

3. THEORITICAL BACKGROUND (36‐46)

3.1. Fundamentals of Boiling 36

3.1.1. Pool Boiling 37

3.1.2. Flow Boiling 39

3.2.

Two‐phase

flow

patterns

42

3.3. Non‐Dimensional Numbers / Parameters Relevant to

Flow Boiling Heat Transfer in Microchannel 45

4. COMPUTATIONAL FLUID DYNAMICS MODEL EQUATIONS (47‐54)

4.1. Single Phase Modeling Equations 47

4.1.1.

Mass Conservation Equation 47

4.1.2. Momentum Conservation Equation 48

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4.1.3. Energy Equation 48

4.2. Two Phase Modeling Equations 49

4.2.1.

Volume of Fluid (VOF) Model 50

4.2.1.1. Volume Fraction Equation 51

4.2.1.2. Material Properties 51

4.2.1.3. Momentum Equation 52

4.2.1.4. Energy Equation 52

4.2.2. Mixture Model 53

4.2.3. Eulerian Model 53

5. SOLUTION METHODOLOGY (55‐61)

5.1. Specification of Problem 55

5.2. Geometry in Ansys Workbench 56

5.3. Meshing of Geometry 56

5.4. Material Properties 57

5.5. Governing Equations 58

5.6.

Boundary Conditions

60

5.7. Method of Solutions 60

5.8. Grid Independence Study 61

6. RESULTS AND DISCUSSION (62‐68)

6.1. Validation 62

6.2. Effect of Various Inlet Velocity on Incipient Heat Flux 63

6.3.

Effect of Various Reynolds No. on Volume Fraction of Vapor,

Static Temperature & Heat Transfer Coefficient at the wall 63

7. CONCLUSIONS AND FUTURE SCOPE OF WORK (69‐70)

7.1. Conclusions 69

7.2. Future scope of Work 70

References (71‐80)

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x

List of Figures

Page No.

Figure 3.1 Typical Boiling Curve & Heat Transfer Process

in Pool Boiling 38

Figure 3.2 Flow Boiling in a Uniformly Heated Circular Tube 40

Figure 3.3 Different flow boiling regimes 44

Figure 5.1 Fluid flow through a rectangular microchannel 55

Figure 5.2 Specification of zone type in ANSYS Workbench 56

Figure 5.3 Two dimensional computational domain with

grid type mesh 57

Figure 5.4 Outlet Velocity Profile at Different Grid Sizes 61

Figure 6.1 Effect of different Inlet Temperature on

Incipient Heat Flux 62

Figure 6.2 Effect of different Inlet Velocity on Incipient Heat Flux 63

Figure 6.3

Volume

Fraction

of

Vapor

at

the

Heated

Wall

Along

the

Flow Direction at Different Reynolds Number 64

Figure 6.4 Static Temperature at the Heated Wall Along the Flow

Direction at Different Reynolds Number 65

Figure 6.5 Surface Heat Transfer Coefficient at the Heated Wall

Along the Flow Direction at Different Reynolds Number 66

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xi

List of Tables

Page No.

Table 5.1 Properties of liquid water at different temperatures 57

Table 5.2 Properties of water vapor at different temperatures 58

Table 5.3 Under‐Relaxation Factors 60

Table 5.4 Error Percentage of Maximum Velocity Value at the Center of the

Pipe for Different Grid Sizes 61

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xii

Nomenclature

2-D Two Dimensional --

Bo Boiling number --

Bn Bond number --

Co Convection number --

Ca Capillary number --

CFD Computational Fluid Dynamics --

CHF Critical Heat Flux W/m2

Dh Hydraulic Diameter μm

Eo Eötvös number --

F External Body Force N

h Heat Transfer Coefficient W/(m2.k)

Ja Jakob number --

K 1 Non-dimensional number --

K 2 Non-dimensional number --

ONB Onset of Nucleate Boiling --

q //

Heat Flux W/m2

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CHAPTER 1

INTRODUCTION

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INTRODUCTION

1

1. INTRODUCTION

With the advent of technology the heat flux generated by various devices are

increasing exponentially. So cooling these devices have become very essential and a

matter of serious consideration. Boiling and two-phase flow in microchannels has

attracted much interest in recent years because of its promising features towards very

high heat flux removal. Utilizing the latent heat of the coolant, two-phase

microchannel heat sinks can dissipate much higher heat fluxes while requiring smaller

rates of coolant flow than in the single-phase counterpart. Better temperature

uniformity across the heat sink can also be achieved. But the complex nature of

convective flow boiling in microchannel heat sinks is still far away from being

completely understood.

1.1. MICROCHANNEL AND ITS USE

Tuckerman and Pease [1] first made use of miniaturization for the purposes of heat

removal, within the scope of a Ph.D. study in 1981. Their publication titled “High

Performance Heat Sinking for VLSI” is believed to be the first study on microchannel

heat transfer. Before proceeding with microchannel flow and heat transfer, it is

appropriate to introduce a definition for the term “microchannel”. The scope of the

term is among the topics of debate between researchers in the field.

Mehendale et al. [54] used the following classification based on manufacturing

techniques required to obtain various ranges of channel dimensions, “D”, being the

smallest channel dimension:

1 μm D 100 μm : Microchannels

100 μm D 1 mm : Minichannels

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INTRODUCTION

2

1 mm D 6 mm : Compact Passages

6 mm D : Conventional Passages

Kandlikar and Grande [56] adopted a different classification based on the rarefaction

effect of gases in various ranges of channel dimensions, “ D” being the smallest

channel dimension:

1μm D 10μm : Transitional Microchannels

10μm D 200 μm : Microchannels

200 μm D 3 mm : Minichannels

3 mm D : Conventional Passages

A simpler classification was proposed by Obot (2003) based on the hydraulic

diameter rather than the smallest channel dimension. Obot classified channels of

hydraulic diameter under 1mm (Dh 1 mm) as microchannels, which was also

adopted by many other researchers.

The classification of microchannel proposed by Obot is considered to be more

appropriate for the purpose of this thesis.

Microchannel heat sinks provide an innovative cooling technology for the removal of

a large amount of heat through a small area. The heat sink is usually made from a high

thermal conductivity solid such as silicon or copper. The micro-channels are

fabricated into its surface by either precision machining or micro-fabrication

technology. A Microchannel heat sink typically contains a large number of parallel

micro channels. Coolant is forced to pass through these channels to carry away heat

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INTRODUCTION

3

from a hot surface. Microchannel heat sinks provide very high surface area to volume

ratio, large convective heat transfer coefficient, small mass and volume, and small

coolant inventory. These aspects of the heat sinks are very suitable for cooling devices

such as high performance microprocessors, laser diode arrays, radars, and high-

energy-laser mirrors. Micro channel heat exchangers could be easier to repair than

their conventional counterparts.

1.2.

APPLICATION

OF

COMPUTATIONAL

FLUID

DYNAMICS

(CFD)

For engineering purposes such as boiling heat transfer analysis in microchannels

Computational Fluid Dynamics (CFD) is widely used. It is a computer-based

numerical tool used to study the fluid flow, heat transfer behavior and other

characteristics associated with a fluid flow analysis. A set of mathematical model

equations are first developed following conservation laws. These equations are then

solved using a computer programmer in order to obtain the flow variables throughout

the computational domain. Examples of CFD applications in the chemical process

industry include drying, combustion, separation, heat exchange, mass transfer,

pipeline flow, reaction, mixing, multiphase systems and material processing.

Validation of CFD models is often required to assess the accuracy of the

computational model. Validation is achieved by comparing CFD results with

available experimental, theoretical, or analytical data. Validated models become

established as reliable, while those which fail the validation test need to be modified

and revalidated.

