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Atomization and Sprays

The document is a comprehensive overview of the book 'Atomization and Sprays' by Arthur H. Lefebvre and Vincent G. McDonell, published by CRC Press in 2017. It includes detailed discussions on various atomization techniques, spray characteristics, and the fundamental processes involved in atomization. The second edition updates the content with new research and contributions from the spray research community while maintaining the practical approach established in the first edition.

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Atomization and Sprays

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Atomization and Sprays

Combustion: An International Series

Norman Chigier, Editor

Bayvel and Orzechowski, Liquid Atomization

Chigier, Combustion Measurements
Kuznetsov and Sabel’nikov, Turbulence and Combustion
Lefebvre, Atomization and Sprays
Atomization and Sprays

Arthur H. Lefebvre and Vincent G. McDonell

CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2017 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
Version Date: 20161115
International Standard Book Number-13: 978-1-4987-3625-1 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and
information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission
to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in
any future reprint.
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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation
without intent to infringe.

Library of Congress Cataloging‑in‑Publication Data

Names: Lefebvre, Arthur H. (Arthur Henry), 1923–2003, author. | McDonell,

Vincent G., author.
Title: Atomization and sprays / Arthur H. Lefebvre and Vincent G. McDonell.
Description: Second edition. | Boca Raton : Taylor & Francis, CRC Press,
2017. | Includes bibliographical references and index.
Identifiers: LCCN 2016028367| ISBN 9781498736251 (hardback : alk. paper) |
ISBN 9781498736268 (ebook)
Subjects: LCSH: Spraying. | Atomization.
Classification: LCC TP156.S6 L44 2017 | DDC 660/.2961--dc23

Visit the Taylor & Francis Web site at

http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents

Preface to the Second Edition..................................................................................................................................................xi

Preface to the First Edition.................................................................................................................................................... xiii
Authors ......................................................................................................................................................................................xv

1. General Considerations.................................................................................................................................................... 1
Introduction......................................................................................................................................................................... 1
Atomization ......................................................................................................................................................................... 1
Atomizers............................................................................................................................................................................. 3
Pressure Atomizers........................................................................................................................................................ 3
Rotary Atomizers........................................................................................................................................................... 4
Air-Assist Atomizers ..................................................................................................................................................... 5
Airblast Atomizers......................................................................................................................................................... 5
Other Types..................................................................................................................................................................... 5
Factors Influencing Atomization ...................................................................................................................................... 6
Liquid Properties ........................................................................................................................................................... 6
Ambient Conditions ...................................................................................................................................................... 9
Spray Characteristics........................................................................................................................................................ 12
Applications....................................................................................................................................................................... 13
Glossary.............................................................................................................................................................................. 13
References .......................................................................................................................................................................... 16

2. Basic Processes in Atomization .................................................................................................................................... 17

3. Drop Size Distributions of Sprays............................................................................................................................... 55

v
vi Contents

Rosin–Rammler............................................................................................................................................................ 59
Modified Rosin–Rammler .......................................................................................................................................... 59
Upper-Limit Function ................................................................................................................................................. 60
Summary....................................................................................................................................................................... 60
Mean Diameters................................................................................................................................................................ 61
Representative Diameters................................................................................................................................................ 63
Drop Size Dispersion........................................................................................................................................................ 67
Droplet Uniformity Index........................................................................................................................................... 67
Relative Span Factor..................................................................................................................................................... 67
Dispersion Index .......................................................................................................................................................... 68
Dispersion Boundary Factor....................................................................................................................................... 68
Joint Size and Velocity Distributions ............................................................................................................................. 68
Concluding Remarks........................................................................................................................................................ 68
Nomenclature.................................................................................................................................................................... 69
References .......................................................................................................................................................................... 69

4. Atomizers .......................................................................................................................................................................... 71
Introduction....................................................................................................................................................................... 71
Atomizer Requirements................................................................................................................................................... 71
Pressure Atomizers .......................................................................................................................................................... 71
Plain Orifice .................................................................................................................................................................. 72
Simplex .......................................................................................................................................................................... 75
Wide-Range Nozzles ................................................................................................................................................... 79
Use of Shroud Air ........................................................................................................................................................ 83
Fan Spray Nozzles........................................................................................................................................................ 84
Rotary Atomizers.............................................................................................................................................................. 86
Slinger System .............................................................................................................................................................. 87
Air-Assist Atomizers........................................................................................................................................................ 89
Airblast Atomizers............................................................................................................................................................ 92
Effervescent Atomizers .................................................................................................................................................... 94
Electrostatic Atomizers .................................................................................................................................................... 95
Ultrasonic Atomizers ....................................................................................................................................................... 96
Whistle Atomizers ............................................................................................................................................................ 98
Manufacturing Aspects ................................................................................................................................................... 99
References .......................................................................................................................................................................... 99

5 Flow in Atomizers ......................................................................................................................................................... 105

6 Atomizer Performance.................................................................................................................................................. 133

Introduction ..................................................................................................................................................................... 133
Plain-Orifice Atomizer................................................................................................................................................... 133
Quiescent Environment ............................................................................................................................................ 133
Crossflow..................................................................................................................................................................... 135
Pressure-Swirl Atomizers .............................................................................................................................................. 135
Effect of Variables on Mean Drop Size ................................................................................................................... 135
Drop Size Relationships .............................................................................................................................................141
Rotary Atomizers............................................................................................................................................................ 146
Drop Size Equations for Smooth Flat Vane-Less Disks........................................................................................ 147
Drop Size Equations for Other Vane-Less Disks................................................................................................... 148
Drop Size Equations for Atomizer Wheels ............................................................................................................ 149
Drop Size Equations for Slinger Injectors .............................................................................................................. 150
Air-Assist Atomizers...................................................................................................................................................... 150
Internal-Mixing Nozzles........................................................................................................................................... 150
External-Mixing Nozzles .......................................................................................................................................... 152
Airblast Atomizers.......................................................................................................................................................... 156
Plain Jet........................................................................................................................................................................ 156
Prefilming.....................................................................................................................................................................161
Miscellaneous Types.................................................................................................................................................. 166
Plain-Jet Atomization by a Crossflow ................................................................................................................ 166
Plain-Jet Impingement Injector ............................................................................................................................167
Other Designs .........................................................................................................................................................167
Effect of Variables on Mean Drop Size ................................................................................................................... 169
Analysis of Drop Size Relationships ....................................................................................................................... 171
Summary of the Main Points ................................................................................................................................... 172
Effervescent Atomizer.................................................................................................................................................... 173
Electrostatic Atomizers .................................................................................................................................................. 175
Ultrasonic Atomizers ..................................................................................................................................................... 175
Nomenclature.................................................................................................................................................................. 177
Subscripts .................................................................................................................................................................... 177
References ........................................................................................................................................................................ 178

7 External Spray Characteristics.................................................................................................................................... 183

Drop Drag Coefficients .................................................................................................................................................. 200

Effect of Acceleration on Drag Coefficient ............................................................................................................. 202
Drag Coefficients for Evaporating Drops ............................................................................................................... 202
Nomenclature.................................................................................................................................................................. 203
Subscripts .................................................................................................................................................................... 203
References ........................................................................................................................................................................ 203

8 Drop Evaporation .......................................................................................................................................................... 207

Introduction..................................................................................................................................................................... 207
Steady-State Evaporation ............................................................................................................................................... 207
Measurement of Evaporation Rate .......................................................................................................................... 208
Theoretical Background............................................................................................................................................ 208
Calculation of Steady-State Evaporation Rates ................................................................................................. 212
Evaporation Constant ........................................................................................................................................... 213
Influence of Ambient Pressure and Temperature on Evaporation Rates............................................................216
Evaporation at High Temperatures ..........................................................................................................................216
Unsteady-State Analysis ................................................................................................................................................ 218
Calculation of Heat-Up Period ................................................................................................................................. 218
Influence of Pressure and Temperature on Heat-Up Period................................................................................ 224
Summary of Main Points .......................................................................................................................................... 225
Drop Lifetime .................................................................................................................................................................. 225
Effect of Heat-Up Phase on Drop Lifetime............................................................................................................. 228
Effect of Prevaporization on Drop Lifetime........................................................................................................... 228
Convective Effects on Evaporation............................................................................................................................... 229
Determination of Evaporation Constant and Drop Lifetime .............................................................................. 231
Drop Lifetime ............................................................................................................................................................. 231
Calculation of Effective Evaporation Constant .......................................................................................................... 232
Influence of Evaporation on Drop Size Distribution ................................................................................................. 234
Drop Burning .................................................................................................................................................................. 235
Multicomponent Fuel Drops ......................................................................................................................................... 237
Nomenclature.................................................................................................................................................................. 239
Subscripts .................................................................................................................................................................... 239
References ........................................................................................................................................................................ 240

9 Spray Size and Patternation Methods....................................................................................................................... 243

Optical Methods......................................................................................................................................................... 252

High Magnification Imaging............................................................................................................................... 252
Holography/Plenoptic .......................................................................................................................................... 254
Time Gating............................................................................................................................................................ 255
X-Ray Methods ...................................................................................................................................................... 256
Single-Particle Counters....................................................................................................................................... 256
Laser Diffraction Technique ................................................................................................................................ 264
Intensity Ratio Method......................................................................................................................................... 268
Planar Methods ..................................................................................................................................................... 269
Calibration Techniques......................................................................................................................................... 270
Spray Pattern ................................................................................................................................................................... 271
Mechanical .................................................................................................................................................................. 271
Optical ......................................................................................................................................................................... 271
Imaging................................................................................................................................................................... 271
Nonimaging ........................................................................................................................................................... 272
Other Characteristics...................................................................................................................................................... 272
Comments Regarding Simulation ................................................................................................................................ 272
Concluding Remarks.......................................................................................................................................................274
References .........................................................................................................................................................................274

