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THESis;

Al LIBRARY
loot, Michigan State
University

This is to certify that the
dissertation entitled

Temperature Measurement Of Aqueous Ammonium Chloride
Solution During Solidification Process Using
Laser-Induced Fluorescence

presented by

Mohammad Behshad Shafii

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Mechanical Engineering

 

 

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2/05 p:/ClRC/DateDue.indd-p.1

Temperature Measurement Of Aqueous Ammonium Chloride Solution
During Solidification Process Using Laser-Induced Fluorescence

By

Mohammad Behshad Shafii

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

2005

ABSTRACT

Temperature Measurement Of Aqueous Ammonium Chloride Solution
During Solidiﬁcation Process Using Laser-Induced Fluorescence

By

Mohammad Behshad Shaﬁi

A wide variety of products are now made of metal alloys. The superior properties
of these alloys permit products to be used in very demanding environments where other
materials would fail. The major quality issues for these alloys are melt-related defects,
such as segregation defects and freckles. Buoyancy-induced ﬂuid ﬂow during
solidiﬁcation, which is primarily responsible for most forms of defects (chimneys), is not
directly controllable. If buoyancy-induced ﬂuid flow is left uncontrolled, natural
convection will contribute to nonuniform distributions of alloy constituents and grain
structure in castings. Materials with acceptable defects can be produced only by trial-and-
error and their acceptability is determined by costly inspection. The quantitative
measurement of the temperature ﬁeld during the solidiﬁcation process will enhance our
understanding of the natural convection phenomena, and provide benchmark temperature
data valuable to other analytical and numerical studies.

Aqueous ammonium chloride is a popular low temperature analog to metal alloys
because of its transparent nature. A IWO-color laser induced ﬂuorescence (LIF) technique
was developed to measure instantaneous whole ﬁeld temperature distribution above the
mushy zone during uni-directional solidiﬁcation of aqueous ammonium chloride that was
cooled from below. The temperature resolution was improved and doubled by using two

temperature sensitive dyes having opposite signs in their sensitivity. The fact that the

intensity of one dye increased and the other decreased with decreasing temperature,
resulted in a higher temperature sensitivity (4% K'l) in the two-color LIF two-dye
approach compared to all previous implementations of the two dye approach (maximum
of 1.7% K’l). This was an important outcome of this study.

In this study, in order to understand some of the observed ﬂow features during the
solidiﬁcation processes of the ammonium chloride solution, two different optical
diagnostic techniques (PIV and MTV) were used to obtain the velocity ﬁelds in these
regions.

The temperature mapping relied on the temperature dependence of ﬂuorescence
intensity, estimated from the intensity ratio of two temperature sensitive dyes. By using
this technique, temperature ﬁelds of some of the complex ﬂow features, such as plumes
and wisps, were obtained that had not been available before.

Along with the fundamental study based on temperature measurements, a novel
technique was also found to enforce the chimney formation at desired locations in the
mushy zone during the solidiﬁcation process of ammonium chloride. This was done by
placing metallic nucleators in particular arrangements on the bottom cooling plate. The
effects of the arrangement and size of the nucleators on the plume structure and
solidiﬁcation process was investigated. Results showed that it is possible to obtain a
relatively large area free of chimneys in the ﬁnal product of the solidiﬁcation process by
placing the nucleators in certain arrangements. The fact that the ﬂow was calm and the
temperature was uniform laterally above this area after t=60 min suggested that the
solidiﬁcation process was taking place uniformly at mush-melt interface, resulting in a

better quality of the ﬁnal product.

This book is dedicated to my mother and father

Mrs. Behnoosh Shaﬁi and Dr. Ahmad Shaﬁi

I want to thank you for always being there for me. You gave me the strength and wisdom

to face any obstacle head on and this book was one of them. I LOVE YOU.

iv

ACKNOWLEDGMENTS

I would not have been able to complete this journey without the aid and support
of countless people over the past few years.

First of all, I would like to thank my mom (Behnoosh), dad (Ahmad) and sisters
(Behnaz, Mahnaz, and Negah) who provided a lot of moral support.

I express my gratitude to my advisor, Dr. Manoochehr Koochesfahani, for his
continuous support of my work and for all the hours spent on the improvement of this
thesis. Much of the research that is presented here would not have been possible without
the encouragement from my supervisor.

I would like to give many thanks to the committee members: Dr. Benard, Dr.
Cloud, Dr. Dykman, and Dr. Golding, who gave me quite a few constructive comments
on my thesis.

Graduate school isn't the most important thing in life, but good friends, good
times and happiness are. I wish to thank my colleagues who provided a lot of technical
support and made my time in the PhD program more fun and interesting. This includes
Chee Lum, Shahram Pouya, Hu Hui, and Jill Drexler.

Finally, and most importantly, my deepest thanks to my wonderful wife,
Parmoon, for all her patience with me and my changing moods. Your support was
essential to the completion of my program.

Financial support for this work was provided by NASA grant NAG-8-1690.

TABLE or CONTENTS it if
it

LIST OF FIGURES ................................................................................ viii
LIST OF TABLES .................................................................................. xiv
NOMENCLATURE ................................................................................. xv
Chapter 1 Introduction .................................................................................................... 1
Chapter 2 Methodology of the solidiﬁcation process ..................................................... 9
2.1 Ammonium chloride characteristics ................................................................... 9
2.2 Solidiﬁcation of ammonium chloride ............................................................... 13
Chapter 3 Diagnostic techniques for temperature and velocity measurements ............. 19
3.1 Laser Induced Fluorescence (LIP) .................................................................... 21
3.1.1 Dye selection in two-color LIF one-dye approach ................................... 27
3.1.2 Spectral conﬂicts in two-color LIF two-dye approach ............................. 30
3.1.3 Selected dyes in two- Color LIF two- -dye approach .................................. 31
3.1.4 pH dependency ......................................................................................... 32
3.1.5 Temperature dependency ......................................................................... 34
3.1.6 Calibration process ................................................................................... 34
3.1.7 Error analysis ............................................................................................ 40

3.2 Particle Image Velocimetry (PIV) .................................................................... 44
3.3 Molecular Tagging Velocimetry (MTV) .......................................................... 45
Chapter 4 Optical setups ............................................................................................... 49
4.1 Optical setup for LIF ........................................................................................ 49
4.2 Optical setup for PIV ........................................................................................ 51
4.3 Optical setup for MTV ..................................................................................... 52
Chapter 5 Temperature maps of the plumes ................................................................. 55
Chapter 6 Comparison between numerical results and LIF results ............................... 72
6.1 Assumptions ..................................................................................................... 72
6.2 Governing equations ......................................................................................... 73
6.3 Boundary conditions ......................................................................................... 77
6.4 Results and discussion ...................................................................................... 79
Chapter 7 Controlling unidirectional solidiﬁcation processes using nucleators ........... 81
7.1 Effect of size and arrangement ......................................................................... 82
7.2 Effect of spacing ............................................................................................... 87
7.3 Obtaining relatively large area free of chimneys .............................................. 98
7.4 Average spacing between plumes .................................................................. 101

vi

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Chapter 8 Temperature maps and velocity ﬁelds of some of the ﬂow features for

different arrangements of the nucleators ................................................... 110

8.1 Temperature of phase locked plumes ............................................................. 110
8.2 Temperature measurement above the area free of chimneys .......................... 117
8.3 Velocity measurement around a single plume using Particle Image Velocimetry
(PIV) technique .............................................................................................. 120

8.4 Velocity measurement above a row of nucleators using Particle Image
Velocimetry (PIV) technique ......................................................................... 123

8.5 Velocity ﬁelds above an area free of plumes ................................................. 125

8.6 Velocity measurement of two phase locked plumes using MTV technique... 131

Chapter 9 Conclusions ................................................................................................ 136
Chapter 10 References .................................................................................................. 142
Appendix A Some Experimental Reports on Double-Diffusive Layer .................. 145
Appendix B Synchronization of Two Cameras .............................................. 151
Appendix C On the Stability of Laminar Plumes ........................................... 153
Appendix D Molecular Tagging Velocimetry and Thermometry (MTV&T) ........... 157
Appendix E Error Analysis .................................................................... 163

vii

LIST OF F IGURS

Figure 2-1: Equilibrium diagram of ammonium chloride ................................................ 10
Figure 2-2: pH of the solution as a function of percent weight of NH4C1 ........................ 11
Figure 2-3: pH variation of ammonium chloride solution as a function of

temperature .................................................................................................. 12
Figure 2—4: Schematic of the container ............................................................................ 13
Figure 2-5: Schematic of the stainless steel plate ............................................................. 14
Figure 2-6: Visualization of solidiﬁcatuion process at different times (Lum et

a1. 2001) ....................................................................................................... 17
Figure 2-7: Shadowgraph image of plumes and the described wisps and DDLs ............. 18
Figure 3-1: Emission spectrum of one dye with one color band (high lighted as

green). .......................................................................................................... 23
Figure 3-2: Two color LIF technique. (a) two-color two-dye, (b) two-color one-

dye (the two color bans are shown as green and red regions) ................... 25
Figure 3-3: Emission spectra of Rhodarnine B ................................................................. 28
Figure 3-4: Average intensity ratio vs. temperature for different ranges of

wavelengths ................................................................................................. 29
Figure 3-5: Spectral conﬂicts. (a) Conﬂict type I, (b) Conﬂict type II ............................ 30
Figure 3-6: Emission (Em) and absorption (Ab) spectra of Fluorescein and

Kiton Red ..................................................................................................... 32
Figure 3—7: Intensity variation of Fluorescein with pH. ................................................... 33
Figure 3-8: Intensity variation of Kiton Red and Fluorescein with Temperature ............ 35

Figure 3-9: Variation of the Intensity ratio of Kiton Red and Fluorescein with
temperature.(Excitation: 514 nm (5x10'7 mol/lit)) ...................................... 37

Figure 3-10: Fluorescent intensity of the imaged area. (ﬂuorescein and kiton
red mixture) ................................................................................................. 38

viii

Figure 3-11: The temperature measurement values if only (a) Fluorescein (one-
color LIF) or (b) Kiton Red (one-color LIF) is used. (c) The
temperature measurement results when the intensity ratio (two-
color LIF) is used ......................................................................................... 39

Figure 3-12: Intensity variation of a pixel vs. number of images ..................................... 42

Figure 3-13: Example of undelayed and delayed lines for line tagging MTV (At

= 35 ms) ....................................................................................................... 47
Figure 4-1: Schematic of the optical setup for LIF technique .......................................... 49
Figure 4-2: Schematic of the optical setup for PIV technique ......................................... 52
Figure 4-3: Optical setup for MTV technique .................................................................. 53
Figure 4-4: Schematic of the test section for MTV technique ......................................... 54
Figure 5-1: Height of mushy region vs. time ................................................................... 55
Figure 5-2: The location and size of the imaged area ....................................................... 56
Figure 5-3: The location of the origin and the imaged area ............................................. 57

Figure 54: Temperature maps corresponding to the imaged area during
solidiﬁcation process ................................................................................... 60

Figure 5-5: Temperature proﬁles along the horizontal line shown in Figure
5-4(a) (average of 10 consecutive pictures with the averaging time
of 300 ms, y = 2.6cm from bottom of plate) ................................................ 61

Figure 5-6: Temperature proﬁle along the horizontal line shown in Figure
5—4(a) (y = 2.6cm from bottom of plate, average of 10 consecutive
pictures with the averaging time of 300 ms and averaged in space,
8x8 pixels) ................................................................................................... 62

Figure 5-7: Temperature Proﬁles along the vertical lines shown in Figure 5-4(j)
(The location of the origin (H=0) is at the bottom of the
temperature map) ......................................................................................... 64

Figure 5-8: Temperature difference AT between vertical lines shown in Figure
5-4 (i) ........................................................................................................... 64

Figure 5-9: The location of the origin and the imaged area .............................................. 65

ix

Figure 5-10: Whole ﬁeld temperature measurement (average of 4 successive
intensity images and averaged in space, average of 8x8 pixels ) ................ 67

Figure 5-11: The location of the origin and the imaged area ............................................ 69

Figure 5-12: Temperature maps of the imaged area (3 x 2.2 cmz), averaged in
time (4 images) and averaged in space (8x8pixels) ..................................... 71

Figure 6-1: Schematic of the plume exiting the mushy zone ........................................... 74

Figure 6-2: Velocity Proﬁle of the Plume at different heights at t = 60 min
(Chee Lum 2001) ......................................................................................... 74

Figure 6-3: Temperature map of the plume exiting the mushy zone (t=60 min) ............. 78

Figure 6-4: Measured temperature proﬁle plus polynomial ﬁt along the vertical
line at r = 3mm (3.5 mm above the mushy zone). .................................. 78

Figure 6-5: Comparison between measured and calculated temperature proﬁles
at the center of the plume ............................................................................. 80

Figure 6-6: The comparison between measured and calculated temperature
proﬁles across the plume at different heights .............................................. 80

Figure 7-1: Different arrangements. (a) First arrangement with small
nucleators, (b) Second arrangement with small nucleators, (c) First
arrangement with big nucleators and ((1) Second arrangement with
big nucleators ............................................................................................... 82

Figure 7-2: Top view of the mushy zone for the case of ﬁrst arrangement with
small nucleators (t = 120 min) ..................................................................... 84

Figure 7-3: Top view of the mushy zone for the case of second arrangement
with small nucleators (t = 120 min) ............................................................. 84

Figure 74: (a) Top view of the mushy zone for the case of second arrangement
with big nucleators(t = 120 min), and 0)) Front view (t = 10min) ............ 86

Figure 7-5: (a) One pair of nucleators, and (b) Two pairs of nucleators .......................... 87

Figure 7-6: Phase locking of two nearby plumes, test # 7 (1800 phase
difference) .................................................................................................... 88

Figure 7-7: Sequence images of the oscillatory mode. (a) t = 8min, (b) t =
12min, (c)t= 16min and (d)t= 18 min ..................................................... 91

Figure 7-8: Height of mushy zone vs. time ...................................................................... 93
Figure 7-9: Schematic top view of one row of nucleators ................................................ 93
Figure 7-10: Schematic front view of one row of nucleators ........................................... 94

Figure 7-11: Stronger ﬁngers were formed above the nucleators compared to

others formed at mush melt interface at t = 6 min ....................................... 94
Figure 7-12: Plumes were formed above the nucleators (t = 30 min) .............................. 95
Figure 7-13: Plumes becoming phase locked (t = 35 min) ............................................... 96
Figure 7-14: Plumes were phase locked at t = 70 min ..................................................... 96
Figure 7-15: Top view of the chimneys ........................................................................... 97
Figure 7-16: Schematic of the locations of the placed nucleators .................................... 98
Figure 7-17: Top view of the chimneys ........................................................................... 99
Figure 7-18: Schematic of the locations of the placed nucleators .................................... 99
Figure 7-19: Top view of the chimneys ......................................................................... 100
Figure 7-20: Schematic of the liquid circulation in the system ...................................... 102
Figure 7-21: variation of the distance 2xL with K (average permeability) ..................... 106
Figure 7-22: Two dimentional porous layer .................................................................... 107

Figure 7-23: Rolls with square cross-sections for minimum Rayleigh number for
neutrally stable cellular convection ........................................................... 109

Figure 8-1: Schematic of the location of the nucleators (a) two-big nucleators
and (b) big-small nucleators ...................................................................... 111

Figure 8-2: the location of the imaged area. (t=70min) ................................................... 111

Figure 8-3: Temperature map of the plumes at t = 70 rrrin for the case of two-big
nucleators (average of 8x8 pixels) ............................................................. 112

Figure 8-4: Temperature proﬁles along horizontal lines for two cases two-big
and big-small nucleators ............................................................................ 113

Figure 8-5: Temperature proﬁles along designated lines ............................................... 113

xi

Figure 8-6: Temperature proﬁles along the indicated vertical lines ............................... 114

Figure 8-7: Temperature map of the plumes ﬁve seconds later ..................................... 116
Figure 8-8: Shadow graph image of the plumes and wisps ............................................ 11.6
Figure 8-9: Temperature proﬁles along horizontal lines ................................................ 117
Figure 8-10: Schematic of the locations of the nucleators ............................................. 118
Figure 8-11: Temperature maps of the imaged area (5.4 x 4 cm2, average of 8

x8 pixels) ................................................................................................... 120
Figure 8-12: PIV image of a plume at t = 120 min (imaged area is 29.3 mm x

21.3 mm) .................................................................................................... 121
Figure 8-13: Measured velocity vectors of the plume at t = 120 min ............................. 122
Figure 8-14: PIV image of the solution at t = 120 min .................................................. 124
Figure 8-15: Measured velocity vectors of the ﬂow above a row of nucleators ............ 124
Figure 8-16: Arrangement of the nucleators and location of the laser sheet .................. 126
Figure 8-17: PIV image of the imaged area above an area free of plumes ..................... 126
Figure 8-18: Velocity vectors at different times above and area free of plumes ............ 130

Figure 8-19:

Figure 8-20:

Figure 8-21:

Figure 8-22:

Figure 8-23:

Line tagging above the mushy zone at t = 25 min for the case of
two phase locked plumes above two big nucleators with a spacing
of 1.2 cm .................................................................................................... 131

Velocity proﬁles of the plumes at t = 25min for the case of two
phase locked plumes above two big nucleators with a spacing of
1.2cm ....................................................................................................... 132

Overlapped velocity proﬁles of the plumes for the case of two big
nucleator pair ............................................................................................. 132

Velocity proﬁles of the plumes at t = 40min for the case of big-
small pair ................................................................................................... 133

Velocity proﬁles of the plumes at t = 60min for the case
of big-small pair ..................................................................... l 34

xii

Figure A-l:

Figure A-2:
Figure B-l:
Figure B-2:
Figure C-l:
Figure C-2:
Figure C-3:

Figure D-l:

Figure D-2:

Figure D-3:

Two-layer salt-stratiﬁed solution (C1 and C2) destabilized by

lateral heating and cooling ......................................................... 146
Double diffusive layers and secondary ﬂow at the interface ................. 146
Schematic for synchronizing two Pulnix cameras ............................. 151

Schematic for synchronizing two PixelFly cameras ........................... 152
Schematic of laminar plume rising from a horizontal line source ........... 153

Wavelength as a function of height along the plume .......................... 155
Wavelength of a plume measured from peak to peak ......................... 156
Normalized lifetime as a function of weight percentage of

the ammonium chloride ........................................................... 159
Variation of normalized lifetime with temperature ............................ 161
Delayed image of a line tagged region .......................................... 162

Images in this thesis are presented in color

xiii

LIST OF TABLES

Table 7-1: The summary of some of experiments carried out for pairs of nucleators ..... 89
Table 7-2: The summarized conclusions ......................................................................... 92
Table 7-3: Parameters used to calculate L ..................................................................... 105
Table C—l: Properties of the Plume ............................................................. 154

xiv

Abbreviations

CCD
DC
DDL
LED
LIF
MTV
MTVT
PIV

RMS

CNH4C1
D
f

Fo

NOMENCLATURE

Charge Coupled Device

Direct Current

Double-Diffusive Layer

Light Emitting Diode

Laser Induced Fluorescence

Molecular Tagging Velocimetry

Molecular Tagging Velocimetry and Thermometry
Particle Image Velocimetry

Root Mean Square

Thermocouples

Thermo—Chromic Liquid Crystal

Length of the sampling volume
Concentration

Concentration of ammonium chloride
Mass diffusivity of the solution
Constant in modiﬁed Poiseuille equation
Fourier number (Dxt/Lz)

gravity

XV

Gr

RaH

1'1

1'2

Modiﬁed Grashof number G = 2J2(Gr)0°25

3 .—
Grashof number [gﬂx (To Roi]

 

V2

Mushy zone height

Height of the container
Incident laser intensity
Average permeability of the mush

Dissociation constant
Optical constant

Constant that depends on the physical property of a dye

Radius of the source area or Width of the container
Lewis number (d/D)
Pressure

Fluorescence quantum yield or Volume ﬂow rate

KgH-IAC

Rayleigh number based on H, Ra H = D
V

Radius of the chimney

Radius of the plume when it exits the chimney

Signal (number of electrons)
Time

Temperature of the base ﬂow (source)

xvi

BC

Br

PB

PE

PP

90

0'shot

Surrounding temperature

Velocity in r direction

Velocity in z direction

Distance from the source in the vertical direction
Path through which the ﬂuorescence intensity travels
Thermal diffusivity or Wave number

Temperature sensitivity of a dye

Solutal expansion coefﬁcients

Thermal expansion coefﬁcient

Absorption coefﬁcient of the ﬂuorescent dye
Viscosity of the ammonium chloride solution

Bulk density of ammonium chloride solution,

Density of the ammonium chloride solution at the eutectic point

Density of the plume at the exit of the mushy zone

Reference density

Dynamic viscosity

Lifetime

Shot noise

xvii

Chapter 1

Introduction

A wide variety of products are now made of metal alloys such as automobile
engine blocks and the compressor and turbine section of an aircraft engine. These alloys
make products strong enough so that they can be used in very demanding environments
where other materials would fail. The major issues for these alloys are melt-related
defects such as segregation defects and freckles formed during the solidiﬁcation process.
The solidiﬁcation process of a binary melt can be inﬂuenced by ﬂuid motion in the
liquid. The solidiﬁcation of binary alloys from a melt is a process that involves ﬂuid ﬂow
and the growth process. As the alloy solidiﬁes, a mushy zone appears at the chilled wall
of a mold and a number of phenomena are associated with the formation of this mush.
The mushy zone is made of numerous dendrites that constitute a porous network that
coarsens as the solidiﬁcation proceeds. An important feature of solidiﬁcation in the
mushy region pertains to rejection of one of the chemical constituents into the liquid.
Solute rejection induces composition gradients which, in combination with existing
temperature gradients and a gravitational ﬁeld, may induce buoyancy driven convection
in the mush (plumes) and the parent melt (ﬁngers). As the mushy zone grows, small
chimneys are formed, from which discrete plumes of interdendritic melt emerge. These
plumes have a very complex ﬂow structure. Since the coupled solid—liquid ﬂow causes
Structural and chemical inhomogeneities in ﬁnal solidiﬁed products, a fundamental
understanding of the multiphase transport phenomena is required. This can be achieved

by computing the appropriate conservation laws or, experimentally measuring the

1

temperature, concentration and velocity ﬁelds in the system. Semi-transparent analog
alloys have been used for experimental studies because they permit optical access to the
sample, which has proven to be useful for ﬂow visualization and morphological studies.
Aqueous ammonium chloride is such a system that behaves in a very similar manner to
metallic alloys.

Mathematical models developed by Worster (1991), Neilson and Incropera (1991)
and Schneider and Beckermann (1995), qualitatively described the temperature and
concentration ﬁelds in the mushy layer and in the liquid by solving coupled and nonlinear
governing equations based on some assumptions, such as two-dimensional ﬂow,
axisymmetric conditions, isotropic permeability in the mush, and local thermodynamic
equilibrium. Some of these assumptions are too limiting; for example, the plumes have
helical motion, therefore assuming two-dimmentional and axisymmetric ﬂow might not
be appropriate. As will be discussed later, the system is not in thermodynamic
equilibrium at early stages of the solidiﬁcation process because substantial ﬂuid under-
cooling exists above the cooled bottom plate. Instability analysis conducted by Feltham
and Worster (1999) showed that a laminar ﬂow in the melt could trigger instability of
mush-melt interface by inducing a ﬂow in the porous mush and melt. It was also shown
that perturbed heat ﬂux from the melt into the mush-melt interface could cause the
growth of instability in the mushy layer. Stability analysis of Heinrich et al. (1989)
revealed that there are critical container widths, below which convection can be
suppressed.

Recent experiments by Chen and Chen (1991) and Magirl and Incropera (1993)

suggested that plume convection and chimneys start forming at the liquidus interface due

to the perturbations induced during the transition from ﬁnger convection to plumes.
Worster (1992) mathematically identiﬁed two instability mechanisms: ‘Boundary layer’
and ‘Mushy-layer’ modes. In boundary-layer mode the ﬂuid within the interstices of the
mushy layer is stagnant and the instability occurs above the mushy layer in the ﬂuid
region. Salt-ﬁnger convection occurs as a result of this mode and is conﬁned to the
compositional boundary layer. The solid fraction does not get perturbed in this mode. The
mushy-layer mode is a mode that is related to the solid—fraction perturbations. It was
shown that this mode is the cause of the formation of the plumes. These mathematical
results can be explored experimentally by embedding nucleators in the cooled bottom
plate to cause the channels to form at these approximate locations (will be discussed
later). It should be noted that the solutal buoyancy force becomes a dominant factor
despite the presence of the stabilizing thermal force. This solutal buoyancy force then
causes large-scale convection to be induced in the bulk ﬂuid.

