Report Final 000

EXPERIMENTAL STUDY OF LIQUID JET BREAKUP AND

ATOMIZATION IN CROSS FLOWS

A PROJECT REPORT

Submitted by

Arvindh R Sharma

Faheem Hussain M

Murugan A

Vishnu Bhadran

Project work carried out at CSIR-NAL, Bangalore - 560017

in partial fulfillment for the award of the degree

of

BACHELOR OF ENGINEERING

IN

AERONAUTICAL ENGINEERING

K.C.G. COLLEGE OF TECHNOLOGY

ANNA UNIVERSITY: CHENNAI 600 025 DECEMBER 2011-APRIL 2012

iii

ANNA UNIVERSITY : CHENNAI 600 025

BONAFIDE CERTIFICATE

Certified that this project work entitled “EXPERIMENTAL STUDY OF

LIQUID JET BREAKUP AND ATOMIZATION IN CROSS FLOWS” is the

bona fide work of Arvindh R Sharma (Reg. No. 31108101009), Faheem Hussain M

(Reg. No. 31108101017), Murugan A (Reg. No. 31108101026) and Vishnu

Bhadran (Reg. No. 31108101052), who carried out the project work under my

supervision.

SIGNATURE SIGNATURE

Prof. R. R. Elangovan Mr. Bikash Kumar Mondal

HEAD OF THE DEPARTMENT SUPERVISOR

Dept. of Aeronautical Engineering Assistant Professor

KCG College of Technology Dept. of Aeronautical Engineering

Chennai-97 KCG College of Technology

Chennai-97

April, 2012

Internal Examiner External Examiner

Experimental Study of Liquid Jet Breakup and Atomization in Cross Flows

iv

Declaration

We hereby declare that the entire work embodied in this dissertation has been

carried out by us and no part of it has been submitted for any degree or diploma of

any institution previously.

Arvindh R Sharma

Faheem Hussain M

Murugan A

Vishnu Bhadran

Date :

Place :


v

Acknowledgements

We wish to express our gratitude to the Director, NAL, for permitting us to

carry out the project at NAL. We thank Mr. C Diwakar, Joint Head, KTMD, Mrs.

Gomathy Sankaran, Group Head, KTMD, and the other staff who helped us in

getting permission to carry out our project at NAL. We also thank the Head of the

Department, Propulsion Division, Mr. M. Jayaraman, and Mr. Manjunath. P,

Deputy Head and Scientist In-Charge, Combustion activities, Propulsion Division,

for allowing us to be a part of the High Speed Combustor Test Facility, Propulsion

Division during our stay at NAL.

Our heartfelt thanks are due to our guides at NAL, Dr. Venkat Iyengar S

(Scientist, PR) and Mr. Sathiyamoorthy K (Scientist, PR), for their constant

support, mentoring, motivation and guidance without which the work attempted

would have been insurmountable. Our special thanks to Mr. J Srinivas (Technical

Officer) and Mr. Pratheesh Kumar (Technical Officer) for their invaluable help in

setting up our experimental facility. We are also grateful to the staff at Combustion

and Gas Dynamics Laboratory and High Speed Combustor Test Facility for

helping us carry out the experiments.

We thank our Principal, KCG College of Technology, Dr. T Rengaraja, for his

support of our endeavor. We sincerely thank the Head of the Department,

Aeronautical Engineering, Prof. R.R. Elangovan, for facilitating our project work

in the midst of a rigorous academic schedule. We are indebted to our guide at KCG

College, Mr. Bikash Kumar Mondal, Aeronautical Department, for his valuable

suggestions and motivation throughout the course of our work.


vi

ABSTRACT The penetration of water jets injected transversely in subsonic cross flows and the

droplet size distributions in the resulting sprays were experimentally studied. The

non-dimensional parameters Weber number(We) and momentum flux ratio(J) were

used to characterize the sprays. A wide range of subsonic Mach numbers and water

mass flow rates(mf) were used. The penetration heights were obtained at cross flow

Mach numbers 0.3 and 0.4, which represent the practical flow conditions in aero-

engines. Two plain orifice injectors with diameters of 0.8 mm and 1mm were used.

Penetration studies were carried out within x/dj=85. The droplet size distribution

studies were carried out at three far-field locations: (x/dj,y/dj)=(330,23),(248,23)

and (310,28.75). High speed photography was used for flow visualization and

penetration studies. Low Angle Laser Light Scattering (LALLS) was used in

studying the droplet size distributions. The penetration increased with increase in J

at a constant We while it decreased with increase in We at a constant J. The effects

of J, We, water mass flow rate and the cross flow velocity(Va) on droplet SMDs

and SMD distributions were analyzed. D32 decreased with increase in J and

increase in mf at constant We. The effect of J and mf decreased as We increased to a

sufficiently high value when aerodynamic breakup and shear stripping began

dominating over column breakup. The percentage of smaller SMD droplets (within

22µm) in the spray increased with increasing Va at a particular mf.


vii

Contents ABSTRACT ...................................................................................................................... vi

Contents ............................................................................................................................ vii

List of Tables ...................................................................................................................... x

List of Figures ................................................................................................................... xi

List of Abbreviations ...................................................................................................... xiii

Symbols .................................................................................................................................... xiii

Subscripts ................................................................................................................................. xiv

1 INTRODUCTION ...................................................................................................... 1

1.1 Atomization....................................................................................................................... 1

1.2 Penetration ........................................................................................................................ 3

1.3 Spray Droplet Size ............................................................................................................ 4

1.4 Liquid Jets in Cross Flows ................................................................................................ 5

1.5 Applications [14] .............................................................................................................. 6

1.5.1. Afterburner ............................................................................................................................ 6

1.5.2. Ramjet ................................................................................................................................... 6

1.5.3. SCRamjet .............................................................................................................................. 7

1.5.4. Reentry Vehicles ................................................................................................................... 7

2 LITERATURE REVIEW .......................................................................................... 9

2.1 Introduction ....................................................................................................................... 9

2.2 Breakup Regimes and Flow Structures ............................................................................. 9

2.3 Penetration Height .......................................................................................................... 14

2.4 Atomization Process ....................................................................................................... 18

2.5 Droplet Properties and Size Distribution ........................................................................ 19


viii

2.6 Effects of Weber Number and Momentum Flux Ratio ................................................... 22

2.7 Effect of Injectant Properties, Injector Geometry and Injection Angle .......................... 25

2.8 Aerated Liquid Jets ......................................................................................................... 30

2.9 Turbulent and Non-Turbulent Liquid Jets ...................................................................... 32

2.10 Conclusion ...................................................................................................................... 33

3 MOTIVATION FOR CURRENT RESEARCH .................................................... 34

4 EXPERIMENTAL SETUP ...................................................................................... 36

4.1 Test Rig ........................................................................................................................... 36

4.2 Water Injection System ................................................................................................... 38

4.3 Injector ............................................................................................................................ 39

4.4 Instrumentation ............................................................................................................... 40

4.5 Coordinate System .......................................................................................................... 40

4.6 Diagnostic Equipment ..................................................................................................... 41

5 EXPERIMENT METHODOLOGY ....................................................................... 43

5.1 Calculation of Flow Parameters ...................................................................................... 44

6 RESULTS AND DISCUSSION ............................................................................... 46

6.1 Visualization of Liquid Jets in Cross Flows ................................................................... 46

6.1.1 Trajectory Details ................................................................................................................ 55

6.2 Characteristics of Spray SMD ........................................................................................ 57

6.2.1 Droplet Size Distribution .................................................................................................... 58

6.2.2 Effect of Momentum Flux Ratio (J) and Weber number (We) ........................................... 62

6.2.3 Effect of Cross Flow Weber number at different Injectant Mass Flow Rates .................... 65

6.2.4 Effect of Cross Flow Velocity ............................................................................................ 66

7 SOURCES OF ERROR ........................................................................................... 71

8 CONCLUSIONS AND FUTURE WORK .............................................................. 72


ix

8.1 Conclusions ..................................................................................................................... 72

8.2 Scope for Future Work.................................................................................................... 73

APPENDIX 1: Particle Size Measurement using Laser Diffraction .......................... 74

A.1 Principle............................................................................................................................. 74

A.2 Apparatus........................................................................................................................... 74

A.3 Optical Models .................................................................................................................. 75

A.4 Advantages of Laser Diffraction ....................................................................................... 75

A.5 Particle Size ....................................................................................................................... 76

APPENDIX 2: Sample Calculation of Experimental Conditions and Parameters ... 77

9 REFERENCES .......................................................................................................... 79


x

List of Tables

Table 2.1 Penetration height correlations for liquid jets in subsonic and supersonic

cross flows ................................................................................................................15

Table 2.2 Effects of Weber number on breakup regime ..........................................25

Table 6.1 Test conditions for the experiments on penetration heights ....................47

Table 6.2 Liquid column trajectory for We=130 and J=35 .....................................55

Table 6.3 Liquid column trajectory for We=130 and J=115 ...................................56

Table 6.4 Test conditions for the experiments on droplet size distributions ...........57

Table 6.5 Test conditions and SMD for Mach 0.3 test case ....................................58

Table 6.6 SMD volume distribution data .................................................................60

Table 6.7 Derived parameters ..................................................................................61

Table 6.8 SMD number distribution data ................................................................62

Table 6.9 Test conditions for effect of cross flow velocity studies .........................67

Table 6.10 Average SMDs and Cumulative Number % at 22.16 µm .....................69


xi

List of Figures

Fig. 2.1 Flow Characteristics of Liquid Jet in Cross Flow ....................................10

Fig. 2.2 Breakup regime map .................................................................................11

Fig. 2.3 General flow topology of jet injection in compressible cross flow .........13

Fig. 2.4 Schematic diagram of the flow structure of liquid jet in hypersonic

crossflow ..................................................................................................................13

Fig. 2.5 Comparison of penetration height for various liquid jet-to-air momentum

flux ratio ...................................................................................................................23

Fig. 2.6 Comparison of penetration heights for various injection angles ..............28

Fig. 2.7 Comparison of penetration heights for different injector diameters ........29

Fig. 2.8 Shadowgraph images of liquid jets at various liquid aeration levels. ......31

Fig. 4.1 Schematic sketch of the test rig ................................................................37

Fig. 4.2 Injector design ..........................................................................................39

Fig. 4.3 Sketch of the test-section showing injector locations ..............................41

Fig. 6.1 Instantaneous image at We=130, J=30 ......................................................48

Fig. 6.2 Averaged image at We=130, J=30 ............................................................49

Fig. 6.3 Outer and inner boundaries from averaged image at We=130, J=30 ........49

Fig. 6.4 Instantaneous image at We=130, J=35 ......................................................50

Fig. 6.5 Averaged image at We=130, J=35 ............................................................51

Fig. 6.6 Outer and inner boundaries from averaged image at We=130, J=35 ........51

Fig. 6.7 Instantaneous image at We=130, J=115 ....................................................52

Fig. 6.8 Averaged Image at We=130, J=115 ..........................................................52


xii

Fig. 6.9 Outer and inner boundaries of the jet from averaged image at We=130,

J=115 ........................................................................................................................53

Fig. 6.10 Instantaneous image at We=240, J=10 ....................................................53

Fig. 6.11 Averaged Image at We=240, J=10 ..........................................................54

Fig. 6.12 Outer and inner boundaries of the jet from averaged image at We=240,

J=10 ..........................................................................................................................54

Fig. 6.13 Comparison of penetration height correlations and experimental data for

We=130 and J=35 ....................................................................................................56

Fig. 6.14 Volume distribution of droplet SMDs .....................................................59

