Study of
Flashing Evaporation
in Liquid Spraying
Qiyiana Tian (992420616)
A thesis submitted in partial fulfilment of requirements for the degree of
BACHELOR OF APPLIED SCIENCE AND ENGINEERING
Supervisor: Professor Ashgriz
Department of Mechanical and Industrial Engineering
University of Toronto
March, 2008
Chapter 1
Introduction
1
1.1 Background
In a kraft recovery boiler, Black liquor is sprayed into the recovery boiler through a set of
splashplate nozzles [1]. These nozzles produce a thin liquid sheet, which breaks up to form
large droplets with a wide size distribution [1]. Many researchers believe that the spray
droplet size and size distribution, as well as factors such as nozzle design, fluid properties
and operating conditions are the key variables in controlling the combustion process in the
furnace [2]. Furthermore, it has been established that flashing within the liquor delivery
system has a significant impact on droplet size and size distribution [2]. However, it is
uncertain whether the flashing phenomenon has any impact on the combustion efficiency.
Flashing is an evaporation phenomenon caused by an abrupt pressure drop below its
saturation pressure as the liquor approaches the nozzle orifice. Due to the sudden drop of
pressure, the liquid temperature is raised above liquid’s boiling point. The heat surplus
that can no longer be sustained in the liquid as sensible heat transforms into latent heat of
vaporization. Vapor bubbles form inside the liquid bulk, evaporation therefore occurs
within the delivery system. [3]
Only a few researches have been conducted on flashing evaporation of a water film. Earlier
on, Aoki [4, 5] investigated the heat flux exchange due to water evaporation under low
pressure conditions.
Harmand et al. [3] carried out an experimental study of flash
evaporation of a water film. Further study on flash evaporation has to be conducted and
insight into the evolution of the flash evaporation has to be acknowledged in order to
2
answer the question if flashing phenomenon has any impact on combustion efficiency.
This study hypothesized that if liquid evaporation occurred at atmospheric pressure, it
should be similar to what happens when it is in a furnace undergoing flashing. Then the
atmospheric pressure results can be applied directly to the furnace condition. Hence, it is
of importance and interest to study the liquor evaporation process at atmospheric pressure.
Flashing evaporation phenomenon happening at atmospheric pressure is very similar to
spray cooling. Spray cooling occurs when liquid is forced through a nozzle orifice, resulting
into liquid droplets which then impinge on a heated surface. The droplets form a thin
liquid layer on the heated surface and then evaporate. A tremendous amount of energy is
removed during spray cooling and transformed to latent heat of evaporation in addition to
substantial convection effects [6].
Unlike flashing evaporation, spray cooling can be
achieved and monitored at atmospheric pressure.
Furthermore, in flashing, liquid
evaporates as it exits nozzle orifice; while in spray cooling, liquid begins to evaporate once it
impinges on the hot surface.
Aiming to apply some findings of spray cooling to the present study, a number of papers
regarding spray cooling have been reviewed. Horacek et al. [6] investigated the single
nozzle spray cooling heat transfer mechanisms. Grissom et al. [7] studied the lowest
surface temperature possible for the existence of spray evaporative cooling. Rybichi [8]
carried out an experimental study on single-phase and two-phase cooling characteristics of
both upward-facing and downward-facing sprays. Chen et al. [9] explained the effects of
3
spray characteristics on critical heat flux in subcooled water spray cooling.
Liu et al. [10] in particular investigated film boiling heat transfer for water jet impinging on
high temperature flat plate. The thermodynamic mechanism at the liquid/solid interface
studied by Liu et al is realized to be the same as the present study. In his analysis,
evaporation heat flux of liquid, qv, convection heat flux of subcooled liquid, ql, and radiative
heat flux in the vapor layer, qr, were accounted to evaluate the total supplied heat flux, qw,
to evaporate the liquid film.
qw = qv + ql +
3
qr
4
(1)
Liu et al proposed a semi-empirical correlation to predict the heat flux supplied to evaporate
liquid at the liquid/solid interface.
qw = (∆Tsatλv)3 / 4 (
hfgVs Re lµl 1/ 4 3
) + qr
3vν
4
(2)
This correlation is employed in the present study. Its application is discussed in more
detailed in 2.0.
1.2 Objective
The purpose of this paper is to study and understand flashing evaporation phenomenon.
Neither the heat transfer mechanisms between the hot surface and the liquid at where a
thin vapor film forms [11] nor between the vapour film layer and subcooled water layer is
addressed in this paper.
This paper also does not address the droplet size and size
4
distribution once the sprayed liquid impinges on a solid surface and breaks into droplets.
Furthermore, the effects of nozzle design, operating conditions and fluid properties are
minimized by fixing these variables to simplify the analysis.
To the author’s knowledge, the study preformed herein is concentrated on independently
varying the liquid spray rate and assessing its impact on the overall evolution of liquid
evaporation.
In summary, the primary purpose of the present study is to study and understand flashing
evaporation phenomenon at room pressure.
The ultimate objective is, once liquid is
sprayed on a surface, to have a portion of liquid evaporates while the rest liquid forms a
water sheet as it leaves the test surface. Experiment was carried out to investigate on
liquid flashing by employing water as the working fluid due to its simple fluid characteristics.
Measurements were taken and analyzed at selected spray rates.
Evolution of several
characteristics parameters such as, water evaporation rate and evaporation fraction of
sprayed water, are presented at the end of this study.
5
Chapter 2
Analytical Model
6
2.1 Analytical Analysis
For water impinges on high temperature metal surface, the heated surface can be divided
into center spray striking zone and surrounding mist zone [10]. In this study, only the spray
striking zone is considered, the assumption here is that the influence of the neighboring
mists on the overall heat removal process is negligible.
The energy supplied to system or the heat transferred from the heating surface to the
sprayed water can be described by the following mechanisms:
(i)
heat absorbed by the evaporating water vapor ( hv ) and
(ii)
energy transferred to heat up the outgoing liquid water or the water sheet ( he ).
The total energy transfer rate by the above two mechanisms can be described by an energy
balance:
.
.
.
Q = Qv + Qe
(3)
While the rate of heat absorbed by the water vapor can be further described as:
.
.
Qv = mv(hs + hfg )
(4)
.
Here, mv denotes the water evaporation rate; hs denotes the sensible heat and hfg
represents the latent heat of vaporization which accounts for the phase change of water
from liquid to vapor.
The sensible heat required to bring water from a lower temperature to the boiling point can
7
be written as:
(5)
hs = Cp (Tb − Ti )
Where Cp denotes the specific heat of water. Tb and Ti denote the boiling
temperature and the initial temperature of sprayed water respectively.
Bring Eq. (4) into Eq. (3),
.
.
Qv = mv[Cp (Tb − Ti ) + hfg ]
(6)
Also, the rate of energy transferred to the water sheet can be described as:
.
.
(7)
Qe = me he
.
Where me denotes the mass flow rate of the water sheet; he denotes the sensible heat.
The sensible heat absorbed by the water sheet can be rewritten as:
he = Cp (Tf − Ti )
(8)
Where Tf denotes the temperature of the water sheet.
Bring Eq. (7) into Eq. (6),
.
.
Qe = me Cp (Tf − Ti )
(9)
Bring Eq. (5) and Eq. (8) into Eq. (2),
.
.
.
Q = me[Cp (Tb − Ti ) + hfg ] + me Cp (Tf − Ti )
8
(10)
In addition, the in flow and out flow water can be related by the following mass balance
equation,
.
.
.
mi = mv + me
(11)
Also, the thermodynamic mechanism occurs at the liquid/solid interface can be described as:
.
Q=
qwAe
t
(12)
.
