an experimental study of heat transfer coefficients and ...336859/fulltext.pdf · ef = enhancement...
Post on 22-Jul-2020
7 Views
Preview:
TRANSCRIPT
An Experimental Study of Heat Transfer Coefficients and
Friction Factors in Airfoil Leading Edge Cooling Cavities
Roughened with Slanted Ribs
A Thesis Presented
By
Benjamin S. Tom
To
The Department of Mechanical and Industrial Engineering
in partial fulfillment of the requirements
for the degree of
Master of Science
In
Mechanical Engineering
Northeastern University
Boston, Massachusetts
June 2014
2
Table of Contents
Nomenclature ......................................................................................................................................... 6
Abstract .................................................................................................................................................. 9
Introduction ............................................................................................................................................ 9
Theory ................................................................................................................................................... 13
Test Environment .................................................................................................................................. 17
Test Section ....................................................................................................................................... 17
Rig 1 .............................................................................................................................................. 18
Rig 2 .............................................................................................................................................. 20
Rig 3A ............................................................................................................................................ 20
Rig 3B ............................................................................................................................................ 21
Turbulator Geometry ......................................................................................................................... 21
Heater Arrangement .......................................................................................................................... 24
Source Pressure Network .................................................................................................................. 26
The Plenum ....................................................................................................................................... 27
Power Source .................................................................................................................................... 28
Test Procedure ...................................................................................................................................... 28
Liquid Crystal Calibration ................................................................................................................... 28
Cold and Heat Transfer Tests ............................................................................................................. 29
Cold Test Procedure .......................................................................................................................... 29
Heat Transfer Test Procedure ............................................................................................................ 30
Data Post-Processing Procedure ............................................................................................................ 30
Image Processing ............................................................................................................................... 30
FORTRAN Code: Determining Average Nusselt Number, Friction Factor, and Enhancement Factor .... 32
Results and Discussion ........................................................................................................................... 32
Test Rig 1 ........................................................................................................................................... 32
Test Rig 2 ........................................................................................................................................... 38
Test Rig 3A......................................................................................................................................... 43
Test Rig 3B ......................................................................................................................................... 48
Comparative Study: Rigs 1, 2, 3A, and 3B ........................................................................................... 52
Conclusions ........................................................................................................................................... 70
References ............................................................................................................................................ 71
3
Appendix A.1: FORTRAN Code for Rig 1 ................................................................................................. 73
Check.f File ........................................................................................................................................ 73
Reduce.F File ..................................................................................................................................... 76
Rig1-reduce-friction.f File .................................................................................................................. 97
Appendix A.2: FORTRAN Codes for Rig 2 .............................................................................................. 118
Check.F ............................................................................................................................................ 118
Reduce.F ......................................................................................................................................... 120
Rig2-reduce-friction.f ....................................................................................................................... 150
Appendix A.3: FORTRAN Codes for Rig 3A ............................................................................................ 158
Check.f ............................................................................................................................................ 158
Rig3a-Reduce-Heat-Transfer.f .......................................................................................................... 160
Rig3a-reduce-friction.f ..................................................................................................................... 191
Appendix A.4: FORTRAN Codes for Rig 3B ............................................................................................ 199
Reduce.f .......................................................................................................................................... 199
Rig3b-Reduce-Heat-Transfer.f.......................................................................................................... 201
Rig3b-reduce-friction.f ..................................................................................................................... 232
Appendix B.1: Rig 1 Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal
Performance) ...................................................................................................................................... 240
Appendix B.2: Rig 2 Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal
Performance) ...................................................................................................................................... 242
Appendix B.3: Rig 3A Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal
Performance) ...................................................................................................................................... 244
Appendix B.4: Rig 3B Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal
Performance) ...................................................................................................................................... 246
4
Table of Figures
Figure 1: High Bypass Turbofan Jet Engine and Turbine Blade [16], [17] ................................................. 10
Figure 2: Thermal Resistance Network (Rig 1) ........................................................................................ 15
Figure 3: Test Section Experimental Setup ............................................................................................. 18
Figure 4: Cross-Section of Test Section 1 ................................................................................................ 19
Figure 5: Layers of Material on Fiberglass Wall ...................................................................................... 19
Figure 6: Cross Section of Test Section 2 ................................................................................................ 20
Figure 7: Cross Section of Test Section 3A .............................................................................................. 20
Figure 8: Cross Section of Test Section 3B .............................................................................................. 21
Figure 9: Staggered 45° Turbulator Arrangement on Sidewalls............................................................... 22
Figure 10: Heater Arrangement for Test Rig 1 ........................................................................................ 25
Figure 11: Heater Arrangement for Test Rig 2 ........................................................................................ 25
Figure 12: Heater Arrangement for Test Rig 3A ...................................................................................... 26
Figure 13: Heater Arrangement for Test Rig 3B ...................................................................................... 26
Figure 14: Parallel Network of Pressure Pipes in Laboratory .................................................................. 27
Figure 15: Plenum Structure .................................................................................................................. 27
Figure 16: Multi-Channel Power Source ................................................................................................. 28
Figure 17: Liquid Crystal Calibration ....................................................................................................... 29
Figure 18: Example of image taken by camera of the backwall and nose surfaces used for image
processing ............................................................................................................................................. 31
Figure 19: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall) ......................................................... 33
Figure 20: Rig 1 Nusselt Number Vs Reynolds Number (Nose)................................................................ 34
Figure 21: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) ........................................... 35
Figure 22: Rig 1 Enhancement Factor Vs. Reynolds Number (Backwall) .................................................. 36
Figure 23: Rig 1 Enhancement Factor Vs. Reynolds Number (Nose)........................................................ 37
Figure 24: Rig 1 Friction Factor Vs. Reynolds Number ............................................................................ 38
Figure 25: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall) ......................................................... 39
Figure 26: Rig 2 Nusselt Number Vs. Reynolds Number (Nose) ............................................................... 40
Figure 27: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) ........................................... 41
Figure 28: Rig 2 Enhancement Factor Vs. Reynolds Number (Backwall) .................................................. 42
Figure 29: Rig 2 Enhancement Factor Vs. Reynolds Number (Nose)........................................................ 42
Figure 30: Rig 2 Friction Factor Vs. Reynolds Number ............................................................................ 43
Figure 31: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall) ....................................................... 44
Figure 32: Rig 3A Nusselt Number Vs. Reynolds Number (Nose) ............................................................ 45
Figure 33: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) ........................................ 46
Figure 34: Rig 3A Enhancement Factor Vs. Reynolds Number (Backwall) ................................................ 47
Figure 35: Rig 3A Enhancement Factor Vs. Reynolds Number (Nose) ..................................................... 47
Figure 36: Rig 3A Friction Factor Vs. Reynolds Number .......................................................................... 48
Figure 37: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall) ....................................................... 49
Figure 38: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)......................................... 50
Figure 39: Rig 3B Enhancement Vs. Reynolds Number (Backwall) .......................................................... 51
5
Figure 40: Rig 3B Friction Factor Vs. Reynolds Number .......................................................................... 52
Figure 41: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall) ............. 54
Figure 42: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose) ................... 56
Figure 43: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall) ...... 58
Figure 44: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose) ............ 59
Figure 45: Friction Factor Vs Reynolds Number for All Rigs at All Blockage Ratios .................................. 61
Figure 46: Thermal Performance of All Four Test Sections at Backwall at All Blockage Ratios ................. 63
Figure 47: Thermal Performance of All Four Test Sections at Nose at All Blockage Ratios ....................... 65
Figure 48: Rig 1 Thermal Performance Vs. Re (Backwall and Nose) ........................................................ 66
Figure 49: Rig 2 Thermal Performance Vs. Re (Backwall and Nose) ........................................................ 67
Figure 50: Rig 3A Thermal Performance Vs. Re (Backwall and Nose) ...................................................... 68
Figure 51: Rig 3B Thermal Performance vs. Re (Backwall and Nose) ....................................................... 69
6
Nomenclature
������ = Cross-section area of the test section
������ = Heater area
�� = Venturi throat cross-sectional area
� = Specific heat at constant pressure
��= Hydraulic diameter
e = Turbulator height
� � = Blockage ratio
EF = Enhancement factor
� ̅���� = Darcy friction factor
��̅���� = Smooth wall friction factor
�� = Proportionality Constant in Newton’s 2nd Law (32.2 �����������)
h = Heat transfer coefficient
ℎ�= Heat transfer coefficient of air at ambient temperature
!= Current applied to heater “i”
"���,�!� = Thermal conductivity of air at ambient conditions
$����� = Length of the heater
Nu = Nusselt number for roughened surface
%&� = Nusselt number for smooth wall
'(�� = Number of turbulators
P = Perimeter of test section
)��� = Ambient pressure
)!*�� = Inlet pressure to test section
)+�* = Venturi pressure
7
Pr = Prandtl number
,-���. = Heat transfer rate from the heater to the ambient air at middle of test section
,-���* = Heat transfer rate from heater to the heated wall surface within leading edge cavity
,-!* = Incoming heat transfer rate from heaters
,-������ = Heat transfer rate of losses
,-�!//�� = Heat transfer rate at middle of test section at camera location
,-*��� = Heat transfer rate at nose
,0! = Heat flux emitted by surface “i”
,0!* = Incoming heat flux
,0������ = Heat flux losses
Re = Reynolds number
1! = Resistance value of material designated by “i”
S = Turbulator pitch (spacing from center of one rib to next)
�� = Turbulator pitch to Turbulator height ratio
23 = Heated wall surface for radiation calculation
24 = Top wall surface for radiation calculation
25 = View wall surface for radiation calculation
26 = Nose projected surface for radiation calculation
7����� = Temperature of the heater
7!* = Average inlet temperature to the test section
7!*3 = Temperature measured by thermocouple #1 at inlet to the test section
7!*4 = Temperature measured by thermocouple #2 at inlet to the test section
7�!8(!/ = Liquid crystal temperature
7���* = Mean temperature at middle of test section (at camera location)
7+�* = Venturi temperature
8
TP = Thermal performance
7�(�� = Surface temperature at surface of heated wall at middle of test section
9! = Voltage applied to heater “i”
9� = Flow mean velocity
μ = Air dynamic viscosity
ρ = Density of air
9
Abstract
In turbine blade design, the use of turbulators in airfoil cavities has been a preferred means to cool the
metal temperatures within the airfoil. Temperatures in the turbine section of a jet engine can easily
reach beyond material temperature capability limits and without any internal cooling, the turbine blades
will begin to creep and eventually lead to engine failure. The introduction of turbulators has provided a
means to increase the heat transfer coefficient within the airfoil cavities and help promote turbulence
and better mixing to facilitate convective cooling. In this study, 4 different test rigs were experimented
upon with each test rig assessing 3 different turbulator blockage ratios (e/Dh). Each test section’s cross
section was based on leading edge cavity geometry scaled up from a “real-life” airfoil. Turbulators were
placed along the backwall and also along the leading edge nose. The backwall turbulators had rounded
corners and staggered, and were placed 45° along the surface of the wall. The nose turbulators also had
rounded corners and staggered, but, unlike the wall turbulators, were placed at 90° along the nose
surface. To determine the reference temperature of the measured wall and nose surfaces, liquid crystals
were used. The liquid crystals were laid on top of the wall and nose surfaces on one wall of the test
section. Electric foil heaters were placed beneath the liquid crystals to simulate a heated wall boundary
condition. The remaining walls were insulated from the environment to simulate adiabatic conditions.
For this study, the heat transfer coefficient, friction factors, enhancement factors, and thermal
performance were calculated based on experimental data collected on the backwall and nose surfaces.
Upon conclusion of this study, it was found that: (a) Rig 1 has the highest thermal performance at the
nose at all blockage ratios. Rig 3A has the highest thermal performance at the backwall at low and high
blockage ratios. (b) Rig 1 had the highest friction factor across the range of Reynolds Numbers. Rig 2 had
the lowest. (c) As the blockage ratio increased, so did the heat transfer coefficient and friction factors. It
was noted, however, in some cases, that as the blockage ratio increased to the maximum blockage the
heat transfer benefit was reduced. (d) The turbulator spacing was suggested to have a potential impact
on the overall heat transfer coefficient as demonstrated by looking at the results between rigs 2 and 3A
and 3B. (e) To validate the test results and trends seen from this experiment, it is recommended that a
CFD analysis be performed on each test section.
Introduction
The use of turbulators in turbine airfoils has been the preferred means of cooling the airfoil metal
temperatures to achieve the design part life. In jet engine design, the leading edge of an airfoil can be
the life limiting location due to high thermal stress. Figure 1 below shows a picture of a high bypass ratio
turbofan jet engine and highlights where in the engine, turbine airfoils are generally located.
10
Figure 1: High Bypass Turbofan Jet Engine and Turbine Blade [16], [17]
As shown in Figure 1, the turbine airfoils are downstream of the combustor module and thus, are
exposed to the extremely high temperatures in the flowpath. To reduce the metal temperature along
the airfoil’s internal walls, it is necessary to provide a means of convectively cooling the internal
passages of an airfoil. This is where the use of turbulators is effective. Turbulators are used to help
facilitate turbulence and enhanced mixing within the internal cavities of the airfoil by “tripping” the
flow. Tripping the flow enhances mixing and the heat transfer coefficient to facilitate heat transfer from
the hot wall to the cooling flow.
Taslim and Lengkong [1] studied the heat transfer coefficient on the surfaces of 45 degree angled ribs
with sharp and rounded corners within a square channel. A comparison was also done to look at the
heat transfer effectiveness of 45 degree vs 90 degree angled turbulators. Taslim and Lengkong
investigated into 3 different blockage ratios (� �) of 0.133, 0.167, and 0.25 and for rib pitch-to-height
ratios (S/e) of 5, 8.5, and 10. The experiment involved measuring the average temperatures on an
electric heated copper rib upstream and midstream location. It was concluded that sharp cornered
turbulators produced higher heat transfer coefficient. In addition, 45° turbulators proved more
beneficial from heat transfer standpoint at smaller blockage ratio. Moreover, Taslim and Lengkong also
showed that small rib pitch to height ratios led to lower thermal performance.
Domaschke et al [2] performed experiments looking at the heat transfer coefficient and pressure drop
measurement for leading edge geometry consisting of both smooth and rib roughened channels.
Staggered 45° angled turbulators were placed on suction and pressure backwalls with constant pitch and
blockage ratio for Reynolds numbers between 20,000 and 50,000. Using the Transient Liquid Crystal
Method, originally developed by Ireland and Jones, Domaschke et al showed that introducing
turbulators increased the local heat transfer at the walls and at the leading edge. The pressure and
suction backwalls showed an increase up to 350%, while the leading edge only showed a 1.5x increase
11
over the smooth wall. The maximum local heat transfer was seen behind the turbulators away from the
leading edge. Overall thermal performance increased with the introduction of the turbulators, but
decreased with increasing Reynolds Numbers.
Rallabandi et al [3] looked at the heat transfer coefficients and frictions factors for a square channel with
45° round-edged ribs at high Reynolds Numbers for land-based gas turbine applications. They looked at
various high blockage ratios and pitch for Reynolds Numbers ranging from 30,000 to 400,000. Using
copper plates and thermocouples, Rallabandi et al found that larger blockage ratios and smaller rib pitch
led to a higher heat transfer coefficient, but also higher pressure drop. Also, increasing the number of
ribs increased the surface area, which enhanced the heat transfer coefficient. In terms of the friction
factor, Rallabandi et al saw that the rounded edge ribs had lower friction factors than that of the sharp
edged ribs.
Lau et al [4] also looked at turbulent heat transfer and friction in a square channel with discrete
turbulator configurations for two rib to pitch ratios and various angles of attack for Reynolds Number of
10,000 to 80,000. Using brass ribs and heated walls, Lau et al determined the Stanton Number and
friction factors for the different rib configurations. Lau et al concluded that the 90° discrete rib case had
about 10-15% higher average Stanton Number than the 90° transverse rib case and that turning the ribs
in the same direction of the core flow increased it further by another 10-20%. Moreover, the thermal
performances of the parallel oblique ribs with 30°, 45°, and 60°angle of attack was about 20% higher
than the 90° discrete rib configuration. The crossed oblique discrete ribs performed the poorest.
Some other works in the field of turbulator heat transfer for 90° ribs included Dees et al [5]. Dees et al
conducted experiments in a closed loop wind tunnel using a “three-vane, two passage cascade” test
section. Rib turbulators were placed within the test airfoil section, which included two different types of
passages; one being of u-bend shape and the other just a straight radial passage. Dees et al concluded
that rib turbulators increased the overall heat transfer effectiveness in both u-bend and radial channels,
with the ribbed radial channel showing between 40-50% increase in effectiveness. Dees et al also
compared the experimental results to their CFD analysis, and concluded that the CFD analysis under
predicted the overall effectiveness, but the trends were similar.
