SCIENCE AND ENGINEERING OF

DROPLETS

Fundamentals and Applications

by

Huimin Liu

spraysoft.com Detroit, Michigan

NOYES PUBLICATIONS

Park Ridge, New Jersey, U.S.A.

WILLIAM ANDREW PUBLISHING, LLC

Norwich, New York, U.S.A.

99-27324 CIP

Copyright © 2000 by Noyes Publications

No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission in writing from the Publisher.

Library of Congress Catalog Card Number: 98-27324 ISBN: 0-8155-1436-0

Printed in the United States

Published in the United States of America by

Noyes Publications / William Andrew Publishing, LLC Norwich, New York, U.S.A.

10 9 8 7 6 5 4 3 2 1

Library of Congress Cataloging-in-Publication Data

Liu, Huimin, 1981–

Science and engineering of droplets : fundamentals and applications / by Huimin Liu.

p . cm .

Includes bibliographical references and index. ISBN 0-8155-1436-0

1. Spraying. 2. Atomization. I. Title. TP156.S6L58 1999

620'.43--dc21

NOTICE

To the best of our knowledge the information in this publication is accurate; however the Publisher does not assume any responsibility or liability for the accuracy or completeness of, or consequences arising from, such information. This book is intended for informational purposes only. Mention of trade names or commercial products does not constitute endorsement or recommendation for use by the Publisher. Final determination of the suitability of any information or product for use contemplated by any user, and the manner of that use, is the sole responsibility of the user. We recommend that anyone intending to rely on any recommendation of materials or procedures mentioned in this publication should satisfy himself as to such suitability, and that he can meet all applicable safety and health standards.

Foreword

Dew droplets scatter the light of the early morning sun like thousands of diamonds. Billions of passing rain droplets, refracting and internally reflecting the sunlight, form the rainbow, stretching across the sky and competing in its magnificence with the red fire ball of the sunset. Droplets are encountered not only in nature but also in a wide range of engineering applications, such as spray combustion, spray drying, spray cooling, etc., etc. The related areas span automotive, aerospace, metallurgy, material, chemicals, pharmaceuticals, paper, food processing, agriculture, meteorology, and power generation. It was these applications that stimulated the fundamental research and development of the technologies associated with discrete droplets. In the past century, droplet-related phenomena have been a subject of considerable scientific interest and practical importance. In recent years, strong research efforts have led to significant strides in theoretical and experimental studies of droplet processes. The drastic developments in high speed, large memory, parallel processing computer systems and advanced computational and measurement techniques have enabled the direct numerical modeling andon-line, insitu measurements of certain droplet properties, and thus largely advanced the design and optimization of droplet processes. These advances have significantly improved our fundamental understanding of the phenomena and processes associated with discrete droplets in general. It is therefore desirable to review these results in a timely manner.

v

vi Foreword

This book presents an updated, systematic review of the recent advances in fundamental science and engineering applications of discrete droplet processes. The objective of this book is to familiarize the reader with the scientific and engineering aspects of discrete droplet processes, and to provide experienced researchers, scientists and engineers in academic and industry communities with the latest developments in this field. The scope of this book encompasses the fundamental science and engineering applications of discrete droplet processes of both normal liquids (i.e., aqueous or oil-based liquids) and melts (i.e., molten metals, alloys, ceramics or polymers). It starts with a systematic survey of various processes and techniques for droplet generation, along with their applications and associated materials systems. It is followed by a through description of the fundamental phenomena and principles involved in droplet processes, with emphasis on the mechanisms of droplet formation and deformation in various processes. The empirical and analytical correlations, theoretical calculations and numerical modeling of droplet properties are outlined and some approaches to intelligent process control are presented along with discussions of recent developments.