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INTRODUCTION

4

1.3. OBJECTIVES OF THE PRESENT WORK

As is evident from the diversity of application areas, the study of flow and heat

transfer in microchannels is very important for the technology of today and the near

future, as developments are following the trend of miniaturization in all fields.

Literature review shows that most experimental & analytical works were carried out

for refrigerant flow boiling. Water flow boiling, especially in microchannel heat sinks,

received less investigation. Also the VOF method of has hardly been used in

microchannel fluid flow and heat transfer simulations. This work is a humble attempt

to investigate some of the microchannel fluid flow and heat transfer characteristics

(with water as the working fluid) using the VOF method.

The present work contributes to the study of the following aspects:

I.

Simulation of Flow Boiling Heat Transfer in a Single Horizontal

Microchannel using commercial flow solver (ANSYS Fluent 13.0).

II. Validation of the CFD model by comparing the present simulated results

with the available literature [22].

III. The effects of various Reynolds no. on “volume fraction of vapor”, “static

temperature along the wall” and “heat transfer coefficient” at the heated

wall is evaluated.

IV.

The Incipient Heat Flux is investigated as a function of fluid inlet velocity

and fluid inlet temperature.

1.4. OUTLINE OF THE REPORT

I. Chapter 1 represents introduction & objective of the project work

including definition & applications of microchannel and the role of

Computational Fluid Dynamics & its applications.

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INTRODUCTION

5

II. Chapter 2 is devoted on the extensive literature survey on experimental &

numerical study of flow boiling heat transfer in microchannel.

III. Chapter 3 deals with theoretical background which includes fundamentals

of boiling, two phase flow patterns and non-dimensional numbers

associated with boiling heat transfer.

IV. Chapter 4 represents computational fluid dynamics (CFD) model equation

of single phase and two phase flow through microchannel. The model

equation includes the continuity equation, momentum equation and energy

equation.

V. Chapter 5 consists of the solution methodology used during the

simulation of flow boiling heat transfer in a microchannel.

VI. Chapter 6 corresponds to validation of the numerical model, results and

discussion.

VII. Chapter 7 deals with overall conclusion and future scope of work.

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CHAPTER 2

LITERATURE REVIEW

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LITERATURE REVIEW

6

2. LITERATURE REVIEW

2.1. EXPERIMENTAL STUDY OF FLUID FLOW AND HEAT TRANSFER IN

MICROCHANNELS

Tuckerman and Pease [1] first introduced the concept of microchannel heat sink.

They demonstrated that the laminar flow in a rectangular microchannel has higher

heat extraction capabilities than turbulent flow in conventional size tubes. This

finding opened up a new research field and it has been followed by many more

studies by numerous researchers.

In their experiments with water in rectangular channels (50-56 μm height

range and 287-320 μm width range) they said that “the flow rate obeyed the

Poiseuille’s equation and that the thermal resistance was independent of power level”.

So this is in good agreement with conventional macro scale theory.

Lazarek & Black [2] investigated the heat transfer coefficient, pressure drop and

critical heat flux of saturated R-113 boiling in a single vertical tube of 3.11 mm

diameter. They concluded that heat transfer coefficient in the saturated boiling region

is independent of the vapor quality.

Cornwell and Kew [3] tested R-113 in parallel rectangular channels (75 nos. channel

of size 1.2 mm X 0.9 mm and 36 nos. channel of size 3.25 mm X 1.1 mm) and

identified 3 flow patterns. These are isolated bubble, confined bubble and annular

slug. They concluded that heat transfer coefficient is dependent on the flow pattern.

Lower values of heat flux have significant effect in confined bubble region and in the

annular slug region convection heat transfer dominates.

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LITERATURE REVIEW

7

Bowers and Mudawar [4] compared between minichannels & microchannels. Their

channel diameter was 2.54 and 0.51 mm and used R-113 as the working fluid in the

input heat flux range of 1000-2000 kW/m2. They find that minichannels are preferable

over microchannels unless liquid inventory or weight constraints are severe.

Tran, Wambsganass and France [5] used circular & rectangular microchannel

constructed of stainless steel. The input heat flux was given via d.c. supply. The heat

transfer coefficient was found to be strongly dependent on the heat flux. Except at the

lowest heat & mass fluxes, both nucleate boiling and convective boiling components

were present.

Kew and Cornwell [6] proposed a non-dimensional parameter named the

“Confinement number” in their experimental analysis. They said that two-phase flow

exhibits different flow and heat transfer characteristics when the confinement number

is greater than 0.5. Confinement of a growing bubble is represented by the restriction

of channel size on bubble growth, such that the bubble length is greater than the

channel diameter. This dimensionless number depends on the diameter as well as

surface tension and density of the liquid and vapor.

Bonjour and Lallemand [7] observed flow patterns of R-113 boiling in a narrow

space between two vertical surfaces. The flow patterns were nucleate boiling with

isolated bubbles, nucleate boiling with coalesced bubbles and partial dryout. They

noted that the Bond number (Bn) effectively identifies the transition of flow patterns

from conventional diameter tubes to minichannels. Also mentioned that for smaller

diameter channels, the gravitational forces become less important and Bond number is

not useful in modeling the flow characteristics.

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8

Peng, Hu and Wang [8] pointed out that nucleation in small channels requires larger

superheats. Bubble generation and growth was said to require a minimum amount of

space, the evaporating space. If missing, what they called fictitious boiling would be

induced before nucleation starts. Later other researchers proposed that the results were

erroneous as no high speed camera/microscope was used.

Lakshminarasimhan, Hollingsworth and Witte [9] performed experiments to

investigate nucleate flow boiling and incipience in a vertical flow channel, 20 mm

wide and 357 mm long. One wall was heated uniformly and others approximately

kept adiabatic. Three channel spacing’s, 2, 1 and 0.5 mm, were investigated. R-11

was the liquid used for the experiments. Liquid crystal thermograph was used to

measure distributions of surface temperature from which the heat transfer coefficients

on the heated surface were calculated. Kandikar’s correlation provided the best fit for

fully developed saturated nucleate boiling in the narrow channels used in these

studies.

Hapke, Boye and Schmidt [10] studied the ONB in a vertical evaporator pipe with

an inner diameter of 1.5 mm using thermographic measurements. They found the

superheat necessary to initiate boiling was essentially higher than that of larger tubes

for the same values of heat and mass flux. Larger heat fluxes lead to an increase in the

wall superheat at the ONB.

Serisawa, Feng and Kawara [11] visualized gas–liquid two-phase flow patterns with

a microscope for air–water flow in circular tubes of 20, 25 and 100 μm internal

diameter and for steam–water flow in a 50 μm internal diameter circular tube.

More than several different flow patterns were observed, namely, dispersed

bubbly flow, gas slug flow, liquid ring flow, liquid lump flow, skewed barbecue

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LITERATURE REVIEW

9

shaped flow, annular flow, frothy or wispy annular flow, rivulet flow and liquid

droplets flow.

The effect of surface contamination and the wet ability between the tube wall

and the fluids was studied experimentally. The cross-sectional average void fraction

was also calculated from photographs, showing a good agreement with the Armand

correlation for air–water flow in larger tubes.

Ghiaasiaan, and Chedester [12] developed a model for the calculation of the boiling

incipience heat flux in water-cooled microtubes. The method is based on the

hypothesis that in microchannels the thermo capillary force, which tends to suppress

the micro bubbles have a tendency to form on the wall cavities, plays an important

role.

