Forced Convective Heat Transfer to Supercritical Water
in Micro-Rocket Cooling Passages
by
Adriane Faust
Bachelor of Science in Aeronautics and Astronautics
Massachusetts Institute of Technology, 1998
Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the
degree of
Master of Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2000
© Massachusetts Institute of Technology, 2000. All Rights Reserved.
Au th o r ..................................................................................................
Department of Aeronautics and Astronautics
January 18, 2000
.........................................
C ertified by ...
Professor Jack L. Kerrebrock
Professor of Aeronautics and Astronautics
Thesis Supervisor
....................
Professor Nesbitt W. Hagood
Associate Professor of Aeronautics and Astronautics
Chair, Departmental Graduate Office
INSTITUTE
Accepte d by .........................................................
MASSACHUSETTS
OFTECHNOLOGY
SEP 0 7 2000
LIBRARIES
2
Forced Convective Heat Transfer to Supercritical Water in MicroRocket Cooling Passages
by
Adriane Faust
Submitted to the Department of Aeronautics and Astronautics in
February, 2000 in partial fulfillment of the requirements for the
degree of Master of Science in Aeronautics and Astronautics
Abstract
An investigation of heat transfer to supercritical fluids in micro-channels was completed to
assess the cooling characteristics of the MIT micro-rocket engine. Previous results from
supercritical ethanol heat transfer tests were compared to water tests to establish a baseline
for future fuel testing. Existing literature on supercritical heat transfer was also consulted
to corroborate the water test results. It was found that the characteristics of the water tests
matched those observed in the literature, as well as those of ethanol tests run at similar
conditions.
Thesis Supervisor: Jack L. Kerrebrock
Title: Professor of Aeronautics and Astronautics
4
Table of Contents
LIST OF FIGURES .......................................................................................................
7
LIST OF TA BLES.......................................................................................................
9
CH A PTER 1: IN TRO D U CTIO N ......................................................................................
1.1 Background ..................................................................................................................
1.2 M otivation ....................................................................................................................
1.3 Objective......................................................................................................................12
1.4 Supercritical Fluid Properties....................................................................................
11
11
12
13
CHAPTER 2: EXPERIMENTAL APPARATUS...........................................................17
2.1 TestRig........................................................................................................................17
2.2 Test Section ..................................................................................................................
18
2.3 Therm ocouples.............................................................................................................20
2.4 Therm ocouple Calibration........................................................................................
20
2.5 Experim ental Procedure...........................................................................................
24
2.5.1 Test Rig Operation...........................................................................................
24
2.5.2 Labview file......................................................................................................
25
CHA PTER 3: D A TA RED U CTION .............................................................................
3.1 Pow er............................................................................................................................27
3.2 W all Temperature....................................................................................................
3.3 Bulk Temperature......................................................................................................
3.4 H eat Transfer Coefficient........................................................................................
3.5 Stanton N um ber......................................................................................................
3.6 Losses...........................................................................................................................32
27
27
30
31
31
CHA PTER 4: RESU LTS AN D D ISCU SSION .............................................................
4.1 Results of Water Tests.............................................................................................
4.1.1 W all and Bulk Tem perature.............................................................................
4.1.2 H eat Transfer Coefficient...............................................................................
4.1.3 Stanton number...............................................................................................
4.1.4 Com parison with Literature.............................................................................
4.2 Results of Low Pressure Ethanol Tests....................................................................
4.2.1 W all and Bulk Tem perature.............................................................................
4.2.2 H eat Transfer Coefficient...............................................................................
4.2.3 Stanton N umber...............................................................................................
4.3 Results of High Pressure Ethanol Tests....................................................................
4.3.1 W all and Bulk Tem perature.............................................................................
4.3.2 H eat Transfer Coefficient...............................................................................
4.3.3 Stanton N umber...............................................................................................
34
34
34
42
45
49
53
53
59
62
65
66
71
74
CH A PTER 5: CON CLU SION S....................................................................................
5.1 Summary ............................ .......................................................
77
77
5.2 F uture W ork .................................................................................................................
78
APPENDIX A: DATA REDUCTION PROGRAMS.........................................................79
APPENDIX B: TEMPERATURE PLOTS FOR CALIBRATION TESTS...................97
RE FERE N C ES ................................................................................................................
6
101
List of Figures
13
P-V plot for a typical fluid...............................................................................................
Thermodynamic properties of water for 300 bar (Pr = 1.36)...........................................14
Thermodynamic properties of ethanol at 100 bar (Pr = 1.6).............................................15
15
Thermodynamic properties of ethanol at 300 bar (Pr = 4.8)...........................................
17
S chem atic of test rig ...........................................................................................................
Test sectio n .........................................................................................................................
19
Detail of heated length of test section.............................................................................
20
Voltage as a function of Temperature for K-type thermocouples..................................21
Calibration test 11 for water. The change in slope indicates the film boiling at the saturation
temperature (222 C).................................................................................................
23
Test section tube heating conditions...............................................................................
28
Thermal conductivity of 304 stainless steel as a function of temperature.......................29
Temperature plots for water at Pr=1.32, mass flow=141 mg/s........................................36
Temperature plots for water at Pr=1.2, mass flow=397 mg/s.........................................37
Temperature plots for water at Pr= 1.3, mass flow= 100 mg/s.........................................38
Temperature plots for water at Pr= 1.45, mass flow= 149 mg/s........................................39
Temperature plots for water at Pr= 1.4, mass flow= 180 mg/s.........................................40
Temperature plots for water at Pr= 1.3, mass flow=623 mg/s.........................................41
Heat transfer coefficient for water at Pr= 1.32, mass flow= 141 mg/s.............................42
Heat transfer coefficient for water at Pr=1.2, mass flow=397mg/s.................................43
Heat transfer coefficient for water at Pr= 1.3, mass flow= 100 mg/s................................43
Heat transfer coefficient for water at Pr=1.45,mass flow= 149mg/s................................44
Heat transfer coefficient for water at Pr=1.4,mass flow= 180mg/s..................................44
Heat transfer coefficient for water at Pr=1.32,mass flow=623mg/s................................45
Stanton number for water at Pr=1.32, mass flow=141 mg/s...........................................46
Stanton number for water at Pr= 1.2, mass flow=397 mg/s.............................................46
Stanton number for water at Pr= 1.3, mass flow= 100 mg/s.............................................47
Stanton number for water at Pr= 1.45, mass flow= 149 mg/s...........................................47
Stanton number for water at Pr= 1.4, mass flow= 180 mg/s.............................................48
Stanton number for water at Pr=1.32, mass flow=623 mg/s...........................................48
Heat transfer coefficient vs. film temperature for water at Pr = 1.32,
mass flow = 14 1 mg/s...............................................................................................
50
Heat transfer coefficient vs. film temperature for water at Pr = 1.3, mass flow = 100 mg/s.51
Temperature plots for ethanol at Pr = 1.64, mass flow = 63 mg/s....................................54
Temperature plots for ethanol at Pr = 1.67, mass flow = 60 mg/s....................................55
Temperature plots for ethanol at Pr = 1.66, mass flow = 32 mg/s....................................56
Temperature plots for ethanol at Pr = 1.65, mass flow = 76 mg/s....................................57
Temperature plots for ethanol at Pr = 1.65, mass flow = 57 mg/s....................................58
Heat transfer coefficient for ethanol at Pr = 1.64, mass flow = 63 mg/s..........................59
Heat transfer coefficient for ethanol at Pr = 1.67, mass flow = 60 mg/s..........................60
Heat transfer coefficient for ethanol at Pr = 1.66, mass flow = 32 mg/s..........................60
Heat transfer coefficient for ethanol at Pr = 1.65, mass flow = 76 mg/s..........................61
Heat transfer coefficient for ethanol at Pr = 1.65, mass flow = 57 mg/s..........................61
Stanton number for ethanol at Pr = 1.64, mass flow = 63 mg/s........................................62
Stanton number for ethanol at Pr = 1.67, mass flow = 60 mg/s........................................63
7
Stanton number for ethanol at Pr = 1.66, mass flow = 32 mg/s........................................63
Stanton number for ethanol at Pr = 1.65, mass flow = 76 mg/s........................................64
Stanton number for ethanol at Pr = 1.65, mass flow = 57 mg/s........................................64
Specific heat of ethanol at supercritical pressures..........................................................66
Temperature plots for ethanol at Pr = 4.86, mass flow = 102 mg/s.................................67
Temperature plots for ethanol at Pr = 4.86, mass flow = 121 mg/s.................................68
Temperature plots for ethanol at Pr = 4.85, mass flow = 71 mg/s....................................69
Temperature plots for ethanol at Pr = 4.89, mass flow = 255 mg/s..................................70
Heat transfer coefficient for ethanol at Pr = 4.86, mass flow = 102 mg/s........................72
Heat transfer coefficient for ethanol at Pr = 4.86, mass flow = 121 mg/s........................72
Heat transfer coefficient for ethanol at Pr = 4.85, mass flow = 71 mg/s..........................73
Heat transfer coefficient for ethanol at Pr = 4.89, mass flow = 255 mg/s........................73
Stanton number for ethanol at Pr = 4.86, mass flow = 102 mg/s......................................74
Stanton number for ethanol at Pr = 4.86, mass flow = 121 mg/s......................................75
Stanton number for ethanol at Pr = 4.85, mass flow = 71 mg/s........................................75
Stanton number for ethanol at Pr = 4.89, mass flow = 255 mg/s......................................76
Calibration test at 20 bar, saturation T = 212 C...............................................................97
Calibration test at 23 bar, saturation T = 220 C...............................................................98
Calibration test at 24 bar, saturation T = 222 C...............................................................99
Calibration test at 24 bar, saturation T = 222 C.................................................................100
8
List of Tables
Critical Conditions.............................................................................................................13
M anual shut-off valve positions...................................................................................
9
24
10
Chapter 1
Introduction
1.1 Background
Microfabrication techniques used to manufacture silicon microprocessors are now being
applied to microelectrical and mechanical systems (MEMS). MEMS technology is capable of manufacturing many wafers of planar geometry simultaneously. These wafers are
then combined to form 3-D devices. The Massachusetts Institute of Technology Gas Turbine Lab (MIT GTL) has applied this technology to propulsion systems such as the MIT
micro-gas turbine and the MIT micro-rocket. MIT is currently testing a bi-propellant
regeneratively cooled p-rocket engine. The current g-rocket is a nozzle, combustion
chamber, and fuel and cooling passages etched onto a silicon chip approximately 8 mm by
12 mm and weighing 2 g. It is designed to produce 15 N of thrust.
There are several advantages to applying MEMS technology to a rocket engine. They
can be manufactured in large quantities in a short period of time at low cost, and the
strength of silicon lends itself to large thrust to weight ratios. The g-rocket will ultimately
consist of a nozzle, pumps, and valves packaged on the same chip. This will eliminate the
need for integration of engine components. Multiple engine packages can be added to a
space vehicle to increase the total thrust.
Since the combustion chamber walls are made from silicon, the surface temperature is
limited to approximately 1000 K. The chamber pressure will be approximately 125 atm
and the heat flux at the walls is expected to reach values as high as 200 W/mm 2. Heat
transfer is therefore a critical issue in the design of the k-rocket. Heat transfer experiments
were necessary to collect data on the behavior of fluids in micro-channels at conditions
above the critical point. Ethanol experiments were completed by Jacob Lopata in Septem-
11
ber, 1998.1 Ethanol is one of the possible fuels being considered for the g-rocket, and was
chosen because it is relatively safe to test in the MIT GTL facilities.
1.2 Motivation
Because the wall temperature of the chamber and nozzle must be kept relatively low,
heat transfer in the wall cooling passages is a primary concern in the design of the grocket. In addition, the high heat fluxes and high pressures mean that the coolant will be at
supercritical conditions. Research on heat transfer to supercritical fluids flowing in circular tubes exists, however, the heat fluxes used in these experiments are small compared to
what the coolant will see in the g-rocket, and the tube dimensions are several orders of
magnitude larger than the ji-rocket cooling passages. Furthermore, the ethanol tests were
originally run because no prior research on heat transfer to supercritical ethanol was available. The ethanol data were checked against an empirical correlation for supercritical
helium. 2 Data and empirical correlations do exist for supercritical water, however. It was
decided that water should be tested in the [t-rocket heat transfer test rig because the results
could be compared to previous water heat transfer research.
1.3 Objective
The objective of this research was to establish a baseline for the ethanol heat transfer
tests by running heat transfer tests on supercritical water and applying a single data reduction scheme to both fluids. Heat transfer data on supercritical water flowing through circular tubes is available, so the results of the water tests can be compared to results from
previous research. The water tests also establish a benchmark for future heat transfer tests
of other possible coolants: JP-7, hydrogen peroxide (H2 02), hydrazine (N2 H4 ), and nitrogen tetroxide (N2 0 4 ).
12
1.4 Supercritical Fluid Properties
The coolant in the g-rocket will be at supercritical pressures and temperatures because
of the high chamber pressures envisioned for the devices. When a fluid is above critical
conditions, there is no phase transition between liquid and vapor. The critical point is the
pressure and temperature at which a phase change will no longer take place, as shown in
figure 1.1. The critical conditions for water and ethanol are listed in table 1.1.
Fluid
Pressure (bar)
Temperature (C)
Water
220.9
374.14
Ethanol
62.55
242.85
Table 1.1: Critical Conditions
P
I Tc
supercritical
critical point
----------------
Pc
vapor
liquid & vapor
Figure 1.1: P-V plot for a typical fluid 3
13
Supercritical fluids are characterized by rapid changes in the fluid properties, as figure 1.2
shows. The temperature at which the sharp peak in specific heat (CP) occurs is called the
pseudocritical temperature. A fluid at the pseudocritical temperature demonstrates remarkable cooling properties due to the C, maximum and resulting increase in the heat transfer
coefficient. In addition, the low viscosity, g, results in an increase in turbulence, and therefore the cooling abilities, of the fluid. Small changes in temperature translate to large variations in the fluid properties and instabilities in the fluid flow. These discontinuities
become less drastic as the pressure of the fluid is increased. The C, maximum decreases as
pressure increases, which leads to a deterioration in the heat transfer coefficient. Figures
1.3 and 1.4 show the fluid properties of ethanol at pressures of 100 bar and 300 bar to
compare the magnitude of the property variations.