In addition to square channels, there also have been experiments performed on triangular leading edge
shaped channels. Liu et al [6] investigated internal cooling of a triangular channel with 45° angled ribs at
high rotation numbers for P/e = 8 and e/Dh = 0.087. Reynolds numbers ranged from 10,000 to 40,000
and the rotational speeds ranged from 0-400 RPM. They concluded that in a rotational channel, the
trailing edge had higher heat transfer coefficient, while in a stationary channel, the leading edge had a
higher heat transfer coefficient.
Luo et al [7] also investigated into triangular ducts with ribbed internal surfaces for blockage ratios of
0.11 to 0.21, and rib spacing to rib height ratios of 3.41 to 13.93 for Reynolds number range of 4,000 to
23,000. The test section was uniformly heated using electrically heated nichrome wire around the
triangular duct and temperatures and pressures were taken using thermocouples and pressure taps
along the axial length of the test section. Luo et al concluded that blockage ratio of 0.18 provided the
12
maximum forced convection and pressure drop increased with blockage ratio. In addition, a rib to rib
spacing of 7.22 provided the best thermal performance.
Taslim and Bethka [8] looked at impingement on the leading edge of an airfoil with axial cross flow. The
experiment measured the heat transfer impact for a range of axial to jet mass flow rates of 1.4 to 6.4
and jet Reynolds Numbers from 8,000 to 48,000. Two types of inlet flows were tested; one in the same
direction as the crossflow and one in the opposite direction of the crossflow. Using copper plates and
thermocouples to measure the local temperature, Taslim et Bethka concluded that (1) For both inlet
flow configurations, the sidewall showed a higher heat transfer coefficient than the leading edge nose.
(2) The heat transfer coefficient for impinging jets with crossflow is less than that of impinging jets
without crossflow.
Bunker and Metzger [9] also performed some studies looking at local heat transfer at airfoil leading edge
with impingement cooling without film cooling extraction. Thin temperature coating was sprayed at the
leading edge and variations in jet Reynolds Number, airfoil leading edge sharpness, jet pitch-to-diameter
ratios, and jet nozzle –to-apex travel distances were tested. 4 different types of airfoils were used with
radius of curvature of 0 (sharp edge), 0.2, 0.4, and 1.0. Pitch-to-jet diameter ratios of 4.67, 3.33, and 0
were tested. Jet nozzle-to-airfoil apex distance to width of slot jet ratios of 18, 24, 30, 36, and 42 were
also tested. Experimental results showed that (1) as the pitch to jet nozzle diameter ratio decreases, the
leading edge heat transfer increased, but severely degrades at pitch to jet nozzle diameter ratio of 0. (2)
Heat transfer at the leading edge apex is increased as the nose radius is increased from 0 to 1.
Bunker and Metzger [10] as a follow-up experiment looked at the local heat transfer at airfoil leading
edge with impingement cooling and film cooling extraction. Similar, to the setup described in the
experiment without film cooling extraction, the only difference was that two rows of bleed holes were
added at +/-45° from the apex centerline for film cooling extraction. Cases were the bleed holes were
directly in-line and out of phase with the impingement jet hole were assessed to determine any
differences in heat transfer performance. Bunker et Metzger concluded that the level of heat transfer
was mainly affected by the impinging jets and secondarily by the amount of bleed air. When the bleed
holes were in-line with the jet holes, the local heat transfer coefficient increased by as much as 50%.
When the bleed holes were 180° out of phase with the impingement jets, the local heat transfer
coefficient decreased. Thus, observations showed that alignment of the bleed holes relative to the jet
holes played an important factor in the local heat transfer coefficient.
Different shaped turbulators and bumps have also been investigated to see what shape turbulator or
bump will provide the optimal thermal performance. Taslim et al [11] investigated into convective heat
transfer coefficient of impingement for 4 different typed surfaces on the leading edge of a channel. The
four different types of surfaces included smooth wall, finely roughened wall, conical surface bumps, and
longitudinal ribs. One sided and two sided inflow, and two sided outflow, crossflow, and one sided
outflow were considered. Thermocouples were embedded into brass test plates that simulated the
backwalls and the nose to measure the surface temperatures. Conclusions showed that (1) crossflow
had a strong impact on the heat transfer coefficient and reduced the heat transfer at the leading edge.
13
(2) The conical shaped bumps proved to be most beneficial out of all the types of surfaces and improved
the heat transfer by 40 percent.
Moreover, Taslim et al [12] also looked at the heat transfer of 45° angled, V-shaped, and discrete ribs
using the liquid crystal methodology to determine surface temperatures. The conclusions of this study
entailed the following: (1) 45° and discrete ribs of lowest blockage had the best thermal performance,
while the 90° angled ribs performed the worst. (2) Low blockage ratio V-shaped ribs facing downstream
produced the highest heat transfer enhancement and friction factors. For all other blockage ratios, the
45° ribs showed the highest heat transfer enhancements with friction factors less than those of the V-
shaped ribs.
Besides looking at heat transfer for a ribbed surface, there have been also a lot of studies on other types
of cooling configurations. One such configuration is looking at heat transfer in a leading edge channel
with crossflow with jet impingment. A study was done by Andrei et al [13] to look at heat transfer of a
trapezoidal channel with racetrack holes and film cooling extraction. Using the thermochromic liquid
crystal method, Andrei et al determined the Nusselt Number for jet Re range of 10k to 40k along the
span of the leading edge. They concluded that the heat transfer coefficient peaks towards the tip of the
blade, where the ratio of jet to crossflow velocity is highest, and that Reynolds number plays a critical
factor in the heat transfer coefficient.
Building upon the works of those aforementioned, this paper will look at 45° staggered rounded corner
wall turbulators and 90° staggered rounded corner nose turbulators for 4 triangular shaped leading edge
test sections at 3 different blockage ratios. This experiment will only be concerned with measuring and
calculating the heat transfer and friction factor at the middle of the test section. Since, each test section
is slightly different from each other, the blockage ratios will be dependent on the hydraulic diameter of
the test section and will change with each test section, except rigs 3A and 3B. Rigs 3A and 3B are
essentially the same test section, but the measured backwall surface for rig 3A is opposite that of rig 3B.
This study will make observations on how the different test section and turbulator geometries impact
the heat transfer coefficient, friction factor of the channel, the enhancement factors at the backwall and
nose surfaces between the turbulators, and the overall thermal performance of each test section.
Theory
In this study, the four major parameters of interest are the Nusselt Number, friction factor,
enhancement factor, and the thermal performance. The Nusselt Number, enhancement factor, and
thermal performance can be determined by first defining the thermal resistance network within the
given system. In terms of the friction factor, there are two types of friction factors of concern. The first
being the Darcy Friction Factor and the second one being the smooth wall friction factor, which can be
expressed by the Dittus-Boelter correlation. This section will briefly explain the details and the main
equations used to determine the Nusselt Number, friction factor, enhancement factor, and the thermal
performance.
14
Before performing the heat transfer calculations, it is necessary to determine the characteristics of the
flow and the heat input into the system. This includes the mass flow rate, the inlet temperature and
pressure, the ambient temperature and pressure, and the upstream venturi temperature and pressure.
The mass flow rate can be determined by equation 1.1 for critical venturi.
:; = �.=43=>?��@ABC�DEFGH@AB (1.1)
Once the mass flow rate is known, the Reynolds Number can also be determined by equation 1.2 below.
1I = 6J@�K , where μ = viscosity of air and P = Test Section Perimeter (1.2)
The inlet temperature is the average of the measured inlet temperature readings from the two
thermocouples placed at the inlet to the test section in the plenum as denoted by equation 1.3 below
7!* = HLBMCHLB�4 (1.3)
In addition to the flow characteristics, the heat transfer rate generated by the heaters also needs to be
known to determine the heat transfer coefficient. To determine the heat transfer rate at the middle of
the test section, the measured voltage and amperage need to be known. The heat transfer rate at the
middle of the test section can be expressed by equation 1.4.
,-�!//�� = 3.413P93 3 +0.594 4T (1.4)
Now, since the input flow characteristics are known and the amount of heat input is calculated, the next
steps are to determine the heat losses due to the radiation, conduction, and convection.
To determine amount of heat loss to the environment, a thermal resistance network needs to be
constructed. Figure 2 shows the thermal resistance network for rig 1. Note this thermal resistance
system can be modified and applied to any of the four different test sections. For simplicity, test section
1 is chosen here to show the thermal resistance network due to its symmetrical nature.
Figure 2 below shows the thermal resistance network of the given system.
15
Figure 2: Thermal Resistance Network (Rig 1)
The thermal resistance network consists of the three different modes of heat transfer: conduction,
convection, and radiation. Conduction occurs in the layers between the leading edge cavity and outside
ambient air. Convection occurs only on the ambient surfaces of the test section walls. Radiation occurs
within the leading edge cavity.
To determine the rate at which heat is leaving the heater due to conduction, a thermal balance needs to
be performed per figure 2. This results in equation 1.5 and 1.6
,-���. = ,-*��� = PH�AD?AU�HVDEFTWFDXY (1.5)
,-���* = ZH�AD?AU�HV[\U]^W]U_B? (1.6)
Furthermore, the equations below indicate which elements compose the conductive resistance
network.
1�` = 1+!�a =1���b! + 1��*+ (1.7)
1���* = 0.51!*� Q1�/���!+�3 Q 1.�`�* Q 1�/���!+�4 Q 1����. Q 1�!8(!/ (1.8)
16
1���. = 0.51!*� +1�/���!+�3 + 1.�`�* + 1�/���!+�5 + 1�!���c���� + 1��*+ (1.9)
The convective resistance of air can be calculated at room temperature by equation 1.10 below
1��*+ = 3�d, where ℎ� = �.5e.
f (Osisik, 443) (1.10)
Where, k= Thermal conductivity of air at ambient temperature and $����� = Length of heater
The radiative resistance network is constructed under the assumption of a 4 sided enclosure. It is
important to note that for the nose, the wall projected from the actual nose surface is assumed to
absorb all the radiation emitted from the actual nose surface. This projected nose surface is represented
by a dashed line in Figure 2. This assumption helps to simplify the geometry of the test section for the
radiative heat transfer calculations. To calculate the radiation view factors in rig 1, we take advantage of
the symmetrical nature of the test section, and also use the view factor correlation for two
perpendicular rectangles with a common edge. This simplifies the problem and only view factors, F1-2
and F2-1 need to be calculated. The remaining view factors can be determined by assuming symmetry.
Once the fractions of radiation leaving the surface i is determined, equation 1.11 is used to determine
the radiative heat flux leaving surface i and radiated away to surfaces j
,0��/,!�g = hiLjLHk\U],Ll �imjmHk\U],ml n3�iL (1.11)
Then, an iterative scheme is used to guess the heat transfer coefficient and the temperatures at the top,
view wall, and the projected nose surface. This iterative scheme is run 30 times or until thermal
equilibrium is reached at both the top and front view walls (net heat transfer rate < .001). Using this
iterative scheme, the total heat loss from each surface can be determined. Knowing the amount of heat
loss, one can calculate the rate at which heat is lost at through each of the four surfaces (top, bottom,
front, and back). In addition, the mean temperature at the middle of the test section can also be
calculated by reducing the 1st Law of Thermodynamics to equation 1.12 below
P,-!* − ,-������T = :+`P7���* − 7�(��T (1.12)
Where 7�(�� =7�!8(!/ −,-���*1�����
Utilizing the mean temperature and the knowing the total heat loss, one can determine the heat
transfer coefficient at the wall using equation 1.13
ℎ = 80 LB�80 p_[[A[H[\U]�HEADB (1.13)
Then, the Nusselt Number at the roughened wall can be calculated using equation 1.14.
%& = P�TP �T.DLU,DEF (1.14)
17
To calculate the smooth wall Nusselt Number, the Dittus-Boelter correlation is used as expressed by
equation 1.15.
%&� = 0.0231I�.q)r�.6 (1.15)
Once the roughened and smooth wall Nusselt Numbers are known, the enhancement factor (EF) also
can be calculated using equation 1.16.
st = u(u(k (1.16)
To determine the thermal performance of a particular test configuration, it is necessary to know the
friction factor besides the enhancement factor. The Darcy and smooth wall friction factors can be
determined by equations 1.17 and 1.18. Equation 1.18 is called the Blasius Correlation.
� ̅���� = 4v� = �� wh �*?\UF�n h�LBpA?��DEF
�.=x;E� ny (1.17)
��̅���� = �.53eW�d.�z (1.18)
Where v�= Fanning Coefficient of Friction and ��= Proportionality Constant in Newton’s 2nd Law
h32.2 ����������� n.
Lastly, the thermal performance (TP) of the system can be determined using equations 1.16, 1.17, and
1.18 and can be expressed by equation 1.19.
7) = {|w ]}~DUX�]}kE__?�y
M/� (1.19)
The calculations and general equations in this section can be applied for the other test sections as well.
The only differences are in the input flow characteristics and the test section geometry, which are
unique to each test configuration.
Test Environment
Test Section
The experimental setup consisted of multiple parts. Figure 3 below shows the individual parts that
comprise together to make up the entire test section.
18
Figure 3: Test Section Experimental Setup
The flow enters the plenum from the venturi network through a 1 ¼” pipe. Once in the plenum, the flow
goes through a flow straightener, which makes the flow uniform prior to entering the actual test section.
The test section is insulated all around with the exception of the front and top viewing windows, which
are transparent to capture images of the liquid crystal surfaces on the heated backwall and nose. The
flow then finally exits out of the test section into atmospheric conditions. Supports are used to hold up
the test section relieving the bending stress created by hanging it off of the plenum forward face. There
are also two cameras set up to take pictures of the liquid crystal color at the backwall and nose section.
The cameras are focused near the center of the test section at one particular section between two
consecutive backwall turbulators.
Rig 1
The cross sectional area of test section 1 is shown below in Figure 4.
19
Figure 4: Cross-Section of Test Section 1
Test section 1 is composed of two “see-through” plexi-glass wall and a fiberglass wall. One of the plexi-
glass walls is positioned directly facing the backwall with the liquid crystal and the other one is
positioned at the top wall directly over the nose. They are “see-through”, so pictures of the liquid crystal
can be taken with a camera normal to the surface of the nose and sidewall. The sidewall and nose
sections, where the liquid crystal, are located are made of fiberglass. On the backside of the fiberglass,
polyurethane foam is sprayed to provide insulation and prevent heat loss to the environment from the
backside. Figure 5 below shows, in general, the different layers that compose the fiberglass backwall and
nose sections.
Figure 5: Layers of Material on Fiberglass Wall
On the front side of the fiberglass wall sits the heaters. They span across the length of the test section.
On top of the heaters is the layer of liquid crystal. It also spans across the entire length of the channel. It
is important to keep the temperature of the heater below the melting temperature of the liquid crystal,
otherwise, the liquid crystal will be damaged. Thus, whenever the heaters are on, cooling air should
always be flowing through the channel.
20
Rig 2
Figure 6 below shows the general composition of test section 2. Unlike test section 1, test section 2 is
slightly asymmetric, however, the composition of test section 2 is same as test section 1.
Figure 6: Cross Section of Test Section 2
Rig 3A
Figure 7 below shows the composition of test section 3A. Only notable difference between test sections
1,2, and 3A is the cross sectional area.
Figure 7: Cross Section of Test Section 3A
21
Rig 3B
Figure 8 below shows the composition of test section 3B. In terms of geometry, test sections 3A and 3B
are exactly the same. Test Section 3B is different from 3A in that 3B examines the heat transfer in what
is 3A’s plexiglass sidewall and fiberglass nose.
Figure 8: Cross Section of Test Section 3B
Turbulator Geometry
The wall turbulator geometry for all four test sections are staggered one after the other on opposing
walls with an angle of attack of 45° and pointing away from inflow as shown in Figure 9 below. The nose
turbulators, however, are staggered and 90° to the flow.
22
Figure 9: Staggered 45° Turbulator Arrangement on Sidewalls
This study investigated into four different test sections. In this paper, they are designated as rigs 1,2, 3A,
and 3B. All the rigs had different cross sectional areas, except for 3A and 3B, which had the same cross
sectional areas and were basically mirror images of each other. Table 1 below outlines the test points
and turbulator geometry for rig 1.
Test Re Rib Angle (°) S/e e/Dh
1 6000 45 14.588 0.114
23
2 10000 45 14.588 0.114
3 15000 45 14.588 0.114
4 20000 45 14.588 0.114
5 30000 45 14.588 0.114
6 40000 45 14.588 0.114
7 6000 45 11.698 0.142
8 10000 45 11.698 0.142
9 15000 45 11.698 0.142
10 20000 45 11.698 0.142
11 30000 45 11.698 0.142
12 40000 45 11.698 0.142
13 6000 45 9.738 0.171
14 10000 45 9.738 0.171
15 15000 45 9.738 0.171
16 20000 45 9.738 0.171
17 30000 45 9.738 0.171
18 40000 45 9.738 0.171
Table 1: Test Points and Turbulator Specifications for Rig 1
Likewise, Table 2 below outlines the test points and turbulator geometry for rig 2.