Index ........................................................................................................................................................................................ 281

Preface to the Second Edition

The Second Edition of the book has been long overdue research direction and analysis. Through these times
and, as a result, it has been quite challenging to even I was able to get to know him better and to appreciate
attempt to address and incorporate numerous impor his perspective regarding engineering, combustion,
tant contributions from the spray research community and atomization and sprays.
since the First Edition. The overarching theme of the In terms of the Second edition, a few points are worth
book’s content has remained connected to the practi mentioning. First, the criticality of liquid properties in
cal, yet physically grounded approach taken by Arthur applying the design tools contained in the book cannot
Lefebvre throughout his incredible career—namely, be overemphasized and hence many new contributions
that as an engineer or practitioner of atomization have been made to Chapter 1. In addition, many new
and spray technology, simple to use design tools that studies have been carried out regarding the basic prin
facilitate hardware development to achieve a particu ciples of internal flow and spray behavior and hence
lar attribute in terms of spray behavior are extremely Chapter 2 has a significant amount of new material.
useful. While the field of atomization and sprays has While some efforts have been carried out in improv
expanded significantly in the last 25+ years, the guid ing the details and subtleties associated with describing
ing principles described in the First Edition remain in the droplet size and size distribution, the basic tools for
the Second Edition. As a result, contributions simply describing these remain largely the same as they existed
reporting observations, new methods, or even analyti in the First Edition. What has changed is the ability to
cal approaches that have not distilled the information rapidly determine coefficients and constants through
into a form that can be readily applied are not high readily available regression analysis tools. In addition,
lighted. While these contributions may have provided a observations regarding the statistical significance of the
path forward to generating a new model or design tool, various distributions (count, surface area, volume) have
emphasis has been given to the new model or tool them been made in regards to extracting typical statistical
selves. And preference is given for the tools in which moments, such as standard deviation, skewness, and
all necessary information to apply it is readily available. so on from these distributions. Chapter 3 contains this
While incredibly detailed information can now be gar information.
nered about spray performance via both measurement In terms of atomizer types, little has changed in
and simulation, it is important to realize that this infor terms of the general classification of the various types.
mation is a means to the end, which in this case is to A few interesting concepts have evolved, but pressure-
innovate, develop, and improve atomization technology. based or twin-fluid approaches remain widely used.
While Arthur Lefebvre had few peers in his field Electrostatic and ultrasonic devices continue to be
during the development of the First Edition, this is no utilized. Thus, Chapter 4 remains similar to the First
longer the case with numerous researchers and devel Edition, but consideration is given regarding innovation
opers now very active in the field. The information he through advanced manufacturing methods.
compiled from his vast research in preparing the First The internal flow of atomizers is an area in which sig
Edition is still very relevant, but others have, and are con nificant progress has been made in recent years due to
tributing. As only one of many contributors to this field, novel diagnostic methods and advancements in simula
I remain humbled about the task of compiling updated tion. Hence, Chapter 5 contains additional details asso
information from throughout the world and trying to ciated with cases in which cavitation is now understood
integrate it in a concise manner among the framework to play a key role in the atomization performance.
established within the First Edition. Undoubtedly, some Drop size and pattern remain a critical aspect of the
fine work has been overlooked, and to those contribu performance of sprays. As a result, Chapters 6 and 7
tors, I can only apologize in advance. provide details on design tools that have evolved for
I had the honor and pleasure of knowing Arthur, describing these aspects. In this area, much progress
having met him at ASME, AIAA, and ILASS confer has been made regarding jets in crossflow, which are
ences. He spent a few weeks each winter in Irvine used in many applications.
where he continued to provide his course on Gas For combustion applications, evaporation remains
Turbine Combustion with assistance from Scott a critical step. The work described in the First Edition
Samuelsen and Don Bahr. He relished his time meet remains highly germane, although other developments
ing with students in the UCI Combustion Laboratory are now included. But for application to complex turbu
and offered many excellent suggestions regarding lent sprays in practical combustion environments, some

xi
xii Preface to the Second Edition

of the simplifications associated with early work remain Scott Parrish, Randy McKinney, Doug Talley, Dom
quite appropriate for design work. Santavicca, Jon Guen Lee, May Corn, Jeff Cohen,
Finally, Chapter 9 is dedicated to instrumentation Corinne Lengsfeld, Norman Chigier, Jiro Senda, Paul
with some consideration for simulations. It has been Sojka, Marcus Herrmann, David Schmidt, Rudi Schick,
well established that, by working together, experimen Jim Drallmeier, Lee Markle, Eva Gutheil, Lee Dodge,
tal measurements and simulations combined offer the Rick Stickles, Muh Rong Wang, and, of course, Arthur
greatest insight. Lefebvre among many others have been helpful in
I would like to thank the growing spray community establishing connections and inspiration throughout.
as a whole and in particular the Institutes for Liquid Thanks to Josh Holt, Ryan Ehlig, Rob Miller, Elliot
Atomization and Spray Systems (ILASS) from around Sullivan Lewis, Max Venaas, and Scott Leask for assis
the world. The ILASS organizations, inspired and tance with various aspects of this edition. Derek Dunn-
founded by the same people who inspired the First Rankin, Roger Rangel, Enrique Lavernia, and Bill
Edition of this book, remain a significant forum for Sirignano have provided perspective and insight and
bringing spray research together. Appreciation is also have been an inspiration. Long-standing colleagues and
given to the journal Atomization and Sprays, which has collaborators Christopher Brown and Ulises Mondragon
provided a suitable means of archiving important spray of Energy Research Consultants have also provided
research in a single place. Of course, many journals friendship and in depth discussions over the years. A
contain relevant works, generally they are application special thank you to Scott Samuelsen who has been
driven and focused, and many new contributions to a great friend, colleague, and mentor. Also, I need to
diagnostic methods and simulation methods are found thank the many graduate and undergraduate students
among numerous sources. and staff of the UCI Combustion Laboratory who have
Ongoing discussions over the decades with Mel provided much enjoyment and discovery.
Roquemore, Hukam Mongia, Don Bahr, Lee Dodge, I must also thank my family, and especially my wife,
Will Bachalo, Mike Houser, Chris Edwards, Bill Sowa, Jan, who remained encouraging and supportive during
Tom Jackson, Barry Kiel, Rolf Reitz, Roger Rudoff, this time consuming, but rewarding process.
Greg Smallwood, Michael Benjamin, Masayuki
Adachi, Yannis Hardapulas, Alex Taylor, Chuck Lipp, Vincent McDonell
Preface to the First Edition

The transformation of bulk liquid into sprays and other which a liquid jet or sheet emerging from an atomizer is
physical dispersions of small particles in a gaseous broken down into drops.
atmosphere is of importance in several industrial pro Owing to the heterogeneous nature of the atomiza
cesses. These include combustion (spray combustion in tion process, most practical atomizers generate drops
furnaces, gas turbines, diesel engines, and rockets); pro in the size range from a few micrometers up to around
cess industries (spray drying, evaporative cooling, pow 500 µm. Thus, in addition to mean drop size, which may
dered metallurgy, and spray painting); agriculture (crop be satisfactory for many engineering purposes, another
spraying); and many other applications in medicine and parameter of importance in the definition of a spray is
meteorology. Numerous spray devices have been devel the distribution of drop sizes it contains. The various
oped, and they are generally designated as atomizers or mathematical and empirical relationships that are used
nozzles. to characterize the distribution of drop sizes in a spray
As is evident from the aforementioned applications, are described in Chapter 3.
the subject of atomization is wide ranging and impor In Chapter 4, the performance requirements and
tant. During the past decade, there has been a tremen basic design features of the main types of atomizers in
dous expansion of interest in the science and technology industrial and laboratory use are described. Primary
of atomization, which has now developed into a major emphasis is placed on the atomizers employed in indus
international and interdisciplinary field of research. trial cleaning, spray cooling, and spray drying, which,
This growth of interest has been accompanied by large along with liquid fuel–fired combustion, are their most
strides in the areas of laser diagnostics for spray anal important applications.
ysis and in a proliferation of mathematical models for Chapter 5 is devoted primarily to the internal flow
spray combustion processes. It is becoming increasingly characteristics of plain-orifice and pressure-swirl atom
important for engineers to acquire a better understand izers, but consideration is also given to the complex flow
ing of the basic atomization process and to be fully con situations that arise on the surface of a rotating cup or
versant with the capabilities and limitations of all the disk. These flow characteristics are important because
relevant atomization devices. In particular, it is impor they govern the quality of atomization and the distribu
tant to know which type of atomizer is best suited for tion of drop sizes in the spray.
any given application and how the performance of any Atomization quality is usually described in terms
given atomizer is affected by variations in liquid prop of a mean drop size. Because the physical processes
erties and operating conditions. involved in atomization are not well understood, empir
This book owes its inception to a highly successful ical equations have been developed for expressing the
short course on atomization and sprays held at Carnegie mean drop size in a spray in terms of liquid properties,
Mellon University in April 1986 under the direction of gas properties, flow conditions, and atomizer dimen
Professor Norman Chigier. As an invited lecturer to this sions. The equations selected for inclusion in Chapter
course, my task was by no means easy because most of 6 are considered to be the best available for the types of
the relevant information on atomization is dispersed atomizers described in Chapter 4.
throughout a wide variety of journal articles and con The function of an atomizer is not only to disintegrate
ference proceedings. A fairly thorough survey of this a bulk liquid into small drops, but also to discharge
literature culminated in the preparation of extensive these drops into the surrounding gas in the form of a
course notes. The enthusiastic response accorded to this symmetrical, uniform spray. The spray characteristics
course encouraged me to expand these notes into this of most practical importance are discussed in Chapter 7.
book, which will serve many purposes, including those They include cone angle, penetration, radial liquid dis
of text, design manual, and research reference in the tribution, and circumferential liquid distribution.
areas of atomization and sprays. Although evaporation processes are not intrinsic
The book begins with a general review of atomizer to the subject of atomization and sprays, it cannot be
types and their applications, in Chapter 1. This chap overlooked that in many applications the primary pur
ter also includes a glossary of terms in widespread pose of atomization is to increase the surface area of
use throughout the atomization literature. Chapter 2 the liquid and thereby enhance its rate of evaporation.
provides a detailed introduction to the various mecha In Chapter 8, attention is focused on the evaporation of
nisms of liquid particle breakup and to the manner in fuel drops over wide ranges of ambient gas pressures