Kandlikar and Steinke [13] proposed a modification of their microchannel flow

boiling correlation to be used for large-diameter tubes. They suggested the modified

correlation may be used for flow boiling in minichannels by using the laminar single-

phase correlation for the heat transfer coefficient for all liquid flow. The trends in heat

transfer coefficient versus quality were also compared in the laminar region.

It was found that the flow with Re < 1600 may be treated as fully developed

laminar flow where single phase correlation is used to find out h which is the single

phase heat transfer coefficient. The flow may be considered in the transition region

for 1600 < Re < 3000. It was suggested that an appropriate interpolation scheme

needs to be developed in the region of 1600 < Re < 3000.

Qu and Mudawar [14] conducted saturated flow boiling experiments on a 21

parallel, rectangular (cross section-- 231 μm X 713 μm) microchannel heat sink,

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LITERATURE REVIEW

10

etched onto a silicon chip. The heater was adhered to the back face. They found that

heat transfer coefficient decreases with increasing equilibrium quality. Droplet

entrainment was seen at the onset of annular flow regime. Boiling mechanism was

found to be forced convection.

Qu and Mudawar [15] studied the critical heat flux in a water-cooled microchannel

heat sink consisting of 21 parallel (cross-section-- 215 μm X 821 μm) microchannels.

They observed that CHF was independent on the inlet temperature but it increased

with increasing the mass flux. They also noticed that, as CHF was approached, flow

instabilities induced backflow into the heat sink’s upstream plenum.

Steinke and Kandlikar [16] reported the local heat transfer coefficients as a function

of heat flux, mass flux, and quality of liquid water / water vapor in parallel

microchannels. The microchannels were etched in silicon and were heated with a

copper heater deposited on the back surface. The heat transfer coefficient was found

to decrease dramatically along the length as quality increased. Considering that the

fluid is water at atmospheric pressure, the fall in heat transfer coefficient with

increasing quality indicated a major departure from the flow boiling characteristics in

conventional channels

The findings of Kandlikar and Balasubramanian [17] are as follows:

Flow boiling consists of nucleate boiling and convective boiling.

Nucleate boiling contribution decreases with quality. Convective

boiling becomes dominant as quality increases.

Heat transfer coefficient trends depend on the boiling number and the

liquid to vapor density ratio.

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LITERATURE REVIEW

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there are pressure drop oscillations, which increase with increasing vapor quality.

This study shows strong dependence of the heat transfer coefficient on the vapor

quality.

Kosar, A., Kuo, C.J., and Peles [20] performed the experiment of boiling heat

transfer in rectangular microchannels with reentrant cavities. They showed that the

deviations between existing data and available correlations are relatively large and

inconsistent. Hence making it is difficult to quantitatively conclude the capabilities of

reentrant cavities to enhance heat transfer.

Depending on the mass velocity and heat flux, both nucleate and convective

dominant boiling mechanisms were detected. These were quantified in terms of the

Reynolds and the Boiling number. For low Re and Bo, Nucleate boiling is dominant.

Two correlations were developed to represent the experimental data for both

nucleate boiling and convective boiling dominant regions. CHF data has been

compared with conventional as well as minichannel correlations.

Kandlikar, Kuan, Willistein and Borrelli [21] studied the effect of pressure drop

elements and artificial nucleation sites on the instability observed during flow boiling

in microchannels. Their individual as well as combined effects were studied

experimentally using high speed video imaging and pressure drop measurements.

It was found that introduction of pressure drop elements alone, partially reduced

the instabilities. Introduction of nucleation sites alone increased the instabilities. Use

of pressure drop elements in conjunction with fabricated nucleation sites is

recommended based on this study.

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LITERATURE REVIEW

13

Liu, Lee and Garimella [22] experimentally investigated the onset of nucleate

boiling under various flow conditions. The microchannels considered were 275 μm

wide by 636 μm deep. They also developed an analytical model to predict the

incipient heat flux as well as the bubble size at the onset of boiling.

They observed that when the incipient heat flux is reached in the experiments,

a single bubble or a few bubbles could be observed simultaneously using the high-

speed imaging system either close to the exit, or even further upstream, in several

microchannels. These bubbles were usually observed to form near but not exactly at

the edges (corners) on the channel bottom surface. Analyzing their experimental data

it is found that the incipient heat flux increases with increased fluid inlet velocity and

decreases with increased inlet temperature.

Kandlikar, S. G., and Balasubramanian [23] studied the influence of gravitational

forces on flow boiling in minichannels. The vertical down flow case exhibited a

higher degree of instability, which resulted in a slightly lower heat transfer

coefficient. In the horizontal and vertical flows, the flow was similar, and the heat

transfer coefficients were identical. This illustrates the insensitivity of the boiling

process to the gravitational orientation in narrow channels. This feature makes the

minichannels and microchannels very attractive for microgravity applications.

Cortina-Díaz, Boye, Hapke, Schmidt, Staate and Zhekov [24] found different

trends of the heat transfer coefficient depending on the nature of the working fluid.

For flow boiling of pure hydrocarbons (n-hexane, n-heptane and n-octane) in a

capillary tube of 1.5 mm in diameter, the heat transfer coefficient was seen to increase

with increasing heat flux. But monotonically decrease with increasing vapor quality.

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LITERATURE REVIEW

14

For water, the heat transfer coefficient increased with increasing vapor quality, and

the same results were observed for an n-hexane/n-octane mixture.

Kandlikar [25] concluded that heat transfer during flow boiling in microchannels is

dictated by the intermittent passage of liquid slugs and expanding bubbles. The heat

transfer mechanism due to periodic movement of the liquid-vapor interface over the

heated surface is similar to the transient conduction mechanism around a nucleating

bubble in pool boiling.

Chen, and Garimella [26] studied the effect of dissolved air on subcooled flow

boiling. They observed the followings:

The dissolved air resulted in a significant reduction in wall temperature at

which bubbles were first observed in the microchannels. This suggested that

the bubbles observed initially in the non-degassed liquid were most likely air

bubbles.

They performed degassing of the working fluid and found that it had a strong

impact on both the measured heat transfer and pressure drop. Larger pressure

drops were measured for boiling with the non-degassed liquid.

For application to electronics cooling, they recommended that liquids be fully

degassed to ensure greater predictability and control of wall temperature and

to ensure lower pressure drops and flow instabilities.

Sobierska, Kulenovic, Mertz and Groll [27] did experiments on flow boiling of

water in a vertical microchannel.

They found the followings:

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LITERATURE REVIEW

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The heat transfer coefficient is the highest one in the bubbly flow regime for

all presented mass fluxes.

With increasing vapor quality the convection mechanism through the liquid

layer starts to play a significant role.

For two-phase flow the heat transfer decreases with increase in vapor quality

(the transition from bubbly to annular flow). As the heat flux is increased, the

heat transfer coefficient increases

Schneider, Kosar, Kuo, Mishra, Cole and Scraringe [28] showed that significant

heat transfer increment (approximately 67%) was obtained under super cavitating

flow conditions in comparison to non-cavitating flow conditions for the same mass

velocity. They found the followings:

No further heat transfer enhancement was obtained with the reduction of the

cavitation index once super-cavitating flow conditions were initiated.

A deviation of 1% - 1.5% in the pressure drop between single-phase flow and

super-cavitating flow conditions were registered.

There was a similarity between the flow patterns in the multipassage

microchannel device used in this study and previously reported patterns in a

single micropassage device under adiabatic conditions. The flow patterns were

dependent on the cavitation number and the longitudinal location in the

channel.

