Experimental Study of Transient Pool Boiling Heat Transfer under Exponential Power Excursion
on Plate-Type Heater
ARCHIVEfi
By
MASSACHUSETTS INSTrTi IFOF rECHNOLOLC-
Guanyu Su
MAY 0 6 2015
B.Sci., Power Engineering (2008)
Chongqing University
LIBRARIES
M.Sci., Nuclear Science and Engineering (2011)
Shanghai Jiao Tong University
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February, 2015
C2015 Massachusetts Institute of Technology
All rights reserved
Signature redacted
Signature of author:
Guanyu Su
Department of Nuclear Science and Engineering
February, 2015
Certified by:
Signature redacted-
Jacopo Buongiorno
Associate Profesor of Nuclear Science and Engineering
Thesis Supervisor
Certified by:
Signature redacte'd
Thomas McKrell
1search Scientist of Nuclear Science and Engineering
Thesis Co-supervisor
Signature redacted
Certified by:
Matteo Bucci
Visiting Scientist for Nuclear Science and Engineering
Thesis Reader
Accepted by:
Signature redacted,.
Mujid S. Kazimi
luc ar Engineering
TEPCO Professor
Department Committee on Graduate Students
2
Experimental Study of Transient Pool Boiling Heat Transfer under
Exponential Power Excursion on Plate-Type Heater
By
Guanyu Su
Submitted to the Department of Nuclear Science and Engineering on February, 2015 in partial
fulfillment for the degree of
MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
Abstract
Conduction and single-phase convective heat transfer are well understood phenomena: analytical
models [1] and empirical correlations [2] allow capturing the thermal behavior of plate-type fuels
or heaters in contact with a single-phase coolant. On the other hand, transient boiling heat transfer
is a scarcely studied and much less understood phenomenon. Although, earlier studies have shown
that important features of the boiling curve (i.e. onset of nucleate boiling (ONB), nucleate boiling
heat transfer coefficient, and critical heat flux (CHF)) in transient conditions. These parameters
significantly differ from those at steady-state. The mechanisms by which these changes occur are
not clear. Furthermore, some of the conclusions from different authors are quantitatively or
qualitatively in disagreement with each other. This work studied transient pool boiling heat transfer
phenomena under exponentially escalating heat fluxes on plate-type heaters, at the time scales of
milliseconds typical of Reactivity Initiated Accidents (RIAs) in nuclear reactors. The investigation
utilized state-of-the-art diagnostics such as Infrared (IR) thermometry and high-speed video
(HSV), to gain insight into the physical phenomena and generate a database that could be used for
development and validation of accurate models for transient boiling heat transfer. The tests with
exponential power escalation periods ranging from 100 ms to 5 ms and subcoolings of OK
(saturation), 25K and 75 K were conducted. The measured pre-ONB heat transfer coefficient
agrees well with the theoretical predictions for transient conduction. The ONB and onset of
significant void (OSV) temperature and heat flux were found to increase monotonically with
decreasing period and increasing subcooling, as expected. The mechanistic ONB model of Hsu
was able to predict the measured ONB temperature and heat flux. The transient pool boiling curves
were measured up to fully developed nucleate boiling (FDNB). Generally two types of boiling
curve were observed: with overshoot (OV) or without overshoot. Data show that, when an OV is
present, the OV temperature increases monotonically with decreasing period and increasing
subcooling. The present study clears the confusions (eg. the trend of ONB temperature and heat
flux versus power period) in previous research, and sheds light to the mechanisms behind transient
boiling heat transfer. This can ultimately reduce the uncertainty in both design and safety analyses
of the research reactors especially under RIAs.
3
THESIS SUPERVISOR: Jacopo Buongiorno, Ph.D.
TITLE: Associate Professor of Nuclear Science and Engineering
THESIS CO-SUPERVISOR Thomas McKrell, Ph.D.
TITLE: Research Scientist of Nuclear Science and Engineering
THESIS READER Matteo Bucci, Ph.D.
TITLE: Visiting Scientist for Nuclear Science and Engineering
4
Acknowledgements
I'm not good at expressing my gratitude, especially when I'm writing in English. My wife
sometimes says that my words of appreciation sound hollow. However, I still try really hard to
squeeze out those solid words and sew them in the simplest way, to give my acknowledgement to
the people who mentored, helped and encouraged me.
I remember two conversations with Prof. Buongiorno which influence me the most. One was the
first time when I remarked a PDE with time dependent boundary condition as "too difficult". Prof.
Buongiorno said "Guanyu, nothing is too difficult in MIT". It was like a loud knock on me that if
I didn't want to challenge myself, why I came to MIT. The other conversation happened at the
night when I got my result for qual in his office. He said that I had passion to do deeper works,
however "you should be clear with everything you put on the screen". After that day, I always ask
myself two questions before I present my works: Do I understand everything I'm going to present?
Have I quantified my "dream" into a blueprint? It's my good fortune to have him as my supervisor.
Another person who gave me tremendous guidance was Dr. McKrell. It was still like yesterday
when he sat down with me and went through my naive and improper designs for hours and hours.
Time after time, he shared with me his incredibly abundant experiences. He always came up with
critical while helpful questions and ideas that helped me examine my works. I remember once he
used "sexy" to describe outstanding result. I personally like the word "sexy", because it means the
result is rich, attractive and in depth. I'd like to thank him for keeping our experimental works
safe, efficient and vivid.
The third person who taught me a lot was Dr. Bucci. He comes from CEA which is the sponsor of
the present study. However, instead of being like an inspector, he was working closely with me in
the same trench. I don't remember how many late nights we spent together in the lab and how
many times we encouraged each other when we failed the tests. From him, I see the pure love for
research. Following his examples, I learned how to organize my works. Once when we wrote
report together, he said "Guanyu, your mind is like a big cloud.. .You have to link them up to
express to other people". He always helps me without any hesitation as if we are brothers.
I would like to thank the members of our group, since I received too much support from them. If
it was not Melanie, I would not have chance to learn surface engineering. I appreciate Andrew for
sharing his knowledge of optics with me. I still remember those early mornings when Carolyn
helped me engineer micro-cavities at 5am. Reza was the actual finder of the nucleation cavity that
worked for our experiments, for which I should name the cavity with his name as those people
who discovered new asteroid. It was Bren who gave me ideas on how to design and prepare heater
and cartridge. It's such a great pleasure for me to be a member of the coolest TH-group.
I also own special thanks to Marina who helped me improve the quality of my writing.
Last but not least, I true heartedly thank my wife Jing. I probably spent much more time in the lab
than with you, however you always gave me a warm hug when I got home.
Although my Master project has finished, these memorable moments keep appearing in my mind
again and again, which are like vigorous boiling bubbles that push me to a higher level of heat
transfer.
5
6
Table of Contents
A bstract ...........................................................................................................................................
3
A cknow ledgem ents.........................................................................................................................
5
List of Figures .................................................................................................................................
9
List of Tables ................................................................................................................................
14
1.
Introduction...........................................................................................................................
15
1.1.
M otivation ......................................................................................................................
15
1.2.
O bjectives.......................................................................................................................
15
2.
Background and Previous Research..................................................................................
17
2.1.
Single Phase Transient H eat Transfer .........................................................................
17
2.2.
Boiling Inception Theory ............................................................................................
19
2.3.
Steady Boiling V .S. Transient Boiling.......................................................................
22
3.
Scope of the W ork ................................................................................................................
27
4.
D esign of the Plate Type H eater ........................................................................................
28
4.1.
Sim ulation of H eater Behavior under Transient Condition ........................................
28
4.2.
Basic H eater Design and Substrate Evaluation ..........................................................
32
4.2.1.
Basic Heater Design.............................................................................................
32
4.2.2.
Evaluation of Substrate M aterials.......................................................................
33
Final Heater Design........................................................................................................
37
4.3.1.
Heater Configuration ..........................................................................................
37
4.3.2.
H eating Surface.......................................................................................................
38
Experim ental Setups .............................................................................................................
40
4.3.
5.
6.
5.1.
Pool Boiling Facility (PBF) .......................................................................................
41
5.2.
Heater Cartridge .............................................................................................................
42
5.3.
Infrared Cam era (IRC) and IR Therm om etry ...........................................................
43
5.4.
H igh Speed V ideo (H SV)..........................................................................................
44
5.5.
H igh Speed DC Power Supply (HD CP).....................................................................
44
5.6.
H igh Speed Data A cquisition System (DA S) ................................................................
45
5.7.
Synchronization of IRC, H SV , HD CP and H DA S .....................................................
47
5.8.
D issolved Oxygen (DO) Control and M easurem ent ...................................................
49
Quantification and Validation of K ey Outputs ..................................................................
6.1.
Power Excursion ............................................................................................................
7
54
54
7.
8.
6.2.
Repeatability of Experim ental Results.......................................................................
56
6.3.
Photon Counts to Tem perature Conversion ................................................................
57
6.4.
D etection of ON B...........................................................................................................
62
Analysis of Experim ental Results......................................................................................
65
7.1.
Boiling Curves................................................................................................................
65
7.2.
Single Phase Heat Transfer........................................................................................
71
7.3.
ON B Heat Flux and Tem perature ...............................................................................
72
7.4.
O SV H eat Flux and Tem perature................................................................................
76
7.5.
O V Temperature.............................................................................................................
78
Conclusion ............................................................................................................................
79
References.....................................................................................................................................
81
Appendix A. Determination of optical properties in non-opaque substrates (sapphire)............ 82
A ppendix B. Coupled radiation-conduction m odel ..................................................................
88
Appendix C. Optical properties of sapphire .............................................................................
95
8
List of Figures
Figure 2-1 Sketch of the one-dimensional multi-layer structure in plate heater, which contains four
layers: air, substrate, heater and water (not to scale). Air layer represents an adiabatic boundary.
Substrate layer has specific thickness. Heater layer is negligible due to its extremely small
thickness. Water layer is semi-infinite. The governing equations are solved in substrate and water
18
lay ers.............................................................................................................................................
Figure 2-2 Hsu's model. The bubble can grow out of the nucleation site if the saturation
temperature corresponding to the internal pressure of the incipient bubble (or vapor embryo) is
20
reached or exceeded all over its surface. ..................................................................................
Figure 2-3 Time dependent temperature distribution in liquid governed by transient conduction
compared with local saturation temperature. As the heat flux escalates with time, the time
dependent temperature distribution in liquid shifts upward and eventually intersects with local
22
saturation tem perature curve.........................................................................................................
Figure 2-4 Typical pool boiling curve [2]. The steady boiling curve includes four regions: natural
23
convection, nucleate boiling, transient boiling and film boiling. .............................................
Figure 2-5 Sketch of generic transient and steady boiling curve. The heat transfer of fully
developed nucleate boiling in steady state is well-understood. Under transient condition however,
only the single-phase pre-boiling regime is well predicted by asymptote analytic solution of
transient conduction. What will happen beyond boiling inception is still unclear.................... 24
Figure 4-1 3-layer geometry of ITO heater: sapphire substrate, ITO heater and water (drawing not
to scale). The finite difference equations are discretized at substrate and water layers. The ITO
layer is represented by planar heat source. The air convection is negligible............................ 29
Figure 4-2 (a) HTC against dimensionless time; (b) Percentage of heat storage rate in sapphire
substrate. During the transient conduction stage, the HTC and heat storage rate are constant. After
ONB happens, HTC increases quickly and heat storage rate in substrate decrease sharply. ....... 31
Figure 4-3 Configuration of wrap-around heater. The wrap-around heater consists of three
components: square sapphire substrate, banded heating element made of wrap-around ITO thin
33
film and a pair of silver electrodes............................................................................................
Figure 4-4 Final heater design (left, not to the scale), and picture (right). The final design replaces
the silver pads with wrap-around gold pads, which minimizes the electro-chemical reaction,
38
reduces local therm al stress and enhances heat flux..................................................................
Figure 4-5 SEM image of wrap-around heater. The grain structure of the ITO thin film is clearly
39
seen. The grain size is approximately 100 to 200 nm ................................................................
Figure 4-6 Engineered cavity pattern (left) and SEM image (right). A hexagonal array of
cylindrical cavities were engineered on the heating surface. The SEM image shows the cavity has
39
4-micron diameter and approx.9-micron depth. .......................................................................
Figure 5-1 Schematic of experimental setup for pool boiling tests. A complete set of equipment
40
used and signal flow s are illustrated .........................................................................................
9
Figure 5-2 Schematic of pool boiling facility (dissolved oxygen control and measurement system
not shown). The PBF consists of two concentric stainless steel cylinders. The inner cylinder
accommodates DI water while the outer enclosure behaves as isothermal bath. Four visualizing
glass windows locate around the outer surface of PBF spacing in 900 to each other............... 41
Figure 5-3 Design of heater cartridge: explosion view (left), assembled view (middle), bottom
view (right). Heater cartridge consists of three components: a pair of graphite electrodes, a pair of
T-shape insulating baffles made by macor, a pair of plate insulating baffles made by macor. A
heater-installation groove is form by graphite electrodes and T-shape macor baffles. ............ 42
Figure 5-4 Schematic of signal chart and wire connections. In HDAS, terminals 1&35 acquire
driven signal for cameras; terminals 2&36 acquire separated voltage of heater; terminals 3&37
acquire shunt signal; terminals 4&38 acquire trigger signal; terminal 39 connects to the ground of
D CP ...............................................................................................................................................
46
Figure 5-5 Synchronization test for IRC and HSV. Visible light bulb and IR light bulb were driven
by FG 2 at the same blinking frequency. HSV and IRC recorded the blinking behaviors of visible
light and IR light respectively..................................................................................................
48
Figure 5-6 Event-line of the synchronization. Four events happen successivelv in time: DAS pretrigger reading, trigger, starting of cameras and HDCP outputs...............................................
49
Figure 5-7 DO control and measurement systems for PBF. The DO control system consists of all
the parts connected to the degassing chimney, which involves with the degassing process, isolation
and volume compensation of PBF. The DO measurement system consists of all the parts connected
to the sampling line, which involves with the measurement of DO concentration in water pool. 50
Figure 5-8 Extech 407510 DO meter. The DO meter measured the water sample extracted from
th e P B F ..........................................................................................................................................
50
Figure 5-9 Change in ONB temperature v.s. DO concentration and cavity diameter. The change
in ONB temperature increases with the increasing of DO concentration and cavity diameter. The
DO concentration at 3.6-ppm has very little effect on change of ONB temperature................ 52
Figure 6-1 Comparison of the ideal and measured voltage, current and power of the ITO heater
(the red dots represent the measured values and the black curves represent the ideal values
calculated by equations. 6.1, 6.2 and 6.3): a) 5ms_75K; b) lOms_75K. The measured values agree
very well w ith the ideal trends......................................................................................................
55
Figure 6-2 Comparison of 2D photon counts contours at the same moment for five runs at 20ms
period and 25K subcooling conducted on a wrap-around heater. Different runs result in similar 2D
contours of photon counts at the same moment which denotes good repeatability of experimental
resu lts............................................................................................................................................
56
Figure 6-3 Comparison of average photon counts increase for different runs at 20ms period and
25K subcooling conducted on wrap-around heater. Five curves converge into one curve within the
measurement uncertainty, which confirms again the repeatability of experimental results......... 57
10
Figure 6-4 Heater radiation towards the IRC. Both the ITO and the substrate emit IR signal. The
latter one is a contamination to the previous one. The level of IR signal contamination also depends
on the temperature distribution within the substrate..................................................................
58
Figure 6-5 IR emission from a heater with sapphire substrate thickness of 250 microns. At constant
temperature distribution condition, approximately 3% of the emission comes from substrate.... 59
Figure 6-6 IR emission from a heater with sapphire substrate thickness of 1 mm (wrap-around
heater). At constant temperature distribution condition, approximately 10% of the emission comes
from sub strate................................................................................................................................
59
Figure 6-7 IR emission in a typical exponential power excursion (5 ms period - 75K subcooling
- 1 mm substrate). At transient heating condition, the temperature distribution in substrate varies
with time which leads to a temporally dependent repartition of IR signal between ITO emission
and substrate em ission..................................................................................................................
60
Figure 6-8 Flow chart of the coupled conduction-radiation inverse problem. Following the flow
chart, the surface-averaged ITO temperature at each time step was converted from photon counts
by iteration. Furthermore, the heat flux to substrate and hence the heat flux to water were calculated
given the surface-averaged ITO temperature.............................................................................