Test Re Rib Angle (°) S/e e/Dh
1 6000 45 12.400 0.067
2 10000 45 12.400 0.067
3 15000 45 12.400 0.067
4 20000 45 12.400 0.067
5 30000 45 12.400 0.067
6 40000 45 12.400 0.067
7 6000 45 9.951 0.084
8 10000 45 9.951 0.084
9 15000 45 9.951 0.084
10 20000 45 9.951 0.084
11 30000 45 9.951 0.084
12 40000 45 9.951 0.084
13 6000 45 8.281 0.101
14 10000 45 8.281 0.101
15 15000 45 8.281 0.101
16 20000 45 8.281 0.101
17 30000 45 8.281 0.101
18 40000 45 8.281 0.101
Table 2: Test Points and Turbulator Specifications for Rig 2
24
Lastly, Table 3 outlines the test points and turbulator geometries for rig 3A and 3B.
Test Re Rib Angle (°) S/e e/Dh
1 6000 45 12.400 0.051
2 10000 45 12.400 0.051
3 15000 45 12.400 0.051
4 20000 45 12.400 0.051
5 30000 45 12.400 0.051
6 40000 45 12.400 0.051
7 6000 45 9.920 0.063
8 10000 45 9.920 0.063
9 15000 45 9.920 0.063
10 20000 45 9.920 0.063
11 30000 45 9.920 0.063
12 40000 45 9.920 0.063
13 6000 45 8.267 0.076
14 10000 45 8.267 0.076
15 15000 45 8.267 0.076
16 20000 45 8.267 0.076
17 30000 45 8.267 0.076
18 40000 45 8.267 0.076
Table 3: Test Points and Turbulator Specifications for Rig 3A and 3B
For all the test sections, it can be seen from tables 1, 2, and 3 that the non-variable elements of the
experiments are the Reynolds Number and the rib angle. The variable elements between each test
section are the pitch or turbulator spacing, rib height, and the cross sectional areas of the test sections
themselves. By carefully observing and comparing the turbulator specifications in tables 1, 2, and 3, it
can be deduced that rig 1 will have the highest blockage ratio (e/Dh) and pitch to rib height ratio (S/e)
out of all the test sections. Rig 2 has the next highest blockage ratio and pitch to rib height ratios and
Rigs 3A and 3B have the lowest. Higher blockage ratios usually result in higher heat transfer coefficients,
however, from previous studies by Taslim and Lengkong (1999), it can be shown that too high of a
blockage ratio can also lead to a decrease in thermal performance due to higher pressure drop.
Heater Arrangement
For each of the 4 test rigs, the heater sizes are chosen based on the sidewall and nose geometries.
Figure 10 below depicts the heater arrangement and sizes for test rig 1:
25
Figure 10: Heater Arrangement for Test Rig 1
For test rig 1, the test section is broken up into 3 equal parts, an inlet, middle, and exit section. A
separate heater is used for each section, and each heater is large enough in width to cover both the
sidewall and nose segments. The use of a single heater for each section is recommended to facilitate in
the amount of heat flux applied to both the sidewalls and nose segments. If 2 separate heaters were
used, the amount of voltage applied to each heater would need to be adjusted to account for the
different heater areas.
Figure 11 below depicts the heater arrangement for test rig 2:
Figure 11: Heater Arrangement for Test Rig 2
The heater arrangement for test rig 2 is different than test rig 1. The most apparent difference is in the
number of heaters used. Unlike test rig 1, test rig 2 has a separate heater for the wall and the nose. The
main reason for using 2 separate heaters is that the heaters only come in certain standard sizes, which
would not be large enough to cover both the wall and nose segments alone. Thus, to facilitate the
application of a constant heat flux across the wall and nose heaters, respectively, three 3”x11” size
heaters were chosen for the wall sections and three 2”x11” heaters were chosen for the nose sections.
It is important to note that since the wall and nose heaters are of different areas, the power applied to
the nose heaters must be a certain amount less than that of the wall heaters in order to output the
same heat flux as the wall heaters.
26
Figure 12 below depicts the heater arrangement for test rig 3A:
Figure 12: Heater Arrangement for Test Rig 3A
For test rig 3A, the heater arrangement is similar to rig 2. Separate heaters are used for each of the wall
and nose sections. They are of equal areas in order to facilitate the application of constant heat across
all the wall and nose sections.
Figure 13 below depicts the heater arrangement for test rig 3B:
Figure 13: Heater Arrangement for Test Rig 3B
The heater arrangement for test rig 3B is similar to rigs 2 and 3A. Some of the notable difference is in
the outlet wall and nose sections of the test section. In the outlet section, there is no nose heater. The
reason for no nose heater in the outlet section is that at the time of the experiment, a 2”x11” heater
was not available. In the absence of a 2”x11” heater, a 3”x11” heater was used to replace it.
Source Pressure Network
The source pressure is generated by a compressor in the mechanical room outside the laboratory. It is
then fed through an air tank which acts as a temporary air storage unit for excess air as it is discharged
and routed to the laboratory for usage. Once the air reaches the laboratory, it enters through a
regulator valve, which controls the amount of air entering the downstream pipe. In the lab, there is a
parallel network of pipes, but only one circuit is used at a time to feed the air downstream towards the
test rig as depicted in Figure 14 below:
27
Figure 14: Parallel Network of Pressure Pipes in Laboratory
Before the air enters the test rig, it is further regulated by a nozzle venturi of a specific diameter. For this
experiment, the two venturi nozzle diameters used were Ø.225” and Ø.320. These specific diameter
venturis were used mainly because they covered the range of Reynolds Number in concern for this
experiment. There are also drain valves at the bottom right and left of the pressure network as depicted
in Figure 14 to facilitate the draining of any additional moisture and condensation. In addition, there is
also a cold water cooling system in place to help cool the passing air during hot and humid days. It is
recommended the air temperature in the system remain relatively cool to the ambient temperature in
the room, because the temperature affects the pressure measured in the system, which in turns impacts
the friction factor calculations.
The Plenum
Figure 15 below shows the general setup of the plenum.
Figure 15: Plenum Structure
28
The plenum is the section of the test rig in between the pressure source and the actual test section. The
plenum is a six-sided enclosure composed of 6 plexi-glass see-thru walls. It is tightened down by bolts at
all interfaces and is sealed up using silicon. The air is supplied to the plenum equally from the left and
right sidewalls of the plenum as shown in Figure 3 by PVC tubes. Once in the plenum, the air is then
straightened and filtered through a honeycomb “diffuser” or “straightener”. After the air has been
filtered and straightened, it then enters the inlet of the test section.
Power Source
A multi-channel power source was used to provide current to the foil heaters within the test sections.
Each heater was connected to a separate channel and two voltmeters were used to measure the voltage
and current through each channel. There were two different types of dials on the power source. One
was the master dial, which controlled all the channels. The second was the “fine tuning” dial, which
varied the voltage at much finer resolution, and only controlled a particular channel. In cases, where the
flux needed to be controlled individually for each heater, the “fine tuning” dial was used. Figure 16
below shows a picture of the multi-channel power source that was used for this experiment.
Figure 16: Multi-Channel Power Source
Test Procedure
Liquid Crystal Calibration
A liquid crystal calibration was performed to determine the reference temperature and color prior to
the start of any testing on any test section. The liquid crystal calibration is important, because the
reference temperature of the liquid crystal will be used to determine the surface temperature. Figure 17
below shows a still-image of liquid crystal calibration video. In the image, one can see that the
calibration is performed in a hot-water bath, and using a thermocouple probe, the temperature is
measured as the bath is cooled naturally by ambient air and “induced stirring”. The calibration is done
until the liquid crystal has turned from black to dark blue (very hot) and to black again (cool). During the
entire calibration, it is important to record the reference temperature at the reference color, which in
this case is green. Note there are different shades of green, so the color “green” is subjective to the
29
experimenter, but it is essential that the experimenter be consistent in determining the color “green”
throughout the image processing step for each test section.
Figure 17: Liquid Crystal Calibration
Cold and Heat Transfer Tests
Two different types of tests were performed for this experiment, heat transfer and cold tests. The cold
tests were done to determine the friction factor at ambient conditions without any effect from heated
wall conditions. Heat transfer tests were done to determine the heat transfer coefficient, enhancement
factors, and also the friction factor at heated wall condition.
Cold Test Procedure
For the cold test, venturi pressure, plenum pressure and temperature, and inlet and exit pressures of
the test sections were measured. The venturi pressures that were decided on encompassed the range of
Reynolds Numbers from the heat transfer tests, and data was taken at increments of 5 psi. In some
cases, two different venturis (Ø 0.225” and Ø 0.32”) needed to be used to cover the range of Reynolds
Numbers of interest. Below outlines the steps in performing the cold test to determine the cold friction
factor at ambient conditions:
1. Turn on the air compressor and wait 2 minutes for the air in the channel to come to equilibrium
2. Set the first test venturi pressure
3. Record the ambient temperature and pressure, venturi pressure and temperature, plenum
temperature, and inlet and exit pressures of the test section.
4. Go to next higher venturi pressure.
5. Repeat steps 3 and 4 until all Reynolds Numbers have been tested. Switch out venturi diameters
if necessary.
30
Heat Transfer Test Procedure
For the heat transfer tests, a range of Reynolds Numbers (Re~6000, 10000, 15000, 20000, 30000, 40000)
were covered. Venturi pressures were determined based on the Reynolds Numbers of concern and the
geometry of the test section. Below outlines the steps in performing the heat transfer tests to
determine the heat transfer coefficient:
1. Turn on the air compressor and set the first test venturi pressure.
2. Turn on the multi-channel power source to turn on the heaters.
3. Wait 5-10 min for thermal equilibrium to be reached within the test section
4. Set the minimum voltage to each heater until a hint of color is seen on liquid crystal at the
midstream wall and nose sections. Note the wall and nose sections liquid crystal may not start
to show color at the same time. If color is seen at either the backwall or nose section, set that as
the minimum voltage.
5. Run the voltage up to the maximum voltage until the nose and backwall liquid crystals are all
blue colored. Wait 1-2 min for the liquid crystal color to stabilize. Record this as your maximum
voltage.
6. Go back to the minimum voltage and wait for 5 minutes until thermal equilibrium is reached.
7. Record voltage and amperage for each heater, ambient temperature and pressure, venturi
pressure, plenum temperature and pressure, and inlet and exit pressure of the test section
8. Take a picture using a digital camera of the liquid crystal of the backwall and nose surfaces.
9. Increment the voltage to each heater using following rule of thumb:
a. Voltage increment = (max voltage – min voltage)/20
i. The voltage increment can be adjusted depending on how quickly the liquid
crystal seems to heat up
10. Repeat steps 7-9 until the liquid crystal on both the backwall and nose sections are all blue
colored.
11. Repeat steps 1-10 for all other venturi test pressures.
Data Post-Processing Procedure
Image Processing
Following the data collection, the next step is to process the data. One of the data processing steps is to
digitize the images collected during the test. Previously, it was noted that to determine the reference
temperature of the liquid crystal, a liquid crystal calibration needs to be done. This calibration
determines the reference temperature and color of the liquid crystal, which will be used for digitizing
the pictures. In this experiment, the color green is chosen as the reference color. Using an image
digitizing software tool called Sigma Scan, the image is processed to calculate the number of pixels that
31
the reference color green takes up in the area of the red box defined in
Figure 18 below. The red box defines one repeated segment of the entire test section or equivalent to
the pitch from the center of one turbulator to the next. The number of pixels is used to determine the
“weighted-average” Nusselt Number and heat transfer coefficient. This image digitization is repeated for
the nose as well as shown in the second picture in Figure 18.
Figure 18: Example of image taken by camera of the backwall and nose surfaces used for image processing
32
FORTRAN Code: Determining Average Nusselt Number, Friction Factor, and
Enhancement Factor
Three FORTRAN codes were used in the data processing. One was called the “Check.f” file, which read
the data input file and searched for any typos or errors. The second code was called the “Reduce.f” file.
The “Reduce.f” file processed the input file and calculated the heat transfer coefficient, Nusselt Number,
Enhancement Factors, and the friction factor at heated wall condition. The last code used was called
“Reduce-Friction.F”, which determined the cold friction factor at ambient conditions. Once all the
results were processed, the output was inputted into Microsoft Excel, which calculated a “weighted-
average” Nusselt Number, Friction Factor, and Enhancement Factor using the number of pixels
determined from the image processing.
Results and Discussion
The following results will be presented for rigs 1, 2, 3A, and 3B.
• Nusselt Number Vs. Reynolds Number (sidewall and nose sections) – Midstream location
• Enhancement Factor Vs. Reynolds Number (sidewall and nose sections) – Midstream location
• Friction Factor Vs. Reynolds Number
Test Rig 1
For test rig 1, there were 3 heaters; one for the inlet, the midsection, and the exit. Each heater spanned
across the wall and nose sections. The results that follow for all test sections are representative of the
midstream section backwall and nose sections. Figure 19 below shows a plot of Nusselt Number Vs.
Reynolds Number for the backwall for all three blockage ratios. The three blockage ratios are 0.114,
0.142, and 0.171.
33
Figure 19: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall)
Figure 19 shows that the Nusselt Number trends upwards with blockage ratio. There is some slight
variation in the data as indicated at the higher Reynolds Number cases, where the medium blockage
data point is nearly the same as the maximum blockage data point. The two Reynolds Numbers, where
this occurrence is seen is at Re ~20,000 and 30,000. Overall the data shows that as the height and width
of the turbulator increases, so does the Nusselt Number, which is as expected. The taller and wider the
turbulator, flow turbulence increases and thus, improving mixing and cooling due to convection at the
backwall.
Figure 20 below shows the Nusselt Number vs. Re plot at the nose for the 3 different blockages.
50.00
80.00
110.00
140.00
170.00
200.00
230.00
260.00
290.00
320.00
350.00
380.00
0 10000 20000 30000 40000 50000
Nu
Re
Rig 1 Nusselt Number Vs. Re (Backwall)
e/Dh = 0.114
e/Dh = 0.142
e/Dh = 0.171
34
Figure 20: Rig 1 Nusselt Number Vs Reynolds Number (Nose)
Similar to Figure 19, the Nusselt Number trends upwards with blockage ratio. The variation in Nusselt
Number between the different blockage ratios is very small. It can be seen that the medium blockage
data point is very close or in some cases exceeds the maximum blockage data point, as indicated at Re
~20000 and 30000. This may be due to some experimental variation at the higher Reynolds Number or
because, at higher Reynolds Number, the positive impact of higher turbulator blockage on Nusselt
Number is diminished. Overall, the Nusselt Number trends as expected, with the maximum blockage
ratio resulting in the most heat transfer benefit.
50.00
80.00
110.00
140.00
170.00
200.00
230.00
260.00
290.00
320.00
350.00
380.00
0 10000 20000 30000 40000 50000
Nu
Re
Rig 1 Nusselt Number Vs. Re (Nose)
e/Dh = 0.114
e/Dh = 0.142
e/Dh = 0.171
35
Figure 21: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)
Figure 21 plots rig 1 backwall and nose Nusselt Numbers together for all three blockage ratios and
shows the differences between the backwall and nose more clearly. The Nusselt Numbers for the nose
for all blockages are substantially higher than that of the backwall. At the lowest Reynolds Number of
approximately 6000, the nose Nusselt Number is about 38% to 43% higher than that of the backwall
depending on the blockage ratio. At the highest Reynolds Number of approximately 40,000, the nose
Nusselt Number is about 24% to 31% higher than that of the backwall depending on the blockage ratio.
Rig 1 turbulator configuration will be best suited for an airfoil design, where the leading edge is the life
limiting location and hottest area as determined by heat transfer analysis.
Figure 22 below shows the trend between the enhancement factor and the Reynolds Number at the
backwall.
50.00
80.00
110.00
140.00
170.00
200.00
230.00
260.00
290.00
320.00
350.00
380.00
0 10000 20000 30000 40000 50000
Nu
Re
Rig 1 Nusselt Number Vs. Re (Backwall Vs. Nose)
e/Dh = 0.114(backwall)
e/Dh = 0.142(backwall)
e/Dh = 0.171(backwall)
e/Dh = 0.114 (nose)
e/Dh = 0.142 (nose)
e/Dh = 0.171 (nose)
36
Figure 22: Rig 1 Enhancement Factor Vs. Reynolds Number (Backwall)
The enhancement factor is defined by eq. 1.16. The ratio of Nu to %&� indicates how much heat transfer
benefit the ribbed wall has over the smooth wall case. If EF > 1, then the test condition has a positive
heat transfer benefit and, if EF < 1, the test condition has a negative heat transfer benefit. In the case of
Rig #1, the EF on average will provide 3-3.5x benefit over a smooth wall channel, depending on the Re of
the flow. This conclusion further proves that the introduction of turbulators in a smooth channel
improves the heat transfer due to convection.