H20 Property Data for 300 bar
400
Temperature (C)
800
Figure 1.2: Thermodynamic properties of water for 300 bar (Pr = 1.36)
14
C2H 60 Property Data for 100 bar
Cp/1 0 (kJ/kg-C)
- - mu*1000 (kg/m-s)
k (W/m-C)
-
i (MJ/kg)
2
1.5
--
-----
0.5
01
0
100
50
150
300
250
200
Temperature (C)
350
400
450
500
Figure 1.3: Thermodynamic properties of ethanol at 100 bar (Pr = 1.6)
C2 H6 0 Property Data for 250-300 bar
2.5
iL
-
L
Cp/1 0 (kJ/kg-C) at 250 bar
mu*1000 (kg/m-s)
k (W/m-C)
i (MJ/kg)
2
1.5
--
1
------------
0.5
-- -- ----
0
50
100
150
200
300
250
Temperature (C)
350
400
450
500
Figure 1.4: Thermodynamic properties of ethanol at 300 bar (Pr = 4.8)
15
The ethanol heat transfer tests were run at pressures of approximately 100 and 300 bar,
or reduced pressures (Pr = P/Pc) of 1.60 and 4.80. The high pressure ethanol data show a
gradual drop in wall temperature at the pseudocritical point, while the low pressure ethanol tests show a sharp drop in wall temperature at the pseudocritical point. The water tests
were run at approximately 300 bar, a reduced pressure of 1.36. The conditions were chosen to match those of the low pressure ethanol tests in order to corroborate the ethanol test
results. These water tests showed a similar drop in the wall temperature to the low pressure
ethanol tests, as well as instabilities in the temperature readings corresponding to the
observations in the literature. The high pressure ethanol tests could not be duplicated with
water since the test rig was not rated for pressures above 6000 psi (414 bar).
16
Chapter 2
Experimental Apparatus
2.1 Test Rig
The test rig located in GTL was designed to measure the outside surface temperature
of the test section tube while varying heat flux and keeping the pressure and mass flow
constant. From the fluid pressure, outside surface temperature, and heat flux into the tube,
the inside wall temperature, bulk fluid temperature, and heat transfer coefficient were
determined. A schematic of the test rig is pictured below.
Control Room: Test Cell
I
sight
I
I
4I
II
I
\.
I
test section
0v
#3
#1
orifice
Tr
w
A
B
manual shut-off valve
vent to atmosphere
solenoid valve
He line
fuel line
Figure 2.1: Schematic of test rig 4
17
heated
waste fuel
The rig occupies two rooms, the g-rocket test cell, and the control room. Instruments
and measurements were represented graphically in Labview on a computer in the control
room so that flow conditions could be altered remotely. The test rig is located in the test
cell and no human intervention is required while a test is running. The fuel tank cylinder
was filled with fuel via the sight glass downstream of the cylinder. Fuel was injected using
a plastic syringe with a 2 ptm filter attached to remove particles from the fluid. The fuel
tank was then pressurized using a 6000 psi helium tank located inside the control room.
This pressure was measured with a pressure transducer located at the top of the fuel tank
and displayed as line pressure on the Labview console. Solenoid valve #1, called the line
flow solenoid, must be opened to begin the flow of fuel through the rig.
Mass flow was controlled by either an orifice located downstream of the test section,
or by a valve located immediately upstream of the orifice. The valve was added to the rig
so that fuel could be vented if the orifice clogged. Mass flow was measured using a MicroMotion, Inc. high pressure, low flow meter. Prior to running the ethanol tests and the water
tests, the mass flow meter was calibrated by measuring the amount of fluid that ran
through the test rig for a set amount of time and comparing that volume to the volume calculated using the average mass flow reading from the meter.
Test section heat flux was applied using resistive heating. Copper leads from a
Hewlett-Packard 1000 W constant voltage DC power supply were attached to the test sec-
tion on either side of the test section tube. The power supply is located in the control room
so that the voltage may be increased remotely. This voltage reading was saved by Labview.
The current running through the test section must also be known to find the power going
into the tube. This was measured using the voltage drop across a metal shunt of known
resistance. Because the test section was heated resistively, an electric insulator was
required along the flow path. A block of G1O fiberglass was installed downstream of the
18
test section. The G10 is pressed between two steel plates to keep it from delaminating at
high pressure.
2.2 Test Section
The test sections were manufactured by MicroGroup, Inc. Each test section consisted
of a 10 mm long 300 pm outer diameter, 95 gm inner diameter 304 stainless steel tube.
This thin tube was silver soldered into a larger 1/16 inch outer diameter tube so that 3 mm
on either side of the test section were inside the larger tube and the center 4 mm length
was exposed. This center length was heated by current introduced by the copper leads on
either side. The 3 mm inlet length allowed the hydrodynamic profile to develop before
heating began.
copper leads
from power supply
0,
0
0
.4-
Figure 2.2: Test section
19
K-type thermocouples
tream
midpoint
downstream
3 mr
/\
1/16"
0
<
0
n->f
1~1.--
46
4mm
heated length
300 gm OD
95 gm ID
Figure 2.3: Detail of heated length of test section
2.3 Thermocouples
The outside surface temperature of the test section was measured and reported in Labview. Three 2 mil diameter K-type thermocouples were spot welded under a microscope
along the 4 mm test section at upstream, midpoint, and downstream positions. Another
thermocouple in the fuel tank cylinder read the fuel temperature inside the tank, which
was assumed to be the inlet fluid temperature.
2.4 Thermocouple Calibration
The non-zero size of the thermocouple spot weld to the outer surface of the test section
led to the thermocouple reading being corrupted by the electric field due to the resistive
heating. This voltage drop across the bead caused the temperature to appear different than
the actual temperature by an amount proportional to the heating current. This error could
be corrected by applying a calibration to each thermocouple.
Figure 2.4 shows the relationship between thermocouple voltage and temperature for
K-type thermocouples.
20
Thermoelectric Voltages for Chromel-Alumel Thermocouples with 0 C Reference Junction
60
50-
40-
E
0)030-
0
0
10-
0
200
400
600
800
Temperature (C)
1000
1200
1400
Figure 2.4: Voltage as a function of Temperature for K-type thermocouples 5
The first step in the calibration was to determine the constant of proportionality. This
constant was a function of the quality, or surface area, of the bead weld. The constant was
multiplied by the power supply voltage to get the actual mV drop across the thermocouple.
This mV drop was then applied to the plot in figure 2.4 to get the corresponding temperature loss in degrees C. This temperature loss was added to the surface temperature
recorded by Labview to get the actual temperature of the test section.
The calibration constant is unique to each thermocouple and must be found by running
a calibration test. In previous work, the constant was found by placing a small voltage on
the order of about 0.001 V across the test section. It was assumed that such a small voltage
did not actually raise the temperature of the tube, and any temperature change recorded
21
was purely the result of a voltage drop across the bead. The ratio of temperature drop to
voltage was used to determine the thermocouple mV reading from the relation in figure
2.4 and therefore, the constant in mV/V.
It was discovered, however, that this method did not correct the thermocouple readings
enough. Upon running several water heat transfer tests at sub critical pressures, it was
observed that the change in slope of the inside wall temperature curve indicating the
change from liquid to vapor did not correspond to the saturation temperature for the given
pressure. The calibration constant was then iterated until the film boiling point occurred at
the saturation temperature. This was determined to be a more accurate calibration method,
so a sub critical pressure calibration test was run before each critical test for a new test
section. It was assumed that the physical characteristics of the weld did not change during
a test, and the calibration constants therefore remained constant throughout the life of a
particular test section. This appeared to be a good assumption until the last water test,
which saw much higher heat fluxes than previous runs. It was observed that the midpoint
thermocouple on the last test section required a larger correction after the first supercritical
test was run. The test section eventually failed at the midpoint because of the high thermal
stresses, and it is assumed that the deformation at the midpoint was responsible for the
change in the thermocouple weld. Previous heat transfer studies have used this same calibration method to correct for thermocouple voltage drop on a resistively heated test section tube. 6 Figure 2.5 is an example of temperature readings from a calibration test. The
film boiling point is readily apparent.
The ethanol test temperatures had to be re-calibrated according to this method without
the existence of calibration tests. This was done by noting that the drop in wall temperature in the supercritical tests corresponded to the pseudocritical temperature, and the calibration constants were adjusted accordingly.
22
11 Temperature upstream vs. Heat Flux 24.03 bar 62. mg/s
300
0
0
250
Outside Surface T emp
Inside Wall Temp
Bulk Fluid Temp
---------------------Saturation Temp
02000
T 150D
2?100-
000 :P~0 00011000
0
[: 000
ooo
PO0
00
E
EP-
99
50
00
00
O~EC
0
-~~--0--~~0
0
0XXwX0
00XOW
0
'00
5
15
10
000 0X('
000
25
20
Heat Flux (W/mm2
11 Temperature midpoint vs. Heat Flux 23.42 bar 62. mg/s
300
0
Outside Surface Temp
Inside Wall Temp
O Bulk Fluid Temp
- - - Saturation Temp
--
o
250
O
o
E
--
0
000
_
~~
OE
0
-
a)
CL
00
o3
b---o---
2 200
C 150
O00000OO
.O0
p0
eq 0
100
50
0
5
0
10
15
Heat Flux (W/mm2
20
25
11 Temperature downstream vs. Heat Flux 22.91 bar 62. mg/s
300
-0
0
Outside Surface Temp
Inside Wall Temp
O Bulk Fluid Temp
- - - Saturation Temp
o
250
oC00
-
~{
o
o
000000000
-
0 ]-a
o
00
Coo
-ff
~~
rn-
- -
200
C 150
a)
00
E
0
a100
99
00
50
0
0)
E
1
5
10
15
Heat Flux (W/mm2)
20
25
Figure 2.5: Calibration test 11 for water. The change in slope indicates the film boiling at
the saturation temperature (222 C).
23
2.5 Experimental Procedure
2.5.1 Test Rig Operation
The following procedure was used to operate the test rig:
The manual shut-off valves should be in the following positions prior to running a test.
The valves are labeled to correspond with figure 2.1.
Position
Valve
A
CLOSED
B
CLOSED
C
CLOSED
D
CLOSED
E
SLIGHTLY OPEN
F
CLOSED
G
CLOSED
H
OPEN IF ORIFICE IS
BLOCKED
Table 2.1: Manual shut-off valve positions
Activate the instruments in the control room by turning the chassis power and the pressure
transducer power supply on. Activate the main power button in the Labview console, then
press the button on the chassis to illuminate the Main Power indicator light. Verify that the
three test section thermocouples are reading room temperature. To fill the fuel tank cylinder, activate solenoid #2 via the Labview console in the control room. On the test rig, open
valve D. Fill the sight glass with fuel using the syringe with the 2g filter. When full, close
valve D, and de-activate solenoid #2. To begin the flow of fuel through the rig, power solenoid #1. To pressurize the system, open the helium tank, and turn the pressure regulator
until the desired pressure (in psi) appears on the Labview console. Turn on the power sup-
24
ply, and begin to slowly increase the voltage, stopping approximately every 1 W/mm 2 to
allow the temperatures to come to equilibrium. Once the data are recorded, shut off the
power supply, and close the pressure regulator on the helium bottle. To vent the line, open
valve A. Power solenoids 1, 2, and 3 to vent all remaining fuel and helium.
2.5.2 Labview file
All measurements taken during a test were displayed graphically in the Labview console. These measurements were line pressure, test section pressure drop, tank temperature,
power supply voltage, current, heat flux, mass flow, and temperature at upstream, midpoint, and downstream positions along the test section. The console also indicated whether
or not main power, and the solenoid valves are on or off. Previously, for the ethanol tests,
each of these measurements was recorded by hand after increasing the heat flux. There
was only one value for mass flow and line pressure recorded for these tests. The Labview
code was modified during the water testing. A save button was added so that measurements could be written to an output file with the date and time when the button was
pushed. After temperature oscillations were observed around the critical point, the code
was further modified to save every time the measurements were re-calculated in Labview
at a frequency of 1 Hz.
25
26
Chapter 3
Data Reduction
The data reduction process was a lengthy one since the heat transfer coefficient must
be determined through only a few measured quantities. Voltage, current, outside surface
temperature, and tank fluid temperature were measured directly. From these, test section
power flux, inside wall temperature, bulk temperature, and heat transfer coefficient were
determined.
3.1 Power
The power into the test section, Q, is a function of the voltage drop across the tube and
the current flowing through the tube:
(3.1)
Q = IV.
It was assumed that the copper block leads on either side of the test section were in good
electrical contact and caused no voltage loss. Previous research assumed losses and calculated the power using a formula for the resistance of the stainless steel as a function of
temperature, however, it was observed that this resistance model broke down at high heat
flux.
3.2 Wall Temperature
A formula for the inside wall temperature of the tube as a function of the outside surface temperature was derived. It was assumed that the electric field in the tube and therefore, the current flowing through the tube were constant. A diagram of the heating
conditions is shown in figure 3.1.
27
V = const.
Q
E
ro= 300gm
I = const.
ri =95 Rm
-.
.
.
.
.
. ---.
.
- . --
--
--
-CL
Figure 3.1: Test section tube heating conditions
The change in temperature across the tube is equal to the energy dissipated in the tube.
The energy balance equation is
rk
sdr
E rdr,
r
(3.2)
where r is the radius from the center line, ks is the thermal conductivity of 304 stainless
steel, T is the temperature of the metal, a is the charge density in the tube, E is the electric
field in the tube, and ro and ri are the outside and inside surface radii. This energy balance
was integrated to get the tube temperature as a function of the radius. The thermal conductivity of steel increases with temperature, so a relation for ks as a function of T was necessary to complete the integration. Figure 3.2 shows this relation.
28
Thermal Conductivity of 304 Stainless Steel
30
0
100
200
300
400
600
500
T (C)
700
800
900
1000
Figure 3.2: Thermal conductivity of 304 stainless steel as a function of temperature. 7
A best fit line was fit to the data points to get the following formula for ks.
ks = 0.0152T + 14.2444
(3.3)
where T is in degrees C and ks is in W/mK. Equation 3.2 becomes
dT
r (0.0152T + 14.2444)
dr
=
P
GE 2rdr.
(3.4)
E and (Twere assumed to be constant in this model, so the integral could be reduced and
the variables separated to get the following:
29
2
(0.0152 T + 14.2444)dT =
2
-E- - r dr.
2
r
(3.5)
This can be integrated to get
0.0152
2
YE _2
2
T + 14.2444T =
r
r- -
E roIn
2
+ C.
(3.6)
C is a constant of integration which can be found using boundary conditions. By setting T
=To at r = ro, and T = Ti and r = ri, where ro is the outside surface of the tube and ri is the
inside wall. The final equation for Ti becomes
T. = -937.13 + 65.79V202.90 + 0.0304X
(3.7)
where
ro
-
X
log -
2l
ri
1
+ 0.0076 T
2
+ 14.2444 To.