61
Figure 6-9 Detection of the ONB moment (scenario 1). The ONB bubble appears on the HSV and
IRC at the same moment, which results in an ONB range of 0.2ms. .......................................
63
Figure 6-10 Detection of the ONB moment (scenario 2). The ONB bubble appears first on the
HSV and then IRC, which results in an ONB range of 0.09ms.................................................
63
Figure 6-11 Detection of the ONB moment (scenario 3). The ONB bubble appears first on the
64
IRC and then H SV, which results in an ONB range of 0.11 ms.................................................
Figure 7-1 Typical boiling curve with temperature overshoot at 10 ms and 75K subcooling. Five
successive steps are distinguished on this type of boiling curve. .............................................
66
Figure 7-2 Typical HSV (top/black & white) and IR (bottom/color) images for each boiling step
of boiling curve with temperature overshoot. HSV images show the boiling/bubble behavior, while
IRC images show the corresponding 2D temperature distribution on the heating surface..... 67
Figure 7-3 Typical boiling curve without temperature overshoot at 10 ms and 25K subcooling.
Three successive steps are distinguished on this type of boiling curve.................................... 68
Figure 7-4 Typical HSV (top/black & white) and IR (bottom/color) images for each boiling step
of boiling curve without temperature overshoot. HSV images show the boiling/bubble behavior,
while IRC images show the corresponding 2D temperature distribution on the heating surface. 69
Figure 7-5 Typical boiling curves for each test condition. For the same subcooling, boiling curves
shift upward and rightward with decreasing power period. For the same power period, boiling
71
curves shift upward and rightward with increasing subcooling...............................................
Figure 7-6 ONB heat flux versus power periods at different subcoolings. For the same subcooling,
ONB heat fluxes varies with period following a trend proportional to 1/T. For the same period,
73
higher subcooling leads to higher ONB heat flux....................................................................
11
Figure 7-7 ONB wall superheat versus power periods at different subcoolings. For the same
subcooling, smaller period leads to higher wall superheat. For the same period, higher subcooling
leads to higher w all superheat...................................................................................................
73
Figure 7-8 Schematic of temperature distribution at ONB moment by Hsu's criterion (drawing not
to the scale). a) For the same subcooling, smaller period leads to higher wall superheat. b) For the
same period, higher subcooling leads to higher wall superheat...............................................
75
Figure 7-9 SEM image of the nucleation cavity. The bigger end of the pear-shape nucleation
cavity has the equivalent diameter of 5 microns.......................................................................
76
Figure 7-10 OSV heat flux versus power periods at different subcoolings. OSV heat flux varies
with period and subcooling similar to ONB heat flux ..............................................................
77
Figure 7-11 OSV wall superheat versus power periods at different subcoolings. OSV wall
superheat varies with period and subcooling similar to ONB wall superheat.......................... 77
Figure 7-12 OV wall superheat versus power periods at different subcoolings. OV was not
observed at period of 5ms and I Oms at subcooling of 25K and OK. OV wall superheat (if exists)
varies with period and subcooling similar to ONB wall superheat. .........................................
78
Figure A.1 Apparent transmissivity of sapphire wafers (320 and 2020 microns). From 3 to 4.5
microns, the apparent transmissivity for both wafers are generally constant. From 4.5 to 5 microns,
the apparent transm issivity slightly decrease...........................................................................
84
Figure A.2 Reflectivity between sapphire and air. The measured reflectivity between sapphire and
air are generally constant between 3 to 5 m icrons....................................................................
85
Figure A.3 Absorption coefficient of sapphire. The spectral absorption coefficient is calculated by
Eq.s A.8 with measured apparent transmissivity. The absorption coefficient increases sharply
between 4.5 to 5 microns which leads to higher emission. The measured values are consistent with
those in literature [18]...................................................................................................................
85
Figure A.4 Sapphire nA compared to dispersion equations for ordinary and extra-ordinary index.
The measured value agrees well with Dobrovinskaya's data and those calculated by Eq. A.9 with
ordinary index and extra-ordinary index....................................................................................
87
Figure A.5 Sapphire extinction index k. The complex part of reflection index is generally
constant from 3 to 4 microns, while it starts to increase after 4 microns. ................................
87
Figure B.1 Heater radiation towards the IRC (reproduction of Figure 6-4). Both the ITO and the
substrate emit IR signal. The latter one is a contamination to the previous one. The level of IR
signal contamination also depends on the temperature distribution within the substrate...... 88
Figure B.2 Multiple reflections and absorption determining apparent transmissivity. The photon
flux emitted by ITO is reflected back and forth between sapphire-ITO interface and sapphire-air
interface. Each time the photon flux goes through sapphire, it is partially absorbed. Each time the
photon flux reaches the sapphire-air interface it is partially transmitted. Each time the photon flux
reaches the sapphire-ITO interface it is partially reflected and partially absorbed. The similar
process happens for the emission from sapphire. .....................................................................
90
12
Figure B.3 Flow chart of the coupled conduction-radiation inverse problem (reproduction of
F igure 6-8)....................................................................................................................................92
Figure B.4 Comparison between measured and calculated radiation is steady-state condition
(uniform temperature profile within the heater). The overlapped region between wet calibration
and dry calibration agrees well with each other, which confirms the consistency of the calibration.
The radiation model agrees very well with the calibration points, which validates the accuracy of
the radiation m odel. ......................................................................................................................
93
Figure C.1 Apparent optical properties of our heater. The apparent optical properties shown are
all direct m easurem ents obtained by FTIR. ..............................................................................
95
Figure C.2 Pure optical properties of interest for our heater. The pure optical properties are
obtained by the methods discussed in Appendix A and Appendix B with the inputs of apparent
96
optical properties in Figure C .1. ..............................................................................................
13
List of Tables
Table 3-1 Major parameters and their range/measuring method .............................................
27
Table 4-1 Properties of substrate candidate materials.............................................................
33
Table 4-2 Evaluation results of different substrate materials...................................................
35
Table 7-1 Number of tests run for each condition in the test matrix for pool boiling ............. 65
Table A.1 Dispersion equation constants for sapphire.............................................................
14
86
1. Introduction
1.1. Motivation
The instantaneous extraction of a control rod from a nuclear reactor core may cause prompt
criticality and an exponential excursion of the thermal power generated within the fuel rods. The
heat is transferred from the fuel to the water coolant which then starts to boil. The heat generation
rate in the fuel can be described as q"'(t) oc e t/T , where t is time and - is the reactor period. The
period can be as short as a few milliseconds. The feedbacks caused by the heating (Doppler in the
fuel and void in the coolant) represent an important insertion of negative reactivity. Depending on
the magnitude and time scale of these feedbacks, either a safe conclusion to the accident is rapidly
achieved or, in extreme cases, the fuel can melt, the molten material be expulsed, fragmented and
possibly lead to steam explosion. Therefore, the time delay between the production of the thermal
energy within the fuel and its transfer to the coolant is key to determining the outcome of the
accident. In turn, this time delay depends on conduction heat transfer within the fuel, single-phase
convective heat transfer and eventually transient boiling heat transfer in the coolant.
Conduction and single-phase convective heat transfer are well understood phenomena:
analytical models [1] and empirical correlations [2] allow capture the thermal behavior of platetype fuel or heaters in contact with a single-phase coolant. On the other hand, transient boiling heat
transfer is a scarcely studied and much less understood phenomenon. Earlier studies have shown
that important features of the boiling curve (i.e. onset of nucleate boiling (ONB), nucleate boiling
heat transfer coefficient (HTC), and Critical Heat Flux (CHF)) in transient conditions significantly
differ from those at steady-state [3]. However, the mechanisms by which these changes occur are
still not clear, which makes this topic very interesting and worthy to be investigated carefully and
thoroughly.
1.2. Objectives
The objective of this work is to study transient boiling heat transfer phenomena under
exponentially escalating heat fluxes on plate-type heaters, at the time scales of milliseconds and
various subcoolings typical of Reactivity Initiated Accidents (RIAs) in pool type nuclear reactors.
15
State-of-the-art diagnostics such as synchronized infrared (IR) thermometry and highspeed video (HSV) were deployed to gain insight into the physical phenomena and generate a
database that could be used for development and validation of accurate models of transient boiling
heat transfer and identification of mechanisms. Specifically, the transient boiling curves were
measured up to fully developed nucleate boiling (FDNB), according to which ONB, OSV and OV
conditions were identified.
16
2. Background and Previous Research
In this chapter, an introduction of previous studies on single phase transient heat transfer,
boiling inception theory, classical steady boiling and transient boiling is presented.
2.1.
Single Phase Transient Heat Transfer
Single phase heat transfer before boiling inception in pool condition has been thoroughly
studied under exponentially heat flux escalations. Both experimental and analytical investigations
were conducted in previous researches.
Exponential transient conduction experiments were first published in 1957 by Rosenthal
[3], who used platinum and aluminum ribbons as heaters immerged in stagnant water at different
temperatures. It was observed that natural convection did not contribute to heat transfer during the
non-boiling phase at short periods (<100 ms) due to rapid temperature rise. The leading heat
transfer mechanism was instead conduction, for which Rosenthal proposed an analytic solution.
Soliman and Johnson [4] investigated the role of forced convection in the non-boiling
regime on a Deltamax@ ribbon (50% nickel, 50% iron). They stated that for short periods, much
smaller than the travel time of the fluid in the heated channel, an estimate of average wall
temperature rise could be obtained by a one-dimensional transversal conduction model combined
with a one-dimension longitudinal advection model.
Johnson [5] reported that for stagnant water or low velocity, a reasonably accurate estimate
of the single-phase heat transfer coefficient could be obtained with the analytic solution by
Rosenthal [3].
In 1977, Sakurai and Shiotsu [6, 7] investigated non-boiling heat transfer with a platinum
wire in subcooled pool conditions. They showed that the heat transfer coefficient before the
inception of boiling can be estimated by conduction at short period or natural convection at longer
periods (> 1 s).
According to the previous experimental works, single phase heat transfer in fast transients
(-
< 100 ms) before boiling inception is governed by transient heat conduction, with negligible
17
contribution from free convection. In such conditions, an asymptotic analytic solution of the onedimensional transient heat conduction problem was achieved by Sargentini et. al.[1].
substrate
air
heater
LO
kCps, ps
Figure 2-1 Sketch of the one-dimensional multi-layer structure in plate heater,
which containsfourlayers: air, substrate, heaterand water (not to scale). Air layer
represents an adiabatic boundary. Substrate layer has specific thickness. Heater
layer is negligible due to its extremely small thickness. Water layer is semi-infinite.
The governing equations are solved in substrate and water layers.
The one-dimensional approximation is only applicable in a large aspect ratio (lateral scale
versus thickness scale) configuration such as the plate heater that was applied in present study. As
shown in Figure 2-1, the region to be solved consists of a substrate, a heater and a semi-infinite
water layer. Due to the small thickness of the heater and henceforth its negligible thermal resistance
and thermal capacity, the heater layer was modeled as a planar surface energy source given by
q'eti/T where q' denotes initial surface energy source. The air/substrate interface was assumed to
be adiabatic because of the low heat transfer coefficient. The equations governing the system,
together with the appropriate initial and boundary conditions are listed below:
=
at
s
at
-ks
a
sT
"s aX2
""
x2
x = = 0 Vt
5
as Xs=0
0
=qOet/T
(2.1)
ks
(2.3)
Tsxs=Ls
(2.5)
TsIt=0 = TwIt=0 = To V xs,xw
-
2T
T
xs.
18
- kw
xT
axW Xw=0
Xw=-W
Vt O
(2.2)
(2.4)
(2.6)
0)
(2.7
)
TWIxW=c = TO V t
where T is the temperature, x is the distance from a reference point, k is thermal conductivity, L is
the thickness of certain layer, a = k/ pcp is the thermal difussivity (p is density and cp is specific
heat), the subscripts 's' and 'w' stand for sapphire and water, respectively.
The asymptotic solution of the transient conduction problem, for short period (r <
100ms), obtained by the Laplace transform method, is given by:
[
Ts (xs, t) = Tbulk
+ q 'et/ VT cosh
x5
/ cosh
Es tanh
q1' (t) = ks
+xs=ss
=
q
(
Es tanh]/+ w
w
1
q' et/s VT/Es tanh
DTwaiL(t) =
- LS 0anh Os
ex
qi'et/T ES tanh
f
(2.8)
+ E
/
- x1
Tw (xw, t) = Tbulk + q1' et/T
1
1
/Es
(2.9)
(2.10)
+ Ew
tanh
+ E
(2.11)
=
q"'' (t) = q f' e t/T Ew
W ~ 01/I
Es tanh -1+
Fs
Ew
w
(2.12)
where E = /k pCp is the thermal effusivity, Fos = as x/Li is the substrate asymptotic Fourier
number, DTwaii(t) = Twaii(t) -
Tbulk
is the rise of wall temperature. Note that Twaii(t)
=
TW (xW = 0, t).
2.2.
Boiling Inception Theory
In heterogeneous boiling, vapor bubbles are usually generated from cavities existing on the
heating surface. In order to activate these cavities and create bubbles, certain thermal conditions
need to be fulfilled close to the heating surface. One of the most widely used model to estimate
such thermal conditions for boiling inception (or ONB) is the so called Hsu's model [8]. Hsu's
model postulates that the bubble can grow out of the nucleation site if the saturation temperature
corresponding to the internal pressure of the incipient bubble (or vapor embryo) is reached or
exceeded all over its surface (normally the top of the bubble):
19
(2.13)
T1(ytOP, 0 >_ Tie(ytop)
where T is the temperature profile; y is the distance away from heating surface; t is the time at
certain moment; p is the pressure. Subscript 1 denotes liquid; le denotes local equivalent
saturation condition; top denotes the bubble apex; sat denotes the saturation condition. The Hsu's
model is shown diagrammatically in Figure 2-2.
T,
4
T 1(0,t)
T1 (yt 0 p,
t)
le (Ytop)
Bubble
Embryo
.Te(Y)
T, (y t)
,
I
y
rb
Figure 2-2 Hsu's model. The bubble can grow out of the nucleation site if the
saturation temperature corresponding to the internal pressure of the incipient
bubble (or vapor embryo) is reached or exceeded all over its surface.
The nucleation at a certain cavity, with radius rb, occurs when the actual liquid temperature
profile T, (y, t) has the first intersection point with the local equivalent saturation temperature
profile. The local saturation temperature profile can be obtained by the combination of YoungLaplace equation and linearized Clausius-Clapeyron equation (more accurately either the
integration of Clausius-Clapeyron equation, or a steam table):
20
P
(2.14)
Pi2a
Tie(Y) = Tsat(Pi) 1
+
-P=-+
-ip
ie
Pi
hfgrb
fq
TsatVg
_
Tsat
where rb is the minimum bubble radius that is determined by wettability of heating surface and
size of cavity during the bubble growth; a is the surface tension of liquid; hfg is the latent heat;
Tsat is the saturation temperature based on liquid pressure pl. rb can be related to y according to
the surface condition.
The liquid temperature profile within the superheated layer can be approximated by a linear
distribution, or more accurately by solving a transient heat transfer problem. Under fast transient,
heat conduction approximation and the one-dimensional analytical solution of single phase liquid
temperature profile at plate-type heater condition has been given by Eq.s (2.8)-(2.12). For a
hemispherical embryo (hydrophilic surface) of radius rb, ONB conditions such as wall superheat
lATsat,onb
=
TwalI,onb - Tsat and wall heat flux qw,onb can be achieved by combination of Eq.s
(2.9), (2.12) and (2.14) [9]:
E
,onb
ATsat,onb
sat(Patm +
2
r
a/rb)
-
[Tsat(Patm + 2 a/rb) - TbUlk]
(2.15)
TbUlk] exp
exp
(
--
sUb
(2.16)
where a is the surface tension of water; Patm is the ambient pressure; ATsUb is the initial bulk
subcooling.
The above mechanistic ONB model sheds light on the requirements of wall super heat and
heat flux at the ONB moment. Generally, the smaller is the cavity, the steeper is the temperature
profile adjacent to the heating surface, which results in higher wall super heat and heat flux. On
the other hand, under the transient condition, as the heating period becomes smaller than the
diffusion time of water, the time lag between the power input and the development of thermal
boundary layer in water becomes more significant. Thus, for the same cavity, ideally shorter period
will result in higher ONB heat flux and hence higher ONB wall super heat. Initial bulk subcooling
could also affect the ONB wall super heat by affecting the ONB heat flux. Figure 2-3 generally
shows the relationship between the time dependent temperature distributions in liquid governed
by transient conduction and the local equivalent saturation temperature.