xiii
xiv Preface to the First Edition

and temperatures. Consideration is given to both Hannifin Corporation, and Roger Tate of Delavan
steady-state and unsteady-state evaporation. The con Incorporated. I am also deeply indebted to my gradu
cept of an effective evaporation constant is introduced, ate students in the School of Mechanical Engineering
which is shown to greatly facilitate the calculation of at Cranfield and the Gas Turbine Combustion
evaporation rates and drop lifetimes for liquid hydro Laboratory at Purdue. They have made significant
carbon fuels. contributions to this book through their research, and
The spray patterns produced by most practical atom their names appear throughout the text and in the lists
izers are so complex that fairly precise measurements of references.
of drop-size distributions can be obtained only if accu Professor Norman Chigier has been an enthusiastic
rate and reliable instrumentation and data reduction supporter in the writing of this book. Other friends and
procedures are combined with a sound appreciation colleagues have kindly used their expert knowledge
of their useful limits of application. In Chapter 9, the in reviewing and commenting on individual chapters,
various methods employed in drop-size measurement especially Chapter 9, which covers an area that in recent
are reviewed. Primary emphasis is placed on optical years has become the subject of fairly intense research
methods that have the important advantage of allow and development. They include Dr. Will Bachalo of
ing size measurements to be made without the insertion Aerometrics, Inc., Dr. Lee Dodge of Southwest Research
of a physical probe into the spray. For ensemble mea Institute, Dr. Patricia Meyer of Insitec, and Professor
surements, the light diffraction method has much to Arthur Sterling of Louisiana State University. In the task
commend it and is now in widespread use as a general of proofreading, I have been ably assisted by Professor
purpose tool for spray analysis. Of the remaining meth Norman Chigier, Professor Ju Shan Chin, and my grad
ods discussed, the advanced optical techniques have uate student Jeff Whitlow—their help is hereby grate
the capability of measuring drop velocity and number fully acknowledged.
density as well as size distribution. I am much indebted to Betty Gick and Angie Myers
Much of the material covered in this book is based for their skillful typing of the manuscript and to Mark
on knowledge acquired during my work on atom Bass for the high-quality artwork he provided for this
izer design and performance over the past 30 years. book. Finally, I would like to thank my wife, Sally, for
However, the reader will observe that I have not hesi her encouragement and support during my undertak
tated in drawing on the considerable practical experi ing of this time-consuming but enjoyable task.
ence of my industrial colleagues, notably Ted Koblish
of Fuel Systems TEXTRON, Hal Simmons of the Parker Arthur H. Lefebvre
Authors

Arthur H. Lefebvre (1923–2003) was Emeritus Professor Vincent G. McDonell is an associate director of the UCI
at Purdue University. With industrial and academic Combustion Laboratory at the University of California,
experience spanning more than four decades, he wrote Irvine, where he also serves as an adjunct professor in the
more than 150 technical papers on both fundamental Mechanical and Aerospace Engineering Department.
and practical aspects of atomization and combustion. He earned a PhD at the University of California, Irvine
The honors he received include the ASME Gas Turbine in 1990 and has served on the executive committees of
and ASME R. Tom Sawyer Awards, ASME George ILASS-Americas and ICLASS International. He has won
Westinghouse Gold Medal, and the IGTI Scholar Award. best paper awards from ILASS-Americas and ASME for
He was also the first recipient of the AIAA Propellants work on atomization. He has done extensive research in
and Combustion Award. the areas of atomization and combustion, holds a patent
in the area, and has authored or coauthored more than
150 papers in the field.

xv
1
General Considerations

various size classes may be required for different appli

cations. For additive manufacturing, a cut between 100
Introduction
and 150 microns may be desired, with material con
The transformation of bulk liquid into sprays and other tained in other size particles and unusable byproduct
physical dispersions of small particles in a gaseous adding cost and inefficiency if it cannot be remelted.
atmosphere is of importance in several industrial pro Efforts associated with quality control, improved
cesses and has many other applications in agriculture, utilization efficiency, pollutant emissions, precision
meteorology, and medicine. Numerous spray devices manufacturing, and the like have elevated atomization
have been developed, which are generally designated as science and technology to a major international and
atomizers or nozzles. In the process of atomization, a interdisciplinary field of research. An evolving array
liquid jet or sheet is disintegrated by the kinetic energy of applications has been accompanied by large strides
of the liquid, by the exposure to high-velocity air or gas, in the area of advanced diagnostics for spray analysis
or by mechanical energy applied externally through and by resulting mathematical models and simulation
a rotating or vibrating device. Because of the random of atomization and spray behavior. It is important for
nature of the atomization process, the resultant spray is engineers to acquire a better understanding of the basic
usually characterized by a wide spectrum of drop sizes. atomization process and to be fully conversant with the
The process is highly coupled and involves a wide range capabilities and limitations of all the relevant atomiza
of characteristics that may or may not be important tion devices. In particular, it is important to know which
depending on the application. To illustrate, Figure 1.1 type of atomizer is best suited for any given applica
summarizes the processes and resultant attributes that tion and how the performance of any given atomizer is
may be found within a typical spray [1]. affected by variations in liquid properties and operating
Natural sprays include waterfall mists, rains, and ocean conditions.
sprays. At home, sprays are produced by shower heads,
garden hoses, trigger sprayers for household cleaners,
propellants for hair sprays, among others. They are com
monly used in applying agricultural chemicals to crops,
paint spraying, spray drying of wet solids, food process
Atomization
ing, cooling in various systems, including nuclear cores,
gas–liquid mass transfer applications, dispersing liquid Sprays may be produced in various ways. Several basic
fuels for combustion, fire suppression, consumer sprays, processes are associated with all methods of atomiza
snowmaking, and many other applications. tion, such as the hydraulics of the flow within the atom
Combustion of liquid fuels in diesel engines, spark- izer, which governs the turbulence properties of the
ignition engines, gas turbines, rocket engines, and emerging liquid stream. The development of the jet
industrial furnaces is dependent on effective atomiza or sheet and the growth of small disturbances, which
tion to increase the specific surface area of the fuel and eventually lead to disintegration into ligaments and
thereby achieve high rates of mixing and evaporation. In then drops, are also of primary importance in deter
most combustion systems, reduction in mean fuel drop mining the shape and penetration of the resulting spray
size leads to higher volumetric heat release rates, easier as well as its detailed characteristics of number density,
light up, a wider burning range, and lower exhaust con drop velocity, and drop size distributions as functions
centrations of pollutant emissions [2–4]. of time and space as illustrated in Figure 1.1. All of these
In other applications, however, such as crop spray characteristics are markedly affected by the internal
ing, small droplets must be avoided because their set geometry of the atomizer, the properties of the gaseous
tling velocity is low and, under certain meteorological medium into which the liquid stream is discharged, and
conditions, they can drift too far downwind. Drop sizes the physical properties of the liquid. Perhaps the sim
are also important in spray drying and must be closely plest situation is the disintegration of a liquid jet issuing
controlled to achieve the desired rates of heat and mass from a circular orifice, where the main velocity compo
transfer. When the objective is creating metal powder, nent lies in the axial direction and the jet is in laminar

1
2 Atomization and Sprays

Pumping characteristics, flow

in tubes and channels, internal
geometry, and flow field
Liquid properties, discharge
coefficient, sheet, cone angle,
thickness, velocity, shear
flow, and turbulence characteristics
Wave instabilities in
the liquid sheet mechanisms
for sheet primary breakup
Breakup length
Drop deformation and
breakup
Secondary breakup
drop collisions and coalescence
Drop size, velocity, number density,
and volume flux distributions
Drop dynamics, drop slip velocities,
induced air flow field, gas phase
flow field with swirl, reversed
flow, and turbulence
Spray interactions with turbulent
eddies, cluster formation, drop
heat transfer and evaporation

FIGURE 1.1
Example of a simple spray illustrating many features that need to be characterized. (From Bachalo, W. D., Atomization Sprays, 10, 439–474, 2000.)