Where Q denotes the energy transfer rate; qw denotes the heat flux supplied to
evaporate water; Ae denotes the water film area.
Eq. (2) proposed by Liu et al correlates the total heat flux, qw , supplied to evaporate water
with superheating temperature as well as water properties in liquid and vapor states. In
the present study, all the physical properties of water vapor and water liquid are assumed to
be constant.
Although some of the parameters are temperature dependent, this
assumption is justified as the dependency is very weak. It is further realized that the first
term on the right hand side of Eq. (2) dominates the equation as sprayed water brings in
high subcooling. Radiative heat flux, qr , becomes negligible compared to conduction and
convection heat flux. Therefore, in present study, Eq. (2) is modified to
qw = (∆Tsatλv) 3 / 4 (
hfgVs Re lµl 1 / 4
)
3vν
(13)
Eq. (13) describes the total heat flux, qw supplied to the metal surface as a function of
∆Tsat , where ∆Tsat = ( Tsurf - Tb ) denotes the surface superheating temperature.
9
Bring Eq. (13) to Eq. (12)
(∆Tsatλv) 3 / 4 (
Q=
hfgVs Re lµl 1/ 4
) Ae
3vν
t
(14)
Table 2.1 Properties of Water Liquid and Water Vapor
ρl
ρv
kv
hfg
μl
μv
νl
νv
Tb
Cpl
Cpv
997
0.5978
0.0251
2257
0.000891
0.00001227
0.000000893681
0.0000205253
100
4.19
4.22
kg/m3
kg/ m3
W ° C /m
KJ/Kg
kg /m s
kg /m s
m2 /s
m2/ s
°C
KJ/ Kg ° C
KJ /Kg ° C
Experiment apparatus was put together in the laboratory aiming to study the evolution of
.
flashing evaporation. Measurements of variables such as mi , Ti and Tf were obtained
and applied to Eq. (10), Eq. (11) and Eq. (14) for further analysis.
10
Chapter 3
Experimental Apparatus
Apparatus and Procedure
11
3.1 Experimental Apparatus
Fig. 3.1 is a schematics of the apparatus used for flashing evaporation experiments. It
consists of a nozzle spray system, power control system, and an aluminum block.
Fig. 3.1 Schematic Diagram of Experimental Apparatus for Flashing Evaporation
An aluminum block was designed and machined to house the heater; its configuration is
illustrated in Fig. 3.2 below. The housing block is a rectangular block measuring 89 mm
long x 30 mm wide x 25 mm thick.
A stainless steel sheath cartridge heater
(CSH-302470/120, Omega) with a 470 W power capacity was selected to be the heating
source. The cartridge heater was inserted into a 10.8 mm hole drilled 68.6mm deep on the
cross section (29.25 mm wide x 25 mm thick). The hole was filled with high thermal
conductivity paste (OT-201-1/2, Omega) to minimize the thermal contact resistance. Heat
12
conduction within the aluminum housing was high enough to provide an almost uniform
temperature profile along its centerline. [12]
The test surface (85 mm long x 30 mm wide ) was polished to a 1200 grit finish employing
water as the polish media using a semi-automatic polisher (Imptech DPS 2000, Boksburg,
South Africa).
Fig. 3.2 Heater Housing Configuration
In the nozzle-spray system, a commercially available spray circular nozzle with a diameter of
d= 2.05 mm (M1, Sprayer Co. Ltd) was used to obtain different values of water spray rate.
The spray nozzle is located 13 degree to the test surface. The distance between the nozzle
orifice and the test face is 1.3 mm horizontally and 0.9 mm vertically.
Electrical power was supplied to the cartridge heater by a variable voltage transformer
13
(3PN126, The superior electric. Co, Bristol Conn, USA).
The rating of the variable
transformer is 120 Volts input/ 140 Volts output at 6 Amps.
3.2 Imaging Visualization
Photographs of flashing phenomenon, sprayed water impinges on a surface resulting in
formation of water sheet and evaporation of water, were taken simultaneously using
FASTCAM-ultima APX High-Speed Video Camera System with a speed of 1200 frames/s.
While a fluorescent lamp was set in place to provide illumination. Photographs were also
taken using a Canon Powershot S410 camera during trial runs. The video camera was
connected to a computer and signals were sent to software Photron Fastcam Viewer 2.438.
Photron Fastcam. Sequences of up to 2488 frames with an area of 128 x 128 pixels can be
recorded from each frame. [13]
3.3 Experimental Procedure
To ensure that the power input to the cartridge heater did not exceed its capacity, variable
transformer was first calibrated.
A multi-meter (Uni-T UT60E DMM, Uni-Trend) was
connected to the heater and variable transformer to create a close-loop circuit. Current
and voltage measurements were taken at each output voltage rating and output power was
acknowledged by applying
Q = IV
(14)
Fig.3.3 illustrates the power output of the variable transformer at each output voltage rating.
It was found that the maximum power output that can be achieved without risking the
14
cartridge heater was 440 W which corresponded to 85% of voltage output capacity of the
variable transformer.
Fig.3.3 Variable Transformer Output
Fig. 3.4 Evolution Of Test Surface Temperature At 440 W Power Input
15
In addition, temperatures of the aluminum surface were measured at 440 W power input
with no water spray on the surface. Results are plotted in Fig.3. 4.
Prior to each experiment, the test surface was cleaned by washing it with acetone and then
with distilled water to remove the oxide depositions. High thermal conductivity paste was
applied to the cartridge heater to ensure good contact between the heater surface and the
housing. [12]
The experiments were conducted at three known water spray rates: 0.0032kg/s, 0.0038kg/s,
and 0.0049kg/s. The water spray rates were measured by recording the volume of water
flowing into a container in a known period of time.
Temperature of the sprayed water was
recorded by a Type K thermocouple. Once the sprayed water reached the desired rate, the
variable transformer was turned on to 85% of the output voltage capacity. Temperature of
the water sheet was measured by the Type K thermocouple.
Photographs of the test surface at selected water spray rate were taken.
All the
measurements were manually recorded and uploaded to an excel file for analysis.
3.4 Uncertainty Analysis
The combinations of the experimental conditions are summarized in Table 3.1.
In the experiments, the aluminum housing was not “guarded” with insulators.
16
Heat
radiation to the surroundings was assumed to be negligible compared to the amount of heat
transferred to the liquid/ solid interface by conduction, convection and radiation
mechanisms. To prevent heat dissipating to the surroundings, thermal conductivity paste
was applied to the cartridge heater to ensure good contact between the heater surface and
the housing.
Another possible source of error may have come from the inaccurate measurements of the
spray water rate. The nozzle was directly connected to the tab where no flow meter was
placed in between. The spray water rate was manually measured by recording the volume
of water flowing into a container in a known period of time. To minimize the impact on
accuracy of the measurements, the average was used.
In addition, due to the failure of the cartridge heaters, only a limited number of results were
obtained during the experiment, making it very difficult to confirm any observations.
Table 3.1 The geometric of Test Section and Experimental Conditions
A
d
s
Pi
Ti
P
Ts
.
0.00267
m2
2.05
mm
water
1.01x105
atm
22.6
°C
__________________________________________________________
440
W
252.6
365.7
440.0
°C
mi
0.0032
0.0038
0.0049
kg/s
Tf
28.2
27.7
26.4
°C
17
Chapter 4
Results and Discussion
Discussion
18
4.1 Flashing Visualization
Figure.4.1 shows a typical front view of the test surfaces at three different water spray rates
at a constant power input of 440 W. In general, the bright portions outline the size and
shape of the water sheet formed. Due to the failure of cartirage heates, evaporation
pheonomenon was not obtained while these photographs were taken. Note that the
photographs were taken at an angle of 17° on a vertical axis. This resulted in the water
sheet on the left side appeared to be thicker than the right; however, in actuality the
thickness across the water sheet is approximately uniform.