21
Hsu Model
140
130
--
NI
NyNN)
T
-
120
110
100
8070
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Distance from Wall [m]
0.9
1
x
10-4
Figure2-3 Time dependent temperature distribution (dashed blue lines) in liquid
governed by transient conduction compared with local saturation temperature
(black solid line). As the heat flux escalates with time, the time dependent
temperature distributionin liquidshifts upwardand eventually) intersects with local
saturationtemperature curve.
2.3.
Steady Boiling V.S. Transient Boiling
Boiling from a heated surface to a fluid at rest is referred to as pool boiling. Steady state
pool boiling heat transfer has been well studied for decades. The "Boiling Curve" is a widely used
method to represent the process of steady state pool boiling by plotting the heat flux versus wall
superheat as shown in Figure 2-4. As the wall super heat increases, steady state pool boiling
experiences 4 stages in succession: natural convection (A to B), nucleate boiling (B to C),
transition boiling (C to D) and film boiling (D to F). Many models and correlations have been
developed to describe and predict the heat transfer behavior at each stage.
22
1.E+01 I
p
Singlephase
natural
convection
S~e
Transition
Transition
-Nucleate
Nucleate
boiling
boiling
C
i
Stable
___________________________________
mm
Stable
fdmn
boiling
n.b..._
__
_
_
1.E+00
.
"r)
-
1.E-01
D't
B
1.E-02
A
I
V
I
_ __ ____ I
-5
-10
I
-25
~75
~400
Wall superheat, ATt (C)
-________ I1
~8000
Figure2-4 Typical pool boiling curve [2]. The steady boiling curve includesfour
regions: naturalconvection, nucleate boiling, transient boiling andfilm boiling.
Compared to steady state pool boiling, transient pool boiling heat transfer is a scarcely
studied and much less understood phenomenon. Earlier studies by Rosenthal [3] and Sakurai [6,
7] have shown that important features of the boiling curve (i.e. onset of nucleate boiling (ONB),
nucleate boiling heat transfer, and CHF) in transient conditions significantly differ from those at
steady-state (see Figure 2-5).
23
Wrt
bubble
10.
(transient) singie-phase heat transfer
(transient) possible boiling heat transfer
(stad~y)-fuly ~ey*1oped nucleate boiling
10
100
ATsat (*C)
Figure 2-5 Sketch of generic transientand steady boiling curve. The heat transfer
of fully developed nucleate boiling in steady state is well-understood. Under
transient condition however, only the single-phase pre-boiling regime is well
predicted by asymptote analytic solution of transientconduction. What will happen
beyond boiling inception is still unclear.
In previous experimental investigations of transient ONB, different researchers obtained
different conclusions, some of which even contradicted with each other.
Rosenthal [3] observed a significant rise in the ONB temperature with respect to the steady
boiling tests. This temperature rise was higher for shorter periods and higher subcooling. However,
for saturation condition, no major differences were observed with respect to steady boiling.
Johnson [5] observed that boiling inception superheat decreases for increasing period and
pressure for both pool boiling and low velocity conditions, whereas for higher velocity, a lower
superheat was unexpectedly reported for higher subcoolings.
Sakurai and Shiotsu [6] found that wall heat flux and superheat at boiling inception increase
with decreasing period and increasing subcooling. Two kinds of boiling incipience models were
developed by extending the formulation of Hsu [8] and Rohsenow [10] to explain this behavior.
24
In 2000, an extensive review on exponential transient heat transfer was published by
Sakurai [II]. He pointed out the difference between highly wetting fluids, water pre-pressurized
to flood the cavities, and non-pre-pressurized water. In particular, he argued that even for non-prepressurized water, for very short period, boiling inception could be triggered by heterogeneous
spontaneous nucleation instead of nucleation in active unflooded cavities. Moreover, contrarily to
Rosenthal, he showed that, also for saturation conditions and relatively long periods, the onset of
nucleate boiling temperature can be significantly higher than in steady boiling.
Other than ONB, unique phenomena in transient boiling were also distinguished from
steady boiling. Along with the improvement of techniques on transient identification, eg. high
speed photography, the investigations on transient boiling went deeper and deeper.
Rosenthal [3] reported that, once boiling had started, for subcooled conditions and
relatively long period (-r> 15 ms), the behavior of the system was not appreciably different than
steady boiling and thus critical heat flux conditions were not influenced by the power excursion
period. He also showed the presence of a temperature overshoot between ONB and the FDNB.
Johnson's observation [5] confirmed that for the FDNB regime with periods of 5 ms or
longer, no major differences with respect to steady boiling were observed as also reported by
Rosenthal.
Hall and Harrison [12] first shed light on the peculiarities of transients at very short periods
(T< 5 ms) by using high speed video. They observed that, even for very short periods, the boiling
crisis was preceded by nucleation of individual bubbles. During this phase the heat flux could
exceed the critical heat flux for steady conditions by an order of magnitude. A similar behavior
was also observed by Tachibana et al. [13] for linear power excursion.
Sakurai and Shiotsu [6, 7] confirmed the presence of a large temperature overshoot after
boiling inception and pointed out the presence of two different boiling processes. The presence of
the overshoot (representing impaired heat transfer) was explained as the result of the time leg of
activation of initially flooded cavities for the increasing rate of heat flux [7]. In the quasi-static
boiling process (i.e. for relatively long periods), fully developed nucleate boiling is attained shortly
after the temperature overshoot. They argued that, in the rapid boiling process, when the power
excursion periods is very short, the critical heat flux conditions are instead reached before potential
25
active cavities are fully activated. Contrarily to Rosenthal, critical heat flux was observed to vary
as a function of power excursion period and pressure in pool boiling. In fact, Sakurai found that,
for subcooled conditions, the CHF increases as the pressure increases and the period decreases,
also for relatively long periods (r> 5ms) [7]. For saturation conditions the trend is more
complicated. Depending on the pressure, the critical heat flux could increase, then decrease and
finally increase again as the power excursion period decreases [11].
Although the previous experimental results form a highly valuable source of database, it
must be remarked that some of the conclusions from different authors are quantitatively or
qualitatively in disagreement with each other. Besides, the mechanisms by which those unique
phenomena at transient boiling occur are not clear. For these reasons, a new experimental work
devoted to the study on exponentially escalation of heat flux in pool boiling condition was
conducted. This work aimed at clearing the conflicts and confusions in previous studies,
establishing a consistent database for the evaluation of numerical models and clarifying the basic
mechanisms of transient boiling phenomena
26
3. Scope of the Work
With the purpose of achieving better understanding of transient pool boiling heat transfer,
in depth investigations on transient pool boiling of deionized (DI) water were done at ambient
pressure. A specially-designed plate-type heater was installed in a cylindrical pool as a mimic of
fuel element surface in pool type reactors. Various periods were tested in the range from 5 ms to
100 ms. The effects of subcooling were also investigated by running tests at saturation condition
(OK), low subcooling (25K) and high subcooling (75K). The present work mainly focus on the
identification of ONB conditions and the mapping of transient boiling curves up to FDNB. In
addition, OSV conditions and OV conditions were also obtained. The range of parameters explored
and the diagnostic tools used are listed below.
Table 3-1 Majorparametersand their range/diagnosticmethods
Parameters
Range/Measurement Method
Boiling Type
Pool
Heat Flux Period T
5 ms, 10 ms, 20 ms, 50 ms, 100 ms
-6 iex.p(t/))
Subcooling
OK, 25K, 75K
Pressure
Ambient pressure
Heater Temperature Field
Subcooling Measurement
Bubble Parameters
Voltage and Current
2D By IR Camera
T Type Thermal Couple
High Speed Video
Speed Data Acquisition System
-IHigh
As shown in Table 3-1, the application of state-of-the-art diagnostics such as synchronized
high speed IR and HSV cameras further extended the spatial and temporal resolution of the
measurement and minimized the uncertainty in the analysis of results. Specially, the 2D
temperature distribution on heating surface was measured by IR camera. The subcooling
temperature was monitored by thermal couple stuck to the heating surface. The bubble parameters
and the ONB moment were measured by HSV. The total power input was obtained from the
measurement of voltage and current over the heater by a high speed data acquisition system (DAS).
The heat flux to sapphire was estimated by solving a transient conduction problem imposing the
initial bulk subcooling and the heating surface temperature as boundary condition. The heat flux
to water was calculated by subtracting the heat flux to sapphire from total planar heat source.
27
4. Design of the Plate Type Heater
In this chapter, the design process of the plate type heater that was implemented in the pool
boiling tests is presented. One-dimensional simulations were carried out for the prediction of
temperature profile inside the heater in prescribed transient conditions, by which the heater design
and an extended range of substrate materials were evaluated and selected. An optimized design
was achieved by considering all the operating requirements.
4.1.
Simulation of Heater Behavior under Transient Condition
A schematic of the heater to be used in experiments is shown in Figure 4-1. A thin indium-
tin-oxide (ITO) film boils off water by Joule-Heating. Such thin film is deposited on a thicker,
electrically insulating substrate which provides structural support to the ITO coating. The back
side of the substrate is open to atmospheric air. In a temporal transient situation, the heat generated
within the ITO film is partially transferred to water and partially to the sapphire substrate.
Unfortunately, the amount of sensible heat stored in the substrate is non-negligible. Therefore, for
a target power delivered to water, the power delivered to the ITO by the power supply have to be
significantly higher. Prior to finalizing the heater design, one-dimensional simulations of transient
conduction within the substrate-ITO-water system were performed with the following objectives:
*
Establish the required output of the DC power supply;
*
Develop a code that can calculate the heat flux to water, given the measured surface
temperature;
*
Explore a range of parameters, i.e. ITO reacting area, substrate materials and
thicknesses, to identify an optimum design that would allow for tests to be achieved all
over the range of periods and subcoolings expected in the experimental matrix.
28
Sphre Substrae
ITO Heater
High Speed
infrared
Camera
x
z-c>
TW.
0
Ls
Figure 4-1 3-layer geometry of ITO heater: sapphire substrate, ITO heater and
water (drawing not to scale). The finite difference equations are discretized in
substrate and water layers. The ITO layer is represented by planar heat source.
The airconvection is negligible.
The reference heater design [14], inherited from previous projects in our research group,
comprises a 0.7 micron ITO thin film on top of a relatively thick (250 microns) sapphire substrate.
Due to the large aspect ratio between lateral scale (1 cm by 2cm) and thickness (250 microns), the
assumption of one-dimensional heat transfer is considered sufficiently accurate for this geometry.
Since the objective of the project is to study transient boiling heat transfer, the heat flux to
water must be known accurately throughout the transient. At any given time, the heat flux to water
(i.e. the instantaneous value of the heat delivered to the fluid per unit time and surface area of the
heater) can be found from the first law of thermodynamics
qW = qst
-
qS
(4.1)
where q" can be discretized as the finite difference equation at the solid-water interface by the
discretized Fourier's conduction law:
ft = q If
/ )ti
= qexp(t/,
) -
t-5k, T(
(4.2)
.
W
29
In Eq.4.1, q" t is the total power input from DC power supply divided by reacting area. In
Eq.4.2, k is the thermal conductivity; 6x is the spatial discretization; T1 is the temperature of solid
node at solid-water interface (wall temperature) and T2 is the temperature of the neighbor solid
node in the substrate; the superscript "t" denotes the time step.
The thermal capacity of the ITO heater was omitted because of its extremely thin thickness.
Convection to air was also verified to be negligible because of the low air heat transfer coefficient.
The main objective of the simulation was to present a numerical solution of transient conduction
within the substrate, which allowed determination of the sensible heat storage rate in the substrate
with the measured wall temperature as the boundary condition, so that through Eq. 4.2 the heat
flux to water could be estimated.
Several strategies were applied to determine the boundary conditions. The adiabatic
codiA
ws
pli1d
LU
theIl heater-air Uoundary since the air convection was negligible. A
constant subcooling temperature was imposed at the right boundary of the water layer, and the
water layer thickness was chosen sufficiently high not to affect the results. However, after ONB
has occurred on the ITO surface (more details below), transient conduction in the water was no
longer simulated; instead the nucleate boiling heat transfer coefficient (h) was estimated from
Rohsenow correlation [2]:
[g(p 1
- p)
h
C
CsfhigPr
- Tsat )2
(4.3)
where p, is the liquid viscosity; hig is the latent heat; g is gravitational acceleration; pi and pg are
liquid and vapor density; a is surface tension coefficient; Cpi is liquid specific heat; Pr is liquid
Prandtl number; Csf is an empirical parameter equal to 0.013. Continuous temperature and heat
flux at the heater-water interface are assumed. ONB is postulated to occur when Rohsenow HTC
is larger than the effective HTC (hetj) calculated from transient conduction, defined as:
heff =
Twaii
-
Tbulk
30
(4.4)
The results of the simulations for the reference heater design at saturation condition are
shown in Figure 4-2 together with the asymptotic analytical values of transient conduction [1],
where a percentage of heat storage rate (PHSR) in substrate is defined as:
PHSR =
q
ot
(4.5)
350000
(a)
-Simulation
O.Is
-Simulation 0.01s
-Simulation 0.003s
- - -Analytic 0.ls
- - AnalytC 0.01s
Analytic 0.003s
300000
250000
200000
150000
100000
ONS
50000
0
1
2
4
t/tau
3
31
5
6
7
8
1
0.7
.E 0.7
S0.6
a.
0.5
-- Simulation
*0.4
60
.
-Simulation
0.3
.3
-Simulation
0.1s
0.015
0.003s
- -- Analytic O.ls
- - - Analytic 0.01s
Analytic 0.003s
0.
i0.1
0
0
1
2
3
4
t/tau
5
6
7
8
Figure 4-2 (a) HTC against dimensionless time; (b) Percentage of heat storage
rate in sapphiresubstrate. Duringthe transientconduction stage, the HTC and heat
storage rate are constant. After ONB happens, HTC increases quickly and heat
storage rate in substrate decrease sharply.
During the transient conduction, the results by one-dimensional simulation agree very well
with the asymptotic analytical values in Figure 4-2 (a) and (b). As Figure 4-2 (b) shows, the
majority of heat generated in the heater is initially stored in the substrate, not transferred to the
fluid. This is due to the high effusivity (Vk p Cp) of the substrate (sapphire was used for these
simulations) compared to the effusivity of water (See table 4-1).
4.2.
Basic Heater Design and Substrate Evaluation
4.2.1. Basic Heater Design
The heater design that could be applied for this study should take into account several
considerations, including heat storage in the substrate, optical properties to allow for accurate
32
access to the ITO by the IR camera, resistance to thermal shock, ITO reacting area, ease of
fabrication and cost. Several design criteria were established:
For the heating material (film coating):
*
It should be opaque and emissive in the IR range from 3 to 5 microns, in order to,
respectively,
screen the IR emission from water and produce
IR radiation
corresponding to the surface temperature;
*
It should be thin enough to have negligible thermal capacity and thermal resistance,
which means negligible temperature drop across the heater, so that the temperature
measured at the back side of the film is essentially equal to the temperature at the
heater-water interface;
"
It should be electrochemically stable in water.
For the substrate material:
"
It should have sufficient mechanical strength for structural support of the extremely
thin heater which is usually <1 microns;
*
It should be as transparent as possible in IR to transmit the light emitted by the heater,
especially in the 3-5 micron range where the IR camera collects the radiation;
"
It should have acceptable effusivity (as small as possible) to minimize heat storage in
the substrate, thus maximizing the heat flux to water, and reducing the power supply
capacity requirements;
"
It should have high resistance to thermal shock, because large temperature gradients
develop in the substrate during transient boiling especially under high subcooling
condition.
Based on the criteria above and the experiences from previous experiments, we chose the
so-called wrap-around heater as basic heater configuration. As Figure 4-3 shows, the lateral size
of the wrap-around heater is 2 by 2 cm 2 and the reacting area is 1 by 2 cm 2 . The ITO thin film, as
heating element, is wrapped from the top of the heater (in contact with water) to the bottom of the
heater (in contact with air). With such configuration, electrical wires can be epoxied to the air side
of the heater which avoids electrode exposure to water as well as disturbance of the fluid. However,
the higher thickness of the substrate (minimum I mm) required to wrap ITO thin film around the
33
fillet leads to higher power storage rate in the substrate. Moreover, the IR emission from a sapphire
substrate with more than 1mm thickness is not negligible.