Fig. 6.15 Number distribution of droplet SMDs .....................................................61

Fig. 6.16 Effect of momentum flux ratio (J) on SMD at various Weber numbers .63

Fig. 6.17 J vs SMD trends .......................................................................................64

Fig. 6.18 Effect of Weber number (We) on SMD at various injectant mass flow

rates ..........................................................................................................................65

Fig. 6.19 Comparison of SMD number distributions at different cross flow

velocities ..................................................................................................................68

Fig. 6.20 Mach number vs Cumulative Number % at 22.16 µm- Trend ................70


xiii

List of Abbreviations

Symbols

D Aerodynamic drag force

ρa Density of the cross flow air

Va Velocity of the cross flow air

d Diameter of liquid droplet

CD Coefficient of drag

FST Force due to surface tension

σ Surface tension of water (0.072 N/m)

SMD, D32 Sauter Mean Diameter of liquid droplet

We Weber number

ρj Density of water (1000 kg/m3)

Vj Velocity of water jet

dj Diameter of injector orifice

J Liquid jet-to-free stream air momentum flux ratio

x,y,z Distances along X,Y,Z axes respectively

M Mach number

θ Injection angle with respect to cross-flow direction

GLR Aerating gas-to-liquid mass ratio (in percentage)

L/D Injector nozzle internal length-to-diameter ratio


xiv

γ Specific heat ratio of air

R Specific gas constant of air

P0 Stagnation pressure of cross flow air

PS Static pressure of cross flow air at the test-section

T0 Stagnation temperature of cross flow air

TS Static temperature of cross flow air at the test-section

mf Mass flow rate of injected water

Aj Nozzle exit orifice area

Subscripts

a Cross flow air property

j Liquid jet property

0 Stagnation condition

S Static condition


1

1 INTRODUCTION

The conundrum of achieving optimum spray characteristics with a simple yet

effective injection scheme has occupied researchers for many decades. The choice

of the injection method depends on the application, which dictates the conditions

prior to injection and the desired flow conditions post injection. From fuel injection

in diesel engines to agricultural sprays, from aerosol sprays to film cooling, sprays

have a wide spectrum of applications. This also necessitates the study of various

injection techniques that can address particular requirements. Transverse injection

in cross flows is one such injection scheme which is particularly suited for

aerospace propulsion applications and promises to address the various requirements

imposed on it yet be simplistic in design and conceptualization.

The liquid spray can be defined as a collection of liquid droplets driven

through a medium, such as air. The spray is formed from the bulk liquid by a

process called atomization. The atomization is the process by which a liquid

droplet, due to the action of forces external and internal to it, undergoes

deformation and breaks down into finer sized droplets. The effectiveness of the

atomization process is the major criteria in deciding the injection scheme. Further,

spray characteristics like spray width, spray cross-sectional area, spray penetration

height, the time or distance required for optimal atomization, the droplet size

distribution across the spray, etc. are parameters that must be analyzed based on the

application.

1.1 Atomization

Lefebvre and Ballal [7] discussed the various factors that affect the atomization

process in detail. The atomization process is the result of the interplay between the


2

consolidating forces that are inherent to a liquid and the disruptive forces acting on

it. In the absence of disruptive forces, the surface tension of the liquid tends to

transform the liquid into a sphere, since it possesses the surface with least surface

energy. The disruptive forces, such as aerodynamic forces, try to deform the liquid.

Thus, atomization is produced when the disruptive forces exceed the consolidating

forces.

In the case of liquid jets in cross flows, the disruptive force is aerodynamic

drag. It is given by:

D

22

a Cd4

V2

1D

a

The consolidating force is that of surface tension and is given by:

dFST

The critical condition when atomization just begins is when

dCd4

V2

1D

22

a

a

From the above critical condition for atomization, it can be inferred that as the

droplets break down and their sizes decrease, the decrease in disruptive

aerodynamic force is relatively larger than the decrease in consolidating surface

tension force. Hence, it becomes progressively more difficult for a droplet to break

down into smaller sized droplets under a given condition.

The atomization process constitutes two regimes: 1) Primary atomization and

2) Secondary atomization. In primary atomization, the liquid jet is broken down

into bag-like structures and ligaments. These structures are further broken down

into finer droplets during secondary atomization.


3

In addition to the effects of surface tension and aerodynamic drag, the liquid

viscosity also affects atomization. Viscosity opposes any relative motion between

various layers in a liquid, thus opposing any change in liquid geometry. This

adversely affects the atomization process.

There are three major factors affecting the atomization process [5]:

1. The relative velocity between the liquid and the surrounding medium, i.e., air.

2. The internal geometry of the injector.

3. The physical properties of the injected liquid and the surrounding medium.

1.2 Penetration

The penetration height of a liquid jet can be defined in a number of ways. One

of the definitions is that the penetration height is the maximum transverse distance

attained by a given spray plume [24]. It can also be defined as the distance from the

wall containing the injector at which the top boundary of the spray plume gets

aligned with the cross flow and becomes parallel to the wall.

The penetration height is necessary for understanding the combustor efficiency

in ramjet and scramjet combustors. It provides an idea about the mixing between

the fuel droplets and the air stream. If a fuel jet penetrates less into the cross flow, a

large area of the combustor remains unutilized for mixing, and the fuel is rather

concentrated in a narrow region of the combustor. On the other hand, with a greater

penetration, a larger area of the combustor is utilized for mixing with air. Thus,

there is better mixing with the surrounding air stream which aids in obtaining a

more uniform droplet distribution in the combustor. This will have a direct bearing

on the flame property and overall combustor operation.

The penetration height is a major factor in deciding applicability of the spray in


4

other spray applications as well.

1.3 Spray Droplet Size

The mean droplet sizes and the size distributions are important parameters that

help in predicting the utility of a spray for a particular application. There are several

mean diameters used to characterize the sprays, such as Arithmetic Mean Diameter

(AMD), Sauter Mean Diameter (SMD) and de Brouckere Mean Diameter. Since

sprays are composed of particles of various shapes and sizes, the different mean

diameters give an idea of different aspects of the droplets such as number, surface

area and volume.

The use of liquid hydrocarbons as fuels in aero-engines such as ramjets,

scramjets and afterburners depends on the ease and completion of combustion of

these fuels in the combustor. The combustion process depends on the surface area of

the droplets, since more the surface area of a droplet for a given volume, more the

exposure to available oxygen for combustion. Thus, a mean droplet size relating the

surface area to volume of the droplets is necessary in characterizing combustion of

sprays.

The SMD or D32 can be defined as the diameter of a droplet sphere having the

same volume-to-surface area ratio as the entire spray. It can also be described as the

mean of the moment of surface area.

2

3

32d

dD

It can be seen that the SMD provides adequately the information about the surface

area available for a given volume of spray. Therefore, SMD is used to study spray

combustion processes.


5

1.4 Liquid Jets in Cross Flows

The transverse liquid injection into gas streams, also called Liquid Jets in

Cross Flows (LJICF), is a promising injection method suited for fuel atomization in

aero-engine combustors. Due to the normal injection, the relative velocity between

the injected liquid and the cross flow is significantly large. This aids in quick

atomization. Moreover, the spray penetration and width can be higher than the case

of angled injection. Other advantages are the simplicity of injector design and

control over the injection parameters. The injectors can produce a high relative

speed between the liquid and cross flow at lower pressures than conventional

pressure atomizers. Thus the problem of clogging of injectors can be addressed to

an extent using cross flow injection. Another important feature that is to be studied

closely is the mixing between the two media, the liquid and the gas cross flow.

The atomization of liquid jets in cross flows depends upon two major non-

dimensional parameters: 1) Weber number (We) and 2) Liquid-to-air momentum

flux ratio (J). The Weber number is the ratio of the aerodynamic force of the cross

flow to the surface tension force of the liquid. Higher the Weber number, higher is

the disruptive force of the cross flow in comparison to the consolidating force

offered by surface tension. The Weber number dictates the breakup mechanism to

some degree. Liquid-to-air momentum flux ratio (J) determines the momentum

exchange between the liquid jet and cross flow.

dVVWe

2

a

2

aa a

d

2

aa

2

jj

V

VJ


6

1.5 Applications [14]

The increased understanding of spray structure resulting from cross flow

injection will help in optimization of combustor design in ramjets, scramjets and

afterburners. LJICF has applications in film cooling of reentry vehicles, thrust

vector control in missiles, rockets and other aircrafts as well.

The jet trajectory plays a main role in different applications. For liquid cooling

applications, a jet that bends more towards the injection wall, grazing it, and having

low penetration is more preferred. But in combustors and afterburners, a jet that

penetrates deeper is desired. The various aspects of transverse liquid jet injection

are utilized in different ways in the different applications.

1.5.1. Afterburner

The turbojet and turbofan engines employ afterburners in order to augment the

thrust by burning additional fuel in a duct downstream of the turbine and before the

exhaust nozzle. In an engine without an afterburner, the turbine blade material

considerations impose limitations on the maximum temperature of the gases leaving

the combustor. However, since the combustion in an afterburner takes place

downstream of the turbine, higher exhaust gas temperatures can be attained.

The fuel injection in an afterburner can be achieved through transverse

injection into the cross flow. This is similar to the classic case of liquid jet injection

in subsonic cross flows.

1.5.2. Ramjet

A ramjet is an engine used to power high subsonic and supersonic aircrafts. It

achieves compression of the incoming air by ram effect, thus eliminating the need

for a mechanical compressor. The air in the inlet is stagnated and enters the

combustor at a speed of about Mach 0.3. Liquid fuels can be injected into this


7

subsonic gaseous cross flow to achieve atomization and combustion. The fuel can

be injected from the combustor walls or from flame stabilizers.

1.5.3. SCRamjet

Supersonic Combustion Ramjet, or SCRamjet, is an engine particularly suited for

supersonic and hypersonic flight regimes. Similar to a ramjet, it compresses air by

ram effect and does without mechanical compressors. However, unlike a ramjet, the

incoming air is not slowed down to subsonic speeds. Instead, the air enters the

combustor at supersonic speeds. Hence, fuel atomization and combustion has to

occur in a supersonic airstream. The use of liquid fuels in SCRamjets will result in

development of longer range supersonic/hypersonic aircrafts since liquid fuels can

be stored more easily and have higher density than gaseous fuels. Hence testing the

viability of using transverse liquid fuel injection in scramjets is of major interest in

hypersonic aircraft development.

On injecting a liquid jet in supersonic airstream, a boundary layer separation

zone is formed upstream of the injector due to the interaction between the boundary

layer and the shock formed due to the presence of liquid jet. This is a zone where

heat transfer rate is very high. Hence, it creates a region favouring combustion.

Also, the shock system decreases the total pressure of the air stream but increases

the static temperature and slows down the air stream. These effects can be utilized

to stabilize the ignition of fuels in supersonic streams and increase overall

combustion efficiency.

1.5.4. Reentry Vehicles

Upon reentry, a hot layer of ionized gases surrounds a reentry vehicle. This layer

may disrupt the working of communication antenna and cause blackout of signals.

To prevent this, cooling of the localized area is necessary. This can be achieved with


8

the help of a liquid jet injected transversely which cools the desired location. The

breakup process of the liquid jet needs to be understood well in order to accurately

design the cooling system.


9

2 LITERATURE REVIEW1

2.1 Introduction

Liquid Jets in Cross Flows (LJICF) have been the focus of many researches for

more than seven decades. A number of researches have focused on various aspects

of the phenomenon and the existing literature cover a wide range of experimental

conditions. Gaining a thorough understanding of the breakup of liquid jets in cross

flows, and identifying the specific focus area of our current research in relation to

the work that has already been done, is the aim of this review.