(a)
19
(b)
(c)
.
.
Fig.4.1 Visulization of Water Sheet Formation: (a) mi =0.0032 kg/s; (b) mi =0.0038 kg/s (c)
.
mi =0.0049kg/s.
Based on the three sets of photographs, once sprayed water impinges on the surface, it is
found that the formation of the water sheet is very similar for all three spray rates. The
water sheet formation process in the present flashing phenomenon can be explained as
follows: it is found that an island shape of water film is first formed on the test surface once
20
water is sprayed onto it; the water film continuously extends its size and flows toward the
bottom edge of the surface due to the force of gravity. As water exits the test surface,
instead of extending itself infinitely, under the action of gravitational force, a triangular
shape of water sheet forms along the bottom edge and it eventually deforms to a water
column. The photographs shown in Fig. 4.1 can be illustrated in sequence. When the
water spray rate is low, it is observed that the small size water sheet levelled off into a
relatively long water column. As water spray rate increases, the size of the water sheet
expands with a shortened water column.
(a)
(b)
Fig.4.2 Visualization of Flash Evaporation Phenomenon at Two Water Spray Rates:
.
.
(a) mi ≈ 0.0031 kg/s; (b) mi ≈ 0.0050 kg/s
Fig.4.2 shows the evaporation phenomenon at a input power of 440 W at two water spray
rates. Photographs were taken during the trial runs using Canon Powershot 4.0 digital
21
camera with not very precise measurement of the water spray rate. Although the details of
the evaporation process cannot be visulized from these photographs, it is believed that at
the liquid/solid interface, heat is absorbed first by water along the edge of the water film
through convection and radiation mechanisms and evaporation begins once the saturation
conditions are reached. Furthermore, these photographs confirm that at a constant power
input, the violence of the flashing phenomenon decreases when water spray rate increases.
4.2 Results of Analytical Analysis
Using Eq. (2), Eq. (10) and Eq. (12) along with measurements of surface superheating
temperature, water evaporation rate over time is predicted and presented in Fig. 4.3, Fig. 4.4
and Fig. 4.5 For simplicity, many values in these figures are not tabulated; to obtain them,
refer to Appendix B for detailed results.
(a)
22
(b)
(c)
Fig. 4.3 Evolution of Water Evaporation at: (a) ∆Tsat = 152.6° C; (b) ∆Tsat = 265.7° C; (c)
∆Tsat = 340° C
Water evaporation rate is plotted against time in Fig. 4.3.
It is noticed that water
evaporation rate increases in a logarithm function of time and leans toward a limit value
23
after a while. In general, water evaporation rate rises to a relatively high value in a short
period of time and then slowly approaches the limit value. It is observed that water
evaporation rate is dependent upon the superheating. As surface superheating rises, the
increase of water evaporation rate becomes significant in a very short period of time; once
the evaporation rate reaches a high value, the increase becomes more gradual over time.
This observation can be explained as follows: the higher the superheating, the more heat
transfers to evaporate the water at liquid/solid interface, the faster the sprayed water
evaporated.
This observation is further confirmed by the fact that higher water
evaporation rate results a reduced subcooling of the water sheet.
(a)
24
(b)
(c)
Fig. 4.4 Evolution of Evaporation Fraction of Sprayed Water at: (a) ∆Tsat = 152.6° C; (b)
∆Tsat = 265.7° C; (c) ∆Tsat = 340.0° C
The evaporation fraction of sprayed water over time is plotted in Fig. 4.4. The evaporation
fractions with different subcoolings are nearly the same except that higher evaporation
25
fraction results in a lower subcooling. As superheating increases, the slope of the curve
becomes steeper, in other words, the evaporation fraction of sprayed water increases
dramatically over time. At superheating temperature of 152.6° C, close to 20% of the
sprayed water is evaporated in a time interval of 100 s. The increase of water evaporation
fraction reaches to 40% during the same time interval at superheating temperature of 340° C.
In addition, the data shows that this superheating effect is insignificant at the beginning and
becomes more significant over time.
(a)
26
(b)
(c)
Fig. 4.5 Fraction of Evaporation Fraction of Sprayed Water Vs t at: (a) ∆Tsat = 152.6° C; (b)
∆Tsat = 265.7° C; (c) ∆Tsat = 340° C
In Fig. 4.5, evaporation fraction of sprayed water is plotted against water spray rate in a
logarithm scale. A strong relationship between the evaporation fraction and superheating
27
is observed. The increase in water evaporation fraction is relatively small at a lower
superheating temperature of 152.6° C, but the increase becomes larger at 265.7° C. The
increase is most significant at superheating temperature of 340° C.
Fig. 4.5 further
modifies the observation made in Fig. 4.3 which shows that not only the water evaporation
rate but also the evaporation fraction of sprayed water increases in a logarithm function of
time and leans toward a limit value after a while.
4.3 Experimental Results
(a)
28
(b)
(c)
.
Fig. 4.6 Comparison Between Predicted and Experimental Results: (a) mv Vs t; (b)
Evaporation Fraction of Sprayed Water Vs t; (c) Evaporation Fraction of Sprayed Water Vs
.
mv
Fig4.6 shows the experimental results and their corresponding predicted values; refer
29
Appendix D for details. It is noticed that, water evaporation rate decreases as water spray
rate rises. Experimental results show that as water spray rate increases from 0.0032 to
0.0049 kg/s , the evaporation fraction decreases from 0.23 to 0.06% while subcooling
decreases from 5.6 to 4.8 ° C. It is found that the predicted values are relatively larger than
the experimental results. Water evaporation rate for small water spray rate (0.0032 kg/s)
correlates relatively well (22% difference) with the predicted result, however, for the larger
water spray rate (0.0049 kg/s), the difference between the experimental and predicted value
reaches 40%. Due to the fact that only a limited number of measurements were taken
during the experiment, it is uncertain if the experiment results would consistently give a
large difference or correlate well with the predicted values. If latter is true, then the
experiment results obtained are just noises.
Also, the observation made previously (4.2) shows that superheating has a very strong effect
on water evaporation rate. However, due to the lack of experimental data, further study
on this observation is not possible.
30
Chapter 5
Conclusion
31
5.1 General Observation and Conclusions
This paper presents an experimental study that concerns the flash evaporation of a water
sheet. Experiments were carried out at 440 W constant power input for a water spray rate
between 0.0032, 0.0038 and 0.0049 kg/s at atmospheric pressure. From the results, a
number of significant observations are noticed and summarized below.
1. Photographs of evaporation phenomenon confirm that at a constant power input, the
violence of the flashing phenomenon decreases as water spray rate increases.
2. It is predicted that water evaporation rate and the evaporation fraction of sprayed water
are strongly dependent upon the superheating. As superheating rises, more significant
increase of both the water evaporation rate and the evaporation fraction is obtained due to
an increased amount of heat transfer occurring at liquid/solid interface.
3. In addition, it is predicted that an increase in water evaporation rate and the evaporation
fraction would result in a decrease in subcooling of the water sheet.
4. Experimental values confirmed that as the water spray rate rises, evaporation rate
increases along with a drop of subcooling of the water sheet.
32
Abstract
An experimental study of flashing evaporation of a liquid sheet has been conducted at
atmospheric pressure using water as the working fluid. The experimental data were taken
for the following conditions: a constant power input of 440 W; a nozzle diameter of d= 2.05
mm; an initial water temperature of Ti= 22.6 ° C and three water spray rate of 00032 kg/s,
0.0038 kg/s, and 0.0049 kg/s. Evaporation was visualized with a high-speed video camera.