Water
SoppdeSubstrate
Sihvw
Elackro
Air
Figure 4-3 Configurationofwrap-aroundheater. The wrap-aroundheaterconsists
of three components: square sapphiresubstrate, banded heating element made of
wrap-aroundITO thin film and a pair of silver electrodes.
4.2.2. Evaluation of Substrate Materials
Since sapphire is not a perfect substrate material due to its high effusivity and slight
emission, a comprehensive evaluation over extended range of substrate materials was conducted
(see Table 4-1). Criteria adopted to determine these disadvantages are detailed in the following.
Table 4-1 Propertiesof substrate candidate materials
K
C
Density
Diffusivity
Effusivity
[W/m-KI
IJ/kg-K
Ikg/m']
1m2 /sI
IW.s"-/m 2 K]
Materials
Thermal
expansion
Il/K]
Young's
modulus
[GPa]
Strength
Limit
[MPa]
Transmittance
at 3-5 microns
wavelength
[%@thickness]
Sapphire
35
761
3980
1.16E-5
1.03E+4
5.30E-6
335
300
>90 @260 pm
Fused Quartz
1.3
720
2200
8.21E-7
1.43E+3
5.50E-7
72
52
90-0 @ 500 gm
34
Spinel
14.7
879
3580
4.67E-6
6.80E+3
6.09E-6
277
200
>85
@ 1mm
1) Power Limit
The 1 D transient conduction code was applied to evaluate the required output of DC power
supply for different substrate materials under the conditions listed in Table 4-1. In particular, the
boiling process was expected to reach OSV. The OSV point was determined as the intersection
between single phase heat transfer and the CATHARE OSV correlation [15]:
hCATHARE =
0.5874
*
(Twaiosv - Tsat)
(4.6)
If the HTC calculated by CATHARE correlation (hCATHARE) was larger than the effective
conduction HTC (he!!), OSV was considered to occur. Once OSV wall heat flux was known, the
required capabilities of the DC power supply could be determined in terms of maximum output
power, voltage, current, voltage slew rate and current slew rate. If the capabilities of the DC power
supply were smaller than any of these limitations, the power supply could not output enough power
(or fast enough) for the occurrence of OSV. Such a deficiency is reported as "Power Limit" in
Table 4-2.
2) Impaired IR Radiation
The optical properties of the substrate material that we concerned are absorption, reflection
and transmission. The probability of a photon emitted by the ITO to reach the IR camera decreases
if the absorption of the substrate material and the reflections at the ITO/substrate and substrate/air
interfaces are high (transmission = 1 - reflection - absorption). Thus, the ideal substrate
has both low absorption and low reflection with air and ITO. Highly reflecting interfaces are not
desirable because they reflect back the light beam emitted by the ITO. Absorption is even less
desirable, because materials that absorb also emit very well. Thus, if a substrate with high
absorption is used, the IR signal emitted by ITO is not only impaired, but also "polluted" by the
IR emission of the substrate.
Obviously, a substrate material with high transmission through the working spectrum of
the IR camera (3-5 microns) is preferred and thus, if a substrate material has high
35
absorption/emission or reflection the "Impaired IR transmission" disadvantage is noted in Table
4-2. However, even if a material suffers from impaired transmission, a radiation-conduction model
(detailed in Appendix B) can be used to post process the recorded IR signal and exclude the
contribution of the substrate emission.
3) Risk of Thermal Shock
The fast exponential power excursion generates a large temperature gradient in the
substrate, which could lead to a cracking of substrate by thermal shock. To check the resistance of
a substrate, a conservative assumption was made, that one side of the substrate (in contact with
air) remained at initial subcooling
(Tblk)
while the other side (in contact with ITO) reached ONB
temperature. The following simple equation was used to estimate the thermal stress (1):
f = aE(Twaiosv - Tbulk)
(4.7)
where a is the thermal expansion coefficient, E is the Young's modulus.
The estimated thermal stress f was compared with the yield strength limit of substrate
materials listed in Table 4-1. In case f is larger than the strength limit, "Risk of thermal shock" is
entered in the corresponding field in Table 4-2.
4) Results of The Substrate Material Evaluation
The results of the substrate evaluation are summarized in Table 4-2 where possible
disadvantages are shown for each condition in the test matrix.
Table 4-2 Evaluationresults of different substrate materials
B0ROSILICATE (180 pm)
Subcooing
-5'
0K
5 ms
Impaired IR Transmission
Impaired IR Transmission Impaired IR Transmission
10 ms
Impaired IR Transmission
Impaired
Material / Perid
36
IR Transmission
Impaired IR Transmission
IR Transmission
IR Transmission
Impaired IR Transmission
Impaired
IR Transmission
50 ms
Impaired
100 ms
Impaired
5 ms
GOOD
GOOD
Power Limit
10 ms
GOOD
GOOD
GOOD
50 ms
GOOD
GOOD
GOOD
100 ms
GOOD
GOOD
GOOD
5 ms
GOOD
GOOD
Power Limit
ms
GOOD
GOOD
GOOD
50 ms
GOOD
GOOD
GOOD
ms
SPINEUl(ama)
GOOD
GOOD
GOOD
axK_____7,K
5 ms
GOOD
GOOD
Power Limit
10 ms
GOOD
GOOD
Power Limit
50 ms
GOOD
GOOD
GOOD
100 ms
GOOD
GOOD
GOOD
10
100
Impaired
JSIrDrQUARTZss(1
IR Transmission
Impaired IR Transmission
pr
Ip)
I:k Tss
Impaired
IR Transmission
Impaired
IR Transmission
IR Transmission
Impaired IR Transmission
Impaired
Impaired IR Transmission
Impaired
100 ms
Impaired JR Transmission
Impaired JR Transmission
Impaired JR Transmission
5 ms
10 ms
GOOD
GOOD
Risk of Thermal Shock
GOOD
GOOD
Risk of Thermal Shock
50 ms
GOOD
GOOD
Risk of Thermal Shock
100 ms
GOOD
GOOD
Risk of Thermal Shock
5 ms
GOOD
GOOD
Power Limit
10 ms
GOOD
GOOD
Power Limit
ms
GOOD
GOOD
Risk of Thermal Shock
GOOD
GOOD
Risk of Thermal Shock
5ims
Impaired IR Transmission
10 ms
Impaired
50 ms
Impaired
50
100 ms
IR Transmission
IR Transmission
IR Transmission
As shown in Table 4-2, there are two promising candidate materials for the substrate which
have comparatively less disadvantages: AMTIR-l and sapphire. AMTIR -1 has the advantages of
both non-emitting nature and low effusivity. But it carries the risk of thermal shock due to high
thermal expansion and low strength limit, which indicates the need to conduct a quenching test for
AMTIR- 1 sample. Sapphire is the other promising material which has a very high transmission
from 3-4.5 micron and slight emission from 4.5 to 5 micron, and also very good mechanical
strength. However the existed heater design with sapphire substrate cannot cover the high
37
subcooling and short period section of the experimental matrix because of insufficient heat flux to
water. An enhancement of heat flux to water is required for the application of sapphire substrate.
In order to finalize the evaluation, quenching tests were conducted to both candidate
substrate materials. Propylene glycol was used to generate a steady liquid pool temperature of
140 *C which was an estimated OV temperature at high subcooling and short period condition.
Test-specimens were dipped into the 140 *C liquid pool from room temperature for multiple times.
AMTIR -1 wafer with 1 inch outer diameter (OD) and 2mm thickness was tested not to survive
more than 3 times dipping. Through crack was formed on the AMTIR- 1 wafer during the
quenching tests. It was also found that after each quenching, some small debris/flakes of the
material shed off the wafer which could be a potential risk leading to loss of sealing or
contamination of the water pool. The AMTIR-I was abandoned after the quenching tests. The
same quenching tests were conducted to 1mm thick sapphire squares which survived the tests as
expected. Eventually, sapphire was still the best choice for substrate material according to our
comprehensive evaluation.
4.3.
Final Heater Design
4.3.1. Heater Configuration
As mentioned before, the application of sapphire comes with two disadvantages. One is
the slight emission from 4.5 to 5 micron wavelength which could pollute the IR emission from the
heater. The other is the insufficient heat flux to water, due to high effusivity, which makes it unable
to cover the test matrix. However, these two disadvantages could be solved.
The solution to the first disadvantage was to post-process the IR camera reading solving
an inverse coupled radiation-conduction problem, so that the emission from the sapphire substrate
was eliminated. The technical details will be discussed in the following section.
The solution to the second disadvantage was to reduce the reacting area from 1 by 2 cm 2
to 1 by 1 cm2 by wrapping gold pads from the top to the bottom of the heater as shown in Figure
4-4. After the downsizing, the scale of the reacting area was still significantly larger than the
Laplace length of water at the conditions of interest, thus edge effects on nucleate boiling could be
neglected. Furthermore, the heater resistance was decreased from 5 Ohms (typical of basic wrap38
around heater) to less than 3 Ohms. With the above modifications, the maximum heat flux to water
achievable was approximately 4 times higher than the value for the basic wrap-around heater.
Before ONB, the ideal maximum heat flux to water is estimated as:
q1 = qfot,maxp = 40p MW/rm2
p = Ew/ Es tanh
+ Ew
0.139-0.29
8
(4.9)
which is sufficient to initiate boiling even in the most penalizing condition (qp = 0.139 at 5ms and
75K subcooling).
ITO Film
Water
Gold Pad
Air
Sapphire Substrate
Figure4-4 Finalheaterdesign (left, not to the scale), andpicture (right). The final
design replaces the silver pads with wrap-aroundgoldpads, which minimizes the
electro-chemicalreaction, reduces local thermal stress and enhances heatflux.
Extra benefits were also obtained through use of the gold pads. In the whole range of
voltages (;
100 V) applied, the gold pads experienced much lower surface damage than the silver
pads. The local thermal stress of the heater fillets at the recess of the heater cartridge was reduced
by constraining the heat generation to the top center of the wrap-around heater.
4.3.2. Heating Surface
The heating surface of the wrap-around heaters is generally nano-smooth with typical grain
size of 100 to 200 nim, as shown by the scanning electron microscope (SEM) image in Figure 45.
The measured static contact angle of this surface is approximately 90 degree.
39
Figure 4-5 SEM image ofwrap-aroundheater. The grain structure of the ITO thin
film is clearly seen. The grain size is approximately 100 to 200 nm.
In the aim to control the ONB conditions and make a clear comparison with theoretical
ONB models, a pattern of cylindrical cavities was engineered on the heating surface using focused
ion beam (FIB). A cavity pattern consisting of 7 cavities in a hexagonal array was etched, as shown
in Figure 4-6 (left). The SEM image of a typical cavity is shown in Figure 4-6 (right). The cavities
had a 4 -micron diameter and approximately a 9-micron depth.
0
0
0
9
I
2mm
Figure 4-6 Engineered cavity pattern (left) and SEM image (right). A hexagonal
array of cylindrical cavities were engineered on the heating surface. The SEM
image shows the cavity has 4-micron diameter and approx.9-micron depth.
40
5. Experimental Setups
The experimental setup used in this study is shown in Figure . Dashed lines denote the
driving signal either from the trigger or from the function generator (FG). A representative signal
is sketched next to each signal line. Solid lines denote the output signals acquired by DAS. Arrows
denote the signal direction. As we can see, the whole system is synchronized by a high level trigger
and two function generators. Precise synchronization of the diagnostics was one of the most
important and challenging activities in this study.
Trigger
- -
2
---- ---------------
-
r-FG
-- FG I
- -r ---------- -- ------------------------
I
-----------~---II
I
I
P1
HSV
IRC-
Figure 5-1 Schematic of experimentalsetup for pool boiling tests. A complete set
of equipment used andsignalflows are illustrated
41
Detailed functions, specifications and operating range for each equipment implemented in
pool boiling tests are presented below.
5.1.
Pool Boiling Facility (PBF)
Isothermal bath
Windos for lawer
4XI and imaging
Bath Rud
ITO heatr
Mirrm
Figure 5-2 Schematic of pool boiling facility (dissolved oxygen control and
measurementsystem not shown). The PBFconsists oftwo concentric stainless steel
cylinders. The inner cylinder accommodates DI water while the outer enclosure
behaves as isothermal bath. Four visualizing glass windows locate around the
outer surface of PBFspacing in 900 to each other.
The pool boiling facility (Figure 5-2) features a concentric-double-cylinder structure:
boiling of DI water takes place in the inner cell, while the outer enclosure functions as an
isothermal bath. The whole facility is further embraced by a layer of 1 inch Buna-N/PVC thermal
insulating foam. The temperature (and thus the degree of subcooling) of the water in the inner cell
is controlled by circulating a temperature-controlled fluid (50% DI water + 50% propylene glycol)
through the isothermal bath with an accuracy of 1 *C. The heater cartridge sits at the bottom of
the cell and accommodates heater samples with the special design described in the Section 4. There
are four glass windows spaced equally at 90' around the outer surface of the PBF which can be
used for imaging the boiling phenomena on the heater surface. Thermocouples are inserted into
the inner cell and the isothermal bath, to monitor the bulk temperatures of the DI water and the
bath liquid. All the metal parts are made of stainless steel grade 316L, to minimize corrosion. The
42
pool boiling facility is typically operated with water at atmospheric pressure. However, other
fluids can also be used, namely FC-72 or other refrigerants.
5.2.
Heater Cartridge
In order to install the wrap-around heater into the PBF, a heater cartridge was designed and
manufactured, since the built-in installation groove of the PBF was made for a 5 by 5 cm 2 heater
while our special designed heater was 2 by 2 cm 2 . The heater cartridge should fulfill the following
requirements:
" It should adapt the 2cm
2cm heater into the installation groove of the PBF and offer
necessary mechanical support;
x
" It should behave as low resistance electrodes to pass current from DC power supply to
the heater while allowing the measurement of corresponding electrical parameters;
" It should insulate the electrically conductive parts from contacting the stainless steel
groove in order to prevent short circuit.
The heater cartridge design is shown below in Figure 5-3.
Macor2
Macorl Graphite
N1 I0.31
031
10-32 UNF
Signal Tap Hole
C 0.16 7 0.31
1-2UF
03
10-32 UNF
Figure 5-3 Design of heater cartridge: explosion view (left), assembled view
(middle), bottom view (right). Heatercartridgeconsists ofthree components: apair
of graphite electrodes, apair of T-shape insulating baffles made by macor, a pair
ofplate insulating baffles made by macor. A heater-installationgroove is form by
graphite electrodes and T-shape macor baffles.
43
1 0.31
Electrode Tar Hole
The heater cartridge was mainly composed of three different modules: graphite electrodes
with installation groove, macor insulating T baffles with installation groove, macor insulating plate
baffles. All the parts were epoxied together with High-Temperature RTV silicone which could
work up to 315 *C.
Graphite blocks with 0.000005" ultrafine grain was used to manufacture the electrodes in
order to decrease the porosity and hence the water permeability. Higher life span and electrical
conductivity were also achieved by such ultrafine grain. One side of the square installation groove
was machined on top of each electrode with 3 spilling pits at the bottom. The spilling pits allowed
excessive epoxy escape downward instead of squeezing upward to the heater surface. Electrically
conductive silver epoxy was utilized as the bonding between the heater and the graphite electrodes.
Two threaded holes were machined on the bottom of each electrode. One of them was used to
connect with copper electrode pad for passing current from DC power supply. The other was used
to connect with copper signal pad for measuring the voltage and resistance over the heater.
Macor ceramic was used to manufacture insulating T baffles and plate baffles, due to its
excellent electrical insulation, nonporous nature and high mechanical strength. One side of the
square installation groove was machined on top of each T baffles. After assembling, the graphite
electrodes are embraced by these 4 macor baffles which prevent the contact between electrodes
and stainless steel PBF.
5.3.
Infrared Camera (IRC) and IR Thermometry
An IRC-800 high-speed infrared camera was used to record the temperature distribution
on the heater surface. The sensor of the IR camera captured Mid-IR (in the 3-5ptm wavelength
range) radiation from the ITO heater surface which was reflected through a gold coated mirror.
The gold coated mirror's reflectivity is more than 0.99 which ensures the purity of the IR signal
after reflection. An optical rail and a rotational stage were applied for the alignment of PBF, gold
coated mirror and IRC, in order to reduce the uncertainty of temperature measurement.
The camera sensor detects the IR radiation intensity and outputs the signal as pixel counts.
A 1 D radiation-conduction model (that will be introduced in the following section and described
in detail in Appendix B) was used for conversion from radiation counts to the temperature field.