2.2 Breakup Regimes and Flow Structures

The breakup process of liquid jets in subsonic cross flows and the regimes in

which they occur have been reported in a number of studies.

The breakup process of liquid jets in subsonic air cross flows can be

considered to occur in three regimes: 1) column, 2) ligament and 3) droplet. After

the liquid injection, the liquid jet undergoes surface breakup with droplets stripped

away from its surface. Acceleration waves then grow on the surface. The liquid

column is flattened and deformed. Subsequently, the column disintegrates into

ligaments and droplets [23]. Gopala et al. [4] also postulated that the surface waves

formed on the liquid surface distort the liquid column. The aerodynamic forces

enhance the growth rate of the disturbances downstream, leading to the formation of

ligaments which breakup into droplets.

1 The symbols representing various parameters like momentum flux ratio, penetration height, air density, etc. are

adapted from the cited references wherever possible. In other instances, the legends used are the authors’ own.


10

Fig. 2.1 Flow Characteristics of Liquid Jet in Cross Flow

Wu et al. [23]

Becker and Hassa [1] observed liquid jets with the help of time-resolved

shadowgraphs. They identified two main breakup mechanisms: 1) column breakup

and 2) surface breakup. In the column breakup zone, waves were observed on the

windward side of the jet. The wave growth leads to the instability in the column,

which fractures at a wave trough. The surface breakup proceeds with the erosion of

the liquid droplets from the jet by the cross flow air. The ligaments and droplets are

stripped off from the sides of the jet.

Becker and Hassa [1] and Wu et al. [23] provided a “break-up map”, a plot of J

vs We, that identified the conditions under which the column and surface break-up

occurred. At high values of J, the liquid jet column is well-defined and relatively

stable. Surface breakup occurs in this case. For a fixed J, the surface breakup is

dominant when the air flow’s dynamic pressure overcomes the conservative action

of surface tension of liquid, thereby stripping away droplets and ligaments. It can be

seen that in this case, the Weber number of the flow is relatively higher. At lower J,

the atomization occurs primarily because of the aerodynamic instabilities in the jet

as the jet bends and aligns with the cross flow. The column breakup mode is


11

dominant in this case. It is expected that for J>100, J ceases to influence the

atomization process and the We decides the mode of breakup. At any point, both the

mechanisms are at work but the dominance of one over the other is mainly

dependent on J and We.

Fig. 2.2 Breakup regime map

Wu et al. [23]

Mazallon et al. [12] reported that for conditions with low liquid viscosities,

five kinds of flows were observed: simple, deformation of the shape and trajectory

of the liquid jet without breakup, breakup of the liquid column as a whole, bag

breakup, bag/shear breakup and shear breakup. For the conditions they

investigated, they found that the column first deforms in the direction normal to the


12

cross flow and yields an elliptical cross section for non-turbulent injection from a

circular injector nozzle. The reduced pressure near the lateral sides of the jet as the

air stream flows past it causes lateral motion of the liquid jet. This motion is

stabilized to an extent by the surface tension of the liquid. The flattening of the

column further increases the aerodynamic drag on it which enhances the liquid jet’s

tendency to be deflected downstream. The breakup regime of non-turbulent round

liquid jets in cross flow and the aerodynamic secondary breakup of spherical drops

were found to be similar. Sallam et al. [19] provided corroborating evidence with

the results from their study of liquid jets in subsonic cross flows using pulsed

shadowgraph photography.

The breakup length, which is the distance between the jet orifice and the

endpoint of liquid jet core, is another important breakup characteristic. Wu et al.

[25], in their discussion on Professor Gerard Faeth’s work in the field of LJICF,

observed that in subsonic cross flows, the column fracture point always occurred at

x/ dj ~ 9, when aerodynamic effects are significant. Becker and Hassa [1]

established that in subsonic flows at elevated pressure, when 2≤J18, the break-up

length was between x/ dj = 6.8 and x/ dj = 9.6.

Masutti et al. [11] investigated liquid injection into a hypersonic cross flow

(Mach 6) and described the flow structure. The presence of liquid jet was found to

cause a bow shock in front of it. The bow shock causes an adverse pressure gradient

which causes the boundary layer upstream to split. A separated flow region with a

separation shock appears in the flow. A velocity gradient in the direction normal to

the wall exists because of the nature of the bow shock, which has varying angle.

This causes a high shear stress. The cross flow’s interaction with the liquid jet

through the shear force on the liquid jet column surface causes it to bend and

disintegrate. There appear waves on the jet surface, which are believed to fold and

form a counter rotating vortex pair.


13

Fig. 2.3 General flow topology of jet injection in compressible cross flow

Masutti et al. [11]

Fig. 2.4 Schematic diagram of the flow structure of liquid jet in hypersonic crossflow

Masutti et al. [11]


14

2.3 Penetration Height

Becker and Hassa [1], from their experiments on liquid jet injection at elevated

pressures (1.5 to 15 bar) and cross flow velocities 50 m/s to 100 m/s, provided some

correlations for the penetration height. The penetration height was correlated with

the liquid-to-air momentum flux ratio, J, and the axial distance, x/ dj.

For J in the range of 1 to 40, and We in the range of 90 to 2120, the penetration

height correlation arrived at was:

d

x56.31lnq48.1

d

y 0.42

When J≤12, the correlation was found to be:

d

x81.31lnq57.1

d

y 0.36

Further, it was suggested that the penetration near the nozzle exit is a function

of the nozzle exit diameter and liquid-to-air momentum flux ratio. For a fixed mass

flow rate of injectant, the penetration increased when the nozzle diameter

decreased.

Tambe et al. [22] conducted penetration studies in subsonic cross flows (0.23

M-0.63M) using water, Jet-A and N-Heptane as injectants. They found that the

penetration increases with an increase in momentum flux ratio but is independent of

cross flow Weber number. They also suggest that the cross flow dynamic pressure

might have an effect on penetration by suppressing it.

Schetz and Padhye [20], from their experiments of liquid jet injection in high

subsonic (0.45M and 0.75M) air streams, observed that the penetration height is

proportional to the square root of liquid injection pressure. When injectant pressure

was held constant, penetration was proportional to injectant density. When the

injector geometry and pressure were held constant, penetration was found to


15

decrease with increasing cross flow Mach number. In their studies, the researchers

assumed a constant drag co-efficient for the jet.

Bunce et al. [2] studied the effects of heating the cross flow air, in subsonic air

speeds (75m/s, 100 m/s and 150 m/s). They suggest that the increased air

temperature, and the resultant increase in air viscosity, causes increased drag forces

on the liquid column. Thus the liquid jet is bent more and penetrates less into the air

stream. Lakhamraju [6], from studies on subsonic cross flows (0.21M to 0.68M),

concluded that increasing air stream’s temperature decreased the penetration height.

Additionally, he suggested that an increase in liquid jet temperature caused a

reduction in penetration height, but an exact relationship was not established

satisfactorily.

Lin et al. [8] studied liquid jets in supersonic cross flows (Mach 1.94). They

postulated that the momentum deficit in the air stream boundary layer can aid in

achieving increased penetration height. Thus, a flow with a large boundary layer

thickness was helpful in getting a good penetration. They suggest that a relationship

exists between boundary layer thickness and penetration height.

Numerous correlations for penetration height and the trajectory exist in the

literature. Table 2.1 lists some of the correlations available in the literature.

Table 2.1 Penetration height correlations for liquid jets in subsonic and supersonic cross

flows

Author(s) Correlation Test-Conditions Methodology

Wu et al.

[23]

1997

qdxCd

yD

J=3.38-148

We=71-1179

Va=68.1-141 m/s

Shadowgraphy


16

Wu et al.

[24]

1998

33.033.0

t

d

xq3.4

d

y

J=5.3-59.1

We=54-217

M=0.2-0.4

Phase Doppler

Particle

Analyzer(PDPA

)

Lin et al.

[8]

2000

0.44

0

0

0 q4.8d

h

J=1-18

M=1.94

x/d0=30

Shadowgraphy

Lin et al.

[9]

2002

24.0

0

0.48

000 dxq42.2dh

M=0.3

J=2-40

x/d0<90

Pulsed

Shadowgraphy

40.0

0

0.33

000 dxq17.3dh

M=0.2-0.4

J=0.5-12

x/d0<200

Phase Doppler

Particle

Analyzer(PDPA

)

21.0

0

0.47

000 dxq94.3dh

M=1.94

J=1-18.5

x/d0<90

Pulsed

Shadowgraphy

Becker and

Hassa [1]

2002

d

x56.31lnq48.1

d

y 0.42

J=1-40

We=90-2120

x/d=2-22

Va=50-100 m/s

Time-resolved

shadowgraphy


17

d

x81.31lnq57.1

d

y 0.36

J=1-12

We=90-2120

x/d=2-22

Va=50-100 m/s

Time-resolved

shadowgraphy

Tambe et

al. [22]

2005

D

z1.661lnq55.1

D

y 0.53

J=0.7-10.2

We=50.5-1725.1

M=0.23-0.63

Shadowgraphy

Dixon [3]

2005

0.63

40.0

0

6

0

qd

xsin1018.0

d

h

θ=45 °,60 °,75°,90°

J=1-15

M=1.94

Shadowgraphy

0.38

38.0

0

4.5

0

qd

xsin1068.0

d

h

θ=45 °,60 °,75°,90°

J=1-14

M=1.94

Laser sheet

illumination

0.31

33.0

0

1.2

0

qd

xsin198.0

d

h

θ=45 °,60 ° ,75 °,90 °

J=1-14

M=1.94

PhaseDoppler

Particle

Analyzer


18

(PDPA)

Miller et al.

[13]

2008

40.0

0

0.33

0

0

0 dxq17.3d

h

J=0.74-4

M=0.07-0.16

x/d=25-50

Digital

holography

Mashayek

et al. [10]

2011

39.0

0.36

d

xq6.2

d

z

J=6.1-34.2

We=47.6-57.2

Va=40.8-53.3 m/s

Pulsed-laser

Shadowgraphy

2.4 Atomization Process

Kihm et al. [5], from their studies on liquid jets in low subsonic cross flows,

suggested that the breakup and atomization of liquid jets depended on three factors:

1) liquid jet nozzle or injector geometry, 2) relative velocity of the jet to that of the

gas into which it is injected and 3) physical properties of the gas and the injected

liquid.

Atomization is produced by column breakup and surface breakup of the liquid

jet. Droplets from the surface breakup are smaller than those generated by column

breakup. Hence a large variation in drop size is observed in the spray plume [23].

Mashayek et al. [10] developed a model for liquid jets in subsonic gaseous

cross flows. In their experiments they observed that the droplets at the lower heights

are formed mainly by mass stripping from the liquid jets and have relatively smaller

droplet sizes. Also, the size of the droplets shed from the liquid jet increase with

height. The droplets near the top boundary of the spray plume are produced mainly

as a result of column breakup. So, they are the largest droplets separated directly


19

from the parent jets.

Tam et al. [21] describe the far field structures of pure and aerated liquid jets in

Mach 2 cross flow in their review of jet in cross flow studies. They state that the

atomization processes of both pure and aerated liquid jets were found to be

complete by x/ dj less than 100. This is due to the interaction between the cross flow

and the spray plumes.

The presence of large drops at the top of the spray plume can be explained on

the basis that the larger drops by virtue of their higher momentum penetrate the

farthest into the cross flow.