(3.8)
r0)
Q is the power into the test section in Watts, 1is the length of the heated tube in meters, To
is the surface temperature in degrees Celsius, ro is the outside surface radius in meters, and
ri is the inside wall radius in meters. This formula was used to calculate the inside wall
temperature in degrees C.
3.3 Bulk Temperature
The bulk temperature was calculated by equating the enthalpy difference between the
tube inlet and outlet to the power per mass flow:
30
Qx
where
= H - H .,
(3.9)
Q is the power in W, x is the fractional distance along the tube length, rh is the
mass flow in kg/s, and Ho and Hi are the outlet and inlet enthalpies in J/kg respectively.
This formula was used to find the outlet enthalpy, which was then used to find the temperature at that point, or bulk temperature. The inlet enthalpy was known because the inlet
temperature, or fuel tank temperature, and the pressure were known. The enthalpy was
read from a fluid property table which lists enthalpy as a function of T and P.8 Once the
outlet enthalpy was calculated, the bulk temperature was read from the same enthalpy
table.
The average of the wall and the bulk temperatures is the film temperature:
T
f
2
b.
(3.10)
3.4 Heat Transfer Coefficient
The heat transfer coefficient was simple to calculate once the inside wall temperature
and bulk temperature were known. Heat transfer coefficient is given by
h =
Ai(Tw-Tb)'
,
(3.11)
where Q is the power into the tube in W, Ai is the inside surface area of the tube in mI2 , TW
is the inside wall temperature (Ti from equation 3.7), and Tb is the bulk temperature.
3.5 Stanton Number
Previous research displayed end results in non-dimensional quantities of Reynolds
number, Re, and Nusselt number, Nu. It was decided that data would be reduced to heat
transfer coefficient and Stanton number to eliminate uncertainties property tables of viscosity and thermal conductivity introduce. Many property tables do not include data in the
31
supercritical regime, and a linear extrapolation may not be accurate. The Stanton number
(St) requires enthalpy table values, however, the enthalpy tables were already necessary in
the calculation of bulk temperature. The following defines St:
St =
A puC (TT - Tb)
(3.12)
where Q is the power in W, A is the inside surface area of the tube in m2, p is the fluid
density in kg/m 3 , u is the fluid velocity in m/s, Tw is the temperature of the fluid at the
inside wall, and Tb is the bulk temperature in degrees C. pu can be found by using
rt = puAe,
(3.13)
where Ae is the tube inlet/outlet area in m2 . (HW-Hb) can be substituted for Cp(Tw-Tb)The equation used for Stanton number is then
St =
(3.14)
Ai M(Hw - Hb)
e
St is a ratio of the amount heat transferred through the walls to the thermal capacity of the
fluid. In these experiments, rn /Ae was held constant, so variation in St was a function of
heat flux and the difference between the wall and bulk temperatures.
3.6 Losses
Potential heat losses include heat flux from radiation and free convection. Radiative
heat loss was previously determined to be approximately 20 kW/m 2 assuming a generous
outside surface temperature of 1000 K. 9 This equates to a test section tube loss of 0.075
W, which is small compared to the actual heat flux, which reaches 380 W. The forced convective heat loss was previously determined to be negligible as well.1 0 Assuming again, an
outside surface temperature of 1000 K and a bulk temperature of 288 K, the convective
32
heat loss would be approximately 0.067 W. Buoyancy effects in the fluid flow are also
negligible for these experimental conditions.1 1 Although buoyancy effects increase with
heat flux, and the heat flux is high, they are also proportional to the tube dimensions.
33
Chapter 4
Results and Discussion
The data reduction algorithms discussed in chapter 3 were applied to both the water
tests as well as the ethanol data measured previously by Lopata.
4.1 Results of Water Tests
A total of six heat transfer tests of water at supercritical conditions were completed.
The pressure for all water tests was kept constant at approximately 300 bar, a reduced
pressure of 1.36, to correspond to the low pressure ethanol tests run at a reduced pressure
of 1.60. The mass flow was varied between 100 mg/s and 623 mg/s. This pressure was
close enough to the critical point that the fluid properties varied severely over small
changes in temperature, as illustrated in figure 1.2. The water test results were therefore
characterized by regions of instabilities caused by the rapid changes in properties. The
tests are labeled 10, 12, 14, 16, 17, and 18. Tests 1 though 8 were preliminary subcritical
calibration tests of the rig, and are therefore not presented here. Tests 9, 11, 13, and 15
were calibration tests of the four test sections used. It should be noted that the upstream
thermocouple in tests 9 and 10 did not work. This was attributed to a poor quality weld.
4.1.1 Wall and Bulk Temperature
The temperature plots show the characteristics of supercritical heat transfer clearly.
The graphs presented in figures 4.1 through 4.6 are plots of the measured outside wall
temperature and the calculated inside wall and bulk temperatures. The bulk temperature
never reaches the pseudocritical temperature or the critical temperature in any test, water
or ethanol. Despite attempts to achieve a critical bulk temperature by increasing the mass
flow and allowing higher heat fluxes, the test section failed due to thermal stress before
reaching this point. In most cases, there is an obvious change in the slope of the wall tem-
34
perature curves around the pseudocritical point. Most tests also show some oscillation and
drift in the wall temperature as well. This oscillation was noticed during tests 10 and 12,
which show some unsteadiness, after the wall temperature reached the critical point. To
get a better representation of this phenomenon, several points were sampled at each heat
flux during test 14. Some instability is apparent around the critical point, where the data
points begin to spread out. The data acquisition program was then altered to record a data
point every time the program ran a calculation cycle at a frequency of 1 Hz. Tests 16
through 18 therefore consist of far more data points than the first 3 tests, and instabilities
are readily apparent, especially in test 16. The rapid increase in the midpoint wall temperature in test 18 is not fluid property related, however. It is believed that this is an anomalous temperature reading caused by a malfunctioning thermocouple. It was observed that
the test section tube shape warped significantly due to the large thermal stresses when this
temperature jump occurred. The midpoint thermocouple was attached at this failure point
and was most likely affected by the changing geometry of the tube.
It is also important to note that some of the water tests experienced a significant pressure drop across the test section. The pseudocritical temperature changes with pressure, so
the pressure drop had to be factored into the data reduction. Tests 12 and 18 had particularly large test section pressure drops accompanied by mass flow rates several times higher
than other tests, both of which were caused by leaks in the G1O block downstream of the
test section. The pressure drop for test 12 remained fairly constant between 55 bar and 65
bar until the test section began to fail around 130 W/mm 2 , at which point the pressure drop
increased rapidly to 140 bar. The epoxy fittings in the G10 block had cracked, and the G10
block was replaced. This G10 block began to leak as well following test 16 due this time
to delamination, but the pressure drop peaked at only 17 bar around 100 W/mm 2 for tests
16 and 17. An attempt was then made to run at a pressure higher than 300 bar for test 18,
35
and this caused the G1O to delaminate substantially, resulting in a mass flow of 623 mg/s,
which increased to more than 800 mg/s after 260 W/mm 2 . The test section pressure drop
for test 18 began at 138 bar and dropped down to 80 bar until the test section began to fail
at 260 W/mm2
10 Temperature midpoint vs. Heat Flux P=1.328 141 mg/s
2
1
1
1
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
0
1.5 -
0
0o
020
00
0
1
I-
-
-
-
-
-
-L
--
-
-9-
00
-
-
00
--
-
0
--
-
-
-
--
0
0
0
----
-
-
40---
-
2
-
0
0. 500K
00
0
0
20
40
qc
60
80
100
Heat Flux (W/mm2)
10 Temperature downstream vs. Heat Flux P=1.319
120
140
141 mg/s
3
o Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
2.5
O
0
2
0
0
00
I--1.5
- -
-
-
-
-
-
-
0
0
0
- 0 -
-0
-
--
-
- -
-
-
-
-
-
----------------
-________O___
0.5
K
9@CK3~~KK
0
0
20
qc
40
0
000>
KKK
0>
60
80
Heat Flux (W/mm2)
0
K
100
120
Figure 4.1: Temperature plots for water at Pr=1.32, mass flow=141 mg/s
36
140
12 Temperature upstream vs. Heat Flux P=1.309
397 mg/s
2
O
o
-
1.5
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
90
0
0
1
I-
00
------------
---
------------------
-----------
0
M
0
K>
moox)
M W(1
MC
0
50
0
2
Heat Flux (W/mm )
K0 K>
3C 0 0>K C>
150
100
qc
12 Temperature midpoint vs. Heat Flux Pr=1.213
397 mg/s
2.E
O
o
-0
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
8o
0
I0
~
0
<(59,
gc
0
>
0
C>
<>@
e>K
0.
50
0
Heat Flux (W/mm
2
150
100
qc
12 Temperature downstream vs. Heat Flux Pr=1.130 397 mg/s
2r
o
Outside Surface Temp
O
o Inside Wall Temp
O> Bulk Fluid Temp
C)
1
I-
~~~------------------
80
8
O
0
0
O
0
0
0
-----------------CoJ E
-------- ---- 9-----------C
-
0. 50o
0
100
50
Heat Flux (W/mm2
qc
Figure 4.2: Temperature plots for water at Pr=1.2, mass flow=397 mg/s
37
150
14 Temperature upstream vs. Heat Flux Pr=1.300 100mg/s
2.5
I
0
0
O
2 -
I
-
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
1.5-
di
C.)
0
I-
e
0.5-
0
0
0
I
10
20
30
40
50
60
qc
Heat Flux (W/mm2
14 Temperature midpoint vs. Heat Flux Pr=1. 2 9 9
70
80
90
80
90
80
90
100 mg/s
2.5
0
0
2
0
1.5
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
I-,
00
0
1z
H-
0.50
0
0
10
I
20
30
40
50
60
70
qc
Heat Flux (W/mm2)
14 Temperature downstream vs. Heat Flux P=1.298 100 mg/s
3
0
2.5-
0
0
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
2-0
.5OO0
o1
0.50
IN
0
0
10
20
qc
I
30
40
50
60
70
Heat Flux (W/mm2)
Figure 4.3: Temperature plots for water at Pr=1.3, mass flow=100 mg/s
38
149 mg/s
16 Temperature upstream vs. Heat Flux Pr=1.451
1.6
-
I
i
t
I
I
1.41.2I
ko
~
~
k
0.8 -
00
Q 0
0.6-
aQ
O Outside Surface Temp
o Inside Wall Temp
O Bulk Fluid Temp
0.40.200
20
100
120
100
60
80
2
Heat Flux (W/mm
16 Temperature downstream vs. Heat Flux P=1.443 149 mg/s
120
60
80
Heat Flux (W/mm2
16 Temperature midpoint vs. Heat Flux P=1.448
qc
2
I
1.5
40
149 mg/s
O Outside Surface Temp
o Inside Wall Temp
O Bulk Fluid Temp
1.
-- No a
0 0o
0
0
0.5
2.5
0
Outside Surface Temp
0 Inside Wall Temp
-
Bulk Fluid Temp
1
C.)
I::
I-
0.5
0
20
40
60
2
Heat Flux (W/mm )
80
100
Figure 4.4: Temperature plots for water at Pr=1.45, mass flow=149 mg/s
39
120
17 Temperature upstream vs. Heat Flux P=1.410
1.
II
Q
o Outside Surface Temp
o Inside Wall Temp
1. 2
O
1
180 mg/s
4r
O
Bulk Fluid Temp
----- -- --
--
V
--
--
0
O
------ 0----------------------- -----
0. 83-
1
0.4
-- --
0
0.2l
0
20
40
60
80
Oc Heat FluxI (W/mm2
III
17 Temperature midpoint vs. Heat Flux Pr=1.403
0II
O Outside Surface Temp
o Inside Wall Temp
- Bulk Fluid T emp
1
-
C ---
0
20
0
20
0
0
0 0 0------
g~P
0.5
4
120
180 mg/s
(9 9
------------------------
0
100
LA - - -
- -
I
09
40
60
80
100
qc
Heat Flux (W/mm2)
17 Temperature downstream vs. Heat Flux Pr=1.394 180 mg/s
40
qc
60
Heat Flux (W/mm2)
80
100
Figure 4.5: Temperature plots for water at Pr=1.4, mass flow=180 mg/s
40
120
120
18 Temperature upstream vs. Heat Flux Pr=1.410 623 mg/s
2.5
O0 Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
-
2
1.5-
0.5 k
9
60
C13nCPE
V
491POP"
em<1 xf
0
18A
~g f
connQ3
ow0
o 0 < 0 <D
250
200
150 qc
Heat Flux (W/mm2
18 Temperature midpoint vs. Heat Flux Pr=1.322 623 mg/s
50
100
3
t::U
1
0
0
O
2. 5
300
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
350
i
O
2 -~1.5-
0.
5
-
6:9DI0EE
V EM
0oo
0
50
0
5
5
2.
250
150
qc
200
(W/mm2
Flux
Heat
18 Temperature downstream vs. Heat Flux P=1.200 623 mg/s
100
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
300
350
0
20
5-
1:~.
-9
500
0.
5-
0
~c
0,Dip__
50
_____
___I
eIww
100
qc
200
150
Heat Flux (W/mm2
250
300
Figure 4.6: Temperature plots for water at Pr=1.3, mass flow=623 mg/s
41
350
4.1.2 Heat Transfer Coefficient
At a reduced pressure of 1.36, the heat transfer coefficient is expected to peak at the
pseudocritical temperature, marking the C, peak maximum shown in figure 1.2. There is a
noticeable peak in the heat transfer coefficient plot for test 12, but for the most part, the
curves are more well-behaved than expected. This pattern was observed in the literature on
supercritical water heat transfer.
10 Heat Transfer Coefficient vs. Heat Flux P=11.328 141 mg/s
x 105
114
-
o midpoint
O downstream
12
10
2
-C
al 8
0
0
0
6
-0
CU
00
4
0
0
A^
00
0
2
0
880
000
6
20
40
60
80
Heat Flux (W/mm2
100
120
140
Figure 4.7: Heat transfer coefficient for water at Pr=1.32, mass flow=141 mg/s
42
12 Heat Transfer Coefficient vs. Heat Flux Pr=1.213 397 mg/s
x 10s
12
I
I
o upstream
o
midpoint
downstream
O
10-
8
0
6-0
0
C
0
0
100
50
150
2
Heat Flux (W/mm )
Figure 4.8: Heat transfer coefficient for water at Pr=1.2, mass flow=397mg/s
14 Heat Transfer Coefficient vs. Heat Flux Pr=1.299 100mg/s
105
3. x
o upstream
* midpoint
-
3
0
C
C
downstream
2.5
0
-
2
8E
1.5
0
o0
0
3ocJ0
C
40
0
Ii
-0.5dt
-1
0
10
20
30
40
50
2
Heat Flux (W/mm )
60
70
80
90
mass flow= 100 mg/s
Figure 4.9: Heat transfer coefficient for water at Pr= 1 .3,
43
16 Heat Transfer Coefficient vs. Heat Flux Pr=1.448 149 mg/s
x 10
aD
0
0
0
20
40
60
Heat Flux (W/mm2)
80
100
120
Figure 4.10: Heat transfer coefficient for water at Pr=1.45,mass flow=149mg/s
x 103
17 Heat Transfer Coefficient vs. Heat Flux P=1.403 180 mg/s
73.