Separate from fundamental issues, some researchers have investigated process-
control options to suppress defects formation (such as freckles and chimneys) in
unidirectional solidiﬁed ingots of binary alloy solutions. Buoyancy forces, which are
mainly responsible for the formation of chimneys and freckles, are not easily
controllable. Kou et al. (1978) performed a numerical analysis, which was conﬁrmed by
experiments, to predict macrosegregation in a rotated vacuum arc remelted ingots of Sn-
Pb. Due to the upward concavity of the liquidus and solidus interfaces, Pb-rich segregates
formed in the center of the ingot. This concavity caused the denser Pb-rich interdendritic
liquid to ﬂow downward and radially inward towards the center line. This indicated that

during the solidiﬁcation process there was a remelting of the dendrites, which, in effect,

left a freckle along the center line. Centrifugal forces due to the rotation of the ingot
prevented the denser Pb-rich ﬂuid to ﬂow toward the center line creating a more uniform
composition proﬁle radially. In fact, they mentioned that by choosing a proper rotational
speed of the ingot, the freckles could be signiﬁcantly reduced. It was also shown that at a
high solidiﬁcation rate, the macrosegregation was slight and centrifugal force had little
effect on the macrosegregation.

Sample and Hellawell (1982) showed that the slow rotation of the cylindrical
ingot about an inclined axis retarded the formation of chimneys and associated
macroscopic composition changes during the solidiﬁcation process of ammonium
chloride solution; however, for higher rotational speeds some chimneys were formed at
the mold walls. They concluded that for freckles to form there must be a convective
circuit within the bulk liquid and interdendritic liquid, and there must be a ﬂow of more
dense solution into the dendritic network around the chimneys to feed the plumes.
Therefore, any interruption in this convection circuit could suppress the chimney
formation. In another set of experiments, Sample and Hellawell (1984) investigated the
mush-melt interface of ammonium chloride that was punctured to various depths by
slowly punching a pointed quill into the mushy zone. These artiﬁcially created channels
failed to propagate and form chimneys and were overgrown and closed within 2 to 4
minutes. However, they could create a new plume, and from that a new chimney, by
lowering down an open capillary to within 1 to 2 mm of the growth front and extracting
some liquid up the tube. They also observed that blocking an established chimney by a

quill could close the chimney and prevent the formation of the plume at that location.

By solving complex and strongly coupled governing equations, Neilson and
Incropera (1990, 1993) supported the ﬁndings of Sample and Hellawell (1982). They
indicated that the quality of unidirectionally solidiﬁed binary alloys may be enhanced
through an intermittent rotation of the mold, which restricts freckling to the centerline
and outer radius of the casting. Experimental observations of Garimella et at. (1995)
showed that low-amplitude vibration to the test section reduced the mushy zone thickness
and the number of chimneys for all concentrations of ammonium chloride solution cooled
from below. They also mentioned that the chimneys’ suppression was inﬂuenced by
vibration amplitude rather than by frequency of oscillation.

Since thermal buoyancy force is one of the main forces that plays an important
role in the creation of the plumes, it is important to understand and measure the
temperature distribution in the solution during the solidiﬁcation process. Some
techniques have been used to carry out temperature measurements during the
solidiﬁcation process of ammonium chloride.

Thermochromic liquid crystal paints (TLC) used in a Hele-Shaw cell (Solomon
and Hartley 1997) enabled simultaneous visualization of temperature ﬁeld at the walls
and the solid fraction in Hele-Shaw cells based on the assumption that the painted TLC
on the walls responded to the ﬂow in the interior due to the rapid diffusion of heat across
the narrow gap. They visualized isotherms both within the mushy layer and in the liquid
region. Distortions in these isotherms revealed ﬂows in the system. Other temperature
measurements have been done by thermocouples. Measured temperature histories on the

test section midline at selected heights (Magirl and Incropera 1993) and at the side wall

(W irtz et a1. 1998) could reveal consistent decay in local temperature, with pronounced
decay occurring at the location closest to the chill plate.

Past experimental, analytical and numerical studies have established that the
convective phenomena present can best be described in terms of complex dynamic
velocity ﬁelds. Most experimental methods applied to date have been poorly suited to
accurately measure these phenomena and do not provide for whole—ﬁeld measurements of
the 2-D temperature distribution. The temperature measurement carried out by Solomon
and Hartley (1997) using TLC paints was in the Hele-Shaw cells, in which one of the side
walls was coated with TLC. The measured temperature was not the actual temperature of
the ﬂuid due to the fact that the ﬂuid is motionless along the sidewalls. In addition, the
convection phenomenon and the plume structure are different in Hele-Shaw cells
compared to those in conventional size containers due to the fact that ﬂow between
closely-spaced parallel plates is affected by wall drag.

This work is the continuation of the work done by Wirtz (1998) and Lum et a1.
(2001) who obtained velocity vectors in the ammonium chloride solution during its
solidiﬁcation process using a molecular tagging velocimetry (MTV) technique. This
current work can be divided into two main goals.

The primary goal of this work was to develop a diagnostic technique to obtain
temperature maps of the ammonium chloride solution during its solidiﬁcation process.
Laser induced ﬂuorescence (LIF) technique was selected to obtain instantaneous two-
dirnensional temperature maps of the whole solution. The use of LIF provides
veriﬁcation of the modeling approaches of some of the previous work, provides

benchmark temperature ﬁeld data valuable to other analytical and numerical studies, and

enhances our understanding of therrnosolutal convection processes. Since some of the
ﬂow features such as plumes and wisps have small temperature difference across them,
the temperature sensitivity of the LIF technique was improved upon for the ﬁrst time by
choosing two temperature sensitive dyes. The detailed temperature ﬁelds quantitatively
characterizing the complex structures previously observed in such solidiﬁcation will be
valuable relative to the development and reﬁnement of numerical models. The energy
equation was simpliﬁed and solved numerically based on some assumptions and
appropriate boundary conditions (obtained from measurements) to obtain temperature
ﬁelds of a plume.

The secondary goal of this work was to investigate the effects of the arrangement
and the size of the nucleators on the plume structure and solidiﬁcation process.
Nucleators are small metallic blocks that are placed on the bottom cooling plate. Wirtz
(1998) showed that plumes could be forced to form above the nucleators for one
particular arrangement. The HP technique was used to obtain temperature ﬁelds of some
of the interesting ﬂow features for some of the nucleators’ arrangements. To obtain
velocity ﬁelds and proﬁles, particle image velocimetry WW) and molecular tagging
velocimetry (MTV) were also used.

In the upcoming chapters of this work, the experimental methodology of the
solidiﬁcation process of the ammonium chloride solution will be discussed. Different
diagnostic techniques for velocity and temperature measurements will be explained. The
LIF technique including dye selection and spectral conﬂicts will be discussed. In later

chapters, the effect of the size and the arrangements of the nucleators on the solidiﬁcation

process will be detailed and some of the temperature and velocity ﬁelds of the interesting

features of the ﬂow will be presented.

Chapter 2

Methodology of the solidiﬁcation process

In this chapter the phase diagram of aqueous ammonium chloride will be
described, the variation of the pH of the ammonium chloride solution with percent weight
of ammonium chloride will be presented (needs to be known for the LIF technique) and

the experimental methodology of the solidiﬁcation process will be detailed.

2.1 Ammonium chloride characteristics

Ammonium chloride is a popular low temperature analog due to the transparent
nature of the ﬂuid. Also, the temperature range at which solidiﬁcation occurs provides a
means for studying the convective mechanisms present in s solidifying system.

The equilibrium diagram for ammonium chloride is shown in Figure 2-1, where
the dashed lines indicate the initial concentration and the ﬁnal equilibrium temperature of
the aqueous ammonium chloride, while the dot above the liquidus line indicates the initial
starting conditions used for all experiments in this study (26% wt). The aqueous
ammonium chloride solution was initially kept at 23°C. When the temperature at the
bottom plate reaches the liquidus temperature (18.60 C), which is determined by the
composition of the salt solution (26% wt), ammonium chloride crystals begin to form and
continue growing as cooling progresses. The process will continue along the liquidus
line, which implies that as the ﬂuid gets cooler, ammonium chloride crystals precipitate

out of the solution forming a mushy zone since the weight percentage of the ﬂuid must

reduce to maintain equilibrium. The mushy zone is composed of solid dendrites and
interdentritic liquid, and it separates fully solidiﬁed and liquid regions during
solidiﬁcation. The permeability of the mushy zone is non-uniform and anisotropic. The
mushy zone is commonly treated as a porous medium. The eutectic region is a mixture of

both ice and ammonium chloride and it is in solid form.

 

  
   
    
  
   
    

 

45 . ﬂ '''''''''''''''''''''''''' I I I T I I .
Initial Starting point for Liquidus Line j
35 - this study (23°C and
26% wt)
A 25 ‘ \
o l I
O
9 15 t 5 j
3 NHiCl-HZO Solution : NH4C1 Crystal Solution ‘
g L E (Mushy Zone) .
o. . I ,
E 5 5 SNllir‘HrL .
m 4 | 1
l— . : 1
-5 . : i
Ice + Solution 5 i
SI . ,+L ? Bottom Plate Temperature
-15 i!— ' ' — " " if: """""""""""""" . """ (it """"""""""""" ‘i
Eutectic Solid 5 1
SNll4Cl+‘ Sin: 5 i

 

 

 

~25 . - -
o 4 a 12 16 2o 24 2a 32 36 40

Weight percentage of NH 4Cl

Figure 2-1: Equilibrium diagram of ammonium chloride

Since the ﬂuorescence intensity of some dyes is greatly affected by pH variation
(this will be discussed later), the pH of the ammonium chloride solution needs to be
known prior to the test. Figure 2-2 shows the pH variation of ammonium chloride

solution as a function of percent weight of ammonium chloride dissolved in the solution.

10

Measurement of pH was carried out by continuously adding a known amount of
ammonium chloride to the distilled water with initial pH of seven and measuring the pH
values with a pH meter (Omega PHH-lZ, accuracy of i 0.05 pH). The ﬁnal pH value of
26% wt ammonium chloride solution is about 4.3 pH. The lack of data points between pH
5 and 7 occurs because of the high sensitivity of the pH to the percent weight of

ammonium chloride in this range.

 

7.5 - ____,__.___ — *L_..___

 

+ Measured
7 . —-—a—— Calculated

 

 

 

 

 

 

6.5 —- —-—~* ———~

 

 

 

 

 

 

 

 

0 5 10 15 20 25 30
Percent weight of NH4CI

Figure 2-2: Measured pH of the solution as a function of percent weight of NH4Cl

The pH of the solution can also be calculated (shown by red squares) from the following

 

equations:
iH+i=JKaXCNH4C1 (2’1)
pH = ‘L0g10([H+]) (2-2)

11

where K, is the dissociation constant and Cch. is the concentration of ammonium

chloride in the solution in mol/lit. The value of the dissociation constant for ammonium
chloride is 5.56x10'1°. Since the temperature of the solution changes during the
solidiﬁcation process, it is important to know the pH variation of the solution with
temperature.

The variation of the pH of 19% wt ammonium chloride solution with temperature
is shown in Figure 2-3. pH is normalized by pHo. pH0 is the pH of the solution at room
temperature (20° C) and is equal to 4.4 for 19% wt of the ammonium chloride solution. It
should be noted that 19% wt ammonium chloride was used in order to avoid crystal
formation of ammonium chloride during the calibration process. It can be seen that the
pH increases slightly as the temperature decreases. This variation is related to the fact
that the dissociation constant of ammonium chloride is slightly temperature dependent.
Since the pH of the solution is slightly temperature dependent, a ﬂuorescent dye should
be chosen such that the emission intensity of the dye does not change with variation in

pH. This will be described in the following chapters.

 

1 .06

 

1.05 -—— - __,_ —
1.04 ~- ~—

1.03 t -——— - ~ \
1.02 .2 »-

1.01 ~» -- -— \

1 l l l T 7

9 11 13 15 17 19
TM

 

 

 

pH/pl-lo

/

 

 

 

Figure 2-3: Measured pH variation of ammonium chloride solution with temperature

12

2.2 A description of the Solidification of ammonium chloride in water

This temperature measurement work is the continuation of the work done by
Wirtz (1998) and Lum et al. (2001) who obtained velocity vectors in the ammonium
chloride solution during its solidiﬁcation process. A schematic of the container used to
conduct experiments is shown in Figure 2-4. The solidiﬁcation system utilized is exactly

the same as the one described in Lum et al (2001).

 

 

 

 

 

 

 

 

 

 

Aqueous NH4C1
———>
Plume > _ _ _ _ _ -1.
/-- ._ ._.._.. m... -1. _.
Mushy Area / u’ a l a
Coolant Outlet / G D ‘ __
o a a o
Nucleators
Plexiglas O

 

 

 

\ Coolant Inlet

Figure 2-4: Schematic of the container

The cooling of the ﬂuid in the container is achieved through the use of a base
stainless steel plate as a heat transfer medium, which is exposed to a coolant bath on one
side to provide for the cooling and aqueous ammonium chloride on the other side within

the test section. An enclosure made of 1/4" quartz glass measuring 52 x 89 x100 mm is

13

placed over the stainless steel base plate and sealed with high vacuum grease and gaskets
to form the test section. Quartz glass is used due to the fact that it absorbs very little of
the laser energy and thus is suitable for the transmission of laser beams in two-color LIF
technique and results in less attenuation.

During initial experimental trials, Wirtz (1998) observed that convective plumes
caused by the instabilities developed within the test section in a random manner.
However, each experimental trial would yield approximately 11 chimneys within the test
section. Eleven square nucleators were embedded in a regular manner in the base
stainless steel plate to induce ﬁnite disturbances to the formation of the mush (Wirtz
1998). These nucleators would cause the channels to form at those approximate locations.
A schematic of the stainless steel plate and the coordinates of the stainless steel
nucleators are provided in Figure 2-5. This resulted in the formation of many ascending
water-rich ﬁngers and the formation of ammonium chloride crystals, which would form

on the bottom of the test section to make up the mushy region.

89 mm

l

11.11m 11.17mm

 

 

 

 

A
J Ill.7lmm
ROW 3 > E?- L: r: ra—L
114.29mm
Row 2 ; E} {E :3 52 mm
ROW 1 ——>———{} 5? [F ?
V

 

 

 

 

 

 

 

 

 

 

 

Figure 2-5: Schematic of the stainless steel plate

14

After the ammonium chloride solution was poured into the container (26% wt
NH4C1), it was cooled from the bottom by means of a heat exchanger. The thermobath
circulated constant temperature coolant (—19°C) through the cooling chamber and this
caused the base stainless steel plate to be at a constant temperature of -14°C. The cooling
ﬂuid is a 50% mix of water and generic automotive anti-freeze (ethylene glycol), which
was refrigerated by this thermobath (Neslab, RTE-140) and pumped through insulated
tubing into the cooling chamber. To reduce the heat transfer to the surroundings, the
cooling chamber was covered with appropriate insulations. The cooling provided to the
test section would then initiate the crystallization process. Rapid growth of the mushy
layer at the initial stages of cooling indicated the presence of substantial ﬂuid under-
cooling (temperature of the ﬂuid with known concentration is below liquidus line shown
in Figure 2-1). The proof of the existence of sub-cooled ﬂuid will be presented later. As
seen in Figure 2-6, which was obtained by Lum (2001) using a shadowgraph technique,
four minutes into the solidiﬁcation process, small ﬁngers started to form around the
nucleators and could be seen rising. At 6 minutes, more ﬁngers maintained their solutal
identity and were able to rise higher. Due to the large Lewis number of ammonium
chloride, the water-rich ﬁngers retained their compositional identity and were clearly
visible to the top of the test section before they would begin to collapse (Magirl and
Incropera 1993). The Lewis number is a measure of the ratio between characteristic

lengths for diffusion of heat and diffusion of mass and can be deﬁned as:

Le=01/D (2-3)

15

where 01 is the thermal diffusivity and D is the mass diffusivity of the solution. The time
when plumes are ﬁrst formed is difﬁcult to determine since this transition from ﬁngers to
plumes is continuous. Fingers are deﬁned as plumes when they become more vigorous
and their size is perceptibly larger than their surrounding neighboring ﬁngers. This
evolution of plumes usually start after 13 min into the process. Initially, there were 2 or 3
plumes and later the number of plumes increased. As neighboring plumes competed for
the supply of water-rich ﬂuid from within the mush, surrounding ﬁngers started to
decrease in quantity. At around 20 minutes, it became apparent that the plumes were
developing above the nucleation sites. Most of the time 11 plumes were formed right
above the 11 nucleators. This is consistent with the mathematical results obtained by
Worster (1992) about mushy—layer instability mode. It was shown that this mode is the
cause of the formation of the plumes. This instability mode happens when the solid
fraction is perturbed. These nucleators located on the bottom plate below the mushy layer
perturbed the solid fraction and from the consequence of that, the plumes were formed
above these nucleators. As the salt-rich ﬂuid adjacent to a plume was cooled, it
descended as a sheath along the plume. These sheaths could not traverse the plume bends,
causing these sheaths to separate from the plume (wisps) and descended freely (Figure
2—7). Other observed regions were the double-diffusive layers shown in Figure 2-7.
Double diffusive layers were formed about 90 min into the process. These layers are
diffusive interfaces, which are slightly inclined from horizontal due to the vertical motion
of the plume. The formation of double diffusive layers (DDL) is a result of the interaction
between the vertical concentration gradient and the horizontal temperature gradient

(Appendix A), both induced by plume convection (Chen 1997).

16

14 minutes

10 minutes ‘

6 minutes

 

 

       

 

26 minutes

, 22 minutes

18 minutes

70 m'nutes ,

g 60 minutes

 

 

mrsnute 120 rnsinute

90 minutes

80 minutes

Figure 2-6: Visualization of solidiﬁcation process at different times (Lum et al. 2001)

17

 

Figure 2-7: Shadowgraph image of plumes and the described wisps and DDLs

Chapter 3

Diagnostic techniques for temperature and velocity measurements

To obtain the temperature maps and the velocity vectors of the ﬂow in this study,
different optical diagnostic techniques were used. In this chapter, these techniques will be

described and some the properties of the selected dyes ’will be detailed.

Temmrature Measurement Technigues

Thermocouples (TC) are widely used as temperature measurement probes. A
carefully calibrated TC probe is capable of measuring temperature with precision better
than i 0.1K. Two primary disadvantages of using TCs are their spatial resolution, on the
order of a few hundred microns at smallest and their physical intrusiveness in the ﬂow.
Their point measurement nature also makes it very difﬁcult to get full-ﬁeld temperature
mapping as a large number of them must be placed and monitored simultaneously.

Thermochromic liquid crystal (TLC) materials have been used as a nonintrusive
tool for full-ﬁeld, temperature measurement. The TLC-based technique is based on the
optical properties of TLC materials. At the heart of LC based thermography systems are
liquid crystal materials called thermochromic liquid crystals (TLCs). Fundamentally, a
liquid crystal is a thermodynamic phase that is between the pure solid and pure liquid
phases of matter and exists in some organic compounds under certain conditions. At
temperatures below the TLC's event temperature, a TLC will be in the solid state and will
appear transparent. When a TLC is at its event temperature, illuminated by white light

and viewed under ﬁxed optical conditions, the TLC material will reﬂect a unique

19

wavelength of visible light (i.e., color). As the temperature rises through the TLC's
bandwidth, the reﬂected color of the TLC will change. Finally, when the temperature
exceeds the TLC's clearing point temperature, the material will enter the pure liquid state
and will revert back to being transparent. The molecular structure of a TLC gives the
material two indices of refraction, causing the material to become birefringent.
Birefringence will cause the selectively reﬂected light emerging from a TLC to become
elliptically polarized. The reﬂected color spectrum for most TLC materials will vary
continuously from the longer wavelengths (i.e., red) corresponding to the event
temperature to shorter wavelengths (i.e., blue) corresponding to the clearing point
temperature. Additionally, a TLC material will also transmit a signiﬁcant amount of the
incident light with virtually no modiﬁcation. Viewing TLCs against a non-reﬂecting (i.e.,
black background prevents this transmitted light from adversely affecting the
interpretation of the selectively reﬂected light. By knowing the relationship between the
reﬂected color and the temperature, one can obtain the full-ﬁeld, temperature map. The
major shortcoming in using TLC is that one has to calibrate each point of test section to
take into account the inﬂuence of the illuminating light variation. Since the color of the
TLC may also depend on the viewing angle and the location of the tested area, the
temperature calibration has to be repeated each time the CCD camera is displaced. The
TLC materials can be made in the form of microencapsulated liquid and used as tracer
particles in ﬂow visualization. In our experiment, microencapsulated TLC materials are
difﬁcult to use in whole ﬁeld temperature measurement since the calibration of TLC is
challenging prior to the test (due to the solidiﬁcation of ammonium chloride and also due

to continuous change of index of refraction of the ﬂuid). As will be shown later in PIV

20

measurements section, another problem that one might encounter using these
microencapsulated TLC particles is that, as they penetrate in mushy zone they become
nucleation sites and crystals form around them. This can change the mushy zone structure
and causes lack of TLC particles in some ﬂow structure.

The Laser Induced Fluorescence (LIF) technique is based on ﬂuorescence of
molecules and atoms, which is induced by absorption of a photon. This absorption causes
a transition from ground state to an excited state. Part of the absorbed energy is released
as re-emitted light (ﬂuorescence) during spontaneous transition from the excited state to
the ground state. The ﬂuorescence occurs at a longer wavelength than that of the
absorption. LIF technique has been widely used for both ﬂow visualization and scalar
measurements (concentration and temperature) of ﬂuid ﬂows in recent years
(Koochesfahani and Dimotakis 1985; Koochesfahani et al. 2000, and Sakakibara and
Adrian 1999). If the ﬂuorescence intensity of a dye is temperature dependent,
ﬂuorescence intensity of known concentration of the ﬂuorescent dye can be calibrated
versus temperature. This calibration curve can be used to obtain a temperature map in the
imaged area (Kim and Kihm 2001). In the next sections the LIF technique will be
explained in detail and some difﬁculties associated with the inherent spectral conﬂicts

will be discussed.

3.1 Laser Induced Fluorescence (LIF)

When the laser beam passes through a liquid medium seeded with an organic
ﬂuorescent dye, the ﬂuorescence intensity is affected by the absorption of the incident

laser beam and by the re-absorption of the ﬂuorescence itself across the absorbing

21

medium. According to Beer’s law, the expression for the ﬂuorescence signal captured by

camera can be expressed as

1 f: Kop,£1QCIOe_C(€‘b+°2°) (3—1)

where Kept is an optical constant, C is the molecular concentration of the ﬂuorescent dye,
81 is absorption coefﬁcient of the ﬂuorescent dye when it is exposed to a laser and b is the
length of the sampling volume along the path of the excitation beam. 82 is the absorption
coefﬁcient of the ﬂuorescent dye when it is exposed to its own emission light and z is the
path through which the ﬂuorescence intensity travels in the solution and gets reabsorbed
by the dye, L, is the incident laser intensity, and Q is the ﬂuorescence quantum yield. If

the concentration is low enough, the above equation can be rewritten as

I f: KoptngClo (3'2)

Both the absorption coefﬁcient 81 and quantum yield Q can be temperature dependent.
Lemoine et al. (1999) used an equation for ﬂuorescence quantum yield based on

the A21 spontaneous emission Einstein coefﬁcient and presented the following equations:

,6
Q = Kspece /T (3-3)
substituting (3-3) in (3-2) results in

.3
I f: KopthpecloCe /T (3‘4)

22

where Kspw depends on the spectroscopic and physical property of the dye and constant B
is the temperature sensitivity of the dye that can be found during the calibration process.
The LIF technique can be applied in two different ways, one-color LIF technique and

two—color LIF technique (known as ratiometlic method), as described below.

One-color LIF technique

In one-color LIF, only one color band of the emission spectrum of a temperature

sensitive dye is used to measure temperature (Figure 3-1).

Emission
Intensity

 

 

 

Wavelength

Figure 3-1: Emission spectrum of one dye with one color band (high lighted as green).

Equation (3—4) can be presented in terms of intensity ratio. Assuming laser intensity IO
and molecular concentration of the ﬂuorescent dye to be constant, equation (3-4) can be

rewritten as

ln(

 

I (7) l l
f

: —_— 3'5
If(T0)) .5(T T0) ( )

23

where T0 is the reference temperature and [f (To) is ﬂuorescence intensity at reference
temperature. This equation is the base equation for temperature measurement of one-
color LIF technique (Lemoine et al. 1999). The drawback of using the one-color LIF
technique is that it is very difﬁcult to maintain the incident laser intensity uniform
throughout the process. During the solidiﬁcation process of ammonium chloride the
index of refraction of ﬂuid continuously changes resulting in non-uniform unsteady laser
illumination ﬁeld and inaccurate temperature measurements. Examples of inaccurate

temperature maps will be displayed later.