2.5 Droplet Properties and Size Distribution

Mashayek et al. [10] report that larger droplets are noticed near the top of the

spray plume. These droplets are formed as a result of column breakup. Also, the

smaller droplets were observed at lower heights. Wu et al. [24] conducted

experiments in subsonic cross flows (0.2 M, 0.3 M, 0.4M) and noted that smaller

droplets were observed near the bottom wall. These droplets are generated from

surface breakup and stripped away from the periphery of the liquid column by

aerodynamic forces. Becker and Hassa [1], from their experiments on subsonic

cross flows (50-100 m/s) at elevated pressure, reasoned that the larger particles, by

virtue of possessing higher momentum, longer velocity relaxation time and higher

inertia, penetrate farther into the air stream. It was also established that the SMD at

elevated pressure cross flows depended on the dynamic pressure of the cross flow

and was independent of J. The dependence was established as:

24.02USMD

where U is the free stream air velocity and ρ free stream air density.

Kihm et al. [5] noted that at low subsonic cross flow speeds, the peak of the


20

SMD size distribution shifted to larger values as the distance from the injector wall

was increased. The spray SMD was seen to monotonically increase with increasing

distance from injector wall, because larger droplets penetrated farther into the

airstream.

The cross-sectional distribution of SMD showed that larger droplets are present

in the centre area of the spray plume. From the bottom wall up, SMD first increases

to a large value, then decreases before increasing again. Near the injector, maximum

SMD is observed in the spray core regardless of the injection condition. With

increasing axial distance, the larger droplets from the spray core penetrate into the

airstream causing the SMD to peak near the top of the spray plume for the cases of

low cross flow velocities. However, for the cases of large cross flow velocities the

larger droplets mostly remain in the central portion of the spray plume. Some larger

droplets still penetrate to the top of the spray plume [24].

Tam et al. [21] noted in their review paper that the droplet size distribution

within the spray was non-uniform. The droplets were found to be concentrated in a

small area of the plume. For cases with high jet/air momentum flux ratio, larger

droplets are found in the upper portion of the spray plume while for cases with low

jet/air momentum ratio, larger droplets are found predominantly in the spray core.

When momentum flux ratio is kept constant, and the cross flow air velocity is

increased, maximum SMD location is shifted from the top of spray plume to the

spray core. This may be due to the transition of column breakup mode and the

resulting liquid-air momentum exchange. For conditions of larger liquid injection

diameter and cross flow air velocity, the momentum exchange will be more intense

thus producing an SMD peak in the spray core [24].

A reduction in maximum SMD was found to have been brought about by

increasing air velocity but the minimum SMD did not vary significantly. Hence,

SMD variation in the spray plume decreased with increasing air velocity. It was also


21

noted that the size of the droplets and ligaments decreased with increasing air flow

Mach number due to the increase in aerodynamic forces [23, 24]. Tambe et al. [22],

with experiments in subsonic cross flows (76-188 m/s) using PDPA measurements,

found that as the cross flow air velocity increased, the minimum SMD as well as the

range of SMDs. This is attributed to the enhanced surface breakup at higher cross

flow velocities, giving better atomization.

From the above literature, it can be concluded that at low cross flow velocities,

the largest droplets penetrate to the top of the plume while for high cross flow

velocities, the largest droplets are concentrated in the spray core. In other words, for

low momentum flux ratio, the SMD peaks in the spray core while for high

momentum flux ratio, the SMD peaks in the spray periphery [21,22,24].

Gopala et al. [4] recorded data concerning total velocity of droplets in low

subsonic cross flows (Mach 0.2) and found that till 50 injector diameters

downstream of the injector, the droplet velocity was different from cross flow

velocity. The droplet velocity reached a maximum of 95% of the cross flow velocity

and stabilized at a downstream distance of 115 injector diameters. Also, they found

that the droplet diameters stabilized at around 35 injector diameters downstream of

the injector and that larger droplets were found within 35 x/ dj.

In Mach 2 supersonic cross flow, atomization was observed to be complete by

x/ dj < 100. This is due to strong interaction between the spray plumes and

aerodynamic forces. Also, flux averaged SMD downstream of this location was

found to be constant and of the order of 10 μm. The centerline droplet size

distribution, normalized by the penetration height, exhibited an S-shape. The upper

inversion point for pure and aerated liquid jets was found to be at y/h = 0.7 and y/h

= 0.5 respectively [21].

Masutti et al. [11] observed that in Mach 6 cross flow, SMD decreased

asymptotically with increasing downstream distance from injection point and


22

reached a constant value at a particular downstream distance. After that SMD did

not vary much with increasing x/ dj. This indicates that the atomization process is

complete at a particular location from injection point.

Wu et al. [25] indicate that in supersonic cross flows, the turbulent flow behind

the shock train caused enhanced mixing between the droplets and free stream air.

2.6 Effects of Weber Number and Momentum Flux Ratio

It has long been theorized that the drop size and penetration are functions of

the momentum flux ratio and the gas Weber number. Many researchers have

attempted to establish the most accurate correlation linking the above mentioned

parameters with the droplet size, column trajectory, breakup regime and other

breakup structures.

Wu et al. [23] noted that the jet penetration decreased as the momentum flux

ratio decreased. This is because the cross flow’s momentum increased relative to

that of the jet. Consequently, the liquid jet cannot penetrate farther. Bunce et al. [2],

Lakhamraju [6] and Miller et al. [13] also asserted that increasing the momentum

flux ratio increased the jet penetration height. Dixon [3], from his studies on angled,

aerated liquid jets in supersonic (Mach 1.94) cross flows, established that for an

increase in liquid-to-air momentum flux ratio, J, there was a small increase in the

penetration height for a normally injected, pure jet (Fig. 2.5).


23

Fig. 2.5 Comparison of penetration height for various liquid jet-to-air momentum flux

ratio

Dixon [3]

Nejad et al. [14], from their experiments in supersonic air cross flows (Mach

3.0), reported that at x/ dj = 48, y/ dj = 15.3, SMD decreased with increasing

momentum flux ratio while the spray penetration height increased. At a downstream

location of x/ dj = 82.9, y/ dj = 13.1, spray penetration again increased with


24

momentum flux ratio but SMD did not show a consistent variation with momentum

flux ratio. Additionally, SMD value was smaller for the downstream location. On

holding the momentum flux ratio constant, it was observed that SMD was smallest

at the spray periphery at x/ dj = 82.9. In effect, a simple relation for the variation of

SMD across spray plume could not be established.

Wu el al. [24] state that the liquid column trajectory is parabolic and the

column breaks always at the same axial location. Thus for lower momentum flux

ratios, there is a sharper curvature of the jet in the downstream direction. The

interaction between column waves and the air stream is intense and there is

significant momentum exchange. For larger momentum flux ratios, the column

curvature is not sharp. The jet penetrates farther due to its larger transverse

momentum.

The spray plume width was also seen to increase with momentum flux ratio,

but not as significant as the increase in penetration height. So, the plume exhibits

higher aspect ratio and higher cross-sectional area at higher momentum flux ratio.

Sallam et al. [18] suggest that there is no significant effect of varying

momentum flux ratio on SMD in the case of aerated liquid jets.

At a fixed momentum flux ratio, the spray penetration decreases with

increasing gas Weber number. For a fixed gas Weber number, the penetration

increases with increasing momentum flux ratio [10]

Kihm et al. [5] observed that increasing the gas Weber number decreased

atomization effectiveness because the jet was bent more and resulted in decreased

shearing area. This caused the SMDs to increase. On increasing the momentum flux

ratio, effective atomization was seen to occur, with higher penetration.

When We < 10, the aerodynamic forces are not large as compared to liquid

surface tension forces. But when We > 10, the aerodynamic forces play a major part

in the breakup process. Bag/multimode column breakup is observed when We is


25

small and shear column breakup dominates when We is large [23].

Gopala et al. [4] suggest that the domination of column breakup mode or shear

breakup mode over the other is decided by the Weber number and the momentum

flux ratio. They also indicate that droplets with larger SMDs are formed at lower

Weber numbers.

Mazallon et al. [12] have identified the various breakup regimes with

corresponding Weber number ranges. For the conditions they investigated (We: 2-

200 and Ohnesorge number: 0.00006-0.3), they identified four liquid column

breakup regimes (Table 2.2).

Table 2.2 Effects of Weber number on breakup regime

Mazallon et al. [12]

Weber

number range We < 5 5 < We < 60 60 < We < 110 110 < We

Breakup

Regime

Liquid column

breakup Bag breakup

Bag/Shear

breakup Shear breakup

They also compared liquid column breakup with secondary drop breakup at

low Ohnesorge number ( Oh < 0.01 ). They found that bag/shear breakup of the

liquid jet is analogous to multimode breakup of drops and thus the original

diameters of liquid jets and drops must be used in the expressions for We and Oh.

2.7 Effect of Injectant Properties, Injector Geometry and Injection

Angle

Wu et al. [23] studied the liquid jet trajectories in subsonic air cross flows

(Mach 0.2, 0.3 and 0.4) for three different liquids- 1) water, 2) 30% alcohol/water


26

solution, and 3) 40% glycerol/water solution. They asserted that the water jet

showed the straightest trajectory and the glycerol/water solution jet curved the

most. The onset of surface breakup was noticed to be closer to the nozzle exit in the

case of alcohol/water solution jet. Further, droplet sizes and ligament non-

sphericities were found to be smaller for the alcohol/water jet.

It had been postulated that the spray characteristics depend on injector

geometry, injection angle, turbulence level of the liquid jet and test-section

characteristics.

Schetz and Padhye [20] examined liquid jets using different injector orifice

shapes with the same exit area. They noticed that the injector with a rectangular

cross-section which is aligned with free stream achieved the highest penetration,

while the circular injector was the next best, closely followed by the rectangular

injector aligned transverse to the free stream direction. The difference in penetration

for the last two injector shapes mentioned was not significantly large. The mean

droplet sizes were also affected by injector geometry. Rectangular injector aligned

with free stream produced droplets with least average size, while the rectangular

injector oriented transverse to the cross flow produced larger sized droplets.

Similarly, Perurena et al. [16] investigated liquid jet injection in Mach 6 hypersonic

cross flow, and observed that a streamwise rectangular injector provided higher

penetration than a circular injector, while a spanwise rectangular injector provided

lower penetration than the other two cases. This is because the lower frontal area for

a lower aspect ratio injectors, like streamwise rectangular injector, facilitate only

lesser momentum exchange between jet and free stream, thus allowing greater

penetration. Also, the lateral extension of the jet was found to increase with aspect

ratio.

Miller et al. [13] recorded the effects of changing the injector diameter in the

case of aerated liquid jets. It was observed that the SMD distribution did not vary


27

much for different injector diameters because SMD distribution was more a

function of thickness of liquid sheet exiting the injector, which is dependent more

on GLR than the injector diameter. However, the number of droplets observed for

the larger diameter injector was almost double the number of droplets for the

smaller diameter injector, due to the increased flow rate in the case of larger

diameter injector.

However, Nejad et al. [14] contended that in supersonic flows, a larger

diameter injector produced droplets with larger SMD.

Kihm et al. [5] observed that as the injector diameter increased, the penetration

decreased due to the decreased injection velocity with accompanying momentum

loss. Also, they reported that there was a dramatic increase in SMD with increasing

injector diameter.

Wu et al. [24] found that a smaller diameter injector with larger liquid injection

velocity contributes to larger cross-sectional area of the plume.

The injection angle is a major factor controlling liquid column fracture height

and fracture distance. As the injection angle decreases, the penetration and column

fracture height decrease while the column fracture distance increases.