2.50
2.80
3.10
3.40
3.70
4.00
4.30
4.60
4.90
5.20
5.50
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
EF
Re
Rig 1 Enhancement Factor Vs. Re (Backwall)
e/Dh = 0.114
e/Dh = 0.142
e/Dh = 0.171
37
Figure 23 below shows the EF at the nose location for the 3 different blockage ratios at various Reynolds
Numbers.
Figure 23: Rig 1 Enhancement Factor Vs. Reynolds Number (Nose)
The EF trends as expected at the nose location. It can be seen that the nose has a higher EF than the
backwall. This results in a higher heat transfer benefit at the nose than the sidewall. On average the
nose will provide roughly 3.5 to 5 times higher heat transfer cooling over the smooth wall case,
depending on the Re of the flow. Thus, if a turbine airfoil design requires more cooling at the leading
edge nose than the sidewall, rig #1 configuration will be the ideal design to provide higher heat transfer
coefficient at the nose.
The experiment also looked at the Cold Friction Factor vs. Reynolds Number for test rig 1. Figure 24
below shows how the friction factor trends with Reynolds Number for the three different blockage
ratios.
2.50
2.80
3.10
3.40
3.70
4.00
4.30
4.60
4.90
5.20
5.50
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
EF
Re
Rig 1 Enhancement Factor Vs. Re (Nose)
e/Dh = 0.114
e/Dh = 0.142
e/Dh = 0.171
38
Figure 24: Rig 1 Friction Factor Vs. Reynolds Number
Figure 24 shows that the Darcy friction factor trends upwards with increasing turbulator size. Darcy
friction factor increases with blockage ratio, because pressure drop across the channel increases with
higher blockage. In addition, there seems to be linear relationship between blockage ratio and Darcy
Friction Factor. This is demonstrated by the fact that the friction factor increases by approximately the
same amount with each incremental change in the blockage ratio.
Test Rig 2
The next series of plots measure the heat transfer coefficient, friction factor, and enhancement
factors of test section 2. For rig 2, the 3 different blockage ratios considered are 0.067, 0.084, and 0.101.
Figure 25 below shows the backwall Nusselt Number for the 3 blockage ratios for a range of Reynolds
Numbers. Figure 20 highlights that the heat transfer coefficient increases with blockage ratio, however,
it can be seen that as the blockage ratio increases, the benefit of increasing the rib height does not
provide much more heat transfer benefit. Going from a blockage ratio of 0.067 to 0.084, the heat
transfer benefit is on average 11%, while going from a blockage ratio of 0.084 to 0.101, the benefit is
only on average 3%. This demonstrates that there is an optimal blockage ratio that provides the best
heat transfer coefficient and if the blockage ratio is too high, it will provide a detrimental or neutral
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10000 20000 30000 40000 50000
f
Re
Rig 1 Cold Friction Factor Vs. Re
e/Dh = .171 (Darcy)
e/Dh = .142 (Darcy)
e/Dh = .114 (Darcy)
e/Dh = .171 (Smooth)
e/Dh = .142 (Smooth)
e/Dh = .114 (Smooth)
39
effect. The detrimental or neutral effect to the heat transfer coefficient can be attributed to most likely
large recirculation or dead zones that develop at the bottom of the turbulators at higher blockage ratios.
These dead zones prevent the core flow from reattaching to the backwall thus, reducing the heat
transfer benefit due to convection in those areas.
Figure 25: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall)
Figure 26 below shows the Nusselt Number for the nose section at the 3 different blockage ratios for a
range of Reynolds Numbers. The trend for the nose section is similar to the backwall in that the Nusselt
Number trends upwards with blockage ratio. It can be deduced, similar to the backwall, that the benefit
of going from a blockage ratio of 0.067 to 0.084, there is greater heat transfer benefit than going from a
blockage ratio of 0.084 to 0.101. Once again, this suggests that if the blockage ratio increases too high, it
is possible that the heat transfer benefit will be reduced or neutralized.
25
50
75
100
125
150
175
200
225
250
0 5000 10000 15000 20000 25000 30000 35000 40000
Nu
Re
Rig 2 Nusselt Number Vs. Re (Backwall)
e/Dh = 0.067
e/Dh = 0.084
e/Dh = 0.101
40
Figure 26: Rig 2 Nusselt Number Vs. Reynolds Number (Nose)
Figure 27 below plots Rig 2 Nusselt Number Vs. Reynolds Number for both the backwall and the nose. By
observing the figure below, it can be seen that the backwall and nose Nusselt Numbers are very similar
across the range of Reynolds Numbers when comparing the same blockage ratio. When comparing the
backwall and the nose at the same blockage ratio, the differences in Nusselt Number across the range of
Reynolds Numbers are for a majority less than 10%. It is only at the highest blockage ratio does one see
a slightly higher Nusselt Number on the nose than on the backwall on average. The fact that the
backwall and nose have similar heat transfer across all blockage ratios, in reality, is beneficial to an
airfoil engineer. This is because, the casting die used to form the leading edge cavity will have a longer
usable life, since the engineer can now tolerate some minimal wear of the casting tooling without having
it impact aero and thermal performance of the airfoil significantly.
25
50
75
100
125
150
175
200
225
250
0 5000 10000 15000 20000 25000 30000 35000 40000
Nu
Re
Rig 2 Nusselt Number Vs Re (Nose)
e/Dh = 0.067
e/Dh = 0.084
e/Dh = 0.101
41
Figure 27: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)
Figure 28 and Figure 29 below highlight the enhancement factors for the backwall and nose sections. As
the blockage ratio increases, so does the enhancement factor. When comparing the backwall and nose
sections, the enhancement factor for the nose is higher than the backwall. At higher Re, however, it can
be seen that the difference in enhancement factor between the nose and the backwall is minimal,
whereas, at lower Re, the difference is more significant, anywhere from 3-10%. This can be attributed to
the tendency of eddies forming at higher Re directly underneath the turbulators leading to a reduction
in heat transfer enhancement.
25
50
75
100
125
150
175
200
225
250
0 5000 10000 15000 20000 25000 30000 35000 40000
Nu
Re
Rig 2 Nusselt Number Vs. Re (Backwall vs. Nose)
e/Dh = 0.067 (backwall)
e/Dh = 0.084 (backwall)
e/Dh = 0.101 (backwall)
e/Dh = 0.067 (nose)
e/Dh = 0.084 (nose)
e/Dh = 0.101 (nose)
42
Figure 28: Rig 2 Enhancement Factor Vs. Reynolds Number (Backwall)
Figure 29: Rig 2 Enhancement Factor Vs. Reynolds Number (Nose)
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
0 5000 10000 15000 20000 25000 30000 35000 40000
EF
Re
Rig 2 Enhancement Factor Vs. Re (Backwall)
e/Dh = 0.067
e/Dh = 0.084
e/Dh = 0.101
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
0 5000 10000 15000 20000 25000 30000 35000 40000
EF
Re
Rig 2 Enhancement Factor Vs. Re (Nose)
e/Dh = 0.067
e/Dh = 0.084
e/Dh = 0.101
43
Figure 30 is a plot of Cold Friction Factor vs. Re for the 3 different blockage ratios. Once again, similar to
rig 1, the Darcy friction factor trends upwards with blockage ratios. The Darcy friction factor for rig 2 is
less than that of rig 1, indicating the pressure loss across the channel is less for rig 2.
Figure 30: Rig 2 Friction Factor Vs. Reynolds Number
Test Rig 3A
The next series of plots measure the heat transfer coefficient, friction factor, and enhancement factors
of test section 3A. For rig 3A, the 3 different blockage ratios considered are 0.051, 0.063, and 0.076.
Figure 31 below shows the backwall Nusselt Number for the 3 blockage ratios for a range of Reynolds
Numbers. In general, an increase in blockage ratio would result in an increase in heat transfer
coefficient. As shown in figure 22, the Nusselt Number along the backwall does not vary much for
blockage ratios 0.051 and 0.063, but for blockage of 0.076, there is a much larger increase in heat
transfer coefficient. On average, the difference in Nusselt Number between blockage of 0.051 and 0.063
is 3.5%, whereas the average difference in Nusselt Number between blockage of 0.063 and 0.076 is
around 11%. It is suggested that the large blockage increases the heat transfer coefficient by creating
turbulence and enhancing mixing.
0
0.1
0.2
0.3
0.4
0.5
0 10000 20000 30000 40000 50000
f
Re
Rig 2 Cold Friction Factor Vs. Re
e/Dh = .101 (Darcy)
e/Dh = .084 (Darcy)
e/Dh = .067 (Darcy)
e/Dh = .101 (Smooth)
e/Dh = .084 (Smooth)
e/Dh = .067 (Smooth)
44
Figure 31: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall)
Figure 32 plots the Nusselt Number Vs. Reynolds Number for the nose section for rig 3A. Similar to the
backwall Nusselt Number trend, the nose exhibits a similar trend. Comparing blockage ratios of 0.051
and 0.063, the difference in Nusselt Number is minimal, whereas between a blockage of 0.051 and
0.063, the Nusselt Number is slightly more distinct. Between blockage of 0.051 and 0.063, there is only a
difference of about 3.5%, and between a blockage of 0.063 and 0.076, there is a difference of 11.2%.
This indicates, like the case with the backwall heat transfer, the large blockage helps to promote a
higher Nusselt Number or heat transfer coefficient.
50
75
100
125
150
175
200
225
250
275
300
0 10000 20000 30000 40000 50000
Nu
Re
Rig 3A Nusselt Number Vs. Re (Backwall)
e/Dh = 0.051
e/Dh = 0.063
e/Dh = 0.076
45
Figure 32: Rig 3A Nusselt Number Vs. Reynolds Number (Nose)
Figure 33 plots rig 3A Nusselt Number vs. Reynolds Number for both the backwall and nose. The nose,
similar to rig 1, is significantly much higher than that of the backwall, anywhere from 7%-30% higher
depending on the Reynolds Number and blockage ratio. Figure 33 also indicates that at the minimum
and medium blockage ratios, the Nusselt Numbers are very similar to each other. The Nusselt Number at
the maximum blockage ratio is substantially higher than that of at the minimum and medium blockage
ratio. This trend will not be beneficial from a manufacturing viewpoint, because it shows that as the
casting die wears from maximum to medium dimension, the thermal performance of the airfoil will
degrade significantly. Nevertheless, similar to rig 1, rig 3A will be an ideal design that has the leading
edge as the hottest area during turbine operation, since the nose has a higher heat transfer than at the
backwall.
50
75
100
125
150
175
200
225
250
275
300
0 10000 20000 30000 40000 50000
Nu
Re
Rig 3A Nusselt Number Vs. Re (Nose)
e/Dh = 0.051
e/Dh = 0.063
e/Dh = 0.076
46
Figure 33: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)
Figure 34 and Figure 35 highlight the enhancement factors for both the backwall and nose sections for
rig 3A. Comparing the backwall and nose sections, the nose has a higher enhancement factor than the
backwall by on average 17.7% across the span of Reynolds Numbers. Usually for turbine blade design,
the leading edge of a blade is the life limiting area due to high thermal stress. Rig 3A exhibits a
turbulator and cavity design that will help improve the heat transfer in the leading edge due to the
higher enhancement factor at the nose.
50
75
100
125
150
175
200
225
250
275
300
0 10000 20000 30000 40000 50000
Nu
Re
Rig 3A Nusselt Number Vs. Re (Backwall Vs. Nose)
e/Dh = 0.051 (backwall)
e/Dh = 0.063 (backwall)
e/Dh = 0.076 (backwall)
e/Dh = 0.051 (nose)
e/Dh = 0.063 (nose)
e/Dh = 0.076 (nose)
47
Figure 34: Rig 3A Enhancement Factor Vs. Reynolds Number (Backwall)
Figure 35: Rig 3A Enhancement Factor Vs. Reynolds Number (Nose)
2.000
2.250
2.500
2.750
3.000
3.250
3.500
3.750
4.000
0 10000 20000 30000 40000 50000
EF
Re
Rig 3A Enhancement Factor Vs. Re (Backwall)
e/Dh = 0.051
e/Dh = 0.063
e/Dh = 0.076
2.000
2.250
2.500
2.750
3.000
3.250
3.500
3.750
4.000
0 10000 20000 30000 40000 50000
EF
Re
Rig 3A Enhancement Factor Vs. Re (Nose)
e/Dh = 0.051
e/Dh = 0.063
e/Dh = 0.076
48
Figure 36 shows the Cold Friction Factor for the 3 blockage ratios for a range of Reynolds Numbers. As
the blockage increases, so does the Cold Darcy friction factor. This trend is similar to the Darcy friction
factor trends for rigs 1 and 2. It is also important to note that the difference in Darcy friction factors
between the medium and lowest blockage is not as high as the difference between the highest and
medium blockage. This can be due to minor experimental variation or if the trend is indeed real, a
significant increase in Darcy friction factor at higher blockage ratios.
Figure 36: Rig 3A Friction Factor Vs. Reynolds Number
Test Rig 3B
For test rig 3B, the same blockage ratios were analyzed as test rig 3A. Test rigs 3A and 3B essentially
have the same geometric cross sections. The only difference is that for test rig 3B, the wall opposite of
the measured wall for rig 3A, is now being measured. The nose section in rig 3B is the same as 3A and
the heat transfer is assumed the same as rig 3A, and will not be assessed for rig 3B.
Figure 37 demonstrates the heat transfer capability of the backwall for rig 3B. The trend is similar to the
other test rigs in that as the blockage ratio increases, so does the heat transfer coefficient. However,
once again, as the highest blockage is approached, the difference in heat transfer capability between the
highest and medium blockage is minimal and is on the average of around 2%. The difference in Nusselt
0
0.1
0.2
0.3
0.4
0.5
0 10000 20000 30000 40000 50000
f
Re
Rig 3A Cold Friction Factor Vs. Re
e/Dh = .076 (Darcy)
e/Dh = .063 (Darcy)
e/Dh = .051 (Darcy)
e/Dh = .076 (Smooth)
e/Dh = .063 (Smooth)
e/Dh = .051 (Smooth)
49
Number between the medium and smallest blockage is much higher in the order of around 8%. This
suggests that the higher blockage ratio does not necessarily lead to higher heat transfer coefficient and
in some cases the higher rib height may produce recirculation zones underneath the ribs that reduce the
heat transfer benefit.
Figure 37: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall)
Figure 38 shows Rig 3B Nusselt Number Vs. Reynolds Number for both the backwall and the nose
surfaces. The nose has a higher Nusselt Number than that of the backwall for mostly across the entire
range of Reynolds Numbers and blockage ratios, ranging anywhere from 0% to 16%. At the medium and
maximum blockage ratios, the backwall Nusselt Numbers are very similar, and at the minimum and
medium blockage ratios, the nose Nusselt Numbers are not much different from each other. This
indicates that if the wall turbulators are designed to max tolerance and the nose turbulators are
designed to nominal tolerance, any minimal wear to the casting die over time will not have a significant
heat transfer impact within the leading edge airfoil cavity.
50
75
100
125
150
175
200
225
250
275
300
0 10000 20000 30000 40000 50000
Nu
Re
Rig 3B Nusselt Number Vs. Re (Backwall)
e/Dh = 0.051
e/Dh = 0.063
e/Dh = 0.076
50
Figure 38: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)
Figure 39 shows the enhancement factor for the 3 different blockage ratio over a range of Reynolds
Numbers for rig 3B. It can be seen that as the blockage ratio increases, so does the enhancement factor.
However, as demonstrated by figure 30 for rig 3A, the enhancement at higher blockage ratios is not as
much as it is at lower blockage ratios. Going from the medium blockage to the highest blockage, the
enhancement in heat transfer performance is only about 2.7%, where going from the smallest blockage
to the medium blockage, the enhancement is greater at roughly 8%. This is indicative that there is an
optimum blockage that provides the best heat transfer benefit.
50
75
100
125
150
175
200
225
250
275
300
325
0 10000 20000 30000 40000 50000
Nu
Re
Rig 3B Nusselt Number Vs. Re (Backwall Vs. Nose)
e/Dh = 0.051 (backwall)
e/Dh = 0.063 (backwall)
e/Dh = 0.076 (backwall)
e/Dh = 0.051 (nose)
e/Dh = 0.063 (nose)
e/Dh = 0.076 (nose)
51
Figure 39: Rig 3B Enhancement Vs. Reynolds Number (Backwall)
Lastly, Figure 40 highlights the friction factor of rig 3B. Essentially, since rigs 3A and 3B share the same
geometric area and cross sectional area, the friction factor for both rigs should be the same. When
comparing Figure 36 and Figure 40, the friction factors are similar, which is to be expected.