flow. Lord Rayleigh, in his classic study [5], postulated is produced by pressure in pressure-swirl and fan spray
the growth of small disturbances that eventually lead to nozzles and by centrifugal force in rotary atomizers.
breakup of the jet into drops having a diameter nearly Regardless of how the sheet is formed, its initial hydro
twice that of the jet. A fully turbulent jet can break up dynamic instabilities are augmented by aerodynamic dis
without the application of any external force. Once the turbances, so as the sheet expands away from the nozzle
radial components of velocity are no longer confined and its thickness declines, perforations are formed that
by the orifice walls, they are restrained only by the sur expand toward one an other and coalesce to form threads
face tension, and the jet disintegrates when the surface and ligaments. As these ligaments vary widely in diame
tension forces are overcome. The role of viscosity is to ter, when they collapse the drops formed also vary widely
inhibit the growth of instability and generally delays in diameter. Some of the larger drops created by this pro
the onset of disintegration. This causes atomization to cess disintegrate further into smaller droplets. Eventually,
occur farther downstream in regions of lower relative a range of drop sizes is produced whose average diam
velocity; consequently, drop sizes are larger. In most eter depends mainly on the initial thickness of the liquid
cases, turbulence in the liquid, cavitation in the nozzle, sheet, its velocity relative to the surrounding gas, and the
and aerodynamic interaction with the surrounding liquid properties of viscosity and surface tension.
air, which increases with air density, all contribute to A liquid sheet moving at high velocity can also disin
atomization. tegrate in the absence of perforations by a mechanism
Many applications call for a conical or flat spray pattern known as wavy-sheet disintegration, whereby the crests
to achieve the desired dispersion of drops for liquid–gas of the waves created by aerodynamic interaction with
mixing. Conical sheets may be produced by pressure-swirl the surrounding gas are torn away in patches. Finally, at
nozzles in which a circular discharge orifice is preceded very high liquid velocities, corresponding to high injec
by a chamber in which tangential holes or slots are used tion pressures, sheet disintegration occurs close to the
to impart a swirling motion to the liquid as it leaves the nozzle exit. However, although several modes of sheet
nozzle. Flat sheets are generally produced either by forc disintegration have been identified, in all cases the final
ing the liquid through a narrow annulus, as in fan spray atomization process is one in which ligaments break up
nozzles, or by feeding it to the center of a rotating disk or into drops according to the Rayleigh mechanism.
cup. To expand the sheet against the contracting force of With prefilming airblast atomizers, a high relative
surface tension, a minimum sheet velocity is required and velocity is achieved by exposing a slow-moving sheet of
General Considerations 3

liquid to high-velocity air. Photographic evidence sug

gests that for low-viscosity liquids the basic mechanisms
Atomizers
involved are essentially the same as those observed in
pressure atomization, namely the production of drops An atomizer is generally used to produce a spray.
from ligaments created by perforated-sheet and/or Essentially, all that is needed is a high relative velocity
wavy-sheet disintegration. between the liquid to be atomized and the surrounding
A typical spray includes a wide range of drop air or gas. Some atomizers accomplish this by discharg
sizes. Some knowledge of drop size distribution is ing the liquid at high velocity into a relatively slow-
helpful in evaluating process applications in sprays, moving stream of air or gas. Notable examples include
especially in calculations of heat or mass transfer the various forms of pressure atomizers and also rotary
between the dispersed liquid and the surrounding atomizers, which eject the liquid at high velocity from
gas. Unfortunately, no complete theory has yet been the periphery of a rotating cup or disk. An alternative
developed to describe the hydrodynamic and aerody approach is to expose the relatively slow-moving liquid
namic processes involved when jet and sheet disinte to a high-velocity airstream. The latter method is gener
gration occurs under normal atomizing conditions, ally known as twin-fluid, air-assist, or airblast atomization.
so that only empirical correlations are available for Other examples may involve heterogeneous processes
predicting mean drop sizes and drop size distribu in which air bubbles or liquid vapor become involved in
tions. Comparison of the distribution parameters in disrupting the liquid phase during the injection process.
common use reveals that all of them have deficien
cies of one kind or another. In one the maximum drop
Pressure Atomizers
diameter is unlimited; in others the minimum possi
ble diameter is zero or even negative. So far, no single When a liquid is discharged through a small aperture
parameter has emerged that has clear advantages over under high applied pressure, the pressure energy is
the others. For any given application the best distri converted into the kinetic energy (velocity). For a typi
bution function is one that is easy to manipulate and cal hydrocarbon fuel, in the absence of frictional losses a
provides the best fit to the experimental data. nozzle pressure drop of 138 kPa (20 psi) produces an exit
The difficulties in specifying drop size distribu velocity of 18.6 m/s. As velocity increases as the square
tions in sprays have led to widespread use of various root of the pressure, at 689 kPa (100 psi) a velocity of
mean or median diameters. A median droplet diam 41.5 m/s is obtained, while 5.5 MPa (800 psi) produces
eter divides the spray into two equal parts by number, 117 m/s.
length, surface area, or volume [6]. Median diameters Plain Orifice. A simple circular orifice is used to
may be determined from different types of cumulative inject a round jet of liquid into the surrounding air. The
distribution curves shown in Figure 3.6. In a typical finest atomization is achieved with small orifices but, in
spray, the value of the median diameter, expressed practice, the difficulty of keeping liquids free from for
in micrometers, will vary by a factor of about four eign particles usually limits the minimum orifice size
depending on the median diameter selected for use. to around 0.3 mm. Combustion applications for plain-
It is important therefore to decide which measure is the orifice atomizers include turbojet afterburners, ramjets,
most suitable for a particular application. Some diam diesel engines, and rocket engines.
eters are easier to visualize and comprehend, while Pressure-Swirl (Simplex). A circular outlet orifice is
others may appear in prediction equations that have preceded by a swirl chamber into which liquid flows
been derived from theory or experiment. Some drop through a number of tangential holes or slots. The swirl
size measurement techniques yield a result in terms of ing liquid creates a core of air or gas that extends from
one particular median diameter. In some cases, a given the discharge orifice to the rear of the swirl chamber.
median diameter is selected to emphasize some impor The liquid emerges from the discharge orifice as an
tant characteristic, such as the total surface area in the annular sheet, which spreads radially outward to form
spray. For liquid fuel fired combustion systems and a hollow conical spray. Included spray angles range
other applications involving heat and mass transfer to from 30° to almost 180°, depending on the application.
liquid drops, the Sauter mean diameter, which repre Atomization performance is generally good. The finest
sents the ratio of the volume to the surface area of the atomization occurs at high delivery pressures and wide
spray, is often preferred. The mass median diameter, spray angles.
which is about 15%–25% larger than the Sauter mean For some applications a spray in the form of a solid
diameter, is also widely used. As Tate [6] has pointed cone is preferred. This can be achieved using an axial jet
out, the ratio of these two diameters is a measure of the or some other device to inject droplets into the center of
spread of drop sizes in the spray. the hollow conical spray pattern produced by the swirl
4 Atomization and Sprays