Two-color LIF technique

The two-color LIF technique can be used to eliminate the effect of laser intensity
variation in the system. In this technique two color bands are chosen. These two color
bands can be chosen either from emission spectra of two ﬂuorescence dyes (two-color
LIF two-dye approach, Figure 3-2 a), or from emission spectrum of one dye at different
locations on its emission spectrum (two-color LIF one-dye approach, Figure 3-2 b).
These color bands should usually be chosen such that the intensity of one is temperature
sensitive and the other temperature insensitive (Sakakibara and Adrian 1999). The
ﬂuorescence signal of temperature sensitive dye provides the temperature distribution in
the measurement region and that of the temperature insensitive dye provides the intensity
distribution of the incident illumination laser light. As will be described later, for the
purpose of this research, two temperature sensitive dyes (with opposite temperature
dependency) are used to increase the temperature sensitivity and also take into account

the non-uniformity of the illumination light.

24

Emission

 

 

 

Intensity
Wavelength
(a)
A
Emission
Intensity .

 

 

 

Wavelength

(b)

Figure 3-2: Two color LIF technique. (a) two-color two-dye, (b) two-color one-dye
(the two color bans are shown as green and red regions)

If two color bands are detected by two aligned cameras, the ﬂuorescence signal

detected on the ﬁrst color band may be written as in equation (3-6)

ﬂ%
If]: Kopthspecllocle (3’6)

and on the second one

25

rz/
If2= KopIZKspec210C2e T (3'7)

the ﬂuorescence ratio can be written as

( —,6)
_ If] _ Koprlepecl ﬂe'ﬂl—T—Z—

If2 K0pt2Kspec2 C2

 

 

(3-8)

C1 is equal to C2 when two color bands are chosen from the emission spectrum of one
dye (two-color LIF one-dye approach). To eliminate Kopt, Kspec and C a reference
temperature T0 needs to be deﬁned. By knowing T0 and corresponding ﬂuorescence

intensity ratio, one can modify the equation (3-8) to obtain ‘

(ﬁr/32) _ (131-162)

 

 

Rf (T) = e T To (3-9)
RAT.»
01'
R (T) 1 1
f
= _ __.__ 3-10
1n[Rf 00)] (,51 .52)[T To] ( )

The value of (Bl-[12) can be calculated from the calibration curve and it is desired to be as
large as possible. The larger this number is, the more sensitive the ratio intensity becomes
to temperature variation. The advantage of using two-color LIF one—dye approach is that,

even if the concentration of the dye changes during the process, equations (3-9) and (3-

26

10) are still valid because the ratio of C1 over C2 is always 1. This might not be true for
two-color LIF two-dye approach. If, during the process, the concentration of one of the
dyes changes locally, then the ratio of C1 over C2 is no longer constant and equations (3-
9) and (3-10) are not valid. The other advantage of two—color LIF one-dye approach, as
shown in equation (3-1), is thatif a low concentration of the dye is used then there is no
need to be concerned about the spectral conﬂicts (will be explained later). A main
difﬁculty in this approach is ﬁnding a dye which has two color bands on its emission
spectrum: one sensitive and the other insensitive to temperature variation. Usually when a
dye is temperature sensitive all color bands on its emission spectrum are temperature

sensitive.

3.1.1 Dye selection in two-color LIF one-dye approach

In order to ﬁnd out if this approach could be used to measure temperature of the
solution during the solidiﬁcation process, Rhodamine B was selected and tested as a
temperature sensitive dye for this approach. Rhodamine B is a useful dye because its
ﬂuorescence is not pH dependent (over pH ranges above 6), but is temperature
dependent. Experimental results obtained by Coppeta and Rogers (1998) indicated that
Rhodamine B is one of the most temperature quenched dyes and over a temperature range
of 0-60 °C the ﬂuorescence intensity changes by approximately —1.54% per degree
Celsius. Figure 3-3 shows the variation of the emission spectrum of Rhodamine B,
dissolved in ammonium chloride solution, with temperature. The emission spectrums of
all dyes presented in this paper were obtained by using a spectrophotometer (Hitachi

4500) located in Michigan State University’s (MSU) Chemistry department.

27

Figure 3—4 shows the variation of the average normalized intensity of Rhodamine
B solution with temperature for different color bands of the emission spectrum (computed
from Figure 3-3). 10 is the intensity at a reference temperature, usually at ambient
temperature (20°C). It can be seen that for the color band that is in the 670-700 nm range
normalized intensity is less sensitive to temperature variation (minimum slope) and the

color band 575-585 nm maximum sensitivity (maximum slope) will be obtained.

 

6000WTL-

 

4000 *

 

 

 

2000 r

I (Intensity In arbitrary units)

 

 

 

 

500 550 600 650 700
1 (nm)

Figure 3-3: Emission spectra of Rhodamine B
Solution of: 5x10’° mol/lit Rhodamine B and 19% wt NH..C1 (excitation=488 nm)

28

Using a single dye such as Rhodamine B in a two—color LIF one dye approach resulted in
poor temperature sensitivity. For example if two color bands are chosen, one 575—585 nm
(high temperature sensitive band) and the other one 670-700 run (low temperature
sensitive band), taking the ratio of these normalized intensity bands results in a low
temperature sensitivity curve (at best 0.33% change in normalized intensity ratio per
degree C). It means that a 1°C temperature variation corresponds to about 0.33%
variation in the normalized ﬂuorescence ratio. Therefore, a two-color LIF two-dye
approach needs to be considered instead. To do so, two appropriate dyes need to be

selected. In order to select two dyes, one should avoid spectral conﬂicts.

 

 

 

 

 

 

 

 

 

 

 

2_o ----.----.----.----r----.ﬁ---
a A 575-585 nm
1 8 x -— — -- 670-700 nm _
' i \-\ ._ —— . 660-700 nm
\ ._ . 650-700 nm +
\. -— - — - 640-700 nm
.\ \ -— —- 620-700 nm
1.6 b Q \o\ “x, o— a 590-700 nm F
il§~;‘ ~l\\ \ -‘\.\
S i \.\:‘\‘!:\ \ 'x 4
'\\\\§° \
1.4 It \ \\ g \\
I\\ A
1 \ \ \
\ \
1.2 ’ \ 7‘~.
.2 \1, 1
1.0 .............................
-1o -5 o 5 1o 15 20

Figure 34: Average intensity ratio vs. temperature for different ranges of wavelengths

29

3.1.2 Spectral conﬂicts in two-color LIF two-dye approach

There are two main spectral conﬂicts that one would usually face when choosing
two dyes and those are related to the overlap between absorption and emission bands
(Coppeta and Rogers 1998). The ﬁrst is shown in Figure 3-5 (a), where there is an
overlap between the emission bands of each dye (conﬂict type I). As shown, some of the
ﬂuorescence from dye 1 will appear in intensity measurement of dye 2 and vice versa.
This implies that, unless optimal ﬁltering is used, one could mistakenly measure
ﬂuorescence from dye 1 as light from dye 2 and ﬂuorescence from dye 2 as light from

dye 1, resulting in inaccurate temperature measurement. One should select two dyes such

that the emission spectra have minimum overlap.

A Emission of
Dye #1

A , ,
Ermssron of

 
 
 
 

Emission of I

Absorption of
Dye #2

Dye #2

...|IIIIII|II'

   

.0

O
O
O
O
O...

 

 

 

L
T r

A A.
(a) (b)
Figure 3-5: Spectral conﬂicts. (a) Conﬂict type I, (b) Conﬂict type II

The second type of spectral conﬂict occurs when the emission band of the ﬁrst
dye and the absorption band of the second dye (or the emission band of the second dye
and the absorption band of the ﬁrst dye) have an overlap (Figure 3-5 (b)). This means the
ﬂuorescence of the ﬁrst dye gets absorbed by the second dye or vice versa, making the

value of the ﬂuorescence ratio become a function of optical path length. One way to

30

decrease the effect of this conﬂict is to use low concentration of both dyes. However, low
concentrations of dyes will decrease the ﬂuorescence intensity, thereby causing the need

for a more powerful laser source or very sensitive cameras.

3.1.3 Selected dyes in two-Color LIF two-dye approach

Many researchers have chosen ﬂuorescent dyes such that one is temperature
sensitive and the other is insensitive to temperature variation (Sakakibara and Adrian,
1999; Kim and Kihm 2001). The most common dyes used so far in two-color LIF two-
dye approach are Rhodamine B (temperature sensitive) and Rhodamine 110 (temperature
insensitive). When these two dyes are mixed in the solution, it has been reported that the
maximum sensitivity (rate of change of the ratio intensity with temperature) of 161.7%
K’1 can be obtained and the resulting random error is 1.0 K. Since some of the ﬂow
features investigated in this study had a temperature difference of less than 2° C across, it
was found necessary to improve the sensitivity of the LIF technique to resolve these
features. After careful research and investigation, ﬂuorescein and kiton red were chosen
as the two ﬂuorescent dyes in the two—color LIF two-dye approach. As will be shown
later, the combination of these dyes will improve the sensitivity of this technique to 4%
K]. By choosing appropriate CCD cameras, the random error can be reduced to 02° C.
In temperature measurement LIF techniques it is very important to ﬁnd ﬂuorescent dyes
that are sensitive to temperature variation but insensitive to pH variation. If the pH of the
solution changes during the process and the dye is pH sensitive, then the measured
temperature values would be inaccurate. In the next section, the pH dependency of these

dyes will be discussed.

3.1.4 pH dependency

Fluorescein is a temperature sensitive dye that has been used by many researchers
(Coppeta and Rogers 1998). It is also one of the pH dependent dyes. Figure 3-6 shows the
relative absorption and emission spectra versus wavelength for both Fluorescein and
Kiton Red. Kiton Red does not exhibit a pH dependent absorption over the range of 3 to
10 pH units. It should be noted that Rhodamine B could have been chosen as one of the
temperature sensitive dyes instead of Kiton Red. The reason for using Kiton Red is
because its absorption and emission spectra are farther shifted to the right in comparison
with Rhodamine B. This reduces spectral conﬂicts (as described before) when used in

combination with Fluorescein.

 

400 450 500 550 600 650 700

Figure 3-6: Emission (Em) and absorption (Ab) spectra of Fluorescein and Kiton Red
(Excitation=514 nm, pH=8)

32

The absorption band of ﬂuorescein is a function of pH over the range of 3 to 8 pH
units.

Figure 3-7 shows the intensity variation of ﬂuorescein with pH. The largest
change in intensity versus pH occurs in the range of 6 to 7 pH units. The ﬂuorescence
intensity remains constant after a pH of 7.4. As will be discussed later, in order to Operate
in the pH-independent range of ﬂuorescein, the pH of all ammonium chloride solutions
was raised to 7.8 by adding Sodium Hydroxide (NaOH). Based on Coppeta and Rogers’s
(1998) ﬁndings, Kiton red’s emission intensity is pH independent over the range of 3 to

10 pH units.

 

21 7 ~— —— _*________ —-~— —— ————~— -—————

 

19
17 z__ _.____ ___ ,__._*_

15

/
13
1. /

 

 

 

 

 

lilo

 

 

 

0001\10

 

 

 

E

l
X
‘ 1

l

l

 

Figure 3-7: Intensity variation of Fluorescein with pH.

(excitation=514 nm, concentration=10‘6 mol/lit))

33

3.1.5 Temperature dependency

Both Fluorescein and Kiton red are temperature sensitive dyes. To minimize the
spectral conﬂicts mentioned before, two spectral bands were selected using two optical
ﬁlters. One spectral band was detected by using a narrow band pass ﬁlter (535-545 nm
half bandwidth). This ﬁlter detects the emitted intensity of Fluorescein in the solution.
The reason for choosing such a color band is to avoid detecting the excitation wavelength
of the laser, which is at 514. The other ﬁlter used is a long pass ﬁlter 0» > 600), which
detects the emitted intensity of Kiton red. As can be seen in Figure 3-6, there is a spectral
conﬂict on the emitted color band of the Fluorescein. The emitted light at the chosen
color band (535-545 nm) of Fluorescein is partially absorbed by Kiton red. To reduce this
conﬂict (as shown in calibration curves later), the concentrations of Fluorescein and

Kiton red were minimized to be 5x10"7 mol/lit.

3.1.6 Calibration process

To obtain the relation between the measured ﬂuorescence intensity and the
solution temperature, the container used for visualizing the solidiﬁcation process was also
used (see Figure 2—4) in the temperature calibration. The test section was ﬁlled with the
solution (Ammonium Chloride 19% wt, 5x10'7 mol/lit Fluorescein and 5x10'7 mol/lit
Kiton Red). Nineteen percent by weight NH4C1 was used to avoid solidiﬁcation during
the calibration process. The temperature could be lowered down to -15°C without
solidifying the ammonium chloride (see Figure 2-1). In order to have a uniform

temperature, the solution in the container was stirred continuously.

34

The solution was excited by an argon-ion laser at 514nm and two Pulnix cameras
(TM-9701) recorded ﬂuorescence images from ﬂuorescein and kiton red by means of the
two described ﬁlters in front of their optical lenses. To ﬁnd the value of the ﬂuorescence
intensity, 30 sequential images were averaged to obtain a time averaged intensity image.
The value of the ﬂuorescence intensity represents an averaged intensity of a small region
of 32 x 32 pixels of this image. Figure 3-8 shows measured intensity variation of both
dyes with temperature for different solutions (with and without Nl-I4Cl) and different

optical paths L.

 

Fluorescein (With no NH 4CL, L=7cm)
Fluorescein (With NH Cl, L=1 cm)
Fluorescein (With no H 4Cl, L=1cm)
Kiton Red (With NH Cl, L=1cm)
Kiton Red (With no H461, L=1cm)
Kiton Red (With no NH 4Cl, L=7cm)

 

1.3 U I I Y t l I ‘ f Tﬁ ‘ V V V
p

  
 
 
   
   

1.2

0040.1)-

 

 

 

1.1 r

1 0 19m: -0.0146T +1.29, max dev:0.00251, r2=1.00
' - n = +0.0175T +0.647, max dev:0.00455, r2=0.999

F Fluorescein

H=|I|20

   

0.9

0.8

 

 

     

 

0.7'l“-.1....l....1..l.1...11....
5.0 7.5 10.0 1 2.5 15.0 17.5 20.0

T (°C)

Figure 3-8: Intensity variation of Kiton Red and Fluorescein with Temperature

(excitation=514 nm, concentration=5x10'° mol/lit)

35

The measured intensities of these two dyes are individually normalized by their
intensity at 20°C. The temperature was not lowered below 3°C because experimental
results obtained by Wirtz (1998) suggested that the temperature of the mush/melt
interface was always above 4°C. The intensity of ﬂuorescein decreases with decreasing
temperature while that of the kiton red increases.

Figure 3-9 presents the same calibration data in terms of the normalized intensity
ratio of kiton red over ﬂuorescein. It can be seen that the optical path length has little
effect on the calibration curve and the error resulted from the optical path length at worst
case is less than 04° C. This error is mainly related to the spectra overlap and re-
absorption of the emitted light as passing through the solution before detection by the
cameras. However, in order to obtain the best accuracy and minimum error possible, for
each experiment an appropriate calibration curve corresponding to its optical path length
L was used to ﬁnd the temperature map of the solution.

The fact that the intensity of one dye increases and the other decreases with
decreasing temperature, results in a higher temperature sensitivity (4% K'l) in the two-
color LIF two-dye approach compared to all previous implementations of the two dye
approach (maximum of 1.7% K!) This means that a 1°C temperature variation
corresponds to about 4% variation in the total ﬂuorescence ratio. This is an important

outcome of this study.

36

 

 

E
g
Ill.
*5
IE
.5.
E
a:
1.2 -
1.0

 

v With NH Cl 19%wt, pH>7.5, L=1cm
A With no NH4CI, pH>7.5, L=1cm

o With NH CI19%wt, pH>7.5, L=7cm .
Rm," Fl in=a exp(b x) max ,

 

dev:0.00575 a=1.92, b=-0.0329

 

 

 

T (°C)

Figure 3-9: Variation of the Intensity ratio of Kiton Red and Fluorescein with

temperature.(Excitation: 514 nm (5><10‘7 mol/lit))

These two dyes were used to measure the temperature distribution in two-

dirnensional planes during solidiﬁcation of ammonium chloride solution. In most of our

experiments the optical path length of the imaged area was 3 cm; therefore, the

calibration curve with the green line (Figure 3-9) was used to minimize the error

associated with the optical path length. As already mentioned, two-color LIF was used so

that the intensity non-uniformities could be taken into account. A good example of these

non-uniformities of this laser is given below.

Since the index of refraction of a ﬁnger or a plume is different than that of the

surrounding ﬂuid as the plume or ﬁnger rises vertically in a helical motion, the curved

37

edges of it causes the laser sheet to diverge and converge results in dark streak patterns in

certain areas of the image (Figure 3-10).

   

(a) (b)

Figure 3-10: Fluorescent intensity of the imaged area. (ﬂuorescein and kiton red mixture)

(a) Before solidiﬁcation, (b) During solidiﬁcation

The two—color LIF technique can suppress the effect of these streaks on the
measured temperature values. Figure 3-11 (a-b) shows the measured temperature values
if only ﬂuorescein (one-color LIF) or kiton Red (one-color LIF) were used individually
as in a single dye approach. Figure 3-11 (c) shows the temperature measurement results
when the two-color LIF was used. It is clear that the two-color LIF reduced many of the
artifacts caused by the streaks on temperature maps, resulting in more accurate results.
The reason for the remaining streaks is the slight miss-alignment of the two cameras,
which was done in the empty container to capture the images of approximately the same
area in the ﬂow ﬁeld. It was realized later that after the solution was poured into the
container, due to difference in index of refraction and the optical path, the images

captured by two cameras became slightly misaligned. Due to this slight misalignment,

38

some streaks still remained in the ﬁnal temperature map. To get the best results, the
cameras were aligned while the solution was already in the container for all of the

experiments.

Fluorescein

T("C)

     

Ratio

   

Figure 3-11: The temperature measurement values if only (a) Fluorescein (one-color
LIF) or (b) Kiton Red (one-color LIF) is used. (c) The temperature measurement results
when the intensity ratio (two-color LIF) is used.

3.1.7 Error analysis

The digital CCD cameras are the most important part of the system and their noise
characteristics have a direct impact on the measurement accuracy of the ﬂuorescent
emission intensity. There are two major noise sources that one should be aware of: shot
noise and dark current noise. The laser intensity variation was less than 0.1%, but was not

important since a ratiometric approach was used.

Shot noise

Shot noise constitutes the major part of the total noise and is the noise associated
with the random arrival of photons at any detector. Since the time between photon arrival
is governed by Poisson statistics, the RMS in number of photons collected during a given

period of time is (Eastman Kodak Company 2001 ):

ashot ‘3 J3:

where oshot is the shot noise and S is the signal, both expressed in either electrons or
photons. For example, a 10000-electron exposure will have a shot noise of 100 electrons.
This implies that the best signal-to-noise ratio possible for a 10,000 electron signal is
10,000/100 = 100. This corresponds to 1.0% uncertainty in measured instantaneous
intensity. The only way to reduce this noise is to use a camera with larger full-well
capacity. The full-well capacity is the maximum number of electrons generated before

the camera is saturated.

40

Dark current noise

Dark current is the result of imperfections or impurities in the depleted bulk
silicon. Electrons can be freed from CCD material through thermal vibration of the CCD
and then trapped in the CCD. The most effective way to reduce dark current is to cool the
CCD. Using small exposure times also reduces this noise. Although the average dark
signal can be subtracted out, the shot noise associated with this signal cannot. As in the
case of photon shot noise, the amount of dark current shot noise is equal to the square

root of the dark signal

O-shot z 5

The image resulting from subtraction of a raw image and a dark frame is more than this

by a factor of J2 since both images have the dark noise embedded in them. The dark
signal, D (electrons/pixel/s), is a characteristic of the camera which is given by the
manufacturer.

A simple test was performed to evaluate the total noise of the 8-bit Pulnix
cameras (TM-9701). These cameras were originally used for some of the experiments
before new 12-bit PixelFly cameras were purchased. An LED (light emitting diode) was
placed in front of a Pulnix camera’s lens and 150 images were taken. Figure 3-12 shows
the time variation of the recorded intensity normalized by average intensity, Iaverage (100
counts in this case). The LED was energized by a DC power supply (Power Designs TP

340A) with voltage stability better than 0.02%. The stability of the luminous intensity of

41

the LED was measured by a photodiode and the RMS of the output voltage of the

photodiode was 0.1%.

 

1.1

1% ll ’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K 0
094——w~%_MeM_L_LL
0%
05 . , T . . . '
0 m 40 m 30 1m mo 1%

Number of Images

Figure 3-12: Intensity variation of a pixel vs. number of images

Since the uncertainty of the output voltage of the photodiode itself was 0.1%, it was
concluded that stability of the LED luminous intensity was at least better than 0.1%. The
intensity of a selected pixel was measured and plotted against the number of images.
From Figure 3-12 the standard deviation was found to be 3.5 counts, or 3.5% of the
average intensity value. This standard deviation results in 08°C uncertainty in
temperature measurement in the two-color LIF technique (using ﬂuorescein and kiton red
as ﬂuorescent dyes). This uncertainty can be reduced by using CCD cameras with lower
shot noise (higher full well capacity), such as the Pixelﬂy cameras (The Cooke

Corporation), which have half of the shot noise of the Pulnix cameras (Appendix E).

42

Averaging the images also reduces the total uncertainty by a factor of the inverse
square root of the total number of averaged images. Pulnix cameras were used initially
for some of the experiments and an averaging technique was used to reduce the total
uncertainty of the temperature values. However, in order to obtain better signal to noise
ratio, two new cameras (Pixelﬂy cameras) were purchased later on and used for the rest
of the experiments. These cameras have a full-well capacity of 20,000 electrons. If half of
this capacity is used, the related shot noise would cause 1% uncertainty in measured
intensity. The combination of shot and dark noises for these cameras will result in a
04°C uncertainty in temperature measurement in two-color LIF technique (using
ﬂuorescein and kiton red as ﬂuorescent dyes). The uncertainty resulted from these
cameras is half of that of Pulnix cameras. Another advantage of using these cameras is
. their resolution. These cameras (1022x1394 pixels) have four times more pixels than
those of Pulnix cameras (480x640 pixels). Therefore, by spatial averaging (averaging of
four pixels) one can reduce the uncertainty of this technique to 02°C per equivalent pixel
of a Pulnix Camera. Therefore. at pixel level, PixelFly cameras perform much better than

Pulnix cameras.

Velocity Measurement Techniques

In this study, in order to understand some of the observed ﬂow features during the
solidiﬁcation processes of the ammonium chloride solution, such as the ﬂow ﬁeld above

a portion of the mushy zone where no plume existed and also the ﬂow ﬁeld between two

43

adjacent plumes (will be discussed later), two different optical diagnostic techniques were

used to obtain the velocity ﬁelds in these regions.

3.2 Particle Image Velocimetry (PIV)

PIV measures whole velocity ﬁelds by taking two images shortly after each other
and calculating the distance that the individual particles traveled within this time. From
the known time difference and the measured displacement the velocity is calculated. The
most common way of measuring displacement, is to divide the image plane into small
interrogation spots and cross-correlate the images from the two time exposures. The
spatial displacement that produces the maximum cross-correlation statistically
approximates the average displacement of the particles in the interrogation cell. The PIV
images were processed using an in-house correlation code written in C (MTV code). In
order to reveal the ﬂow motion, generally the ﬂow is seeded with particles which will
scatter the light sheet and are imaged two or more times from the side by a CCD camera.
However, in this study, neutrally buoyant particles (i.e. impurities) that already existed in
the ammonium chloride solution were used for velocity measurements and no additional
particles were seeded in the ﬂow. The size of the impurities or particles in the solution
was less that 20 pm. The resulting double or multi-exposed image, taken in a known time
interval, provided a displacement record of the particles within the measurement plane,
which is then analyzed and scaled to velocity. The velocity information produced in this
way tends towards the instantaneous velocity distribution, as camera exposure time is
smaller than the delayed time between two images.

As will be discussed later, due to the lack of seeding particles in the plumes

during the solidiﬁcation process of ammonium chloride solution, PIV technique could not

44

be used to obtain velocity information in the plumes. Therefore, Molecular Tagging
Velocimetry (MTV) technique was chosen as an alternative technique to obtain the

velocity proﬁle of the plumes.