Dixon [3] studied penetration of angled, aerated liquid jets in supersonic cross

flows. He observed liquid jets injected at angles 45°, 60°, 75° and 90° using

shadowgraphy, laser sheet illumination and Phase Doppler Particle Analyzer

(PDPA). He established that the spray penetration increases considerably with an

increase in injection angle towards 90° (Fig. 2.6). He also observed that with an

increase in injector diameter, the penetration height and the effective momentum of

the jet increases (Fig. 2.7). He concludes his thesis with the observation that the

correlations of penetration height derived from PDPA measurements are more

accurate than those obtained from shadowgraphy and laser-sheet illumination

methods. Also, he suggests that PDPA is better suited for far-field measurements


28

whereas shadowgraphy and laser-sheet illumination are better for near-field

measurements.

Fig. 2.6 Comparison of penetration heights for various injection angles

Dixon [3]


29

Fig. 2.7 Comparison of penetration heights for different injector diameters

Dixon [3]

The effects of nozzle length/diameter (L/D) on the surface properties of

turbulent jets were studied by Osta and Sallam [15]. When the injector diameter was

constant, increase in L/D resulted in a decrease in breakup length of the jet. Also, an

increase in L/D resulted in an increase in surface activity of the jet.

Reichel et al. [17] compared a sharp-edged injector with l/d = 10 (Injector 1)


30

and a smooth injection orifice with l/d ~1 (Injector 2). It was observed that the

spray from the Injector 1 oscillated at 60 injector diameters downstream of the

injector by about 10 diameters. The jet from Injector 2 penetrated farther due to less

turbulence. The flow through Injector 1 was highly erratic and spread out than that

from Injector 2.

2.8 Aerated Liquid Jets

Effervescent atomization is produced by injecting an amount of gas along with

the liquid jet, at a location upstream of the liquid jet nozzle exit, in order to produce

a two-phase flow. The aeration level depends upon the ratio of aerating gas-to-

liquid mass ratio.

It is suggested that a typical aerated liquid jet produces a good spray in the far

field which is characterized by smaller droplet sizes, larger cross-sectional area,

high droplet velocities and fairly uniform volume flux distribution at lower injection

pressures than pure liquid jets, within a relatively short distance after injection [18].

In fact, aeration was shown to help achieve combustion in a direct-connect

supersonic combustor using cold JP-7 fuel, while under the same conditions, a pure

liquid jet failed to achieve combustion [25].

It was also observed that as the amount of aerating gas increased, the discharge

co-efficient decreased while the spray penetration height increased (Fig. 2.8). This

was postulated to be due to the increase in the effective momentum flux ratio due to

the aerating gas. In a highly aerated liquid jet, which is a two-phase, co-annular

flow, the liquid forms a thin, annular film around the aerating gas and travels at a

high speed [21].


31

Fig. 2.8 Shadowgraph images of liquid jets at various liquid aeration levels.

Injectant: water, M = 0.3, d0 = 1.0 mm, q0 = 4.2

Tam et al. [21]

Miller et al. [13] differentiated the jet characteristics of a low GLR jet and high

GLR jet in a subsonic airstream, in more detail. They indicate that a liquid jet with

low GLR will exit the injector as a plume with gas bubbles traveling in the center of

the jet. In the case of a high GLR jet, the liquid will exit the injector as an annular,

thin film surrounding the gas core. The spray was found to be constituted of densely

packed, small droplets and was difficult to analyze. It was also found that changing

the GLR resulted in a change in the SMD of droplets in the immediately

downstream of the injector(0-50d). On increasing the GLR from 4% to 8%, the

SMD reduced from 151 μm to 71 μm, under the conditions they investigated. The


32

reason is that the liquid film is squeezed into a thinner sheet by the increased gas

flow rate. Also, another flow characteristic, the penetration height, was found to be

15 diameters higher at 8% GLR than at 4% GLR, because the thinner liquid jet

exited the orifice at a higher velocity than the thicker liquid jet at lower GLR. But

GLR changes did not have much effect on spray width. These results effectively

show how aerated liquid jets can be utilized for obtaining a spray with desirable

characteristics.

2.9 Turbulent and Non-Turbulent Liquid Jets

Turbulent liquid jets are produced by injectors with high length-to-diameter

ratios, typically greater than 10. Highly contracted, converging flow passages, with

L/D~0, are used to produce non-turbulent liquid jets with highly laminar internal

flow in the nozzle. Turbulence has been found to enhance the break-up process of

the liquid jets [25].

Osta and Sallam [15] investigated turbulent liquid jets in gaseous cross flows

and reported that the breakup region consists of two major regimes: 1) aerodynamic

breakup regime, which includes column, bag, multimode, shear breakup (similar in

appearance to breakup of non-turbulent liquid jets in cross flow) 2) turbulent

breakup regime. They also gave a dimensionless number that divided the two

regimes.

where, WeL Λ is the jet Weber number.

17000qWe 3

1

L


33

2.10 Conclusion

While the numerous experiments and investigations on LJICF throw light on

various aspects, there is still some obscurity and scope for further research. The

breakup regimes, the atomization process, the liquid jet penetration and the

behaviour of the SMD of the droplets on varying the parameters like Weber number

and liquid-to-air momentum flux ratio needs to be understood better. Also, the SMD

distribution of the spray, after the droplets have undergone secondary breakup, is

expected to throw new light on the jet atomization process in the far-field region.

The current research attempts to bring these aspects of jet atomization into focus.


34

3 MOTIVATION FOR CURRENT RESEARCH

The fuel injection scheme is a critical aspect in the design of ramjet, SCRamjet

combustors and afterburners. The thrust developed in these combustors depends

upon the combustion efficiency. The effective mixing between the fuel droplets and

the air stream will go a long way in improving combustion efficiency. To

understand the mixing characteristics better, knowledge of the breakup regime, the

penetration and droplet size distribution in the fuel spray is of paramount

importance.

The combustor performance also depends on other aspects such as fuel spray

droplet velocity, residence time and burning time of the fuel droplet. In supersonic

combustors, the burning time has to be very short since the residence time inside the

combustor will be very small. The fuel has to be injected, atomized, mixed with the

air and burnt within a very short span of time. The candidacy of the transverse fuel

injection scheme has to be examined and established, taking into consideration the

above mentioned considerations.

The breakup regimes give an idea of the atomization method and the drop sizes

resulting from the breakup. The understanding of dominance of one breakup regime

over another, based on parameters like J and We, help in understanding the flow

structure of liquid jets in cross flows. The penetration, on the other hand, influences

the mixing characteristics and the overall combustor performance.

The SMDs of fuel sprays and the SMD distribution give insight into the

effectiveness of the injection method. Wu et al. [24] observed that the SMD

distribution of sprays formed from transverse injection is not very three

dimensional. The authors suggest that line-of-sight measurements such as laser


35

diffraction can be used to satisfactorily analyze droplet size distribution. To study

the SMD distribution, Malvern Instruments’ Spraytec™ is used in the current

research. It is a diagnostic equipment working on the principle of laser diffraction

using the Mie theory optical model.

The objective of the current research is to further the understanding of the

spray characteristics resulting from liquid injection in subsonic and supersonic cross

flows. It is expected that the current research will help in the optimization of

aerospace engine combustor design.


36

4 EXPERIMENTAL SETUP

The experiments were carried out at the Combustion and Gas Dynamics

Laboratory at CSIR- National Aerospace Laboratories, Bangalore, India. The test

rig was assembled in order to produce both subsonic and supersonic flows. The test

facility consists of the following components:

Centrifugal compressors at National Trisonic Aerodynamic Facilities (NTAF)

deliver pressurized air at room temperature through pipelines to the Combustion

and Gas Dynamics Laboratory. The pressurized air delivered from NTAF is

controlled by an electrical motor-operated gate valve to supply the air at required

total pressure to the test rig through a 6 inch pipeline. The test rig comprises the

apparatus to produce air cross flow at desired Mach number and the water injection

system.

4.1 Test Rig

The air flow through the rig can be controlled with the help of a gate valve

positioned at the upstream end of the test rig. Downstream of the gate valve, the

pipeline cross-section is changed from circular to rectangular using a circular-to-

rectangular transition pipe. The 6 inch diameter circular cross-section is reduced to

a rectangular cross-section (50 mm X 70 mm) and its dimensions downstream of

the transition pipe remain the same.


37

Fig. 4.1 Schematic sketch of the test rig


38

The transition pipe is followed by a C-D nozzle capable of producing a steady

flow of Mach number 2. The C-D nozzle is used when supersonic cross flow

conditions are required.

The test-section is attached to the downstream end of the nozzle. The test-

section is 200 mm long and has a cross-section of dimensions 50 mm span X 70

mm height. Quartz glass windows are used as the side walls of the test section. The

glass windows are 3 mm thick and provide high transmission to the laser beam for

the drop size measurements. The test-section contains a port at the upstream end

where an injector can be inserted.

4.2 Water Injection System

The water injection system consists of a water reservoir with a capacity of 20

litres. The water in the reservoir is pressurized using compressed air from the

compressor, so that water can be injected at a constant pressure. The compressed air

delivered to the reservoir can be controlled using a ball valve. The pressurized air

line to the reservoir also contains a gate valve for venting excess pressure inside the

reservoir before refilling the reservoir with water. This valve is also useful to know

if the reservoir is full since excess water from the reservoir overflows through this

vent.

The pressurized water from the reservoir exits through ½ inch aluminium

pipeline. Two gate valves in series are used to accurately control the mass flow rate

of water through the pipeline. The aluminium pipe is then connected to a ½ inch

flexible hose. The flexible hose delivers the water to the ¼ inch aluminium pipe that

is connected to the injector.


39

4.3 Injector

Fig. 4.2 Injector design

The injector consists of a nozzle that is welded to the ¼ inch pipe. The nozzle

consists of an exit orifice of diameter d (0.5 mm, 0.8 mm and 1.0 mm). The hole of

diameter d extends from the exit orifice to a length of 10d inside the nozzle,

followed by a bore of ¼ inch, into which the ¼ inch pipe is inserted and welded.

The orifice length-to-hole diameter ratio, l/d, is maintained the same for all the

nozzles tested so as to reduce the geometric effect on the atomization between the

different injectors. Kihm et al. [5] used similar l/d orifices in conducting liquid jet

experiments in subsonic cross flows.


40

4.4 Instrumentation

The electronic instrumentation is used to measure the total pressure of the air

entering the test-rig, the static pressure of the cross flowing air at the entrance to the

test-section, the water injection pressure and the mass flow rate of water. This is

accomplished with the help of three pressure transducers and a coriolis mass flow

meter.

The total pressure of the air is measured using a differential pressure

transducer, open to atmosphere on one side, and placed just upstream of the

transition pipe. The static pressure at the entrance to the test-section is measured by

another differential pressure transducer placed at that location. This transducer is

also open to the atmosphere on one side and thus measures the gauge pressure at

that location.

The water mass flow rate is measured using a mass flow meter placed

downstream of the two control valves in the ½ inch water pipeline. The water

injection pressure is measured using an absolute pressure transducer.

The data acquisition from the transducers and the mass flow meter, and logging

are carried out using the hardware National Instruments USB-6218 and the software

National Instruments LabVIEW™ 8.6. NI USB-6218 is a bus-powered,

multifunction data acquisition (DAQ) system. It delivers good accuracy at fast

sampling rates. It can handle 8 analog inputs, 2 analog outputs, 8 digital inputs and

8 digital outputs with a 250 kS/s single-channel sampling rate. More information on

USB-6218 can be found in Ref. [30].

4.5 Coordinate System

A right-handed coordinate system, centered at the injection orifice, is used to

orient the measurements. The positive X-axis points in the direction of the incoming


41

air, the Y-axis points in the direction of water injection and the Z-axis is lies on the

plane containing the orifice such that it completes a right-handed coordinate system.