chamber. These two modes of injection create a bimodal Spill Return. This is essentially a simplex nozzle, but
distribution of drop sizes, droplets at the center of the with a return flow line at the rear or side of the swirl
spray being generally larger than those near the edge. chamber and a valve to control the quantity of liquid
Square Spray. This is essentially a solid-cone nozzle, removed from the swirl chamber and returned to sup
but the outlet orifice is specially shaped to distort the ply. Very high turndown ratios are attainable with this
conical spray into a pattern that is roughly in the form design. Atomization quality is always good because the
of a square. Atomization quality is not as high as the supply pressure is held constant at a high value, reduc
conventional hollow-cone nozzles but, when used in tions in flow rate being accommodated by adjusting the
multiple-nozzle combinations, a fairly uniform coverage valve in the spill return line. This construction provides
of large areas can be achieved. a hollow-cone spray pattern, with some increase in the
Duplex. A drawback of all types of pressure nozzles spray angle as the flow is reduced.
is that the liquid flow rate is proportional to the square Fan Spray. Several different concepts are used to pro
root of the injection pressure differential. In practice, duce flat or fan-shaped sprays. The most popular type
this limits the flow range of simplex nozzles to about of nozzle is one in which the orifice is formed by the
10:1. The duplex nozzle overcomes this limitation by intersection of a V groove with a hemispheric cavity
feeding the swirl chamber through two sets of distribu communicating with a cylindrical liquid inlet [6]. It pro
tor slots, each having its own separate liquid supply. duces a liquid sheet parallel to the major axis of the ori
One set of slots is much smaller in cross-sectional area fice, which disintegrates into a narrow elliptical spray.
than the other. The small slots are termed primary and An alternative method of producing a fan spray is
the large slots secondary. At low flow rates all the liquid by discharging the liquid through a plain circular hole
to be atomized flows into the swirl chamber through onto a curved deflector plate. The deflector method pro
the primary slots. As the flow rate increases, the injec duces a somewhat coarser spray pattern. Wide spray
tion pressure increases. At some predetermined pres angles and high flow rates are attainable with this type
sure level a valve opens and admits liquid into the swirl of nozzle. Because the nozzle flow passages are rela
chamber through the secondary slots. tively large, the problem of plugging is minimized.
Duplex nozzles allow good atomization to be achieved A fan spray can also be produced by the collision of
over a range of liquid flow rates of about 40:1 without impinging jets. If two liquid jets are arranged to collide
the need to resort to excessively high delivery pressures. outside the nozzle, a flat liquid sheet is formed that is
However, near the point where the secondary liquid is perpendicular to the plane of the jets. The atomization
first admitted into the swirl chamber, there is a small performance of this type of injector is relatively poor,
range of flow rates over which atomization quality is and high stream velocities are necessary to approach
poor. Moreover, the spray cone angle changes with flow the spray quality obtainable with other types of pres
rate, being widest at the lowest flow rate and becoming sure nozzles. Extreme care must be taken to ensure that
narrower as the flow rate is increased. the jets are properly aligned. The main advantage of
Dual Orifice. This is similar to the duplex nozzle except this method of atomization is the isolation of different
that two separate swirl chambers are provided, one for liquids until they collide outside the nozzle. These are
the primary flow and the other for the secondary flow. commonly used for hypergolic propellant systems in
The two swirl chambers are housed concentrically within which an oxidizer and fuel component will react upon
a single nozzle body to form a nozzle within a nozzle. At low contact
flow rates all the liquid passes through the inner primary
nozzle. At high flow rates liquid continues to flow through
Rotary Atomizers
the primary nozzle, but most of the liquid is passed
through the outer secondary nozzle that is designed for a One widely used type of rotary atomizer comprises a
much larger flow rate. As with the duplex nozzle, there is high-speed rotating disk with means for introducing
a transition phase, just after the pressurizing valve opens, liquid at its center. The liquid flows radially outward
when the secondary spray draws its energy for atomiza across the disk and is discharged at high velocity from
tion from the primary spray, so the overall atomization its periphery. The disk may be smooth and flat or may
quality is relatively poor. have vanes or slots to guide the liquid to the periphery.
Dual-orifice nozzles offer more flexibility than the At low flow rates, droplets form near the edge of the
duplex nozzles. For example, if desired, the primary and disk. At high flow rates, ligaments or sheets are gener
secondary sprays can be merged just downstream of the ated at the edge and disintegrate into droplets. Small
nozzle to form a single spray. Alternatively, the primary disks operating at high rotational speeds and low flow
and secondary nozzles can be designed to produce dif rates are capable of producing sprays in which drop
ferent spray angles, the former being optimized for low sizes are fairly uniform. A 360° spray pattern is devel
flow rates and the latter optimized for high flow rates. oped by rotating disks that are usually installed in a
General Considerations 5

cylindrical or conical chamber where an umbrella-like Other Types

spray is created by downward gas currents [6].
Most practical atomizers are of the pressure, rotary, or twin-
Some rotary atomizers employ a cup instead of a disk.
fluid type. However, many other forms of atomizers have
The cup is usually smaller in diameter and is shaped
been developed that are useful in special applications.
like an elongated bowl. In some designs, the edge of
Electrostatic. A liquid jet or film is exposed to an
the cup is serrated to encourage a more uniform drop
intense electrical pressure that tends to expand its area.
size distribution in the spray. A flow of air around the
This expansion is opposed by the surface tension forces.
periphery is sometimes used to shape the spray and to
If the electrical pressure predominates, droplets are
assist in transporting the droplets away from the atom
izer. In contrast to pressure nozzles, rotary atomizers formed. Droplet size is a function of the electrical pres
allow independent variation of flow rate and disk speed, sure, the liquid flow rate, and the physical and electrical
thereby providing more flexibility in operation. properties of the liquid. The low liquid flow rates asso
ciated with electrostatic atomizers have tended to limit
their practical applications to electrostatic painting and
Air-Assist Atomizers nonimpact printing.
In this type of nozzle, the liquid is exposed to a stream Ultrasonic. The liquid to be atomized is fed through
of air or steam flowing at high velocity. In the internal- or over a transducer and horn, which vibrates at ultra
mixing configuration, gas and liquid are mixed within sonic frequencies to produce the short wavelengths
the nozzle before discharging through the outlet orifice. necessary for fine atomization. The system requires a
The liquid is sometimes supplied through tangential high-frequency electrical input, two piezoelectric trans
slots to encourage a conical discharge pattern. However, ducers, and a stepped horn. The concept is well suited
the maximum spray angle is limited to about 60°. The for applications that require very fine atomization and a
device tends to be energy inefficient, but it can produce low spray velocity. At present, an important application
a finer spray than simple pressure nozzles. of ultrasonic atomizers (nebulizers) is for medical inha
As its name suggests, in the external-mixing form of lation therapy, where very fine sprays and the absence of
air-assist nozzle the high-velocity gas or steam impinges gas to effect atomization are important attributes.
on the liquid at or outside the liquid discharge orifice. Sonic (Whistle). Gas is accelerated within the device
Its advantage over the internal-mixing type is that to sonic velocity and impinges on a plate or annular cav
problems of back pressures are avoided because there ity (resonation chamber). The sound waves produced
is no internal communication between gas and liquid. are reflected into the path of the incoming liquid [7]. The
However, it is less efficient than the internal-mixing frequency of the sound waves is around 20 kHz, and
concept, and higher gas flow rates are needed to achieve this serves to disintegrate the liquid into small droplets
the same degree of atomization. Both types of nozzles ranging downward in size from 50 μm. The sonic and
can atomize high-viscosity liquids effectively. pneumatic effects are difficult to isolate from each other.
Efforts have been made to design nozzles that operate
above the audible frequency limit to reduce the nuisance
Airblast Atomizers of noise [8]. However, in some applications the attendant
These devices function in a very similar manner to air- sound field may benefit the process (e.g., combustion)
assist nozzles, and both types fall in the general category for which the resultant spray is required.
of twin-fluid atomizers. The main difference between Windmill. Many aerial applications of pesticides
air-assist and airblast atomizers is that the former use require a narrow spectrum of drop sizes. The conven
relatively small quantities of air or steam flowing at very tional rotary disk atomizers can provide such a spec
high velocities (usually sonic), whereas the latter employ trum, but only when operating in the ligament mode
large amounts of air flowing at much lower velocities at low flow rates. By making radial cuts at the periph
(<100 m/s). Airblast nozzles are thus ideally suited for ery of a disk and twisting the tips of the segments, the
atomizing liquid fuels in continuous-flow combustion disk can be converted into a windmill that will rotate
systems, such as gas turbines, where air velocities of this rapidly when inserted into an airflow at aircraft flight
magnitude are usually readily available. The most com speed. According to Spillmann and Sanderson [9], the
mon form of airblast atomizer is one in which the liquid disk windmill constitutes an ideal rotary atomizer for
is first spread into a thin conical sheet and then exposed the aerial application of pesticides. It provides a narrow
to high-velocity airstreams on both sides of the sheet. spectrum of drop sizes in the range most suitable for
The atomization performance of this prefilming type of herbicides, at relatively high flow rates.
airblast nozzle is superior to that of the alternative plain- Vibrating Capillary. This type of droplet generator
jet airblast nozzle, in which the liquid is injected into the was first used to study the collision and coalescence of
airstream in the form of one or more discrete jets. small water droplets. It consists of a hypodermic needle
6 Atomization and Sprays

Liquid Plain-orifice

Liquid Liquid
Simplex Internal-mixing
Air Air assist

Primary
Secondary Duplex
Liquid External-mixing
Air Air assist
Secondary
Primary Dual-orifice Liquid

Liquid
Liquid Plain-jet
Liquid Fan spray Air Airblast

Supply Liquid
Air Prefilming
Spill Spill return
Airblast
Disk Cup
(a) (b) (c)

FIGURE 1.2
(a) Pressure atomizers, (b) rotary atomizers, and (c) twin-fluid atomizers.

vibrating at its resonant frequency and can produce injection pressures than the values normally associated
uniform streams of drops down to 30 μm in diameter. with pressure atomization.
The size and frequency with which the droplets can be Schematic diagrams illustrating the principal design
produced depend on the flow rate of the liquid through features of the most important of the atomizers described
the needle, the needle diameter, the resonant frequency, above are shown in Figure 1.2. The relative merits of
and the amplitude of oscillation of the needle tip. these and other atomizers are listed in Table 1.1.
Flashing Liquid Jets. An orifice downstream of which
a high-pressure liquid flash vaporizes to shatter the liq
uid into small droplets can produce a fairly regular spray
pattern. Flashing dissolved gas systems have been stud Factors Influencing Atomization
ied by Brown and York [10], Sher and Elata [11], Marek The performance of any given type of atomizer depends
and Cooper [12], and Solomon et al. [13]. The results have on its size and geometry and on the physical properties
shown that flashing even small quantities of dissolved gas of the dispersed phase (i.e., the liquid being atomized)
(mole fractions <15%) can effect a significant improvement and the continuous phase (i.e., the gaseous medium into
in atomization. However, these beneficial effects cannot which the droplets are discharged).
be realized unless they are promoted by fitting an expan For plain-orifice pressure nozzles and plain-jet airblast
sion chamber just upstream of the discharge orifice. The atomizers, the dimension most important for atomiza
need for this expansion chamber stems from the low bub tion is the diameter of the final discharge orifice. For
ble growth rate for dissolved gas systems. This low bubble pressure-swirl, rotary, and prefilming airblast atomizers,
growth rate appears to pose a fundamental limitation to the critical dimension is the thickness of the liquid sheet
the practical application of flashing injection by means of as it leaves the atomizer. Theory predicts, and experiment
dissolved gas systems but applications such as recipro confirms, that mean drop size is roughly proportional to
cating engines are looking to exploit the phenomena to the square root of the liquid jet diameter or sheet thick
improve performance. ness. Thus, provided the other key parameters that affect
Effervescent Atomization. This method of atomi atomization are maintained constant, an increase in
zation overcomes the basic problems associated with atomizer scale (size) will impair atomization.
flashing dissolved gas systems. No attempt has been
made to dissolve any air or gas in the liquid. Instead,
Liquid Properties
the gas is injected at low velocity into the flowing liq
uid stream at some point upstream of the discharge The flow and spray characteristics of most atomizers are
orifice. The pressure differential between the atomiz strongly influenced by the liquid properties of density,
ing gas and the liquid into which it is injected is only viscosity, and surface tension. In theory, the mass flow
a few centimeters of water and is only what is needed rate through a pressure nozzle varies with the square
to prevent the liquid from flowing back up the gas line. root of liquid density. However, as Tate [6] has pointed
Studies by Lefebvre and coworkers [14] have shown that out, in practice it is seldom possible to change the den
good atomization can be achieved at much lower liquid sity without affecting some other liquid property, so
General Considerations 7