3.3 Molecular Tagging Velocimetry (MTV)

Molecular Tagging Velocimetry (MTV) is a whole-ﬁeld optical technique which
uses molecules that can be turned into long lifetime tracers upon excitation by photons of
an appropriate wavelength. Typically a pulsed laser is used to tag the regions of interest
and those tagged regions are interrogated at two successive times within the lifetime of
the tracer by taking two successive images. The displacement of the tagged region
between the two interrogation times is determined and the measured Lagrangian
displacement vector provides the estimate of the velocity vector. A description of this
measurement technique is given by Gendrich and Koochesfahani (1996) and
Koochesfahani (1999).

There are several chemicals which can be applied as tracer molecules for MTV.
Caged ﬂuorescent compounds are ﬂuorescent molecules covalently modiﬁed by the
addition of a chemical group that renders them nonﬂuorescent. This modiﬁcation has the
additional property that it can be removed by exposing the molecule to ultraviolet light,
which cleaves the bond between the modifying group and the ﬂuorescent molecule,
restoring the original molecule and its ﬂuorescence. Caged ﬂuorescein is one of these
chemicals. After cleaving the bond, ﬂuorescein molecules can be tagged by an additional
laser (Argon Ion 488 nm). Thus, for uncaged ﬂuorescent dyes, two sources of photons are

needed, one to break the cage (UV laser) and the other to excite the uncaged ﬂuorescent

45

dye (Argone Ion laser). The use of caged ﬂuorescein and similar compounds was ﬁrst
introduced by Lempert e. al. (1995). The advantage of using this chemical is that the
ﬂuorescence of the uncaged dye persists (practically inﬁnite) for a very long time and can
be interrogated for very low ﬂow velocity. One of the disadvantages of using this
chemical is that the cage-breaking process is irreversible. The other disadvantage of using
this chemical is that it requires two laser sources and makes it more expensive to use.

The bleaching method is another way to measure velocity vectors in the ﬂow. The
bleaching method uses a high energy UV laser to bleach tracer molecules in a certain
region of interest. The principle of determining the velocity is the same as the caged
ﬂuorescent dyes. A ﬂuorescent dye such as ﬂuorescein will be excited by a laser (Argon
lone) and then get bleached by high energy UV laser. The bleached area (dark area) will
be interrogated within an illuminated (bright) area. The bleaching technique has the same
advantages and disadvantages as the caged ﬂuorescent dyes.

In this work, MTV based on phosphorescent tracers was utilized. The
phosphorescent compound (MTV Triplex) used for the purpose of this research consists
of a lumophore, l-Br-Np; an alcohol, cyclohexanol; and a sugar, cyclodextrin; and is
collectively known as 1-Ber.MB-CD.ROH. The concentrations of the MTV triplex used
in this study are 2 x 10'4M for Maltosyl-Cyclodextrin, 0.06M for alcohol and a saturated
amount of bromo-napthalene was added (Gendrich et al. 1997). This tracer was added
into the ammonium chloride solution. Due to the small concentrations of the tracer, the
solidiﬁcation process was not affected by the presence of the tracer. When excited with

an excimer laser (308nm), these tracers emit light that has a lifetime of ~5ms. In this

46

case, only one source of photons (laser) is needed, and the excitation/emission process is
reversible.

Line or grid patterns created with the laser can be imaged at two successive times
and are correlated to obtain the velocity proﬁles, or the velocity vectors of the plumes
(Lum, 2001). Line tagging written into the ﬂow ﬁeld provides a measurement of the
velocity component perpendicular to the line and it provides one dimensional velocity
values. An example of line tagging is shown in Figure 3-13. As will be shown later, this

method was used to obtain velocity proﬁles of some plumes.

Undelayed Delayed

 

V

 

Figure 3-13: Example of undelayed and delayed lines for line tagging MTV (At = 35 ms)

The typical concentration of the ammonium chloride solution is 26% by weight, whereas
the highest concentration of the three components of the MTV triplex is less by at least
three orders of magnitude (in molar concentration). To conﬁrm this, experiments with
and without using the tracer were performed by Lum et al. 2001. A comparison between

the experiments did not indicate any change in behavior including the variation of mushy

47

zone height with time. Thus, the solidiﬁcation behavior is not noticeably inﬂuenced by

the presence of the tracer molecules.

48

Chapter 4

Optical setups

In this chapter, the three different experimental setups for LIF, PIV and MTV

techniques will be described.

4.1 Optical setup for LIF

The experimental setup for the LIF technique is shown schematically in Figure

Argon-Ion Laser Mirror

Cylindrical Converging
f =20 m f =15 mm

 

 

Test Section
Mirror
Coolant Outlet

 

 

 

 

Coolant Inlet
Beam Splitter CCD Camera

  

Green Filter for
Fluorescein

  

Red Filter for
Kiton Red

CCD Camera

Figure 4-1: Schematic of the optical setup for LIF technique

The main objects in this setup are an argon—ion laser, mirrors to direct the laser
beam, a converging lens, a cylindrical lens to create a laser sheet with a thickness of 0.3

mm, a beam splitter, two CCD cameras (Pulnix TM9701, 30 frames/s or PixelFly, 12

49

frames/s), and two optical ﬁlters (Edmund Industrial Optics). The excitation wavelength
of the argon-ion laser is set to 514 nm with a power of 1.5 Watts. The test section is the
same as the one described in Figure 2—4. The width of the sheet is 0.3mm. The CCD
cameras are mounted on translational stages and adjusted to capture images of
approximately the same area in the ﬂow ﬁeld (within one pixel). This can be done by
subtracting the two images from two cameras simultaneously and aligning the cameras
until the resulting image has minimum intensity values (subtracting two identical images
results in an image with pixel values of zero count). To obtain sub-pixel accuracy after
aligning the cameras, a calibration plate, which has an equally spaced grid pattern at 1-
mm intervals on its surface, is placed in the plane of the laser sheet (the plane in which
temperature is measured) and illuminated by a halogen lamp. One image captured from
one camera is assumed to be the base image and the other image captured by the other
camera is assumed to be the deformed image. The displacement between grid points on
the base image and the deformed image gives a mapping equation. This mapping
equation maps the location of all pixel points of the deformed image on to the base
image. The displacement between grid points of base image and deformed image is found
using an in-house correlation code written in C (MTV code). This correlation code was
developed at the TMUAL (Turbulent Mixing and Unsteady Aerodynamics Laboratory,
Gendrich et al. 1997) at Michigan State University and can produce a sub-pixel accuracy
of 0.1 pixels. After obtaining the displacements between each grid point in the base
image and that in the deformed image, a 3’°-order polynomial function was ﬁtted by the
least-squares method (MATLAB Code) to ﬁnd the mapping equation. Since the intensity

ratio obtained from two cameras is needed to obtain the temperature map, a bi~linear

50

interpolation scheme was used to obtain intensities at sub-pixel locations. This alignment
procedure is the same for both Pulnix cameras and PixelFly cameras. The framing rate of
the 8-bit Pulnix cameras is 30 frames/second and that of the 12-bit PixelFly cameras is 12
frames/second. Pulnix cameras have a special resolution of 480x640 pixels and PixelFly
cameras have a special resolution of 1024x1392 pixels. It should be noted that the laser
sheet should not intersect with the mushy zone during the solidiﬁcation process, because
the resulting reﬂection from the mushy zone contaminates the true LIF signals. The
procedure of synchronizing the Pulnix and PixelFly cameras is detailed in Appendix B.
Some bleaching effects were observed at early stages of the solidiﬁcation process
(0 to 8 min) where convection was slow above the ﬁngers. The intensity of ﬂuorescein
would drop 1% at some locations on the imaged plane when it was exposed to the laser
sheet for more than 2 seconds. To eliminate this effect, a shutter was used to minimize

the amount of time that ﬂuorescein was exposed to the laser sheet (less than 0.5 second).

4.2 Optical setup for PIV

The experimental setup is similar to that of the LIF technique except that only one
camera is used to capture scattered light from the particles (Figure 4-2). It should be
noted that there is no need for an optical ﬁlter in this setup since the particles scatter light
with the same wavelength as that of the laser sheet. The same in-house correlation code
used to ﬁnd displacement between grid points of the base image and the deformed image
in the aligning procedure is used to ﬁnd the average velocity of the interrogating cell in
the PIV technique. As mentioned before, this results in a sub—pixel accuracy of 0.1

pixels.

51

Argon-Ion Laser Mirror

Cylindrical Converging

 

 

 

 

 

 

Test Section f =20 m f =15 mm
Mirror
Coolant Outlet , .
n n 11
Coolant Inlet
CCD Camera

Figure 4-2: Schematic of the optical setup for PIV technique

4.3 Optical setup for MTV

In this work, a line tagging technique was used to obtain velocity proﬁles of some
plumes. Creating the appropriate line tagging pattern for velocity measurements involves
a setup of optics. To make ﬁne laser lines, two lenses were used to manipulate the laser
beam and to make a laser sheet that is as thin as possible. As shown in Figure 4-3, a VFL
(Variable Focal Length) setup consisting of a 150mm and 50mm cylindrical lens were
used to increase the aspect ratio of a 20ns, lOOmJ/pulse beam from an excimer laser
(Lambda Physik LPX 220 iCC ﬁlled with XeCl). The thickness of the laser sheet passing
through this optical setup would be about 0.5mm. To obtain multiple laser lines, the laser
sheet is passed through a beam blocker to create the line patterns. The beam blocker is
basically a plate with an array of slots that are very thin. This optics setup was used to
measure the ﬂow ﬁeld near the mushy zone where the velocities are slow - on the order
of 0.5mrn/s. In order for the smaller features within the ﬂow ﬁeld to be resolved, the

beam blocker with the slot spacing of 0.8mm and slot width of 0.15mm was used.

52

  
  
  

UV laser

Beam blocker 50mm 150mm

Laser lines

Figure 4-3: Optical setup for MTV technique

In imaging the ﬁelds of view, an intensiﬁed camera and various electronics were
used in order to detect the tagging pattern in low light conditions. A 105mm Micro
Nikkor ( f / 2.8 ) lens with an additional close-up lens was used in conjunction with an
intensiﬁed camera (DiCam-Pro). This is a l2—bit, high-resolution (1280x1024 pixels),
gated, intensiﬁed camera with a fast-decay phosphor (P46). The detector was operated in
the dual-frame mode, where two full-frame images of luminescence are acquired in quick
succession from the same laser pulse (the delayed time can be speciﬁed manually in the
software). A four Channel Digital Delay/Pulse Generator (SRS) was used to generate
5Hz TTL pulses to synchronize the camera and laser. For this work, the ﬁrst frame
integrates the ﬂuorescence signal of MTV Triplex for a period of 0.2ms starting at a 0.2
ms delay after the laser pulse, whereas the second frame integrates the phosphorescence
signal for a period of 5 ms starting at 35 ms delay after the laser pulse.

As will be discussed later, the MTV technique was used to measure the velocity
proﬁle of two adjacent plumes simultaneously. In order to be able to adjust the container
such that the laser lines passed through the center of the plumes, the container was placed

on rotational and translational stages. During the experiments, the stages were moved and

53

rotated such that the maximum displacement of the line tagged region in the delayed
images was obtained at the location of the plumes and this was done visually. Maximum
displacements indicated that the laser lines were passing through the center of both

plumes. Schematic of the test section is shown in Figure 44.

Maximum displacements of
tagged regions in delayed image

 

 

 

\f‘ 3*

 

Laser+optics

 

Plumes_

 

 

UV laser lines

 

 

 

 

 

 

 

Translational stag [7
Rotational stage

Figure 4-4: Schematic of the test section for MTV technique

54

Chapter 5

Temperature maps of the plumes

After aligning the two Pulnix cameras, the ammonium chloride solution was
poured in the container (26% wt NH4C1, 5x10'7 mol/lit Fluorescein, 5x10‘7 mol/lit Kiton
Red) and cooled from the bottom. The thickness of the mushy zone as a function of time
is plotted against that obtained by Lum et al (2001) to show the consistency between all
experiments (Figure 5-1). Due to the small concentrations of ﬂuorescent dyes, the
physical properties do not change signiﬁcantly. Therefore, the thermal and ﬂow behavior

of the solution with ﬂuorescent dyes is the same as the one without ﬂuorescent dyes.

 

 

 

 

 

 

 

 

 

3o - . - e . . . . - . LL -
l
/ 75:: % '__-_-_- ___—._ E
25 ’ / (a 37.3’ V’
A /e o”
E ,9’
E. 29’
c 20 . 48 ,
7‘; ﬂ
2 l ,3/
5' 15 ~ /
G)
g .
3 v — - - v With 5x10'7 moi/lit of Fluorescein
E 10 . and Kiton Red pH=7.8
O!
I 13 - - - -1:l Lum et. al. (2001) trial#2
5 _ o — — o Lum et. al. (2001) trial#1
o r" i A A . A A r A A A A A A A A . A A
0 20 40 60 80 100 120

Time (min)

Figure 5—1: Height of mushy region vs. time

55

As mentioned before, one of the interesting ﬂow features of the solidiﬁcation
processes of ammonium chloride solution is the formation of the ﬁngers and the plumes.
In order to characterize the detailed temperature ﬁeld of these features, the LIF technique
was used to obtain the temperature map of a plume in the test section. The imaged area is
2.5 x 1.9 cm2 and located above the second nucleator on the ﬁrst row (Figure 5-2). The
imaged area was selected above a nucleator because, based on Wirtz (1998) observation,
a plume would form above it. The bottom left comer of the imaged area is at (18mm,
11.71mm, 22.5mm). The origin as shown in Figure 5-3 is located at the front bottom left
comer of the test section. The spatial resolution of the measurement in the plane of
illumination is, therefore, 40 um per pixel. The exposure time used in this case was 15

ms.

 

Size of the Nucleators
1.59mm x 1.59mm x 3.18mm

‘
10 cm \ Quartz

2.25cm

 

 

 

8.9 cm

Figure 5-2: The location and size of the imaged area

56

89 mm

 

A

+
11.11mm 11.17mm
H H

I 11.71mm

a a J 1r
Y I 14.29mm
lmaged area T T T

\-11¥'=éti=+

Origin (0,0,0)/v Va
X

 

 

52mm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5-3: The location of the origin and the imaged area

Temperature maps corresponding to this imaged area during the solidiﬁcation
process at different times are shown in Figure 5-4 (a-l). The temperature maps are
presented in three different ways. The ones in the left column (Figure 5-4 a,d,g and i)
show the instantaneous temperature maps of the plume. The ones in the middle column
(Figure 5-4 b,e,h and k) were obtained from averaging ten successive intensity images in
time (300 ms). The last columns on the right (Figure 5—4 c,f,i and l) are a result of
ﬁltering in space and were obtained from ﬁltering the time averaged temperature maps
(middle temperature maps) using Wiener method (8x8 pixels). The color bars display
temperature values between 4°C to 24°C.

At t=17 min there are four ﬁngers in the imaged area and one of them seems to
have lower temperature than the rest of the ﬁngers (the third ﬁnger from the left above
,1.5cm). This ﬁnger is right above the described nucleator and will become a plume after

t = 20 min. Plume has a signature characterized by its temperature. Its temperature is

57

cooler than the surrounding ﬂuid. The reason for not seeing as many ﬁngers in the
temperature maps as in the shadow graph technique is because, in the shadow graph
technique the ﬁeld of view is integrated across the depth of the test section; whereas, in
the LIF technique the resultant temperature maps are obtained from a single plane (the
thickness of the laser sheet is small).

At t=30 min while the plume strengthens, adjacent ﬁngers weaken and continue to
decline in number. The temperature of the plume is also cooler since the mushy zone has
grown (1.5cm in height) and it is getting close to the bottom of the imaged area (0.75 cm
below the imaged area).

At t=40 min three of the four ﬁngers subside and only one ﬁnger survives as a
plume. The mushy zone height is about 1.8 cm and is reaching towards the bottom of the
imaged area (0.45 cm below the imaged area). The missing portion of the plume on the
top portion of this temperature map is due to the helical motion (Appendix C) of the
plume, causing the center of plume to move out of the illuminated sheet.

At t=60 min, one distinct plume can be observed. At this time the mushy zone is
right below the imaged area and there is a layer of cooled liquid (thickness of 0.3mm)
right above the mushy zone around the plume exit. The feature on the right side of the
plume is speculated to be a ﬁnger that is about to form. At this time the temperature of
the plume at the exit of the mush is about 78° C and the mush interface has a temperature

of 8.40 C.

58

. . Ave e of 10 'ctures and

Average of 10 pictures With ﬁligred in 5;“ using

the averaging time of 300 ms Wiener method (8x8 pixels)
T

An instantaneous picture

138-

141-

047—

   

Temperature profile along
which temperature data are
extracted in Figure 5-5

lmaged area

1.88-
1.41—
50.94-

047—

   

(d)

Imaged area

 

Figure 54: Temperature maps corresponding to the imaged area during solidiﬁcation
process

59

. . Average of 10 pictures and
Average of 10 pictures wrth ﬁltered in space using

the averaging time 0‘ 30° "'5 Wiener method (8x8 pixels)
'r ("C)

An instantaneous picture

1.88- . . _22

   
 
     
 
 
  
    
   

1.41—
50.94-
0.47—

0 - I I .1 1 I
0 . . . . D 0.5 1 1.5 2 2.5
cu] cm

Imaged area

Vertical lines along which
temperature data are
extracted in Figure 5-8

1.88 —
1.41—
E o.s4 —

0.47 '

  

Figure 54: Temperature maps corresponding to the imaged area during solidiﬁcation
process

60

The temperature proﬁles along a horizontal line on the laser sheet at different
times are extracted in Figure 5-5 in order to measure the temperature difference across
the plume and understand how cold the plume is compared to its surrounding ﬂuid. The
location of this line is shown in Figure 5—4 (a) and is 2.6 cm above the cooling plate along
H = 0.3 cm. It is clear from these proﬁles that the location of the ﬁnger that later becomes
the plume does not change during the solidiﬁcation process (minimum peak always
remains at X = 1.5 cm). It seems that at t = 25 rrlin the second ﬁnger from the right had
moved out of the plane of illumination because the temperature proﬁle is ﬂat; however, it

reappears later on the image plane.

 

e-—--e t=60min

 

24 ' ' ' ' ' ' + — - + t=50min
A — A t=40min
22 e — - ~e t=30min

v—--V t=25min
Cl-—--Cl t=20min
20 o—-—o t=17min

 

 

 

T (C)

 

 

0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
X cm
Figure 5-5: Temperature proﬁles along the horizontal line shown in Figure 5—4(a)

(average of 10 consecutive pictures with the averaging time of 300 ms, y = 2.6cm from
bottom of plate)

61

Figure 5-6 shows the same temperature proﬁles but for spatially averaged images
of the time averaged temperature maps. This ﬁgure shows smoother temperature proﬁles
due to the spatial averaging. As mentioned before, averaging reduces the error by a factor
of the inverse square root of the number of averaged images or number of averaged
pixels. Space averaging uses a pixelwise adaptive Wiener method based on statistics
estimated from a local neighborhood of each pixel. Matlab’s built in routine was used for
implementing the Wiener ﬁlter. The performance of the ﬁlter depends upon the size of

the NxM local neighborhood. Larger block size results in a more smoothed image;

 

20.0

 

 

e—--e t=60min
v—--v t=40min
15.0- U—---Cl t=30min
O——O 1: 17min

 

 

 

 

T (°C)

 

 

 

X (cm)

Figure 5-6: Temperature proﬁle along the horizontal line shown in Figure 5-4(a) (y =
2.6cm from bottom of plate, average of 10 consecutive pictures with the averaging time
of 300 ms and averaged in space, 8x8 pixels)

62

smaller block size results in a relatively sharp image. The local mean and the variance

around each pixel is estimated using

1
WW Io,d(n,.n2) (5-1)
nl,n2
l
aZ=—— 120/d(’11,"2)-.112 (5-2)
NM
nl,n2
2 2
a —v
[new("1’"2)=iu+—3_'—(lold(nlrn2)_.u) (5-3)
0'

where v2 is noise variance. n, and n2 represent the row and column numbers. N and M
represent the total number of pixels in each row and each column. Iold(111,n2) is the
intensity value of a given pixel in the image and Incw(n1,n2) is the new intensity value of
this pixel after ﬁltering. Usually, if the noise variance is not given, the average of all the
local estimated variances calculated from equation (5-2) is taken as default value.

Figure 5-7 shows the temperature distributions along a vertical line on the plume
and along a vertical line adjacent to the plume at t = 60 min and t = 17 min extracted
from Figure 5-4 (1) (see Figure 5-4 (i) for the location of these lines). At t = 60 min, the
mushy zone is right below the imaged area and the temperature of the plume is very
close to the temperature of the adjacent ﬂow at the location where the plume exits from
the mushy zone. At this time there is a cold layer of ﬂuid above the mushy layer (see
Figure 5-4 (1)) and a steep temperature gradient can be observed in this layer (Figure 5-7

from H = 0 to H = 0.6cm on the black curve, H is measured from Mush-melt interface).

63

 

 

 

 

 

 

 

 

 

 

l‘ - 1‘ e t=60min on the plume
15 v t=60min adjucent to the plume
A o t=17min on the finger
a o t=17min adjucent to the finger
._ 13
11
A4
9Luanil-nanupan—--———-—"-—
7 i
0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

H (cm)

Figure 5-7: Temperature Proﬁles along the vertical lines shown in Figure 5-4(j) (The
location of the origin (H20) is at the bottom of the temperature map)

5.0

 

4.5

4.0 :1 t=60min
o t=17min

3.5
3.0
2.5
2.0

ATCC)

1.5
1.0 '

 

0.5
0

 

 

 

0.2 0.4 0.6 0.8 1 .0 1 .2 1.4 1.6
H (cm)
Figure 5-8: Temperature difference AT between vertical lines shown in Figure 54 (j)

(The location of the origin (H20) is at the bottom of the temperature map)

64

Figure 5-8 shows temperature difference AT between these two lines at t = 17 min
and t = 60 min. The maximum temperature difference is about 2.7 °C and occurs when
the plume is formed. The temperature difference right at the exit of the mushy zone
(H=0mm and t=60min) is about 0.8 °C.

To understand the temperature variation with time above the mushy zone, the
whole ﬁeld temperature maps at different times have been obtained by Pulnix cameras
over a much larger area above the ﬁrst row of nucleators (Figure 5-9). The imaged area is
8 x 6 cm2, and the bottom left corner of the image has a coordinate of (0.4mm, 11.71mm,
3mm) with respect to the origin. The spatial resolution of the instantaneous measurement
(with no ﬁltering in space) in the plane of illumination is, therefore, 125 um per pixel.

The results are shown in Figure 5-10.

1‘ 89 mm

4’
11.11mm 11.17mm
H H

1L r as J:

Y I 14.29mm 52 mm

 

 

 

lmaged area

Origin (0,0,0)/v >

 

 

 

 

 

 

 

 

 

 

 

Figure 5-9: The location of the origin and the imaged area

65

 

 

 

 

1:
cm cm
(c) (D

Figure 5-10: Whole ﬁeld temperature measurement (average of 4 successive intensity
images and averaged in space, average of 8x8 pixels )

66

cm

cm

cm

 

 

 

6 -. , . 6 _
f _' " 18-16mm =30min H20
6 ‘ ' 5 ' 1e
4 16
3 .‘14
12
2 10
8
1 -
6
o 'l 4
0
cm cm
(s) (i)
T (°C)
6 -' . 6 2' . n”
t = 20mm ‘ t = 40mm 20
5 ‘ " 1e
4 .16
~ 14
3 12
2 10
8
1 6
o l l l I l l l l | o I l l i l T 7 I 'ﬁ T" l 4
o 1 2 3 4 5 6 8 o 1 2 3 4 5 e 7 a
CH] cm
0!) (k)
T (“O
6 . . 6 . 22
t = 26mm ‘ t = 50min . .20
5 ~ _
18
4 . 16
14
3 _
12
2 ‘ 10
1 8
6
o " ' ' I ' I ' ‘ ' ‘rr‘rr‘rru l fkrur 7*‘1’*‘ I "—1
1 2 3 4 5 5 8 0 o 1 2 3 4 5 e 7 8 ‘
cm £111..
0) (1)

Figure 5—10: Whole ﬁeld temperature measurement (average of 4 successive intensity
images and averaged in space, average of 8x8 pixels )

67

It should be noted that the red solid region on the bottom portion of the
temperature maps does not represent the thickness of the mushy layer. The mushy layer is
about 4 or 5 mm below the interface of the red solid region because the laser sheet was
always kept 4 or 5 mm above the mushy layer to avoid reﬂection of the ﬂuorescent light
off of the mushy layer onto the imaged area. Therefore, the red solid region represents the
mushy zone plus the dark area below the laser sheet.