Kuo, Kos, Peles, Virost, Mishra and Jensen [29] experimentally found the

followings:

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The experiments on two microchannel devices with identical global

geometrical configurations (i.e., one having reentrant cavities and one with

plain smooth walls) is a better way to evaluate the inherent capabilities in

reentrant cavities in enhancing heat transfer in microchannels.

In microchannels and macrochannels, active nucleation site density, bubble

departure diameter & its frequency and flow patterns during forced flow with

enhanced reentrant cavities are similar.

The active nucleation site density varies with the heat flux and mass velocity

and which shifts towards the inlet region when increased.

The wall superheat temperatures do not seem to strongly affect the nucleation

site density unlike large-scale channels.

There is a major difference between the activation mechanisms of bubble

nucleation sites in microchannels and macrochannels. And possibly it is

related to the increasing bubble-departure-diameter to channel-hydraulic-

diameter ratio in microchannels.

Wojtan L., Revellin R. Thome [30] investigated critical heat flux during saturated

flow boiling of R-134a and R-245fa in horizontal 0.5 and 0.8 mm microchannels.

They found that for fixed inlet subcooling, CHF increased with increasing the mass

flux and was higher for the 0.8 mm than for the 0.5 mm diameter tube. The effect of

the inlet subcooling was found insignificant for the range of experimental conditions.

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Nucleation characteristics during flow boiling in microchannels were studied by

K andilkar [31]. Also expressions for local wall superheat and liquid subcooling at

the nucleation location were proposed.

The unique flow characteristics in microchannels and minichannels were

further analyzed and their influence on flow boiling stability was investigated

experimentally using visual images generated with a high-speed camera. Stabilizing

the flow by introducing a pressure drop element and artificial nucleation sites was

discussed clearly.

Huh and Kim [32] experimentally studied flow boiling in an asymmetrically heated

rectangular microchannel. They found that the saturated flow boiling is governed by

nucleate boiling and the forced convection boiling. The heat transfer mechanism of

thin liquid film evaporation between the vapor core and the heated surface might

contribute to the boiling heat transfer. High mass flux and high heat flux resulted in

pressure drop oscillations.

Wang, Cheng and Wu [33] performed simultaneous visualization and measurements

of temperature, pressure and mass flux variations during their investigation of flow

boiling instabilities of water in microchannels at various heat fluxes and mass fluxes.

A flow boiling map, in terms of heat flux vs. mass flux, showing stable flow

boiling regime and unstable flow boiling regime were presented. The data was for

both parallel microchannels as well as for a single microchannel.

Comparison of results of flow boiling in parallel microchannels and in a single

microchannel showed that flow interaction effects from neighboring channels at the

headers are significant.

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Chang and Pan [34] experimentally explored the two-phase flow instability in a

microchannel heat sink with 15 parallel microchannels. The hydraulic diameter for

each channel was 86.3 μm.

Flow boiling in their study showed significantly different two-phase flow

patterns under stable or unstable conditions. For unstable cases forward or reversed

slug or annular flows appeared alternatively in every channel.

The study also showed that if the deviation between the maximum instant pressure

drop and the minimum instant pressure drop is greater than about 6 kPa, two phase

flow instability with reversed flow to the inlet chamber appears.

Muwanga, Hassan and Mcdonald [35] studied detailed flow characteristic of flow

boiling instabilities in two different silicon microchannel heat sinks. One is a straight

standard microchannel configuration and the second contains cross-links between the

channels. Their findings are as follows:

Both configurations showed a decreasing frequency of oscillation with

increasing heat flux.

Flow oscillations for inlet temperature, outlet temperature, and inlet pressure

are at the same frequency.

At two different inlet temperatures and a range of flow rates for the straight

standard heat sink, the instability data was presented and the data showed that

with increasing flow rate, the frequency of oscillations increased, whereas

with decreasing inlet temperature, the oscillation frequency increased.

The frequency and amplitude characteristics of these oscillations were

correlated with two different inlet temperatures, with the boiling number, with

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the inlet subcooling temperature and with the weber number. The oscillations

had relatively large amplitudes, which could have damaging effects on the

electronic chip being cooled.

Flow boiling of water in microchannels is experimentally investigated by Liu and

Garimella [36]. The fluid inlet temperatures, microchannel wall temperatures and the

pressure drop across the microchannel were measured. The boiling heat transfer

coefficients for subcooled and saturated boiling regimes were determined. Heat

transfer correlations in the literature were assessed critically for applicability to

microchannels. A new correlation suitable for the saturated boiling regime is

developed.

It was found that the fluid inlet conditions, i.e., degree of subcooling and velocity,

affect the onset of nucleate boiling, but have little impact on the boiling curve once

the onset nucleate boiling has occurred.

Experiments on CHF of R-123 conducted in a microchannel heat sink by Kosar and

Peles [37]. They showed that dryout is the leading CHF mechanism for boiling of R-

123. They found the followings:

Depending on the heat flux, location and mass velocity different flow regimes

like bubbly, slug, intermittent annular, and annular are identified.

CHF tends to reduce with reduction in surface tension and latent heat of

vaporization. CHF increases with mass velocity and decreases with exit vapor

quality.

CHF increases as pressure is increased to a certain value, beyond which CHF

declines.

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Boiling number, the dimensionless pressure ratio, and the exit mass quality

can successfully represent the experimental data.

Pressure Drop, Boiling Heat Transfer and Flow Patterns during Flow Boiling in a

Single Microchannel were experimentally investigated by Huh and Kim [38]. A

horizontal rectangular microchannel with hydraulic diameter of 100 μm and length of

40 mm was used for the experiments. Flow patterns were obtained from real-time

flow visualizations made during the flow boiling experiments. The effects of mass

flux and vapor quality on the local flow boiling heat transfer coefficient and two-

phase frictional pressure gradient were studied. The evaluated experimental data were

compared with existing correlations. Most of the existing correlations did not provide

reliable heat transfer coefficient predictions for different vapor quality values. Also

prediction of the two-phase frictional pressure gradient deviated except under some

limited conditions.

Wang, Cheng and Bergles [39] studied the effects of inlet/outlet configurations on

flow boiling instability in parallel microchannels. They found that for microchannels

where flow entering to the microchannels is restricted, steady flow boiling with no

oscillations of temperature and pressure can be achieved. In these microchannels, no

reversed flow of vapor bubbles was observed under the experimental conditions. This

configuration is recommended for high-heat-flux microchannel applications to avoid

large temperature fluctuations and early burnout.

In their experimental study Kuan and Kandilkar [40] observed that the pressure

drop elements (PDE) at the inlet of each microchannel stabilizes the flow boiling

process and avoid the backflow phenomena. The PDE decreases the CHF in case of

R123 and had no effect on the CHF value of water. Also their theoretical analysis of

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The heat flux increases slowly with the flow rate for single-phase flow and the

diverging microchannel shows a significantly higher heat transfer rate at the

same rate.

After boiling begins, heat flux and the heat transfer coefficient are elevated

sharply but the mass flow rate show insignificant effect.

The diverging microchannel presents better performance in boiling heat

transfer than that of the uniform cross-section microchannel with the same

mean hydraulic diameter and under similar operating conditions due to much

more stable two-phase flow.

The single-phase pressure drop of the diverging microchannel is higher than

that for that with a uniform cross section and the difference decreases with

increasing the mass flow rate. Contrarily, the two-phase pressure drop after

boiling begins is approximately the same at the same heat flux for both types

of microchannel.

Singh, Kulkarni, Duttagupta, Puranik and Agrawal [43] studied the impact of

aspect ratio on the pressure drop in rectangular microchannels.