44
A 100mm germanium lens (f/2.3) with a 3/4" extension ring was used to achieve the desired spatial
resolution at the optimal camera distance from the reference plane. The IRC has a maximum image
resolution of 640 x 512 pixels. In experiments, only a small window was needed for imaging the
whole ITO heater surface, allowing for a high frame rate of 2500 fps. The spatial resolution was
approximately 115 microns.
5.4.
High Speed Video (HSV)
A Phantom 12.1 high speed video camera (Vision Research) was used for imaging the
boiling process. The camera's CMOS sensor has a maximum image resolution of 1280
x
800
pixels with 20ptm pixel size. This camera is capable of taking 6,242 fps at full resolution of 1280
x
800, and I million fps at windowed down resolution of 128 x 8. An AF Micro-Nikkor 200mm
f/4D lens (Nikon) was used for "close-up" imaging of the flow fields on the boiling area. The long
working distance of the lens allowed for the camera to be placed safely away from the experiment,
and when used with extension rings can achieve spatial resolutions as low as 15 um. A nonstroboscopic LED light source was applied for the illumination of the boiling area. Such
continuous high luminance lighting allowed to utilize small aperture of the lens which enhanced
the depth of the field thus the quality of the image.
In the present study, a sampling rate of 5,000 fps was applied with spatial resolution of 25
[trm and exposure time of 90 ps. Such high spatial and temporal resolutions allowed for accurate
identification of the ONB moment together with IRC image, the detailed identifying algorithm of
which will be introduced in the following section.
5.5.
High Speed DC Power Supply (HDCP)
During the transient boiling tests, the generation of exponentially escalating heat flux
required the DC power supply to output both high power and high slew rate near the end of the
escalation. Searching for such a DC power supply was a difficult task, since conventional DC
power supplies focused on either high power at constant output or low power at fast transient
output. Eventually, the Chroma 62050P-100-100 HDCP was found capable of fulfilling both
requirements. The maximum output power of the HDCP is 5kW, with maximum current and
45
voltage of I OOA and 1 OOV respectively. The nominal maximum voltage and current slew rates are
1 OV/ms and 2A/ms if the power supply is working under constant voltage mode or constant current
mode separately. However, if the HDCP works under constant voltage mode, the current slew rate
will follow the voltage variation with respect to the electrical resistance, which can be much higher
than the nominal value of 2A/ms.
Constant voltage mode was applied in the transient boiling tests. These high power and
high slew rate features enabled the exponential heat flux excursion with a period as small as 5ms.
In present study, the HDCP was driven by an external function generator as shown in Figure 5-1
(the HDCP was represented with a battery sign).
5.6.
High Speed Data Acquisition System (DAS)
Due to the transient nature of the present experiment, the simultaneous acquisition of
voltage and current through the heater, trigger signal and camera driving signal was crucial for
synchronized measurement of surface temperature profile and heat flux to water. In addition, a
higher sampling rate was required to reduce the temporal uncertainty of the measurement and
enhance the consistency between surface temperature and heat flux to water. Thus, the Agilent
U2542A USB modular high speed data acquisition system (HDAS) was selected to undertake the
task. The HDAS has four simultaneous voltage acquisition channels with I6bit resolution,
maximum I OV input limit and highest 125 kHz sampling rate for each channel. The schematic
signal chart is shown in Figure 5-4.
46
HDASTerminals
2
34
36
35
37
38
39
R2
RI
DCP
Cameras
3
2
1
+
36
Shut
Heata
DCP
A
A
+
CHI
+
FG2
FG1
EXT Trigger
EXT Trigger
i092
CHI
* 'O Triseff
Figure 5-4 Schematic of signal chart and wire connections. In HDAS, terminals
1&35 acquire driven signal for cameras; terminals 2&36 acquire separated
voltage of heater; terminals 3&37 acquire shunt signal; terminals 4&38 acquire
triggersignal; terminal 39 connects to the groundof DCP.
Since the HDAS only acquires voltage signal, the electrical current has to be converted to
voltage for measurement. The linear conversion was achieved by cascading the heater with a
current shunt (see Figure 5-4) which was essentially a standard electrical resistor with very low
resistance in order to reduce the voltage/power loss over itself. The conversion range of the current
shunt was from 0-30 Amps input to 0-50mV output with a manufacturing accuracy of 0.25%.
A voltage separator was applied to reduce the voltage signal of the heater (up to 1 00V) to
the range of HDAS input (0-1OV). As shown in Figure 5-4, the heater was paralleled with two
serial resistors RI (5.55 kOhms) and R2 (80.7 kOhms), so that the voltage signal was reduced by
a factor of 15.52 and well-adjusted into the HDAS input range.
47
In the present study, a sampling rate of 50 kHz (50 samples/ms) for each channel was used
during the tests, which was more than sufficient even for the most rapid condition (-r = Sms).
Considering an initial power of I W and typical heater resistance of 3 Ohms, the lower bound of
voltage and current signal at the heater were 1.732V and 0.577A corresponding to HDAS input
values of 0.1 12V and 0.962mV. According to these two lower bound values, 0-1OV range was
selected for the measurement of heater voltage which resulted in a resolution of 0.00015V
(corresponding to 1 V), while the range 0-1.25V was selected for the measurement of heater
current which resulted in a resolution of 0.0 19mV (corresponding to
5.7.
1.25E3
21
mV), that is 0.0114 A.
Synchronization of IRC, HSV, HDCP and HDAS
The rapid transient nature of the exponentially escalating heat flux input and the consequent
heat transfer process require simultaneous measurement of multiple parameters, in order to
determine all the features of the transient boiling curve at certain moments. Such simultaneous
measurements can be achieved only if all the sensors are well synchronized. The synchronization
of IRC, HSV, HDCP and DAS is a characteristic challenge for the present study (see Figure 5-1).
As shown in Figure 5-1, the synchronization network starts with a high level trigger signal
generated by a trigger circuit which consisted of a 5V DC power source and a switch. The high
level trigger signal then triggers FGI, FG2 and HDAS. FGI will drive IRC and HSV to work
simultaneously but at different frame rate. FG2 will drive HDCP to output an exponentially
escalating power. Each step of the synchronization process was examined separately.
The input high level trigger signal and output function of FG1 and FG2 were recorded and
examined by the HDAS with sampling rate of 50 kHz. The results showed no time lag between
the input and output signal of FG 1 and FG2, which means that the two function generators were
synchronized with an accuracy of 0.02 ms
The synchronization of IRC and HSV were tested by using synchronized visible light bulb
and IR light bulb as shown in Figure 5-5. The periodic blinking of the visible and IR light bulbs
were recorded by HSV with 5000 fps and IRC with 2500 fps separately. The recorded videos
showed that HSV and IRC always saw the lighting up and darkening down of two light bulbs at
48
the same moment, which meant HSV and IRC were well synchronized. In addition, by calculating
the duration of the first flashing period of each light bulb, it showed that the time delay between
receiving trigger signal and starting recording for each camera was negligible.
5V
FGI
FG2
Figure 5-5 Synchronization test for IRC and HSV Visible light bulb and IR light
bulb were driven by FG 2 at the same blinkingfrequency. HSV and IRC recorded
the blinking behaviors of visible light and IR light respectively.
The input and output of HDCP was also tested by HDAS with sampling rate of 50 kHz.
The recorded data showed that the delay between the input and output was proportional to the
initial voltage. This delay did not constitute a problem since it was measurable for each test that
we ran.
In the present study, the DAS was set to record certain pre-trigger readings in order to make
sure every data during the transient could be recorded including the high level trigger signal. The
output of FGI was delayed for 2ms to distinguish the starting moment of cameras from the trigger
moment. The output of FG2 was also delayed for 2ms to be consistent with FG1. However the
intrinsic delay between the input and output of HDCP made it start working later than the cameras.
The event-line is shown in Figure together with a sample DAS data. With such cascade-delay
49
technique, the DAS successfully monitored the rest of the equipment while IRC and HSV could
record the full range of the transient boiling process. To the best of our knowledge, this is the first
time that synchronized HSV photography and IR thermometry have been used to investigate
boiling heat transfer process under such rapid transient conditions.
DAS
Pre-trigger reading
Trigger
Cameras start
I
I
HDCP outputs
I
2ms
'0
P
3-4ms
lime
6
-Trigger
-FG1
5
-
Signal
Output
HDCP Output
4
3
W,
I
/
2
n
0.00
-1
1.00
2.00
4.00
3.00
5.00
6.00
7.00
Time [ms]
Figure 5-6 Event-line of the synchronization. Four events happen successively in
time: DASpre-triggerreading, trigger, starting of cameras and HDCPoutputs.
5.8.
Dissolved Oxygen (DO) Control and Measurement
Dissolved non-condensable gases reduce the wall superheat required for ONB by reducing
the partial pressure of vapor necessary for the bubble embryo to grow, as shown in Eq. 5.1 (YoungLaplace equation with non-condensable gas), where pg is the partial pressure of non-condensable
gas; pv is the vapor pressure in the bubble; pi is the liquid pressure; a is the water surface tension;
rb
is the critical bubble radius (also cavity radius for a hydrophilic surface such as wrap-around
heater). To quantify the presence of non-condensable gas and minimize its effect, a system to
measure and control the dissolved oxygen (DO) concentration was installed on the lid of the PBF
50
(see Figure 1)). During the transient pool boiling tests, this system limited the contact between the
water in the PBF and air from the environment.
2(5.1)
Pg + Pv - Pi =-
Degassing Chimney
Rebalance Branch
"Sample Bottle
Ball Valve
Ball Valve
Pressure Gauge
3 Way Valve
PBF
Volume Compensation
Syringe
Lid
piing Line
Figure 5-7 DO control and measurement systemsfor PBF. The DO control system
consists of all the parts connected to the degassing chimney, which are involved
with the degassingprocess, isolation and volume compensation of PBF. The DO
measurement system consists of all the parts connected to the sampling line, which
are involved with the measurement of DO concentrationin water pool.
Figure 5-8 Extech 407510 DO meter. The DO meter measured the water sample
extractedfrom the PBF.
51
For the pool boiling facility, sampling was performed from the region adjacent to the heater
surface. The sampling line consisted of a 1/8" tube, so that the amount of water remaining in the
line was minimized. A syringe was used to extract the water sample and deliver it to a sampling
bottle. A three way valve was utilized to separate the suction and ejection processes. In the center
of the PBF lid, a degassing chimney made of a 3/4" clear PVC tube was installed to release the
gases that came out of solution. A ball valve was installed on the degassing chimney to isolate the
system. A volume rebalance branch with a reduced size semitransparent tube (1/4") was connected
to the root of the degassing chimney so that it could quickly rebalance the pressure of the PBF (if
necessary) by opening the ball valve. Two 140-ml syringes filled with deaerated water were
connected to the rebalance branch in order to compensate the volume change of the water (volume
reduction of approximately 190 ml from saturation to room temperature) when the PBF was
isolated and cooled down. A pressure gauge was used to monitor the pressure of the PBF.
A precise procedure was followed for DO measurement and control. Firstly, deionized (DI)
water was vigorously boiled outside and inside the PBF for approximately one hour. Steady boiling
on the test surface was also carried out for 15 min to eliminate non-condensable gases trapped
inside the surface cavities. After degassing, the PBF still needed to be further filled with predeaerated water until the water level was above the ball valve on the degassing chimney (also
above the ball valve on the rebalance branch). The ball valves were then closed to isolate the PBF.
The PBF was maintained at atmosphere pressure by the two compensation volumes (syringes).
The rebalance branch could be opened briefly, only if the volume compensation from the syringes
was not fast enough.
The DO concentration was monitored with the Extech 407510 DO meter (see Figure 5-8)
before and after each series of experiments for both pool and flow boiling. The DO concentration
measured at the operating temperatures was always steady (typically 3.6 ppm) and much lower
than saturation value.
With the measured DO concentration in hand, the effect of DO on the ONB temperature
can be quantified by using Eq. 5.1 and Henry's law. Henry's law states that at a constant
temperature, the amount of a given gas that dissolves in a given type and volume of liquid is
directly proportional to the partial pressure of that gas in equilibrium with that liquid, according to
which the DO partial pressure can be calculated by the following equation:
52
p0 2 = kH(T)
*
(5.2)
c0 2
.
where kg is Henry's constant in units of L -atm/mol whose value depends on temperature; C0 2
is oxygen concentration in water in units of mol/L; T is the temperature (in Kelvin degrees)
Henry's constant and the DO concentration can be calculated by the following equations:
1
1(53
kH(T) = kH( 2 9 8 .15) * exp(1700 * (- -5.) 8.15)
0*(T- T9
(5.4)
6
C2 = Pw * PPM * 10- /molar-mass
2 9 8 .1 5 ) = 769.23 L -atm/mol;
where the molar mass of the oxygen molecule is 32 glmol; kH(
PPM=3.6 is the typical DO concentration (in ppm) measured by the DO probe in our facility.
Cavity
Cavity
Cavity
Cavity
Cavity
C
1.2
-
-9-
LU
-
Dameter = 3tn
Diameter = 4tsn
D(ameter = Sum
Diameter = 6um
Dameter =7um
0.8-
Z 0.6
0.20
0
1
2
6
5
4
3
DO CONCENTRATION [PPM]
7
8
9
Figure 5-9 Change in ONB temperature v.s. DO concentration and cavity
diameter. The change in ONB temperature increases with the increasing of DO
concentration and cavity diameter. The DO concentration at 3.6-ppm has very little
effect on change of ONB temperature.
In presence of dissolved oxygen, the local ONB saturation temperature can be calculated
by iterating on Eq. (5.1) through Eq. (5.4). The change in ONB temperature, which is the difference
53
between the ONB temperature with dissolved oxygen and the ONB temperature without dissolved
oxygen, is plotted in Figure 5-9 as a function of DO concentration and cavity diameters. The
results in Figure 5-9 suggest that at 3.6 ppm the DO concentration has very little effect on the
expected ONB temperature. Moreover, the ONB temperature does not vary much with the oxygen
concentration (roughly 0.13 K/ppm for a cavity diameter of 5 microns). Therefore, a DO
concentration of 3.6 ppm was acceptably low for our experiments.
54
6. Quantification and Validation of Key Outputs
Although all the techniques that we developed for transient pool boiling tests were
examined separately, it was still important to prove the correctness and accuracy of the key outputs
in the exact operating experimental conditions after we combined all the techniques together. This
section discusses the quantification methods and the validation efforts we made.
6.1.
Power Excursion
The first step of the validation was to make sure that the power excursion of the ITO heater
followed the expected exponential curve with the prescribed period. During the experiments, the
voltage excursion (instead of the power excursion) was precisely prescribed, since the HDCP
worked at the constant voltage mode. The power of the ITO heater is estimated by the measured
voltage and current using QITO
= VITO X
Ideal voltage, current and power exponential
IITO .
excursions are shown as equations 6, 7 and 8, where r is the prescribed power excursion period.
OITOi =
VITOi
=
ITOi =
where
RITO
0 , exp
V1 Riro
N0
(T)
(6.1)
exp (A)
(6.2)
t
(6.3)
exp(-)
is the electrical resistance of the ITO heater and
00
is the initial power, which we
imposed I watt. All the periods we expect to run in the boiling experiments were tested in the
wrap-around heater. Two representative examples for the most challenging conditions (5 ms and
10 ms at 75K subcooling) are shown in Figure -L. In Figure -1, the red dots represent the measured
data and the black lines represent ideal trends (as reported in Eqs. 6.1, 6.2 and 6.3) used as input
to the DC power supply. Note that the measured voltage, current and power data overlap very well
with the ideal trends, which confirms that the power output of the ITO heater is correct and
accurate.
55
voltage
-
10000
current
-----
----power.
1000
0
100
cc
U
10 V
0:
0.11
-10 0
-50
0
50
TIME [m8]
100
150
200
100
150
200
a) 5ms_75K
10000
voltage
current ------power ----
1000 :-
0
100
z
:
uL
10
C,
'
0.1
-10 0
-50
0
50
TIME [msj
b) JOms_75K
Figure 6-1 Comparison of ideal and measuredvoltage, current and power of the
ITO heater (the red dots represent the measured values and the black curves
represent the ideal values calculatedby equations. 6.1, 6.2 and 6.3): a) 5ms 75K
b) 1 Oms 75K. The measured values agree very well with ideal trends.
56
6.2.