Within the ﬁrst 4 minutes of applying coolant to the bottom heat exchanger, no
crystals form. However, as seen in Figure 5-10 (b), the temperature of the ﬂuid close to
the bottom plate corresponding to 26% wt concentration of ammonium chloride, which is
186° C, is well below the liquidus line shown in Figure 2-1. This liquid near the bottom
plate is subcooled. At t=6 min onset of solidiﬁcation takes place and some dendritic
crystals begin to form on the nucleators. Within another 2 minutes (at t = 8 min), the
surface is covered with a crystalline mush about 5 mm thick and the small ﬁngers and
their temperature characteristics are vigorous. The rapid growth of the mushy layer is
because of the existence of substantial ﬂuid undercooling. This is qualitatively in good
agreement with the results obtained by Neilson and Incropera (1993) using numerical
analysis. Their results were presented in terms of wavy isothermal lines near the mushy
zone at initial stages of the solidiﬁcation process (signature of the ﬁngers).

Between t = 8 min and t = 50 min, the neighboring plumes compete for the supply
of water rich ﬂuid from within the mush surrounding and the ﬁngers start to decrease in
number. At t = 50 min all ﬁngers have subsided and four vigorous plumes can be seen.
These plumes are located right above the nucleators and remain there until the end of the

experiment.

68

All temperature maps presented up to this point were taken using two 8-bit Pulnix
cameras. As mentioned before in the noise analysis section (3.1.7), using Pulnix cameras
resulted in 08°C uncertainty in instantaneous temperature measurement (with no ﬁltering
in time and space). The two PixelFly cameras, with described speciﬁcations, were used to
carry out the rest of the experiments because of their better noise characteristic and
resolution.

A smaller region above a nucleator was selected for temperature measurement in
order to better characterize the temperature of the ﬁngers (Figure 5-11). Figure 5-12
shows temperature maps of the solution during the solidiﬁcation process using new
Pixelﬂy cameras over this imaged area. The imaged area is 3 x 2.2 cm2 and located above
the second nucleator on the second row. The bottom left corner of the image is at (31mm,
26mm, 7mm). The spatial resolution of the instantaneous measurement (with no ﬁltering
in time and space) in the plane of illumination is, therefore, 21 um per pixel. The origin

as shown in Figure 5-11 is located at the front bottom left comer of the test section.

A

89mm ll.llmm11.l7mm

4 D
H H

 

 

A
I 11.71mm

W *1

 

Y 14.29mm

 

lmaged area

 

 

 

 

 

 

 

 

 

 

 

1 r 11,...

Origin (40,0.O)//v >
X

 

Figure 5-11: The location of the origin and the imaged area

69

 

1.5 2 2.5

         

Fin er above cm
the incleator (c) (d) T (°C)
22
2“ t = 15min 2* . t = 25min H20
-18
1.5—1 1 5 . j16
; E ‘~ 14
u 1 - 9 1 12
10
0.5- 0.5' 8
6
0- . 0 - . . 4
0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3
cm cm
(1:) (D

Figure 5-12: Temperature maps of the imaged area (3 x 2.2 cmz), averaged in time (4
images) and averaged in space (8x8pixels)

7O

      

0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3
cm cm

(g) (b)

Figure 5-12: Temperature maps of the imaged area (3 X 2.2 cmz), averaged in time (4
images) and averaged in space (8x8pixels)

These images show the temperature characteristic of the ﬁngers at initial stages of
the solidiﬁcation process. At t = 5 and t = 7 min, temperature maps show simple diffusion
of the temperature into the solution and no temperature characteristic of the ﬁngers can
be seen, even though the bottom plate is entirely covered with dendrites. Since the
imaged area is 7 mm above the bottom plate, the ﬁngers are short in length and small in
velocity at the early stages; therefore, the temperature characteristics of ﬁngers don’t
show up in the temperature maps. Later in time (t = 9min and t = 11min) the ﬁngers can
be seen in the temperature maps. It seems that the ﬁnger, which is formed above the
nucleator at this stage, is more pronounced because of a higher solidiﬁcation rate around
the nucleator. Due to the formation of the plume out of the laser sheet, the temperature
characteristic of the plume cannot be seen clearly in the temperature maps; however, the
shadow of the plume is presented in the Figure 5-12 (h) above X = 1.3 cm. It should be
noted again that the red solid region on the bottom of the temperature maps represents the

mushy zone plus the dark area below the laser sheet.

71

Chapter 6

Comparison between numerical results and LIF results

In the literature, the issue of the temperature ﬁeld in and around the plumes has
not been the topic of many studies. One reason is that there has not been an existing
measurement tool to measure in-situ temperature quantitatively. The task of this work is
to use the measured thermal boundaries of the plume and predict the temperature
distribution across the plume at different heights right above the mushy zone with
numerical simulation. The results from this simulation will be compared with LIF
temperature data. Hellawell er al. (1993) explained in their study the idea of an analytical
approach which described the velocity proﬁle associated With plumes. Following that
work, Wirtz (1998) obtained the velocity proﬁle by assuming a balance between
buoyancy and friction forces in the momentum equation using appropriate boundary
conditions. In this section, the energy equation will be solved numerically, based on some
assumptions, and the data of this simulation will be compared to the results of the LIF

experiment.

6.1 Assumptions

In order to solve the energy equation, the following assumptions are made
1) The flow is steady (not time dependent). This assumption is valid late into the
experiment when the velocity and temperature variations are very small (t >

60min).

72

2) The ﬂow is assumed to be one dimensional flow (only one component of
velocity Vz exists, therefore it is fully developed (no entrainment, Wirtz
(1998)).

3) The plume is moving upward on a straight line. This assumption is valid for
regions very close to the mush-melt interface.

4) The physical properties are assumed to be constant.

5) Average concentration across the plume is constant along the plume. Since
the Lewis number is large (small solutal diffusivity), the plume retains its
compositional identity.

6) Symmetry around 2 axis.

6.2 Governing equations

The governing equations for the ﬂow shown in Figure 61 can be written as

Continuity:

O 0
an+V +3VZ =0—->Vz=f(r) (6-1)
3r r dz

Assuming the ﬂow to be one dimensional dictates that Vz = f(r); therefore, the ﬂow is
fully developed. Velocity proﬁles of a plume at different heights obtained by Lum (2001)
using the MTV technique showed that the velocity proﬁle of the plume near the mush-
melt interface for short distances (3mm) along the plume does not change with height

(Figure 6-2). It is assumed that these results are valid for longer distances (1.1 cm).

73

Thermal boundary

 

  

 

 

 

‘r = R = 3mm (location 6f
thermal boundary)

Figure 6-1: Schematic of the plume exiting the mushy zone

Velocity (mm/sec)

0— »- —-- Line 7 (~25.6mm from the base plate, ~ 6.6mm from the solidiﬁcation front)
.__ —— -v Line 5 (~24r1mm from the base plate. ~5.1mm from the solidiﬁcation front)
a ------ a Line 3 (~22.5mm from the base plate, ~3.5mm from the solidiﬁcation front)

 

Length (mm)

Figure 6-2: Velocity Proﬁle of the Plume at different heights at t = 60 min (Chee Lum
2001)

74

Momentum:

Even though the result from this section is not used in this numerical analysis, the
momentum equation will be simpliﬁed to show how Wirtz (1998) obtained the ﬁnal
simpliﬁed differential equation for the velocity proﬁle of the plume. Using the
Boussinesq approximation (last two terms in eq (6-2)) and assuming asymmetric flow,

the z-momentum equation can be written as

0 0 0

v a 82v- 18v aZZi
v —Z- V724: ~' ——Z Z T—Too C—Coo 6-2
A, + z {arz +r 8r + 22 +gﬂT( )+g,BC( ) ( )

The last two terms in equation (6-2) show how the buoyancy forces, which drive the

 

 

plume upward, are related to temperature and concentration differences. Br and [3c are the
volumetric thermal and solutal expansion coefﬁcients. These thermodynamic properties
of ﬂuid provide a measure of the amount by which the density changes in response to
changes in temperature and concentration under constant pressure.

From continuity Vr = O and 8V) /82 = 0. Since Br is 10 times smaller than BC for
ammonium chloride solution and AT z AC (AT z 2°C, base on our ﬁndings and AC 2 2%
wt, speciﬁed by Hellawell et al. 1993), the thermal buoyancy force can be neglected
compared to the solutal buoyancy force. Therefore, the momentum equation can be

simpliﬁed as

183V

—_ __.£ = _ -
Vr[dr[r 3r D g'BC(C C00) (63)

75

where BC is the solutal expansion coefﬁcient and (C-C...) is the concentration difference
between the plume and the surrounding ﬂuid. Since the solutal diffusivity is very small

(aC = 1.3x10'9 mzs'l), one can conclude from the species equation a uniform

concentration across the plume, and the right term in the above equation is a constant.
Therefore, the velocity VZ can be obtained by integrating the above equation. Wirtz
(1998) used the exact same equation to obtain the velocity proﬁle of the plume by using
some experimental results and appropriate velocity boundary conditions. The velocity
proﬁle resulting from the above differential equation is not parabolic since the buoyancy
term (C-Cm "~" 0) outside of the plume is equal to zero (Wirtz, 1998).

In this study the analytical velocity proﬁle obtained from the integration of the
above equation cannot be used since the exact value of (CC...) is unknown. However, the
velocity proﬁle obtained experimentally by Lum (2001) will be used to solve the energy

equation in the next step.

Eneggy equation:

Assuming axially symmetrical ﬂow, the energy equation can be written as

 

 

0
3]“ ar 3% 1 ar 3% (64)
V’a_r+VZE:a[a,2 "We—N 3.52]

Neglecting conduction along the plume in the z direction, the energy equation can be

written as the following:

V2 (r)

—+

31. BZT 191 (6-5)
82- 3,2 rar

76

where a is the thermal diffusivity of the ammonium chloride solution. This partial
differential equation can be solved numerically by knowing the boundary conditions and

velocity proﬁle Vz(r) that was obtained by Lum (2001) experimentally.

6.3 Boundary conditions

Boundary conditions for the flow ﬁeld shown in Figure 6-1 can be written as

T=T(r) @ z=0
T=T(z) @ r=R

aT_

— 0 @ =0
Br r

R is the distance between the thermal boundary and the center of the plume. Figure 6-3
shows the temperature map of the plume right above the mushy zone at t = 60 min.
Temperature proﬁles T(r) and T(z) are extracted from this temperature map. The location
of the imaged area and the dimensions (2.5 x 1.9 cm2) of this temperature map were
discussed in the previous chapter (Figure 5-4 (1)). The locations of the corresponding
boundary conditions are also shown as dashed lines. The vertical thermal boundary is
placed at a location where the horizontal temperature proﬁles of the plume become ﬂat
(3mm away from the center of the plume). The temperature along the horizontal line,
found experimentally at z = 0, is T = 8.40 C, except in the plume region where T = 7.80 C.
The temperature proﬁle, found experimentally along r = 3mm, is shown in Figure 6—4. A
second—order polynomial function is used to curve ﬁt the temperature data. Velocity Vz(r)

is found by curve ﬁtting a velocity data set in Figure 6-2 obtained by Lum (2001)

77

450

 

  
 
 

 

”-5 W T = 1.717823 - 5.993822 + 7.64542 + 8.2219
12 . R2 = 0.9896
11.5 i

0 Thermal Boundary Proﬁle

 

 

:3 10.5 at r = 3mm
" 1° ‘ —Poly. (Thermal Boundary
9.5 _ Profile at r = 3mm)
9 ..
3.5 I
8 T T T l l T
o 0.25 0.5 0.75 1 1.25 1.5
2 (cm)

Figure 6-4: Measured temperature proﬁle plus polynomial ﬁt along the vertical line at
r = 3mm (3.5 mm above the mushy zone).

78

6.4 Results and discussion

Using Euler’s method, the energy equation was solved numerically with given
boundary conditions and the velocity proﬁle. Figure 6-5 shows the comparison between
the measured and calculated temperature proﬁles of the plume along the center line. As
can be seen, the measured and calculated temperature proﬁles are in good agreement. The
only unknown parameter in the energy equation is the value of thermal diffusivity of the
ammonium chloride solution (a), which was assumed to be constant. The thermal
diffusivity of the 26% wt ammonium chloride is about a = 1.45 x 10'7 mzls. In Figure
6-5, temperature proﬁles of the plume at the center line are plotted for two different
values of a (1.4 x 10’7 mz/s, 1.7 x 10’7 mZ/s). As can be seen the temperature proﬁle is not
very sensitive to the value chosen for a and both proﬁles are in good agreement with the
experimental result. Figure 6-6 shows the comparison between measured and calculated
temperature proﬁles across the plume at different heights. The slight deviation of the
temperature proﬁle for positive r is due to the fact that on the right hand side of the plume
(seen in Figure 6-3), a ﬁnger was about to form in the plane of the measurement.
Therefore, the measured temperature values of the plume are lower compared with those
of the calculated values. The overall agreement between measured and calculated
temperature proﬁles (from a simpliﬁed model) is good. These results show that the
temperature proﬁles of a plume can be obtained for short distances along the plume using

the described simpliﬁed model if appropriate boundary conditions are given.

79

. Temperature of the boundary
(used at 3.0. 0 r=3mm,Fig 6-4)

- Curve titted temperature of the
boundary

It Measured temperature at the
center line

1 Calculated temperature at the
center of the plume a=1.7x10'7mzls

- Caculated temperature at the
comer 0f the plume a=1.4x10'7m2/s

 

0 0.25 0.5 0.75 1 1.25 1.5
z(cm)

Figure 6—5: Comparison between measured and calculated temperature proﬁles at the
center of the plume

o Calculated(z=0.31cm)

I |Veasured(z=0.31cm)

‘ Wasured(z=1.1cm)
x Calsulated(z=1.1cm)

T (°C)

      

-0.005 -0.009 -0.001 0.001 0.003 0.005
r (m)

Figure 6-6: The comparison between measured and calculated temperature proﬁles
across the plume at different heights

80

Chapter 7

Controlling unidirectional solidification processes using nucleators

As discussed in previous chapters, the LIF technique in combination with
nucleators (for one particular arrangement of the nucleators, Wirtz, 1998) was used to
quantify the temperature maps of a plume during the solidiﬁcation process. The objective
of this study is to investigate the effects of the arrangement and size of the nucleators on
the plume structure and solidiﬁcation process.

Quantitative measurements of the velocity proﬁles and temperature maps will be
made using described diagnostic techniques to enhance our understanding of the effect of
these arrangements on ﬂow structures during the solidiﬁcation process. A buoyancy-
induced ﬂuid ﬂow, which is primarily responsible for most forms of macro-segregation
(chimneys), is not easily controllable. If left uncontrolled, natural convection will
contribute to nonuniform distributions of alloy constituents and grain structure in casting.
Materials with acceptable defects can be produced only by trial-and-error, and their
acceptability is determined by costly inspection. In this chapter, it will be shown that a
relatively large area free of chimneys in the ﬁnal product of the solidiﬁcation process can
be obtained by placing nucleators in a certain arrangement. Quantitative measurements of
velocity ﬁelds and temperature maps of the solution were made for this arrangement to

better understand the ﬂow structure above this area.

81

7.1 Effect of size and arrangement

The shape of the test section was essentially described in previous chapters and
consisted of 1/4" quartz glass measuring 52 x 89 x 100 mm placed over a stainless steel
base plate (430 stainless steel). Small nucleators measuring 1.59 x 1.59 x 3.19 mm in size
and big nucleators measuring 3.19 x 3.19 x 3.19 mm in size were made of Neodymium
rare-earth magnets. Magnets were chosen to be nucleators so that they could be arranged

and placed easily on the stainless steel bottom plate.

8.9 cm 8.9 cm

5.2cm 5.2cm

   

8.9 cm 8.9 cm

 

5.2cm 5.20m

   

(C) ((0
Figure 7—1: Different arrangements. (a) First arrangement with small nucleators, (b)

Second arrangement with small nucleators, (c) First arrangement with big nucleators and
(d) Second arrangement with big nucleators

82

To examine the effects of the size and arrangement of the nucleators on the
solidiﬁcation process of ammonium chloride, two different arrangements were used in
the following experiments. The ﬁrst arrangement with small nucleators, as shown in
Figure 7-1(a), is the same as that used by Wirtz (1998) in his experiment. A second
arrangement with small nucleators as shown in Figure 7-1(b), is used with that of Wirtz
(1998) for the purpose of comparison. Figure 7-1(c) and Figure 7-1(d) show the ﬁrst and
second arrangement with big nucleators.

A detailed study of the general features of the solidiﬁcation process of the
ammonium chloride has already been described in the second chapter. Four minutes into
the solidiﬁcation process, small ﬁngers started to form around the nucleators and could
be seen rising. This was true for all nucleator arrangements. In the case of the ﬁrst
arrangement with small nucleators (Figure 7-1[a]), eleven chimneys and plumes were
formed above the nucleators as expected. This is consistent with Wirtz’s (1998)
observation.

Figure 7-2 shows the top view of the mushy zone. The white region is the surface
of the mushy zone and the dark spots are the chimneys. As can be seen, the eleven
chimneys (marked with red circles) were formed above the nucleators. The second
arrangement with small nucleators exhibited different behavior of the ﬂow compared to
that of the ﬁrst one, even though they were only slightly different. Not all the chimneys
and plumes formed above the nucleators in this arrangement (Figure 7-1[b]). As seen in
Figure 7-3, four out of the twelve chimneys (marked with blue circles) formed randomly

in the test section. Even though the two arrangements are only slightly different, the

83

results turned out to be completely different. These simple tests illustrated that the

arrangement of the nucleators plays an important role during the solidiﬁcation process.

 

Figure 7—2: Top view of the mushy zone for the case of ﬁrst arrangement with small
nucleators (t = 120 min)

 

Figure 7-3: Top view of the mushy zone for the case of second arrangement with small
nucleators (t = 120 min)

84

By keeping the same arrangement (second arrangement) but using the big
nucleators (Figure 7-1 (d)), plumes and chimneys could be forced to form above the
nucleators. Figure 7-4 (a) shows the location of these chimneys and, as can be seen, they
were well arranged above the nucleators. This experiment clearly showed that with a
bigger nucleator, more perturbation at the location of the nucleator is induced and,
therefore, a plume tends to form at that location. This can be seen clearly in Figure 7-4
(b). As shown in the early stages, ﬁngers that are formed at the mush-melt interface
above the nucleators seem to be stronger and thicker than the rest of the ﬁngers. Chen et
al (1994) concluded that plume convection is possible if a vigorous enough salt-ﬁnger
convection is present along with a mushy layer of large permeability. Sample and
Hellawell (1984) reported that they could create a new plume, and from that a new
chimney, by lowering down an open capillary to within 1 to 2 mm of the growth front
and extracting some liquid up the tube. These ﬁngers behave very similar to that of the
capillary tube. Since these ﬁngers are stronger, they entrain more liquid at the mush-melt
interface, creating a convective circuit within the bulk liquid and interdendritic liquid. It
should be noted that these stronger ﬁngers are formed above the nucleators due to the fact
that the solidiﬁcation rate is higher around these nucleators. As mentioned before, these
nucleators are made of metallic alloys. These nucleators act as thermal ﬁns and they
enhance heat transfer from the surrounding ﬂuid to the bottom plate, therefore enhancing
the solidiﬁcation rate locally around them. These ﬁngers also look thicker in comparison

to those above the small nucleators (Figure 2-6).

85

 

Figure 7-4: (a) Top view of the mushy zone for the case of second arrangement with
big nucleators(t = 120 min), and (b) Front view (t = 10min)

86

7.2 Effect of spacing

To examine the effect of nucleator spacing on the plume structure, two different
arrangements were used in the following experiments. Either one pair (Figure 7-5 [a]) or
two pairs (Figure 7-5 [b]) of nucleators were used. In the case of two pairs, the pairs of
nucleators were placed far enough apart (h > 3cm) so that one pair did not inﬂuence the
other. Different experiments were carried out by changing the spacing, L, between the
nucleators. It was generally observed that when the two nucleators were close to each
other, the plumes generated above them were always phase locked with 180° phase
difference (Figure 7-6). The reason for phase locking was due to the coupling between
nearby jets. Entrainment of ﬂuid and counter-propagating shear ﬂow produce dynamical
instabilities, and results in synchronization of phases of the nearby plumes (Dombrowski
et al. 2004). Based on experimental results obtained by Dombrowski et al. (2004), it is
speculated that phase locking of the plumes (with 180° phase difference) occurs when the
two adjacent plumes have the same Reynolds number, and they are identical. The
temperature and velocity proﬁles across these phase locked plumes, found

experimentally, will be shown later.

Next
adjacent
plume

 

One pair (a) Two pairs (b)

Figure 7-5: (a) One pair of nucleators, and (b) Two pairs of nucleators

87

Two pairs of phase
locked plumes

 

Figure 7-6: Phase locking of two nearby plumes, test # 7 (180° phase difference)

Some of the experimental results are summarized in Table 7-1 with the ﬁrst and
the second columns containing the test number and the size of each pair. The third
column indicates the distance between nucleators of each nucleator pair. The fourth
column indicates whether two plumes were generated or only one was formed on each
pair of nucleators. The ﬁfth column shows whether the two generated plumes were phase
locked or not, and the sixth column illustrates the time the phase locking occurred (before
this locking time, two ﬁngers or two plumes existed with no clear relationship between
their phases). The last column represents the shortest distance (d) between a next
adjacent plume and one of the plumes formed on the pair of nucleators (Figure 7-5[a]). It
should be noted that the two adjacent plumes are phase locked with 180° phase difference
as long as a third randomly formed plume is far way from them; otherwise, there would
be no clear relationship between their phases. It should be noted that every single

arrangement was carried out four times to make sure that the results are repeatable.

88

Table 7-1: The summary of some of experiments carried out for pairs of nucleators

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Test Test Distance Final Phase status Time when d
# on apart number of phase locking (cm)
Nucleators L (cm) plumes occurred
(min)
1 A pair of 0.42 l oscillatory 1.2
big ones
2 A pair of 0.52 2 Locked and 30 1.6
big ones 180°
3 A pair of 0.6 2 Locked and 35 1.21
big ones 180°
4 A pair of 1 2 Not Locked 0.8
big ones
5 A pair of 0.6 1 oscillatory 1.19
small ones
6 A pair of 1 2 Locked and 35 1.31
small ones 180°
7 Two pairs 0.52 2 30 1.4
of big Locked and
ones 0.76 2 180° 30 1.67
8 A pair of 0.46 l 1.24
big ones
A pair of 0.48 1 1.25
small ones

 

From Table 7-1 and other observations, the following results were concluded:

For a pair of small nucleators:

If the distance between nucleators of each pair was less than about 0.6 cm, only

one plume was formed on one of the nucleators. The transition from ﬁngers to plume

formation was either oscillatory or non-oscillatory. In oscillatory mode, initially two

ﬁngers were formed above the nucleators. Later in time, one of the ﬁngers on the ﬁrst

nucleator disappeared while the other one on the second nucleator was still ascending.

89

 

After some time, the ﬁnger that had disappeared grew back again on the ﬁrst nucleator.
This process only repeated itself once or twice. The ﬁnger that survived became a plume
later in time. Figure 7-7 shows the sequence images of the oscillatory mode of test # 5.
Initially, two ﬁngers were formed above the nucleators. Later in time, one of the ﬁngers
on the left nucleator disappeared while the other one on the right nucleator was still
ascending (t = 12 min). After a while (t = 16 min), the ﬁnger that disappeared grew back
again on the left nucleator. At t = 18 min this ﬁnger started to get weaker again and
disappeared at t = 20 min. The ﬁnger that survived became the plume on the right
nucleator.

In non-oscillatory mode, two ﬁngers grew initially and later one disappeared
while the other remained and later formed a plume until the end of the experiment. Most
of the time, for distances in the range of 0.6 cm 5 L S 1.2 cm, two plumes were formed
above the nucleators. If the distance between the next adjacent plume and one of these
plumes was larger than (I = 1.2 cm, then the plumes on the pair of nucleators were always
phase locked with 1800 phase difference and had the same amplitude of oscillation until
the end of the experiment. If another plume randomly formed closer than (1 = 1.2 cm to
the pair of plumes, the phase between the plumes was no longer locked. They were out of
phase until the end of experiment. The coupling of nearby plumes becomes complicated

with the existence of the third plume.

90

 

      

(c?

Figure 7-7: Sequence images of the oscillatory mode. (a) t = 8min, (b) t = 12min, (0) t =
16 min and (d)t= 18 min

For a pair of big nucleators:

The results for pairs of big nucleators are similar to those for small ones, except
that the minimum distance between nucleators that can generate two separate plumes
becomes shorter (L = 0.5 cm). This indicates that the bigger the nucleators are, the closer
they can be brought to obtain two separate plumes. The summary of the conclusions is

written in Table 7-2.