2.000
2.250
2.500
2.750
3.000
3.250
3.500
3.750
4.000
0 10000 20000 30000 40000 50000
EF
Re
Rig 3B Enhancement Factor Vs. Re (Backwall)
e/Dh = 0.051
e/Dh = 0.063
e/Dh = 0.076
52
Figure 40: Rig 3B Friction Factor Vs. Reynolds Number
Comparative Study: Rigs 1, 2, 3A, and 3B
In this study, it is essential to compare the heat transfer, friction factors, and thermal performance
between all the rigs. Each rig provides a different performance due to their geometric differences in the
channel and turbulator geometries. This comparative study assesses the Nusselt Number, friction
factors, and thermal performance over a Reynolds’ Number range of 6000 to 40,000 at all blockage
ratios for all four rigs.
In analyzing the backwall for all the rigs, Figure 41 shows that rig 1 demonstrates the highest heat
transfer coefficient based on the Nusselt Number Vs. Reynolds Number relationship. After rig 1, rig 3B,
then, rig 2, and lastly rig 3A have the next highest heat transfer coefficient. This is mostly likely due to
the higher blockage ratios (e/Dh) of rig 1, which helps to promote more turbulence. In terms of blockage
ratios, rig 1 has the highest blockage ratio, followed by rig 2 and then rigs 3A and 3B. If it is safe to
assume that blockage ratio has a large effect on the heat transfer coefficient, one would question why
rig 2 performed similar to rig 3B on the sidewall. It can be suggested that blockage is not the only factor
that impacts the heat transfer coefficient, but also perhaps the pitch or spacing between turbulators.
0
0.1
0.2
0.3
0.4
0.5
0 10000 20000 30000 40000 50000
f
Re
Rig 3B Cold Friction Factor Vs. Re
e/Dh = .076 (Darcy)
e/Dh = .063 (Darcy)
e/Dh = .051 (Darcy)
e/Dh = .076 (Smooth)
e/Dh = .063 (Smooth)
e/Dh = .051 (Smooth)
53
Looking at Table 2 and Table 3, it can be seen that rig 2 turbulator pitch to rib height ratio is slightly
higher than rigs 3A and 3B, however, the actual turbulator spacing from the test geometry indicates that
rig 2 has a slightly smaller turbulator spacing than rigs 3A and 3B by about .070”. This slight difference in
turbulator spacing between rigs 2 and 3B may influence the heat transfer capability. As indicated in
Taslim and Lengkong (1999), one of the findings was that if the turbulator spacing was too close it
actually reduced the heat transfer coefficient due to the introduction of wakes behind the turbulators.
This prevents the flow from reattaching to the backwall easily and reduces the local heat transfer
coefficient.
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
Nu
Re
Nusselt Number Vs. Re (Backwall, Min e/Dh)
Rig 1 Wall Min e/Dh
Rig 2 Wall Min e/Dh
Rig 3A Wall Min e/Dh
Rig 3B Wall Min e/Dh
54
Figure 41: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall)
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
Nu
Re
Nusselt Number Vs. Re (Backwall, Med e/Dh)
Rig 1 Wall Med e/Dh
Rig 2 Wall Med e/Dh
Rig 3A Wall Med e/Dh
Rig 3B Wall Med e/Dh
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
Nu
Re
Nusselt Number Vs. Re (Backwall, Max e/Dh)
Rig 1 Wall Max e/Dh
Rig 2 Wall Max e/Dh
Rig 3A Wall Max e/Dh
Rig 3B Wall Max e/Dh
55
Figure 42 compares the heat transfer capability at the nose sections for all the rigs. Similar to the trend
seen in Figure 41 on the backwall, rig 1 nose possesses the highest heat transfer coefficient. Rig 3A and
3B nose is slightly higher than rig 2 nose. It is important to note again that since rigs 3A and 3B have the
same channel and turbulator geometry, the results at the nose apply to both rigs 3A and 3B. The reason
why rigs 3A and 3B nose has slightly higher heat transfer coefficient than rig 2, can be attributed to
possibly the smaller pitch or turbulator spacing in rig 2. As mentioned previously, though rig 2 has a
higher blockage, the slightly smaller pitch, may actually reduce the heat transfer coefficient overall,
because it may not allow the flow to reattach to the nose surface after going over the turbulators.
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
Nu
Re
Nusselt Number Vs. Re (Nose, Min e/Dh)
Rig 1 Nose Min e/Dh
Rig 2 Nose Min e/Dh
Rig 3A/3B Nose Min e/Dh
56
Figure 42: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose)
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
Nu
Re
Nusselt Number Vs. Re (Nose, Med e/Dh)
Rig 1 Nose Med e/Dh
Rig 2 Nose Med e/Dh
Rig 3A/3B Nose Med e/Dh
0
50
100
150
200
250
300
350
400
0 10000 20000 30000 40000 50000
Nu
Re
Nusselt Number Vs. Re (Nose, Max e/Dh)
Rig 1 Nose Max e/Dh
Rig 2 Nose Max e/Dh
Rig 3A/3B Nose Max e/Dh
57
Figure 43 and Figure 44 show the enhancement factor for all the rigs at the backwall and nose sections.
The enhancement factor is greatest for rig 1 at both the backwall and nose sections. After rig 1, at the
backwall, rig 3B has the next highest enhancement factor, and then, followed by rig 2 and rig 3A, which
have similar enhancement factors at the backwall. At the nose location, rig 1 has the highest
enhancement factor, followed by rigs 3A and 3B, and lastly rig 2. Rigs 3A and 3B have a slightly higher
enhancement factor than rig 2 due to once again the minimal difference in turbulator spacing.
2
2.5
3
3.5
4
4.5
5
5.5
0 10000 20000 30000 40000 50000
EF
Re
Enhancement Factor Vs. Re (Backwall, Min e/Dh)
Rig 1 Wall Min e/Dh
Rig 2 Wall Min e/Dh
Rig 3A Wall Min e/Dh
Rig 3B Wall Min e/Dh
2
2.5
3
3.5
4
4.5
5
5.5
0 10000 20000 30000 40000 50000
EF
Re
Enhancement Factor Vs. Re (Backwall, Med e/Dh)
Rig 1 Wall Med e/Dh
Rig 2 Wall Med e/Dh
Rig 3A Wall Med e/Dh
Rig 3B Wall Med e/Dh
58
Figure 43: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall)
2
2.5
3
3.5
4
4.5
5
5.5
0 10000 20000 30000 40000 50000
EF
Re
Enhancement Factor Vs. Re (Backwall, Max e/Dh)
Rig 1 Wall Max e/Dh
Rig 2 Wall Max e/Dh
Rig 3A Wall Max e/Dh
Rig 3B Wall Max e/Dh
1.5
2
2.5
3
3.5
4
4.5
5
5.5
0 10000 20000 30000 40000 50000
EF
Re
Enhancement Factor Vs. Re (Nose, Min e/Dh)
Rig 1 Nose Min e/Dh
Rig 2 Nose Min e/Dh
Rig 3A/3B Nose Min e/Dh
59
Figure 44: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose)
In Figure 45, the cold friction factors are plotted up against the Reynolds Number for all four test rigs at
the minimum, medium, and maximum blockage ratios. In general, the Darcy Friction Factor increases
with increasing blockage ratio as expected. At medium and maximum blockage ratios, Rig 1 has the
1.5
2
2.5
3
3.5
4
4.5
5
5.5
0 10000 20000 30000 40000 50000
EF
Re
Enhancement Factor Vs. Re (Nose, Med e/Dh)
Rig 1 Nose Med e/Dh
Rig 2 Nose Med e/Dh
Rig 3A/3B Nose Med e/Dh
1.5
2
2.5
3
3.5
4
4.5
5
5.5
0 10000 20000 30000 40000 50000
EF
Re
Enhancement Factor Vs. Re (Nose, Max e/Dh)
Rig 1 Nose Max e/Dh
Rig 2 Nose Max e/Dh
Rig 3A/3B Nose Max e/Dh
60
highest Darcy friction factor, followed by rig 3A and 3B, and lastly, rig 2. The reason why Rig 1’s friction
factor is the highest is because, it has the highest rib height to hydraulic diameter ratio out of all the rigs.
A higher e/Dh usually increases the friction factor. One interesting results is why rigs 3A/3B have a
higher friction factor than rig 2. According to tables 2 and 3, rig 2 has a higher e/Dh than rigs 3A/3B, so
as a result, the assumption is that rig 2 should have a higher friction factor. Though, rigs 2 and 3 may
have slightly rib-to-rib spacing, the differences are not great enough to show why rig 2 friction factor is
less than that of rigs 3A and 3B. The reason is most likely to the geometric differences in the cross
sectional areas between rigs 2 and 3A/3B. Rig 2 has a more asymmetrical cross sectional area and has
the turbulators lying at angle to the incoming flow, while rigs 3A/3B has the wall and nose turbulators
lying more perpendicular to the incoming flow, which may lead to higher pressure drop. The higher
pressure drop in rigs 3A/3B is the most likely reason why it has a higher friction factor than that of rig 2.
In turbine blade design, a high pressure drop is usually not recommended, because it usually requires
more cooling flow to cool the entire cavity. This takes away precious cooling from other turbine
hardware downstream of the jet engine, and thus, not recommended.
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0 10000 20000 30000 40000 50000 60000
f
Re
Friction Factor Vs. Re (Min e/Dh)
Rig 1 Min e/Dh (Darcy)
Rig 1 Min e/Dh (smooth)
Rig 2 Min e/Dh (Darcy)
Rig 2 Min e/Dh (Smooth)
Rig 3A Min e/Dh (Darcy)
Rig 3A Min e/Dh (Smooth)
Rig 3B Min e/Dh (Darcy)
Rig 3B Min e/Dh (Smooth)
61
Figure 45: Friction Factor Vs Reynolds Number for All Rigs at All Blockage Ratios
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0 10000 20000 30000 40000 50000 60000
f
Re
Friction Factor Vs. Re (Med e/Dh)
Rig 1 Med e/Dh (Darcy)
Rig 1 Med e/Dh (smooth)
Rig 2 Med e/Dh (Darcy)
Rig 2 Med e/Dh (Smooth)
Rig 3A Med e/Dh (Darcy)
Rig 3A Med e/Dh (Smooth)
Rig 3B Med e/Dh (Darcy)
Rig 3B Med e/Dh (Smooth)
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0 10000 20000 30000 40000 50000 60000
f
Re
Friction Factor Vs. Re (Max e/Dh)
Rig 1 Max e/Dh (Darcy)
Rig 1 Max e/Dh (smooth)
Rig 2 Max e/Dh (Darcy)
Rig 2 Max e/Dh (Smooth)
Rig 3A Max e/Dh (Darcy)
Rig 3A Max e/Dh (Smooth)
Rig 3B Max e/Dh (Darcy)
Rig 3B Max e/Dh (Smooth)
62
The thermal performance of each test section is also calculated. The thermal performance takes into
account not only the heat transfer enhancement, but also the pressure drop across the test section
length. Thermal performance can be calculated using eq. 1.19. Figure 46 shows the thermal
performance at the heated wall for all four test rigs for minimum, nominal, and maximum blockage
ratios. It is important to note for this comparison, the blockage ratios are specific to each test section as
specified in tables 1-3.
0.6
0.8
1
1.2
1.4
1.6
1.8
0 10000 20000 30000 40000 50000
TP
Re
Thermal Performance Vs. Re (Backwall, Min e/Dh)
Rig 1 Min Wall e/Dh
Rig 2 Min Wall e/Dh
Rig 3A Min Wall e/Dh
Rig 3B Min Wall e/Dh
0.6
0.8
1
1.2
1.4
1.6
1.8
0 10000 20000 30000 40000 50000
TP
Re
Thermal Performance Vs. Re (Backwall, Med e/Dh)
Rig 1 Med Wall e/Dh
Rig 2 Med Wall e/Dh
Rig 3A Med Wall e/Dh
Rig 3B Med Wall e/Dh
63
Figure 46: Thermal Performance of All Four Test Sections at Backwall at All Blockage Ratios
Figure 46 shows that rigs 2 has the highest thermal performance at the wall out of all the test sections at
all blockage ratios. Rig 1 has the second highest thermal performance, Rig 3B has the 3rd highest, and rig
3A has the lowest thermal performance at the wall. Rig 2 has the highest thermal performance, because
it has a very low friction factor. Rig 1 has the next highest thermal performance, because of its blockage
ratio is much higher than that of the other rigs, which increases the enhancement factor. However, the
higher blockage ratio induces a higher pressure drop across the test channel, which slightly reduces the
overall thermal performance of rig 1. It is important to note that though rigs 3A and 3B share the same
blockage ratio, rig 3B has a higher thermal performance than rig 3A, because rig 3B has a smaller
backwall surface area for convection. Smaller surface area results in a higher heat transfer coefficient,
which means higher Nusselt Number and higher thermal performance.
The thermal performance at the nose is also determined for all four test sections for minimum, nominal,
and maximum blockage ratios. Figure 47 below compares the thermal performance for each test
section.
0.6
0.8
1
1.2
1.4
1.6
1.8
0 10000 20000 30000 40000 50000
TP
Re
Thermal Performance Vs. Re (Backwall, Max e/Dh)
Rig 1 Max Wall e/Dh
Rig 2 Max Wall e/Dh
Rig 3A Max Wall e/Dh
Rig 3B Max Wall e/Dh
64
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Thermal Performance Vs. Re (Nose, Min e/Dh)
Rig 1 Min Nose e/Dh
Rig 2 Min Nose e/Dh
Rig 3A/3B Min Nose e/Dh
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Thermal Performance Vs. Re (Nose, Med e/Dh)
Rig 1 Med Nose e/Dh
Rig 2 Med Nose e/Dh
Rig 3A/3B Med Nose e/Dh
65
Figure 47: Thermal Performance of All Four Test Sections at Nose at All Blockage Ratios
Figure 47 shows that the thermal performance at the nose is highest for rig 1 for all blockage ratios and
at all Reynolds numbers at the nose. Rig 2 has the next highest thermal performance. Rigs 3A and 3B
follow closely behind rig 2. At higher Reynolds Numbers, rigs 3A and 3B have equivalent or slightly
higher thermal performance than rig 2. The thermal performance trends slightly downwards with higher
blockage ratio for all test sections. This is due to the higher pressure drop across the test channel with
larger blockage ratios.
Another interesting comparison to observe is the thermal performance between backwall and nose for
each rig for minimum, nominal, and maximum blockage ratios.
Figure 48 looks at the thermal performance for rig 1 backwall and nose at the three blockage ratios.
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Thermal Performance Vs. Re (Nose, Max e/Dh)
Rig 1 Max Nose e/Dh
Rig 2 Max Nose e/Dh
Rig 3A/3B Max Nose e/Dh
66
Figure 48: Rig 1 Thermal Performance Vs. Re (Backwall and Nose)
Figure 48 shows that the thermal performance of the nose is higher than that of the backwall. On
average, at minimum e/Dh, the nose is 37% higher than that of the backwall; at nominal e/Dh, the nose
is 34.6% higher than that of the backwall; at maximum e/Dh, the nose is 31.2% higher than that of the
backwall. This trend indicates that as the blockage increases, the thermal performance decreases. This is
due to the increase in pressure drop due to the higher blockage. In addition, as the blockage increases,
the nose’s thermal performance seems to decrease relatively more than that of the backwall. This
behavior would not be beneficial to die wear, as it indicates that as the die wears overtime, the
performance of subsequent cast airfoils would decrease. Regardless, rig 1 would still be an ideal design,
where the nose needs more cooling than that of the backwall, to meet life requirements.
Figure 49 highlights the thermal performance of rig 2 backwall and nose.
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Rig 1 Thermal Performance Vs. Re
Rig 1 Min Wall e/Dh
Rig 1 Nom Wall e/Dh
Rig 1 Max Wall e/Dh
Rig 1 Nose Min e/Dh
Rig 1 Nom Nose e/Dh
Rig 1 Max Nose e/Dh
67
Figure 49: Rig 2 Thermal Performance Vs. Re (Backwall and Nose)
Figure 49 shows that, unlike rig 1, the wall and nose thermal performance are relatively similar. On
average across the range of Reynolds Number, at minimum e/Dh, the nose is 1% higher than that of the
backwall; at nominal e/Dh, the nose is 1.1% higher than that of the backwall; at maximum e/Dh, the
nose is 2.3% higher than that of the backwall. One thing to note is that at the lower Reynolds Number,
the nose is higher than that of the backwall, but as the Reynolds Number crosses beyond around 15,000,
the backwall thermal performance seems to exceed that of the nose. Rig 2 would be the optimal design
for balance in thermal performance on both the backwall and nose.
Figure 50 below plots the thermal performance vs. Reynolds Number for Rig 3 backwall and nose.