Temperature measurements of the test surface and the water sheet were taken. The water
evaporation rate and evaporation fraction of sprayed water were first predicted using a
numerical analysis. Comparisons were made between experimental results and predicted
values. Overall, study results show that as water spray rate increases, the violence of the
flashing phenomenon decreases.
In addition, rising superheating would result in a
significant increase of both water evaporation rate and evaporation fraction of sprayed
water; an increase in water evaporation rate would result in a decrease in subcooling of the
water sheet.
Acknowledgements
The author gratefully acknowledges the assistance provided by the following person:
Prof. Nasser Ashgriz
Reza Karami
Rajeev Dhiman
Len Roosman
Thank you for your help.
-i-
Table of Contents
List of Symbols ............................................................................................................................. iii
List of Figures .............................................................................................................................. iiii
List of Tables ................................................................................................................................. iv
Chapter 1 Introduction ................................................................................................................. 1
1.0. Background .............................................................................................................................. 2
1.1. Objective .................................................................................................................................. 4
Chapter 2 Analytical Model ......................................................................................................... 6
2.0. Analytical Analysis ................................................................................................................... 7
Chapter 3 Experimental Apparatus and Procedure ................................................................ 11
3.1. Experimental Apparatus ...................................................................................................... 12
3.2. Imaging Visualization ........................................................................................................... 14
3.3 Experimental Procedure ....................................................................................................... 14
3.4 Uncertainty Analysis .............................................................................................................. 16
Chapter 4 Results and Discussion .............................................................................................. 18
4.1. Flashing Visualization ........................................................................................................... 19
4.2. Results of Analytical Analysis .............................................................................................. 22
4.3. Experimental Results ............................................................................................................ 28
Chapter 5 Conclusion .................................................................................................................. 31
5.1. General Observation and Conclusions ............................................................................... 32
References ................................................................................................................................... 33
Appendix A Calibration of Variable Transformer:
................................................................. 36
Appendix B Analytical Model: ................................................................................................... 37
Appendix C Temperature Measurements: ............................................................................... 51
Appendix D Summary of Experimental Results: ...................................................................... 52
-ii-
List of Symbols
Nomenclature
A
surface area [m2]
Cp
specific heat [KJ/kg° C]
d
nozzle diameter [m]
hfg
latent heat of vaporization [KJ/kg]
k
thermal conductivity [J/m° Cs]
m
mass flow rate [kg/s]
P
pressure [Pa]
q
heat flux [J/m2s]
Re
Reynolds number [-]
s
substance [-]
T
temperature [° C]
t
Time [s]
Greek Symbols
μ
viscosity [Pa s]
ν
kinematics viscosity [m2/s]
ρ
density [kg/m3]
Subscripts
a
atmospheric
b
boiling state
e
excess water
f
final state
i
initial position
l
liquid
r
radiation
s
saturation state
sat
superheating
sub
subcooling
surf
surface
v
vapour state
-iii-
List of Figures
Chapter 3 Experimental Apparatus and Procedure
Fig. 3.1 Schematic Diagram of Experimental Apparatus for Flashing Evaporation ………………12
Fig. 3.2 Heater Housing Configuration ……………………………………………………………………………….13
Fig.3.3 Variable Transformer Output ………………………………………………………………………………….15
Fig. 3.4 Evolution Of Test Surface Temperature At 440 W Power Input ………………………………15
Chapter 4 Results and Discussion
Fig.4.1 Visulization of Water Sheet Formation:
.
.
.
(a) mi =0.0032 kg/s; (b) mi =0.0038 kg/s (c) mi =0.0049kg/s …………………………………..19
Fig.4.2 Visualization of Flash Evaporation Phenomenon at Two Water Spray Rates:
.
.
(a) mi ≈ 0.0031 kg/s; (b) mi ≈ 0.0050 kg/s …………………………………………………………………21
Fig. 4.3 Evolution of Water Evaporation at:
(a) ∆Tsat = 152.6° C; (b) ∆Tsat = 265.7° C; (c) ∆Tsat = 340° C ………………………….……22
Fig. 4.4 Evolution of Evaporation Fraction of Sprayed Water at:
(a) ∆Tsat = 152.6° C; (b) ∆Tsat = 265.7° C; (c) ∆Tsat = 340.0° C ……………………………24
Fig. 4.5 Fraction of Evaporation Fraction of Sprayed Water Vs t at:
(a) ∆Tsat = 152.6° C; (b) ∆Tsat = 265.7° C; (c) ∆Tsat = 340° C …………………………….26
Fig. 4.6 Comparison Between Predicted and Experimental Results:
.
(a) mv Vs t; (b) Evaporation Fraction of Sprayed Water Vs t; (c) Evaporation Fraction of
.
Sprayed Water Vs mv ………………………………………………………………………………………………………………28
-iiii-
List of Tables
Chapter 3 Experimental Apparatus and Procedure
Table 2.1 Properties of Water Liquid and Water Vapor……………………………………………………….10
Table 3.1 The geometric of Test Section and Experimental Conditions ……………………………….17
-iv-
References
[1]Miikkulainen, P., Kankkunen, A. & Jarvinen, M. 2002, The Effect of Excess
Temperature and Flashing on Black Liquor Spray Properties, IFRF Finnish- Swedish
Flamed Days 2002, Vaasa, Finland, 24-25 September
[2]Terry N. Adams, Kraft Recovery Boilers, Atlanta, GA : Tappi Press ; [New York] :
AF&PA, c1997.