Repeatability of Experimental Results
Repeatability is an important standard to examine the quality of the experimental data. The
photon counts from the IR camera, which have a one-to-one correspondence with temperature, are
a primary output of the experiments. In order to verify the repeatability of photon counts, each
experiment was repeated for three to five times under the same setup and the same conditions (i.e.,
fixed period and subcooling). Sample results at the same moment (i.e. the same IRC frame number)
are shown in Figure for a representative set of conditions (20 ms period and 25K subcooling)
run I
run 2
run 3
run 4
run 5
Figure 6-2 Comparison of 2D photon counts contours at the same moment (right
qfter ONB).for five runs at 20ms period and 25K subcooling conductedon a wraparound heater. Different runs result in similar2D contours ofphoton counts at the
same moment which denotes good repeatabilityof experimental results.
As shown, the 2D contours of photon counts from different runs at the same moment are
very similar to each other. There are several signature bubbles appearing at the identical position
on every picture. Figure 6-3 shows the surface-averaged photon counts increase (measured photon
counts minus initial photon counts) versus time for different runs. All five runs overlap in a single
curve within experimental uncertainty. The repeatability of the experimental results is thus
confirmed.
57
1000
100
N
0 20ms TestOl
*20ms
Test02
10
N
20msTestO3
20msTestO4
20msTestOs
1
1
21
41
61
Time [ms)
81
101
121
Figure 6-3 Comparison of average photon counts increasefor different runs at
20ms period and 25K subcooling conducted on wrap-around heater. The five
curves converge into one curve within the measurement uncertainty, which
confirms again the repeatabilityof experimentalresults.
6.3.
Photon Counts to Temperature Conversion
The conversion algorithm of the IR photon counts to temperature is one of the most critical
parts of the project.
As discussed in Section 4.2.2, due to the slightly emissive nature of sapphire, both the ITO
coating and the substrate (sapphire) contribute to the total infrared emission received by the IRC
(see Figure 6-4). However, only the emission from ITO is the signature of the actual temperature
on the boiling surface. Emissions from the substrate "contaminate" the signal from the ITO.
Typically the more IR absorptive is the substrate material, the larger is the contamination; also,
the thicker is the substrate, the larger is the contamination. Moreover, the contamination of the IR
signal depends on the temperature profile within the substrate.
58
-------
ITO
- --
SUBSTRATE
X
LENS
MIRROR
CAMERA
Figure 6-4 Heater radiationtowards the IRC. Both the ITO andthe substrate emit
IR radiation. The substrate radiationis a contamination to the ITO one. The level
of IR signal contaminationalso depends on the temperature distributionwithin the
substrate.
In the wavelength range of the IRC measurement (3 to 5 microns), sapphire was measured
to be partially opaque, in particular between 4.5 and 5 microns (see Figure 6-4). In a sapphire
substrate 250-micron thick with a uniform steady temperature profile (case A, Figure ),
approximately 3% of the IR radiation collected by the IRC is emitted by the substrate. If the same
steady temperature is applied to a sapphire substrate 1 -mm thick (case B, Figure 6-6), the
contamination would increase to 10%.
Figure 6-7 depicts the repartition of IR emission in a typical exponential power excursion
transient in a wrap-around heater (sapphire 1-mm thick), with period of 5 ms and subcooling of 75
K. As the ITO (wall) temperature in the figure increases during the transient, the repartition
between the IR signal emitted from the ITO and the signal emitted by the sapphire changes
(decreases).
59
STEADY-STATE - 250 um substrate
Ii
- -- ITO
90
Sapphire
80
70
Q
T(x)
60
50
E
A
a)
40
30
10
x
D
20
10
0
20
40
100
80
60
140
120
160
ITO Temperature [C)
Figure 6-5 IR emission from a heater with sapphire substrate thickness of 250
microns. At constant temperature distribution condition, approximately 3% of the
emission comes from substrate.
STEADY-STATE - 1000 um substrate
100
901
SphIre
80
70
C
.7
-n
E
T(x)
60
50
-
40
0
30
20
-B
lix
B
-
is-
10
0
20
40
80
100
60
ITO Temperature (C)
120
140
160
Figure 6-6 IR emission from a heater with sapphire substrate thickness of 1 mm
(wrap-around heater). At constant temperature distribution condition,
approximately 10% of the emission comes from substrate.
60
TRANSIENT (Sms period) - DTsub = 75K - 1000 um substrate
100
90
SapphIre
60
70
T(x)
60
50
C
40
30
20
X
2~
100
In
_________
10
0
20
40
60
80
100
ITO Temperature (C)
120
140
160
-
Figure 6-7 IR emission in a typical exponential power excursion (5 ms period
75K subcooling- 1 mm substrate). At transientheating conditions, the temperature
distribution in substrate varies with time, which leads to a time dependent
repartitionof IR signal between ITO emission and substrateemission.
The simplest way to correlate the infrared radiation received by the infrared camera with
the temperature of the ITO thin film is to use a steady state calibration curve. This approach is
satisfactory only if the substrate is very thin (e.g. 250 microns), such that its contribution to the IR
signal is small. However, for wrap-around heaters (1 -mm thick), the use of a steady-state
calibration curve would lead to a significant underestimation of the temperature on the boiling
surface. In particular, in the case illustrated in Figure 6-7, the use of a calibration curve obtained
in steady conditions will lead to temperature underestimations as large as 2 *C at the ONB moment.
To solve this issue, the coupled conduction-radiation inverse problem depicted in Figure
6-8 has to be solved. At a given time step, the radiation collected by the IR camera is known (as
counts). Based on the counts, we guess the ITO temperature that serves as boundary condition for
the conduction problem. By solving the conduction problem with that boundary condition, the
temperature profile within the substrate is estimated. With this tentative temperature profile in
hand, the total radiation from the heater is calculated according to the radiation model and hence
compared to the value measured by the infrared camera. If the measured radiation and calculated
61
radiation differ significantly, the process continues with a new guess of the surface temperature,
until the iterations converge within an acceptable error. Finally, once the converged temperature
profile is known, the heat flux to the substrate at the ITO-substrate interface can be simply
calculated by the discretized Fourier's conduction law:
Ts(2) - Ts(1)
skXS(2) - Xs(1)
,,s
(6.4)
and thus an estimation of the instantaneous heat flux to water can be obtained as:
i f e
if It
q',' =: qt'ot - q'' =he
Ts(2) - Ts(1)
sl
(6.5)
e1x p(t /T ) + ks Xs2
Counts IR Camera
Guess of ITO temperature
&
Conduction
-
Temperature Profile of the Substrate
-
Radiation
rCounts of the C/R
-
ITO --
SUBSTRAEo
Radatton
uction
X
NO
Counts IR Camera - Counts
C/R Code! <s ?
YES
MIRROR
LENS
Next Time Step
CAMERA
Figure 6-8 Flow chart of the coupled conduction-radiation inverse problem.
Following the flow chart, the surface-averagedITO temperature at each time step
was converted from photon counts by iteration. Furthermore, the heat flux to
substrate and hence the heal flux to water were calculated given the surfaceaveragedtime-dependent ITO temperature.
More details about the coupled radiation-conduction model can be found in Appendix B.
The measurement procedure for the optical properties required to implement this model is
discussed in Appendix A. All the optical properties required are shown in Appendix C.
62
6.4.
Detection of ONB
The precise detection of ONB moment is crucial to accurately determine ONB temperature
and heat flux. At short period and high subcooling conditions (eg. 5ms and 75K subcooling) the
ITO temperature increases rapidly near ONB. The temperature difference from one IRC frame to
the next can be as high as 10 degree (if 2500 fps frame rate is used). Limited by the frame rate of
the present IRC, a methodology needs to be developed for enhancing the precision of ONB
moment detection.
In the present investigation, a 2500 frame rate was applied with two objectives. The first
objective was to decrease the noise-to-signal ratio by using as high integration time (0.2 ms) as
possible. The second objective was to view the entire heating area: at higher frame rate, the IRC
viewing window could not cover the whole heating area.
To increase the accuracy in the determination of the ONB moment, a HSV frame rate of
5000 fps (2 HSV frames for each IR frame) was used. With this configuration, three different ONB
detection scenarios are possible depending on when the first bubble appears on the HSV and the
IRC recordings, as shown in Figure 6-9 through Figure 6-11. In scenario 1 (Figure 6-9), the ONB
bubble appears on HSV and IRC recordings at the same moment. In scenario 2 (Figure 6-10), the
ONB bubble first appears on the HSV recording and then the IRC recording. In scenario 3 (Figure
6-11), the ONB bubble first appears on the IRC recording and then the HISV recording. The lower
limit and the upper limit of the ONB moment could be identified according depending on the
scenario. The ONB time range is thus defined as the time duration between the upper and the lower
limit. The time in the middle of the range is taken as the nominal ONB time.
For scenarios 1, 2 and 3, the durations of the ONB ranges are 0.2 ms, 0.09 ms and 0.11 ms,
respectively. If the HSV frame rate were not doubled, the ONB range would be typically as large
as 0.24 ms.
63
.
Lower Upper
l t
limit
Cn--
Cout
3
2
1
IRC
I
I
I
I
HSV
0
1
2
Extrapolation
3
5
ONB Range
Figure 6-9 Detection of the ONB moment (scenario 1). The ONB bubble appears
on the HSV and IRC at the same moment, which results in an ONB range of 0. 2ms.
Lower Upper
limit
limit
Extrapolation
Counts
IRC
1
HSV
0
1
2
3
2
4
5
ONB Range
Figure 6-10 Detection of the ONB moment (scenario 2). The ONB bubble appears
first on the HSV and then IRC, which results in an ONB range of 0. 09ms.
64
Lower Upper
.limit
....
Counts
IRC
1
Extrapolation
pla--
-2i3
IR
HSV
0
1
M
2
4
5
ONB Range
Figure 6-11 Detection of the ONB moment (scenario3). The ONB bubble appears
first on the IRC and then HSV, which results in an ONB range of 0. 1rms.
To estimate the nominal ONB temperature, the temperature before ONB is extrapolated up
to the higher limit of the ONB range, using the temperature rate of change at the time before ONB.
Uncertainties on the ONB temperature take into account the temperature change between the socalled lower limit and upper-limit of the ONB range.
65
7. Analysis of Experimental Results
The transient pool boiling tests were conducted according to the test matrix in Table 7-1.
Various periods were tested in the range from r=5 ms to 100 ms. The effect of subcooling was
also investigated by running tests at saturation condition (OK), low subcooling (25K) and very high
subcooling (75K). Each test condition was run several times (3 or 5 times) to check the
repeatability of the measurements. In total 70 tests were successfully run and analyzed.
Table 7-1 Number of tests run for each condition in the test matrix for pool boiling
Pool Boiling
2
m
s 7m
OK (saturation)
25K (low subcooling)
75K (high subcooling)
The quantities of interests for this study were the boiling curves (heat flux to water versus
wall superheat), the single phase heat transfer coefficient, the ONB heat flux and temperature, the
OSV heat flux and temperature, the OV temperature, all reduced from the analysis of the
experimental data, and presented in the following sections. Before running transient tests, the
heater was tested under steady state boiling. The steady-state boiling curve obtained in the fully
developed nucleate boiling regime was in good agreement with the Rohsenow correlation.
7.1.
Boiling Curves
In transient boiling tests there are generally two types of boiling curves observed: boiling
curves with temperature overshoot and without temperature overshoot.
66
iO
-
-----
Bo4ng Qarve
TrnSmnt GOno&
Transkent
--
x
ONS
o OSV
107
4) TBL Depletion
5) Towards FDNB
3) OV
Rohsenow
/
-L
S
1052
1) ONB
10 41-
100
10'
102
WALL SUPERHEAT (K)
Figure 7-1 Typical boiling curve with temperature overshoot at 10 ms and 75K
subcooling. Five successive steps are distinguishedon this type of boiling curve.
Figure 7-1 shows a typical boiling curve with temperature overshoot, where the subcooling
is 75K and the period is 10 ms. Five steps can be identified. The corresponding HSV and IR images
of each step are shown in Figure 7-2. Details of boiling behavior and surface temperature
distribution are illustrated. By linking Figure 7-1 with Figure7-2, an overall understanding of this
kind of boiling curve is achieved and explained in the following.
1) ONB
2) OSV
3) OV
p
*44
~win'wh
mU4j..41
67
4) TRI, Denletion
5) Towards FDNB
Figure 7-2 Typical HSV (top/black & white) and IR (bottom/color) imagesfor each
boiling step of boiling curve with temperature overshoot. HSV images show the
boiling/bubble behavior, while IRC images show the corresponding 2D
temperature distributionon the heating surface.
Before ONB the boiling curve closely follows single-phase transient conduction, whose
characteristics will be introduced in the next section. While heat flux to water and wall superheat
keep increasing (and so does the thermal boundary layer (TBL) thickness in water), at a certain
moment ONB occurs (step 1). We can see several small standalone bubbles on the HSV image but
barely see any change in the IR image since boiling is still highly localized.
Shortly after ONB, the boiling curve starts to deviate from the transient conduction
asymptote. When several bubbles are generated, the heat transfer coefficient (HTC) increases
significantly and so does the heat flux, whereas the wall superheat does not show a significant
increase. The combination of heat flux to water and wall superheat results in an inflection of the
boiling curve. Such inflection denotes the occurrence of OSV (step 2). We can clearly see several
big bubbles and their temperature footprints in the HSV and IR images.
After OSV, boiling becomes more and more vigorous. The heat flux to water increases
sharply while the heat flux to substrate decreases significantly. The substrate can also release its
sensible heat to the water. Such conjugate heat transfer among water, substrate and power input
causes the wall temperature to drop; this is the OV point (step 3). We can see from the
corresponding HSV image that lots of big bubbles cover the heater surface. The yellow color on
the IR image denotes the consumption of the previously established TBL by boiling.
68
After the OV, wall superheat keeps decreasing due to the cooling effect of vigorous boiling.
However, heat flux to water still increases sharply. This rapid process reaches an end when the
TBL is fully depleted (step 4). After that, boiling is suppressed. The HSV image shows that bubbles
condense and become smaller, while the IR image shows a cooler surface temperature.
Finally, when the exponential increase of power input catches up with the energy
consumption of the system, heat flux to water and to substrate reach a new balance. The boiling
curve progresses towards FDNB (step 5) which is predicted by Rohsenow correlation (Eq. 4.3).
108
Transient Boling Curve
-
-- -
Transient Conduckmn
x
ONO
0
OSV
107
E
3) towards FDNB
D10
i0
100
101
102
WALL SUPERHEAT [K]
Figure 7-3 Typical boiling curve without temperature overshootat 10 ms and 25K
subcooling. Three successive steps are distinguishedon this type of boiling curve.
Figure 7-3 shows a typical boiling curve without temperature overshoot, where the
subcooling is 25K and the period is 10 ms. This type of boiling curve usually exists at small period
and low subcooling. At such conditions, the boiling process presents three steps. HSV and IR
images of each step are shown in Figure 7-4. A different approach other than five-step boiling
curve is observed from OSV towards FDNB.
69
1) ONR
2) OSV
3) Towards FDNB
Figure 7-4 Typical HSV (top/black & white) and IR (bottom/color) imagesfor each
boiling step of boiling curve without temperatureovershoot. HSV images show the
boiling/bubble behavior, while IRC images show the corresponding 2D
temperature distributionon the heating surface.
Before OSV, the heat transfer regimes are basically the same as for the case with overshoot.
However, the boiling process differs after OSV. Instead of progressing through OV and
TBL depletion, there is no visible temperature overshoot (see Figure 7-3). Wall superheat increases
monotonically at these conditions, which means the power input is always sufficiently high and
the TBL is thick enough to support vigorous boiling.
Eventually, the boiling curve also progresses toward FDNB.
The typical boiling curves for three different subcoolings are plotted in Figure 7-5 (1 to 3).
For each subcooling, the boiling curve is plotted for each period along with the corresponding
analytic transient conduction curve (colored dashed line). The corresponding values predicted by
Rohsenow correlation (Eq. 4.3) are also plotted with black dash line. For the same subcooling, the
boiling curve is shifted towards higher heat fluxes and higher wall superheats as the period
becomes smaller. For the same period, the boiling curve is also shifted towards higher heat fluxes
and higher wall superheats with increasing subcooling. Such kind of shift in the boiling curve will
be correlated to the values of the single phase heat transfer coefficient, ONB, OSV and OV heat
fluxes and temperatures in the following section.
70
108
-/
Rohs-ow
10
twon!