.2
0 2.
a)
T 1.
120
Heat Flux (W/mm 2)
Figure 4.11: Heat transfer coefficient for water at Pr=1.4,mass flow=180mg/s
44
18 Heat Transfer Coefficient vs. Heat Flux P=1.322 623 mg/s
106
1.4 -
0
1.20
0
000
oE
a>
~1
0
.
_
g
0
0.6(
0.4
~al
0.4
o upstream
o
.
0
50
100
200
150
2
Heat Flux (W/mm )
midpoint
downstream
250
300
350
Figure 4.12: Heat transfer coefficient for water at Pr=1.32,mass flow=623mg/s
4.1.3 Stanton number
The data were reduced to the Stanton number because a non-dimensional quantity can
be used for direct comparison with any other fluid. Stanton number is proportional to
((heat transferred) / (thermal capacity of the fluid) }. In these experiments, the heat transfer
is the dependent variable and the mass velocity, pu, is held constant, therefore the variations in the plots of St are a function of C, and the temperature difference (Tw-Tb) according to equation 3.12. As the fluid temperature approaches the pseudocritical point, the C,
rises sharply, which would result in a decrease in St. However, because the heat transfer
around this temperature is enhanced, the wall temperature drops sharply, reducing the (TwTb) term. This results in an overall increase in the St curve. Figures 4.13 through 4.18 are
plots of St for the water tests. When compared to the temperature plots in figures 4.1
through 4.6, the St plots all show an increase at the heat flux corresponding to the wall
temperature drop. Tests 14 and 17 are particularly clear examples.
45
10 St vs. Heat Flux Pr=1.328
x 10-3
18
0
0
141 mg/s
midpoint
downstream
0
16
14
12
10
0
8
0
6
0
4
0
0
2
0
0
-
0
0
000
ElO0
C'
0
20
40
60
80
Heat Flux (W/mm 2)
100
120
140
Figure 4.13: Stanton number for water at Pr=1.32, mass flow= 141 mg/s
12 St vs. Heat Flux Pr=1.213 397 mg/s
x 10-3
4.5
o upstream
0
midpoint
-0 downstream
4
3.5
-0
3
2.5
-
-0
2
(OD 00
0
0
0
1.5
0
1
OcO
0.5
0
0
50
100
150
Heat Flux (W/mm2
Figure 4.14: Stanton number for water at Pr=1.2, mass flow=397 mg/s
46
14 St vs. Heat Flux Pr=1.299
x 10-3
100 mg/s
o upstream
0
midpoint
O downstream
C
o
4
0
8
3
0
0
0
08
0
0
Qi
A
0o
13
-0
0
10
20
30
40
50
2
Heat Flux (W/mm )
60
70
80
90
Figure 4.15: Stanton number for water at Pr=1.3, mass flow=100 mg/s
16 St vs. Heat Flux Pr=1.448 149 mg/s
x 10-3
8
o
o
0
7
upstream
midpoint
downstream
6
1 10
5
~
0
00
0
0O0
0n
0
0
3
p I
-
00
0
O.
2
80e
-0
0
O
VV
1i
0
0
40
O
20
40
60
Heat Flux (W/mm2
80
100
120
Figure 4.16: Stanton number for water at Pr=1.45, mass flow=149 mg/s
47
17 St vs. Heat Flux Pr=1.403 180 mg/s
x10_3
0
20
40
60
Heat Flux (W/mm2
80
100
120
Figure 4.17: Stanton number for water at Pr=1.4, mass flow=180 mg/s
x 10.3
18 St vs. Heat Flux Pr=1.
32 2
623 mg/s
350
Heat Flux (W/mm 2)
Figure 4.18: Stanton number for water at Pr=1.32, mass flow=623 mg/s
48
4.1.4 Comparison with Literature
Previously conducted water heat transfer research was reviewed to compare to the
water tests. Establishing a baseline was difficult, however, due to several differences
between the test rigs described in the literature and the g-rocket test rig, as well as differences in the test conditions.
Several articles on heat transfer to supercritical water flowing in circular tubes were
used for comparison. 12, 13, 14 Each experimental test apparatus described differed from the
g-rocket test rig in several ways. First, several rigs described used vertical tubes instead of
horizontal tubes. 15 , 16, 17, 18 The test section tube dimensions were substantially larger; on
the order of 10 mm diameter and 1 to 2 m in length. More importantly, in each case, the
fluid was heated to near critical temperatures prior to entering the test section, making the
heat fluxes much lower (-0.1 - 2 W/mm 2 ) than the ji-rocket test conditions (-1 - 350 W/
mm 2 ). 19 , 20, 21,
22, 23, 24
The inlet temperature was regulated while the heat flux, pressure,
and mass flow rate were held constant. In the case of the g-rocket test rig, the heat flux is
the independent variable and the inlet temperature was kept constant.
Several papers discussed a heat transfer deterioration phenomenon, which occurred at
high heat fluxes. 25 , 26,27 High heat flux, in their case was approximately 0.5 - 1 W/mm2 ,
which is far exceeded in the p-rocket tests. It is therefore expected that a deterioration in
the heat transfer coefficient can be observed in the water tests.
Deterioration of the heat transfer coefficient is a phenomenon governed by the heat
flux only. Swenson, et al. noticed that the heat transfer coefficient peaked when the film
temperature reached the pseudocritical temperature, however, increasing the pressure of
the fluid lowered the peak, and increasing the heat flux from 0.788 W/mm 2 to 1.74 W/
mm 2 lowered the peak heat transfer coefficient from 45,400 W/m 2 K by a factor of 2 to
22,700 W/m 2 K. The tests for which the film temperature reached the pseudocritical tem-
49
perature (-400 C for water at 300 bar), tests 10 and 14, are shown in figures 4.19 and 4.20.
The heat transfer coefficient does have a maximum at approximately 400 C, however, it is
not a sharp peak discontinuity, like the C, curve. Koshizuka, et al. and Tanaka, et al. offer
an explanation for the mechanism of heat transfer coefficient deterioration. As the heat
flux increases, the difference between the wall temperature and the bulk temperature
increases. The fluid in the g-rocket test sections is heated from room temperature, so the
bulk temperature is much lower than the wall temperature, which reaches a gas-like state
almost immediately upon entering the heated tube length. The increasing temperature drop
across the gas-like wall fluid causes the heat transfer coefficient to decrease. It was
observed in the literature that the heat transfer coefficient will increase, resulting in
enhanced cooling capabilities as the bulk temperature exceeds the pseudocritical temperature. This never occurred in the g-rocket experiments.
10 Heat Transfer Coefficient vs.
X10s
Pr=1.319 141 mg/s
x
Ix
x
x
X
x
xx
2
x
x
xx
- .5
1.
-
xX
16
X
xX
x
X
0
a
Cl
I-
X
X
0.5-
0
100
200
300
Downstream Tf (C)
400
500
600
Figure 4.19: Heat transfer coefficient vs. film temperature for water at Pr = 1.32, mass
flow = 141 mg/s
50
Pr=1 .298 100 mg/s
14 Heat Transfer Coefficient vs.
X 10s
2.
I
2x
X
X
X
x
X
a)
0
X
oX
a
01.5 -
X
tX
xCl
X
:X
XX
X X
0
XX
X
0
100
200
XX
,X
300
Downstream Tf (C)
XXX X
I
II
400
500
Figure 4.20: Heat transfer coefficient vs. film temperature for water at Pr
600
=1.3,
mass flow
= 100 mg/s
Yamagata et al. wrote that the deterioration occurred when a particular heat flux, called
the critical heat flux, qc, was exceeded. The authors developed a relationship for the critical heat flux is a function of the mass velocity, G:
qc = 0.20G 1.2
(4.1)
The critical heat flux is labeled on the plots of temperature in figures 4.1 through 4.6. This
relationship was developed using data from vertical tube experiments with bulk temperatures that reached the critical point, so this correlation might not be accurate for this situation. It is worth noting, however, that for both tests 10 and 14, the critical heat flux was
surpassed, meaning the deterioration in the heat transfer peak was expected.
Rapid fluctuations in wall temperature were observed during several of the water tests
while the heat flux was held constant. The effect is most prominently shown in figure 4.4,
51
the 1.45 reduced pressure, 149 mg/s mass flow test. At constant heat flux, the temperature
plot shows a drift-like pattern around the critical point. This phenomenon was also
observed in the literature at high heat flux. 28 Temperature oscillations were recorded in
vertical tube supercritical water heat transfer experiments for heat fluxes above the critical
heat flux. The oscillations are the result of the mixing of the gas-like wall layer and the
cold bulk temperature within the viscous layer at the walls. The high wall temperatures
cause the viscosity of the water to drop, the turbulence to decrease, and the heat transfer
coefficient to break down. This further raises the wall temperature and increases the thickness of the boundary layer. The larger boundary layer then begins to mix with the cooler
bulk temperature, and the heat transfer coefficient in the boundary layer increases, lowering the temperature. This shrinks the thickness of the wall layer, creating a cycle for temperature oscillation at the wall. The effect becomes more pronounced as the bulk
temperature reaches the pseudocritical temperature where the heat transfer is enhanced.
The thermal entrance region is also of concern. The literature states that the thermal
entrance region length is extended significantly for near-critical or supercritical fluids. 29
This means that the thermal profile may still be developing through most of the measured
test section tube length. The 3mm long section was placed in front to avoid entrance
region effects due to a developing velocity profile, but the heating begins at the inlet of the
measured 4mm long section. One experiment observed that the thermal entrance region
effects progressed as far as 1/3 of the length of the test section. 30 This figure may be larger
for the g-rocket experiments, however. One article indicates that the entrance region also
increases significantly if the bulk temperature is lower than the wall temperature and the
critical temperature. This was the case for all p-rocket tests. The thermal entrance region
is characterized by a drop in the heat transfer coefficient, which rises again once the flow
has developed. 3 1 It is therefore expected that the downstream heat transfer coefficient
52
curves and Stanton number curves should be lower than the midpoint and upstream curves
if the thermal entrance region extends that far into the tube. This does not occur in the
water tests. The upstream heat transfer coefficient is greater than that at the midpoint and
downstream positions. It can therefore be concluded that the entrance region stays within
the first segment of heated length upstream of the first thermocouple.
4.2 Results of Low Pressure Ethanol Tests
The reduced pressure for the low pressure ethanol tests (1.6) corresponds approximately to the reduced pressure for the water tests. It is expected that the ethanol tests
should show similar heat transfer coefficient increases at the pseudocritical temperature.
4.2.1 Wall and Bulk Temperature
The temperature plots of the low pressure ethanol tests show a dramatic decrease in the
wall temperature at the pseudocritical temperature, about 270 C at this pressure. This is
caused by the sharp increase in the C, curve, shown in figure 1.3. A trend in the curve that
resembles film boiling is visible in the downstream temperature plots. As the temperature
approaches the C, maximum, the heat transfer coefficient begins to rise at an increasing
rate with the C, curve, creating a steady drop in the rise of the wall temperature until the
peak is reached.
Unlike the water temperature plots, the ethanol data show no sign of temperature drift
or oscillation. The previous research on the ethanol tests reported some pressure oscillations, but the temperature readings remained steady. 32 The critical heat flux is not displayed on either set of ethanol plots because it is not useful to know where oscillations
may begin.
53
1010 Temperature upstream vs. Heat Flux P=1.642 63 mg/s
2
o Outside Surface Temp
o Inside Wall Temp
0
00
-O Bulk Fluid Temp
1.5
0
0 0
OoD 0
I-
00
0
0
0
--------------------------------
1
0
0
0
0.5
0
5
10
15
20
Heat Flux (W/mm2)
1010 Temperature midpoint vs. Heat Flux P=1.642 63 mg/s
0
25
2.5
0
0
2
-
0
00
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
0
0
0
0
0 0
O:
1.5
-
00
0
-
I-
1
0
-3
0 0
9 0
0
0.5
0
5
0
10
15
20
Heat Flux (W/mm2)
1010 Temperature downstream vs. Heat Flux Pr=1.642 63 mg/s
25
1.5
0
0
0
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
00
0
0
0
0
O
0
O
0
0
-----------------------------f-----------------------------
8
0j
0
0
0
0
C-
o o
8
0.5
c>K 8>K
0
0
5
0
0
>K
>K
>K
>K
10
15
Heat Flux (W/mm2)
0
>K
>
0
>>KK
20
Figure 4.21: Temperature plots for ethanol at Pr = 1.64, mass flow = 63 mg/s
54
25
1021 Temperature midpoint vs. Heat Flux P=1.675 60 mg/s
3
0 Outside Surface Temp
-01 Inside Wall Temp
K Bulk Fluid Temp
2.5
2
0
-0
IZ 1.5
1
-
-
0.5
0
2
1.5
0
:
O
8
0
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
0
O
O
00
-8
-8
0
e
H
0
-- - -
C- -- --O'
- - - - - - - - - - - -- -- -- -- - --
1
0.5
0
2
20
18
16
14
12
10
Heat Flux (W/mm 2)
1021 Temperature downstream vs. Heat Flux Pr=1.675 60 mg/s
6
4
2
-
4
0
-
6
8
12
10
Heat Flux (W/mm2)
14
16
18
Figure 4.22: Temperature plots for ethanol at Pr = 1.67, mass flow = 60 mg/s
55
20
66 4
3010 Temperature upstream vs. Heat Flux Pr=1.
32 mg/s
2. 5
0
Outside Surface Temp
o Inside Wall Temp
2 -
0
Bulk Fluid Temp
00
00
1.
0
00 0
5
H
0
0
0
0
-------------------------------
000
--------------
0
0
00
------------------
0.
0
3010 Temperature midpoint vs. Heat Flux
P=1.664 32 mg/s
2. 5
0 Outside Surface Temp
13 Inside Wall Temp
2 -
O
0
01:
Bulk Fluid Temp
0
1.