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35
Appendix A - Calibration of Variable Transformer
Variable Transformer Output Table
t [s]
10
20
30
40
50
60
70
80
85
90
100
I (Amp)
0.469
0.914
1.356
1.777
2.195
2.625
3.054
3.46
3.62
3.76
4.16
V (Yolt)
15.19
29.6
44
57.8
71.8
84
100
114.8
121.6
128.5
142.8
P (Watt)
7.12411
27.0544
59.664
102.7106
157.601
220.5
305.4
397.208
440.192
483.16
594.048
Variable Transformer Output Plot
36
Power-ideal (Watt)
4.971
27.141
60.111
103.881
158.451
223.821
299.991
386.961
434.496
484.731
593.301
Appendix B – Analytical Model
Summary of Analytical Model
Re=Vs*d/ν-l
ν= μ/ρ
qw= [(Tw-Ts)*kv/d]^3/4*(1/3*hfg*Vs*Rel*μ-l*t/ν-v)^1/4+3/4*qr in [W/m2]
q*A= mv[Cp1(Tb-Ti)+hfg]+ meCp2(Tf-Ti)
mv=[Q/1000-miCp2(Tf-Ti)]/[Cp1(Tb-Ti)+hfg-Cp2(Tf-Ti)]
ρ-l@25 degree C ρ-l
kg/m3
kg/m3
997
957.9
hfg
V-s
KJ/kg
2257
Tw
Ts
k-v
d
hfg
Vs
Re-l
μ-l
ν-v
Ts
k-v
d
degree C W/m° C
m
100
0.0251 0.00205
μ-v
ν-l
ν-v
m2/s
m2/s
1.2E-05 8.9E-07 2.1E-05
kg/s
°C
m^2
0.00267
°C
100
m2
0.00067
W/m° C 0.0251
kg/s
m
0.00205 KJ/Kg° C
4.22
KJ/Kg
2257
°C
100
m/s
°C
22.6
KJ/kg
2257
kg/ms 0.00089
kg/s
m2/s
2.1E-05 KJ/Kg° C
4.19
37
Area-nozzle
3.3E-06
Tsurf
174.479
252.599
365.697
440.013
m2
°C
Analytical Result at Tsurf = 252.6 ° C and Tf = 35 ° C
constant heat flux
Tw
t
252.599
3.5
5
7
10
13
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.54271
0.45407
0.38376
0.32107
0.2816
0.26216
0.22703
0.20306
0.18537
0.17162
0.16054
0.15136
0.14359
0.13691
0.13108
0.12594
0.12135
0.11724
0.11352
0.11013
0.10702
0.10417
0.10153
149813
Re
1244.92
1041.57
880.291
736.504
645.957
601.353
520.787
465.806
425.221
393.678
368.252
347.191
329.375
314.046
300.677
288.881
278.372
268.933
260.394
252.619
245.501
238.954
232.903
Qtotal
mi
0.00179
0.00149
0.00126
0.00106
0.00093
0.00086
0.00075
0.00067
0.00061
0.00056
0.00053
0.0005
0.00047
0.00045
0.00043
0.00041
0.0004
0.00039
0.00037
0.00036
0.00035
0.00034
0.00033
38
400
Tf
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
Qwetted
mv
2.86674E-06
8.85034E-06
1.35962E-05
1.78273E-05
2.04917E-05
2.18042E-05
2.4175E-05
2.57928E-05
2.69871E-05
2.79153E-05
2.86634E-05
2.92832E-05
2.98074E-05
3.02585E-05
3.06519E-05
3.0999E-05
3.13082E-05
3.1586E-05
3.18373E-05
3.20661E-05
3.22755E-05
3.24682E-05
3.26462E-05
100
mv/mi*100%
0.16059986
0.59260962
1.07718838
1.68814244
2.21245222
2.52877434
3.23745981
3.86182425
4.42629285
4.9453753
5.42852546
5.88231001
6.31151011
6.71973515
7.10978926
7.48390242
7.84388269
8.19122018
8.5271602
8.85275614
9.16890847
9.47639414
9.77588908
Analytical Result at Tsurf = 252.6 ° C and Tf = 40 ° C
constant heat flux
Tw
t
252.599
6
8
10
13
15
17
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.4145
0.35897
0.32107
0.2816
0.26216
0.24625
0.22703
0.20306
0.18537
0.17162
0.16054
0.15136
0.14359
0.13691
0.13108
0.12594
0.12135
0.11724
0.11352
0.11013
0.10702
0.10417
0.10153
149813
Re
950.823
823.437
736.504
645.957
601.353
564.873
520.787
465.806
425.221
393.678
368.252
347.191
329.375
314.046
300.677
288.881
278.372
268.933
260.394
252.619
245.501
238.954
232.903
Qtotal
mi
0.00136
0.00118
0.00106
0.00093
0.00086
0.00081
0.00075
0.00067
0.00061
0.00056
0.00053
0.0005
0.00047
0.00045
0.00043
0.00041
0.0004
0.00039
0.00037
0.00036
0.00035
0.00034
0.00033
39
400
Tf
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Qwetted
mv
2.41004E-07
5.54481E-06
9.16431E-06
1.29343E-05
1.47914E-05
1.63103E-05
1.81458E-05
2.0435E-05
2.21248E-05
2.34381E-05
2.44967E-05
2.53736E-05
2.61154E-05
2.67536E-05
2.73103E-05
2.78014E-05
2.82389E-05
2.8632E-05
2.89875E-05
2.93112E-05
2.96076E-05
2.98802E-05
3.01321E-05
100
mv/mi*100%
0.01767758
0.4696296
0.86780733
1.39649206
1.71545364
2.01377013
2.43005254
3.0596268
3.62880545
4.15221923
4.6394009
5.09697192
5.52975336
5.94138472
6.33469352
6.71192836
7.07491239
7.42514814
7.76389131
8.09220409
8.41099447
8.72104586
9.02303985
Analytical Result at Tsurf = 252.6 ° C and Tf = 45 ° C
constant heat flux
Tw
t
252.599
10
13
15
17
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
95
100
qw
Vs
0.32107
0.2816
0.26216
0.24625
0.22703
0.20306
0.18537
0.17162
0.16054
0.15136
0.14359
0.13691
0.13108
0.12594
0.12135
0.11724
0.11352
0.11013
0.10702
0.10417
0.10153
0.10417
0.10153
149813
Re
736.504
645.957
601.353
564.873
520.787
465.806
425.221
393.678
368.252
347.191
329.375
314.046
300.677
288.881
278.372
268.933
260.394
252.619
245.501
238.954
232.903
238.954
232.903
Qtotal
mi
0.00106
0.00093
0.00086
0.00081
0.00075
0.00067
0.00061
0.00056
0.00053
0.0005
0.00047
0.00045
0.00043
0.00041
0.0004
0.00039
0.00037
0.00036
0.00035
0.00034
0.00033
0.00034
0.00033
40
400
Tf
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
35
35
Qwetted
mv
3.55533E-07
5.2497E-06
7.66058E-06
9.63237E-06
1.20153E-05
1.4987E-05
1.71807E-05
1.88856E-05
2.02599E-05
2.13983E-05
2.23613E-05
2.31898E-05
2.39125E-05
2.455E-05
2.5118E-05
2.56282E-05
2.60898E-05
2.651E-05
2.68947E-05
2.72486E-05
2.75757E-05
3.24682E-05
3.26462E-05
100
mv/mi*100%
0.03366692
0.56680023
0.88844569
1.18927234
1.60905752
2.24392929
2.81789725
3.34571526
3.83699628
4.2984175
4.73484055
5.14993554
5.54655382
5.92696287
6.2930012
6.64618398
6.98777749
7.31885283
7.64032564
7.95298594
8.25752103
9.47639414
9.77588908
Analytical Result at Tsurf = 365.7 ° C and Tf = 40 ° C
constant heat flux
Tw
t
365.697
1.5
1.7
2
2.3
2.5
2.7
3
5
7
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.36083
0.33894
0.31249
0.2914
0.2795
0.26895
0.25515
0.19764
0.16703
0.13975
0.11411
0.09882
0.08839
0.08068
0.0747
0.06988
0.06588
0.0625
0.05959
0.05705
0.05481
0.05282
0.05103
0.04941
0.04793
0.04658
0.04534
0.04419
149813
Re
827.712
777.5
716.819
668.438
641.143
616.94
585.281
453.356
383.156
320.571
261.745
226.678
202.747
185.082