Imm
-
E
D106
x
6
10ms
10
20ms
50ma
YOM
1oon*
10
I
101
100
102
10,
WALL SUPERHEAT [K]
1) 75K subcooling
Rohsenow
/
108
10
E
-J 10 6
J/
U.
----
10
-
ms
10ms
20ms
so=s
70mis
looms
100
101
WALL SUPERHEAT [K]
2) 25K subcooling
71
102
Rohsenow
/
108
107
X
6
D 10/
-J
Ia.
~~11ms
20mu
10 5
5ms
--
70s
100-ms
104
100
102
101
WALL SUPERHEAT [K]
3) OK subcooling
Figure 7-5 Typical boilingcurves for each test condition. For the same subcooling,
boiling curves shift upward and rightwardwith decreasingpower period. For the
same power period, boiling curves shift upward and rightward with increasing
subcooling.
7.2.
Single Phase Heat Transfer
As discussed in Section 2.1, single phase heat transfer under exponentially escalating heat
flux can be well represented by the asymptotic analytical solution of transient conduction, if the
period is much shorter ( T < 100 ms) than the time scale of free convection. By setting x, = 0 in
Eq. 2.9, the wall temperature and heat flux are achieved as below:
Twaii (t) = TbUk + qI' eti
'
+ 8w]
E tanh
1
1/
q" (t) = q ' et/T EW1 es tanh
(7.1)
+ E'
(2.12)
The analytical curves plotted with dash lines in Figure 7-5 (1 to 3) were calculated from
Eq. (7.1) and Eq. (2.12). The same color represents the same period as the boiling curve. As shown,
72
the experimental boiling curves agree very well with the analytical solution, which confirms the
correctness of the analytic solution. By combining Eq. (7.1) and Eq. (2.12), the single phase HTC
during transient conduction is given by:
HT CCOnl =
7.3.
(7.2)
ONB Heat Flux and Temperature
The ONB conditions are determined by synchronized IRC and HSV images, as discussed
in Section 6.4. For each test, a temporal uncertainty (ete) is calculated by half the difference
between the upper limit and lower limit temperature of the ONB range. In addition to temporal
uncertainty, there is an uncertainty related to the test repeatability. The standard deviation of ONB
temperatures from repeated runs is used to represent such repeatability uncertainty ( ere ).
Compared to the temporal and repeatability uncertainties, the nominal instrument uncertainties are
much smaller, and therefore can be safely neglected in the present analysis. Since the temporal
uncertainty and the repeatability uncertainty are independent and assumed to be Gaussian, the total
uncertainty etot is calculated as below:
etot =
ete + ere
(7.3)
Usually, at short periods the total uncertainty is dominated by temporal uncertainty while
at long periods by repeatability uncertainty. The ONB heat flux and corresponding uncertainty are
calculated using the same procedure of the ONB temperature. The ONB heat flux and wall
superheat are plotted below.
73
107
*ONB OK
*
o
ONB25K
ONB75K
Model OK
Model 25K
Model 75K
i6
UI-
x i05
Or
IA/zz4
10
10 1
10 0
103
PERIOD [ms)
Figure 7-6 ONB heatflux versus power periods at different subcoolings. For the
same subcooling, ONB heatfluxes varies with periodfollowing a trend close to
1 /-fi. For the same period, higher subcooling leads to higher ONB heatflux.
+
30
*
o
ONBOK
ONB25K
ONB75K
Model OK
Model 25K
Model 75K
25-
-
20
-LJ
-
15
-
100
-
.
.
.
-
. I
-
-
-
,
-
,
10l-
102
101
PERIOD [ms]
Figure 7-7 ONB wall superheatversus power periods at different subcoolings. For
the same subcooling, smaller period leads to higher wall superheat. For the same
period, higher subcooling leads to higher wall superheat.
74
In Figure 7-6, ONB heat fluxes as a function of the period are shown for tests with OK,
25K and 75K of subcooling (error bars shown in the plots correspond to
etot). We observe that
under the same period the higher is subcooling, the higher is the heat flux required to start boiling.
Moreover, for a given subcooling, the heat flux varies with the period following a trend close to
1/VTh (black solid line). In Figure 7-7, ONB wall superheats show qualitatively the same
dependency as heat fluxes. The trend of ONB heat flux and wall superheat confirm the discussion
of the mechanistic ONB model in Section 2.2 that given the same cavity condition, shorter period
will ideally result in steeper temperature gradient that means higher ONB heat flux and higher
ONB wall super heat. Initial bulk subcooling also affects the ONB wall super heat by affecting the
ONB heat flux. The schematic of such trends are shown in Figure 7-8.
In order to quantify the ONB mechanism, the mechanistic ONB model was applied to
predict the ONB heat flux and wall superheat. For a slightly hydrophilic surface such as our ITO
coating, the critical bubble radius rb is equal to the cavity radius r, and the bubble embryo is
hemispherical. The final expressions of the mechanistic ONB model for ONB heat flux and wall
superheat after substituting rb with r, are as below:
c
,q11[sat(Patm
LdTsat, onb ~ Msat (Patm + 2u/rc)
-
Tbulk
1
exp
bulk]
exp
(7.4)
c
ATsub
(7.5)
Application of the ONB model requires knowledge of the radius (or the distribution of
radii) of the micro-cavities (nucleation sites) on the heating surface. In our case the coordinates of
the ONB nucleation site were first identified from the IRC image. Then, the heater was examined
with the SEM, making it possible to identify the cavity that served as nucleation site at ONB (see
Figure 7-9). Unexpectedly, boiling inception did not occur on engineered cavity, but on another
surface imperfection. The size of the imperfection is approximately 5 microns which corresponds
to rc ~ 2.5 pum. Using this value in the ONB model, the ONB heat flux and wall superheat could
be predicted and plotted in Figure 7-6 and Figure 7-7 (solid color lines). As shown, the predictions
of the ONB model agree reasonably well with the experimental results.
75
At The Same Subcooling
-
- - -
Shorter Period
Longer Period
ONB Reauirement
L
E
Bulk TemDerature
Distance Away From Wall
Wall
a) Same subcooling different periods
-
At The Same Period
- Higher Subcooling
- -
Lower Subcooling
ONB Requirement
CL
FT
Wall
Bulk Temoeratures
Distance Away From Wall
b) Same perioddifferent subcoolings
Figure 7-8 Schematic of temperature distribution at ONB moment by Hsu's
criterion (drawing not to the scale). a) For the same subcooling, smaller period
leads to higher wall superheat and heat flux. b) For the same period, higher
subcooling leads to higher wall superheat and heatflux.
76
Figure 7-9 SEM image of the nucleation cavity. The bigger end of the pear-shape
nucleation cavity has the equivalent diameter of 5 microns.
7.4.
OSV Heat Flux and Temperature
OSV marks the start of significant negative reactivity feedback during the RIAs. As
introduced in the boiling curve section, the signature of OSV is associated with an inflection point
on the boiling curve. In addition, OSV is related to a significant decrease of the heat flux to
substrate due to vigorous boiling. According to these characteristics, OSV was determined by the
inflection of boiling curve.
The methodology to calculate the OSV heat flux, OSV temperature and associated
uncertainties is the same used for ONB. The results are plotted in Figures 7-10 and 7-11. Although
the trends for OSV and ONB are very similar, the values of heat flux and wall superheat for OSV
are higher than the ones for ONB, as expected. On a heater with a distribution of cavity sizes, the
ONB bubbles are always generated on the biggest unflooded cavities which require the lowest heat
flux and wall superheat according to Eq. 7.4 and Eq. 7.5. However, higher heat flux and wall
superheat are required to nucleate the remaining smaller cavities which will contribute to OSV.
77
10
+
*OSV
0
10
25K
OSV 75K
6
*
x
*
E
OSV CK
I-
00*
:
1041
10 0
102
10i
PERIOD [msJ
Figure 7-10 OSV heatflux versus powerperiods at different subcoolings. OSV heat
flux varies with periodand subcooling similarto ONB heatflux.
30
+
OSV OK
*
0
OSV 75K
OSV 25K
-
25
FI
20
+I
15
10
100
102
101
103
PERIOD [ms]
Figure 7-11 OSV wall superheat versus power periods at different subcoolings.
OSV wall superheat varies with period and subcooling similar to ONB wall
superheat.
78
7.5.
OV Temperature
OV wall superheats (if OV is present) are obtained by searching for the highest temperature
on the boiling curve between OSV and TBL Depletion. The methodology to calculate wall
superheat and the corresponding uncertainties is the same used for ONB. The results are plotted in
Figure 7-12 as a function of the period for tests with OK, 25K and 75K of subcooling (error bars
shown in the plots correspond to +etot).
30
+1
OV OK
*
0
OV 715K
OV 25K
25
I-
+
20Co,
15
101
100
101
102
10
3
PERIOD [ms]
Figure 7-12 OV wall superheat versus power periods at different subcoolings. OV
was not observedat periodof 5ms and 1 Oms at subcooling of 25K and OK. OV wall
superheat (if exists) varies with period and subcooling similar to ONB wall
superheat.
As shown in Figure 7-12, there is usually no temperature overshoot at short periods and
small subcoolings. The variation trend for the OV wall superheat is also similar to ONB wall
superheat. For a given subcooling, the OV wall superheat increases with decreasing power
excursion periods. For a given power excursion period, the OV wall superheat increases with
increasing subcooling.
79
8. Conclusion
The study of transient pool boiling heat transfer phenomena under exponentially escalating
heat fluxes on plate-type heaters was conducted, at the time scales of milliseconds typical of
Reactivity Initiated Accidents (RIAs) in nuclear reactors. Due to the fast transient nature of such
phenomena, the investigation required significant improvements to the operating and measuring
techniques. A specially designed wrap-around heater with engineered cavities was applied to cover
all the test conditions. A state-of-the-art diagnostic system was constructed by synchronizing IRC,
HSV, HDCP and DAS. Systems to monitor and minimize the concentration of the noncondensable gases in water were built. A coupled radiation-conduction model was developed for
accurate conversion from photon counts to temperature. Moreover, a methodology for the precise
determination of the ONB moment was achieved. The implementation of all the improved
techniques above ensured the accuracy of the experimental output.
The transient boiling tests were carried out under the same wrap-around heater. Various
exponential periods in the range from 5 ms to 100 ms were tested. The effect of subcooling was
also investigated by running tests at saturation condition (OK), low subcooling (25K) and very high
subcooling (75K). The quantities of interest were achieved, including boiling curve, single phase
heat transfer coefficient, ONB heat flux and temperature, OSV heat flux and temperature and OV
temperature.
Experimental results show two types of transient boiling curves: with temperature OV and
without temperature OV. Five specific steps are distinguished on the boiling curve with
temperature OV, while three specific steps are distinguished on the boiling curve without
temperature OV. From the boiling curve, other quantities of interest are reduced. The measured
single phase HTC under transient follows the analytical solutions obtained for transient conduction
heat transfer which has the form:
cw/V7.
The ONB heat flux and wall superheat increase as the
subcooling increases and the power excursion period decreases. For the heat flux in particular, the
trend is close to 1 / -J. A mechanistic ONB model that is based on Hsu's criterion is used to
interpret the ONB mechanism. The prediction of this ONB model is consistent with observed
trends for ONB heat flux and wall superheat. OSV heat fluxes and temperatures, as well as
overshoot temperatures (whenever temperature overshoot is present) also follow a trend similar to
the ONB heat fluxes and temperatures. The clear trends of ONB and OSV heat fluxes and
80
temperatures versus power period observed in the present study clarify the conflicts and confusions
in previous researches. The validated mechanistic ONB model sheds light to the mechanisms
behind transient pool boiling heat transfer. Furthermore, with the abundant generated data base, it
is a good chance to reduce the uncertainty of models applied in both design and safety analyses of
the research reactors especially under RIAs.
In order to explore deeper and broader transient boiling heat transfer phenomena, further
follow-up studies could be done. First, the same tests should be run in flow boiling condition,
because in actual reactor condition, the coolant flows over the heating surface, which could affect
the development of thermal boundary layer and hence the corresponding ONB, OSV and OV
conditions. Another idea is to investigate the pool and flow boiling critical heat flux under
exponentially escalating heat flux, because critical heat flux is a key parameter for the safety
margin of reactor. A third possibility is to study the effects of surface characteristics (roughness,
wettability, porosity) on transient boiling through the use of engineered surfaces reproducing fresh
and/or irradiated fuel cladding conditions, since our ONB model has already revealed that the ONB
and OSV conditions are highly affected by heating surface conditions. With these follow-up works,
the understanding of transient boiling heat transfer in reactor conditions will be more in depth and
complete.
81
References
[1] L.Sargentini, M.Bucci, G.Su, J.Buongiorno, T.J.Mckrell, "Experimentaland analyticalstudy
ofexponentialpower excursion in plate-typefuel". International Topical Meeting on Advances
in Thermal Hydraulics - 2014 (ATH '14). June 15-19, 2014, Reno, NV.
[2] Neil E. Todreas and Mujid S. Kazimi, "Nuclear Systems - Volume 1 ", Taylor and Francis,
2012.
[3] M.W.Rosenthal,
"An experimental study of transient boiling", Nuclear
Science and
Engineering, vol.2, pag.640-656 (1957).
[4] A.Sakurai, L.Shiotsu, "Transient pool boiling heat transfer, Part 1: Incipient boiling
superheat", Journal of heat transfer, vol.99, pag.547-553 (1977).
[5] A.Sakurai, L.Shiotsu, "Transientpool boiling heat transfer, Part2: Boiling heat transfer and
burnout", Journal of heat transfer, vol.99, pag.640-656 (1977).
[6] A.Sakurai, "Mechanisms of transitionsto film boiling at CHFs in subcooled and pressurized
liquids due to steady and increasingheat inputs", Nuclear Engineering and Design, vol.197,
pag.301 -356 (2000).
[7] M.Bucci, L.Sargentini, "Theoretical and computationalanalysis of transientheat transfer in
plate-type core nuclear reactors", CEA report RT/1 1-017/A.
[8] M.Bucci,
A.Guion,
"Characterization of transient heat transfer phenomena during
exponentialpower excursion", CEA report RT/ 12-024/A.
[9] M.Bucci, A.Guion, "Recommendationsfor the modeling of transientheat tranfer phenomena
in the CA THARE code ", CEA report RT/12-033/A.
[10] Van P. Carey, "Liquid-Vapor Phase-ChangePhenomena", Taylor and Francis, 2008.
[11] G.R. Fowles, "Introductionto Modern Optics". Holt, Rinehart and Winston, 1975.
[12] T.H. Kim, E. Kommer, S. Dessiatoun, J. Kim, "Measurement of two-phase flow and heat
transferparametersusing infraredthermometry ". International Journal of Multiphase Flow,
40 (2012), 56-67.
[13] E.R. Dobrovinskaya, L.A. Lytvynov, V. Pishchik, "Sapphire. Material, Manufacturing,
Properties". Springer, 2009.
82
Appendix A. Determination of optical properties in non-opaque
substrates (sapphire)
The transmission of radiation of wavelength A through a non-opaque substrate is limited
by reflections at the interface between the substrate and the surrounding medium (air) and
absorption in the substrate.
Reflection
Reflections depend on physical properties, surface roughness, wavelength and angle of
incidence & of the radiation. To characterize reflections at an interface, the reflectivity p,,a is thus
defined as the ratio between the reflected and the incident photon flux.
For electrically conducting materials (most metals, unless oxidized or with a rough
surface), the normal reflectivity with vacuum (0 = 0) is given by [16]
(na - 1)2 + kA
P-L)
(nI + 1)2 + k
(A.)
where n and k are the real and the imaginary part of the refraction index N
Na = na + ika
(A.2)
For dielectric materials that are poor electrical conductors (liquids, plastics, paints, glasses,
woods and also metal oxides), the complex part k known as extinction index approaches zero, and
the normal reflectivity with vacuum can be estimated by
(n,- 1)2
Pi,aVIA-(nA
= (a+12
+ 1)2
(A.3)
Absorption
According to the Beer-Lambert law, the radiation intensity I (W/m2) transmitted through
a layer of thickness x is given by
Ix,, = Ioae-ax
83
(A.4)
where aa (m-1) is the absorption coefficient of the material. Thus, the transmissivity x, for a layer
of thickness L is defined as
A-
- e-aAL
(A.5)
It can be demonstrated that the absorption coefficient depends on the real and the complex
part of the refraction index as follows
a
4
k
(A.6)
A nA
Evaluation of reflectivity and absorption coefficient
The transmission of a radiation through a non-opaque wafer is a combination of continued
reflections and absorption. It can be shown that, for normal radiation, the resulting apparent
transmissivity of the substrate is given by [17]:
*
*
(1 -pa) 2 7., - _
-1-pj'T
-p e-2aL
T-p2 ,1
p )
2
e-aaL
pj'e-;L(A.7)
A7
Fourier transform infrared spectroscopy (FTIR) spectrometers can directly be used to
measure the apparent transmissivity of a specific substrate made of a single material. To obtain
reflectivity and absorption coefficient, one can measure the apparent transmissivity rTR
of two
wafers with different thicknesses and solve the algebraic equation set below (only one root is
acceptable).