The distances along the X, Y and Z axes are denoted using the variables x, y and z

respectively.

Fig. 4.3 Sketch of the test-section showing injector locations

4.6 Diagnostic Equipment

The particles’ size and distribution are measured using Malvern Instruments’

Spraytec particle size analyzer. The principle of laser diffraction is used in the

measurement of particle size. The optical model employed in Spraytec is Mie


42

theory.

The laser beam is produced by a 632.8 nm, 2 mW helium-neon laser, which

passes transversely through the spray plume. The laser beam from the transmitter on

passing through the spray plume gets diffracted to different angles based on the

particle sizes. These diffracted rays are picked up by detectors, which feed the data

to a computer. The computer then presents the processed data in the form of particle

sizes and distributions. Spraytec is chosen in this study to analyze particle size

because it can measure a wide size range of 0.1µm to 2000µm. A purge system is

also employed to prevent contamination of the optical lenses by spray particles

during operation. The optical alignment and background check are done

automatically by the Spraytec software.

A Photron FASTCAM™ SA5 high speed camera is used to capture the images

of the spray. A sigma lens with a focal length of 105 mm was used. The camera is

capable of capturing 1,024 * 1,024 pixels images at 3600 frames/second and 504 *

396 pixels images at 10000 frames/second. The Phantom FASTCAM Viewer

software can save the data in video file or picture format (in JPEG, TIFF and other

formats). The data for the entire recorded duration or a small fractional duration can

be saved in the computer. The Phantom software provides control options to setup

camera operating parameters such as frame rate and exposure time before the

camera operation.

The camera is placed on a tripod such that it captures the image of the spray

through the side glass walls of the test-section. The lighting is provided with the

help of a 500 W halogen lamp and a white background.


43

5 EXPERIMENT METHODOLOGY

The experiment is conducted by following a procedure for obtaining desired

initial test conditions. The data on total pressure of the air cross flow, the air static

pressure at the test-section, the water injection pressure and mass flow of injected

water are the parameters available to set the required flow conditions.

The required cross flow conditions are first established before the water is

injected. This is because the cross flow will blow down any debris in the rig and

will help evaporating any moisture in the test-section. The air flow into the test rig

is controlled by the gate valve at the upstream end. The gate valve is opened slowly

so that a stable cross flow at the desired Mach number is established in the test-

section. The calculation of Mach number and other flow parameters are described in

detail in Appendix 2. The Mach numbers range from Mach 0.2 to Mach 2.0 during

the different test runs.

Once the desired cross flow conditions are established, the valve that controls

the supply of compressed air to pressurize the water is opened. The two valves that

control the water flow through the water injection system are controlled in order to

obtain a required mass flow rate of the water. Care must be taken to ensure that the

water jet does not impinge on the upper, side or lower walls of the test-section,

since it will result in the formation of accumulated droplets in the walls which

might get entrained into the spray.

The non-dimensional parameters, We and J, depend upon the cross flow

properties and liquid jet properties. For a given Mach number and the injector

diameter, We does not change during a test run. To increase the Weber number, the

cross flow speed can be increased. When the Weber number is fixed at a particular

Mach number, the water injection speed is varied to vary J. On increasing the water


44

injection pressure, the water jet speed is increased thereby increasing J.

The high-speed camera is positioned on a tripod stand and so placed as to get

images through the optically transparent side walls of the test-section. The images

were obtained at a speed of 10000 fps to 13500 fps. The focus lamps and the white

background are suitably arranged to obtain high contrast images of the spray.

Spraytec is positioned such that the laser beam passes transversely through the

spray at a desired downstream location from the injector orifice. This is done with

the help of a calibrated scale to measure axial distance from the injector and the

height above the orifice.

5.1 Calculation of Flow Parameters

The flow parameters that are calculated during the experiment include the

Mach number, the Weber number, We, and the liquid-to-air momentum flux ratio, J.

The data acquisition and the calculation of these parameters are done with the help

of National Instruments LabVIEW™ 8.6 software.

The Mach number is calculated from the total pressure of air entering the test

rig, P0 and the static pressure of air in the test-section, PS using the formula:

The total temperature of the air, T0, which is the room temperature, is noted down.

Then, the static temperature at the test-section, TS, is given by:

2

1

1

S

0 1P

P

1-

2M

2

0S

M2

11

TT


45

From these values, the cross flow air velocity, Va, can be calculated as:

The density of the cross flowing air, a , is calculated using the formula:

The jet injector area is calculated from the jet injector exit diameter. Since the

density of injected liquid, water in this case, is known, the liquid injection velocity

can be calculated using the formula:

Where fm is given in terms of kg/min.

After obtaining the above values, the liquid-to-air momentum flux ratio, J, and

the Weber number, We, can be calculated using the following formulae.

2

1

Sa RTMV

S

Sa

RT

P

jj

f

jA

60

m

V

2

aa

2

jj

V

VJ

j

2

a dVWe

a


46

6 RESULTS AND DISCUSSION

6.1 Visualization of Liquid Jets in Cross Flows

In order to develop fuel injection systems with well defined mixing

characteristics leading to maximum possible combustion efficiency, a good

knowledge of the two-phase flow (spray) physics is of fundamental importance.

Visualization techniques with high spatial and temporal resolution can be used to

analyze the spray structure (breakup modes, penetration, spread), size and velocity

of the droplets and develop velocity correlations at a variety of operating

parameters such as fuel and air flow rates, pressure, and temperature.

In this study, a 500 W Halogen lamp combined with Phantom FASTCAM

high-speed camera is used for the visualization of the injection of liquid jet in cross

flows to assess the penetration heights and breakup modes. In this method

instantaneous images of the jet are captured at extremely high frame rates and

information regarding the jet column penetration, breakup modes, outer and inner

boundary of the jet is extracted. The effects of the major dimensionless parameters,

Weber number and liquid jet-to-air momentum flux ratio, are studied for a limited

set of conditions.

To examine the liquid jet behavior in cross flows, tests were conducted at two

typical mach numbers of 0.3 and 0.4, which are close to the practical situations

encountered in aero engine applications. As indicated, the backlight illumination

technique along with high speed imaging is used for flow visualization and analysis.

The Photron FASTCAM™ SA5 high speed camera is used in capturing the spray

images. 1000 images of 504 by 396 pixels with 256 gray levels were recorded for

each test run. The field of view was 70 mm by 90 mm.


47

The results on the injection of liquid jet in subsonic cross flows (M = 0.3,0.4)

are presented in this thesis. The results presented in this paper are obtained with the

injectant liquid water, using a plain orifice injector with a diameter of 0.8 mm. A

steady run time of about 3-5s is obtained at M = 0.3 and 0.4 which is adequate for

image analysis and recording after a startup and stabilization run time of 10s which

is required to stabilize the liquid flow at the set mach number condition.

The test conditions for the experiments on penetration heights are given in

Table 6.1.

Table 6.1 Test conditions for the experiments on penetration heights

Test Case Mach number

(M)

Weber Number

(We)

Momentum Flux

Ratio (J)

A 0.3 130 30

B 0.3 130 35

C 0.3 130 115

D 0.4 240 10

Fig. 6.1 and Fig. 6.2 show typical instantaneous and averaged images of

water jet in subsonic cross flow for Mach No 0.3 and a momentum ratio of J = 30

(Test Case A). The averaged image was obtained from 10 instantaneous images

over a 10µs time period at subsonic conditions. The averaged image is used for the

determination of the penetration height of the jet. Fig. 6.3 gives the outer and inner

boundaries obtained from the averaged image. The upper edge of the average image

represents the penetration height (y) of the jet. The lower edge of the image

represents the lower or leeward surface trajectory. This coupled with the upper

surface trajectory provides an idea about the spray plume area in the test section.


48

It is to be noted that the images obtained show the penetration heights of the jet

for a normalized longitudinal distance between 0 < x/dj < 85, where x is the

longitudinal distance from the jet exit and dj is the injector diameter. The average

error on the penetration height of the jet can be estimated to be less than 5%, which

would include the error in the image processing (determination of the upper/lower

edge of the image), volume flow rate measurements and the determination of the

Mach number. The freeware ImageJ was used for the visualization and image

processing of the jet breakup and further development.

Case A: We=130, J=30

Fig. 6.1 Instantaneous image at We=130, J=30


49

Fig. 6.2 Averaged image at We=130, J=30

Fig. 6.3 Outer and inner boundaries from averaged image at We=130, J=30

Typical results of the penetration height of water jets in subsonic cross flow for

different jet/cross flow momentum flux ratios at the same Weber number of 130


50

(Test Cases B and C) are shown in Fig. 6.4 to Fig. 6.9. The results show an

increase in the penetration height of the liquid jet (y) as the jet/cross flow

momentum flux ratio increases from 30 to 115 for water at We=130. For a given J,

the increase in the Weber number lowers the jet penetration. Fig. 6.10, Fig. 6.11

and Fig. 6.12 show the jet penetration height for the case We=240 and J=10 (Test

Case D).

Case B: We=130 J=35



51

Fig. 6.5 Averaged image at We=130, J=35

Fig. 6.6 Outer and inner boundaries from averaged image at We=130, J=35


52

Case C: We=130 J=115


Fig. 6.8 Averaged Image at We=130, J=115


53

Fig. 6.9 Outer and inner boundaries of the jet from averaged image at We=130, J=115

Case D: We=240 J=10



54

Fig. 6.11 Averaged Image at We=240, J=10

Fig. 6.12 Outer and inner boundaries of the jet from averaged image at We=240, J=10

The jet trajectories for Cases B and C are given in Table 6.2 and Table 6.3


55

respectively.

6.1.1 Trajectory Details

Case B: We=130 J=35

Baseline: (0,0)=50.49,74.32

Table 6.2 Liquid column trajectory for We=130 and J=35

Lower Trajectory Upper Trajectory

x y x

mm

y

mm

x/dj y/dj x y

x

mm

y

mm

x/dj y/dj

51.83 71.49 1.34 2.83 1.675 3.5375 50.04 71.79 -0.45 2.53 -

0.5625 3.1625

52.43 70.45 1.94 3.87 2.425 4.8375 50.19 70.89 -0.3 3.43 -0.375 4.2875

53.17 69.40 2.68 4.92 3.35 6.15 50.79 67.91 0.3 6.41 0.375 8.0125

54.06 68.66 3.57 5.66 4.4625 7.075 51.38 65.83 0.89 8.49 1.1125 10.6125

54.81 67.91 4.32 6.41 5.4 8.0125 51.83 64.64 1.34 9.68 1.675 12.1

55.85 66.87 5.36 7.45 6.7 9.3125 52.57 63.45 2.08 10.87 2.6 13.5875

56.74 66.13 6.25 8.19 7.8125 10.2375 53.32 62.40 2.83 11.92 3.5375 14.9

58.09 65.09 7.6 9.23 9.5 11.5375 54.21 61.51 3.72 12.81 4.65 16.0125

59.13 64.04 8.64 10.28 10.8 12.85 55.11 60.62 4.62 13.7 5.775 17.125

60.47 62.70 9.98 11.62 12.475 14.525 57.49 58.98 7 15.34 8.75 19.175

62.40 61.81 11.91 12.51 14.8875 15.6375 59.13 58.23 8.64 16.09 10.8 20.1125

64.49 60.91 14 13.41 17.5 16.7625 60.77 57.64 10.28 16.68 12.85 20.85

66.13 60.32 15.64 14 19.55 17.5 62.55 57.49 12.06 16.83 15.075 21.0375

From the trajectory details in Table 6.2, a comparison was made between the

experimental data obtained and the correlations from the literature review in Table

2.1. Three correlations from the literature which matched the experimental

conditions were chosen for the comparison. It was observed that the obtained results

are closer to the correlation given by Becker and Hassa [1], while they are much


56

lower than the values predicted by Lin et al. [9] and Wu et al. [24]. The comparison

is presented in Fig. 6.13.