171.353
160.286
151.119
143.364
136.692
130.873
125.738
121.165
117.056
113.339
109.955
106.857
104.007
101.374
Qtotal
mi
0.00119
0.00111
0.00103
0.00096
0.00092
0.00088
0.00084
0.00065
0.00055
0.00046
0.00038
0.00033
0.00029
0.00027
0.00025
0.00023
0.00022
0.00021
0.0002
0.00019
0.00018
0.00017
0.00017
0.00016
0.00016
0.00015
0.00015
0.00015
41
400
Tf
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Qwetted
mv
5.36682E-06
7.45743E-06
9.9839E-06
1.19983E-05
1.31348E-05
1.41425E-05
1.54606E-05
2.09534E-05
2.38762E-05
2.6482E-05
2.89312E-05
3.03913E-05
3.13877E-05
3.21232E-05
3.26948E-05
3.31556E-05
3.35372E-05
3.38601E-05
3.41379E-05
3.43802E-05
3.4594E-05
3.47844E-05
3.49555E-05
3.51102E-05
3.52511E-05
3.53801E-05
3.54988E-05
3.56084E-05
100
mv/mi*100%
0.45220671
0.66894108
0.97138063
1.25186726
1.42878203
1.59875078
1.8423045
3.22339057
4.34598713
5.7613503
7.70879529
9.35056737
10.7969976
12.1046705
13.3071998
14.4264868
15.4777442
16.4720481
17.4177603
18.3213768
19.1880639
20.0220101
20.8266675
21.604921
22.3592109
23.0916234
23.8039583
24.4977815
Analytical Result at Tsurf = 365.7 ° C and Tf = 45 ° C
constant heat flux
Tw
t
365.697
2
3
5
6
7
8
9
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.31249
0.25515
0.19764
0.18042
0.16703
0.15625
0.14731
0.13975
0.11411
0.09882
0.08839
0.08068
0.0747
0.06988
0.06588
0.0625
0.05959
0.05705
0.05481
0.05282
0.05103
0.04941
0.04793
0.04658
0.04534
0.04419
149813
Re
716.819
585.281
453.356
413.856
383.156
358.41
337.912
320.571
261.745
226.678
202.747
185.082
171.353
160.286
151.119
143.364
136.692
130.873
125.738
121.165
117.056
113.339
109.955
106.857
104.007
101.374
Qtotal
mi
0.00103
0.00084
0.00065
0.00059
0.00055
0.00051
0.00048
0.00046
0.00038
0.00033
0.00029
0.00027
0.00025
0.00023
0.00022
0.00021
0.0002
0.00019
0.00018
0.00017
0.00017
0.00016
0.00016
0.00015
0.00015
0.00015
42
400
Tf
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
Qwetted
mv
1.41952E-06
8.52932E-06
1.566E-05
1.7795E-05
1.94544E-05
2.07919E-05
2.18998E-05
2.28371E-05
2.60167E-05
2.79121E-05
2.92056E-05
3.01605E-05
3.09025E-05
3.15007E-05
3.19962E-05
3.24154E-05
3.2776E-05
3.30905E-05
3.3368E-05
3.36153E-05
3.38373E-05
3.40382E-05
3.42211E-05
3.43886E-05
3.45426E-05
3.4685E-05
100
mv/mi*100%
0.13811173
1.01636393
2.40907103
2.99880096
3.5411136
4.04588589
4.5199784
4.96838624
6.93221787
8.58780451
10.0464056
11.3650818
12.5777298
13.7064349
14.766538
15.7692084
16.7228782
17.6340982
18.5080779
19.3490413
20.1604694
20.9452715
21.7059083
22.4444836
23.1628124
23.8624737
Analytical Result at Tsurf = 365.7 ° C and Tf = 50 ° C
constant heat flux
Tw
t
365.697
3
4
5
6
7
8
9
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.25515
0.22096
0.19764
0.18042
0.16703
0.15625
0.14731
0.13975
0.11411
0.09882
0.08839
0.08068
0.0747
0.06988
0.06588
0.0625
0.05959
0.05705
0.05481
0.05282
0.05103
0.04941
0.04793
0.04658
0.04534
0.04419
149813
Re
585.281
506.868
453.356
413.856
383.156
358.41
337.912
320.571
261.745
226.678
202.747
185.082
171.353
160.286
151.119
143.364
136.692
130.873
125.738
121.165
117.056
113.339
109.955
106.857
104.007
101.374
Qtotal
mi
0.00084
0.00073
0.00065
0.00059
0.00055
0.00051
0.00048
0.00046
0.00038
0.00033
0.00029
0.00027
0.00025
0.00023
0.00022
0.00021
0.0002
0.00019
0.00018
0.00017
0.00017
0.00016
0.00016
0.00015
0.00015
0.00015
43
400
Tf
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
Qwetted
mv
1.4804E-06
6.70872E-06
1.02767E-05
1.29105E-05
1.49575E-05
1.66075E-05
1.79742E-05
1.91304E-05
2.30527E-05
2.53909E-05
2.69866E-05
2.81644E-05
2.90799E-05
2.98178E-05
3.0429E-05
3.09461E-05
3.13909E-05
3.17789E-05
3.21213E-05
3.24263E-05
3.27002E-05
3.2948E-05
3.31737E-05
3.33802E-05
3.35703E-05
3.37459E-05
100
mv/mi*100%
0.17640577
0.92308954
1.58093115
2.17566543
2.72258003
3.23163574
3.70975131
4.16196427
6.14246063
7.8120963
9.28307485
10.6129411
11.8358794
12.9741625
14.0432614
15.0544404
16.0162028
16.9351553
17.8165515
18.6646511
19.4829649
20.2744266
21.0415181
21.7863608
22.5107852
23.2163837
Analytical Result at Tsurf = 365.7 ° C and Tf = 55 ° C
constant heat flux
Tw
t
365.697
4
5
6
7
8
9
10
11
12
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.22096
0.19764
0.18042
0.16703
0.15625
0.14731
0.13975
0.13325
0.12757
0.11411
0.09882
0.08839
0.08068
0.0747
0.06988
0.06588
0.0625
0.05959
0.05705
0.05481
0.05282
0.05103
0.04941
0.04793
0.04658
0.04534
0.04419
149813
Re
506.868
453.356
413.856
383.156
358.41
337.912
320.571
305.653
292.64
261.745
226.678
202.747
185.082
171.353
160.286
151.119
143.364
136.692
130.873
125.738
121.165
117.056
113.339
109.955
106.857
104.007
101.374
Qtotal
mi
0.00073
0.00065
0.00059
0.00055
0.00051
0.00048
0.00046
0.00044
0.00042
0.00038
0.00033
0.00029
0.00027
0.00025
0.00023
0.00022
0.00021
0.0002
0.00019
0.00018
0.00017
0.00017
0.00016
0.00016
0.00015
0.00015
0.00015
44
400
Tf
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
Qwetted
mv
5.46125E-07
4.80131E-06
7.94236E-06
1.03836E-05
1.23514E-05
1.39814E-05
1.53603E-05
1.65466E-05
1.75813E-05
2.0038E-05
2.28266E-05
2.47295E-05
2.61343E-05
2.7226E-05
2.8106E-05
2.8835E-05
2.94516E-05
2.99822E-05
3.04449E-05
3.08532E-05
3.12169E-05
3.15436E-05
3.18392E-05
3.21083E-05
3.23546E-05
3.25813E-05
3.27907E-05
100
mv/mi*100%
0.07514436
0.73861607
1.33844035
1.89003571
2.40344814
2.88565565
3.34173884
3.77553319
4.19001847
5.33918519
7.02311036
8.50667822
9.84792609
11.0813308
12.2293559
13.3076047
14.3274377
15.2974313
16.2242486
17.1131882
17.9685463
18.7938635
19.5920989
20.3657555
21.116973
21.8475973
22.5592347
Analytical Result at Tsurf = 440.0 ° C and Tf = 40 ° C
constant heat flux
Tw
t
440.013
0.6
0.7
0.8
0.9
1
1.3
1.5
1.7
2
2.5
3
3.5
4
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.39411