TABLE 1.1
Relative Merits of Various Types of Atomizers
Type Description Advantages Drawbacks Applications
Pressure Plain orifice 1. Simple, cheap 1. Narrow spray angle Diesel engines, jet engine
atomizer afterburners, ramjets
2. Rugged 2. Solid spray cone
Simplex 1. Simple, cheap 1. Needs high supply pressures Gas turbines and industrial
furnaces
2. Wide spray angle (up to 180°) 2. Cone angle varies with
pressure differential and
ambient gas density
Duplex Same as simplex, plus good Spray angle narrows as liquid Gas turbine combustors
atomization over a very wide flow rate is increased
range of liquid flow rates
Dual orifice 1. Good atomization 1. Atomization poor in transition Wide range of aircraft and
range industrial gas turbines
2. Turndown ratio as high as 50:1 2. Complexity in design
3. Relatively constant spray 3. Susceptibility of small
angle passages to blockage
Spill return 1. Simple construction 1. Spray angle varies with flow Various types of combustor
rates
2. Good atomization over entire 2. Power requirements higher Has good potential for slurries
flow range than with other pressure and fuels of low thermal stability
nozzles except at maximum
discharge
3. Very large turndown ratio
4. Large holes and flow passages
obviate risk of blockage
Fan spray 1. Good atomization Needs high supply pressures High-pressure coating operations
2. Narrow elliptical pattern Annular combustors
sometimes advantageous
Rotary Spinning disk 1. Nearly uniform atomization Produces a 360° spray pattern Spray drying
possible with small disks
rotating at high speeds
2. Independent control of Crop spraying
atomization quality and flow
rate
Rotary cup Capable of handling slurries May require air blast around Spray drying
periphery
Spray cooling
Air-assist Internal mixing 1 Good atomization 1. Liquid can back up in air line Industrial furnaces
2. Large passages prevent 2. Requires auxiliary metering Industrial gas turbines
clogging device
3. Can atomize high-viscosity 3. Needs external source of
liquids high-pressure air or steam
External Same as internal mixing, plus 1. Needs external source of air Same as internal mixing
mixing construction prevents backing or steam
up or liquid into the air line
2. Does not permit high liquid/
air ratios
Airblast Plain jet 1. Good atomization 1. Narrow spray angle Industrial gas turbines
2. Simple, cheap 2. Atomizing performance
inferior to prefilming airblast
Prefilming 1. Good atomization especially Atomization poor at low air Wide range of industrial and
at high ambient air pressures velocities aircraft gas turbines
2. Wide spray angle
Ultrasonic 1. Very fine atomization Cannot handle high flow rates Medical sprays
2. Low spray velocity Humidification
(Continued)
8 Atomization and Sprays

TABLE 1.1 (CONTINUED)

Relative Merits of Various Types of Atomizers
Type Description Advantages Drawbacks Applications

spray drying
Acid etching
combustion
Electrostatic Very fine atomization Cannot handle high flow rates Paint spraying
Printing

this relationship must be interpreted cautiously. The 0.028

significance of density for atomization performance is Relative
diminished by the fact that most liquids exhibit only density
minor differences in this property. Moreover, the mod- 0.024 0.84
est amount of available data on the effect of liquid den 0.80
sity on mean drop size suggests that its influence is 0.76
0.020
quite small.
0.72
One way of defining a spray is in terms of the
increase in liquid surface area resulting from atomiza Surface tension, kg/s2 0.016
tion. The surface area before breakup is simply that
of the liquid cylinder as it emerges from the nozzle.
After atomization, the area is the sum of the surface 0.012
areas of all the individual droplets. This multiplica
tion factor provides a direct indication of the level of
atomization achieved and is useful in applications that 0.008
emphasize surface phenomena such as evaporation
and absorption. Surface tension is important in atomi
zation because it represents the force that resists the 0.004
formation of new surface area. The minimum energy
required for atomization is equal to the surface ten
sion multiplied by the increase in liquid surface area. 0
300 400 500 600 700
Whenever atomization occurs under conditions where
Temperature, K
surface tension forces are important, the Weber num
ber, which is the ratio of the inertial force to the sur
FIGURE 1.3
face tension force, is a useful dimensionless parameter Surface tension–temperature relationship for hydrocarbon fuels of
for correlating drop size data. Commonly encountered varying relative densities.
surface tensions range from 0.073 kg/s2 for water to
0.027 kg/s2 for petroleum products. For most pure liq
uids in contact with air, the surface tension decreases The effect of viscosity on flow within the nozzle is
with an increase in temperature and is independent of complex. In hollow-cone nozzles, a modest increase
the age of the surface [15]. This is illustrated clearly in in viscosity can actually increase the flow rate. It does
Figure 1.3. this by thickening the liquid film in the discharge ori
In many respects, viscosity is the most important liq fice, thereby raising the effective flow area. At high
uid property. Although in an absolute sense its influ viscosities, however, the flow rate usually diminishes
ence on atomization is no greater than that of surface with increasing viscosity. With pressure-swirl nozzles,
tension, its importance stems from the fact that it affects an increase in viscosity generally produces a narrower
not only the drop size distributions in the spray but also spray angle. At very high viscosities the normal coni
the nozzle flow rate and spray pattern. An increase in cal spray may collapse into a straight stream of rela
viscosity lowers the Reynolds number and also hinders tively large ligaments and drops. An increase in liquid
the development of any natural instability in the jet or viscosity invariably has an adverse effect on atomiza
sheet. The combined effect is to delay disintegration and tion quality, because when viscous losses are large,
increase the size of the drops in the spray. less energy is available for atomization and a coarser
General Considerations 9

spray results. In airblast atomizers, liquid velocities are Ambient Conditions

usually much lower than in pressure nozzles. In con
sequence, the drop sizes produced by airblast nozzles The ambient gas into which sprays are injected can vary
tend to be less sensitive to variations in liquid viscosity. widely in pressure and temperature. This is especially
Table 1.2 lists the relevant physical properties of some true of liquid fuel fired combustion systems. In diesel
of the liquids used in spray applications. The viscosity engines, critical and supercritical pressure and temper
of these liquids ranges from 0.001 kg/m·s for water to ature conditions are encountered. In gas turbine com
0.5 kg/m·s for heavy fuel oil. The viscosity of liquids bustors, fuel sprays are injected into highly turbulent,
generally decreases with an increase in temperature. It swirling recirculating streams of reacting gases. In indus
is customary to heat up many of the heavier fuel oils, trial furnaces, the fuel is sprayed into high-temperature
partly to reduce pumping power requirements but also flames of recirculating combustion products. With pres
to improve atomization. sure-swirl atomizers, the spray angle decreases markedly
Some fluids, for example slurries of liquids and solid with increase in ambient gas density until a minimum
powders, are characterized by a nonlinear relationship angle is reached beyond which any further increase in
between shear stress and shear strain rate. For such liq the ambient gas density has no effect on the spray angle.
uids, which are called non-Newtonian, it is necessary to The ambient gas density also has a strong influence on
specify the shear rate with the viscosity. The apparent the mean drop sizes produced by pressure-swirl atom
reduction in viscosity with increasing shear rate high izers. If the ambient pressure is raised continuously
lights the need to minimize pressure losses in the supply above the normal atmospheric value, the mean drop size
lines and nozzles. This reduction is also desirable because increases initially until a maximum value is reached and
the viscosities of non-Newtonian fluids have less effect then slowly declines. The reasons for this unusual rela
on atomization if a high shear rate is produced in the liq tionship between ambient pressure and mean drop size
uid film formed by the nozzle [15]. Very little secondary are discussed in Chapter 6.
atomization will occur once the drops are formed, due to The spray patterns generated by pressure-swirl atom
the increase in apparent viscosity at the lower shear rate. izers are also affected by the liquid injection pressure
To successfully correlate or simulate atomization differential ∆PL. The ejector action of the high-velocity
behavior, it is imperative to know the key physical prop spray generates air currents, which causes the spray
erties at the point of atomization. Table 1.2 provides angle to contract. This effect is aggravated by the increase
some information for an array of liquids as a starting in spray velocity that accompanies an increase in ∆PL.
point. However, for many applications, the temperature Thus, although increasing ∆PL has no effect on the spray
dependency must be established. Also, in the case of angle immediately downstream of the nozzle, it causes
mixtures of pure liquids, the behavior of the mixture appreciable contraction of the spray pattern farther
must be understood. In some cases, the properties of downstream.
the mixture are simple mass weighted averages, but for With plain-orifice atomizers an increase in the ambi
some liquids (e.g., alcohols) an azeotrope may result, ent gas density leads to a wider spray angle. This is
which has highly nonlinear behavior. Hence, for the because the increase in aerodynamic drag on the drop
best results, the researcher/end-user is urged to estab lets, created by an increase in gas density, tends to pro
lish measurement capability for the physical proper duce a greater deceleration in the axial direction than in
ties using various ASTM, ISO, or SAE methods (e.g., the radial direction.
ASTM D 1343-93 for viscosity, ASTM D971; D3825-09 or The spray patterns produced by airblast atomizers
D7541-11 for surface tension; ASTM D4052 for density). tend to be fairly insensitive to variations in the ambient
Extensive information (CRC Report 635) is available for gas density. All but the largest drops in the spray tend to
the temperature-dependent properties of jet fuels due to follow the streamlines of the airflow pattern generated at
its critical role in aircraft and associated need for ensur the nozzle exit by the various swirlers and shaped pas
ing safety [16]. Yet, as an illustration of the importance sages within the nozzle. This airflow pattern generally
of knowing the actual physical properties of the liquids remains fixed and independent of air density, apart from
being worked with, the information in CRC 635 is still second-order Reynolds number and Mach number effects.
only representative and the variability in properties from However, if the natural cone angle of the spray, that is, the
batch to batch of jet fuel still requires an independent spray angle with no air flowing, is markedly different
measurement to have full confidence in the actual prop from that of the air, then the change in aerodynamic drag
erties of the jet fuel being worked with. forces produced by a change in air density will affect the
In summary, it is imperative that the physical proper resulting spray pattern. In general, an increase in air den
ties of the liquids used are well understood in order to sity will cause the spray pattern to adhere more closely to
apply the concepts within this book. the streamlines of the atomizing air.
10 Atomization and Sprays