There have been books on droplet-related processes. However, the present book is probably the first one that encompasses the fundamental phenomena, principles and processes of discrete droplets of both normal liquids and melts. The author has attempted to correlate many diverse mechanisms and effects in a single and common framework in an effort to provide the reader with a new perspective of the identical basic physics and the inherent relationship between normal liquid and melt droplet processes. Another distinct and unique feature of this book is the comprehensive review of the empirical correlations, analytical and numerical models and computer simulations of droplet processes. These not only provide practical and handy approaches for engineering calculations, analyses and designs, but also form a useful basis for future in-depth research. Therefore, the present book covers the fundamental aspects of engineering applications and scientific research in the area.

UniversityofBremen,Germany Prof.Dr.-Ing.KlausBauckhage

January,1999

Contents

1 General Introduction ...........................................................		1
2 Processes and Techniques for Droplet Generation ...........		19
2.1.0 ATOMIZATION OF NORMAL LIQUIDS ....................................		20
2.1.1	Pressure Jet Atomization ....................................................	22
2.1.2	Pressure-Swirl Atomization ................................................	28
2.1.3	Fan Spray Atomization ......................................................	35
2.1.4	Two-Fluid Atomization ......................................................	37
2.1.5	Rotary Atomization ............................................................	44
2.1.6	Effervescent Atomization ...................................................	47
2.1.7	Electrostatic Atomization ...................................................	49
2.1.8	Vibration Atomization .......................................................	52
2.1.9	Whistle Atomization ..........................................................	59
2.1.10	Vaporization-Condensation Technique ...............................	61
2.1.11	Other Atomization Methods ...............................................	63
2.2.0 ATOMIZATION OF MELTS ........................................................		65
2.2.1	Gas Atomization ................................................................	73
2.2.2	Water Atomization .............................................................	90
2.2.3	Oil Atomization .................................................................	95
2.2.4	Vacuum Atomization .........................................................	96
2.2.5	Rotating Electrode Atomization .........................................	98
2.2.6	Rotating Disk Atomization ...............................................	101
2.2.7	Electron Beam Rotating Disk Atomization .......................	102

ix

x	Contents
	2.2.8	Roller Atomization ..........................................................	104
	2.2.9	Centrifugal Shot Casting Atomization ..............................	106
	2.2.10	Centrifugal Impact Atomization .......................................	107
	2.2.11	Spinning Cup Atomization ...............................................	108
	2.2.12	Laser Spin Atomization ....................................................	110
	2.2.13	Durarc ® Process ...............................................................	110
	2.2.14	Vibrating Electrode Atomization ......................................	112
	2.2.15	Ultrasonic Atomization ....................................................	113
	2.2.16	Steam Atomization ..........................................................	116
	2.2.17	Other Atomization Methods .............................................	116
3 Fundamental Phenomena and Principles in Droplet
	Processes	...........................................................................	121
	3.1.0 DROPLET FORMATION ...........................................................		121
	3.1.1 ......	Droplet Formation in Atomization of Normal Liquids	122
	3.1.2 ....................................................	Secondary Atomization	169
	3.1.3 ......................	Droplet Formation in Atomization of Melts	182
	3.2.0 DROPLET ..........................DEFORMATION ON A SURFACE		193

3.2.1Deformation of a Single Droplet on Flat and Non-Flat

Surfaces ..........................................................................

194

3.2.2Splashing of a Single Droplet on Flat and Non-Flat

Surfaces ..........................................................................

203

3.2.3Droplet Deformation and Solidification on a Cold Surface 206

3.2.4 Droplet Deformation and Evaporation on a Hot Surface ... 217

3.2.5Interaction, Spreading and Splashing of Multiple Droplets

on a Surface .....................................................................	229
3.2.6 Sessile Droplet Deformation on a Surface .........................	233

3.2.7Spreading and Splashing of Droplets into Shallow and

	Deep Pools ......................................................................	235
4 Empirical and Analytical Correlations of Droplet
Properties	.........................................................................	238
4.1.0 CONCEPT AND DEFINITIONS OF DROPLET SIZE
DISTRIBUTION .........................................................................		238
4.2.0 CORRELATIONS FOR DROPLET SIZES
OF NORMAL LIQUIDS ..............................................................		253
4.2.1	Pressure Jet Atomization ..................................................	254
4.2.2 Pressure-Swirl and Fan Spray Atomization .......................		257
4.2.3	Air-Assist Atomization ....................................................	261
4.2.4	Air-Blast Atomization ......................................................	264
4.2.5	Rotary Atomization ..........................................................	270
4.2.6	Effervescent Atomization .................................................	275
4.2.7	Electrostatic Atomization .................................................	276
4.2.8	Ultrasonic Atomization ....................................................	276

