Dynamics of Droplets

298 Pages·2000·9.638 MB·English

by  Prof. Dr. rer. nat. Arnold Frohn, Dr.-Ing. Norbert Roth (auth.)

Experimental Fluid Mechanics
R.J. Adrian · M. Gharib · W. Merzkirch
D. RockweH · J.H. Whitelaw
Springer-Verlag Berlin Heidelberg GmbH
ONLINE LIBRARY
http:// www.springer.de/engine/
Arnold Frohn · No rbert Roth
Dynamics of Droplets
With 193 figures
Springer
Series Editors
Prof. R.J.Adrian Prof. Dr. D. RockweH
University of Illinois at Urbana-Champaign Lehigh University
Dept. of Theoretical and Applied Mechanics Dept. of Mechanical Engineering and
216 Talbot Labaratory Mechanics
104 South Wright Street Packard Lab.
Urbana, IL 61801 19 Memorial Drive West
USA Bethlehem, PA 18015-3085
Prof. M. Gharib USA
California Institute of Technology Prof. J.H. Whitelaw
Graduate Aeronautical Laboratories Imperial College
1200 E. California Blvd. Dept. of Mechanical Engineering
MC205-45 Exhibition Road
Pasadena, CA 91125 London SW7 2BX
USA UK
Prof. Dr. Wolfgan Merzkirch
Universität Essen
Lehrstuhl für Strömungslehre
Schützenbahn 70
45141Essen
Germany
Authors
Prof. Dr. rer. nat. Arnold Frohn
Dr.-Ing. Norbert Roth
Universität Stuttgart
Institut für Thermodynamik der Luft-und Raumfahrt
Pfaffenwaldring 31
70550 Stuttgart
Germany
Cataloging-in-Publication Data applied for
Frobn, Arnold: Dynamics of droplets I Arnold Frohn ; Norbert Roth.
ISBN 978-3-642-08516-1 ISBN 978-3-662-0404o-9 (eBook)
DOI 10.1007/978-3-662-04040-9
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Preface
The main purpose of this book is the description of dynamic aspects of droplet
behavior under various ambient conditions. Engineers and scientists from a
large variety of disciplines have become interested in this topic during the last
years. Many new applications have been found in different modern technolo
gies as combustion, ink jet printing, spray drying, net shape forming, or mi
croencapsulation and manufacturing. The numerical simulation of dynamic
properties of single droplets or droplet systems depends often on informa
tion, which must be gained in experiments. The book describes experimental
tools, which are appropriate for the investigation of droplets. The book, which
has been written for the experimental worker, contains research results from
many different scientific fields. A large amount of the presented results is
based on experiments performed at Institut für Thermodynamik der Luft
und Raumfahrt, University of Stuttgart (ITLR).
The first chapter, Chapter 1, of this book gives abrief review of the the
oretical background, which is essential for the understanding of the behavior
of droplets in various environments. A simple approach has been chosen,
which provides a short but comprehensive survey of the various mechanical,
thermodynamical, physical, and physico-chemical phenomena. The basis for
the derivations has been outlined. Ample references have been provided for
those, who wish a deeper understanding of the fundamentals. Chapter 2 is de
voted to the generation of droplets. The generation of sprays, droplet streams,
and single droplets is discussed. In Chapter 3 droplet systems, sprays, linear
and planar droplet arrays are discussed. Three-dimensional droplet arrays
are considered as a model for the simulation of sprays. Different experimen
tal arrangements for the study of single droplets are considered. The most
important measurement techniques for studying the various droplet systems
are discussed in Chapter 4, whereas Chapter 5 deals with mechanical inter
actions of droplets with the surrounding gas, with solid walls, and with other
droplets. In Chapter 6 experiments for studying phase transition processes are
presented. Experimental setups for the investigation of evaporation or com
bustion, condensation, and freezing are described and results are presented.
Chapter 7 deals with a selected set of practical applications. The material
of this chapter may help to avoid the impression that the subject of droplet
dynamics is a definitive closed body of knowledge.
VI
The authors are indebted to Professor Dr. Merzkirch for the encourage
ment to write this book. Gontributions of Klaus Anders during the initial
planning phase will not be forgotten. Klaus Anders contributed results on
evaporating droplets, especially at low Knudsen numbers. Many scientists at
ITLR contributed experimental results. Gerd Bauer performed droplet ex
periments near the critical point, Nils Widdecke and Wolfgang Klenk studied
interactions between shock waves and droplets, Guido Funcke interactions
between acoustic waves and droplets, Alexander Karl droplet-wall interac
tions, Thomas Kraut performed wind-tunnel experiments. Frank Herrmann
studied the glare points of droplets and developed several electronic devices
necessary for various experiments.