TABLE 1.2
Properties of Liquids
Liquid Temperature (K) Viscosity (kg/m·s) Density (kg/m3) Surface Tension (kg/s2)
Acetone 273 0.000400 0.0261
293 0.00032 792 0.0237
300 0.000300
303 0.000295
313 0.00028 0.02116
Ammonia 284 0.0234
300 0.00013 0.0181
307 0.0181
Aniline 283 0.0065 0.0441
288 0.0053 1,000 0.040
323 0.00185 0.0394
373 0.00085
Benzene 273 0.00091 899 0.0302
283 0.00076
293 0.00065 880 0.0290
303 0.00056 0.0276
323 0.00044
353 0.00039
Butane 300 0.00016 0.0116
Carbon tetrachloride 273 0.00133
293 0.00097 799 0.0270
373 0.00038 0.0176
Castor oil 283 2.42
288 969
293 0.986
303 0.451
313 0.231
373 0.0169
Chloroform 273 0.0007
293 0.00058 1,489 0.02714
303 0.00051 926
Cottonseed oil 289
293 0.0070
Creosote 313 0.0070
n-Decane 293 0.00092
300 0.0233
Ethane 300 0.000035 0.0007
Ethyl alcohol 273 0.00177 0.02405
293 0.0012 791 0.02275
303 0.0010 0.02189
323 0.0007
343 0.00050
Ethylene glycol 293 0.01990
313 0.00913
333 0.00495
353 0.00302
373 0.00199
Fuel oil (light) 288 0.172 930 0.0250
313 0.047 916 0.0230
356 0.0083 880 0.0210
Fuel oil (medium) 313 0.215 936 0.0230
378 0.0134 897 0.0200
(Continued)
General Considerations 11

TABLE 1.2 (CONTINUED)

Properties of Liquids
Liquid Temperature (K) Viscosity (kg/m·s) Density (kg/m3) Surface Tension (kg/s2)
Fuel oil (heavy) 313 0.567 970 0.0230
366 0.037 920 0.0210
400 0.015 900 0.0200
Gas oil 288 0.0060 850 0.0240
313 0.0033 863 0.0230
Glycerin 273 12.1 1,260 0.0630
288 2.33
293 0.622 0.0630
Heptane 273 0.00052
300 0.00038 0.0194
313 0.00034
343 0.00026 0.0194
Hexane 273 0.00040
293 0.00033 0.0184
300 0.00029 0.0176
323 0.00025
Hydrazine 274 0.00129
293 0.00097
298 0.0915
Kerosene 293 0.0016 800 0.0260
Linseed oil 288 942
303 0.0331
363 0.0071
Machine oil (light) 288.6 0.114
310.8 0.0342
373 0.0049
Machine oil (heavy) 288.6 0.661
310.8 0.127
Mercury 273 0.0017 13,600
293 0.00153 13,550 0.480
313 0.00045
Methyl alcohol 273 0.00082 810 0.0245
293 0.00060 0.0226
300 0.00053 0.0221
323 0.00040
Naphthalene 353 0.00097
373 0.00078
400 0.0288
Nonane 300 0.0223
n-Octane 293 0.00054 0.0218
300 0.0005 0.0210
Olive oil 283 0.138
288 918
291 0.0331
293 0.0840
343 0.0124
Pentane 273 0.00029
300 0.00022 0.0153
Propane 300 0.000098 0.0064
Toluene 273 0.00077 0.0277
293 0.00059 0.0285
303 0.00053 0.0274
(Continued)
12 Atomization and Sprays

TABLE 1.2 (CONTINUED)

Properties of Liquids
Liquid Temperature (K) Viscosity (kg/m·s) Density (kg/m3) Surface Tension (kg/s2)
343 0.00035
Turpentine 273 0.00225 870
283 0.00178 0.0270
303 0.00127
343 0.000728
Water 291 0.073
300 0.00085 0.0717

holography are being used to study drop size distribu

tions and spray structure. Much of the tedium normally
Spray Characteristics
involved in detailed studies of drop size distributions in
The spray process is inherently chaotic and random in various regions of the spray can now be alleviated using
nature. Further, the resulting spray is a result of sev automatic image analysis. The method has the impor
eral complex steps, starting with behavior within the tant advantage of being nonintrusive, and can also give
atomizer itself. The transformation of intact liquid to the temporal distribution of drop sizes as produced by
droplets involves a number of dynamic processes. The the atomizer. In recent years, considerable advances
resulting spray droplets sizes and distribution of the have been made in the development of laser diagnostic
material are often the characteristics that are of inter techniques for measuring particle size and velocity in
est in many applications, yet the steps to generating sprays.
the size and spatial distribution of material is a result A ubiquitous and effective method for assessing and
of the upstream behavior. In recent years, the focus of comparing sprays is the Fraunhofer diffraction particle
both simulations and measurements has moved farther sizing, which uses a line-of-sight measurement through
upstream. However, the importance of drop size for the spray. Various models of this instrument are com
the many processes that utilize liquid sprays remains mercially available for applications to both continuous
key. Both instrumentation and simulation are driven and intermittent sprays.
by a desire to better understand the overall atomization More detailed information can be generated using
process. interferometric methods both at a point as well as
In the internal flow region, it is now possible to mea within a plane. Phase Doppler interferometry provides
sure actual flow behavior within the flow passages highly detailed results for the spray behavior at a point
using novel x-ray methods. The region immediately within the spray including size, multiple components of
following the atomizer liquid exit is now being studied velocity, and inferred quantities such as concentration
using various evolving methods [17]. The resulting drop or volume flux. Such results are ideal for validation of
size characteristics and spray spatial (and temporal) dis simulations. Planar methods can capture information
tributions are characterized using a variety of methods. about size and velocity of droplets, providing additional
In terms of measuring drop size, due to its importance insight into the dynamic processes within the spray and
as critical parameters in atomization, a wide range of adding insight into coupling between the gas phase
techniques have been developed over the decades. No aerodynamics and the spray. In fact, the subject of laser
single technique is completely satisfactory, but each diagnostics for measurement of spray has broadened
technique has its own advantages and drawbacks, to the point where it warrants its own textbook. Recent
depending on the application. Classic direct methods reviews of the subject are available [17, 18]. Summaries
include those in which individual drops are collected of the methods used in spray analysis prior to 1980 have
on slides for subsequent measurement and counting or been prepared by Chigier [19]. Even earlier methods are
in which droplets are frozen and sized as solid parti summarized by Putnam et al. [20] and Tate [21]. These
cles. With the impaction method, the drops are sorted and more recent developments are described in some
on the basis of inertial differences. Depending on its detail in Chapter 9.
size, a droplet may impact or fail to impact a solid sur Ever evolving computational resources have facili
face or may follow a different trajectory. This allows tated detailed simulation capability which can imple
all the drops in a spray to be sorted into different size ment sophisticated models developed to describe the
categories. High-speed imaging can be used to provide atomization process and transport of the resulting
instantaneous images of the drops in a spray, which are droplets. Evaporation, droplet impact with surfaces and
recorded for subsequent counting or analysis. High- each other, and reaction of the liquid/vapor with sur
speed pulsed microphotography, cinematography, and faces and gases can also be readily computed.
General Considerations 13