They said that there are two kinds of pressure drop inside the channel called

the frictional pressure drop and acceleration pressure drop. And these oppose each

other for different aspect ratio which results in a minimum pressure drop. The above

results were demonstrated theoretically as well as through experiments. The result

obtained have practical significance in that for a given hydraulic diameter, an aspect

ratio range close to 1.56 may be employed to minimize the pressure drop penalty.

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The paper of Wang and Cheng [44] presents a study of Flow Boiling in a single

Microchannel. They identified three flow regimes which were Isolated Bubble,

Confined Bubble and Annular Slug.

The heat transfer coefficient was a strong function of heat flux and system

pressure, while effects of mass flux and vapor quality are small. Heat flux was mainly

through nucleate boiling.

At low Reynolds number the flow trends in boiling heat transfer coefficient

were similar to that observed in nucleate boiling.

The effect of mass flux and vapor quality on the local flow boiling heat

transfer coefficient and two phase frictional pressure gradient were studied, and the

prediction capability of conventional macro-channel correlations was assessed.

The heat transfer coefficient was found to be independent of mass flux and

vapor quality but the flow resembled annular flow. This finding according to them

was a disagreement with available literature.

Macro-channel correlations cannot be used to predict the boiling heat transfer

coefficient in micro-channel applications. However at vapor quality of 0.1 correlation

proposed by Liu and Winterton predicted the experimental data with reasonable

accuracy.

Lee and Garimella [45] conducted experiments to find out the characteristics of

saturated flow boiling heat transfer and pressure drop in silicon microchannel arrays.

The presented their results in terms of temperatures and pressure drop as a function of

imposed heat flux. The microchannels considered for their experimental run, range in

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width, from 102 μm to 997 μm, with the channel depth being nominally 400 μm in

each case. Key findings from this work are given below:

The pressure drop across the microchannels increases rapidly with heat flux

when the incipience heat flux (for the onset of nucleate boiling) is exceeded.

At low to medium heat fluxes, the local heat coefficient increases almost

linearly with heat flux. At higher heat fluxes, the saturated heat transfer

coefficient becomes largely insensitive to heat flux. This may indicate a

change in the dominant boiling mechanism, from nucleate boiling to

convective boiling.

A critical review of correlations in the literature suggests that existing

correlations in the literature do not match the experimental results obtained for

two-phase pressure drop and heat transfer associated with flow boiling in

microchannels.

Lu and Pan [46] experimentally explored the possibilities of stabilizing of flow

boiling in ten parallel microchannel heat sinks with a diverging cross-section design.

Flow visualization showed that heat flux and mass flux significantly affect the

stability of flow boiling in the parallel microchannels. The extent of pressure drop

oscillations may be regarded as an index for the onset of flow boiling instability.

Their study confirmed that, in terms of stability performance, the flow boiling

in the parallel microchannel heat sinks with a diverging cross-section design is

superior to a uniform cross-section design.

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Harirchian and Garimella [47] experimentally studied the effects of channel

dimension, heat flux, and mass flux on flow boiling regimes in microchannels. They

found the followings:

As channel width increases, bubbly flow replaces slug flow and discontinuous

churn/wispy-annular flow replaces irregular churn/annular flow.

As mass flux increases, the bubbles become smaller and more elongated in the

bubbly region, and the liquid layer thickness in the wispy-annular and annular

regimes decreases.

The transition between specific flow patterns occurs at a higher heat flux for

higher mass fluxes.

Bertsch, S.S., Groll, E. A., and Garimella [48] experimentally studied the effects of

heat flux, mass flux, vapor quality, and saturation temperature on flow boiling heat

transfer in microchannels. They used R-245fa and R-134a as the working fluid and

found the followings:

The heat transfer coefficient for R-245fa in comparison with R-134a in flow

boiling is lower as a result of its higher molecular mass and surface tension.

The onset of nucleate boiling (ONB) is shifted towards higher heat fluxes with

increasing mass flux.

The flow boiling heat transfer coefficient strongly increases with increasing

heat flux and seems to be dominated by nucleate boiling. It also shows a

strong dependence on thermodynamic vapor quality.

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Zhao and Bansal [49] used CO2 –lubricant mixtures as the working fluid in their

experimental study of flow boiling heat transfer. Their findings are as follows:

Addition of lubricant in CO2 sharply decreases the flow boiling heat transfer

coefficient, even with very low oil concentrations.

At high oil concentrations, the flow boiling heat transfer coefficient is almost

independent of vapor quality.

The deterioration of the flow boiling heat transfer due to lubricant increases

with increasing saturation temperature.

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2.2. THEORITICAL, NUMERICAL AND OTHER STUDIES RELATED TO FLUID FLOW

AND HEAT TRANSFER IN MICROHANNELS

Palm [55] in his paper titled “Heat Transfer in Microchannel” published in 2001,

reviewed the available literature on heat transfer and pressure drop for one and two

phase flow. He emphasized on reports presented during the last few years.

The flow boiling heat transfer is often assumed to be the result of two different

mechanisms, nucleate boiling and convective boiling. Nucleate boiling is dominant at

high heat flux and low vapor quality, while convective boiling is important at high

mass flux and high vapor quality, where nucleate boiling is suppressed. Fluids with

low molar mass are expected to give the highest heat transfer coefficients for two-

phase cooling systems.

Kandlikar [56] studied the fundamental issues related to the “presence of nucleate

boiling and characteristics of flow boiling in microchannels and minichannels” in

comparison to that in the conventional channel sizes (3 mm and above). Also, the

effect of heat exchanger configuration (single-channel and multichannel) on the heat

transfer and pressure drop performance was reviewed.

They found that three flow patterns are commonly encountered during flow

boiling in minichannels i.e. isolated bubble, confined bubble or plug/slug, and

annular. It was also found that the effect of surface tension is quite significant in flow

boiling in microchannel causing the liquid to form small uniformly spaced slugs that

fill the tube, sometimes forming liquid rings. The heat transfer rate in multichannel

evaporators was found to be different from that in single-channel evaporators under

the same set of operating conditions.

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Kandilkar [58] proposed two new dimensionless groups in his study titled “Heat

Transfer Mechanisms During Flow Boiling in Microchannels”. The dimensionless

numbers are useful at arriving at basic relationships among system variables that are

valid for different fluids under different operating conditions. Heat flux at the wall

causes evaporation of the working fluid and the resulting momentum change

introduces a force on a liquid interface. Other forces are inertia of flow and surface

tension at contact line. Gravity force is assumed to be negligible. Viscous forces are

not considered here but their effect is important in determining the stability of micro

channels.

The conclusions derived from this study are as follows:

Wall superheat increases with channel diameter.

Heat transfer is found to be nucleate boiling (dominating)

Immediately after nucleation a sudden increase in heat transfer coefficient is

experienced due to release of accumulated super heat into the liquid prior to

nucleation.

Thome [59] reviewed the available literature on experiments and theory on

evaporation in microchannels.

What best defines a microchannel is not yet clear. But the threshold to

confined bubble flow is a good working definition for the upper limit. The lower limit

may be the complete suppression of nucleation and hence the threshold to

nanochannels, from a two-phase flow and heat transfer perspective. The primary flow

regimes observed are elongated bubble flow (also referred to as slug flow or confined

bubble flow) and annular flow.

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Flow boiling heat transfer coefficients have been shown experimentally to be

dependent closely on heat flux and saturation pressure. This is similar to nucleate pool

boiling heat transfer and only slightly dependent on mass velocity and vapor quality.

This has led to the conclusion that nucleate boiling controls evaporation in

microchannels.

Numerical simulation of the growth of a single vapor bubble, during flow of water

through a microchannel was performed Mukherjee and Kandilkar [60]. The

objective of the numerical simulations was to obtain flow and thermal fields around a

single vapor bubble inside a microchannel.