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Rig 2 Thermal Performance Vs. Re
Rig 2 Min Wall e/Dh
Rig 2 Nom Wall e/Dh
Rig 2 Max Wall e/Dh
Rig 2 Nose Min e/Dh
Rig 2 Nom Nose e/Dh
Rig 2 Max Nose e/Dh
68
Figure 50: Rig 3A Thermal Performance Vs. Re (Backwall and Nose)
Figure 50 shows that the nose has a higher thermal performance than that of the backwall. On average
across the range of Reynolds Numbers, at the minimum e/Dh, the nose’s thermal performance is 18.2%
higher than that of the backwall; at the nominal e/Dh, the nose is 21.8% higher than that of the
backwall; at the maximum e/Dh, the nose is 22.2% higher than that of the backwall. One interesting
finding to note is that, compared to rig 1 nose, the thermal performance for rig 3A nose does not
decrease as much with increasing Reynolds’ Number. This is beneficial to an airfoil engineer, because it
means that the airfoil’s thermal performance will not degrade much with increasing flow velocity or
engine operation.
Figure 51 shows the thermal performance of rig 3B’s backwall and nose.
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Rig 3A Thermal Performance Vs. Re
Rig 3A Min Wall e/Dh
Rig 3A Nom Wall e/Dh
Rig 3A Max Wall e/Dh
Rig 3A Nose Min e/Dh
Rig 3A Nom Nose e/Dh
Rig 3A Max Nose e/Dh
69
Figure 51: Rig 3B Thermal Performance vs. Re (Backwall and Nose)
Figure 51 depicts, similar to rig 2, the thermal performance of rig 3B backwall and nose are similar to
each other across the range of Reynolds Numbers. On average across the range of Reynolds Numbers, at
the minimum e/Dh, the nose is 7.2% higher than that of the backwall; at the nominal e/Dh, the nose is
1.6% higher than that of the backwall; at the maximum e/Dh, the nose is 10.4% higher than that of the
backwall. This type of design is a very well balanced configuration, which provides almost equivalent
thermal performance to both the backwall and the nose areas.
In conclusion, rig 1 has the highest potential thermal performance at the leading edge nose, while rig 2
has the highest thermal performance at the backwall. Rigs 2 and 3B have a relatively well balanced
configuration in that in provides almost equivalent thermal performance on both the backwall and nose
areas. Rigs 1 and 3A, on the other hand, provide better thermal performance at the nose surfaces. One
key learning from these results is that though, higher Nusselt Number is indicative of high heat transfer
capability, it is also important to observe the pressure drop as well. Thus, the reason why thermal
performance is examined in this study. In turbine blade design, there exists a tradeoff between heat
transfer coefficient and pressure drop. Higher pressure drop requires more cooling flow to be able to
drive the cooling air from the inlet to the exit of the cooling channels. As a result, this reduces the
overall engine performance and more bleed air needs to be taken from the compressor to cool the
turbine section. A good design is where the heat transfer enhancement is high, but the pressure drop
across the channel is minimized.
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 10000 20000 30000 40000 50000
TP
Re
Rig 3B Thermal Performance vs. Re
Rig 3B Min Wall e/Dh
Rig 3B Nom Wall e/Dh
Rig 3B Max Wall e/Dh
Rig 3B Nose Min e/Dh
Rig 3B Nom Nose e/Dh
Rig 3B Max Nose e/Dh
70
Conclusions
In this study, 45° wall turbulators and 90° nose turbulators at various blockage ratios for 4 different test
sections were assessed. It looked at how the blockage ratio and the pitch to turbulator height ratio
affected the heat transfer coefficient, friction factor, and the enhancement factors of the wall and nose
sections between turbulators. The following are the conclusions from this study:
1. Rig 1 has the highest thermal performance at the nose at all blockage ratios. Rig 2 has the
highest thermal performance at the backwall at all blockage ratios.
2. Rig 1 had the highest friction factor across the range of Reynolds Numbers. Rig 2 had the lowest.
3. As the blockage ratio increased, so did the heat transfer coefficient and friction factors. It was
noted, however, that as the blockage ratio increased to the maximum blockage the heat
transfer benefit was reduced.
4. The turbulator spacing was suggested to have a potential impact on the overall heat transfer
coefficient as demonstrated by looking at the results between rigs 2 and 3A and 3B. Though, rigs
3A and 3B possessed smaller blockage ratios than rig 2, the fact that the turbulator spacing of rig
3 was slightly larger may have increased the heat transfer coefficient slightly beyond that of rig
2.
5. To validate the test results and trends seen from this experiment, it is recommended that a
future effort be conducted to model each test section and perform a CFD analysis.
71
References
[1] Taslim, M.E., and Lengkong A., 1999, “ 45 deg Round-Corner Rib Heat Transfer Coefficient
Measurements in a Square Channel”, ASME Journal of Turbomachinery, Vol. 121.
[2] Domaschke, Norbert, Wolfersdorf, Jens von, and Semmler, Klaus, 2012, “Heat Transfer and Pressure
Drop Measurements in a Rib Roughened Leading Edge Cooling Channel”, Vol. 134.
[3] Rallabandi Akhilesh P., Alkhamis, Nawaf, and Han, Je-Chin, 2011, “Heat Transfer and Pressure Drop
Measurements for a Square With 45 deg Round-Edged Ribs at High Reynolds Numbers”, Vol. 133
[4] Lau, S.C., McMillin, R.D., Han, J.C., 1991, “Turbulent Heat Transfer and Friction in a Square Channel
With Discrete Rib Turbulators”, Vol. 113.
[5] Dees, Jason E., Bogard, David G., Ledezma, Gustavo A., Laskowski, Gregory M., and Tolpadi, Anil K.,
2012, “Experimental Measurements and Computational Predictions for an Internally Cooled Simulated
Turbine Vane With 90 Degree Rib Turbulators”, Vol 124.
[6] Liu, Yao-Hsien, Huh, Michael, Rhee, Dong-Ho, Han, Je-Chin, and Moon, Hee-Koo, 2009, “Heat
Transfer in Leading Edge, Triangular Shaped Cooling Channels With Angled Ribs Under High Rotation
Numbers”, Vol. 131.
[7] Luo, D.D, Leung, C.W., and Chan T.L., 2004, “Forced convection and flow friction characteristics of air-
cooled horizontal equilateral triangular ducts with ribbed internal surfaces”, Int. J. Heat and Mass
Transfer, 47, pp. 5439-5450
[8] Taslim, M.E., and Bethka, D., 2009, “Experimental and Numerical Impingement Heat Transfer in an
Airfoil Leading-Edge cooling Channel With Cross-Flow”, Vol. 131.
[9] Metzger, D.E., Bunker, R.S., 1990, “Local Heat Transfer in Internally Cooled Turbine Airfoil Leading
Edge Regions: Part I – Impingement Cooling Without Film Coolant Extraction”, ASME Journal of
Turbomachinery, Vol. 112, pp. 451-458
[10] Metzger, D.E., Bunker, R.S., 1990, “Local Heat Transfer in Internally Cooled Turbine Airfoil Leading
Edge Regions: Part II – Impingement Cooling With Film Coolant Extraction”, ASME Journal of
Turbomachinery, Vol. 112, pp. 459-466
[11] Taslim, M.E, Setayeshgar, L., and Spring, S.D., 2001, “An Experimental Evaluation of Advanced
Leading Edge Impingement Coolilng Concepts”, Vol. 123.
[12] Taslim, M.E., Li, T., and Kercher, D.M., 1996. “Experimental Heat Transfer and Friction in Channels
Roughened With Angled, V-Shaped, and Discrete Ribs on Two Opposite Walls”, Vol. 118.
72
[13] Luca, Andrei, Carcasci, Carlo, Soghe, Riccardo Da, Facchini, Bruno, Maiuolo, Francesco, Tarchi,
Lorenzo, and Zecchi, Stefano, 2013, “Heat Transfer Measurements in a Leading Edge Geometry With
Racetrack Holes and Film Cooling Extraction”, Vol. 135.
[14] Kaminski, Deborah A., and Jensen, Michael K. Introduction to Thermal and Fluids Engineering. John
Wiley & Sons, INC. Hoboken, NJ, 2005.
[15] Ozisik M. Necati. Heat Transfer A Basic Approach. McGraw-Hill. New York, NY, 1985.
[16] “CF6-6_engine_cutaway.jpg” . 8 Jan 2007. Photograph. Wikipedia. Web. 18 Mar 2014.
http://en.wikipedia.org/wiki/File:CF6-6_engine_cutaway.jpg
[17] “Turbine blade with a thermal barrier coating”. 11 July 1979. Photograph. Wikipedia. Web. 18 Mar
2014. http://en.wikipedia.org/wiki/File:ThermalBarrierCoating.JPG
73
Appendix A.1: FORTRAN Code for Rig 1
Author: Professor Mohammad Taslim
Check.f File
implicit real*8(a-h,o-z)
real*8 i1,i2,i3,i4,new1,new2,new3,new4
character*25 filename
character*80 title
open(2, file='output.dat', status='old') ! output file
write(6,*)'enter the name of the data file that u',
&' want to check'
read(5,10)filename
10 format(a25)
open(unit=4,file=filename,status='old')
read(4,*)n
do i=1,11
read(4,20)title
20 format(a80,/,/)
enddo
DO I=1,n
read(4,*)Ph1,Pven,Tven,Tin1,Tin2,Tamb,
&V1,i1,V2,i2,V3,i3,SG,Pplen,DP,Pamb,Dthroat
if(Tamb.lt.40.or.Tamb.gt.80)
&write(2,9)Pven,ph1
9 format(' Check Tamb for Pven=',f6.1,' ph1',f6.1)
if(Pamb.lt.29.or.Pamb.gt.32)
&write(2,19)Pven,ph1
19 format(' Check Pamb for Pven=',f6.1,' ph1',f6.1)
if(Tin1.lt.40.or.Pamb.gt.80)
&write(2,29)Pven,ph1
29 format(' Check Tin1 for Pv=',f6.1,' ph1',f6.1)
if(Tin2.lt.40.or.Pamb.gt.80)
&write(2,28)Pven,ph1
28 format(' Check Tin2 for Pv=',f6.1,' ph1',f6.1)
if(old1.eq.0)goto 43
74
new1=V1/i1
new2=V2/i2
new3=V3/i3
err1=abs((new1-old1)/old1)
err2=abs((new2-old2)/old2)
err3=abs((new3-old3)/old3)
if(err1.gt..01)then
write(6,37)pven,ph1
new1=old1
endif
37 format('error in heater 1 entry,Pv,Ph1 #',F4.1,f5.0)
if(err2.gt..01)then
write(6,38)pven,ph1
new2=old2
endif
38 format('error in heater 2 entry,Pv,Ph1 #',F4.1,f5.0)
if(err3.gt..01)then
write(6,39)pven,ph1
new3=old3
endif
39 format('error in heater 3 entry,Pv,Ph1 #',F4.1,f5.0)
43 write(2,41)ph1,v1/i1,v2/i2,v3/i3
write(6,41)ph1,v1/i1,v2/i2,v3/i3
if(flag.eq.1)goto 32
old1=V1/i1
old2=V2/i2
old3=V3/i3
flag=1.
go to 30
32 old1=new1
old2=new2
old3=new3
75
30 continue
ENDDO
41 format(1x,f4.1,4(1x,f7.3))
write(6,*)
write(6,*)' NOTE : THE RESISTANCES FOR ALL HEATERS ARE',
&' IN FILE output.dat'
stop
end
76
Reduce.F File
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,Nu,NoseR,NoseL,Losses
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,
&Side,Top,BOt,NoseR,Perim,Dh
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
FAC1=3.413 ! converts Watts to BTU/hr
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1, FILE='input.dat',STATUS='old')
OPEN(UNIT=4,FILE='nu-plots.dat',STATUS='old')
OPEN(UNIT=5, FILE='uncertain.out',STATUS='old')
OPEN(UNIT=7, FILE='output.dat',STATUS='old')
OPEN(UNIT=8, FILE='friction.out',STATUS='old')
OPEN(UNIT=10,FILE='nu-pictures.dat',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
NoseR=0.504 ! inches
NoseR=NoseR/12. ! feet
Angle=144. ! degrees
RigL=36. ! inches
C
C FIBERGLAS
C
Side=3. ! inches
Side=Side/12. ! feet
C
C PLEXI
C
77
Top=2.813 ! inches
Top=Top/12. ! feet
Pitch=3.72 ! inches
nturb=9
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side+Top
Bot=SQRT(2*(NoseR**2)*(1-COS(Angle*PI/180)))
H1=SQRT((SIDE**2)-(0.5*(Top-Bot))**2)
Area1=0.5*(Top+Bot)*H1
Area2=(PI*(NoseR**2)*(Angle/360))-
&(0.5*Bot*NoseR*COS(0.5*Angle*PI/180))
Across=Area1+Area2
Dh=4*Across/Perim
! EACH HEATER
Hlength=11.
Hlength=Hlength/12.
Hwidth=4.26
Hwidth=Hwidth/12.
Harea=Hlength*Hwidth
Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,
&12.*Top,12.*Bot,12.*Hlength,12.*Hwidth,
&144.*Harea,12.*Perim,144.*ACross,12*Dh,Pitch,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Nose Length=',f8.3,' inches',/,
&2x,'Side 1 (Plexi)=',f8.3,' inches',/,
&2x,'Side 2 (LC)=',f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Bottom Flat Line=',f8.3,' inches',/,
&2x,'Heater Length=',f8.3,' inches',/,
&2x,'Heater Width=',f8.3,' inches',/,
&2x,'Heater area=',f8.3,' Sq.in',/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
! R E A D I N D A T A
78
read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid
Poe=Pitch/TurbH
eoDh=(TurbH/12)/Dh
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
DO 333 I=1,11
READ(1,10)TITLE
WRITE(5,10)TITLE
WRITE(7,10)TITLE
333 WRITE(10,10)TITLE
10 FORMAT(A80,//)
WRITE(10,451)
451 FORMAT(' no. Re Nu h uncer',
&' Nu_smooth EF',/)
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3
&,SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' V1,A1,V2,A2,V3,A3'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,201)V1,A1,V2,A2,V3,A3
201 FORMAT(5X,3(' ',F5.2,' ',F6.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
79
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
Mv=F(Athroat,Pven+Pamb,Tven+460)
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
C HEAT FLUX, BTU/(sqft.hr)
Flux=V2*A2*FAC1/(Harea)
C TOTAL HEAT GENERATED FROMINLET TO cAMERA LOCATION , BTU/hr
Q=(A1*V1+0.5*A2*V2)*FAC1
CALL HTC(Q,Flux,Tm,Tsurf,h,Losses)
TmR=Tm+460.
CALL AIRPROP(TmR,gamm,CONm,VISm,PRm,CPm)
VISm=VISm/3600.
C REYNOLDS NUMBER
Re=4.*Mv/(Perim*VISm)
! NUSSELT NUMBER
Nu=h*Dh/CONm
SmoothNu=0.023*(Re**0.8)*(Prm**0.4)
! ENHACEMENT
EF=Nu/SmoothNu
! NUSSELT NUMBER UNCERTAINTY ANALYSIS
CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,Dthroat,Harea,
&Tsurf,Tin,Losses,Uncer)
WRITE(10,305)testno,Re,Nu,h,uncer,SmoothNu,EF
80
305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)
WRITE(4,*)Re,Nu
WRITE(7,300)Tm,MV,Re
C***************************************************
! DARCY FRICTION FACTOR CALCULATIONS
Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb
Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb
Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/
&(0.5*Rho*(Um**2))
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Inlet Pressure=',f9.4,' psia',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)
STOP
END
81
C**********************************************************************C
SUBROUTINE HTC(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,
&Side,Top,BOt,NoseR,Perim,Dh
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
82
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! BIRK
tinc = 1.0e-03/12. ! BIRK
tadh1= 1.0e-03/12. ! BIRK
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
83
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Top*Hlength ! Top surface
Afront=1.5*Side*Hlength ! Front surface
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
84
C THE POINT IN QUESTION
Anose=1.5*PI*NoseR*(Angle/360)*Hlength ! Nose surface
Aback=1.5*Side*Hlength ! Side surface
C write(6,*)Atop,Afront,Anose,Aback
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=h
htop=0.8*h ! Guess
hnose=h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
C write(6,*)Frtop,Frfront,Frnose,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
85
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fnose=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Ftop*Atop+Fnose*Anose+Ffront*Afront+Fback*Aback
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frnose
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
86
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=h
htop=0.8*h
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' LEADING-EDGE CHANNEL',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
87
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,h,hfront,htop
120 FORMAT(5x,'hside=',F8.3,1X,'hnose=',F8.3,1X,'hfront=',F8.3,1X,
&'htop=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)Fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frnose
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C***************************************************************
SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)
PI=4.*ATAN(1.E00)
W=H1
H=0.5*(Bot+Top)
T(1)=Tsurf + 460.
T(2)=Ttop + 460.
T(3)=Tfront+ 460.
88
T(4)=Tbot + 460.
W=W/(3.*Hlength)
H=H/(3.*Hlength)
C Emissivities
E(1)=.85 ! Liquid Crystal Foil, Back Wall
E(2)=.9 ! Plexiglas, Top Wall
E(3)=.9 ! Plexiglas, Front Wall
E(4)=.85 ! Liquid Crystal Foil, Nose Wall
C
N=4
SIGMA=0.1712E-08
C WRITE(7,150)
150 FORMAT(//,20X,'SHAPE FACTORS',//)
C
F11=0.