H
-
0
0
-
5-
51
1
1
0.
0
5
15
20
25
Heat Flux (W/mm2)
3010 Temperature downstream vs. Heat Flux P=1.664 32 mg/s
-H
0
1.6
1.4
0
10
0
-
0.6
-
0.4
-
0.2
0
00
0 0
0O
00
O 0
0
0
0
9
0 0
0
0
8
10.8
30
8r
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
1.2
H
10
0
0
0
0
-
-0--
9
00
5
0
10
I
15
Heat Flux (W/mm2
I
20
25
Figure 4.23: Temperature plots for ethanol at Pr = 1.66, mass flow = 32 mg/s
56
30
4010 Temperature upstream vs. Heat Flux Pr=1.653 76 mg/s
2
ri
Outside Surface Temp
Inside Wall Temp
O Bulk Fluid Temp
0
0
1.5
0
0
1
--
-
-----------
0c-
Oo
0.5 [-
99
0'
0
5
00000000O0
0T0--------------
0
0
00
0
000
0
0000
0
0
I!-3
-I
20
25
Heat Flux (W/mm2)
4010 Temperature midpoint vs. Heat Flux P=1.653
10
15
|
1
2
76 mg/s
1
1
1
I
40
35
30
0
Outside Surface Temp
O Inside Wall Temp
O Bulk Fluid Temp
1.5
0
0
0 0
0
0
0
El0
0
0
1
0
S00
00
0.5
0
10
5
25
20
15
40
35
30
Heat Flux (W/mm2 )
4010 Temperature downstream vs. Heat Flux
P=1.653
76 mg/s
2
0
Outside Surface Temp0
c
Inside Wall Temp
O
Bulk Fluid Temp
1.5
0
H
0
e 00 00
[]
3
] :]0
0
0
l
0
1
I
I
0 0
O
I 00000 000 I
0
0
0
0000000
I
0.5
-
0
0
5
10
15
25
20
Heat Flux (W/mm2)
30
35
Figure 4.24: Temperature plots for ethanol at Pr = 1.65, mass flow = 76 mg/s
57
40
5010 Temperature upstream vs. Heat Flux Pr=1.653
2
0
1.5
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
57 mg/s
1
r
O
0
O
E]
0 000
00
OO
0
I-
O
I
0 0 0
0000
---- []- In- El- Q- -0 - -0 -13
o
Oo
98
0.5f
K>~K>K>K> K>K>K>K> K>K>
~K>K>
0I
)
5
10
15
20
25
Heat Flux (W/mm2)
5010 Temperature midpoint vs. Heat Flux P=1.653 57 mg/s
2
30
35
r1
o
o
O
1.5
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
0
0 0 0
0
S
0000
000
Oo 0o
I-
K>
0
0
0
00
3
00
0
O o
0o
1
0
9
0.5
0
5
0
10
15
20
25
30
Heat Flux (W/mm2
5010 Temperature downstream vs. Heat Flux P=1.653 57 mg/s
35
2
0
0
1.5
Outside Surface Temp
Inside Wall Temp
BulkFluidTemp
0
O
0
0 00
oOO0
0
0
-9
000 00
00
0
11
0
0
0
1
0.5
00
00
0 0
0
A
-
0>KKK>>>
0
0
5
10
15
20
25
30
Heat Flux (W/mm2)
Figure 4.25: Temperature plots for ethanol at Pr = 1.65, mass flow = 57 mg/s
58
35
4.2.2 Heat Transfer Coefficient
As expected, the heat transfer coefficient shows a sharp increase corresponding to the
point where the wall temperature dropped. The heat transfer plots also indicate the presence of the thermal entrance region as the heat flux increases. The literature indicated that
heat flux did not have a large effect on the thermal entrance region length, however, the
heat fluxes reached here are considerably larger than those in the literature.3 3 The heat
transfer coefficient downstream drops below the upstream measurement slowly over a
range of more than 10 W/mm 2 , so the dependence of thermal entry length on the heat flux
may not have been noticed over the test conditions in previous experiments.
x 10o
1010 Heat Transfer Coefficient vs. Heat Flux Pr=1.642 63 mg/s
~3S2.5-
2 -
71.5 -
0
0.50
5
15
10
Heat Flux (W/mm2)
20
25
Figure 4.26: Heat transfer coefficient for ethanol at Pr = 1.64, mass flow = 63 mg/s
59
1021 Heat Transfer Coefficient vs. Heat Flux Pr=1.675 60 mg/s
x 104
2I
o midpoint
O downstream
11
1
10
9
C
8
A)
7
0
0-
0
-0
6
5
0
1
0~
-0
4
3
0
I
1
2
4
6
8
0
|
10
12
Heat Flux (W/mm2)
14
16
18
20
Figure 4.27: Heat transfer coefficient for ethanol at Pr = 1.67, mass flow = 60 mg/s
3010 Heat Transfer Coefficient vs. Heat Flux P=1.664 32 mg/s
x 10
7
o
o
0
upstream
midpoint
downstream
O O
6
-5
4
0
I-2
000
0
1
-O
88
0
0
8
5
0
10
0
0
0
OO
0
0
00
15
Heat Flux (W/mm2
20
25
30
Figure 4.28: Heat transfer coefficient for ethanol at Pr = 1.66, mass flow = 32 mg/s
60
76 mg/s
4010 Heat Transfer Coefficient vs. Heat Flux P=1.653
r
1
X 105
o
upstream
-
downstream
O midpoint
2
0
c
0
LI
1.8 F
0-
2'1.6
0
01
0
Li
1.4 -
0
0
0
o
0
Q
a 1.2 -
000
0 0
0
0
: 0.8
0.6 -
00
03
00
ElO
00
0.4-
0.2'0
15
10
5
20
Heat Flux (W/mm2
35
30
25
40
Figure 4.29: Heat transfer coefficient for ethanol at Pr = 1.65, mass flow = 76 mg/s
5010 Heat Transfer Coefficient vs. Heat Flux P=1.653 57 mg/s
10
0
upstream
L
midpoint
O downstream
2
00
0
00
00
c.
0O
0
0
0
0
0
08
0
0.
-
01.
0
00 0oo
0 0 0
5
10
8
0oo
8 80
0-
88
15
20
Heat Flux (W/mm2)
25
30
35
Figure 4.30: Heat transfer coefficient for ethanol at Pr = 1.65, mass flow = 57 mg/s
61
4.2.3 Stanton Number
The behavior of the Stanton number is governed by the difference between the bulk
and the wall temperatures, and therefore shows an increase around the pseudocritical temperature as the wall temperature drops. In addition, the Stanton number plots show the
development of a thermal entrance region at the upstream and midpoint positions indicated by the decrease in the Stanton number below the downstream position.
1010 St vs. Heat Flux Pr=1.642 63 mg/s
x 10-3
o upstream
0 midpoint
-0 downstream
10
8
5
6
4
00
2
o0o0o0o
0 00
0
0
0D
0
5
00
0
0 03
0
0
011
11
10
15
2
Heat Flux (W/mm )
0
00
0
0 0
0
0
0
00
20
25
Figure 4.31: Stanton number for ethanol at Pr = 1.64, mass flow = 63 mg/s
62
1021 St vs. Heat Flux Pr=1.675 60 mg/s
X 10-3
2.4
o
midpoint
downstream]
2.2
2
1.8
-o
1.6
-0
1.4
0D
0
-0
0
1.2.
1
00
0
0.8
2
4
6
8
10
12
Heat Flux (W/mm2)
14
16
18
20
Figure 4.32: Stanton number for ethanol at Pr = 1.67, mass flow = 60 mg/s
3010 St vs. Heat Flux Pr=1.664 32 mg/s
X 10.3
30:
0
0
O
upstream
midpoint
downstream
25 -
20 k
65
15
10
0
0
5
0 000
60
0
0
-
5
0
0
o
0
~00
3
8
0
1OO0 o
10
0
15
2
Heat Flux (W/mm )
20
25
30
Figure 4.33: Stanton number for ethanol at Pr = 1.66, mass flow = 32 mg/s
63
4010 St vs. Heat Flux Pr=1.653 76 mg/s
x 10.3
5
o upstream
o
midpoint
downstream
-
4.5
0
0
0
4
0
3.5
3
80
0
2.5
2
0001:00000
0
0
00o
00
40
og
o
1.5
0
0000
0
0
0
De
00000000
1
L
0.5
0
I
I
5
10
15
20
Heat Flux (W/mm2
35
30
25
40
Figure 4.34: Stanton number for ethanol at Pr = 1.65, mass flow = 76 mg/s
5010 St vs. Heat Flux Pr=1.653 57 mg/s
X 10-3
0
o
4.5
O
upstream
midpoint
downstream
0
4
00
>2>00
0
3.5
c00
0
0
0
90
90
0
0
0
0
00
2.5
00
000 000
0l
2
0
0
0~
1.5
10
5
0
10
02
0
15
20
Heat Flux (W/mm2
25
30
35
Figure 4.35: Stanton number for ethanol at Pr = 1.65, mass flow = 57 mg/s
64
4.3 Results of High Pressure Ethanol Tests
The graph of fluid properties for ethanol at 300 bar in figure 1.4 indicates that there are
no large variations in the properties at a reduced pressure of 4.80. There is a maximum in
the C, curve at approximately 320 C, but the peak C, value has been severely degraded at
these extreme pressures. The C, curve in figure 1.4 is actually for a pressure of 250 bar,
since C, data for 300 bar was unavailable. Figure 3.3 shows C, plotted over a range of
pressures above the critical point. The maximum value of C, decreases as pressure
increases. From this plot, it can be concluded that the C, curve at 300 bar would closely
resemble the C, curve at 250 bar, and the pseudocritical temperature would remain close
to 330 C.
65
C vs. T for C2H6 0 at Supercritical Pressures
p
14000
-
100 bar
150 bar
--
200 bar
....
250 bar
12000-
10000-
:
8000 -
6000 ---
-
4000-
2000
180
1
200
220
240
260
280
300
Temperature (C)
320
340
360
380
Figure 4.36: Specific heat of ethanol at supercritical pressures
4.3.1 Wall and Bulk Temperature
As expected, the lack of variation in the ethanol fluid properties at 300 bar results in a
smooth temperature profile with no sudden decrease due to specific heat and viscosity
changes. There is little variation in the slope of the wall temperature to mark the pseudocritical temperature, as observed in figures 4.22 through 4.25. The temperature plots
show that the fluid at this pressure is stable and predictable, although there is no enhanced
heat transfer in the pseudocritical region.
66
1017 Temperature upstream vs. Heat Flux Pr=4.861
102 mg/s
2.5
O Outside Surface Temp
o Inside Wall Temp
- Bulk Fluid Temp
2
0
0
-
00
1.5
00000
OO
00
I-
00
Do
0
1
0
5
0
10
15
20
25
Heat Flux (W/mm2
1017 Temperature midpoint vs. Heat Flux P=4.861 102 mg/s
o Outside Surface Temp
0
0 0
Inside Wall Temp
-> Bulk FluidTemp
00
0
30
00 O 0 0
O
00
0
0
0 0
35
0
00
0
0000
F-
00
0
0
1
0.5
0
0
5
10
15
20
25
30
Heat Flux (W/mm2
1017 Temperature downstream vs. Heat Flux P=4.861 102 mg/s
2
35
ir
0
0
Outside Surface Temp
0 Inside Wall Temp
-> Bulk Fluid Temp
00
00
0 D
0 0
0
0
0
0
0
0
0
00
0
000
:
0
0
00
0 0
U-
1
----
----
----------------------------------------
8
8 O
o
0.5
>
K
>
K
>
K
K>
0 0> 0>
0
1
-
0
5
10
o
1
1
20
15
Heat Flux (W/mm2
25
30
Figure 4.37: Temperature plots for ethanol at Pr = 4.86, mass flow = 102 mg/s
67
-
35
2017 Temperature upstream vs. Heat Flux Pr=4.861
121 mg/s
3
O
0
O
2.5
Outside Surface Temp
Inside Wall Temp :O0
Bulk Fluid Temp
O00
000
O
co00
2
0 O0
O
IZ 1.5
000 E 000
0
1
0.5
0
5
10
15
20
25
30
Heat Flux (W/mm2)
2017 Temperature midpoint vs. Heat Flux P=4.861
35
40
45
121 mg/s
2.5
0
0
2
-
1.5
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
co co o00000
O
0
00
00000
~
000
000
00
~
0
0.5
0
5
0
10
15
20
25
30
Heat Flux (W/mm2
2017 Temperature downstream vs. Heat Flux Pr=4.861
35
40
45
121 mg/s
2.5
0
0
2
-
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
1.5
-
000
00000
o000OOO
00000
0 0
00
O000
0
00000000
0
1
------- -9 - ------------------------------------------------
0.5
0
0
oo
5
10
15
20
25
Heat Flux (W/mm2)
30
35
ooc
OO
40
Figure 4.38: Temperature plots for ethanol at Pr = 4.86, mass flow = 121 mg/s
68
45
3017 Temperature upstream vs. Heat Flux P=4.85
71 mg/s
3
o
0
0
2.5
Outside Surface Temp
Inside Wall Temp
0
Bulk Fluid Temp
0
O OO
0
0 0 0 0 0 0 OO
o
o
O
0000000
_
2
000
-0
1.5
1
03o
-0
-
0.5
0
5
0
35
20
25
30
Heat Flux (W/mm2)
3017 Temperature midpoint vs. Heat Flux Pr= 4 .85
10
15
40
45
40
45
71 mg/s
2.5
2
0
Outside Surface Temp
0
Inside Wall Temp
Bulk Fluid Temp
-
0 0
00
00
00000000000000000800
0 0 000000
00
El0
1:
00
1.5
0
1
0.5
0
0
5
25
30
20
Heat Flux (W/mm2
3017 Temperature downstream vs. Heat Flux P=4.85
10
35
15
71 mg/s
3
0
2.5
0
O
00
Outside Surface Temp
Inside Wall Temp
Bulk FluidTemp
0
0
@O
0o
2
-DO
000000og
1.5
0
80
1
o
0
K>K>>K>>K>KK>KK>K>>
-
0.5
0
0
5
10
15
20
25
Heat Flux (W/mm2
30
35
40
Figure 4.39: Temperature plots for ethanol at Pr = 4.85, mass flow = 71 mg/s
69
45
4017 Temperature upstream vs. Heat Flux P=4.888 255 mg/s
3
0
2.5
0O
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
0
0
0
2
O
O
0
0000
17 1.5
1-
0
0
-~0
0 c0 0
00000
0.5 1-
I~XKK
0
0
3
0 0
>
>xK1
K>>K 00
K>1000
60
80
100
Heat Flux (W/mm2)
4017 Temperature midpoint vs. Heat Flux P=4.888 255 mg/s
20
40
120
0 Outside Surface Temp
2.5
0
Inside Wall Temp
Bulk Fluid Temp
01
O
0
0 0
2
00
0
1.5
00
0 01
0
5a:000
0
Wo
00
000
)20
40
60
80
100
Heat Flux (W/mm2)
4017 Temperature downstream vs. Heat Flux P=4.888
0
0
4
O
O ]
-
5
OO O1
120
14l0
255 mg/s
Outside Surface Temp
Inside Wall Temp
Fluid Temp
KBulk
0 0
---60
0----20----40
900
~~xxHet
3
0
00
gee00
000
1
0
0
00000
C]1
0.5
140
----
80-----100-----
120-----
Flu (W/mm2>>
14--
K
I-
2
-
08000000
0
20
0
-IWo0
0
0
40
60
80
Heat Flux (W/mm2)
100
120
Figure 4.40: Temperature plots for ethanol at Pr = 4.89, mass flow = 255 mg/s
70
140
4.3.2 Heat Transfer Coefficient
Both the pressure and the heat flux affect the heat transfer coefficient by reducing the
pseudocritical peak value as pressure and heat flux are increased. These tests were run at
pressures significantly above the critical point and at high heat flux, so, as expected, the
heat transfer coefficient curves are smooth and show little variation. These plots also show
a clear thermal entrance region development, particularly test 2017. The downstream heat
transfer curve increases at a smaller rate due to the increasing length of the thermal
entrance region. Eventually, the midpoint and downstream curves overtake the downstream curve indicating that the thermal entrance region has expanded into the test section
as far as the downstream and eventually midpoint thermocouples. This seems to indicate
that the thermal entrance length is dependent on heat flux and the fluid, since it appears in
the ethanol tests and not the water tests. Pressure does not seem to be as important because
both the thermal entrance region transitions for the low and high pressure ethanol tests
occur at nearly the same heat flux.