91

Table 7-2: The summarized conclusions

 

 

 

 

 

Big nucleators Small nucleators
3.19 x 3.19 x 3.19 mm 1.59 x 1.59 x 3.19 mm
One plume oscillatory or non-oscillatory One plume oscillatory or non-oscillatory
when when
L505 cm L30.6cm
Two Plumes Phase locked with the same Two Plumes Phase locked with the same
amplitude when amplitude when
0.5cmSLSl.2cm 0.6cm.<_L_<_l.2cm
No relationship between phases and No relationship between phases and
amplitude. They don’t see each other amplitude. They don’t see each other
when when
1.2cmSL 1.2cm_<_L
Not phase locked with different Not phase locked with different

 

 

 

amplitude of oscillation When (1 < 1 cm amplitude of oscillation When d < 1 cm

 

As ammonium chloride solution crystallizes, the height of the mushy zone
increases, which reduces the weight percentage of the solute. The height of the mushy
zone with time for some of the tests in Table 7-1 is provided in Figure 7-8. The height of
the mushy zone at a given time is measured to be the distance from the base stainless
steel plate to the average location of the mush—melt interface. It is clear from this ﬁgure
that all of the experiments carried out had the same solidiﬁcation growth rate. Even
though the spacing and the size of the nucleators is different from one test to another, the
resulting mushy growth rate is about the same for all of them. It should be noted that in
these tests only two or four nucleators were placed on the bottom plate and plumes
associated with them were forced to form above them. The rest of the plumes were free to

form randomly anywhere in the test section.

92

 

 

    
  
  
  
  
    

A
E o Testtﬂ
3 1 5 I TesttH
I A Testtl2
1 x Test“
0 T951115

Lum eta I. (2001)

0 25 50 75 100

t (min)

 

Figure 7-8: Height of mushy zone vs. time

 

 

In order to verify the previous conclusion regarding the phase locking of two

adjacent plumes, an experiment was carried out by placing 7 equally spaced big

nucleators in a row as shown schematically in Figure 7-9. The front view is shown in

Figure 7-10.

1.llcm

 

Figure 7-9: Schematic top view of one row of nucleators

93

 

Figure 7-10: Schematic front view of one row of nucleators

As expected, initially (t = 6 min), some ﬁngers that are stronger (more water rich
ﬂuid) than the rest of the other ﬁngers were formed above the nucleators and can be seen

in Figure 7-11.

 

Figure 7-11: Stronger ﬁngers were formed above the nucleators compared to others
formed at mush melt interface at t = 6 min

94

These ﬁngers became plumes at t = 20 min; however, some remained out of phase.
Figure 7-12 shows these plumes at t = 30 min, where some were out of phase and the
amplitudes were different. Other plumes seen in the test section were formed randomly

(since only seven of the eleven plumes are controlled, the rest will form randomly).

 

Figure 7—12: Plumes were formed above the nucleators (t = 30 min)

At t = 35 min these plumes started to become equal in amplitude, but with 180° phase
difference with respect to each other. This is shown in Figure 7-13. At t = 40 min these 7
plumes are equal in amplitude, but 180° out of phase. They remained phase locked until
the end of the experiment. Figure 7-14 shows this phase locking at t = 70 min. Some of

the randomly formed plumes disappeared and a new one formed after t = 40 min.

95

 

Figure 7-13: Plumes becoming phase locked (t = 35 min)

New randomly
formed plume

Old randomly
formed plume

 

Figure 7-14: Plumes were phase locked at t = 70 min

96

As mentioned before, in the absence of nucleators, the experimental trial would yield
approximately 11 chimneys within the test section. In this experiment, seven plumes were
forced to be formed above the row of nucleators; therefore, the remaining plumes would
be free to form randomly within the test section. Two additional chimneys associated
with these plumes (seen on the left side of the Figure 7-14) were formed randomly within

the test.

Chimneys associated with ,
randomly formed plumes

 

Figure 7—15: Top view of the chimneys

As can be seen clearly from Figure 7-15, 7 chimneys were formed above the row of
nucleators. The reason the chimneys were not exactly in a straight line was due to the fact
that the plume formation could occur at any location around the periphery of the
nucleators. The two chimneys on the left side, which are not in the row, show the

locations of the two randomly formed plumes described in Figure 7-14.

97

7 .3 Obtaining relatively large area free of chimneys

In order to obtain a relatively large area free of chimneys and to push out the

chimneys to the sidewalls, some big nucleators were placed at locations speciﬁed in

 

 

 

Figure 7-16.
2.22 cm
4—>
0.86 cm I l .1: n l
I

 

 

 

 

 

 

 

 

 

 

 

 

 

111* 1

Figure 7-16: Schematic of the locations of the placed nucleators

 

In this case, ten plumes were formed above the nucleators as seen in Figure 7—17. A more
uniform composition proﬁle of the ﬁnal product (free of chimneys) would be obtained
over a relatively large area (6.66 cm x 3.44 cm). In the next chapter the temperature maps
and velocity ﬁelds will be shown to qualitatively conﬁrm this relative uniformity. This is
an interesting result since materials with acceptable defects can be produced only by trial-
and-error process development, or by costly inspection knowing the location of the
defects (chimneys) has obvious economic and environmental beneﬁts. Other researchers
have used “artiﬁcial” means to redirect the formation of chimneys through rotation
(Samme and Hellawell, 1982) or vibration (Garimella et a1, 1995) of the test section. The
advantage of the present use of nucleators in dictating the formation of the chimneys is

that it is less intrusive and more cost effective in implementation.

98

 

Figure 7-17: Top view of the chimneys

Another experiment was carried out by keeping the same number of nucleators
and placing them slightly closer to the side walls (Figure 7-18). With the exception of
one, all of the plumes formed above the nucleators; however, some more plumes were
formed in the middle of the test section (marked with blue circles) as can be seen from
the top view in Figure 7-19. A total number of 13 plumes formed during the solidiﬁcation

process.

2.22 cm
<—>

0.86 cm t

 

Figure 7-18: Schematic of the locations of the placed nucleators

99

 

Figure 7-19: Top view of the chimneys

For this case, placing more nucleators on the periphery next to the other nucleators did
not change the results. Still, some chimneys were observed in the middle of the test
section. This experiment shows how sensitive the results are to the wall boundary
condition and when the nucleators are placed very close to the side walls. The results
presented in this study are valid for the case of 26% wt ammonium chloride solution
cooled from below with a bottom temperature of -l4°C. It is obvious that changing any
physical property of the ﬂuid would affect these results. The size of an area free of
chimneys that one can obtain depends on the pumping effect of the plumes (caused by
buoyancy difference between the plumes and the surrounding ﬂuid) and the permeability
of the mushy zone. More pumping effect of the plumes and more permeability of the
mush could result in a larger area free of chimneys by placing nucleators around the

periphery of that area.

7.4 Average spacing between plumes

As mentioned before, based on our observations and other researchers’ reports,
the average spacing between plumes, in the absence of nucleators, is approximately 1cm.
It should be possible to calculate in a quantitative manner the maximum area of the
mushy zone around the plume that can provide the supply ﬂow of water to the plume.
From that, the average spacing between the plumes would be known.

Figure 7-20 shows a schematic of the proposed model. Since there is a continuous
circulation in the system, it is necessary to identify the pressures that are available to
drive the system. It is assumed that the ﬂow is in steady state condition.

In Figure 7-20, P is the pressure, pH is the bulk density of ammonium chloride
solution, pH is the density of the ammonium chloride solution at the eutectic point at the
bottom plate and pp is the density of the plume at the exit of the mushy zone. The radius
of the chimney is r1, and r2 is the radius of the plume when it exits the chimney. The
radius r2 is larger than r1 due to the expansion of the jet ﬂow at the exit of the mush. The
parameter 2L is the diameter of the source area. H is the height of the container and h
represents the mushy zone height. Referring to Figure 7-20, it can be seen that the driving
force for circulation must come from the total density difference between the plume and
its surrounding ﬂuid. The following equations can be written for this system:

the pressure balance can be expressed in terms of an identity equation

(P6-Pl)+ (PS-P6) + (P3-P5) + (P2-P3) + (Pl-P2) = 0 (7-1)

101

_,
l
I
I
l
l
w:
"I
l
I
l
1

PP
133 113

1111 1111

——-———-—_—-—-—_———-
\
———-————_—_————————_—
\

 

 

 

 

 

 

Figure 7-20: Schematic of the liquid circulation in the system

At the top of the container, the ﬂuid is open to the ambient air. Therefore,

PZzPlzP

(Hm

(7-2)

Since the downward velocity of bulk ﬂuid surrounding the plume is very small, we can

assume that the pressure is dictated by the hydrostatic pressure, therefore
P6 z pBg(H - h) + P1 (7-3)
There is a pressure drop across the mushy zone due to its porous nature; therefore, from

Darcy’s law we have

102

 

h
P5=P6+J'[pE+-p—B—;E—E—z]gdz- -ZQ/Ihz. (74)
0 h ”l "1 lK

where K is the average permeability of the mush, Q the volume ﬂow rate and u is the
viscosity of the ammonium chloride solution (assumed to be a constant everywhere in the
test cell). The second term takes into account the hydrostatic pressure and it is assumed
that the density is changing linearly across the mushy zone. The last term in eqution (7-4)
is the pressure drop across the mushy zone and is obtained by integrating Darcy’s law
across the depth of the mushy zone. Assuming the plume is a ﬂow in a circular pipe, the
pressure drop along the plume in the mush can be found from Poiseuille’s equation (Liu

and Hellawell, 1999)

4

h
P3 = P5— (p5 +szgdz-m (7-5)
0 h ”I

Since the ﬂow rate in the chimney varies from 0 to Q, the Poiseuille equation was
modiﬁed by introducing a factor f, which varies from 0 to 1 in this region and can be seen
in the second term of equation (7-5). The integral of this equation is based on the
assumption that the density of the plume in the mushy zone varies linearly with height.
Assuming the plume is a ﬂow in a circular pipe outside of the mushy zone, the
pressure drop along the plume can be also found from Poiseuille’s equation (Liu and

Hellawell, 1999)

8Qﬂ(H - h)

71724

P2 = P3— ppg(H — h) — (7-6)

 

Substituting all equations into equation (7-1) yields

103

 

h
PBg(H-h)+j[pE+BB—_—p£z)gdz- -2Qﬂh2-
0 h ”(L —I'1 )K

 

h
_ H-
0 h ”I 7172

which reduces to

 

h
(103 -pp)g(H—h)+j1-l)i—p£z]gdz= * ZQ‘th‘

+ 8071014- h) + Sfotlh (,8)
7V2 7V1
the density difference (pB- pp) in equation (7-7) can be written in terms of a concentration

difference as shown in equation(7-8). {3 is the volume solutal expansion coefﬁcient; po is

the reference density; AC is the concentration difference between plume and bulk ﬂuid.

 

_ h _ ,Q/lh, 33le”! 8Q#(H-h)
poﬂAC(H h)+p0,6ACA—ﬂ(L2_r]2)K+ ”14 + ”24 (7-9)

- Qﬂh
ﬂ(L2 — r1

 

- _ h _ 8fQﬂh _ 8Qﬂ(H -h)
2)K _ poﬂAC(H —h)+p0,6ACA ”14 7:724 (740)

From equation (7-10), L can be estimated using available experimental data on
the various parameters need in the model. The following parameters shown in Table 7-3

are used to calculate L.

104

Table 7-3: Parameters used to calculate L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Value Reference
H 10 cm Lum (2001)
h 2 cm Lum (2001)
Ac 4 wt% Liu and Hellawell (1999)
p 1.2x10‘3 mzs'l
p 1000 kg/m3
r1 0.5 mm Lum (2001)
r2 1 mm Lum (2001)
f 0.5
Q 11 mm3/s Lum (2001)
13 2.82“? wt%'1 Liu and Hellawell (1999)
K 2x10'9 m2 Chen and Chen (1991)

 

Using speciﬁed parameters in table 3 results in

This result is in good agreement with meaured average spacing between plumes (1 cm).
This work illustrates that the proposed simple model can be used to predict the spacing
between plumes using available experimental data on the various parameters. It should be
noted that most of the parameters used in this model can be measured easily using
experimental methods. However, permeability K is a parameter that people have had

difﬁculties in measuring experimentally. Keeping all the variables constant, Figure 7-21

2xL = 1.0491 cm

shows the variation of the spacing 2xL with K (average permeability).

105

 

 

 

 

 

10 f l l r T l l l l
9.1 -
.15 1
7 r 1 -
5 " 4
2L (cm)
5 .. .1
4 ~ \ —
\\
\\
3 ~ “ ~
2 _ \\\\ -4
1 l l l l l l l l
o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2 x109
K (m )

Figure 7-21: variation of the distance 2xL with K (average permeability)

This ﬁgure shows that as K decreases (resistivity to ﬂow current increases), the distance
L increases. To have the same pressure drop in the mushy zone, the velocity of ﬂow in
the mushy zone must decrease as resistivity to ﬂow current increases. Therefore, a larger
source is needed to feed the plume.

The average spacing between plumes can also be predicted based on stability
analysis of the system. As described before, linear stability of a mushy layer analyzed by
Worster (1992) in directional solidiﬁcation showed two modes of convection. One, called
the boundary-layer mode, is associated with the compositional buoyancy in a thin
boundary layer above the mush-liquid interface (ﬁngers). The other, called the mushy-

layer mode, is driven by the buoyancy in the interior of the mushy layer (plumes). It was

106

also mentioned that once the mushy layer has become thick enough, it must become
unstable to the mushy-layer mode; and it will do so irrespective of the pre-existence of
the boundary-layer mode (ﬁngers) of instability. In other words, the existence of ﬁngers
above the mush-melt interface does not cause the formation of the plumes inside the
mushy zone. If this is true, then the formation of plumes can be explained in a simpler
way. Imagine a porous layer with thickness of H that has a lower concentration of
solution on the bottom and higher concentration of the solution on the top as shown in
Figure 7-22. The ﬂow in this region can become unstable in the presence of

perturbations.

Co+AC

 

Co

Figure 7 -22: Two dimentional porous layer

The detailed analysis of this ﬂow can be found in Bejan (1995) for a porous layer
heated from below and cooled from above. Since the energy and solutal equations are
similar, the analysis described in Bejan (1995) is also valid for this case. Assuming a
linear concentration distribution across the porous layer, this ﬂow is neutrally stable

when

 

Ra” =

107

and 01 is the wave

where Ra” is the Rayleigh number based on H, Ra H =ﬂgiA—C
v

number of disturbances. K is an empirical constant called permeability, D is the effective
solutal diffusivity of the medium, v is dynamic viscosity, ,8 is the volume solutal
expansion coefﬁcient, and g is gravity.

The above equation says that the assumed disturbance (n,a) is likely to exist,
neither growing nor decaying, if the Rayleigh number is as high as in the above equation.

As Ran increases above zero, the ﬁrst chance of ﬂow convection materializes (minimum

RaH = 0. The minimum value of Rayleigh

 

Ran) at n = l and a = it found by setting 8

number for these values would be Ra H = 39.5 .

As shown in Figure 7-23 and mentioned by Bejan (1995), the disturbance (n = 1,
01 = 7r) represents rolls with square cross-sections; that is, rolls whose horizontal
dimension is equal to the porous layer thickness H. This means the average spacing
between the plumes is more likely to be equal to the mushy zone thickness.

Experimental results obtained by Chen et al. (1994) showed that the onset of
plume convection for different concentration of ammonium chloride solution occurred
when the height of the mushy zone was about 1cm (our experimental observations
confurn their results). Therefore, the average spacing of the plumes based on the above
stability analysis should be 1cm. This is indeed in good agreement with experimental

results that show the average spacing between plumes is approximately 1cm.

108

Co+AC

 

 

 

 

 

 

+———>
H Co

Figure 7-23: Rolls with square cross-sections for minimum Rayleigh number for
neutrally stable cellular convection

109

Chapter 8
Temperature maps and velocity ﬁelds of some of the flow features for

different arrangements of the nucleators

As mentioned before, the reason for phase locking with 180° phase difference is
believed to be due to the coupling between nearby plumes. To understand whether or not
the two adjacent plumes are identical in their features and behavior, the temperature and
velocity characteristics of two phase locked plumes with 1800 phase difference were
quantitatively measured.

It was also proven in previous chapters that it is possible to obtain a relatively large
area free of chimneys and plumes. The velocity vectors and temperature maps of the ﬂow
above this area will be studied to better understand the difference between the velocity
vectors and temperature distribution of the ﬂow above this area and that of randomly

distributed plumes.

8.1 Temperature of phase locked plumes

To understand whether or not the two adjacent plumes are identical, temperature
measurements of the plumes were made using the LIF technique for the cases of big-big
and big-small nucleator pairs as shown in Figure 8-1. The spacing between nucleators
was 1.1 cm. The imaged area is 3 x 4 cm2, and the bottom left comer of the image has a
coordinates of (29.5mm, 26mm, 28mm) with respect to the origin. The origin is located at

the front bottom left comer of the test section. Figure 8-2 shows the location of the

110

imaged area at t = 70 min for the case of big-big nucleators at t = 70 min. The imaged

area was 4mm above the mushy zone at this time.

1.11cm 1.11cm

 

Figure 8-1: Schematic of the location of the nucleators (a) two-big nucleators and (b)
big-small nucleators

70min

t

 
     

lmaged area
3x4 cm2

Figure 8—2: the location of the imaged area. (t=70min)

111

 

0 0.5 1 1 .5 2 2.5 3 3.5 4
cm

Figure 8-3: Temperature map of the plumes at t = 70 min for the case of two—big
nucleators (average of 8x8 pixels)

Figure 8-3 shows a temperature map of two plumes at t=70min. Phase locking
with 1800 phase difference can be clearly seen in this ﬁgure. Since plumes rise vertically
in helical motions, they move in and out of the laser sheet continuously. That is why the
temperature characteristic of the plumes is less pronounced in the upper portion of this
temperature map for heights greater than 3 cm (the temperature of the plumes slightly
fades out in the upper portion). The animation of the temperature maps of the plumes, as
they rise up, has been obtained and saved on an attached CD to this thesis. The duration
of the movie is 5 seconds in real time. Temperature proﬁles of the plumes along
horizontal lines on the laser sheet at different times are shown in Figure 8-4 for both
cases (two-big and big-small nucleators). The locations of these lines are shown in Figure

8-5.

112

e Big-unall nucleators
H=0.36cm

‘ A Big-anall nucleators
H=1.24cm

. I Two big nucleators
H=0.36cm

. I 0 Two big nucleators
V H=1.24CITI

 

 

0 0.5 1 1 .5 2 2.5 3 3.5 4
Width (cm)

Figure 8-4: Temperature proﬁles along horizontal lines for two cases two big and big-
small nucleators

 

Location of the big Location of the big Location of the big Location of the
nucleator nucleator nucleator small nucleator
(a) Two big nucleators (t=70min) (b) Big-small "UCICatOFS (t=70min)

Figure 8—5: Temperature proﬁles along designated lines

113

As can be seen in Figure 8—4, temperature proﬁles of two plumes are very similar
for the case of big-big nucleators, which are shown with green and red dots for different
heights. For the case of big-small nucleators, the plume on the big nucleator was formed
slightly out of the laser sheet (The left plume in Figure 8-5 (b)) and temperature
characteristic of the plume could not be obtained. However, by comparing the
temperature proﬁles of the plume on the small nucleator (case (b)) with that of the
plumes on the big nucleator (case (a)), one can see that they are similar, even though they
were obtained from different experiments.

Temperature proﬁles along indicated vertical lines are shown in Figure 8-6. Since
there is a good agreement in temperature proﬁles, it can be concluded that the

solidiﬁcation processes were similar for both cases.

15

r (°0)

 

Height (cm)

Figure 8-6: Temperature proﬁles along the indicated vertical lines

114

As mentioned before, one of the interesting features of the solidiﬁcation process
of ammonium chloride is falling wisps. In order to obtain a temperature map of these
wisps, the temperature map of the plumes was obtained ﬁve seconds after the image in
Figure 8-3 was taken. During this time plumes had ascended from below; and the bends
had moved slightly upward. Therefore, the temperature characteristic of these wisps
started to appear on the temperature map. Figure 8-7 demonstrates the temperature map
of these wisps. As described by Dombrowski et al. (2004), the complex ﬂow ﬁelds arise
from remarkably simple ingredients. Due to the small solutal diffusivity of anunonium
chloride, the water-rich plumes retained their compositional identity and moved upward.
As the plume ascends into the density stratiﬁed surroundings, the entrained ﬂow around
the plume (jet) builds a conduit in which ﬂow moves upward with the jet. However, as
the heavier ﬂow in the conduit moves upward, it encounters the surrounding ﬂuid that is
less dense (density stratiﬁed surrounding). Therefore, due to the buoyancy effect, the
ﬂow in the conduit starts to move downward at the edges of the conduit. The wisps seen
in the temperature map formed as a result of downward ﬂow in the conduit. Magirl and
Incropera (1993) also described the formation of the wisps in this way: as salt-rich ﬂuid
adjacent to the plume is cooled, it descends as a sheath along the plume. These sheaths
cannot traverse the plume bends (due to shearing force), causing these sheaths to separate
from the plume (wisps) and descend freely. Based on our observation, the formation of
these wisps is a combination of both phenomena described by Dombrowski er al. (2004)
and Magirl and Incropera (1993).

The image of these wisps as obtained from a different experiment using the

shadow graph technique is shown in Figure 8-8.

115

 

0 0.5 1 1.5/’2 2.5 3 3.5 4
Wisp ,’, cm

Figure 8-7: Temperature map of the plumes ﬁve seconds later

 

Figure 8-8: Shadow graph image of the plumes and wisps

Temperature proﬁles along the horizontal lines at different heights corresponding

to Figure 8-7 are shown in Figure 8-9. The temperature proﬁle of each plume has two

116

spikes in it. One spike is related to the plume itself and the other belongs to the wisp
(blue dotted line). The temperature proﬁles of the wisps are not clear at H=l.82cm
(yellow dotted line) because the wisps had fallen and were mixed with the solution. From
Figure 8-9 one can see that the maximum temperature difference between the center of

the plume and the center of the wisp could be as high as 0.5° C.

 

0 0.5 1 1.5 2 2.5 3 3.5 4
Width (cm)

Figure 8-9: Temperature proﬁles along horizontal lines

8.2 Temperature measurement above the area free of chimneys

Up to now, temperature maps of the solution above the nucleators, where the
plumes exist, were obtained and presented. In the previous chapter it was proven that by
arranging the nucleators as shown in Figure 8-10, a relatively large area free of chimneys

was obtained. In order to verify that a more uniform composition proﬁle of the ﬁnal

117

product of the solidiﬁcation process can be obtained with such an arrangement of the
nucleators, an experiment was carried out to measure the temperature of the solution

above this area, which is free of plumes.

2.22 cm
<———>

WM 1 H;
4 / 1-
+4 =—+

Figure 8—10: Schematic of the locationsof the nucleators

 

, lmaged
area

 

 

 

 

 

 

 

 

 

 

 

 

 

The imaged area is 5.4 x 4 cm2, and the bottom left corner of the image has a coordinate
of (17.5mm, 26mm, 5mm) with respect to the origin. Temperature maps at different times
are shown in Figure 8-11. At early stages of the solidiﬁcation process, the temperature
maps are very similar to those obtained above the nucleators in the previous chapters
because ﬁngers exist at mush-melt interfaces for all cases. However, after t = 60 min, the
temperature becomes stratiﬁed and, unlike the previous cases, there is no signature of
plumes in the temperature maps (Figure 8-11 (g)) and (b)). Since temperature is almost
uniform laterally at this time, it is expected to produce a more uniform composition
proﬁle of the ﬁnal product. The velocity ﬁelds associated with this area will be presented

later.

118

 

t = 25min

11.9 1.8 2.7 3.6
cm

(e)

 

Figure 8-11: Temperature maps of the imaged area (5.4 x 4 cm2, average of 8 x8 pixels)

119

 

II 0.9 1.8 2.? 3.5 4.5 5.4 11 0.9 1.11 2.7 3.6 4.5 5.4
cm cm

(8) (b)

Figure 8-11: Temperature maps of the imaged area (5.4 x 4 cm2, average of 8 x8 pixels)

8.3 Velocity measurement around a single plume using Particle Image
Velocimetry (PIV) technique

Detailed and accurate velocity measurements obtained by Lum (2001) for small
regions of some plumes revealed some interesting ﬂow features in and around those
plumes. However, in this section, in order to better understand the ﬂow structure around a
single plume, velocity ﬁelds will be presented that were obtained by using the PIV
technique during the solidiﬁcation process for a larger imaged area.