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F12=Z1*(Z2+Z3+Z4+Z5)
F14=F12
F13=1.-F11-F12-F14
C
F31=F13
F32=F12
F33=0.
F34=F14
C
DUM=W
W=H
H=DUM
W2=W*W
89
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F21=Z1*(Z2+Z3+Z4+Z5)
F22=0.
F23=F21
F24=1.-F21-F22-F23
C
F41=F21
F42=F24
F43=F23
F44=0.
C
C WRITE(7,110)F11,F12,F13,F14
C WRITE(7,120)F21,F22,F23,F24
C WRITE(7,130)F31,F32,F33,F34
C WRITE(7,140)F41,F42,F43,F44
C
110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,
&5X,'F14=',F6.4,/)
120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,
&5X,'F24=',F6.4,/)
130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,
&5X,'F34=',F6.4,/)
140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,
&5X,'F44=',F6.4,//)
C WRITE(7,160)
160 FORMAT(/,20X,'EMISSIVITIES',//)
C WRITE(7,100)(I,E(I),I=1,N)
C WRITE(7,170)
170 FORMAT(/,20X,'TEMPERATURES IN R',//)
C WRITE(7,100)(I,T(I),I=1,N)
A(1,1)=F11-1./(1.-E(1))
A(1,2)=F12
A(1,3)=F13
90
A(1,4)=F14
C
A(2,1)=F21
A(2,2)=F22-1./(1.-E(2))
A(2,3)=F23
A(2,4)=F24
C
A(3,1)=F31
A(3,2)=F32
A(3,3)=F33-1./(1.-E(3))
A(3,4)=F34
C
A(4,1)=F41
A(4,2)=F42
A(4,3)=F43
A(4,4)=F44-1./(1.-E(4))
C
C WRITE(7,180)
180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)
C WRITE(7,200)((A(I,J),J=1,N),I=1,N)
DO I=1,N
B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))
ENDDO
C WRITE(7,250)
C WRITE(7,100)(I,B(I,1),I=1,N)
200 FORMAT(1X,4E15.6)
250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)
C WRITE(7,55)
55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)
CALL EQSOLVE(A,B,N,N,1)
C WRITE(7,50)
C WRITE(7,100)(I,B(I,1),I=1,N)
DO I=1,N
Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))
ENDDO
Frback =Q(1)
Frtop =Q(2)
Frfront=Q(3)
Frnose=Q(4)
C WRITE(7,350)
C WRITE(7,100)(I,Q(I),I=1,N)
100 FORMAT(4(I3,E15.6))
50 FORMAT(/,20X,'RADIOCITIES',/)
350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)
RETURN
END
C**********************************************************************C
91
SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,Dth,Harea,Tsurf,
&Tin,Losses,Uncer)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 i1,i2,Losses,M1,M2
PI=4.*ATAN(1.E00)
C FAC=491.3744
FAC1=3.413 ! converts Watts to BTU/hr
C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)
C=0.24*0.5215*3600
C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J
P1=Pven+Pamb
T1=Tven+460.0
TI=Tin
TS=Tsurf
a=Harea
f=0.5
ATH=PI*(Dth**2)/4.
DATH=PI*((Dth+0.001)**2)/4. -ATH
h=((FAC1*(V2*i2)/a)-Losses)/
&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+f*V2*i2)))/(C*P1*ATH))
WRITE(5,*)' '
WRITE(5,*)' h =',h,' BUT/hr.sqft.F'
H2=h*h
C
C i2 v2
C ------- - Floss
C a
C -------------------------------------
C sqrt(T1)(i1 v1 + f i2 v2)
C Ts-Ti - -------------------------
C C P1 A_throat
C
DLOSS=0.1*Losses
92
dv1=0.1
dv2=0.1
di1=0.01
di2=0.01
da=1./(32.*32.*144)
dts=0.5
dti=0.5
dt1=0.5
dp1=0.5
Df=0.1
C1=FAC1*(V2*i2/a)-Losses
Q1=C*P1*Ath
Q2=Q1*sqrt(T1)
M1=(Ts-Ti)*Q1
A=FAC1*(i1*v1)
B=FAC1*(i2*v2)
M2=M1-sqrt(T1)*(A+f*B)
DHDF=B*Q1*C1*sqrt(T1)/(M2**2)
DHDTI= C1*(Q1**2)/(M2**2)
DHDTS=-C1*(Q1**2)/(M2**2)
DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))
DHDLOSS=-Q1/M2
DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)
DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)
DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDATH=C1*C*P1*(M2-M1)/(M2**2)
DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)
DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))
ZF=(DF*DHDF)**2
ZA=(DA*DHDA)**2
ZI1=(DI1*DHDI1)**2
ZV1=(DV1*DHDV1)**2
ZI2=(DI2*DHDI2)**2
ZV2=(DV2*DHDV2)**2
ZTS=(DTS*DHDTS)**2
ZTI=(DTI*DHDTI)**2
ZATH=(DATH*DHDATH)**2
93
ZP1=(DP1*DHDP1)**2
ZT1=(DT1*DHDT1)**2
ZLOSS=(DLOSS*DHDLOSS)**2
Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+
&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
RETURN
END
C**********************************************************************C
SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(NDIM,NDIM),B(NDIM,NB)
DO 291 J1=1,NA
C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE
C VALUE IN PIVOTAL COLUMN.
101 TEMP=0.
DO 121 J2=J1,NA
IF(ABS(A(J2,J1))-TEMP) 121,111,111
111 TEMP=ABS(A(J2,J1))
IBIG=J2
121 CONTINUE
IF(IBIG-J1)5001,201,131
C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE
C VALUE IN PIVOT POSITION.
131 DO 141 J2=J1,NA
TEMP=A(J1,J2)
A(J1,J2)=A(IBIG,J2)
141 A(IBIG,J2)=TEMP
DO 161 J2=1,NB
TEMP=B(J1,J2)
94
B(J1,J2)=B(IBIG,J2)
161 B(IBIG,J2)=TEMP
C COMPUTE COEFFICIENTS IN PIVOTAL ROW.
201 TEMP=A(J1,J1)
DO 221 J2=J1,NA
221 A(J1,J2)=A(J1,J2)/TEMP
DO 231 J2=1,NB
231 B(J1,J2)=B(J1,J2)/TEMP
IF(J1-NA)236,301,5001
C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.
236 N1=J1+1
DO 281 J2=N1,NA
TEMP=A(J2,J1)
DO 241 J3=N1,NA
241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)
DO 251 J3=1,NB
251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)
281 CONTINUE
291 CONTINUE
C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.
301 IF(NA-1)5001,5001,311
311 DO 391 J1=1,NB
N1=NA
321 DO 341 J2=N1,NA
341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)
N1=N1-1
IF(N1-1)5001,391,321
391 CONTINUE
5001 CONTINUE
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
95
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
96
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
97
Rig1-reduce-friction.f File
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,Nu,NoseR,NoseL,Losses
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,
&Side,Top,BOt,NoseR,Perim,Dh
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
FAC1=3.413 ! converts Watts to BTU/hr
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1, FILE='input.dat',STATUS='old')
OPEN(UNIT=4,FILE='nu-plots.dat',STATUS='old')
OPEN(UNIT=5, FILE='uncertain.out',STATUS='old')
OPEN(UNIT=7, FILE='output.dat',STATUS='old')
OPEN(UNIT=8, FILE='friction.out',STATUS='old')
OPEN(UNIT=10,FILE='nu-pictures.dat',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
NoseR=0.504 ! inches
NoseR=NoseR/12. ! feet
Angle=144. ! degrees
RigL=36. ! inches
C
C FIBERGLAS
C
Side=3. ! inches
Side=Side/12. ! feet
C
C PLEXI
C
98
Top=2.813 ! inches
Top=Top/12. ! feet
Pitch=3.72 ! inches
nturb=9
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side+Top
Bot=SQRT(2*(NoseR**2)*(1-COS(Angle*PI/180)))
H1=SQRT((SIDE**2)-(0.5*(Top-Bot))**2)
Area1=0.5*(Top+Bot)*H1
Area2=(PI*(NoseR**2)*(Angle/360))-
&(0.5*Bot*NoseR*COS(0.5*Angle*PI/180))
Across=Area1+Area2
Dh=4*Across/Perim
! EACH HEATER
Hlength=11.
Hlength=Hlength/12.
Hwidth=4.26
Hwidth=Hwidth/12.
Harea=Hlength*Hwidth
Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,
&12.*Top,12.*Bot,12.*Hlength,12.*Hwidth,
&144.*Harea,12.*Perim,144.*ACross,12*Dh,Pitch,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Nose Length=',f8.3,' inches',/,
&2x,'Side 1 (Plexi)=',f8.3,' inches',/,
&2x,'Side 2 (LC)=',f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Bottom Flat Line=',f8.3,' inches',/,
&2x,'Heater Length=',f8.3,' inches',/,
&2x,'Heater Width=',f8.3,' inches',/,
&2x,'Heater area=',f8.3,' Sq.in',/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
! R E A D I N D A T A
99
read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid
Poe=Pitch/TurbH
eoDh=(TurbH/12)/Dh
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
DO 333 I=1,11
READ(1,10)TITLE
WRITE(5,10)TITLE
WRITE(7,10)TITLE
333 WRITE(10,10)TITLE
10 FORMAT(A80,//)
WRITE(10,451)
451 FORMAT(' no. Re Nu h uncer',
&' Nu_smooth EF',/)
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3
&,SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' V1,A1,V2,A2,V3,A3'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,201)V1,A1,V2,A2,V3,A3
201 FORMAT(5X,3(' ',F5.2,' ',F6.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
100
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
Mv=F(Athroat,Pven+Pamb,Tven+460)
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
C HEAT FLUX, BTU/(sqft.hr)
Flux=V2*A2*FAC1/(Harea)
C TOTAL HEAT GENERATED FROMINLET TO cAMERA LOCATION , BTU/hr
Q=(A1*V1+0.5*A2*V2)*FAC1
CALL HTC(Q,Flux,Tm,Tsurf,h,Losses)
TmR=Tm+460.
CALL AIRPROP(TmR,gamm,CONm,VISm,PRm,CPm)
VISm=VISm/3600.
C REYNOLDS NUMBER
Re=4.*Mv/(Perim*VISm)
! NUSSELT NUMBER
Nu=h*Dh/CONm
SmoothNu=0.023*(Re**0.8)*(Prm**0.4)
! ENHACEMENT
EF=Nu/SmoothNu
! NUSSELT NUMBER UNCERTAINTY ANALYSIS
CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,Dthroat,Harea,
&Tsurf,Tin,Losses,Uncer)
WRITE(10,305)testno,Re,Nu,h,uncer,SmoothNu,EF
101
305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)
WRITE(4,*)Re,Nu
WRITE(7,300)Tm,MV,Re
C***************************************************
! DARCY FRICTION FACTOR CALCULATIONS
Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb
Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb
Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/
&(0.5*Rho*(Um**2))
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Inlet Pressure=',f9.4,' psia',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)
STOP
END
102
C**********************************************************************C
SUBROUTINE HTC(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,
&Side,Top,BOt,NoseR,Perim,Dh
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
103
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! BIRK
tinc = 1.0e-03/12. ! BIRK
tadh1= 1.0e-03/12. ! BIRK
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
104
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Top*Hlength ! Top surface
Afront=1.5*Side*Hlength ! Front surface
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
105
C THE POINT IN QUESTION
Anose=1.5*PI*NoseR*(Angle/360)*Hlength ! Nose surface
Aback=1.5*Side*Hlength ! Side surface
C write(6,*)Atop,Afront,Anose,Aback
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=h
htop=0.8*h ! Guess
hnose=h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
C write(6,*)Frtop,Frfront,Frnose,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
106
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fnose=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Ftop*Atop+Fnose*Anose+Ffront*Afront+Fback*Aback
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frnose
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
107
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=h
htop=0.8*h
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' LEADING-EDGE CHANNEL',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
108
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,h,hfront,htop
120 FORMAT(5x,'hside=',F8.3,1X,'hnose=',F8.3,1X,'hfront=',F8.3,1X,
&'htop=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)Fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frnose
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C***************************************************************
SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)
PI=4.*ATAN(1.E00)
W=H1
H=0.5*(Bot+Top)
T(1)=Tsurf + 460.
T(2)=Ttop + 460.
T(3)=Tfront+ 460.
109
T(4)=Tbot + 460.
W=W/(3.*Hlength)
H=H/(3.*Hlength)
C Emissivities
E(1)=.85 ! Liquid Crystal Foil, Back Wall
E(2)=.9 ! Plexiglas, Top Wall
E(3)=.9 ! Plexiglas, Front Wall
E(4)=.85 ! Liquid Crystal Foil, Nose Wall
C
N=4
SIGMA=0.1712E-08
C WRITE(7,150)
150 FORMAT(//,20X,'SHAPE FACTORS',//)
C
F11=0.
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F12=Z1*(Z2+Z3+Z4+Z5)
F14=F12
F13=1.-F11-F12-F14
C
F31=F13
F32=F12
F33=0.
F34=F14
C
DUM=W
W=H
H=DUM
W2=W*W
110
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F21=Z1*(Z2+Z3+Z4+Z5)
F22=0.
F23=F21
F24=1.-F21-F22-F23
C
F41=F21
F42=F24
F43=F23
F44=0.
C
C WRITE(7,110)F11,F12,F13,F14
C WRITE(7,120)F21,F22,F23,F24
C WRITE(7,130)F31,F32,F33,F34
C WRITE(7,140)F41,F42,F43,F44
C
110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,
&5X,'F14=',F6.4,/)
120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,
&5X,'F24=',F6.4,/)
130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,
&5X,'F34=',F6.4,/)
140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,
&5X,'F44=',F6.4,//)
C WRITE(7,160)
160 FORMAT(/,20X,'EMISSIVITIES',//)
C WRITE(7,100)(I,E(I),I=1,N)
C WRITE(7,170)
170 FORMAT(/,20X,'TEMPERATURES IN R',//)
C WRITE(7,100)(I,T(I),I=1,N)
A(1,1)=F11-1./(1.-E(1))
A(1,2)=F12
A(1,3)=F13
111
A(1,4)=F14
C
A(2,1)=F21
A(2,2)=F22-1./(1.-E(2))
A(2,3)=F23
A(2,4)=F24
C
A(3,1)=F31
A(3,2)=F32
A(3,3)=F33-1./(1.-E(3))
A(3,4)=F34
C
A(4,1)=F41
A(4,2)=F42
A(4,3)=F43
A(4,4)=F44-1./(1.-E(4))
C
C WRITE(7,180)
180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)
C WRITE(7,200)((A(I,J),J=1,N),I=1,N)
DO I=1,N
B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))
ENDDO
C WRITE(7,250)
C WRITE(7,100)(I,B(I,1),I=1,N)
200 FORMAT(1X,4E15.6)
250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)
C WRITE(7,55)
55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)
CALL EQSOLVE(A,B,N,N,1)
C WRITE(7,50)
C WRITE(7,100)(I,B(I,1),I=1,N)
DO I=1,N
Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))
ENDDO
Frback =Q(1)
Frtop =Q(2)
Frfront=Q(3)
Frnose=Q(4)
C WRITE(7,350)
C WRITE(7,100)(I,Q(I),I=1,N)
100 FORMAT(4(I3,E15.6))
50 FORMAT(/,20X,'RADIOCITIES',/)
350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)
RETURN
END
C**********************************************************************C
112
SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,Dth,Harea,Tsurf,
&Tin,Losses,Uncer)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 i1,i2,Losses,M1,M2
PI=4.*ATAN(1.E00)
C FAC=491.3744
FAC1=3.413 ! converts Watts to BTU/hr
C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)
C=0.24*0.5215*3600
C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J
P1=Pven+Pamb
T1=Tven+460.0
TI=Tin
TS=Tsurf
a=Harea
f=0.5
ATH=PI*(Dth**2)/4.