71
1017 Heat Transfer Coefficient vs. Heat Flux P=4.861
x104
102mg/s
o upstream
o midpoint
-> downstream
11
10
9
0
2
00 0 0
al
8
000 0 0
0
K0
0
0
0
0
00
7
0
000
6
0
C3
0
~0
0 0 0 0000
O>
-
0K
00
0
00
-
5
4
3
0
5
10
15
20
Heat Flux (W/mm2
25
30
35
Figure 4.41: Heat transfer coefficient for ethanol at Pr = 4.86, mass flow = 102 mg/s
14
2017 Heat Transfer Coefficient vs. Heat Flux P=4.861
x 104
I
0
upstream
midpoint
> downstream
I
121 mg/s
I
I
KO
0
12
00
0 0
S10
00
0
0l
00
0 0
0
0
0
0
D8
0000080000
0
000
C
000
0
C
0000OOOO
OO
0
09
-A0
756
000
00
0
0 00c
00
4
9
20
I
5
I
10
I
15
I
I
20
25
Heat Flux (W/mm2
I
30
I
35
40
45
Figure 4.42: Heat transfer coefficient for ethanol at Pr = 4.86, mass flow = 121 mg/s
72
71 mg/s
3017 Heat Transfer Coefficient vs. Heat Flux P=4.85
x 104
11
o
upstream
o
0 0
midpoint
O downstream
0
10
00
9
OO
-
2
0
0
0 0
8
O
0
7
0
00
30
000
0
0
00
0000 000
0
aO
00 0
6
0
~ o 00
000C00
000000O
5
0~00000
0
00
000
I0 I
L
4
-
3
5
0
10
25
20
Heat Flux (W/mm 2)
15
30
35
40
45
Figure 4.43: Heat transfer coefficient for ethanol at Pr = 4.85, mass flow = 71 mg/s
4017 Heat Transfer Coefficient vs. Heat Flux P=4.888
x 105
3.5
0 upstream
0
0
midpoint
0
downstream
0
3
0
0
0
*0
0
0
0 0
O
O
O
~00
0
O
<>
OOO>>KK>
C
0
2
0
a
0
0
O O
O
000
0l
0
0 0
0
0
0
0
0
0
a
0
0
00
C
000
a
Ia
I
00
0
7
2.5-
255 mg/s
1.5 F
0
0
0
O
1
0
0
20
40
60
80
2
Heat Flux (W/mm )
100
120
140
Figure 4.44: Heat transfer coefficient for ethanol at Pr = 4.89, mass flow = 255 mg/s
73
4.3.3 Stanton Number
The Stanton number curves, like the heat transfer coefficient curves, are well behaved.
For the midpoint and downstream points, the Stanton number rises as the film boiling phenomenon starts, since the difference between the bulk and the wall temperatures drops.
The upstream curve shows a different trend. It drops, indicating the continued increase in
the temperature difference. This, again, is the result of the extended thermal entrance
region.
1.8
1017 St vs. Heat Flux Pr=4.861
x 10-3
102 mg/s
o upstream
0
-
1.7
midpoint
downstream
0
0
0
0
1.6
00
00
0
00
00
1.5
0
1.4
000
1.3
0~
-l
O
0
00
1.2
1.1
00
0
0
00
0.9
0.8
0
5
10
15
20
Heat Flux (W/mm 2)
25
30
35
Figure 4.45: Stanton number for ethanol at Pr = 4.86, mass flow = 102 mg/s
74
4 86 1
1.8
121 mg/s
2017 St vs. Heat Flux Pr= .
x10-
0 upstream
o midpoint
O downstream
1.6
0oo
0000
001
000
35
40
1.4
00
0
1.2
00
cI
0
o
-
00
O
1
0.8
0r
c
-~c
0
oc
15
10
5
000o
000
0000000a0
30
25
20
Heat Flux (W/mm2
45
Figure 4.46: Stanton number for ethanol at Pr = 4.86, mass flow = 121 mg/s
2.6
x
71 mg/s
3017 St vs. Heat Flux Pr=4.85
10_-3
0 upstream
0
midpoint
O downstream
2.4
2.21
0
o
2
0
0
O
O
0
1.8
0
0
00
0
0
0
0
0
0
00
00
0
1.6
000
1.4
0
0ooo
0.8
ooo
0
0
-
1
0
0
5
0
00
0
0
00
1.2
00
0
0
10
0
oooo
00
0
0 00
15
0
25
20
Heat Flux (W/mm2
30
35
40
45
Figure 4.47: Stanton number for ethanol at Pr = 4.85, mass flow = 71 mg/s
75
2.6
x
4017 St vs. Heat Flux Pr=4.888 255 mg/s
10-3
o upstream
midpoint
downstream
0
2.4
-
0
0
2.2
0
0
0
-
0
0
0 00
2
0
0 0
o
1.8
M51.6|
0
O
O
0
0ooQ
0
O
0
0
1.4
0
0
A
O O
O
1.2
1
0.8 I-
VU0
20
40
60
80
Heat Flux (W/mm2)
100
120
140
Figure 4.48: Stanton number for ethanol at Pr = 4.89, mass flow = 255 mg/s
76
Chapter 5
Conclusions
5.1 Summary
The purpose of the water heat transfer tests was to extend to higher heat fluxes existing
data on supercritical water heat transfer and compare the previously acquired ethanol data
with these results. The water tests showed some features that were observed in the literature. The phenomenon of deterioration of the heat transfer coefficient at high heat fluxes
was present in the water data, as well as oscillations in the temperature within a constant
heat flux value. A discontinuity in the wall temperature plot as the wall temperature
reached the pseudocritical point was also observed.
The water test reduced pressures were similar to those of the low pressure ethanol
tests, and similarities existed between the two data sets. The ethanol wall temperature
plots showed the same discontinuity around the pseudocritical temperature. The ethanol
data, however clearly showed a thermal entrance region while the water data did not.
The high reduced pressure ethanol tests cannot be compared to water tests because the
test rig is unable to duplicate the test conditions. Although, the high pressure ethanol tests
showed characteristics observed in the literature. The heat transfer coefficient was
degraded due to the high pressure. The thermal entrance region was present and occurred
at heat fluxes close to those of the low pressure ethanol.
The water tests seemed to display characteristics seen in previous research, indicating
that the difference in test conditions did not make a comparison impossible. The literature,
as well as the water tests show that high heat fluxes cause instabilities in the fluid flow,
which appear when the bulk temperature is much lower than the wall temperature. To
achieve large heat transfer coefficients, the bulk temperature must reach the pseudocritical
77
temperature. In addition, discontinuities decrease as the reduced pressure increases. The
water and low pressure ethanol tests demonstrate that heat transfer at reduced pressures
close to 1 is unstable and unpredictable. The high pressure ethanol tests showed stable
flow, but the enhanced heat transfer coefficient cannot be achieved since the fluid properties have no large changes leading to a sudden increase in cooling ability.
5.2 Future Work
The next step in the heat transfer experimentation is to begin a series of tests using
other propellants to observe the supercritical behavior of the fluids. JP-7 is one of several
fuels being considered for the g-rocket. It has the advantage that it does not coke, which is
vital because the cooling passages are so small, and therefore are easily clogged. The heat
transfer tests will most likely begin after the current g-rocket testing has been completed.
The test rig was designed to investigate the cooling passage effectiveness by varying
the coolant pressure and the mass flow, but keeping the tube dimensions constant. The
actual g-rocket cooling passages have a set coolant pressure and mass flow, so the passage
dimensions must be changed to alter the cooling abilities. It is unclear at this time how
accurately the test rig can predict the heat transfer conditions in light of this fundamental
difference. It is therefore suggested that running a series of tests using test sections with
different internal diameters at a constant pressure would provide a better understanding of
how supercritical heat transfer scales as a function of tube dimensions. This may provide a
more accurate representation of the rocket engine.
78
Appendix A
Data Reduction Programs
These programs were written for Matlab.
% HEAT TRANSFER DATA REDUCTION PROGRAM FOR WATER
clear;
%%%%%%%%%%%%%%CONSTANTS %%%%%%%%%%%%%%%%%%%%%
tccor = 24576; % thermocouple correction for K type t.c.'s
OD = 300e-6; % outer diameter of tube in m
ro = OD/2; % outer radius of tube in m
ID = 95e-6; % inner diameter of tube in m
ri = ID/2; %inner radius if tube in m
1= 4e-3; % length of the tube in m
Vol = l*pi*((ro)A2-(ri)A2); % volume of steel tube wall (mA3)
Ai = pi*ID*l; % inside surface area of the tube (mA2)
Ao = pi*OD*l; % outside surface area of the tube (mA2)
Ae = pi*riA2; %inlet / exit area of the tube
Pc = 220.9; % Critical pressure of water in bar
Tc = 374.14; % Critical temperature of water in C
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%Read data from spreadsheet-like file%%%
filename = ['data/water/test09.txt'
'data/water/test 10.txt'
'data/water/test 11 .txt'
'data/water/test 12.txt'
'data/water/test 13.txt'
'data/water/test 14.txt'
'data/water/test 15.txt'
'data/water/test 16.txt'
'data/water/test 17.txt'
'data/water/test 18.txt'];
output-filename = ['data/reduceddata/water/test09.dat'
'data/reduceddata/water/test 10.dat'
'data/reduceddata/water/test 11.dat'
'data/reduceddata/water/test 12.dat'
79
'data/reduceddata/water/test
'data/reduceddata/water/test
'data/reduceddata/water/test
'data/reduceddata/water/test
'data/reduceddata/water/test
'data/reduceddata/water/test
13.dat'
14.dat'
15.dat'
16.dat'
17.dat'
18.dat'];
for i = 1:10,
%%%%%%%%%%%%%CLEAR OLD ARRAYS %%%%%%%%%%%%%%%%%
clear T3, clear T4, clear T5;
clear T3w, clear T4w, clear T5w;
clear T3b, clear T4b, clear T5b;
clear T3f, clear T4f, clear T5f;
clear yr, clear day, clear hr, clear minute, clear sec;
clear Tin, clear mdot, clear P, clear ts_P, clear V, clear I, clear power;
clear P3, clear P4, clear P5;
clear Q, clear heatflux, clear h_in, clear C3, clear C4, clear C5;
clear h3_out, clear h4_out, clear h5_out, clear h3, clear h4, clear h5;
clear cp, clear St3, clear St4, clear St5, clear G;
clear data;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
testnum = file name(i,16:17);
disp(testnum);
fid = fopen(file name(i, 1:21),'r');
testcond(1:6) = str2num(fgetl(fid));
c3 = testcond(1); % thermocouple calibration constansts
c4 = testcond(2);
c5 = testcond(3);
xd3 = testcond(4); %l/d for thermocouples
xd4 = testcond(5);
xd5 = testcond(6);
x3 = xd3*ID/l; % fractional distance of t.c. location
x4 = xd4*ID/l;
x5 = xd5*ID/l;
line = fgetl(fid);
j = 1;
while line ~= -1
linestr = str2num(line);
yr(j) = linestr(1);
% year
80
day(j) = line-str(2);
% day
% hour
hr(j) = linestr(3);
minute(j) = linestr(4);
% minute
% second
sec(j) = line_str(5);
% supply tank temp (degrees C)
T_in(j) = linestr(6);
m_dot(j) = line_str(7)./le6; % mass flow (kg/s)
P(j) = line-str(8) * 6.894757e-2; % line pressure in bar (from psi)
tsP(j) = linestr(9) * 6.894757e-2; % test section pressure drop in bar (from psi)
% voltage (V)
V(j) = linestr(10);
% current (A)
1(j) = line str( 11);
power(j) = line-str(12);
% heat_flux (W/mmA2)
T5(j) = line_str(13);
T4(j) = linestr(14);
T3(j) = line_str(15);
%T5 (degrees C)
%T4 (degrees C)
%T3 (degrees C)
%%%%%%%%%%%%PRESSURE DROP ACCOUNTING %%%%%%%%%%%%
P3(j) = P(j)-tsP(j)*x3;
P4(j) = P(j)-tsP(j)*x4;
P5(j) = P(j)-tsP(j)*x5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%THERMOCOUPLE CALIBRATION %%%%%%%%%%%%%
milliV = V(j)*c3;
Tcfactor = tccor*milli_V;
T3(j) = T3(j) + Tcfactor;
milliV = V(j)*c4;