Numerical calculations are due to Peter Drtina, Markus Schelke, and Mar
tin Rieber. Markus Schelkle developed a lattice Boltzmann code and Martin
Rieber the Navier-Stokes code. Thesecodes were used in Chap. 5 for the sim
ulation of droplet-droplet and droplet-wall interactions. Martin Rieber con
tributed describing numerical results in Sects. 5.3.5 and 5.4.3. The authors
are indebted to Ulrike Sehröderand Jutta Schöllhammer for technical assis
tance received in many experiments described in this book. Harald Hettrich
designed devices to examine droplets in shock tubes and under high pressure,
the corresponding three-dimensional schematical views in Figs. 5.11 and 6.52
have been drawn by him. Without the help of Peter Fischer it had been
impossible to provide so many references. The authors are very grateful to
Professor Gouesbet and Professor Grehan from INSA Rouen for their kind
permission to use their computer code for calculations of light scattering by
droplets illuminated with a laser beam with Gaussian intensity distribution.
Table of Contents
Preface....................................................... V
1. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Surface Tension and lnternal Pressure . . . . . . . . . . . . . . . . . . . . . 1
1.2 Liquid-Liquid and Solid-Liquid Interfaces . . . . . . . . . . . . . . . . . . 8
1.3 Charged Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Small-Amplitude Droplet Oscillations . . . . . . . . . . . . . . . . . . . . . 12
1.5 Internal Circulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 Iustability of Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1. 7 Iustability of Jets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.8 Relaxation Phenomena.................................. 16
1.8.1 Relaxation of velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.8.2 Relaxation of temperature . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.9 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.9.1 Multiphase Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.9.2 Kelvin-Helmholtz Equation . . . . . . . . . . . . . . . . . . . . . . . . 24
1.9.3 Thermodynamics of the Interface. . . . . . . . . . . . . . . . . . . 25
1.9.4 Gibbs Isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.10 Phase Transition Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.11 Evaporation of a Single Droplet . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.11.1 Diffusion-controlled evaporation of a single droplet . . . 32
1.11.2 Combustion of a single droplet . . . . . . . . . . . . . . . . . . . . . 34
1.11.3 Evaporation of multicomponent droplets . . . . . . . . . . . . 37
1.11.4 Evaporation through films . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.11.5 Evaporation and combustion in droplet arrays . . . . . . . 38
1.12 Interaction with Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.12.1 Geometrical approximation . . . . . . . . . . . . . . . . . . . . . . . . 40
1.12.2 Glare Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.12.3 Rainbow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.12.4 Mie scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.12.5 Influence of Gaussian Intensity Distribution. . . . . . . . . . 52
1.12.6 Radiation Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1.12.7 Partial Wave Resonances.......................... 58
VIII Table of Contents
2. Droplet Generation....................................... 63
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.2 Spray Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.3 Droplet Stream Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.3.1 Physical Principle and Technical Performance........ 65
2.3.2 Operation Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3.3 Operation Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.4 Droplet on Demand Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.5 Dropper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3. Droplet Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2 Sprays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3 Droplet Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.1 Monodisperse Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.2 Droplet Arrays................................... 91
3.3.3 Deflection with Electrical Field. . . . . . . . . . . . . . . . . . . . . 92
3.4 Single Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.1 Single Moving Droplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.2 Aerodynamically Suspended Droplets . . . . . . . . . . . . . . . 93
3.4.3 Droplet Suspension with Thin Fibers . . . . . . . . . . . . . . . 93
3.4.4 Electrostatic Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.5 Electrodynamic Levitation ....................... , . 95
3.4.6 Electromagnetic Levitation . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4. 7 Dielectrophoretic Levitation . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.8 Ferrofluid Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.9 Optical Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.10 Acoustic Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.11 Microgravity experiments .......................... 102
3.4.12 Combined Levitation Techniques ................... 102
4. Experimental and Measurement Techniques .............. 105
4.1 Introduction ........................................... 105
4.2 Photographie Observation Techniques ..................... 106
4.3 Droplet stroboscope .................................... 108
4.4 Video Observation Techniques ........................... 110
4.5 Velocity ............................................... 112
4.5.1 Laser-Doppler Velocimetry ........................ 112
4.5.2 Laser-Two-Focus Velocimetry ...................... 113
4.5.3 Partide-Image Velocimetry ........................ 114
4.5.4 Young's fringes ................................... 115