Fig. 6.13 Comparison of penetration height correlations and experimental data for We=130

and J=35

Case C: We=130 J=115

Baseline: (0,0)=50.49,74.32

Table 6.3 Liquid column trajectory for We=130 and J=115

Lower Trajectory Upper Trajectory

x y x

mm

y

mm

x/dj y/dj x y

x

mm

y

mm

x/dj y/dj

51.38 71.94 0.89 2.38 1.1125 2.975 49.74 71.94 -0.75 2.38 -0.9375 2.975

51.98 68.81 1.49 5.51 1.8625 6.8875 50.04 67.91 -0.45 6.41 -0.5625 8.0125

52.43 67.17 1.94 7.15 2.425 8.9375 50.19 65.23 -0.3 9.09 -0.375 11.3625

53.02 65.38 2.53 8.94 3.1625 11.175 50.49 63.45 0 10.87 0 13.5875


57

53.62 63.30 3.13 11.02 3.9125 13.775 50.94 61.21 0.45 13.11 0.5625 16.3875

54.96 61.21 4.47 13.11 5.5875 16.3875 51.68 58.53 1.19 15.79 1.4875 19.7375

56.15 59.13 5.66 15.19 7.075 18.9875 53.02 55.55 2.53 18.77 3.1625 23.4625

57.34 57.34 6.85 16.98 8.5625 21.225 54.96 51.68 4.47 22.64 5.5875 28.3

58.68 56.45 8.19 17.87 10.2375 22.3375 56.60 50.19 6.11 24.13 7.6375 30.1625

60.32 55.11 9.83 19.21 12.2875 24.0125 58.68 49.15 8.19 25.17 10.2375 31.4625

61.06 54.21 10.57 20.11 13.2125 25.1375 60.91 48.11 10.42 26.21 13.025 32.7625

6.2 Characteristics of Spray SMD

The experiments to study the droplet size distributions covered a wide range of

Mach numbers, water injection mass flow rate, liquid-to-air momentum flux ratio

(J) and Weber number (We). These test conditions are listed in Table 6.4.

Table 6.4 Test conditions for the experiments on droplet size distributions

Test

Case

Mach

Number mf

kg/min

dj mm

x/dj y/dj We J

No. of

Test

Runs

1 0.30 0.4-0.6 0.8 310 28.75 125 24-36 5

2 0.35 0.7-1.5 1 330 23 212 13-69 5

3 0.40 0.7-0.8 0.8 310 28.75 238 26-31 2

4 0.40 0.7-1.5 1 330 23 296 11-46 5

5 0.50 0.7-1.5 1 330 23 460 6-30 4

6 0.55 0.9-1.5 1 330 23 550 8-28 4

Two injectors with orifice diameters 0.8 mm and 1mm were used. The

experiments were conducted at two axial distances downstream of the injector


58

orifice, x=330 mm and x=248 mm. The injector with 0.8 mm diameter orifice was

only used at x=248mm. This corresponds to a x/dj of 310. The height above the

injector wall where the laser beam diagnosed drop sizes was y=23 mm for all cases.

This gives a y/dj of 23 for 1mm injector and y/dj of 28.75 for 0.8 mm injector.

Similarly, for the 1mm injector, there were two x/dj locations: 248 and 330. The

mass flow rate of injected water was varied from 0.4 kg/min to 1.5 kg/min for the

six test cases.

6.2.1 Droplet Size Distribution

The droplet size distributions are obtained with the help of the Malvern

Instruments’ Spraytec particle analyzer and the software. The software generates the

distribution data at different time instances of an experimental run. It also generates

the SMD and other derived parameters both at time instances of multiples of 2s and

the average values for the entire test run.

To illustrate, consider a set of distribution data from Test Case 1. The test

conditions are given in Table 6.5.

Table 6.5 Test conditions and SMD for Mach 0.3 test case

Mach

number

mf

kg/min J We

SMD

μm

0.3 0.5 23.99 129.4544 60.85

Fig. 6.14 displays the volume distribution of the particle SMD sizes at 4s after

the laser diagnosis was begun. The volume frequency gives the percentage of

volume of a particular SMD sized droplets in the entire volume of the spray. The

cumulative volume graph at an abscissa indicates the percentage of total volume of

the spray constituted by all droplet sizes at and below the droplet size at that point.


59

It can be noticed from the graph that the distribution is uni-modal, with a longer

forward tail. The distribution peaks at an SMD of about 100 μm, corresponding to

the location of maximum volume frequency (about 8.77%). This is the mode of the

distribution. The long forward tail indicates the presence of a range of smaller SMD

droplets. However, these droplets have relatively smaller volume frequency due to

their smaller sizes.

Fig. 6.14 Volume distribution of droplet SMDs

Table 6.6 condenses the distribution data corresponding to Fig. 6.14. The table

indicates the values of “%V<” and “%V” for various droplet SMDs. These values

indicate the cumulative volume percentage and the volume frequency percentage

respectively. For instance, it can be seen that the SMD with highest volume

frequency is 101.22 μm, with %V=8.77 %. Thus, this is the mode of the

distribution. The %V< value at this point is 54.19%, which means that 54.19% of

volume of the spray contains droplets of SMD lesser than and equal to 101.22 μm.

Further, it can be seen that at SMD=462.33 μm, the cumulative volume reaches

100%. This indicates that the spray contains droplets of SMDs up to 462.33 μm

only.


60

Table 6.6 SMD volume distribution data

Table 6.7 displays the SMD, transmission of laser, etc. at a time instance (in

this case, +4s). The transmission percentage is an indicator of the transmission

efficiency of the laser beam through the spray. “Dv(10)” indicates the SMD at

which cumulative volume reaches 10%. That is, in the table below, 10% of the total

volume constituted by the smallest SMD droplets is composed of SMDs 31.19 μm

and lesser. “Dv(50)” and “Dv(90)” give analogous SMD values at which

cumulative volume reaches 50% and 90% respectively. “D[4][3]” is the de

Brouckere mean diameter of the spray and “D[3][2]” is the SMD of the spray.


61

Table 6.7 Derived parameters

Fig. 6.15 gives the number distribution of the droplets. The number

distribution from laser diffraction experiments should be taken as only indicators

and not absolute results. However, they give a good idea of how the spray droplets

differ in number and how they contribute to the volume of the spray.

The cumulative number % and the number frequency % are analogous to the

cumulative volume % and volume frequency %. From the graph below, it can be

seen that the mode of the distribution is around 8 μm.

Fig. 6.15 Number distribution of droplet SMDs


62

Analogous to Table 6.6, Table 6.8 gives the cumulative number % and number

frequency % for different SMDs. It can be seen that the mode is 8.05 μm with a

number frequency of 17.04%. Clearly, a large difference in the modes of volume

and number distributions exists. This is because of the fact that although the spray

contains a large number of smaller SMD droplets, their volume is relatively smaller

than the volume of few large droplets.

Table 6.8 SMD number distribution data

6.2.2 Effect of Momentum Flux Ratio (J) and Weber number (We)

The effect of momentum flux ratio on the SMD of the spray has been an

important focus of research. Kihm et al. [5] studied effect of varying J in subsonic

flows (about 11 m/s to 43 m/s) while Nejad et al. [14] investigated effects of

varying J in Mach 3 supersonic cross flow. In both investigations, the observed

trend was that an increase in momentum flux ratio brought about effective


63

atomization and decreased the SMD of droplets.

In the current study, the SMD variation was studied in subsonic cross flows,

with Mach number ranging from 0.3 M-0.6M. The SMD values were studied by

varying momentum flux ratio while holding the Weber number constant. The

experiments were conducted at various Weber numbers at the location

(x/dj,y/dj)=(330,23) and with a nozzle having orifice diameter dj=1mm.

Fig. 6.16 Effect of momentum flux ratio (J) on SMD at various Weber numbers

Fig. 6.16 is a plot of J vs SMD at various Weber numbers. The SMD values

are shown with 5% experimental error bars. It is clearly observed that the SMD of

the droplets decrease with increasing momentum flux ratio, J. This trend is more

prominent in lower Weber numbers, We=211 and We=294, than in the higher Weber

numbers, We=510 and We=585.


64

At lower Weber numbers, the reduction in SMD with increasing momentum

flux ratio (J) is significant. However, a predictable trend in the slopes of the curves

at different Weber numbers could not be discerned. For example, when a linear fit

was fitted on the data for the different Weber numbers, with 6% error bars for SMD

at We=211 and 5% error bars for We=294,510,585, the absolute value of the

negative slope increased from 0.311 for We=211 to 0.440 for We=294, then

decreased to 0.113 for We=510 before further decreasing to 0.062 for We=585. This

is shown in Fig. 6.17. The results indicate that a definite quantitative prediction of

the behavior of increasing Weber number on the SMD is not possible with available

data. However, it can be inferred qualitatively that increasing the Weber number

will result in a decrease in droplet SMDs at comparable J ratios.

Fig. 6.17 J vs SMD trends

Further, Fig. 6.16 shows that at very high Weber numbers, the dependence of


65

SMD on momentum flux ratio may be lessened. The data points for We=510 and

We=585 reveal that the SMD is almost constant for various J values. It can be

inferred that at some point, the aerodynamic breakup due to the increased Weber

number dominates over the column breakup. While the column breakup is

dependent on momentum flux ratio, aerodynamic breakup is influenced by Weber

number. Thus, there exists a Weber number at which the effect of momentum flux

ratio is nullified and the SMD depends on aerodynamic breakup alone.

6.2.3 Effect of Cross Flow Weber number at different Injectant Mass Flow

Rates

The data from Table 6.4 were compiled to study the effect of Weber number on

SMD at various injectant mass flow rates. The experiments were conducted at the

location (x/dj,y/dj)=(330,23) and with a nozzle having orifice diameter dj=1mm.

Fig. 6.18 Effect of Weber number (We) on SMD at various injectant mass flow rates


66

Fig. 6.18 is a plot of We vs SMD at three different water mass flow rates,

mf=0.9 kg/min, 1.3kg/min and 1.5 kg/min. The data set is fitted with 5%

experimental error bars for all the test cases. It can be seen that the SMD of the

droplets decrease with increasing Weber number for all three cases of water mass

flow rates until about We≈500. This decrease in SMD is more prominent for the

lower mass flow rate, mf=0.9 kg/min than the higher mass flow rate, mf=1.5 kg/min.

This is due to the interplay between the momentum flux ratio, which increases with

water mass flow rate for a given Weber number, and SMD.

The data also reveals that the SMD for all three cases approach a value of

about 25 µm at We≈500. The SMD value is relatively stagnant at this value even for

higher Weber numbers. As mentioned earlier, this may be due to the dominance of

aerodynamic breakup at high Weber numbers over column breakup.

6.2.4 Effect of Cross Flow Velocity

The effect of cross flow velocity on the jet breakup process was studied by

comparing the numerical SMD distributions for different cross flow Mach numbers

at fixed water injection mass flow rates. The results suggest that as the cross flow

velocity increases, the number frequencies of smaller SMD droplets increase and

the overall SMD range of the distribution shrinks.

The test conditions for these cases are given in Table 6.9.