The PIV images were processed with 50% overlap for enhanced spatial sampling
and 21 x 21 pixel interrogation window and 31 x 31 pixel search window sizes. This
resulted in a vector spacing of 0.259 mm. Overall, the vector ﬁeld map covered an area of
29.3 mm x 21.3 mm. Usually, the ﬂow medium must be seeded with particles, droplets,
or bubbles. However, in this case, particles already existed as impurities in the

ammonium chloride solution and were used for velocity measurements. The size of the

120

impurities or particles in the solution was less that 20 um. Figure 8-12 shows the PIV
image of a plume at t = 120 min and velocity vectors related to this image are shown in
Figure 8-13.

Since the vector spacing is 0.259 mm and the diameter of the plume is about 1
mm, four vectors would fall in the plume area. A problem that one might encounter using
the PIV technique to measure the plume velocity is the lack of particles in the plume as
seen in Figure 8-12. As particles move into the mushy zone, they become nucleation sites
and crystals form around them. As they grow, they attach to the mushy zone and cannot
ﬂow into the chimney, or into the plume from there. If there is a particle in the plume, it
is due to the fact that entrainment takes place as the plume exits the mushy zone and
particles are entrained from the surrounding into the plume. Usually, the number of
particles in the plume is not high enough to get accurate velocity measurements.
Therefore, a larger interrogation window size is needed to include more particles. This

results in averaging the actual velocity of the plume.

 

Figure 8—12: PIV image of a plume at t = 120 min (imaged area is 29.3 mm x 21.3 mm)

121

  
  

25
V(mm/s)
3.5
a— 20 3
2.5
E 2
s.— 1.5
E 15 1
.91 0.5
0 0
I -0.5
10 '1
-1.5
v
5 L
U
5 1o 25 30

   

1 5 20
Width (mm)
Figure 8-13: Measured velocity vectors of the plume at t = 120 min

It should be emphasized that the purpose of these measurements is not to obtain
accurate velocity ﬁelds of the plume itself, but of the surrounding ﬂuid.

Figure 8-13 shows the velocity vectors associated with the imaged area of Figure
8-12. The color bar represents the magnitude of the v-component of the velocity vector.
The height axis is measured from the bottom of the imaged area, not from the bottom
plate. It is clear from Figure 8-13 that as the plume moves upward in a helical motion
(red areas), the ﬂuid moves downward in an opposite helical motion wrapping itself
around the plume. As described before, the downward ﬂow is a result of both thermal and
solutal buoyancy effects. In the case of thermal effect, the ﬂuid in contact with the plume
becomes cooler than the bulk ﬂuid. The cooler ﬂuid has a higher density than the bulk

ﬂuid, causing it to move downwards. In the case of solutal effect, as the plume ascends

122

into the density stratiﬁed surroundings, the entrained heavier ﬂow around the plume (jet)
encounters the lighter surroundings and, due to the negative buoyancy effect, it starts
falling downwards. This results in a maximum downward velocity of -1.5 mm/s. This is
in good agreement with measured maximum downward velocity of the ﬂow obtained by
Lum (2001) and is approximately four times less than the maximum upward velocity of
the plume (6mm/s). It should be noted that since the plume is moving in a helical motion,
it continuously moves in and out of the laser sheet. That is why the upward velocity is
discontinued and replaced by downward velocity vectors. The animation of the velocity

vectors has been obtained and saved on the attached CD to this thesis.

8.4 Velocity measurement above a row of nucleators using Particle Image

Velocimetry (PIV) technique

In order to understand some of the ﬂow features between two phase locked
plumes, a similar experiment to that in the previous chapter (Figure 7-9) was carried out
to obtain whole ﬁeld velocity vectors above the mushy zone and on a row of nucleators
using the PIV technique. The imaged area (8.5 x 6.2 cm2) is 3 cm above the bottom plate,
and it is directly above the mushy zone. A 15 x15 pixel interrogation window and a 21 x
21 pixel search window were used to obtain these velocity vectors. This resulted in a
vector spacing of 0.44 mm. Not all of the plumes formed within the laser sheet. Only ﬁve
of them seemed to form on the imaged plane. Figure 7-14 shows the PIV image of the

solution.

123

 

Figure 8-14: PIV image of the solution at t = 120 min

 

60
3—anIs
V (mm/s)
“ 40 3
E 2.5
E 2
E ‘1|.5
% 0.5
:I: 20 0
-0.5
-1
-1.5
-2
V
0
20 40 60 80
Width (mm) L. U

Figure 8-15: Measured velocity vectors of the ﬂow above a row of nucleators

124

It is clear from the PIV image that there is a lack of particles in the plumes; therefore,
accurate velocity measurements can be obtained only in the surrounding ﬂuid, not in the
plumes. As can be seen in Figure 8-15, when two adjacent phase locked plumes diverge
as they move upward in a helical motion, the velocity of the ﬂow between them is
downward with a negative sign (blue color). As the plumes get closer, the velocity of the
ﬂow starts to increase and, eventually, the velocity at the regions of closest approach

between the two plumes is upward (green color).

8.5 Velocity fields above an area free of plumes

It was shown by using the LIF technique in section 8.2 that after t = 60 min the
temperature of the ﬂow above the mushy zone and above an area free of chimneys is
almost uniform laterally. This is expected to result in a more uniform composition proﬁle
of the ﬁnal product of the solidiﬁcation process. In order to have a better understanding
of the velocity ﬁelds above this area, an experiment similar to that discussed in section
8.2 was carried out to measure the velocity vectors in an area where plumes do not form
(Figure 8-16). The bottom left comer of the image is at (27 .75mm, 30mm, 4mm). The
images were processed with a 50% overlap for enhanced spatial resolution, and 11 x 11
pixel interrogation window and 17 x 17 pixel search window sizes. This resulted in a
vector spacing of 0.41 mm. Overall, the vector ﬁeld map covered an area of 52 mm x 38
mm. Since no plume exists on the image plane, accurate velocity values can be obtained
using the PIV technique. Velocity vectors measured at different times are shown in

Figure 8-17. The height is measured from the bottom of the imaged area, not from the

125

bottom of the plate, and the color bar shows the magnitude of the v-component of the

velocity vectors.

2.22 cm
<—>

0.86 cm I

 

Figure 8-16: Arrangement of the nucleators and location of the laser sheet

 

Figure 8-17: PIV image of the imaged area above an area free of plumes

126

Right before crystallization begins (t = 4min), there is an evidence of large scale ﬂow
circulation in the container as shown in Figure 8-18(a) due to the thermal buoyancy
effect. Once the ﬁngers are formed, the upward velocity vectors next to the downward
ﬂow can be observed as seen in Figure 8-18(b). The maximum velocity of these ﬁngers is
about 1.5 mm/s. As time goes by, the number of ﬁngers increases, but their maximum
velocities remains constant. At t = 20 min, the maximum velocity of the ﬁngers starts to
decrease and the ﬁngers become weaker. This is due to the fact that the plumes are
forming on the arranged nucleators and more ﬂow has to penetrate into the mushy zone
to feed the plumes through the chimneys within the mushy zone. Later in time, ﬁngers
decrease in number as they get weaker (Figure 8—18 (g)) and some disappear. At t = 60
min, no ﬁngers can be observed on the imaged plane. The upward velocity vectors seen
at this time are very small (compared with that of the ﬁngers, 1.5 mm/s). A small
maximum positive V-velocity component of 0.06 mm/s exists because solidiﬁcation is
still taking place at the mush-melt interface; therefore, some water-rich ﬂuid ascends
locally at the interface. Velocity vectors seen at this time are small in magnitude.

The ﬂow structure at t = 90 min is similar to that of t = 60 min, and the height of
the mushy zone has increased. The fact that ﬂow is calm and temperature is uniform
laterally above this area suggests that the solidiﬁcation process is uniform above this
area, and better quality of the ﬁnal product can be obtained. As was mentioned before,
velocity proﬁle of the plume cannot be obtained accurately by using PIV measurements
due to the lack of particles inside the plume. Molecular Tagging Velocimetry has the
potential to give additional insight by providing valuable data that quantiﬁes the velocity

ﬁeld within and around phase locked

127

.. lmmls

40

Height (mm)

 

 

o l A l J l l l I l l A 1 1 l l l l l l l l l l A _L
0 10 20 _ 30 40 50
Width (mm)
(a)
40 —o1mm/s

(a)
0

Height (mm)
8

 

 

or_1_rr_L
o 10 20_ 30 40 50
Width(mm)
(b)
—olmm/s
4o -

t = 10 min

30

Heightlmm)

_|
O

 

 

 

o....r....r11.1....1...._L
10 2O 30 40 50
Widﬂi(mm)
(C)

Figure 8-18: Velocity vectors at different times above and area free of plumes

128

40 t = 12 min —.lmm/s

lvlr'

Heuhtlmm)

 

 

Hebhtlmm)

 

 

Height (mm)

 

 

oirrrjrrrrlrrrrlirrrlrir1|

Figure 8-18: Velocity vectors at different times above and area free of plumes

129

40 - t = 40 min —‘ 0-4mm/S

Height (mm)

 

 

 

 

 

 

o k r r r r I i I r r I 1 r r I I l r r r I 1 l r L_L
10 20 30 40 50
Width (mm)
(g)
40 — t = 60 min —- 0.4mm/s
I .5
E I
E 024
5 2° ' 0:00
g’ 0
.012
I _ -0.3
10 - V
' L U
0 . | l r I r l l r 2I0 l l r r 310 r 1 r I I r r i 1_L
10 40
Width (mm)
(11)
40 t = 90 min —-> 0.4mm/s

 

 

E 06
.2 0
-0.12
I .03
10 V
LU
o.._._.r....1....1....r...._1_
0 10 20 40
Width(mrn)
(1)

Figure 8-18: Velocity vectors at different times above and area free of plumes

130

plumes. In the following section, the results from using the MTV technique will be

described.

8.6 Velocity measurement of two phase locked plumes using MTV technique

It was shown before that the temperature proﬁles of two phase locked plumes
with 180° phase difference were the same. The aim of this experiment was to ﬁnd out
whether or not the two phase-locked plumes were also identical in velocity proﬁle. Two
big nucleators were placed in the middle of the test section on the bottom plate with
spacing of 1.2 cm. The UV laser had a pulse repetition rate of 10 Hz. Figure 8—19 shows
the delayed image of the tagged lines at t = 25 min in the test section above the mushy
zone. This image is obtained from averaging ﬁve successive images. As can be seen in
this ﬁgure, the maximum displacement of the lines occurs at the locations where plumes
exist. At this time the plumes were phase locked with a 180° degree phase difference.
Velocity proﬁles of the plumes 5.3mm above the mushy zone are shown Figure 8-20.

Both plumes have almost the same maximum velocity values of 3.5mm/s.

 

Figure 8-19: Line tagging above the mushy zone at t = 25 min for the case of two phase
locked plumes above two big nucleators with a spacing of 1.2 cm

131

 

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5
Width (mm)

Figure 8-20: Velocity proﬁles of the plumes at t = 25min for the case of two phase
locked plumes above two big nucleators with a spacing of 1.20m

 

1.2

1 _
0.8 -
0.6 ~' -
0.4 —

 

 

 

 

 

 

Didance from center (mm)

Figure 8-21: Overlapped velocity proﬁles of the plumes for the case of two big nucleator
pair

132

A similar experiment was carried out by using the big-small nucleator pair in the middle
of the test section. The spacing between nucleators was 1.2 cm. An initial observation
revealed that most of the time the two plumes generated above the two nucleators were
phased locked with a 180° phase difference. However, in some occasions during the
experiment, they fell out of phase (is not clear why) with no relation between phases.
Figure 8-22 shows the velocity proﬁle of the plumes at t = 40 min when the plumes were
phase locked with 180° phase difference. Again, delayed and undelayed images were
obtained from averaging ﬁve successive images. As can be seen, the maximum velocity
values of the plumes are almost identical. The velocity proﬁle on the left belongs to the
plume formed above the small nucleator and the one on the right belongs to that formed

above the big nucleator.

 

 

 

 

 

 

V (mmls)

 

 

 

 

 

O 2.5 5 7.5 10 12.5 15 17.5 20
Width (mm)

Figure 8—22: Velocity proﬁles of the plumes at t 2 40min for the case of big-small pair

133

At t = 60 min suddenly the two plumes fell out of phase. Figure 8-23 shows the velocity
proﬁles of these plumes at this time. The maximum velocity values changed slightly. The
velocity of the plume above the small nucleator slightly decreased; whereas, the one

above the big nucleator slightly increased.

 

 

 

 

 

 

 

 

 

 

 

 

 

0 2.5 5 7.5 10 12.5 15 17.5 20
Width (m)

Figure 8-23: Velocity proﬁles of the plumes at t = 60min for the case of big-small pair

It seems that this small variation in velocity difference (0.5mm/s) was enough to
force the two plumes out of phase. These results show that when the two plumes are
phase locked with 180° phase difference their velocity proﬁles are very similar.

A Molecular Tagging Velocimetry and Thermometry (MTVT) technique has been
developed recently at the TMUAL (Turbulent Mixing and Unsteady Aerodynamics
Laboratory) at Michigan State University by Hu and Koochesfahani (2002). This
technique is capable of measuring velocity and temperature of the ﬂow simultaneously.

134

Unfortunately, because the sensitivity of the life time to temperature variation was small,
and also because the lifetime of the chemical depends on the concentration of ammonium
chloride, the MTV&T technique could not be used to obtain simultaneous temperature
and velocity measurements of the plumes. This optical diagnostic technique and its

reasons for not being applicable to this study are detailed in the Appendix D.

135

Chapter 9
Conclusions

In the solidiﬁcation process of a simple binary alloy, solutal and thermal
buoyancy forces play an important role in the creation of plumes and imperfections
(freckles) in the ﬁnal product. Therefore, it is important to know the temperature
distribution in the liquid regions during the solidiﬁcation of aqueous ammonium chloride.
Whole-ﬁeld temperature maps have not been obtained in the past for the liquid region in
a conventional size container during solidiﬁcation process. The temperature map
obtained by Solomon and Hartley (1997) using thermochromic liquid crystal paints
(TLC) was in a Hele—Shaw cell. The ﬂow ﬁeld velocities in Hele-Shaw cells are different
from those in conventional size containers due to the viscous effect imposed by walls on
the ﬂow. Since liquid crystals were painted on the wall surface, the temperature map
obtained was not the actual temperature map of the ﬂuid itself but of the wall boundaries.

To address the lack of appropriate experimental data in this ﬁeld, a two—color LIF
technique was developed and used to measure temperature distribution during the
solidiﬁcation process of aqueous ammonium chloride. As the plume rises vertically in
helical motion, the curved edge of the plume causes the laser sheet to diverge and results
in dark streak patterns in certain areas of the image. It was shown that the two-color LIF
technique can suppress the effect of these streaks on the measured temperature values.
Two color bands should usually be chosen such that one is temperature sensitive and the
other is temperature insensitive (Sakakibara and Adrian 1999). The ﬂuorescence signal of
temperature sensitive dye provides the temperature distribution in the measurement

region and that of the temperature insensitive dye provides the intensity distribution of

136

the incident illumination laser light. For the ﬁrst time in two-color LIF technique,
temperature resolution has been improved and doubled by using two temperature
sensitive dyes with opposite sensitivity to temperature variation. The two dyes used were
ﬂuorescein and kiton red. The calibration curve showed that if exited at 514nm, the
intensity of ﬂuorescein decreases with decreasing temperature and that of kiton red
increases.

The initial measurements of the solidiﬁcation process yielded some interesting
results. The temperature distribution in the plume region was clearly captured and the
temperature proﬁle indicated a minimum temperature value at the center of the plume.
The temperature of the center of the plume and that of the surrounding ﬂuid
monotonically increased as the plume was moving upward away from the mushy zone
and merging eventually at the top section of the container. The maximum temperature
difference between plume and the surrounding ﬂuid was found to be 27° C.

The energy equation was simpliﬁed based on some assumptions and solved
numerically. It was shown that the simpliﬁed energy equation could be used to obtain the
temperature proﬁles across a plume for a short portion of the plume close to the mushy
zone when appropriate boundary conditions were given (found experimentally). The
temperature proﬁles obtained from the numerical study agreed well with the
measurements. Most of the proposed numerical models for solidiﬁcation processes of
ammonium chloride use equilibrium phase diagram to ﬁnd temperature and concentration
values of the solution within the mushy zone, assuming that the ﬂow is in equilibrium
state. However, whole-ﬁeld temperature measurement showed that within 4 minutes of

applying coolant to the bottom heat exchanger, when no crystals are formed, the

137

temperature of the solution (7° C) close to the bottom plate corresponding to 26% wt
concentration of ammonium chloride was well below the liquidus line (18.6° C).
Therefore, the liquid close to the bottom plate was subcooled and not in equilibrium. The
fact that the ﬂuid is subcooled near the bottom cooling plate needs to be taken into
account in numerical modeling. Whole-ﬁeld temperature measurement also clearly
showed the temperature characteristic of the ﬁngers for the ﬁrst time. Due to the
existence of the ﬁngers above the mushy zone, the temperature distribution was non-
uniform, which was in good qualitative agreement with numerical results obtained by
Neilson and Incropera (1993). The evolution of ﬁngers into the plumes could be seen
from the whole ﬁeld temperature maps. As salt-rich ﬂuid adjacent to the plume is cooled,
it descends as a sheath along the plume. These sheaths cannot traverse the plume bends,
causing them to separate from the plume and descend freely. The sheaths are called
wisps. The temperature of the wisps was captured by using the LIF technique and the
results showed that these wisps could be approximately 05° C warmer than the center of
the plume itself.

It was shown experimentally that the location of the plumes and chimneys can be
controlled during the solidiﬁcation process of ammonium chloride by placing metallic
nucleators on the bottom cooling plate. Plumes could be formed above the nucleators
because, at initial stages of the solidiﬁcation process, stronger ﬁngers were formed above
the nucleators. This was due to the fact that these nucleators acted as thermal ﬁns and
they enhanced the solidiﬁcation rate locally. This enhanced heat transfer from the
surrounding ﬂuid to the bottom plate would trigger one of the instability modes at the

locations of the nucleators. It was not clear if this instability mode was in the form of the

138

‘mushy-layer’ mode or ‘boundary layer’ mode as identiﬁed by Worster (1992)
mathematically.

To examine the effects of size and arrangements of nucleators on the
solidiﬁcation process of ammonium chloride. two different arrangements and sizes (big
and small nucleators) were used. The experiments clearly showed that with a bigger
nucleator, more perturbation at the location of the nucleator was induced and therefore, a
plume was more probable to form at that location. When the distance between two
nucleators was less than 0.5 cm for big nucleators and 0.6 cm for small nucleators, only
one plume formed above them. If the distance between nucleators was less than 1.2 cm,
the two plumes were always phase locked with 180° phase difference. The phase locking
was due to the hydrodynamic coupling between nearby jets. Entrainment of ﬂuid and
counter-propagating shear ﬂow produce dynamical instabilities, and result in
synchronization of phases of the nearby plumes. It was also demonstrated that it is
possible to obtain a relatively large area free of chimneys by placing nucleators around
the side walls but not very close to the walls. It is not clear yet why more plumes were
formed randomly elsewhere when nucleators were placed very close to the side walls.
The size of an area free of chimneys that can be obtained depends on the pumping effect
of the plumes (caused by buoyancy difference between the plumes and the surrounding
ﬂuid) and the permeability of the mushy zone. With a larger concentration difference
between the plumes and the surrounding ﬂuid (more pumping effect), and more
permeability of the mush, a larger area free of chimneys can be obtained by placing
nucleators around the periphery of that area. This experiment has demonstrated a novel,

cheap, and easy technique to enhance the quality of unidirectionally solidiﬁed binary

139

alloys and obtain a more uniform composition proﬁle of the ﬁnal product of the
solidiﬁcation process by pushing the chimneys out to the sidewalls and leaving a large
area in the center free of defects.

To have a better understanding of ﬂow structure around the plume, particle image
velocimetry (PIV) technique was used to measure the velocity vectors in the solution
during the solidiﬁcation process. The problem that one might encounter using the PIV
technique to measure the plume velocity is the lack of particles in the plume. As particles
move into the mushy zone, they become nucleation sites and crystals form around them.
As they grow, they attach to the mushy zone and cannot ﬂow into the chimney and from
there into the plume. Thus, the plumes are left out without particles in them and PIV
measurements can not be carried out inside the plumes. Our PIV measurements around
the plumes in the surrounding ﬂuid showed that as the plume moved upward in helical
motion, another ﬂow adjacent to it moved downwards with slower speed (3 to 4 times
slower than the maximum velocity of the plume) in helical motion and both ﬂows were
twisted around each other.

The PIV measurements also showed that the maximum velocity of the ﬁngers was
1.5 mm/s at initial stages of the solidiﬁcation process located above a relatively large area
free of plumes (in good agreement with results obtained by Lum, 2001). After t = 60min
the upward velocity of the ﬂow was very small 0.06 mm/s (no ﬁnger was observed). The
whole ﬁeld temperature maps also showed that in this region, where no plume existed
after t = 60min, the temperature was well stratiﬁed. The fact that the ﬂow was calm and

the temperature was uniform laterally above this area suggested that the solidiﬁcation

140

process was taking place uniformly at mush-melt interface, resulting in a better quality of
the ﬁnal product.

To compare the velocity proﬁles of two adjacent phase locked plumes, molecular
tagging velocimetry (MTV) technique was used to obtain one dimensional velocity
proﬁles of the plumes. The PIV technique could not be implemented to measure the
velocity of the plumes due to the lack of particles in the plume. The results showed that
the velocity of the two phase locked plumes with 1800 phase difference is identical (the
overlapping between two velocity proﬁles was good). The LIF technique also showed
that their temperature proﬁles were identical. When the two plumes were out of phase,
the velocity proﬁles looked slightly different. In one example the difference between
maximum velocities of two plumes was about 0.5mm/s. That small variation in velocity
difference was enough to force the two plumes out of phase.

It is believed that the nucleators can be used in other solidiﬁcation processes to
enforce the freckle formation at desired locations. However, experiments need to be

conducted to conﬁrm this hypothesis.

141

Chapter 10

References

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Bergman, TL, and Ungan, A., 1988, “A note on lateral heating in a double-diffusive
system”, J. Fluid Mech, Vol. 194, PP. 175-186.

Chee Leong Lum, 2001, "Velocity ﬁeld measurement for a uni-directional solidiﬁcation
of an ammonium chloride (NH4Cl) solution using Molecular Tagging Velocimetry
(MTV)", master thesis, conducted at Mechanical Engineering Department, Michigan
State University.

Chen, CR, and Chen, R, 1991, "Experimental Study of directional Solidiﬁcation of
Aqueous Ammonium Chloride Solutions", J. Fluid Mech, Vol. 227, PP. 567-586.

Chen, Y. M., and Liou, J. K. (1997). "Time—dependent double-diffusive convection due
to salt-stratiﬁed ﬂuid layer with differential heating in an inclined cavity" Int. J. Heat
Mass Transfer 40, 711-725.

Chen, F., Lu, J.W., and Yang, TL, 1994, "Convection Instability in Ammonium
Chloride Solution Directionally Solidiﬁed from Below", J. Fluid Mech, Vol. 276, PP.
163-187.

Dombrowski, C., Lewellyn, B., Pesci A. 1., Restrepo, J. M., Kessler, J. O., and Goldstein,
R. E., (2004). "Coiling, Entrainment, and Hydrodynamic Coupling of Decelerated Fluid
Jets" Int. J. Heat Mass Transfer 33, 367-380.

Falin Chen, (1997). "Formation of double-diffusive layers in the directional solidiﬁcation
of binary solutions" Journal of Crystal Growth 179, 277-286.

Garimella, S.V., McNulty, J .P., and Schlitz, L.Z., 1995, "Formation and Suppression of
Channels during Upward Solidiﬁcation of a Binary Mixture", Metallurgical and
Materials Transactions A, Vol. 26A, PP. 971-981.

Gendrich, C. P. and Koochesfahani, M. M., 1996, "A spatial correlation technique for
estimating velocity ﬁelds using Molecular Tagging Velocimetry (MTV)," Exp. in Fluids,
22(1), 67-77.

Hellawell, A., Sarazin, J. R., and Steube, R. S., 1993."Channel convection in partly
solidiﬁed systems" Phil. Trans. R. Soc. Lond. A345, 507-544.

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Hu, H., Koochesfahani, M.M., 2002, "A novel Technique for quantitative temperature
mapping in liquid by measuring lifetime of laser induced phosphorescence", The 10’”
International Symposium on Flow Visualization, August 26-29, Kyoto, Japan. .

Kay Wirtz, 1998, "Experimental study of convection phenomena associated with
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Kim, H]. and Kihm, K.D., 2001, "Application of a Two-Color Laser Induced
Fluorescence (LIF) Technique for Temperature Mapping", Proceedings of ASME
IMECE, November 11-16 - New York, USA.

Koochesfahani, M. M., 1999, "Molecular Tagging Velocimetry (MTV): Progress and
Applications", AIAA Paper No. AiAA-99-3786 (invited).