0.36487
0.34131
0.32179
0.30527
0.26774
0.24925
0.23413
0.21586
0.19307
0.17625
0.16318
0.15264
0.13652
0.09654
0.07882
0.06826
0.06105
0.05574
0.0516
0.04827
0.04551
0.04317
0.04116
0.03941
0.03786
0.03649
0.03525
0.03413
0.03311
0.03218
0.03132
0.03053
149813
Re
904.035
836.973
782.917
738.141
700.262
614.171
571.762
537.077
495.16
442.885
404.297
374.306
350.131
313.167
221.442
180.807
156.583
140.052
127.85
118.366
110.721
104.389
99.032
94.4233
90.4035
86.8568
83.6973
80.8593
78.2917
75.9541
73.8141
71.8454
70.0262
Qtotal
mi
0.0013
0.0012
0.00112
0.00106
0.001
0.00088
0.00082
0.00077
0.00071
0.00064
0.00058
0.00054
0.0005
0.00045
0.00032
0.00026
0.00022
0.0002
0.00018
0.00017
0.00016
0.00015
0.00014
0.00014
0.00013
0.00012
0.00012
0.00012
0.00011
0.00011
0.00011
0.0001
0.0001
45
400
Tf
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Qwetted
mv
2.18907E-06
4.98121E-06
7.23189E-06
9.09616E-06
1.06733E-05
1.42578E-05
1.60235E-05
1.74676E-05
1.92128E-05
2.13894E-05
2.2996E-05
2.42447E-05
2.52512E-05
2.67903E-05
3.06093E-05
3.23012E-05
3.33097E-05
3.3998E-05
3.45061E-05
3.49009E-05
3.52192E-05
3.54829E-05
3.57059E-05
3.58978E-05
3.60652E-05
3.62128E-05
3.63444E-05
3.64625E-05
3.65695E-05
3.66668E-05
3.67559E-05
3.68378E-05
3.69136E-05
100
mv/mi*100%
0.16887811
0.41507058
0.64422094
0.85944367
1.06300638
1.61905323
1.95452268
2.26827856
2.70610569
3.36826361
3.96690013
4.51740322
5.02979901
5.96623172
9.64031346
12.4595355
14.8362497
16.9301769
18.8232318
20.5640754
22.1844132
23.7062676
25.1456734
26.5147352
27.8228573
29.0775183
30.284782
31.4496456
32.5762856
33.6682347
34.7285129
35.7597257
36.76414
Analytical Analysis Result at Tsurf = 440.0 ° C and Tf = 45 ° C
constant heat flux
Tw
t
440.0129
1
1.3
1.5
1.7
2
2.3
2.5
3
3.5
4
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.305274
0.267743
0.249255
0.234134
0.215861
0.201291
0.193072
0.17625
0.163176
0.152637
0.136523
0.096536
0.078821
0.068261
0.061055
0.055735
0.051601
0.048268
0.045508
0.043172
0.041163
0.039411
0.037865
0.036487
0.03525
0.034131
0.033112
0.032179
0.03132
0.030527
149812.7
Re
700.2622
614.1705
571.7617
537.0766
495.1601
461.7392
442.8847
404.2965
374.3059
350.1311
313.1668
221.4423
180.8069
156.5834
140.0524
127.8498
118.3659
110.7212
104.3889
99.03202
94.42333
90.40345
86.85683
83.69734
80.85931
78.29169
75.95409
73.81411
71.84538
70.02622
Qtotal
mi
0.001004
0.000881
0.00082
0.00077
0.00071
0.000662
0.000635
0.00058
0.000537
0.000502
0.000449
0.000318
0.000259
0.000225
0.000201
0.000183
0.00017
0.000159
0.00015
0.000142
0.000135
0.00013
0.000125
0.00012
0.000116
0.000112
0.000109
0.000106
0.000103
0.0001
46
440
Tf
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
Qwetted
100
mv
mv/mi*100%
2.31446E-06 0.23050846
6.96779E-06 0.79123412
9.26003E-06 1.12952636
1.11348E-05 1.44592231
1.34004E-05 1.8874335
1.52069E-05 2.2968971
1.6226E-05
2.5551631
1.83117E-05 3.1588368
1.99327E-05 3.71397206
2.12394E-05 4.23067937
2.32373E-05 5.17499162
2.81951E-05 8.87998864
3.03915E-05 11.7229329
3.17008E-05 14.1196457
3.25943E-05 16.2311921
3.32539E-05 18.1401759
3.37665E-05 19.8956678
3.41797E-05 21.5296397
3.4522E-05 23.0642997
3.48115E-05 24.5158173
3.50606E-05 25.896399
3.52779E-05 27.2155281
3.54696E-05 28.4807464
3.56404E-05 29.6981685
3.57938E-05 30.8728338
3.59326E-05 32.0089538
3.60589E-05 33.110091
3.61746E-05 34.1792908
3.6281E-05 35.2191807
3.63793E-05 36.2320466
Analytical Analysis Result at Tsurf = 440.0 ° C and Tf = 50 ° C
constant heat flux
Tw
t
440.0129
1.5
1.7
2
2.3
2.5
2.7
3
3.5
4
4.5
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.249255
0.234134
0.215861
0.201291
0.193072
0.185784
0.17625
0.163176
0.152637
0.143907
0.136523
0.096536
0.078821
0.068261
0.061055
0.055735
0.051601
0.048268
0.045508
0.043172
0.041163
0.039411
0.037865
0.036487
0.03525
0.034131
0.033112
0.032179
0.03132
0.030527
149812.7
Re
571.7617
537.0766
495.1601
461.7392
442.8847
426.166
404.2965
374.3059
350.1311
330.1067
313.1668
221.4423
180.8069
156.5834
140.0524
127.8498
118.3659
110.7212
104.3889
99.03202
94.42333
90.40345
86.85683
83.69734
80.85931
78.29169
75.95409
73.81411
71.84538
70.02622
Qtotal
mi
0.00082
0.00077
0.00071
0.000662
0.000635
0.000611
0.00058
0.000537
0.000502
0.000473
0.000449
0.000318
0.000259
0.000225
0.000201
0.000183
0.00017
0.000159
0.00015
0.000142
0.000135
0.00013
0.000125
0.00012
0.000116
0.000112
0.000109
0.000106
0.000103
0.0001
47
400
Tf
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
Qwetted
100
mv
mv/mi*100%
2.3818E-06 0.29052848
4.6945E-06 0.60960932
7.48936E-06 1.05486709
9.71777E-06 1.46780533
1.09749E-05 1.72826293
1.20897E-05 1.97849445
1.35479E-05 2.3370593
1.55476E-05 2.89690535
1.71595E-05 3.41799734
1.84946E-05 3.90741764
1.96241E-05 4.37032286
2.574E-05
8.10675986
2.84495E-05 10.9738288
3.00646E-05 13.3908797
3.11669E-05 15.5203443
3.19805E-05 17.4455275
3.26129E-05 19.2159161
3.31226E-05 20.8637537
3.35448E-05 22.4114366
3.3902E-05 23.8752715
3.42093E-05 25.2675685
3.44773E-05 26.5978916
3.47138E-05 27.8738463
3.49245E-05 29.1015992
3.51137E-05 30.2862325
3.52849E-05 31.4319935
3.54408E-05 32.5424748
3.55834E-05 33.6207476
3.57147E-05 34.6694618
3.5836E-05 35.6909227
Analytical Analysis Result at Tsurf = 440.0 ° C and Tf = 60 ° C
constant heat flux
Tw
t
440.0129
2.5
2.7
3
3.3
3.5
4
4.5
5
5.5
6
6.5
7
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.193072
0.185784
0.17625
0.168048
0.163176
0.152637
0.143907
0.136523
0.130169
0.124627
0.119738
0.115383
0.096536
0.078821
0.068261
0.061055
0.055735
0.051601
0.048268
0.045508
0.043172
0.041163
0.039411
0.037865
0.036487
0.03525
0.034131
0.033112
0.032179
0.03132
0.030527
149812.7
Re
442.8847
426.166
404.2965
385.4816
374.3059
350.1311
330.1067
313.1668