67

Table 6.9 Test conditions for effect of cross flow velocity studies

Trial

Number

Mach

Number

Cross

Flow

Velocity

(Va)

m/s

Mass

Flow

Rate

(mf)

kg/min

dj

mm

x/dj y/dj

1 0.35 120.12 0.90 1 330 23

2 0.52 175.94 0.90 1 330 23

3 0.56 188.70 0.91 1 330 23

4 0.733 241.95 0.90 1 330 23

To study the effect of increasing cross flow velocity on the numerical size

distribution, consider the following plots given in Fig. 6.19. The labels in the

figure, (a), (b), (c) and (d) correspond to the Test Trials 1,2,3 and 4 in Table 6.9.

It is clearly observed from the figure that as the cross flow velocity increases,

the range of the SMDs in the distribution gets smaller. This fact is illustrated by the

cumulative number % curve, which attains the 100% mark at lower SMD values as

the cross flow velocity is increased. Further, the number frequency of the smaller

SMD droplets, in the range of 4 µm-20 µm, increases from case (a) to case (d) as

the cross flow velocity increases.

These results corroborate the findings of Wu et al. [24], who conducted

experiments in subsonic cross flows (0.2M-0.4M) and found that the maximum

SMD decreased with increasing cross flow velocity while the minimum SMD

remained relatively unchanged. This resulted in a decrease in the variation of SMD

as the cross flow velocity increased.


68

Fig. 6.19 Comparison of SMD number distributions at different cross flow velocities

mf=0.9 kg/min, d=1mm, x/dj=330, y/dj=23


69

Table 6.10 Average SMDs and Cumulative Number % at 22.16 µm

Trial

Number

Mach

Number

Cross

Flow

Velocity

(Va)

m/s

Mass

Flow

Rate

(mf)

kg/min

Average

SMD

µm

Cumulative

Number %

at 22.16 µm

(%N<)

%

1 0.35 120.12 0.90 41.92 87.69

2 0.52 175.94 0.90 25.02 92.56

3 0.56 188.70 0.91 24.99 93.97

4 0.733 241.95 0.90 23.87 95.76

Table 6.10 gives the values of average SMDs and the cumulative number % at

22.16 µm. The values correspond to the graphical data given in Fig. 6.19. A rising

trend in the cumulative number % at 22.16 µm is observed as the cross flow

velocity increases. The behavior of the average SMD values with increasing cross

flow velocity is similar to the variation of average SMD with increasing Weber

number.

Another interesting aspect was the analysis by fitting a trend line to a “Mach

number vs. Cumulative number% at 22.16 µm” plot for the experiment conducted

at x/dj=330, y/dj=23 and mf=0.90 kg/min. The plot is given in Fig. 6.20.

When the trend was extrapolated to find the Mach number at which the

cumulative number% will reach 99% for 22.16 µm, it yielded 0.935 M with the

logarithmic trend and 0.921 with the power trend. When similar analyses were done

for the cases at different water mass flow rates but at the same (x/dj,y/dj) and with

the same injector, it was found that it took higher Mach numbers to attain a


70

cumulative number % of 99% for cases with higher water mass flow rates. For

example, at mf=1.5 kg/min, the trend lines indicated that the required Mach number

would be 1.625 M according to logarithmic trend and 1.544 M according to power

trend. These trends suggest that as the injectant mass flow rate increases, a higher

Mach number cross flow is required to complete atomization that yields low SMD

droplets, ie, fine atomization. At lower injectant mass flow rates, a lower Mach

number cross flow can achieve the same purpose.

Fig. 6.20 Mach number vs Cumulative Number % at 22.16 µm- Trend


71

7 SOURCES OF ERROR

In the course of the experiments, it was noticed that the spray touched the side-

walls or the top/bottom wall of the test-section for certain injection conditions. This

caused the accumulation of water droplets at the ends of the test-section. The large,

accumulated droplets sometimes got entrained in the cross flow and passed through

the laser beam. This slightly skewed the droplet size distribution data for certain test

cases. In order to filter this error, the number distributions were used as indicators to

note when the droplets with extremely large SMD showed up in the results. While

all efforts have been taken in obtaining accurate results, a certain level of

arbitrariness has been introduced by the filtering process. However, the results were

compared with available data in the literature for conformance and the qualitative

assessment of the data is expected to be sufficiently accurate for the analysis

presented in this thesis.

For the flow visualization using high speed photography, the images obtained

over a period of time were averaged to eliminate any error that may have crept in

due to vibration of the test-rig and the liquid jet oscillations.


72

8 CONCLUSIONS AND FUTURE WORK

8.1 Conclusions

An experimental investigation of the penetration and the droplet size

distributions resulting from liquid jet injection in subsonic cross flows has been

carried out with water as the test liquid. The experiments encompassed a wide range

of cross flow Mach numbers and water injection mass flow rates. Two plain orifice

injectors with diameter 0.8 mm and 1.0 mm were used in the study. The

experiments on droplet SMDs were carried out at locations

(x/dj,y/dj)=(330,23),(248,23) and (310,28.75). The non-dimensional parameters

Weber number (We) and liquid jet-to-air momentum flux ratio (J) were used to

characterize the sprays. High speed photography was used for flow visualization in

order to study penetration of the jets while Malvern Instruments’ Spraytec,

operating on Low Angle Laser Light Scattering (LALLS) was used to study droplet

SMD distributions. The results of the investigation can be summarized as follows:

1. For a particular Weber number, the penetration height increased with an

increase in the liquid jet-to-air momentum flux ratio.

2. When the momentum flux ratio was held constant, an increase in Weber

number lowered the jet penetration.

3. The SMD number distributions are uni-modal with the mode less than 10µm

for all the conditions investigated in the study.

4. At a fixed Weber number, the droplet SMDs decreases with increasing

momentum flux ratio (J). The reduction in SMD with increase in J was more

prominent at lower Weber numbers (We=211, 294) than at higher Weber

numbers (We=510,585).


73

5. At very high Weber numbers, the effect of J on SMD reduces drastically. This

is believed to be due to the dominance of aerodynamic breakup over the

column breakup at higher Weber numbers.

6. At a fixed injectant mass flow rate, droplet SMD decreased on increasing the

Weber number. The decrease in SMD is prominent for the cases with lower

water mass flow rates.

7. The SMD of droplets approached a constant value for different water mass

flow rates as the Weber number increased to a particular value. This

phenomenon suggests that the SMD may depend more upon the aerodynamic

breakup and shear droplet stripping at higher Weber numbers than on column

breakup.

8. On increasing the cross flow velocity at a particular water mass flow rate, the

percentage of smaller SMD droplets in the spray was seen to increase. The

range of the SMD number distribution was also seen to reduce. At higher

cross flow velocities, atomization yielded a spray with finer SMD droplets.

9. As the injectant mass flow rate increases, a higher Mach number cross flow is

required to produce the same level of fine atomization that can be produced

by a lower Mach number cross flow at a lower injectant mass flow rate.

8.2 Scope for Future Work

The current study examined penetration and droplet size distributions from

transverse injection at atmospheric temperature and pressure. Future work can be

directed in studying the spray structures of liquid jets from angled injectors. Also,

the effects of heating the cross flow air can provide a more fundamental

understanding of the actual injection processes in an aero engine.


74

APPENDIX 1: Particle Size Measurement using Laser

Diffraction

Particle size analysis laser diffraction has emerged as a reliable, economic and

simple to use diagnostic technique in the recent years. Also called Low Angle Laser

Light Scattering (LALLS), it is non-intrusive and caters to the needs of many

industries which require repetitive, accurate sampling of particles. The standard ISO

13320 provides guidelines on the use of laser diffraction for scientific analysis

purposes. Various industry sources and researchers have attested to its utility in

particle size measurements [26, 27, 28, 29].

A.1 Principle

Instruments working on the principle of laser diffraction, such as Malvern

Instruments’ Spraytec, which is used in the present study, depend on the scattering

of laser by the particles. The scattering angle of the incident laser light is inversely

proportional to the particle size and increases logarithmically with decreasing

particle size. The intensity of the scattered light is also a function of the particle

volume. Large particles scatter light at low angles and high intensity while small

particles scatter light at larger angles and low intensity.

A.2 Apparatus

The required apparatus consists of a laser source of suitable wavelength, an

array of detectors to measure the angular scattering of the laser by the particles, a

method by which the laser is passed through the particles and a means of

interpreting the optical signals, which is usually done with the help of a software.

The wavelength of the laser light source influences the sensitivity of the instrument.

Lower wavelengths, such as blue lasers, provide more sensitivity to smaller


75

particles in the sub-micron scale. The angular measuring range of the detectors

determines the particle size range that can be measured.

A.3 Optical Models

The data from laser diffraction can be interpreted using two major optical

models: 1) Fraunhofer approximation and 2) Mie theory.

Fraunhofer approximation was used in older instruments. It assumes the following:

Particle size is larger than the wavelength of laser source.

Particles are opaque, transmit no light through them and scatter light at low

angles.

Scattering efficiency is the same for all particle sizes.

Consequently, Fraunhofer approximation is not suitable for measuring finer

particles. It does not take into consideration the refractive index of the particle

medium, either.

Mie theory, on the other hand, provides a more rigorous solution of the

equations governing light interaction with matter. This enables the measurement of

a wider range of particle sizes, typically from 0.02-2000μm.

However, for using Mie theory, the refractive indices of both the particles and

the medium are to be known.

A.4 Advantages of Laser Diffraction

This method can be used to measure a wide dynamic range of particle sizes,

typically from 0.1 to 2000 microns.

Dry powders as well as particles in liquid suspensions and emulsions can be

studied.

It can generate rapid and reproducible results.


76

The instrument does not need calibration. However, the results can be

validated against a standard.

A.5 Particle Size

Before proceeding to the measurement of particle sizes, it is important to

understand the meaning of a particular particle size measurement. A particle, which

is non- spherical, will need more than one-dimension to specify it completely.

However, for many applications, it is impractical and unnecessary to collect and

process so many dimensions. Hence, we use the concept of equivalent sphere. For

example, the volume equivalent sphere diameter of a cube with sides 1 cm will be

equal to 1.24 cm. Here, the volume of the cube is equated to the volume of an

imaginary equivalent sphere and the diameter of this equivalent sphere replaces the

actual dimensions of the cube in our considerations.

In combustion studies, we are concerned with knowing the available surface

area of a spray for a given volume. In this case, then, we use the mean of the

moment of surface area, which is the SMD, to represent the particle size. Here, we

do not consider the actual dimensions of the particles. Nor does the SMD require

the actual number of particles in the spray. Instead, it denotes the diameter of the

equivalent sphere having the same specific surface area as the entire spray.


77

APPENDIX 2: Sample Calculation of Experimental

Conditions and Parameters

Let P0=0.99204 bar

PS=0.92538 bar

mf=0.51284 kg/min

T0=300 K

The parameters that are already known are:

=1.4

R=287.3 J kg−1

K−1

dj =0.0008 m=0.8 mm

jA =0.0000005024 m2 (for a 0.8 mm diameter injector nozzle)

ρj=1000 kg/m3

=0.072 N/m

M=0.3168

ST =294.0968 K

2

1

4.1

14.1

192538.0

0.99204

1-4.1

2M

K

0.31682

14.11

300T

2S

s

m0968.294287.34.10.3168V 2

1

a


78

aV =108.9588 s

m

ρa=1.09523m

kg

jV =17.0130 s

m

J=22.26

W

We=144.47

3am

kg

294.0968287.3

0.92538

s

m

10000008.04

60

0.51284

V2

j

2

2

108.95881.0952

0130.171000J

072.0

0008.0108.95880952.1We

2


79

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