Kou, S., Poirier, D. R., and Flemings, M. C., 1978, "Macrosegregation in rotated
remelted ingots". Metall. Trans, B 103, 331-339.

Kranenborg, E. J., and Dijkstra, H. A. 1998, "On the evolution of double-diffusive
intrusions into a stably stratiﬁed liquid: a study of the layer merging process" Int. J. Heat
Mass Transfer 41, 2743-2756.

Lum, C.L., Koochesfahani, M.M., and McGrath, 1.1., 2001, "Measurements Of The
Velocity Field With MTV During The Solidiﬁcation Of An Alloy Anolog With Mushy
Region", Proceedings of ASME IMECE, Vol. 31, PP. 1-7.

Magirl, CC, and Incropera FR, 1993, "Flow and Morphological Conditions Associated
With Unidirectional Solidiﬁcation of Aqueous Ammonium Chloride", Transactions of
the ASME, Vol. 115, PP. 1036-1043.

Neilson, D. G., and Incropera, F. P. 1993, "Effect of rotation on ﬂuid motion and channel
formation during unidirectional solidiﬁcation of binary alloy" Int. J. Heat Mass Transfer

36, 489-505.

Neilson, D. G., and Incropera, F. P.,1990, "Numerical simulation of solidiﬁcation in a
horizontal cylindrical annulus charged with an aqueous salt solution" Int. J. Heat Mass
Transfer 33, 367-380.

Pera, L., and Gebhart, B., 1971, "On the stability of laminar plumes: some numerical
solutions and experiments" Int. J. Heat Mass Transfer 14, 975-984.

Popvich, A. T., Hummel, R.L. 1967, "A New Method for Non-Disturbing Turbulent
Flow Measurement Very Close to Wall" Chem. Eng. Soc, Vol. 22, 21-25.

Pringsheim P. 1949, "Fluoresence and Phosphorescence", Interscience publishers, INC.
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Sakakibara, J. and Adrian, R. J .1999, "Whole ﬁeld measurement of temperature in water
using two-color laser induced ﬂuorescence", Experiments in Fluids, 26, 7-15.

Sample, A. K., and Hellawell, A.,1982, "The effect of mold precession on channel and
macro-segregation in ammonium chloride-water analog castings", Metall. Trans., B 133,
495-501.

Sample, A. K., and Hellawell, A. 1984, "The mechanisms of formation and prevention of
channel segregation during alloy solidiﬁcation", Metall. Trans., A 13A, 2163-2173.

Shaﬁi, M. and Koochesfahani, M. M. 2003, "Temperature Measurement of Aqueous
Ammonium Chloride Solution during Solidiﬁcation Process Using Laser Induced
Fluorescence (LIF)", Bull. Am. Phys. Soc., 48(10), 180.

Tanny, Y., and Yakubov, B., (1999), "Experimental study of a double-diffusive two-layer
system in a laterally heated enclosure", Int. J. Heat Mass Transfer 42, 3619-3629.

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solidiﬁcation of alloys", J. Fluid Mech, Vol. 237, PP. 649-669.

144

Appendix A

Some Experimental Reports on Double-Diffusive Layer

The nature of double-diffusive natural convection, seen in the solidiﬁcation
process of ammonium chloride, will be explained in this section. The formation of double
diffusive layers (DDL) is a result of the interaction between the vertical concentration
gradient and the horizontal temperature gradient. When a parcel of liquid near a heated
wall moves upward, it retains almost all of its salt due to the very small salt diffusivity.
The parcel rises to a level where its density is equal to that of the surrounding liquid, and
because of the buoyancy effect, it is then forced to move laterally, and a layered ﬂow
pattern eventually results. These ﬂow patterns create double diffusive cells.

Bergman and Ungan (1988) performed experiments of double-diffusive
convection in a two-layer, salt-stratiﬁed solution (Figure A-l, C1 > C2) destabilized by
lateral heating and cooling of side walls. Two ﬂuid layers with two different
concentrations were contained within an enclosure and the sidewall temperature were
kept at T1 and T2 (T1>T2). Polystyrene-encapsulated liquid crystals were mixed with
solutions to visualize temperature changes in the layers. The interface was the location of
signiﬁcant upward heat transfer and thermally unstable density distributions, resulting
from cool ﬂuid traveling from the cold wall to the warm wall above the interface.
Bergman and Ungan (1988) mentioned that the salinity interface was not horizontal.
Figure A-l below shows a schematic of their experimental observation. The salt transport

continuously occurred from the salty bottom layer to the water-rich top layer. After some

145

time, the vertical boundary layers on the heated and cooled sidewalls began to penetrate

the salinity interface as seen in Figure A-2.

 

C2
T1
//\ T2
Interface

C1

 

 

 

Figure A-l: Two-layer salt-stratiﬁed solution (C 1 and C2) destabilized by lateral heating
and cooling

At this time the interface was tilted and secondary ﬂow at the interface became very

evident. Eventually, both ﬂuids got mixed and no double-diffusion effect was observed.

 

Penetrated I
boundary layer in l l
salinity interface T1 V T2

1 1
1 1
Salinity interface I‘ C1 ‘

secondary ﬂow \ '

 

 

 

Figure A-2: Double diffusive layers and secondary ﬂow at the interface

146

This mixing time (complete mixing) was characterized by three parameters: Rayleigh
number, Solutal to Thermal buoyancy forces, and Fourier numbers. Fourier number is a

time scale associated with mixing.

2 8161(T1_T2)L3

 

 

 

Ra -
r ya (A1)
Rp : ﬂC(C2—Cl) (A-2)
ﬁr (T1 _ T2)
F0 : lezm (A-3)

In these expressions, C2-C1 is the difference in the layer 'solute concentration, a is the
thermal diffusivity, v is the kinematic viscosity , [3c and Br are solutal and thermal
expansion coefﬁcients of the solution, L is the width of the container and D is species
diffusivities. The dimensionless mixing time decreases as RaT increases. This seems to be
obvious since a more salt is transferred through the interface due to an increase of AT and
natural convictive velocities. The dimensionless mixing time increases as Rp increases
due to more stable interface.

Kranenborg and Dijkstra (1998) performed a direct numerical simulation. They
assumed liquids initially stratiﬁed through a constant salt gradient. Their numerical
results showed that as time proceeded, convection cells formed near the heated left wall
and gradually ﬁlled up the cavity forming double-diffusive cells. Their results showed

that as Rp decreased, the number of convection cells decreased and as a result the

147

convective transport of salt became stronger. It was also shown that the concentration
within each convective cell was uniform.

An experimental study was carried out by Tanny and Yakubov (1999) to
investigate the mixing process of a two-layer stratiﬁed ﬂuid in a laterally heated
enclosure. They concluded that the appearance of vortices at the interface separating the
layers was an instability phenomenon. The critical Rayleigh number for the onset of

interfacial instabilities shown in Figure A-2 was proposed as

Rac =108'2 x R pm (A-4)

Chen and Liou (1995) performed a numerical study on time-dependent double-
diffusive convection of NaCl-H2O concerning the stably stratiﬁed salt ﬂuid layer with
lateral heating in an inclined cavity. Their results showed that at early time, the
convective cells are generated near the bottom and top walls, and then, some
simultaneous cells appear in the middle portion at the hot wall and intrude toward the
interior region. The onset of instability was more pronounced at the negative angles (hot
wall on top) than the positive ones (hot wall at the bottom). When the angle increased, the
effect of heating-from-below was more and more vigorous. The ﬂuid parcel near the hot
wall raised up more and more along the sidewall, making the bottom cell larger in size
and reducing the cell numbers in the cavity. The convective ﬂow would occupy the

whole domain at positive angles, but only part of the domain at negative angles. Their

148

results showed that the average Nusselt number was higher for positive angles than for
negative angels.

The double diffusive layers formed in this study during the solidiﬁcation process
of ammonium chloride were a result of the concentration gradient along the test section
and the temperature difference between the plumes and the surrounding ﬂuid. It was
shown in previous chapters that the double-diffusive layers usually formed around the
plumes and the side walls, where lateral temperature gradients existed.

Falin Chen (1997) carried out some experiments on the solidiﬁcation process of
ammonium chloride. From his observations, several features were delineated as
summarized below. DDLs (double diffusive layer) were observed in the upper half of the
bulk ﬂuid. As a new layer was formed on top, the layer interface moved downward
continuously until it reached the melt/mush interface and broke down. The ﬂow pattern
of the plume was not changed by the presence of the DDLs. The onset of the formation of
DDLs occurred a couple of minutes after the salt ﬁngers vanished (50 min, bottom plate
temperature Tb: -9.8° C, H = 100m, top plate temperature T, = 29.6° C, initial
concentration 28% wt). There were 7 layers in the system with an average thickness of
0.7 cm each (almost constant during the experiment). The averaged propagating speed
was about 0.075 cm/min initially and decreased with time (minimum of 0.043 cm/s). As a
general rule, they found out that the onset of DDL occurred when the number of plumes
reached the maximum. Due to the break down of the DDLs at the mush/melt interface,
the overall thickness of the mush decreased about 0.15 cm. The reason for remelting is
that the concentration of DDLs formed on the top region remained unchanged during

their propagation downwards because of the small diffusivity across the layer interfaces.

149

The less-concentrated ﬂuid of the DDL interacted with the mush/melt interface and
remelted it. After plumes formed, the concentration of ammonium chloride was less at
the top of the test section and uniform in the center. This resulted in a negative
concentration gradient on the top region of the test section. The lower concentration
gradient was due to the fact that the plumes brought less-concentrated ﬂuid into the upper
region. The DDL thickness (0.6-1cm) did not change with constant bottom plate
temperature. However, the time evolution of the plumes was inﬂuenced by the bottom
plate temperature, Tb. The DDL appeared when the concentration gradient was negative
everywhere in the test section. If plumes broke up before they reached the top region, it
caused a positive gradient on the top region and from the consequence of that, no DDL
formed. It should be noted that the experimental set up of Chen was slightly different
from that of used in this study since the top boundary of his was ﬁxed at 30° C and that of

in this study is open to ambient.

150

Appendix B

Synchronization of Two Cameras

To capture two simultaneous images from the two Pulnix cameras (8—bit, 30
frames/s), the outputs of the two cameras are connected to the red and green channels of
an RGB frame grabber (Mutech MV-1300) and then digitized (8 bits) as a color image
and saved on a disk. The green and red intensities of this color image are subsequently
separated using a MATLAB code to restore the two images captured by the two cameras.
To acquire a color image, two cameras have to be synchronized by means of an external
SYNC generator (standard RS—170). The framing rates of these cameras are ﬁxed at 30

frames/second. Figure B-l shows the schematic for synchronizing two cameras.

  
     
     
 
   
   

  

Pulnix Pulnix
Camera Camera #2
HD

VD HD VD To RGB

Frame Grabber

 

 

  

Synch
Generator

Figure B- 1: Schematic for synchronizing two Pulnix cameras

151

In order to capture two simultaneous images from two PixelFly (12-bit) cameras,
the cameras are connected to two separate PCI boards on two separate computers. Each
camera can be controlled on each computer separately by related software (CamWare).
To synchronize the two cameras, the provided SYNC cables are ﬁrst connected to each
separate PC! board. The other ends of the cables, which are BNC type, are connected to a
signal generator that generates TTL signals (5 Volts). Then, the trigger of each camera is
set to external mode (Extem) through the software (CamWare). When the record buttons
are selected on the software, the cameras are ready to take images. For every TTL signal,
each camera takes one image. A burst of signals can also be given, but one should make
sure that the time delay between each TTL signal is longer than 80ms + exposure time.

Figure B-2 shows the schematic for synchronizing the two PixelFly cameras.

 

 

 

 

 

 

 

 

PixelFly PixelFly
Camera Camera #2

 

 

 

 

 

 

 

 

 

 

 

 

_l_lLl_l

TTL 1 To PCI board TO PCI board
S gnal On computer it 1 On computer it 2

 

 

 

 

 

Generator

 

 

 

 

Figure B-2: Schematic for synchronizing two PixelFly cameras

152

Appendix C

On the Stability of Laminar Plumes

As mentioned before, plumes move upward in helical motion during the
solidiﬁcation process of ammonium chloride solution. The helical motion of these
plumes, which has a resemblance to the stability of buoyant jet ﬂows, is due to the
hydrodynamic instability.

An investigation of the hydrodynamic stability of a laminar plume arising from a
horizontal line source of heat was carried out by Pera and Gebhart (1970). Inviscid
solutions of the Orr-Sommerfeld equation were obtained for both symmetric and
asymmetric disturbances. They assumed a steady locally periodic ﬂow (the amplitude of
disturbances does not vary with time, but with x). The computed neutral stability curve
(a) for coupled governing equations and asymmetric disturbances was presented in terms

of modiﬁed Grashof number (G) and Prandtl number (Pr).

x
‘1

Asymmetric

 

To Y
Line source

Figure C-l: Schematic of laminar plume rising from a horizontal line source

153

The modiﬁed Grashof number G was deﬁned as

 

V2

3 0.25
G : 242(0)“)0'25 = 2ﬁ[ 875‘ (To "'Too )] (C-l)

where g is gravity, [3 is coefﬁcient of volumetric expansion, To is the temperature of the

base ﬂow (source), T00 is surrounding temperature, and v is kinematic viscosity of the

ﬂuid. It was shown that

LE7:
x aG

(C-2)

where x is distance from the source in the vertical direction and 0. and G parameters were
obtained from the computed neutral curve. Since the energy and species equations are
very similar, one can use the same theory to calculate the wavelength of the oscillation of
a plume as a function of height (x). For this scenario, AT and thermal expansion B in
Equation (C-l) has to be replaced by AC and solutal expansion coefﬁcent. Schmidt

number (analogous to the Prandtl number in heat transfer) also needs to be used. The

physical properties of the plume are summarized in Table C-l

Table C-l: Properties of the Plume

 

AC (%wt) solutal expansion v (ml/s) Schmidt

[3 (%Wt'l) number

 

2% 0.003 106 800

 

 

 

 

 

 

154

Assuming the location of the point source to be at the exit of the plume on the
mush-melt interface, one can use Equation (C-2) and the plotted curve by Pera and
Gebhart (1970) to calculate the wavelengths of the disturbances as a function of height

(Figure C-2). This is a valid assumption since the Reynolds number is very small at the

exit of the mush-melt interface (Re=4)

 

 

4
IErperimentalttt
3'5 I A Experimental #2
3 - IExperimental#3
E 0 From analytical solution (Para
3 2-5 and Gebhart, 19970)
5 I I ' I
g 21 I
2 A ‘
§ 1.5 - - t I
3 A
11 0000.........
Q 0
0.5
0 r 4

 

 

O
_r
N
(A)
A

Height (cm)

Figure C-2: Wavelength as a function of height along the plume

As can be seen in Figure C-2, the calculated wavelengths of the plumes based on
Pera and Gebhart (1970) predictions are almost twice as small as those measured

experimentally (Figure C—3). This mismatch is due to the fact that the plume is bounded

155

on the top surface of the container, which inﬂuences the motion of the plume. The
shearing force between the plume and the descending ﬂuid also makes the plume more

unstable.

Wavelength

 

Figure C-3: Wavelength of a plume measured from peak to peak

156

Appendix D

Molecular Tagging Velocimetry and Thermometry (MTV&T)

Molecular Tagging Velocimetry and Thermometry (MTV&T) has been developed
at Michigan State University by Hu and Koochesfahani (2002). As mentioned in the body
of this work, when a substance is exposed to incident photons, a fraction of the molecules
in the appropriate lower energy level absorbs the incident light and are excited to a higher
energy state. These molecules return to the equilibrium ground state by emitting photons.
Compared with ﬂuorescence, which typically has a lifetime in the order of nanoseconds,
phosphorescence has a much longer lifetime in the order of microseconds to minutes. As
described in this work, the emitted phosphorescent can be used in the MTV technique to
measure the velocity vectors in the ﬂow ﬁeld. The lifetime of the phosphorescent dye
used in MTV technique (l-Ber-GB-CD-ROH) is also temperature dependent. As in the
MTV measurements, the phosphorescence signal is imaged at two successive times
within the lifetime of the tracer. The phosphorescence lifetime, estimated from the
intensity ratio of the two images at each point, is calibrated against the temperature.
While the displacements of the tagged regions between two interrogations provide the
estimate of ﬂow velocity vectors, the intensity ratio of the two images represents the ﬂuid
temperature distribution. Therefore, simultaneous velocity ﬁelds and temperature maps

can be obtained.

157

Phosphorescence life time

According to quantum theory, the decrease of emission intensity follows an
exponential law (Pringsheim 1949). Therefore, the intensity decay of a

photoluminescence process (ﬂuorescence or phosphorescence) can be expressed as

-t

[m =10e T (D-l)
Where lifetime (I) refers to the time when the intensity drops to 37% (l/e) of the initial

intensity. Therefore, the ratio intensity at two different times, t1 and t2 will be

 

= 6
(DZ
Ieml )

From Equation (D-2), it is clear that the intensity ratio of the two successive
phosphorescence images is only a function of phosphorescence lifetime, not the initial
intensity 10 (or laser power). It should be noted that the Equation (D-2) is valid when the
exposure times for two successive phosphorescence images are the same. If the exposure
times are different, this equation will change slightly and the expression for it can be
found in Hu and Koochesfahani (2002). Thus, the lifetime of the chemical, r, can be
found by two successive images with known delay time (At = t2-t1) and equal exposure

time. This lifetime is temperature dependent and can be calibrated against temperature.

Lifetime with ammonium chloride
During initial experimental trials of the solidiﬁcation process of the ammonium
chloride solution, Lum (2001) observed that in the presence of ammonium chloride, the

phosphorescent intensity of the MTV Triplex (chemical used in our experiments)

158

appeared brighter and yielded longer delay times between the undelayed and delayed
images. This prompted the investigation of lifetime variation of the MTV chemicals in
aqueous ammonium chloride solutions. The lifetime of the MTV Triplex (chemical used
here) in the presence of different concentrations of ammonium chloride was determined

and the results are shown in Figure D-l. The lifetime is normalized with the lifetime of

the chemicals at T = 20° C.

 

 

 

 

 

 

 

 

 

2
3: oTrail #1 l I, .
" 1 I O
1.8 1» ——. - Chee Lum (2001)]. _.__. A
4» I
E 1: .
E 1 6 1 l .
'_r f “ _ a
8 .
.u -_ a.
g 1.4 a
3 if
z +-
1.2 ’5 .. i
i: I
1.

 

0 5 10 15 20 25
Amnonium Chloride Concentration (%wt)

Figure D-l: Normalized lifetime as a function of weight percentage of the ammonium
chloride

It can be seen that the lifetime increases signiﬁcantly by adding ammonium chloride to
the solution. The lifetime tapers off at 20% wt and after 22% wt it is almost constant. The
lifetime at this point is approximately 6.7 ms. Interestingly, based on the equilibrium

phase diagram of ammonium chloride solution, the concentration of the solution never

159

goes below 21% wt during the solidiﬁcation process. Therefore, one can conclude that
the lifetime of the MTV chemicals is almost independent from the ammonium chloride
concentration during the solidiﬁcation process, which that simpliﬁes the application of

MTV&T.

Calibration of the lifetime of MTV Triplex with temgrature variation

In order to know if the MTV&T technique could be used to measure velocity and
temperature proﬁles of two phase-locked plumes simultaneously, the lifetime of the MTV
Triplex was calibrated with temperature variation. A XeCl excimer ultraviolet (UV) laser
(wavelength 1. = 308 nm, energy 50 mj/pulse) and appropriate optics were used to
illuminate the test section (the same container used in the solidiﬁcation studies),
containing an aqueous solution of l-Ber-GB-CD-ROH complex, with a laser sheet. The
solution was stirred to achieve thermal equilibrium. A thermocouple was placed in the
solution to measure the actual temperature. The same camera used in MTV measurement
was used here to conduct phosphorescence image recording. To acquire temperature data,
the aqueous solution of the l-Ber-GB-CD-ROH complex was cooled from below. After
the thermal equilibrium was established, the phosphorescence lifetime was measured by
taking two successive images with a 5 ms delay between them, 500 us after the laser
pulse, and 500 as exposure time for each image. Then, Equation (D-2) was used to
calculate lifetime (t2-t1 = 5 ms). Figure D-2 shows the variation of the normalized
lifetime with temperature. As can be seen, the sensitivity of the normalized lifetime to
temperature in the absence of ammonium chloride was very high (10%°C'l). Adding

ammonium chloride to the solution reduced this sensitivity signiﬁcantly. After 22% wt,

160

the sensitivity (1.5%°C") no longer decreased with additional ammonium chloride.
Therefore, the maximum sensitivity one can have during the solidiﬁcation process of
ammonium chloride for temperature measurement is 1.5% °C'l. This sensitivity is three
times less than the LIF technique described in previous chapters. Besides, the intensiﬁed
cameras (DiCam-Pro) usually have less signal/noise ratio than the non-intensiﬁed

(Pixelﬂy) CCD cameras, which were used for the LIF technique.

x 0% wt N-l401 (Hi and Koochesfahani 2002)

 

 

 

 

 

 

 

 

 

 

 

3.25 1 I With l‘b N440
3 ,, XWrth-N-l4019%wt
’* ° ..___.___-__ “"7— . th-N-l4019°/owt
2,75 -2.-_ -—. “1a-..- -———oWrth-N-l4022%wt
0 Q +WIth-Nr140 24%
e 2.5 4.2 *u —-——-——
B
3 x
'5 2.25 ~r * - - I
8 ' x
.5 2 i-F
'3 x
E I.-
g 1 I75 K—— ‘ ‘ ~— _ — — — A x d ——_ ‘——'——‘
5 .
15 , -2- I! - .2--- __ 22.. -
+ H §
+ + a u
1.25 -— — — - %~-4——.——— 3 —~--
9 . : x3»:
1 "___—__'T——7—' ' _ '1 _ T — T T ' —'.
O 5 10 15 20 25 30

Temperature (C)

Figure D-2: Variation of normalized lifetime with temperature

MTV&T technique was used to measure the temperature of a plume at t = 25 min.
the tagged line was 5 mm above the mushy zone. The delayed time used to take two
successive images was 30 ms with 3 ms exposure time for each image. Unfortunately, the

measured temperature proﬁle of the plume showed the plume being warmer than the

161

surroundings. As can be seen in Figure D-3, the intensity of the tagged line in the plume
region looks dimmer compared with that of the surroundings. Assuming the intensity of
the tagged line in the undelayed image to be uniform and referring to the calibration

curve, this

 
   

Dimmer region
(in the plume)

Figure D-3: Delayed image of a line tagged region

means that the lifetime should be shorter in the plume and should look warmer. This
discrepancy is because of low sensitivity of the calibration curve to temperature variation
(1.5%°C'1). Suppose that the concentration of the plume is 3% wt less than that of the
surrounding. This will result in 0.1 difference in normalized life time, as seen in Figure
D-2 which is a 5% variation in normalized lifetime (0.1/1.8 x100). Thus, as seen in
Figure D-2, the plume will appear 3°C warmer than what it should be. Unfortunately, 1-
Ber-GB-CD-ROH cannot be used in ammonium chloride solution due to its unique
characteristics. For implementation of the MTV&T technique in ammonium chloride

solution, an alternative chemical needs to be found and studied in the future.

162

Appendix E

Error Analysis

In two—color LIF technique, the temperature mapping relies on the temperature
dependence of ﬂuorescence intensity, estimated from the intensity ratio of two
temperature sensitive dyes. The actual value of temperature would correspond to an
R f (T)
Rf (T0)

 

equivalent value from the calibration proﬁle if the CCD cameras are free of

Rfm
Rf(T0)

 

noise. However, due to the noise of the CCD cameras the measured value is not

the actual value, and the predicted temperature is not exactly correct. As mentioned
before, the ﬂuorescence intensity can be written as a function of the temperature and

reference conditions:

 

R T
ln[ f( )]=(Bl—le[i—i] (E-l)

R f (To) T To
the above equation can be rewritten as

T = (13-2)

 

 

163

 

 

 

 

R T
The “error” in the f ( ) , associated with the noise of the CCD cameras, will result
. . 8T
rn an error AT, Wthl’l can be found from AT = AR f (T) + HOT.
aRf (T)

Therefore from equation (E-2) one can show that

_1_ 1

AB R f (T)
AT = 2 ARf (T) (E-3)

 

1 Rf(T) 1
—1n +—
AB Rf(T0) T0

01'

ALI/“rm
T2 AB Rf(T)

 

(E4)

in whichAB = 2682 K (in this study).

From equation (E-4) one can conclude that 1% variation in intensity ratio

ARf (T)

(Rf(T)

 

=1%) at room temperature (T2300 K) will result in AT: 0.3 K error in the

measured temperature value.

164

   

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