	Contents	xi
4.3.0 CORRELATIONS FOR DROPLET SIZES OF MELTS ...............		278
4.3.1	Gas Atomization ..............................................................	279
4.3.2	Water Atomization ...........................................................	289
4.3.3	Centrifugal Atomization ...................................................	291
4.3.4	Solidification and Spheroidization ....................................	295
4.4.0 CORRELATIONS FOR DROPLET DEFORMATION
CHARACTERISTICS ON A SURFACE .....................................		297
4.4.1	Viscous Dissipation Domain ............................................	307
4.4.2	Surface Tension Domain ..................................................	308
4.4.3	Solidification Domain ......................................................	310
4.4.4 Partial Solidification Prior to Impact ................................		314
5 Theoretical Calculations and Numerical Modeling of
Droplet Processes .............................................................		315
5.1.0 ENERGY REQUIREMENTS AND EFFICIENCY ......................		316
5.2.0 MODELING OF DROPLET PROCESSES
OF NORMAL LIQUIDS ..............................................................		318
5.2.1 Theoretical Analyses and Modeling of Liquid Jet
	and Sheet Breakup ...........................................................	320
5.2.2 Modeling of Droplet Formation, Breakup, Collision
	and Coalescence in Sprays ...............................................	324
5.2.3 Theories and Analyses of Spray Structures
	and Flow Regimes ...........................................................	331
5.2.4 Modeling of Droplet-Gas and Droplet-Droplet Interactions ..		335
5.2.5 Modeling of Multiphase Flows and Heat
	and Mass Transfer in Sprays ............................................	340
5.3.0 MODELING OF DROPLET PROCESSES OF MELTS ...............		349
5.3.1 Modeling of Melt Flows and Heat Transfer
	in Near-Nozzle Region .....................................................	350
5.3.2 Modeling of Gas Flows in Near-Nozzle Region ................		355
5.3.3 Modeling of Droplet Formation and Breakup in Sprays ....		360
5.3.4 Modeling of Multiphase Flows and Heat Transfer
	in Sprays ..........................................................................	367
5.4.0 MODELING OF DROPLET DEFORMATION
ON A SURFACE .........................................................................		381
5.4.1 Modeling of Deformation of a Single Droplet
	on a Flat Surface ..............................................................	381
5.4.2 Modeling of Droplet Deformation and Solidification
	on a Cold Surface .............................................................	385

5.4.3Modeling of Interactions of Multiple Droplets on Flat

and Non-Flat Surfaces ......................................................

389

5.4.4Modeling of Droplet Deformation and Evaporation

on a Hot Surface ..............................................................

394

xii Contents
6 Measurement Techniques for Droplet Properties and
Intelligent Control of Droplet Processes..........................		397
6.1.0 MEASUREMENT TECHNIQUES FOR DROPLET SIZE ...........		399
6.1.1	Mechanical Methods ........................................................	401
6.1.2	Electrical Methods ...........................................................	407
6.1.3	Optical Methods ..............................................................	409
6.1.4	Other Methods .................................................................	428
6.2.0 MEASUREMENT TECHNIQUES FOR DROPLET VELOCITY ...		430
6.3.0 MEASUREMENT TECHNIQUES FOR DROPLET NUMBER
DENSITY ..........................................................................		433
6.4.0 MEASUREMENT TECHNIQUES FOR DROPLET
TEMPERATURE ........................................................................		436
6.5.0 MEASUREMENT TECHNIQUES FOR DROPLET
DEFORMATION ON A SURFACE ............................................		439
6.6.0 INTELLIGENT CONTROL OF DROPLET PROCESSES ...........		446
References ..............................................................................		451
Index .......................................................................................		508