Tcfactor = tccor*milli_V;
T4(j) = T4(j) + Tcfactor;
milliV = V(j)*c5;
Tcfactor = tccor*milli_V;
T5(j) = T5(j) + Tcfactor;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q(j) = I0).*Vj);
heat_flux(j) = Q(j)/(Ai* 1e6);
% W/mmA2
%%%%%%%%%%%PROPERTY TABLE INDEPENDENT %%%%%%%%%%%%
h_in(j) = tp2h_h2o(P(j),T_in(j)); %enthalpy at tube inlet (J/kg)
C3(j) = -1*(Q(j)/(2*pi*l)*((log(ro/ri)/(1-(ri/ro)A2))-0.5)
81
+0.0076*T3(j)A2+14.2444*T3(j);
T3w(j)=(- 14.2444+sqrt(1 4.2444^A2+4*0.0076*C3(j)))/(2*0.0076); %wall temp(C)
C4(j) = -1*(Q(j)/(2*pi*l)*((log(ro/ri)/(1-(ri/ro)A2))-0.5))
+0.0076*T4(j)A2+14.2444*T4(j);
T4w(j)=(- 14.2444+sqrt(1 4.2444A2+4*0.0076*C4(j)))/(2*0.0076);
C5(j) = -1*(Q(j)/(2*pi*l)*((log(ro/ri)/(1-(ri/ro)A2))-0.5))
+0.0076*T5(j)A2+14.2444*T5(j);
T5w(j)=(- 14.2444+sqrt(14.2444A2+4*0.0076*C5(j)))/(2*0.0076);
h3_out(j) = hin(j) + ((Q(j).*x3)./m dot(j)); %enthalpy at tube exit (J/kg)
h4_out(j) = h_in(j) + ((Q(j).*x4)./mdot(j));
h5_out(j) = hin(j) + ((Q(j).*x5)./m_dot(j));
T3b(j) = hp2tLh2o(h3_out(j),P3(j)); %bulk fluid temperature (degrees C)
T4b(j) = hp2t-h2o(h4_out(j),P4(j));
T5b(j) = hp2t-h2o(h5_out(j),P5(j));
h3(j)= Q(j)./(Ai.*(T3w(j) - T3b(j))); %heat transfer coefficient (W/mA2.K)
h4(j)= Q(j)./(Ai.*(T4w(j) - T4b(j)));
h5(j)= Q(j)./(Ai.*(T5w(j) - T5b(j)));
G(j) = mdot(j)/Ae; % mass velocity (kg/s.mA2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%
PROPERTY TABLE DEPENDENT %%%%%%%%%%%%
if testnum == '09' I testnum == '10'
St3(j) = 0;
else
h3w(j) = tp2hh2o(P3(j),T3w(j)); %Wall enthalpy (J/kg)
h3b(j) = tp2hh2o(P3(j),T3b(j)); % Bulk enthalpy (J/kg)
St3(j) = (Q(j)/Ai)/((mdot(j)/Ae)*(h3w(j)-h3b(j))); % Stanton number
end
h4w(j) = tp2h-h2o(P4(j),T4w(j));
h5w(j) = tp2hh2o(P5(j),T5w(j));
h4b(j) = tp2h_h2o(P4(j),T4b(j));
h5b(j) = tp2h-h2o(P5(j),T5b(j));
St4(j) = (Q(j)/Ai)/((m-dot(j)/Ae)*(h4w(j)-h4b(j)));
St5(j) = (Q(j)/Ai)/((m-dot(j)/Ae)*(h5w(j)-h5b(j)));
82
j =j + 1;
line = fgetl(fid);
end
L=j-1;
P3_ave = 0;
P4_ave = 0;
P5_ave = 0;
m_dotave = 0;
for index=1:L,
P3_ave = P3(index)+P3_ave;
P4_ave = P4(index)+P4_ave;
P5_ave = P5(index)+P5_ave;
mdot-ave = mdot(index)+mdotave;
end
P3_ave = P3_ave/L;
P4_ave = P4_ave/L;
P5_ave = P5_ave/L;
p3_str = num2str(P3_ave./Pc);
p4_str = num2str(P4_ave./Pc);
p5_str = num2str(P5_ave./Pc);
m_dotave = mdotave/L* 1e6; %converts to mg/s from kg/s
m_dotstr = num2str(m dot ave);
m_dotstr = m_dot str(1:3);
st = fclose(fid);
%%%%%%%%%%%WRITE DATA TO FILE%%%%%%%%%%%%%%%%%%%%
data = [ID];
fid = fopen(outputfilename(i,1:34),'w');
fprintf(fid, '% 12.6f\n',,data);
st = fclose(fid);
data = [P3; P4; P5; m_dot; heat_flux; T3; T4; T5; T3w; T4w; T5w; T3b; T4b; T5b;
St3; St4; St5; G];
fid = fopen(outputfile_name(i,1:34),'a');
fprintf(fid, '%12.4f %12.4f %12.4f %12.6f %12.4f %12.4f %12.4f %12.4f %12.4f
%12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f\n',data);
st = fclose(fid);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
83
%%%%%%%%%%%%%PLOT DATA%%%%%%%%%%%%%%%%%%%%%%%
fig = 0;
% plot surface temp, inside wall temp, and bulk fluid temp vs. heat flux
plt = input('Do you want to plot temperature vs. heat flux? (y/n def = n) ','s');
if isempty(plt) == 1
plt = 'n';
end
if plt == 'y'
fig =fig+1;
figure(fig)
hold off, clf
subplot(3,1,1), plot(heat-flux(1:L), T3(1:L)./Tc, 'bo');
hold on
plot(heat-flux(1:L), T3w(1:L)./Tc, 'rs');
plot(heat-flux(1:L), T3b(1:L)./Tc, 'gd');
ti(1:2) = testnum;
ti(3:44) = ' Temperature upstream vs. Heat Flux P r=';
ti(45:49) = p3_str(1:5);
ti(50:52) = '
';
ti(53:55) = mdotstr;
ti(56:60) = ' mg/s';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('TTc');
legend('Outside Surface Temp', 'Inside Wall Temp', 'Bulk Fluid Temp',2);
subplot(3,1,2), plot(heat-flux(1:L), T4(1:L)./Tc, 'bo');
hold on
plot(heat_flux(1:L), T4w(1:L)./Tc, 'rs');
plot(heatjflux(1:L), T4b(1:L)./Tc, 'gd');
ti(1:2) = testnum;
ti(3:44)= ' Temperature midpoint vs. Heat Flux P_r=';
ti(45:49) = p4_str(1:5);
ti(50:52) = ' ';
ti(53:55) = m_dotstr;
ti(56:60) = ' mg/s';
84
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('T/T_c');
legend('Outside Surface Temp', 'Inside Wall Temp', 'Bulk Fluid Temp',2);
subplot(3,1,3), plot(heat_flux(1:L), T5(1:L)./Tc, 'bo');
hold on
plot(heat_flux(1:L), T5w(1:L)./Tc, 'rs');
plot(heat_flux(1:L), T5b(1:L)./Tc, 'gd');
ti(1:2) = test-num;
ti(3:46) = ' Temperature downstream vs. Heat Flux P r=';
ti(47:51) = p5_str(1:5);
ti(52:54) = ' ';
ti(55:57) = m-dot str;
ti(58:62) =' mg/s';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('T/T_c');
legend('Outside Surface Temp', 'Inside Wall Temp', 'Bulk Fluid Temp',2);
end
% plot heat transfer coefficient vs. heat flux
plt = input('Do you want to plot heat transfer coefficient vs. heat flux? (y/n def = n)
if isempty(plt) == 1
plt= 'n';
end
if plt == 'y'
fig =fig+1;
figure(fig)
hold off, clf
plot(heat_flux(1:L), h3(1:L), 'bo');
hold on
plot(heat-flux(1:L), h4(1:L), 'rs');
plot(heat flux(1:L), h5(1:L), 'gd');
ti(1:2) = test num;
ti(3:49) = ' Heat Transfer Coefficient vs. Heat Flux P-r=';
ti(50:54) = p4_str(1:5);
85
ti(55:57) = ' ';
ti(58:60) = m_dotstr;
ti(61:65) = ' mg/s';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Heat Transfer Coefficient (W/mA2.K)');
legend('upstream', 'midpoint', 'downstream',2);
end
% plot Tw-Tb vs. heat flux
plt = input('Do you want to plot Tw-Tb vs. heat flux? (y/n def = n) ','s');
if isempty(plt) == 1
plt= 'n';
end
if plt ==Y
fig = fig+1;
figure(fig)
hold off, clf
plot(heatflux(1:L), T3w(1:L)-T3b(1:L), 'bo');
hold on
plot(heat-flux(1:L), T4w(1:L)-T4b(1:L), 'rs');
plot(heat_flux(1:L), T5w(1:L)-T5b(1:L), 'gd');
ti(1:2) = testnum;
ti(3:29) = ' Tw-Tb vs. Heat Flux P r=';
ti(30:34) = p4_str(1:5);
ti(35:37) = ' ';
ti(38:40) = mdotstr;
ti(41:45) = ' mg/s';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Tw-Tb (C)');
legend('upstream', 'midpoint', 'downstream',2);
end
% plot Stanton Number vs. heat flux
plt = input('Do you want to plot St vs. heat flux? (y/n def= n) ','s');
if isempty(plt) == 1
plt = 'n';
86
end
if plt ==y
fig = fig+1;
figure(fig)
hold off, clf
plot(heat_flux(1:L), St3(1:L), 'bo');
hold on
plot(heat-flux(1:L), St4(1:L), 'rs');
plot(heat-flux(1:L), St5(1:L), 'gd');
ti(1:2) = test num;
ti(3:26) = ' St vs. Heat Flux Pr=';
ti(27:31) = p4_str(1:5);
ti(32:34) = ' ';
ti(35:37) = m_dotstr;
ti(38:42) = ' mg/s';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('St');
legend('upstream', 'midpoint', 'downstream',2);
end
end
87
% HEAT TRANSFER DATA REDUCTION PROGRAM FOR ETHANOL
clear;
%%%%%%%%%%%%%%%%%CONSTANTS %%%%%%%%%%%%%%%%%%
tccor = 24576; % thermocouple correction for K type tc's ***CHECK***
OD = 300e-6; %outer diameter of tube in m
ro = OD/2; %outer radius of tube in m
ID = 95e-6; % inner diameter of tube in m
ri = ID/2; % inner radius if tube in m
1 = 4e-3; % length of the tube in m
Vol = 1*pi*((ro)A2-(ri)A2); % volume of steel tube wall (mA3)
Ai = pi*ID*1; % inside surface area of the tube (mA2)
Ao = pi*OD*l; % outside surface area of the tube (mA2)
Ae = pi*riA2; % inlet / exit area of the tube
Tpc = 243; % Critical temperature of ethanol in C
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%Read data from spreadsheet-like file%%%
filename = ['data/ethanol/1010.txt'
'data/ethanol/1017.txt'
'data/ethanol/ 1021 .txt'
'data/ethanol/2017.txt'
'data/ethanol/30 10.txt'
'data/ethanol/3017.txt'
'data/ethanol/40 10.txt'
'data/ethanol/4017.txt'
'data/ethanol/50 10.txt'];
output-filename = ['data/reduceddata/ethanol/1010.dat'
'data/reduceddata/ethanol/1017.dat'
'data/reduceddata/ethanol/1021.dat'
'data/reduceddata/ethanol/2017.dat'
'data/reduceddata/ethanol/3010.dat'
'data/reduceddata/ethanol/3017.dat'
'data/reduceddata/ethanol/40 10.dat'
'data/reduceddata/ethanol/4017.dat'
'data/reduceddata/ethanol/50 10.dat'];
88
for i = 1:9,
%%%%%%%%%%%%%CLEAR OLD ARRAYS %%%%%%%%%%%%
clear T3, clear T4, clear T5;
clear T3w, clear T4w, clear T5w;
clear T3w_o, clear T4w_o, clear T5w_o;
clear T3b, clear T4b, clear T5b;
clear T3f, clear T4f, clear T5f;
clear V, clear I, clear power;
clear Q, clear heatflux, clear h_in, clear C3, clear C4, clear C5;
clear h3_out, clear h4_out, clear h5_out, clear h3, clear h4, clear h5;
clear cp, clear St3, clear St4, clear St5, clear G;
clear data;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
testnum = filename(i,14:17);
disp(test-num);
fid = fopen(filename(i,1:21),'r');
line = fgetl(fid);
testscond(1:9) = str2num(fgetl(fid));
P = testcond(1) * 6.894757e-2; %line pressure in bar (from psi)
p_str = num2str(P);
m_dot = test cond(2) / le6;
c3 = testcond(3);
c4 = testcond(4);
c5 = testcond(5);
xd3 = test cond(6);
xd4 = testcond(7);
xd5 = test cond(8);
x3 = xd3*ID/Il;
x4 = xd4*ID/Il;
x5 = xd5*ID/Il;
T_in = test-cond(9); % Temperature at the inlet of the test section in degrees C
h_in = tp2h-c2h6o(P,Tin); %enthalpy at tube inlet (J/kg)
line = fgetl(fid);
j = 1;
while line ~= -1
linestr = str2num(line);
V(j) = linestr(1); %voltage (V)
89
1(j) = line str(2); % current (A)
T3(j) = line str(3); % T3 (C)
T4(j) = line-str(4); % T4 (C)
T5(j) = line str(5); % T5 (C)
power(j) = line-str(6); % heat flux (W/mmA2)
%%%%%%%%%%%THERMOCOUPLE CORRECTION %%%%%%%%%%%%%%
milli_V = V(j)*c3;
Tcfactor = tccor*milliV;
T3(j) = T3(j) + Tcfactor;
milli_V = V(j)*c4;
Tcfactor = tccor*milliV;
T4(j) = T4(j) + Tcfactor;
milli_V = V(j)*c5;
Tcfactor = tccor*milliV;
T5(j) = T5(j) + Tcfactor;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q(j)
= I0).*Vj);
heatflux(j) = Q(j)/(Ai*1e6); % W/mm^2
%%%%%%%%%PROPERTY TABLE INDEPENDENT %%%%%%%%%%%%%%
C3(j) = -1*(Q(j)/(2*pi*l)*((log(ro/ri)/(1-(ri/ro)A2))-0.5))
+ 0.0076*T3(j)A2 + 14.2444*T3(j);
T3w(j) = (-14.2444 + sqrt(14.2444A2+4*0.0076*C3(j)))/(2*0.0076); % wall temp (C)
C4(j) = -1*(Q(j)/(2*pi*l)*((log(ro/ri)/(1-(ri/ro)A2))-0.5))
+ 0.0076*T4(j)A2 + 14.2444*T4(j);
T4w(j) = (- 14.2444 + sqrt( 14.2444A2+4*.0076*C4(j)))/(2*.0076);
C5(j) = -1*(Q(j)/(2*pi*l)*((log(ro/ri)/(1-(ri/ro)A2))-0.5))
+ 0.0076*T5(j)A2 + 14.2444*T5(j);
T5w(j) = (-14.2444 + sqrt(14.2444A2+4*.0076*C5(j)))/(2*.0076);
h3_out(j) = h-in + ((Q(j).*x3)./m dot); % enthalpy at tube exit (J/kg)
h4_out(j) = hin + ((Q(j).*x4)./m_dot);
h5_out(j) = hin + ((Q(j).*x5)./m dot);
T3b(j) = hp2t c2h6o(h3_out(j),P); % bulk temperature in degrees C
T4b(j) = hp2t_c2h6o(h4_out(j),P);