4.6 Size ................................................... 115
4.6.1 Images .......................................... 115
4.6.2 Phase Doppler Technique .......................... 116
4.6.3 Interference Method .............................. 117
Table of Contents IX
4.6.4 White-Light Method .............................. 119
4.6.5 Glare Point Method .............................. 119
4.6.6 Rainbow ........................................ 120
4.6. 7 Other Techniques ................................ 121
4. 7 Refractive Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.7.1 Introducing Remarks ............................. 123
4.7.2 Phase Doppler Based Instruments .................. 124
4.7.3 Glarepoints ..................................... 125
4.7.4 Rainbow ........................................ 125
4.8 Temperature ........................................... 129
4.8.1 Thermocouples ................................... 129
4.8.2 Schlieren Method ................................. 129
4.8.3 Infrared Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.8.4 Thermochromie Liquid Crystals .................... 130
4.8.5 Other Methods ................................... 130
4.9 Surface Tension ........................................ 131
4.10 Size Change Rates ...................................... 131
5. Experiments to Study Mechanical Interactions ........... 135
5.1 Introduction ........................................... 135
5.2 Droplet-Gas Interaction with surrounding fluids ............ 135
5.2.1 Wind tunnels for the investigation of droplet systems . 136
5.2.2 Interaction with Acoustic Field ..................... 140
5.2.3 Shock Tube Experiments .......................... 145
5.2.4 Droplet Deformation .............................. 147
5.2.5 Droplet Fragmentation by Shock Waves ............. 147
5.2.6 Ignition Delay Times of Droplets inShock Tubes ..... 150
5.3 Droplet Interaction with Solid and Liquid Surfaces .......... 151
5.3.1 Cold Solid Surfaces ............................... 152
5.3.2 Cold Liquid Surfaces .............................. 153
5.3.3 Heated Surfaces .................................. 153
5.3.4 Wetting of Solid Walls During Droplet Impact ....... 168
5.3.5 Comparison with Numerical Results ................ 173
5.4 Droplet-Droplet Interaction .............................. 178
5.4.1 The dynamics and geometry of a binary encounter .... 179
5.4.2 Experimental Setup and Results .................... 180
5.4.3 Numerical Results for Binary Droplet Collisions ...... 186
6. Experiments to Study Phase Transition Processes ........ 191
6.1 Introduction ........................................... 191
6.2 Experimental Setups .................................... 192
6.2.1 Arrangementsand Sensors to Detect Scattered Light .. 192
6.2.2 Optically Levitated Droplets ....................... 194
6.2.3 Acoustically Levitated Droplets .................... 197
6.2.4 Droplet Streams .................................. 198
X Table of Contents
6.3 Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6.3.1 Measurements on Single Droplets ................... 200
6.3.2 Measurements on Droplet Streams .................. 210
6.4 Combustion ........................................... 214
6.4.1 Burning Rates ................................... 218
6.4.2 Droplet Temperature ............................. 222
6.4.3 Flame Propagation ............................... 223
6.4.4 Microexplosions .................................. 229
6.5 Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
6.5.1 Droplet Size and Shape ........................... 235
6.5.2 Depolarization ................................... 237
6.6 Droplet Streams in High Pressure Environments ............ 240
7. Miscellaneous Applications ............................... 245
7.1 Introduction ........................................... 245
7.2 Interna! Combustion Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
7.3 Fire Suppression ....................................... 245
7.4 Spray Cooling .......................................... 246
7.5 Fuel-Coolant Interaction in Nuclear Reactors ............... 246
7.6 Cleaning with High Pressure Jets ......................... 246
7.7 Medicine and Health .................................... 246
7.8 Bioaerosols ............................................ 247
7.9 Production of Small Solid Particles ....................... 248
7.10 Applications in Agriculture .............................. 248
7.11 Acid Rain ............................................. 249
7.12 Cloud Physics .......................................... 249
7.13 Air Thaffic and Condensation Thails ....................... 250
7.14 Effects of Heavy Rain and Ice Accretion on Aircraft Wings .. 250
7.15 Applications in Space ................................... 251
7.16 Droplets in a Microgravity Environment ................... 252
7.17 Droplets as Chemical Reactor ............................ 252
7.18 Atomization of Alloy Powders ............................ 252
7.19 Ink-Jet Printing ........................................ 253
7.20 Solder Jet Technology ................................... 253
7.21 Picoliter Fluid Dispenser in Biotechnology ................. 254
7.22 Micro-Jet Printing of Microlenses ......................... 254
7.23 Applications in Medicine ................................ 254
7.24 Droplet-Based Manufacturing ............................ 254
7.25 Thermal Spraying ...................................... 256
7.26 Compound droplets ..................................... 256
7.27 Microencapsulation ..................................... 256
7.28 Submicron Particles and Microspheres .................... 257
7.29 Slurry Droplets ........................................ 257
7.30 Emulsions ............................................. 258
7.31 Aerosols ............................................... 258