2
p,aALl
A8
_LL
*,FTIR
2
p)
*,FTIR
(1
e-aaL,
2
A
2
-aaL2
(A.8)
1AL2
_ p
e - 2aAL2
This strategy was adopted to determine the reflectivity with air and the absorption
coefficient of sapphire. Two wafers have been used, 320 and 2020 microns thick, whose apparent
transmissivity for wavelength from 3 to 5 microns is shown in Figure 1. Sapphire reflectivity and
the absorption coefficient are shown in Figure 2 and Figure 3, respectively. Absorption coefficients
are compared to those reported by Dobrovinskaya et al. [18]. As it can be seen, transmission is
84
essentially impaired by reflections. Absorption plays a relevant role only for wavelength longer
than 4.5 microns. Indeed, above 4.5 microns, sapphire absorbs and re-emits part of the infrared
radiation.
SAPPHIRE OPTICAL PROPERTIES
1.0
2020 microns
320 microns
-
-
0.9
0.8
0.7
0.6
.....
.... .... 4-...
..-
z0.5
.......
..
...
...
.......
.....
.......
0.4
00.3
0.2
0.1
0% 4
2
2.5
3
4.5
4
3.5
WAVELENGTH [microns]
5
5.5
6
Figure 1 Apparent transmissivity of sapphire wafers (320 and 2020 microns).
From 3 to 4.5 microns, the apparent transmissivityfor both wafers are generally
constant. From 4.5 to 5 microns, the apparenttransmissivityslightly decrease.
85
SAPPHIRE OPTICAL PROPERTIES
1.0
measured
0.9
.
..
..
-.
-.
.
4
0.8
-.
- .....
0.7
0.6
-.
.. ........... ...
.
- ........
0.5
0.4
.. .
.
-.
0.3
0.2
0.1
A l
2.5
2
6
5.5
5
4.5
4
3.5
WAVELENGTH [microns]
3
Figure 2 Reflectivity between sapphireand air. The measured reflectivity beiween
sapphireand air are generally constant between 3 to 5 microns.
SAPPHIRE OPTICAL PROPERTIES
100
90
80
70
Q
60
U
....
-.
40
O
---
-..
50
--
-..
-......
..
.....
-----..
.....
.....-----.
E
30
20
measured
10
Dobrovinskaya et al 181
A
2
2.5
3
4.5
4
3.5
WAVELENGTH [microns]
5
5.5
6
Figure 3 Absorption coefficient of sapphire. The spectral absorption coefficient is
calculated by Eq.s A.8 with measured apparent transmissivity. The absorption
coefficient increases sharply between 4.5 to 5 microns which leads to higher
emission. The measured values are consistent with those in literature[18].
86
Evaluation of the complex index of refraction
Once reflectivity and absorption coefficient are obtained, Eq.A. 1 and Eq.A.6 can be used
to calculate the real part nA and the complex part kA of the refraction index .1a. The results are
shown in Figure 4 and Figure 5. Data reported by Dobrovinskaya et al. [18] for the same
temperature condition (room temperature) are also shown. In Figure 4, dispersion equations for
ordinary and extraordinary index, n, and ne are also reported, expressed by a Sellmeier series
i-
A=2-
(A.9)
B?
where Ai and Bi are constants. The values of these empirical constants are listed in Table A.1.
Table A.1 Dispersion equationconstants for sapphire
coefficient
A,
A2
extra-ordinary index
1.5030759
0.55069141
B,
ordinary index
1.4313493
0.65054713
0.53414021
0.0726631
B2
B3
0.1193242
0.1216529
18.0228251
20.072248
A3
6.5927379
0.07402288
Experimental values for na are in good agreement with those of Dobrovinskaya et al. [18]
and with the dispersion equations.
87
SAPPHIRE OPTICAL PROPERTIES
2.0
1.8
*
measured
ordinary Index, EqA9
extra-ordinary lndex, EqA9
Dobrovinskaya St al. [181
1.9
1.7
ii
1.6
1.5
- --
-
1.4
C
....-.
-
1.3
4
--i --- -
--
1.2
1.1
In
2
4.5
4
3.5
WAVELENGTH [mlcrons
3
2.5
5
6
5.5
Figure 4 Sapphirena compared to dispersion equationsfor ordinaryand extraordinary index. The measured value agrees well with Dobrovinskaya's data and
those calculatedby Eq. A.9 with ordinary index and extra-ordinaryindex.
SAPPHIRE OPTICAL PROPERTIES
5.0e041
measured
4.S0-04
-
4.Se-04
3.00-04
-.
2.50-04
-.
I.25.04....
S2.00-04
1.50-041.00-04--
-
....
.....
..
5.00-05
o.00+00L
2
2.5
3
4.5
4
3.5
WAVELENGTH [microns]
5
5.5
6
Figure 5 Sapphire extinction index ka. The complex part of reflection index is
generally constantfrom 3 to 4 microns, while it startsto increase after 4 microns.
88
Appendix B. Coupled radiation-conduction model
TO
-
-------
T(x)
- ---
SUBSTRATE_
X
LENS
MIRROR
CAMERA
Figure B.1 Heater radiationtowards the IRC (reproductionof Figure 6-4). Both
the ITO and the substrate emit IR signal. The latter one is a contamination to the
previous one. The level of IR signalcontaminationalso depends on the temperature
distributionwithin the substrate.
Conduction Model
The heat transfer equation is discretized with a finite volume scheme in the physical heater
domain sketched in Figure B.1. For the transient conduction phase, a simple 1D model can be
adopted. The adiabatic boundary condition is applied at the interface between the substrate and air.
The temperature of the ITO is fixed according to the photon counts recorded by the infrared
camera, as described below. Once the converged solution is achieved for a prescribed ITO
temperature, the heat flux to sapphire at the ITO-sapphire interface can be simply calculate by the
discretized Fourier's conduction law
it -k
s
Ts(2) - Ts(1)
s
Xs(2) - Xs(1)
(B.1)
An estimate of the instantaneous heat flux to water can thus be obtained as
T (2) - Ts(1)
q'=
Aheated exp(t/x) + ks Xs(2) - Xs(1)
89
(B.2)
Radiation Model
Photons are emitted by the ITO layer and by the substrate. Water emissions are completely
shielded by the ITO layer, which is opaque in the range 3 to 5 microns used in our investigations.
The spectral hemispherical photon flux per wavelength emitted by a black body is
2 rc
4
NpA = Npa(T,A) =
(B.3)
2
Since ITO is thick enough to be considered opaque, the spectral photon flux emitted at the
interface between the ITO and the substrate is
(B.4)
- PA,hs)
Np,,rT - (
where PA,hs is the spectral reflection coefficient at the interface ITO/substrate and
Th
is
temperature of the ITO, wvhich can be considered constant through its thickness. Then, to obtain
the effective photon flux emitted by the ITO, one must take into account multiple reflections at the
ITO/substrate and substrate/air interfaces and absorption within the substrate (see Figure B.2)
A= NPA,Tf (1
PA,hs) TA,s(1
-
- PA,sa)
I(PAs
PA,sa
n=O
Np,1,(i
=
- PA,hs) T2,s(1 -
PA,sa)
PAhs PA,sa TZs
1
(B.5)
NPa,Th,aPP
A substrate layer of thickness dx emits a photons flux equal to axNpXT(x)dx in two
directions. Half of the flux is emitted forward, towards the camera, half is emitted backward,
towards the ITO heater. In the first case, the spectral photons flux reaching the substrate/air
interface is
L
N
+ 1
aA NpA,T(x) exp(-aA(L - x)) dx
=
(B.6)
0
In the second case, the photons flux reaching the ITO/substrate interface is instead given
by
L
Ns
N 2
= aA
NpI,T(x) exp(-aAx) dx
0
90
(B.7)
AIR
(iPA.?,,)(i
-.
0x.AwP
PIAm
TA.NPATh
Figure B.2 Multiple reflections and absorption determining apparent
transmissivity. The photonflux emitted by ITO is reflected back andforth between
sapphire-ITO interface and sapphire-airinterface. Each time the photon flux goes
through sapphire, it is partiallyabsorbed Each time the pholon flux reaches the
sapphire-airinterface it is partiallytransmitted Each time the photonflux reaches
the sapphire-ITO interface it is partially reflected and partially absorbed. The
similarprocess happensfor the emissionfrom sapphire.
Part of this flux is reflected back at the substrate/ITO interface and crosses the substrate to
reach the substrate/air interface. At the substrate/air interface, the two light beams can be
transmitted or reflected. Once multiple reflections and absorptions are accounted for, the effective
NpsPss2
-
s+
(i
PAsa) +
-,(x)
1-PA,hs PA,sa I'~s
91
,-PA,sa) -
-'+
N=,T x)EA4app
+1-
+
NpA,T(x)EA,app
B.8
(
P~ a) + N
NJ,
sNA, T(x) PAhs TAs(
,
spectral photons flux crossing the substrate/air interface is
Part of the signal reaching the IR camera is due to reflection of the background emission
at the ITO/substrate and substrate/air interfaces. The atmosphere emits like a blackbody, and the
spectral photons flux reflected by the heater is given by
(PA,sa
P2s A( PA,sa)2
+
ah
NPa = Np.A,T
5
-
1 -
2
Pa,hs PA,sa TAs
Npaa Pa,app
(B-9)
The spectral overall photons flux emitted at the substrate/air interface is thus given by
NpA = NpA,ThTa,app + NpA,TaPA,app + NArsjx)Eapp + Ns,+x)Qapp
(B.10)
The spectral flux can be integrated over the range of interest (3 to 5 micrometers) to obtain
the effective photons flux
=p
fp 2Npad
INpApTaPA,appd'{ + JNsi, (xjEiappdA
,
=fNpA,ThTAL,appdll
+
(B. 11)
+ A2 N~~)ap~
Finally, only a fraction of the photons emitted by the heater is directed towards the lens
and can reach the camera sensor. The final flux depends essentially on the lens focal number nf
and can be estimated by
S2 TOS
4
(B.12)
ni
where the transmission efficiency of the optical setup
Tos
(mirror and lens) is also accounted for.
Conversion from camera counts to photons
An IRC800 high-speed infrared camera with an InSb photon detector is used. Each pixel
of the InSb sensor has a well of 7 million electrons. Every time a photon hits the pixel, one electron
is moved from the valence to the conduction band and creates a voltage difference, which is the
signal measured as camera counts. The quantum efficiency of the sensor, QE, which is determined
by the photon/electron conversion efficiency, as well as reflection on the surface of the sensor,
must be also taken into account.
92
To convert camera counts to photons, the contribution of the noise must be cancelled. This
is given by the empty well counts when the integration time int_time is zero (approximately 300
counts) and the dark current (9570 counts/second), whose noise is proportional to the integration
time (0.2 ms). The effective photons flux measured by the camera is thus given by
N IRC
1
7. E + 6
ncounts - (ewell + darkcurrent- int-time)
(fwell - ewell) QE -pixelarea (B.13)
inttime
where fwell is the counts when the signal is saturated (approximately 16000 counts).
Conduction/Radiation Coupling
At a given time step, the photon counts from the IR camera are obtained. Then a guess of
the heater temperature is made based on the temperature distribution at the previous time step. The
temperature distribution through the substrate is solved by the heat conduction code. The emission
from the ITO and the substrate are calculated from the temperature distribution within the substrate
and then converted to photon counts. Then the photon counts obtained by the conduction/radiation
model are compared to the camera reading. If the difference of photon counts is less than a
prescribed tolerable error, the guessed temperature of ITO heater is accepted and the code is moved
to the next time step, otherwise, the code keeps iterating with another guess of the ITO temperature
as boundary condition. The flow chart of the code is shown in Figure B.3.
joe
SCounts R0.
---
ouess ofITO tenmertj
Conduclion
46
Tenperature Profile
ofthe Substnat
-Rodkffion
I -_
| Co.unts
|f
S
rrsTE
SBSTRF~Zf
N
Rodidon
riounts IR Carnere - Counts C/A Code;C
X
Next Tune Skep
MIRROR
LENS
CAMERA
Figure B.3 Flow chart of the coupled conduction-radiation inverse problem
(reproductionof Figure 6-8).
93
It should be noted that verification of the conduction/radiation coupling is required before
every experimental campaign (every heater and camera position). Fine tuning of the quantum
efficiency and the transmissivity of lens and mirror is also necessary to reduce the error on the
measured photons flux. This is normally achieved by steady-state calibration, to be run before
every transient experiment (see Figure B.4).
RADIATION MEL
40M
-
COMISN WITH WEASRDEMTS
radiation w&de
Cal
.. ... . . ..
3000
. .. .
.
measued - we
00
0
20
40
60
90
100
Teperature [C]
120
140
160
Figure B.4 Comparisonbetween measuredand calculatedradiationis steady-state
condition (uniform temperatureprofile within the heater). The overlapped region
between wet calibrationand dry calibration agrees well with each other, which
confirms the consistency of the calibration. The radiationmodel agrees very well
with the calibrationpoints, which validates the accuracy of the radiationmodel.
It must be emphasized that the implementation of the radiation model requires the
knowledge of three fundamental optical properties:
*
ax spectral absorption coefficient in sapphire (to calculate us);
*
Px,,a spectral
"
PAhs
reflectivity between sapphire and air;
spectral reflectivity between sapphire and ITO.
94
In Appendix A, we have discussed how to obtain the first two properties. To obtain the
reflectivity at the interface between ITO and sapphire (PX,hs), we only need to measure the apparent
reflectivity with the FTIR and then solve for PX,hs by the equation below.
PA,app = PA,sa + PAhs TAs (1 - Psa)2
1 - PA,s PA,sa Tas
95
(B. 14)
Appendix C. Optical properties of sapphire
Apparent
optical properties are measured through Fourier Transform
InfraRed
spectroscopy. An FTIR Bruker spectrometer was used to measure the apparent transmissivity of
sapphire and the reflectivity of ITO through sapphire. Other properties have been estimated as
discussed in Appendix A and Appendix B.
In Figure C. 1, apparent optical properties of interest for our heater are shown:
0
is labeled ito reflectivity (through sapphire), as measured with the FTIR;
STappp is labeled sapphire transmissivity, as measured with the FTIR;
" EXapp is labeled sapphire emissivity (backward), calculated as discussed in Appendix B;
*
EXapp is labeled sapphire emissivity (forward) , calculated as discussed in Appendix B.
PAapp
WRAPPED AROUND HEATER: APPARENT OPTICAL PROPERTIES
1
0.9
0.8
0.7
CL
4-
0.6
0.5
CL
L
0.4
0.3
0.2
ito reflectivity (through sapphire)
sapphire transrnissivity
sapphire emissivity (backward)--~~-~sapphire ernissivity (forward)
0.1
2
2.5
3
3.5
4
4.5
Wavelength [um]
5
5.5
6
Figure C.J Apparent optical properties of our heater. The apparent optical
propertiesshown are all direct measurements obtainedby FTIR.
96
In Figure C.2, pure optical properties of interest for our heater are shown:
*0
0
0
rus is labeled sapphire transmissivity (obtained as discussed in Appendix A);
PA,sa is labeled air-sapphire reflectivity (obtained as discussed in Appendix A);
P,hs is labeled ito-sapphire reflectivity (obtained as discussed in Appendix B).
OPTICAL PROPERTIES OF SAPP1IRE
I
air-sapphire ref lectivitV
ite-sapphire reflectivit-V
_sapphire transpissivituj
0.9
0.8
:
...
............
.....................
0.7
0.6
4-)
'I
U
0.5
0.4
0.3
0.2
0.1
0,
2
2.5
3
3.5
4.5
4
iavelength (um)
5
5.5
6
Figure C.2 Pure optical properties of interestfor our heater. The pure optical
properties are obtainedby the methods discussed in Appendix A and Appendix B
with the inputs of apparentopticalproperties in Figure C.1.
97