T5b(j) = hp2tc2h6o(h5_out(j),P);
h3(j)= Q(j)./(Ai.*(T3w(j) - T3b(j))); % heat transfer coefficient (W/mA2.K)
h4(j)= Q(j)./(Ai.*(T4w(j) - T4b(j)));
h5(j)= Q(j)./(Ai.*(T5w(j) - T5b(j)));
90
G(j) = mdot/Ae; %mass velocity (kg/s.mA2)
%%%%%%%%%%%PROPERTY TABLE DEPENDENT %%%%%%%%%%%%%%
T3f(j) = (T3w(j)+T3b(j))/2; % film temperature of fluid (C)
T4f(j) = (T4w(j)+T4b(j))/2;
T5f(j) = (T5w(j)+T5b(j))/2;
h3w(j) = tp2h-h2o(PT3w(j)); % wall enthalpy (J/kg)
h3b(j) = tp2h-h2o(PT3b(j)); %bulk enthalpy (J/kg)
St3(j) = (Q(j)/Ai)/((mdot/Ae)*(h3w(j)-h3b(j))); % Stanton number
h4w(j) = tp2h-h2o(PT4w(j));
h5w(j) = tp2h-h2o(PT5w(j));
h4b(j) = tp2h-h2o(PT4b(j));
h5b(j) = tp2hh2o(PT5b(j));
St4(j) = (Q(j)/Ai)/((mdot/Ae)*(h4w(j)-h4b(j)));
St5(j) = (Q(j)/Ai)/((mdot/Ae)*(h5w(j)-h5b(j)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
j =j +
1;
line = fgetl(fid);
end
L =j-1;
st = fclose(fid);
%%%%%%%%%%%WRITE DATA TO FILE %%%%%%%%%%%%%%%%%%%
data = [P; m_dot; ID];
fid = fopen(output-file-name(i, 1:34),'w');
fprintf(fid, '%12.4f %12.6f %12.6f\n',data);
st = fclose(fid);
data = [heatflux; T3; T4; T5; T3w; T4w; T5w; T3b; T4b; T5b; St3; St4; St5; G];
fid = fopen(output-file-name(i,1:34),'a');
fprintf(fid, '%12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f
%12.4f %12.4f %12.4f %12.4f %12.4f\n',data);
st = fclose(fid);
91
PLOT DATA %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
fig = 0;
% plot surface temp, inside wall temp, and bulk fluid temp vs. heat flux
plt = input('Do you want to plot temperature vs. heat flux? (y/n def = n) ','s');
if isempty(plt) == 1
plt = 'n';
end
if plt ==y
fig = fig+1;
figure(fig)
hold off, clf
subplot(3,1,1), plot(heat_flux(1:L), T3(1:L), 'bo');
hold on
plot(heat-flux(1:L), T3w(1:L), 'rs');
plot(heat-flux(1:L), T3b(1:L), 'gd');
ti(1:4) = test num;
ti(5:42) = ' Temperature upstream vs. Heat Flux ';
ti(43:45) = pstr(1:3);
ti(46:49) = ' bar';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Temperature (C)');
legend('Outside Surface Temp', 'Inside Wall Temp', 'Bulk Fluid Temp',2);
subplot(3,1,2), plot(heat_flux(1:L), T4(1:L), 'bo');
hold on
plot(heat-flux(1:L), T4w(1:L), 'rs');
plot(heatjflux(1:L), T4b(1:L), 'gd');
ti(1:4) = testnum;
ti(5:42) = ' Temperature midpoint vs. Heat Flux ';
ti(43:45) = pstr(1:3);
ti(46:49) = ' bar';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Temperature (C)');
92
legend('Outside Surface Temp', 'Inside Wall Temp', 'Bulk Fluid Temp',2);
subplot(3,1,3), plot(heat_flux(1:L), T5(1:L), 'bo');
hold on
plot(heat_flux(1:L), T5w(1:L), 'rs');
plot(heat_flux(1:L), T5b(1:L), 'gd');
ti(1:4) = testnum;
ti(5:44)= ' Temperature downstream vs. Heat Flux ';
ti(45:47) = pstr(1:3);
ti(48:51) = ' bar';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Temperature (C)');
legend('Outside Surface Temp', 'Inside Wall Temp', 'Bulk Fluid Temp',2);
end
% plot heat transfer coefficient vs. heat flux
plt = input('Do you want to plot heat transfer coefficient vs. heat flux? (y/n def
if isempty(plt) == 1
plt = 'n';
end
if plt== 'y'
fig = fig+1;
figure(fig)
hold off, clf
plot(heatflux(1:L), h3(1:L), 'bo');
hold on
plot(heat flux(1:L), h4(1:L), 'rs');
plot(heat_flux(1:L), h5(1:L), 'gd');
ti(1:4) = testnum;
ti(5:47) = ' Heat Transfer Coefficient vs. Heat Flux
ti(48:50) = p-str(1:3);
ti(51:54) = ' bar';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Heat Transfer Coefficient (W/mA2.K)');
legend('upstream', 'midpoint', 'downstream',2);
93
';
=
n)
end
% plot Tw-Tb vs. heat flux
plt = input('Do you want to plot Tw-Tb vs. heat flux? (y/n def = n) ','s');
if isempty(plt) == 1
plt = 'n';
end
if plt ==y
fig = fig+1;
figure(fig)
hold off, clf
plot(heat-flux(1:L), T3w(1:L)-T3b(1:L), 'bo');
hold on
plot(heatflux(1:L), T4w(1:L)-T4b(1:L), 'rs');
plot(heat-flux(1:L), T5w(1:L)-T5b(1:L), 'gd');
ti(1:4) = testnum;
ti(5:27) = ' Tw-Tb vs. Heat Flux ';
ti(28:30) = pstr(1:3);
ti(31:34) = ' bar';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('Tw-Tb (C)');
legend('upstream', 'midpoint', 'downstream',2);
end
%plot Stanton Number vs. heat flux
plt = input('Do you want to plot St vs. heat flux? (y/n def= n) ','s');
if isempty(plt) == 1
plt = 'n';
end
if plt ==y
fig = fig+1;
figure(fig)
hold off, clf
plot(heat-flux(1:L), St3(1:L), 'bo');
hold on
plot(heat-flux(1:L), St4(1:L), 'rs');
plot(heatjflux(1:L), St5(1:L), 'gd');
ti(1:4) = testnum;
94
ti(5:24) = ' St vs. Heat Flux ';
ti(25:27) = pstr(1:3);
ti(28:31) = ' bar';
title(ti);
clear ti;
xlabel('Heat Flux (W/mmA2)');
ylabel('St');
legend('upstream', 'midpoint', 'downstream',2);
end
end
95
96
Appendix B
Temperature Plots for Calibration Tests
These plots are the temperature as a function of heat flux plots for the calibration tests
that were conducted for the water runs. Test 09 is the calibration test for water test 10, calibration test 11 corresponds to test 12, calibration test 13 corresponds to test 14, and calibration test 15 corresponds to tests 16, 17, and 18. The dotted line on each plot shows the
location of the saturation temperature for the given pressure.
09 Temperature midpoint vs. Heat Flux 20.83 bar 98. mg/s
350
2o
300
0
O
-250
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
Saturation Temp
0
200
E
0
OO
C]o
0
0
150
-E
100
9
0
50
0
2
0
4
6
8
10
Heat Flux (W/mm2)
12
14
16
18
09 Temperature downstream vs. Heat Flux 19.23 bar 98. mg/s
300
I
0
250
-
200
-t
0
O
Outside Surface Temp
Inside Wall Temp
Bulk Fluid Temp
Saturation Temp
Oo
OD
0
00
0-
-0
0
O
O0
-0 - - - - - - - - - - -
00 Go
000
150
-
00
E1-
(D 10050
0
0
II
2
I
4
6
I
I
8
10
Heat Flux (W/mm2)
I
12
I
14
Figure B.1: Calibration test at 20 bar, saturation T = 212 C
97
16
18
11 Temperature upstream vs. Heat Flux 24.03 bar 62. mg/s
-I
300
Outside Surface T emp
Inside Wall Temp
Bulk Fluid Temp
------------------Saturation Temp
0
0
250
O
(-)200
a,
150 -
10
C5PO
~~
P0 )0 EP
tli
0
0
Q
ccO
0
000
O
C
o:
or
~~
~
~VE]
~D~OO
0-
E
~c 0
--------------6P 00
100
99
50
0-
000000Kc
5
0
15
10
20
25
Heat Flux (W/mm2
11 Temperature midpoint vs. Heat Flux 23.42 bar 62. mg/s
300
O Outside Surface Temp
0 Inside Wall Temp
O Bulk Fluid Temp
Saturation Temp
250
O
o
C:5-'
200
O
E
OCO
o
-
0
0So
El-0
Li
EL00 0
,0
-
EP
-O
T 150
000
O0Ot 00
-PH
100
50
C
0
5
10
15
Heat Flux (W/mm2
20
25
11 Temperature downstream vs. Heat Flux 22.91 bar 62. mg/s
30C
0
Outside Surface Temp
o eO
01 Inside Wall Temp
250
Bulk Fluid Temp
Saturation Temp
0
C>0
Oo o00
COD 0
O
--~o-Id -~od ~-~
-~-~-- -o
~-
-
200
CP E
*,
150
0
00
0
5
10
15
Heat Flux (W/mm2
20
Figure B.2: Calibration test at 23 bar, saturation T = 220 C
98
25
13 Temperature upstream vs. Heat Flux 24.64 bar 58. mg/s
300
o
Outside Surface Temp
Inside Wall Temp
<2 Bulk
Temp
_0
___________a
Sat Fluid
uionTemp-----------------------------------.
_
250
Saturation Temp
200
00
OEI
Oo
100
9
0 0 900
-
0
0
0
0
-
50
-3
01
00
0C
ca.
E
2
_0
(
-
2 150
0
0
t3-oGd3J-
0
0
4
6
000
-0
-
0
8
10
Heat Flux (W/mm2)
12
14
16
13 Temperature midpoint vs. Heat Flux 24.44 bar 58. mg/s
500
0
Outside Surface Temp
o Inside Wall Temp
400
-
Bulk Fluid Temp
Saturation Temp
-
o
300
0-200
-
-
9Ge
geg 9
100
0
0
2
4
6
10
8
Heat Flux (W/mm2)
12
14
16
13 Temperature downstream vs. Heat Flux 24.13 bar 58. mg/s
500
400
O Outside Surface Temp
o Inside Wall Temp
-0 Bulk Fluid Temp
Saturation Temp
00Q
C9
2 300
0-200
100
0
0
-
-------------------------
000
2
--------------------
g 9
4
6
10
8
2
)
(W/mm
Flux
Heat
-
12
Figure B.3: Calibration test at 24 bar, saturation T = 222 C
99
14
16
15 Temperature upstream vs. Heat Flux 24.71 bar 96. mg/s
500
O
Outside Surface Temp
o Inside Wall Temp
400
-
Bulk Fluid Temp
Saturation Temp
2 300
ca
E 200
a)
100
0
0
5
10
15
20
Heat Flux (W/mm2
25
30
5
15 Temperature midpoint vs. Heat Flux 24.04 bar 96. mg/s
600
O Outside Surface Temp
o Inside Wall Temp
O Bulk Fluid Temp
Saturation Temp
50C
O
0
40C
T 30C
E
-- - - - - - - -
---
-~
- - -
-
20C
~~88
100
C
0
5
10
15
20
Heat Flux (W/mm2
25
30
35
15 Temperature downstream vs. Heat Flux 23.12 bar 96. mg/s
500
O
Outside Surface Temp
o Inside Wall Temp
400
-
0
O
Bulk Fluid Temp
Saturation Temp
-
2 300
-- - - - - - -
--
---
0-20(
-
a)
<*
4
W0
0000O
100
X~'~X
OK>0
5
10
-
>~x ~
20
15
Heat Flux (W/mm2
25
30
Figure B.4: Calibration test at 24 bar, saturation T = 222 C
100
35
References
1: Lopata, J. B. "Characterization of Heat Transfer Rates in Supercritical Ethanol for
Micro-Rocket Engine Regenerative Cooling." S.M. Thesis, Massachusetts Institute
of Technology, 1998.
2: Lopata, J. B., 1998.
3: London, A. P. "Supercritical Fluids: Properties and Heat Transfer." 16.540 Term Project,
Massachusetts Institute of Technology, 1998.
4: Lopata, J. B., 1998.
5: Dally, J. W., Riley, W. F., McConell, K. G. Instrumentation for Engineering
Measurements, 2nd ed. John Wiley and Sons, Inc., 1993.
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1965.
7: Incorpera, F. P., DeWitt, D. P. Fundamentalsof Heat and Mass Transfer, 4th ed. John
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10: Lopata, J. B., 1998.
11: Lopata, J. B., 1998.
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15: Yamagata, K., 1972.
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17: Tanaka, H., 1971.
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19: Yamagata, K., 1972.
20: Koshizuka, S., 1995.
21: Tanaka, H., 1971.
101
22: Popov, V. N., Valueva, E. P. "Distinctive Features of Heat Exchange During Turbulent
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Energiya, Vol. 70, pp. 329-335, May 1991.
23: Valyuzhinich, M. A., Eroshenko, V. M., Kuznetsov, E. V. "Heat Transfer to Fluids at
Supercritical Pressure in the Entrance Region Under Conditions of Strong
Nonisothermicity." Teploenergetika, Vol. 32, pp. 64-66, 1985.
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Research, Vol. 17, pp. 21-26, March-April, 1985.
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28: Koshizuka, S., 1995.
29: Schnurr, N. M., Sastry, V. S., Shapiro, A. B. "A Numerical Analysis of Heat Transfer
to Fluids Near the Thermodynamic Critical Point Including the Thermal Entrance
Region." Journal of Heat Transfer, pp. 609-615, November 1976.
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31: Swenson, H. S., 1965.
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33: Schnurr, N. M., 1976.
102