Behavior of liquid vapor interface and its interaction with the constraining

walls was studied.

Effect of gravity, wall superheat and Reynolds number on the bubble growth

rate was determined.

Numerical results are obtained while keeping total mass flux constant, show

that backward bubble expansion causing reverse flow occur in multiple micro

channels whereas bubble formation is not simultaneous in each channel. Reverse

flow is found to increase when contact angle decreases and wall superheat increases.

The paper of Thome [61] focuses on the advantages and drawbacks of two-phase

flow boiling heat transfer as compared to other cooling methods.

Some notable advantages are as follows:

Lower pressure drop and mass flow rate, hence lesser pumping power.

Increase of the heat transfer coefficient with heat flux

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The amplitude and frequency of fluctuations during unstable flow boiling has

been attributed to inlet/exit configurations and vapor quality.

The data obtained for flow boiling in microchannels is found to vary largely

from that of macrochannels at high vapor quality.

The upstream compressible volume has been identified as the source of flow

boiling instability in microchannels.

Stable Flow Boiling has been found to occur at low vapor quality.

Nucleate boiling dominates at outset of nucleation while annular two phase

flow prevails at downstream.

The local boiling heat transfer coefficients have been found to peak at low

vapor qualities.

Macrochannel correlations have been found to overestimate boiling heat

transfer coefficients in microchannels.

The parametric study of Revellin and Thome [68] showed that the best solution for a

particular application will be to find a design with the following combination of

characteristics: (i) a short channel length, (ii) a low saturation temperature, (iii) a large

mass flux, (iv) a large subcooling, and (v) a large microchannel diameter for a chosen

fluid to achieve higher value of CHF.

Zhuan and Wang [69] numerical simulated multiphase flow model to investigate the

nucleate boiling of water in a single micro channel. They had used the VOF (Volume

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of Fluid) method for the purpose of simulation. They also investigated the influences

of roughness elements on nucleation and frictional pressure drop.

They noted that there are some differences between micro and macro two-

phase flow. The feature of nucleate boiling in common channel is free bubble

flowing, while in micro channels it is confined bubble flowing. They showed that the

incipient heat flux affect the bubbles growth rates. Also the higher heat flux makes the

small bubbles coalescence more quickly.

Roughness elements increase the nucleation cavities on the wall. The nucleate

boiling in micro channel is intensified on roughness surface contrast to the smooth

surface. But the frictional pressure drop increases on roughness surface.

They presented that with the increase of vapor quality and volume fraction,

mass flux decreases at initial time. Also, as vapor quality rise, frictional pressure drop

also increases due to the jam of large bubbles in micro channel.

Zhuan and Wang [74] simulated bubble behavior to analyze the mechanism of

subcooled boiling in a microchannel. Bubble growth, condensation and collapse were

analyzed in subcooled boiling flow. They also discussed the function of the degree of

subcooling, lift-off diameter, different heat flux and mass flux. They had used the

VOF (Volume of Fluid) method for the purpose of simulation.

They noted that there are some differences in bubble behavior between subcooled

boiling and saturated boiling. In subcooled boiling, bubble growth and collapse are

controlled by degree of subcooling, lift-off diameter, heat flux and mass transfer. In

saturated boiling, lift-off bubbles expand and coalesce quickly and form a slug flow.

In subcooled boiling, due to the subcooled liquid, an annular flow seldom occurs in

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the wide range of mass and heat fluxes. But in saturated boiling, the slug and annular

flows usually appear in the microchannel.

At high degree of subcooling, surface tension influences the growth of subcooled

boiling to some extent. Also a high degree of subcooling delays ONB to some extent.

ONB is also influenced by microchannel size. With high aspect ratio, the nucleation

process is delayed and the bubbles begin to grow slowly.

A numerical study Mukherjee, Kandlikar and Edel [75] had been performed to

analyze the wall heat transfer mechanisms during growth of a vapor bubble inside a

microchannel. The microchannel was of 200 m square cross section and a vapor

bubble begins to grow at one of the walls, with liquid coming in through the channel

inlet. The complete Navier-Stokes equations along with continuity and energy

equations were solved using the SIMPLER method. The liquid vapor interface was

captured using the level set technique.

The observations made are as follows:

The wall heat transfer improved with increase in wall superheat and the bubble

growth rates.

The wall heat transfer remained unaffected by the changes in the incoming

liquid flow rates.

Insignificant effect of the liquid surface tension on bubble growth was

observed. The bubble shapes were affected by the liquid surface tension values

with lower surface tension producing longer and thinner bubbles. The effect of

surface tension on wall heat transfer found to be negligible.

A decrease in contact angle causes formation of a liquid layer between the

bubble downstream interface and the wall that has significant influence on

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bubble growth and wall heat transfer. The bubble with the lowest contact

angle exhibited the highest growth rate and also the highest wall heat transfer.

The bubble growth is found to push the liquid against the microchannel walls,

thus preventing the growth of the thermal boundary layers.

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CHAPTER 3

THEORITICAL B ACKGROUND

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3. THEORETICAL BACKGROUND

3.1. FUNDAMENTALS OF BOILING

Boiling is defined as the process of phase changing just like evaporation, but there are

significant differences between the two. Evaporation occurs at the liquid-vapor

interface when the vapor pressure is less than the saturation pressure of the liquid at a

given temperature. Boiling on the other hand occurs at the solid-liquid interface when

a liquid is brought into contact with a surface maintained at a temperature sufficiently

higher than saturation temperature of the liquid.

Boiling process is characterized by the rapid formation of vapor bubbles at the solid-

liquid interface that detach from the surface when they reach a certain size and

attempt to rise to the free surface of the liquid. The boiling process in practice does

not occur under equilibrium conditions, and normally the bubbles are not in

thermodynamic equilibrium with the surrounding liquid. That is the temperature and

pressure of the vapor in a bubble is usually different than that of the liquid. The

pressure difference between the liquid and vapor is balanced by the surface tension at

the interface. The temperature difference between the vapor in a bubble and the

surrounding liquid is the driving force for heat transfer between the two phases. When

the liquid is at lower temperature than the bubble, heat is transferred from the bubble

to the liquid, causing some of the vapor inside the bubble to condense and the bubble

eventually to collapse. When the liquid is at higher temperature than the bubble, heat

is transferred from the liquid to the bubble, causing the bubble to grow and rise to the

top under the influence of buoyancy.

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If the temperature of the liquid is below the saturation temperature, the process is

called Subcooled boiling, whereas if the liquid is maintained at the saturation

temperature the process is known as saturated boiling.

The three different boiling heat transfer mechanisms are nucleate boiling, where heat

is transferred by means of vapor bubbles nucleating, growing and finally detaching

from the surface; convective boiling, where heat is conducted through the liquid and

heated liquid evaporates at the liquid-vapor interface without bubble formation; and

film boiling, where the heat is transferred by conduction and radiation through a film

of vapor that covers the heated surface and the liquid vaporizes at the vapor liquid

interface. Nucleate boiling and film boiling may occur in both pool boiling and flow

boiling, while forced convective boiling occurs only in flow boiling.

Boiling can be defined according to the geometric situation and to the mechanism

occurring. Regarding the geometry, it is possible to distinguish between pool boiling,

where the heat is transferred to a stagnant fluid; and flow boiling, where the fluid has

a velocity relative to the heating surface. A brief discussion on both these boiling

processes is as follows:

3.1.1. POOL BOILING

In pool boiling the fluid is not forced to flow by a mover such as pump. Any motion

of the fluid is by natural convection currents and the motion of the bubbles under the

influence of buoyancy. The relationship between heat flux q// and the wall superheat

(ΔTsup = Twall – Tsat) is known as the boiling curve which is illustrated for saturated

pool boiling in Figure 3.1.