(turndown ratio); required mean drop size and drop

size distribution; liquid or gas pressures available for
Applications
nozzles, or power required for rotary atomizers; condi
A compilation by Tate [6] of some of the most important tions that may contribute to wear and corrosion; size
applications is contained in Table 1.3. While this per and shape of vessel, enclosure, or combustor containing
spective is more than four decades old, it is still quite spray; economics of spray operation taking into account
relevant. As the cost, complexity, atomizing perfor initial cost, operating expenses, and depreciation; and
mance, and energy consumption vary widely between safety considerations [6].
different types of atomizers, it is important to select the
best atomizer for any given application. The following
factors enter into the proper selection: properties of the
liquid to be atomized, for example, density, viscosity,
surface tension, and temperature; ambient gas proper
ties, such as pressure, temperature, and flow pattern;
Glossary
particle sizes and percent solids in suspensions, slur Some of the terms frequently used in descriptions of
ries, and pastes; maximum flow rate; range of flow rates atomizers and sprays are defined in the following.
These definitions are necessarily brief, and no attempt
TABLE 1.3
has been made to include all qualifying considerations.
Spray Applications
Production or processing Air-assist nozzle: Nozzle in which high-velocity air or
Spray drying (dairy products, coffee and tea, starch steam is used to enhance pressure atomization
pharmaceuticals, soaps and detergents, pigments, etc.) at low liquid flow rates.
Spray cooling Airblast atomizer: Atomizer in which a liquid jet or
Spray reactions (absorption, roasting, etc.) sheet is exposed to air flowing at high velocity.
Atomized suspension technique (effluents, waste liquors, etc.) Air core: Cylindrical void space within the rotating liq
Powdered metals uid in a simplex swirl chamber.
Treatment Arithmetic mean diameter: Linear mean diameter of
Evaporation and aeration drops in spray.
Cooling (spray ponds, towers, reactors, etc.) Atomization: Process whereby a volume of liquid is dis
Humidification and misting integrated into a multiplicity of small drops.
Air and gas washing and scrubbing Beam steering: Refraction of a laser beam due to den
Industrial washing and cleaning sity gradients in the continuous phase.
Coating Breakup length: Length of continuous portion of jet
Surface treatment
measured from nozzle exit to point where
Spraypainting (pneumatic, airless, and electrostatic)
breakup occurs.
Flame spraying
Cavitation: Formation of bubbles by gas or vapor
Insulation, fibers, and undercoating materials
released in flow regions of low static pressure;
Multicomponent resins (urethanes, epoxies, polyesters, etc.)
affects discharge coefficient and jet breakup.
Particle coating and encapsulation
Cavitation number: Ratio of pressure differential to
Combustion
downstream pressure; indicator of propensity
Oil burners (furnaces and heaters, industrial and marine boilers)
for cavitation.
Diesel fuel injection
Combined spray: Spray produced when both stages
Gas turbines (aircraft, marine, automotive, etc.)
flow simultaneously in a dual-orifice or piloted
Rocket fuel injection
airblast nozzle.
Miscellaneous
Continuous phase: Medium, usually gaseous, in which
Medicinal sprays
atomization occurs.
Dispersion of chemical agents
Critical flow rate: Liquid flow rate corresponding to
Agricultural spraying (insecticides, herbicides, fertilizer solutions,
etc.) the transition from one mode of atomization to
Foam and fog suppression another.
Printing Critical Weber number: Value of Weber number above
Acid etching which a single drop will split into two or more
drops.
Source: Tate, R. W.: Sprays, Kirk-Othmer Encyclopedia of Chemical Cumulative distribution: Plot of percentage by num
Technology. pp. 634–654. 1969. Copyright Wiley-VCH Verlag GmbH & ber, surface area, or volume of drops whose
Co. KGaA. diameter is less than a given drop diameter.
14 Atomization and Sprays

Discharge coefficient: Ratio of actual flow rate to theo flow rate to the square root of injection pressure
retical flow rate. differential.
Discharge orifice: Final orifice through which liquid is Flow rate: Amount of liquid discharged during a given
discharged into the ambient gas. period of time; normally identified with all fac
Dispersed phase: Liquid to be atomized. tors that affect flow rate, such as pressure dif
Dispersion: Ratio of the volume of a spray to the vol ferential and liquid density.
ume of the liquid contained within it. Frequency distribution curve: Plot of liquid volume
Drooling: Sluggish dripping of liquid from a nozzle per size class.
while spraying, usually caused by impingement Heat transfer number: Indicator of rate of evaporation
of the spray on some surface other than the ori due to heat transfer to droplet from surround
fice from which the liquid is discharging [22]. ing gas.
Drop coalescence: Collision of two drops to form a sin Heat-up period: Initial phase of droplet evaporation
gle drop. prior to attainment of steady-state conditions.
Droplet size: Diameter of a spherical droplet, usually Hollow-cone spray: Spray in which most of the droplets
expressed in micrometers. are concentrated at the outer edge of a conical
Droplet uniformity index: Indication of the range of spray pattern.
drop sizes in a spray relative to the median Impingement: Collision of two round liquid jets or colli
diameter. sion of a jet of liquid with a stationary deflector.
Drop saturation: Droplet population exceeding the Impinging jet atomizer: Atomizer in which two liquid
capability of the sizing instrument or method. jets collide outside the nozzle to produce a liq
Dual-orifice atomizer: Atomizer consisting of two sim uid sheet perpendicular to the plane of the jets.
plex nozzles fitted concentrically one inside Internal mixing nozzle: Air-assist atomizer in which
other. gas and liquid mix within the nozzle before dis
Duplex nozzle: Nozzle featuring a swirl chamber with charging through the outlet orifice.
two sets of tangential swirl ports, one set being Mass transfer number: Indicator of rate of evaporation
the primary ports for low flows and the other due to mass transfer.
the larger secondary ports for handling high Mass (volume) median diameter: Diameter of a drop
flow rates. below or above which 50% of the total mass
Effective evaporation constant: Value of evaporation (volume) of drops lies.
constant that includes heat-up period and con Mean drop size: A given spray is replaced by a ficti
vective effects. tious one in which all the drops have the same
Electrostatic atomizer: Atomizer in which electrical diameter while retaining certain characteristics
pressure is used to overcome surface tension of the original spray.
forces and achieve atomization. Monodisperse spray: Spray containing drops of uni
Equivalent spray angle: Angle formed by drawing two form size.
straight lines from the nozzle discharge orifice Multiple scattering: When spray number density is
through the center of the liquid mass in the left high some drops obscure part of signal gen
and right lobes of the spray. erated by others, leading to biased diffraction
Evaporation constant: Indication of the rate of change patterns.
of drop surface area during steady-state Normal distribution: Distribution of drop sizes based
evaporation. on the random occurrence of a given drop size.
External mixing nozzle: Air-assist atomizer in which Obscuration: Percentage of light removed from original
high-velocity gas impinges on a liquid at or out direction; indicator of the extent to which mea
side the final orifice. surements of mean drop size are affected by
Extinction: Percentage of light removed from original multiple scattering. Also known as extinction.
direction; indicator of the extent to which mea Ohnesorge number: Dimensionless group obtained
surements of mean drop size are affected by by dividing the square root of the Weber num
multiple scattering. Also termed obscuration. ber by the Reynolds number, which eliminates
Fan spray: Spray in the shape of a sector of a circle of velocity from both; indicator of jet or sheet
about 75° angle; elliptical in cross section. stability.
Film thickness: Thickness of annular liquid sheet as it Patternation: A measure of the uniformity of the cir
discharges from the atomizer. cumferential distribution of liquid in a conical
Flat spray: Same as fan spray. spray. The term radial patternation is also used to
Flow number: Effective flow area of a nozzle, usually describe the radial distribution of liquid within
expressed as the ratio of mass or volumetric a conical spray.

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Atomization and Sprays

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Atomization and Sprays

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Atomization and Sprays

Combustion: An International Series

Bayvel and Orzechowski, Liquid Atomization

Arthur H. Lefebvre and Vincent G. McDonell

Library of Congress Cataloging‑in‑Publication Data

Names: Lefebvre, Arthur H. (Arthur Henry), 1923–2003, author. | McDonell,

Visit the Taylor & Francis Web site at

Preface to the Second Edition..................................................................................................................................................xi

2. Basic Processes in Atomization .................................................................................................................................... 17

3. Drop Size Distributions of Sprays............................................................................................................................... 55

5 Flow in Atomizers ......................................................................................................................................................... 105

6 Atomizer Performance.................................................................................................................................................. 133

7 External Spray Characteristics.................................................................................................................................... 183

Drop Drag Coefficients .................................................................................................................................................. 200

8 Drop Evaporation .......................................................................................................................................................... 207

9 Spray Size and Patternation Methods....................................................................................................................... 243

Optical Methods......................................................................................................................................................... 252

Index ........................................................................................................................................................................................ 281

various size classes may be required for different appli­

Pumping characteristics, flow

liquid to high-velocity air. Photographic evidence sug­

cylindrical or conical chamber where an umbrella-like Other Types

TABLE 1.1 (CONTINUED)

this relationship must be interpreted cautiously. The 0.028

spray results. In airblast atomizers, liquid velocities are Ambient Conditions

TABLE 1.2 (CONTINUED)

TABLE 1.2 (CONTINUED)

holography are being used to study drop size distribu­

(turndown ratio); required mean drop size and drop

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various size classes may be required for different appli

liquid to high-velocity air. Photographic evidence sug

holography are being used to study drop size distribu