298.5928
285.8808
274.6654
264.6742
221.4423
180.8069
156.5834
140.0524
127.8498
118.3659
110.7212
104.3889
99.03202
94.42333
90.40345
86.85683
83.69734
80.85931
78.29169
75.95409
73.81411
71.84538
70.02622
Qtotal
mi
0.000635
0.000611
0.00058
0.000553
0.000537
0.000502
0.000473
0.000449
0.000428
0.00041
0.000394
0.00038
0.000318
0.000259
0.000225
0.000201
0.000183
0.00017
0.000159
0.00015
0.000142
0.000135
0.00013
0.000125
0.00012
0.000116
0.000112
0.000109
0.000106
0.000103
0.0001
48
400
Tf
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
Qwetted
100
mv
mv/mi*100%
2.00885E-07 0.03163412
1.74875E-06 0.28618581
3.77349E-06 0.65094116
5.51543E-06 0.99787087
6.55011E-06 1.22045276
8.78829E-06 1.75054123
1.06422E-05 2.24841121
1.22106E-05 2.71930834
1.35599E-05 3.16719267
1.47368E-05 3.59514075
1.57751E-05 4.00559922
1.67001E-05 4.40055178
2.07027E-05 6.52025367
2.44648E-05 9.43682161
2.67075E-05 11.8956021
2.8238E-05 14.0618312
2.93677E-05 16.020252
3.02458E-05 17.8212058
3.09536E-05 19.4974928
3.15398E-05 21.0718959
3.20358E-05 22.5610034
3.24625E-05 23.977338
3.28346E-05 25.3306286
3.3163E-05 26.6286123
3.34555E-05 27.8775619
3.37183E-05 29.0826475
3.3956E-05 30.2481897
3.41724E-05 31.377843
3.43705E-05 32.4747319
3.45528E-05 33.5415518
3.47212E-05 34.5806479
Analytical Analysis Result at Tsurf = 440.0 ° C and Tf = 70 ° C
constant heat flux
Tw
t
440.0129
4
4.3
4.5
4.7
5
5.5
6
6.5
7
7.5
8
8.5
9
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.152637
0.147216
0.143907
0.140812
0.136523
0.130169
0.124627
0.119738
0.115383
0.11147
0.107931
0.104708
0.101758
0.096536
0.078821
0.068261
0.061055
0.055735
0.051601
0.048268
0.045508
0.043172
0.041163
0.039411
0.037865
0.036487
0.03525
0.034131
0.033112
0.032179
0.03132
0.030527
149812.7
Re
350.1311
337.6964
330.1067
323.0068
313.1668
298.5928
285.8808
274.6654
264.6742
255.6996
247.5801
240.1879
233.4207
221.4423
180.8069
156.5834
140.0524
127.8498
118.3659
110.7212
104.3889
99.03202
94.42333
90.40345
86.85683
83.69734
80.85931
78.29169
75.95409
73.81411
71.84538
70.02622
Qtotal
mi
0.000502
0.000484
0.000473
0.000463
0.000449
0.000428
0.00041
0.000394
0.00038
0.000367
0.000355
0.000344
0.000335
0.000318
0.000259
0.000225
0.000201
0.000183
0.00017
0.000159
0.00015
0.000142
0.000135
0.00013
0.000125
0.00012
0.000116
0.000112
0.000109
0.000106
0.000103
0.0001
49
400
Tf
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
Qwetted
100
mv
mv/mi*100%
1.22985E-07 0.02449748
1.60768E-06 0.33202494
2.51387E-06 0.53111402
3.3616E-06 0.72582591
4.53649E-06 1.01028386
6.27661E-06 1.46603661
7.79441E-06 1.90150288
9.13352E-06 2.31917226
1.03265E-05 2.72106334
1.1398E-05 3.10883969
1.23675E-05 3.48389162
1.32501E-05 3.84739516
1.40581E-05 4.20035561
1.54883E-05 4.8780041
2.03401E-05 7.84581021
2.32324E-05 10.3477865
2.52062E-05 12.5520719
2.66632E-05 14.5448982
2.77955E-05 16.3774911
2.87083E-05 18.083227
2.94644E-05 19.6852892
3.0104E-05 21.2005572
3.06543E-05 22.641774
3.11342E-05 24.0188392
3.15577E-05 25.3396258
3.19349E-05 26.610517
3.22738E-05 27.8367735
3.25804E-05 29.0227918
3.28595E-05 30.1722909
3.3115E-05 31.2884499
3.33501E-05 32.3740116
3.35673E-05 33.4313625
Analytical Analysis Result at Tsurf = 440.0 ° C and Tf = 80 ° C
constant heat flux
Tw
t
440.0129
6
6.3
6.5
6.7
7
7.3
7.5
7.7
8
8.5
9
10
11
12
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
qw
Vs
0.124627
0.121624
0.119738
0.117938
0.115383
0.112987
0.11147
0.110013
0.107931
0.104708
0.101758
0.096536
0.092043
0.088125
0.078821
0.068261
0.061055
0.055735
0.051601
0.048268
0.045508
0.043172
0.041163
0.039411
0.037865
0.036487
0.03525
0.034131
0.033112
0.032179
0.03132
0.030527
149812.7
Re
285.8808
278.9911
274.6654
270.5349
264.6742
259.1786
255.6996
252.357
247.5801
240.1879
233.4207
221.4423
211.137
202.1483
180.8069
156.5834
140.0524
127.8498
118.3659
110.7212
104.3889
99.03202
94.42333
90.40345
86.85683
83.69734
80.85931
78.29169
75.95409
73.81411
71.84538
70.02622
Qtotal
mi
0.00041
0.0004
0.000394
0.000388
0.00038
0.000372
0.000367
0.000362
0.000355
0.000344
0.000335
0.000318
0.000303
0.00029
0.000259
0.000225
0.000201
0.000183
0.00017
0.000159
0.00015
0.000142
0.000135
0.00013
0.000125
0.00012
0.000116
0.000112
0.000109
0.000106
0.000103
0.0001
50
400
Tf
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
Qwetted
100
mv
mv/mi*100%
6.03767E-07 0.14729331
1.61776E-06 0.40440938
2.25439E-06 0.57243151
2.8623E-06 0.73788797
3.72484E-06 0.98150926
4.53364E-06 1.21996367
5.04567E-06 1.37621987
5.53762E-06 1.53040619
6.24066E-06 1.75797853
7.32859E-06 2.12798228
8.32455E-06 2.48725441
1.00875E-05 3.1770207
1.16041E-05 3.83307801
1.29271E-05 4.45993288
1.6068E-05 6.19789749
1.9633E-05 8.74461444
2.2066E-05 10.9883171
2.38619E-05 13.0167794
2.52577E-05 14.8821429
2.63828E-05 16.618381
2.73147E-05 18.2490915
2.81031E-05 19.7914558
2.87814E-05 21.2584445
2.9373E-05 22.6601346
2.9895E-05 24.0045397
3.036E-05
25.2981571
3.07777E-05 26.5463416
3.11556E-05 27.7535685
3.14996E-05 28.9236231
3.18146E-05 30.0597413
3.21043E-05 31.1647153
3.2372E-05 32.2409738
Appendix C – Temperature Measurements
Table of Temperature Measurements at Test Surface
t [s]
10
20
30
40
50
60
70
80
85
Tsurf (° C)
32.4
42.7
67
99.1
114
180
230
330
442
Tsurf 2 (° C) Tsurface-ideal (° C)
27
27.43457095
43.2
39.717978
57
57.50109157
75.2
83.24632065
122
120.51858
180
174.4789199
246
252.5991719
338
365.6965648
480
440.0128502
Plot of Temperature Measurements
51
Appendix D – Summary of Experimental Results
Summary of Experimental Results and Corresponding Predicted Values
Tw
Predicted 252.559
Exp
t
7
15
20
252.559 7
mv
mv/mi*100% Error%
9.73188E-06 0.304121142
7.33642E-06 0.1930636
5.36619E-06 0.109514046
0.0000076
0.2375
21.9061
52
ΔTsub
5.6
5.1
4.2
5.6