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Fig. 3.1, Typical Boiling Curve & Heat Transfer Process in Pool Boiling [64]

As the input heat flux to the surface is increased there’s no bubble formation and heat

is transferred by natural convection between the hot surface and the liquid vapor

interfaces (O-A). At a certain value of wall superheat (A) bubble nucleation is

initiated on cavities present on the heater surface. This condition is called Onset of

Nucleate Boiling (ONB) and the corresponding heat flux is known as Incipient Heat

Flux. In liquids that wet the surface well, the onset of nucleation may be delayed (A /).

Because for these liquids a sudden activation of a large number of cavities, at an

increased wall superheat, causes a reduction in the surface temperature while the heat

flux remains constant (A/-.A//). After inception, the slope of the curve increases. At

first, discrete bubbles are released from randomly located active sites (A-B). At higher

heat flux the density of active sites and the frequency of bubble release increase.

Transition from isolated bubbles to fully developed nucleate boiling (B-C) occurs

when bubbles at a given site begin to merge in the vertical direction and with bubbles

ΔTsup = Twall – Tsat (K)

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from the neighboring sites. Further increasing the heat flux, intense evaporation near

the bubble base leads to periodic dry patches on the surfaces that are re-wetted by the

surrounding liquid (C-D). This results in a reduction in the slope of the curve.

Eventually, liquid is unable to rewet the heating surface and a large area becomes

covered by a vapor blanket, causing a large temperature excursion on the heating

surface (F). The heat flux corresponding to this condition (D) is known as the critical

heat flux (CHF), and represents the upper limit of fully developed nucleate boiling or

safe operation of equipment. If the temperature at F exceeds the melting temperature

of the heating material, the heater will fail (burn out). The curve E-F represents the

stable film boiling. The heating surface is totally covered with vapor film and the

liquid does not comes in contact with the solid and the system can be made to follow

this curve by reducing the heat flux. With a reduction in heat flux in film boiling, a

condition is reached when the vapor film can no longer be sustained and collapses.

The heat flux corresponding to this condition (E) is called the minimum heat flux. The

region falling between nucleate and film boiling (D-E) is known as the transition

boiling region. Transition boiling is very unstable and essentially inaccessible with

constant heat flux boundary condition.

3.1.2. FLOW BOILING

For flow boiling process the boiling curve obtained is similar to the pool boiling. The

underlying mechanisms however, are more complex as the liquid-vapor flow

configurations change due to the addition of vapor along the flow direction.

Figure 3.2, shows a conceptual picture of forced flow boiling process with

temperature profile for a circular tube with uniform heat flux boundary condition in

which subcooled liquid enters the tube.

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Fig. 3.2, Flow Boiling in a Uniformly Heated Circular Tube [53].

The first mode of heat transfer as subcooled liquid enters the tube is single-phase

convection. The heat transfer coefficient in this region is constant except for the

variations due property change with increasing liquid temperature in the flow

direction. Boiling will not occur until the wall temperature reaches a certain value

above the saturation temperature. The primary formation of bubbles is known as onset

of nucleate boiling, ONB. Subcooled flow boiling exists when the bulk liquid

temperature remains below its saturation value but the surface is hot enough for

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bubbles to form. Bubbles formed at the wall will condense as they move out of the

developing saturation boundary layer, but the appearance of these bubbles will affect

the heat transfer between the wall and the fluid. Initially, only few nucleation sites are

active and a portion of the heat is transferred by single-phase convection between

patches of bubbles. As more nucleation sites are activated the contribution to heat

transfer from nucleate boiling increases while the single-phase convective

contribution diminishes. This region is termed partial nucleate boiling. When the

surface becomes fully active for nucleation, fully developed nucleate boiling, is

established. In addition, as the bulk fluid is heated the saturation boundary layer

continues to grow and eventually covers the entire channel and the saturated nucleate

boiling region is reached. Further downstream, the addition of vapor to the flow leads

to a transition in the heat transfer mechanism. The thickness of the thin liquid film in

annular flow is often such that the effective thermal conductivity is enough to prevent

the liquid from being superheated to the temperature needed to sustain nucleate

boiling. Heat is transferred from the wall by forced convection to the liquid-vapor

interface, where evaporation occurs. The suppression of nucleate boiling indicates the

beginning of the convective boiling region. Ultimately, at some critical vapor quality

complete evaporation of the liquid film will occur. This transition is known as dryout

and is accompanied by a rise in the wall temperature. The area between the dryout

point and the transition to dry saturated vapor is commonly referred to as the liquid

deficient region.

The critical heat flux (CHF) condition in flow boiling is a major research area. It is

characterized by a sharp reduction of the local heat transfer coefficient as a result of

the replacement of liquid by vapor adjacent to the heat transfer surface [53]. The CHF

condition in low boiling can be of different nature [73]:

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At low vapor quality, it has strong similarities to pool boiling critical heat flux,

both in mechanism and in behavior. It is associated with subcooled boiling or

saturated boiling at high heat fluxes encountered for example in nuclear reactor

applications.

At medium or high quality, it is commonly called dryout and it is

characterized by the discontinuation of the liquid film on the tube wall, usually in

annular flow. It is associated to moderate heat flux conditions. Dryout condition may

occur due to interruption of the liquid layer caused by surface wave instabilities (at

medium vapor qualities) or by dry up of the liquid layer on the heated wall due to

entrainment and vaporization (at high vapor qualities).

Critical heat flux has been extensively studied and vast amounts of data have been

collected, in particular for steam-water flow in vertical tubes. The CHF for a

uniformly heated tube usually varies linearly with the inlet subcooling degree,

increases with mass flux and tube diameter and asymptotes to zero as the tube length

increases.

3.2. TWO‐PHASE FLOW PATTERNS

Two-phase vapor-liquid flow can take on many geometrical configurations according

to the spatial distribution of the vapor and liquid phases in the channel. These

configurations are known as flow patterns.

In the study of microchannels, flow patterns observed via high speed visualizations

are categorized into five major flow regimes [47] – bubbly, slug, churn, wispy-annular,

and annular flows; a post-dry-out regime of inverted-annular flow is also identified.

Although these flow patterns have a slightly different appearance in different channel

sizes and for different mass fluxes and flow rates, each is characterized by certain

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common features. Figure [2.3.] represents different liquid and vapor phases in the

flow patterns which are represented below:

Figure [2.3.(a)] shows bubbly flow in which isolated round and elongated

bubbles that are smaller than the cross section of the microchannels move in the flow

direction. Bubbles generally nucleate at the microchannel walls and detach from the

walls after growing. The shape and size of the bubbles vary with flow rate and heat

flux.

As the heat flux increases, the bubble generation rate at the walls increases and

bubbles become larger as a result of bubble coalescence. At higher heat fluxes or in

smaller microchannels, bubbles occupy the entire cross section of the channels,

resulting in slug flow as shown in Figure [2.3. (b)]. Also small bubbles exist in the

liquid slugs between the elongated bubbles.

The churn flow regime is demonstrated in Figure [2.3. (c)]. This flow regime

consists of vapor chunks transported downstream and large bubbles nucleating at a

high rate at the channel walls. However, at high heat fluxes, the nucleation at the

walls may be suppressed.

In wispy-annular flow as in Figure [2.3. (d)], a vapor core is separated from

the channel walls with a relatively thick and unstable liquid film. Large, irregular-

shaped droplets are entrained into the vapor core. Very few nucleation sites remain in

the liquid film and result in small vapor bubbles in the liquid layer.

In annular flow, as illustrated in Figure [2.3. (e)], the liquid layer is thinner

than in wispy-annular flow, and the interface between the vapor core and the liquid

film may become wavy. The liquid film thickness decreases as the heat flux increases.

Small, round droplets are entrained into the vapor core, while no vapor bubbles are

seen in the liquid annulus.

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At very high heat fluxes, when critical heat flux is reached, the walls can

completely dry out under certain conditions and a vapor blanket forms at the walls

around a liquid core flowing through the center of the channels. This flow regime is

called inverted annular flow Figure [2.3. (f)]. This flow regime is to be avoided since

it is accompanied with a sudden rise in the wall temperature and a significant drop in

the heat transfer coefficient.

Under some conditions, these flow patterns may alternate in a single channel,

resulting in an intermittent flow. In channels with large aspect rations, two different

flow patterns may also be present alongside each other across the width of the

channels.

Fig. 3.3, Different Flow Boiling Regimes [47]

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3.3. NON‐DIMESIONAL NUMBERS / PARAMETERS RELEVENT TO FLOW BOILING

HEAT TRANSFER IN MICROCHANNEL

Non-Dimensional

Numbers / Parameters

Significance

Martinelli Parameter (Xm)

V F

LF

m

dz

dpdz

dp

X

⎟

⎠

⎞⎜

⎝

⎛

⎟ ⎠

⎞⎜⎝

⎛

=2

This parameter [62] is an empirical expression. It is the

ratio of frictional pressure drops between liquid and gas

flow. This parameter has been successfully employed in

two-phase model.

Convection number (Co)

( )5.08.0

1⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡ −=

L

V

x x

Co ρ

ρ

Convection number is a modified Martinelli Parameter

[62]. But its usage is limited to flow boiling heat transfer

only. This non-dimensional number was also proposed

empirically based on extensive data analysis.

Boiling number (Bo)

LV Gh

q Bo

//

=

Kandlikar and Balasubramanian [17] proposed this

number. Heat transfer coefficient trends depend on the

boiling number and the liquid to vapor density ratio. It is

used as an empirical relationship because heat flux is non-

dimensionalized with mass flux and latent heat without

fundamental study.

K 1

V

L

LV Gh

qK

ρ

ρ 2

//

1 ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =

Kandlikar [56] proposed this number based on

fundamental considerations, for flow boiling heat

transfer, when surface tension forces become an

important consideration. It is the ratio of evaporation

momentum to inertia forces at the liquid–vapor interface.

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K 2

σ ρ V LV

D

Gh

qK

2//

2 ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =

Kandlikar [56] derived this number and suggested to use

it in modeling interface motion, such as critical heat flux.

It is the ratio of evaporation momentum to surface tension

forces at the liquid–vapor interface.

Bond number (Bn)

( )σ

ρ ρ V L

gD Bn

−=

2

Bonjour and Lallemand [7] proposed this non-

dimensional number. They noted that the Bond number

effectively identifies the transition of flow patterns from

conventional diameter tubes to minichannels.

Eötvös number (Eo)

( )σ

ρ ρ V LgL Eo −

=2

“Eo” is same as Bond number [62], except that the

characteristic dimension L could be Dh or any other

suitable parameter.

Capillary number (Ca)

σ

V Ca =

It is the ratio of viscous force to surface tension force

[62]. This non-dimensional number is very important in

microchannel flow since both the numbers have

significance effect during the flow.

Weber number (We)

ρσ

2 LG

We =

“We” represents the ratio of the inertia to the surface

tension forces [62]. For flow through channels, L may be

replaced by Dh. this non-dimensional number is

commonly employed in analyzing the gas-liquid adiabatic

flows.

Jakob number (Ja)

LV

L p

V

L

h

T c Ja

Δ= ,

ρ

ρ

“Ja” represents the ratio of the sensible heat required for

reaching a saturation temperature to the latent heat [62].

This non-dimensional number is helpful in analyzing the

bubble growth phenomenon.

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CHAPTER 4

COMPUTATIONAL FLUID

DYNAMICS MODEL EQUATIONS

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COMPUTATIONAL FLUID DYNAMICS MODEL EQUATIONS

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4. COMPUTATIONAL FLUID DYNAMICS MODEL EQUATIONS

In this study both the single phase and multiphase models are used for solving the

problems. The simulated flow is supposed to be fully developed [69]. At first the

single phase model is used to obtain fully developed velocity profile at outlet of the

pipe and then this velocity profile is used as the inlet profile of multiphase pipe flow

simulation. The theories for all the models used in this chapter are adopted from the

ANSYS Fluent 13.0 [70, 71].

4.1.

SINGLE

PHASE

MODELING

EQUATIONS

The single phase model equations include the equation of continuity, momentum

equation and energy equation (ANSYS Fluent 13.0). The continuity and momentum

equations are used to calculate velocity vector. The energy equation is used to

calculate turbulent kinetic energy & turbulent dissipation rate. The equations are as

follows:

4.1.1. MASS CONSERVATION EQUATION

The equation for conservation of mass, or continuity equation, can be written as

follows:

mS v =⎟ ⎠ ⎞⎜⎝ ⎛ Δ+∂

∂ → ρ ρ .

t (4.1)

Equation (4.1) is the general form of the mass conservation equation, and is valid for

both incompressible & compressible flows. The source S m is the mass added to the

continuous phase from the dispersed second phase (e.g., due to vaporization of liquid

droplets) and any user defined sources.

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4.1.2. MOMENTUM CONSERVATION EQUATION

Conservation of momentum in an inertial (non-accelerating) reference frame is

described by

( ) PF g ∇−∇++=⎟ ⎠

⎞⎜⎝

⎛ ∇+⎟ ⎠

⎞⎜⎝

⎛ ∂

∂ →→→τ ρ υ υ ρ υ ρ ..

t (4.2)

Where p is the static pressure, τ is the stress tensor (described below), and ρ g and

F are the gravitational body force and external body forces (e.g., that arise from

interaction with the dispersed phase), respectively. F also contains other model

dependent source terms such as porous-media and user-defined sources.

The stress tensor τ is given by

( ) ⎥⎦

⎤⎢⎣

⎡∇−∇+∇= I T υ υ υ μ τ .

3

2 (4.3)

Where μ is the molecular viscosity, I is the unit tensor, and the second term on the

right hand side is the effect of volume dilation.

4.1.3. ENERGY EQUATION

ANSYS FLUENT solves the energy equation in the following form:

( )[ ] ( )heff

j

j jeff S J hT k p E E +⎥

⎦

⎤⎢⎣

⎡+−∇∇=+∇+⎟

⎠

⎞⎜⎝

⎛

∂

∂∑ υ τ ρ υ ρ ...

t (4.4)

Where κ eff is the effective conductivity (κ eff = κ + κ t, where κ t is the turbulent thermal

conductivity, defined according to the turbulence model being used), and j J is the

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diffusion flux of species J . The first three terms on the right-hand side of Equation

represent energy transfer due to conduction, species diffusion, and viscous

dissipation, respectively. S h includes the heat of chemical reaction, and any other

volumetric heat sources.

In Eq. (4.4)

2

2υ

ρ +−=

ph E (4.5)

Where sensible enthalpy h is defined for ideal gases as

∑= j j jhY h (4.6)

Y j is the mass fraction of species j.

dT ch j p j ∫= , (4.7)

T ref is used as 298.15 K.

4.2. TWO PHASE MODELING EQUATIONS

A large number of flows encountered in natur

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