DATH=PI*((Dth+0.001)**2)/4. -ATH
h=((FAC1*(V2*i2)/a)-Losses)/
&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+f*V2*i2)))/(C*P1*ATH))
WRITE(5,*)' '
WRITE(5,*)' h =',h,' BUT/hr.sqft.F'
H2=h*h
C
C i2 v2
C ------- - Floss
C a
C -------------------------------------
C sqrt(T1)(i1 v1 + f i2 v2)
C Ts-Ti - -------------------------
C C P1 A_throat
C
DLOSS=0.1*Losses
113
dv1=0.1
dv2=0.1
di1=0.01
di2=0.01
da=1./(32.*32.*144)
dts=0.5
dti=0.5
dt1=0.5
dp1=0.5
Df=0.1
C1=FAC1*(V2*i2/a)-Losses
Q1=C*P1*Ath
Q2=Q1*sqrt(T1)
M1=(Ts-Ti)*Q1
A=FAC1*(i1*v1)
B=FAC1*(i2*v2)
M2=M1-sqrt(T1)*(A+f*B)
DHDF=B*Q1*C1*sqrt(T1)/(M2**2)
DHDTI= C1*(Q1**2)/(M2**2)
DHDTS=-C1*(Q1**2)/(M2**2)
DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))
DHDLOSS=-Q1/M2
DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)
DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)
DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDATH=C1*C*P1*(M2-M1)/(M2**2)
DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)
DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))
ZF=(DF*DHDF)**2
ZA=(DA*DHDA)**2
ZI1=(DI1*DHDI1)**2
ZV1=(DV1*DHDV1)**2
ZI2=(DI2*DHDI2)**2
ZV2=(DV2*DHDV2)**2
ZTS=(DTS*DHDTS)**2
ZTI=(DTI*DHDTI)**2
ZATH=(DATH*DHDATH)**2
114
ZP1=(DP1*DHDP1)**2
ZT1=(DT1*DHDT1)**2
ZLOSS=(DLOSS*DHDLOSS)**2
Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+
&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
RETURN
END
C**********************************************************************C
SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(NDIM,NDIM),B(NDIM,NB)
DO 291 J1=1,NA
C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE
C VALUE IN PIVOTAL COLUMN.
101 TEMP=0.
DO 121 J2=J1,NA
IF(ABS(A(J2,J1))-TEMP) 121,111,111
111 TEMP=ABS(A(J2,J1))
IBIG=J2
121 CONTINUE
IF(IBIG-J1)5001,201,131
C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE
C VALUE IN PIVOT POSITION.
131 DO 141 J2=J1,NA
TEMP=A(J1,J2)
A(J1,J2)=A(IBIG,J2)
141 A(IBIG,J2)=TEMP
DO 161 J2=1,NB
TEMP=B(J1,J2)
115
B(J1,J2)=B(IBIG,J2)
161 B(IBIG,J2)=TEMP
C COMPUTE COEFFICIENTS IN PIVOTAL ROW.
201 TEMP=A(J1,J1)
DO 221 J2=J1,NA
221 A(J1,J2)=A(J1,J2)/TEMP
DO 231 J2=1,NB
231 B(J1,J2)=B(J1,J2)/TEMP
IF(J1-NA)236,301,5001
C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.
236 N1=J1+1
DO 281 J2=N1,NA
TEMP=A(J2,J1)
DO 241 J3=N1,NA
241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)
DO 251 J3=1,NB
251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)
281 CONTINUE
291 CONTINUE
C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.
301 IF(NA-1)5001,5001,311
311 DO 391 J1=1,NB
N1=NA
321 DO 341 J2=N1,NA
341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)
N1=N1-1
IF(N1-1)5001,391,321
391 CONTINUE
5001 CONTINUE
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
116
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
117
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
118
Appendix A.2: FORTRAN Codes for Rig 2
Author: Professor Mohammad Taslim
Check.F
character*25 filename
character*80 title
write(6,*)'enter the name of the data file that u',
* ' want to check'
read(5,10)filename
10 format(a25)
open(unit=1,file=filename,status='old')
open(unit=2,file='output.dat',status='old')
write(6,*)'is there a title for this file? enter 1=yes, 0=no'
read(5,*)ans
if(ans.eq.0)goto 30
read(1,*)NTESTS
do i=1,11
read(1,20)title
20 FORMAT(A80,//)
enddo
30 do i=1,NTESTS
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3
&,SG,Pplen,Pinlet,Pamb,Dthroat
if(Tven.lt.45.or.Tven.gt.90)write(6,*)
&' ** CHECK Tven IN TEST ',i
if(Tin1.lt.50.or.Tin1.gt.90)write(6,*)' ** CHECK Tin1 IN TEST '
if(Tin2.lt.50.or.Tin2.gt.90)write(6,*)' ** CHECK Tin2 IN TEST '
if(Tamb.lt.60.or.Tamb.gt.80)write(6,*)' ** CHECK Tamb IN TEST '
if(Pamb.lt.28.or.Pamb.gt.31)write(6,*)' ** CHECK Pamb IN TEST '
if(old1.eq.0)goto 31
err1=abs((v1/a1)-old1)/old1
err2=abs((v2/a2)-old2)/old2
err3=abs((v3/a3)-old3)/old3
if(err1.gt..0125)write(6,*)'error in heater 1 entry, test #'
*,testno
if(err2.gt..0125)write(6,*)'error in heater 2 entry, test #'
*,testno
if(err3.gt..0125)write(6,*)'error in heater 3 entry, test #'
119
*,testno
31 write(6,35)testno,v1/a1,v2/a2,v3/a3
write(2,35)testno,v1/a1,v2/a2,v3/a3
C if(flag.eq.1)goto 32
old1=v1/a1
old2=v2/a2
old3=v3/a3
flag=1.
32 continue
enddo
35 format(2x,f4.0,2x,3(1x,f10.6))
write(6,*)' '
write(6,*)' '
write(6,*)' Resistances are in file : output.dat'
stop
end
120
Reduce.F
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,NuS,NuN,NoseR,NoseL,LossesS,LossesN
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
FAC1=3.413 ! converts Watts to BTU/hr
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1,FILE='input.dat',STATUS='old')
OPEN(UNIT=2,FILE='nu-plots-side.dat',STATUS='old')
OPEN(UNIT=3,FILE='nu-plots-nose.dat',STATUS='old')
OPEN(UNIT=4,FILE='uncertain-side.out',STATUS='old')
OPEN(UNIT=5,FILE='uncertain-nose.out',STATUS='old')
OPEN(UNIT=7,FILE='output.dat',STATUS='old')
OPEN(UNIT=8,FILE='friction.out',STATUS='old')
OPEN(UNIT=9,FILE='nu-pictures-side.dat',STATUS='old')
OPEN(UNIT=10,FILE='nu-pictures-nose.dat',STATUS='old')
OPEN(UNIT=11,FILE='convergence.dat',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
NoseR=0.969 ! inches
NoseR=NoseR/12 ! feet
Angle=125. ! degrees
RigL=36. ! inches
Side=3. ! inches
Side=Side/12 ! feet
121
Side2=3.226 ! inches
Side2=Side2/12 ! feet
C
C CALCULATION
hypo1=sqrt(NoseR**2 + SIDE2**2)
hypo2=sqrt(NoseR**2 + SIDE**2)
beta1=atan(NoseR/SIDE2)*180/PI
beta2=atan(NoseR/SIDE)*180/PI
alpha1=90-beta1
alpha2=90-beta2
gamma1=180-65-alpha1
gamma2=180-60-alpha2
theta1=43.28255
theta2=180-gamma1-gamma2-theta1
sigma1=180-gamma1-theta1
Top=sqrt(hypo1**2 + hypo2**2 -
&2*hypo1*hypo2*COS((gamma1+gamma2)*PI/180))
Pitch=2.418 ! inches
nturb=9
Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +
&NoseR*COS(60*PI/180)
Wave=0.5*Top+NoseR*SIN(60*PI/180)
Bot=NoseR*(SIN(60*PI/180)+SIN(65*PI/180)) ! Flat projected bottom for radiation losses only
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side2+Top
Area1=0.5*NoseR*SIDE2
Area2=0.5*NoseR*SIDE
AreaNose=(PI*(NoseR**2)*(Angle/360))
AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)
Across=Area1+Area2+AreaNose+AreaTop
Dh=4*Across/Perim
! EACH HEATER
122
HlengthS=11.
HlengthS=HlengthS/12.
HwidthS=3.
HwidthS=HwidthS/12.
HareaS=HlengthS*HwidthS
HlengthN=10.9
HlengthN=HlengthN/12.
HwidthN=1.95
HwidthN=HwidthN/12.
HareaN=HlengthN*HwidthN
Write(7,101)12*NoseR,Angle,12*Side,12*Side2,
&12*Top,12*HlengthS,12*HwidthS,144*HareaS,12*HlengthN,
&12*HwidthN,144*HareaN,alpha1,alpha2,beta1,beta2,sigma1,
&gamma1,gamma2,theta1,theta2,12*Perim,144*ACross,12*Dh,
&Pitch,12*Have,12*Wave,12*Bot,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Side 1 (LC)=',f8.3,' inches',/,
&2x,'Side 2 (Plexi)=',f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Side Heater Length=',f8.3,' inches',/,
&2x,'Side Heater Width=',f8.3,' inches',/,
&2x,'Side Heater area=',f8.3,' Sq.in',/,
&2x,'Nose Heater Length=',f8.3,' inches',/,
&2x,'Nose Heater Width=',f8.3,' inches',/,
&2x,'Nose Heater area=',f8.3,' Sq.in',/,
&2x,'alpha1 and alpha2=',f8.3,5x,f8.3,/,
&2x,'beta1 and beta2=',f8.3,5x,f8.3,/,
&2x,'sigma1=',f8.3,/,
&2x,'gamma1 and gamma2=',f8.3,5x,f8.3,/,
&2x,'theta1 and theta2=',f8.3,5x,f8.3,/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Average Test Section Height=',f8.3,' inches',/,
&2x,'Average Test Section Width=',f8.3,' inches',/,
&2x,'Flat projection bottom for rad losses=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
! R E A D I N D A T A
read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid
Poe=Pitch/TurbH
123
eoDh=(TurbH/12)/Dh
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
WRITE(10,401)ntests
401 FORMAT(I4)
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
DO 333 I=1,11
READ(1,10)TITLE
WRITE(5,10)TITLE
WRITE(7,10)TITLE
333 WRITE(10,10)TITLE
10 FORMAT(A80,//)
WRITE(10,451)
451 FORMAT(' no. Re Nu h uncer',
&' Nu_smooth EF',/)
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,
&V4,A4,V5,A5,V6,A6
&,SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' V1,A1,V2,A2,V3,A3'
WRITE(7,*)' V4,A4,V5,A5,V6,A6'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,201)V1,A1,V2,A2,V3,A3
WRITE(7,201)V4,A4,V5,A5,V6,A6
201 FORMAT(5X,3(' ',F5.2,' ',F6.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
124
Athroat=PI*(Dthroat**2)/4. ! square inches
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
Mv=F(Athroat,Pven+Pamb,Tven+460)
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
C HEAT FLUX, BTU/(sqft.hr)
FluxS=V2*A2*FAC1/(HareaS)
FluxN=V5*A5*FAC1/(HareaN)
C TOTAL HEAT GENERATED FROMINLET TO CAMERA LOCATION , BTU/hr
Q=(A1*V1+A4*V4+0.5*A2*V2+0.5*A5*V5)*FAC1
CALL HTCSIDE(Q,FluxS,TmS,TsurfS,hS,LossesS)
CALL HTCNOSE(Q,FluxN,TmN,TsurfN,hN,LossesN)
TmRS=TmS+460.
CALL AIRPROP(TmRS,gammS,CONmS,VISmS,PRmS,CPmS)
VISmS=VISmS/3600.
TmRN=TmN+460.
CALL AIRPROP(TmRN,gammN,CONmN,VISmN,PRmN,CPmN)
VISmN=VISmN/3600.
C REYNOLDS NUMBER
ReS=4.*Mv/(Perim*VISmS)
ReN=4.*Mv/(Perim*VISmN)
! NUSSELT NUMBER
NuS=hS*Dh/CONmS
NuN=hN*Dh/CONmN
RatioNu=NuN/NuS
125
SmoothNuS=0.023*(ReS**0.8)*(PrmS**0.4)
SmoothNuN=0.023*(ReN**0.8)*(PrmN**0.4)
! ENHACEMENT
EFS=NuS/SmoothNuS
EFN=NuN/SmoothNuN
! UNCERTAINTY ANALYSIS
IND=1
CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,A4,V4,A5,V5,
&Dthroat,HareaS,TsurfS,Tin,LossesS,UncerS,IND)
IND=2
CALL UNCERTAIN(Pamb,Pven,Tven,A4,V4,A5,V5,A1,V1,A2,V2,
&Dthroat,HareaN,TsurfN,Tin,LossesN,UncerN,IND)
WRITE( 9,305)testno,ReS,NuS,hS,uncerS,SmoothNuS,EFS
WRITE(10,305)testno,ReN,NuN,hN,uncerN,SmoothNuN,EFN
305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)
WRITE(2,*)ReS,NuS
WRITE(3,*)ReN,NuN
WRITE(7,300)TmS,MV,ReS
WRITE(7,301)TmN,MV,ReN
WRITE(7,302)RatioNu
302 format(5x,'Nu_Nose/Nu_Side=',f8.3)
C***************************************************
! DARCY FRICTION FACTOR CALCULATIONS
Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb
Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb
TmR=0.5*(TmRS+TmRN)
Re=0.5*(ReS+ReN)
Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/
&(0.5*Rho*(Um**2))
fsmooth=0.316/(Re**0.25) ! Blasius correlation
126
write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Inlet Pressure=',f9.4,' psia',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm_Side=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReS=',F8.2)
301 FORMAT(30X,'Tm_Nose=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReN=',F8.2)
STOP
END
C************************************************************************************
**************C
C********************************** ON THE SIDE WALL
**********************************************C
C************************************************************************************
**************C
SUBROUTINE HTCSIDE(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
127
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
128
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! BIRK
tinc = 1.0e-03/12. ! BIRK
tadh1= 1.0e-03/12. ! BIRK
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
129
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Top*HlengthS ! Top surface
Afront=1.5*Side2*HlengthS ! Front surface
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Aback=1.5*Side*HlengthS ! Back surface
Abot =1.5*PI*NoseR*(Angle/360)*HlengthN ! Bottom surface
C write(6,*)Atop,Afront,Abot,Aback
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
130
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=h
htop=0.8*h ! Guess
hbot=1.2*h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Top,Bot,Have,HlengthN,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)Frtop,Frfront,Frbot,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
131
Fbot=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frbot
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
132
hfront=h
htop=0.8*h
hbot=1.2*h
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' ON THE SIDE WALL',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',
&/,10x,4F10.2,' F')
133
write(7,120)h,htop,hfront,hbot
120 FORMAT(5x,'hside=',F8.3,1X,'htop=',F8.3,1X,'hfront=',F8.3,1X,
&'hnose=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C****************************************************************************C
C****************************ON THE NOSE ************************************C
C****************************************************************************C
SUBROUTINE HTCNOSE(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
134
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
135
tkap = 1.0e-03/12. ! BIRK
tinc = 1.0e-03/12. ! BIRK
tadh1= 1.0e-03/12. ! BIRK
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
136
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Side2*HlengthS ! Top surface (since NOSE is now the back surface)
Afront=1.5*Top*HlengthS ! Front surface (since NOSE is now the back surface)
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Abot =1.5*Side*HlengthS ! Bottom surface
Aback=1.5*PI*NoseR*(Angle/360)*HlengthN ! Back surface
C write(6,*)Aback,Atop,Afront,Abot
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=(0.8/1.2)*h
htop=(1/1.2)*h ! Guess
hbot=(1/1.2)*h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
137
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Side2,Side,Wave,HlengthS,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)Frtop,Frfront,Frbot,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fbot=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
138
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frbot
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=(0.8/1.2)*h ! Guess
htop=(1/1.2)*h ! Guess
hbot=(1/1.2)*h ! Guess
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
139
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' ON THE NOSE',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Nose, Top, Front and Back Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,hbot,hfront,htop
120 FORMAT(5x,'hnose=',F8.3,1X,'hback=',F8.3,1X,'htop=',F8.3,1X,
&'hfront=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from Nose, Front, Ftop and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
140
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C****************************************************************************
C****************************************************************************
C**********************************************************************C
SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)
PI=4.*ATAN(1.E00)
W=H1
H=0.5*(Bot+Top)
T(1)=Tsurf + 460.
T(2)=Ttop + 460.
T(3)=Tfront+ 460.
T(4)=Tbot + 460.
W=W/(3.*Hlength)
H=H/(3.*Hlength)
C Emissivities
E(1)=.85 ! Liquid Crystal Foil, Back Wall
E(2)=.9 ! Plexiglas, Top Wall
E(3)=.9 ! Plexiglas, Front Wall
E(4)=.85 ! Liquid Crystal Foil, Nose Wall
C
N=4
SIGMA=0.1712E-08
C WRITE(7,150)
150 FORMAT(//,20X,'SHAPE FACTORS',//)
C
F11=0.
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
141
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F12=Z1*(Z2+Z3+Z4+Z5)
F14=F12
F13=1.-F11-F12-F14
C
F31=F13
F32=F12
F33=0.
F34=F14
C
DUM=W
W=H
H=DUM
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F21=Z1*(Z2+Z3+Z4+Z5)
F22=0.
F23=F21
F24=1.-F21-F22-F23
C
F41=F21
F42=F24
F43=F23
F44=0.
C
142
C WRITE(7,110)F11,F12,F13,F14
C WRITE(7,120)F21,F22,F23,F24
C WRITE(7,130)F31,F32,F33,F34
C WRITE(7,140)F41,F42,F43,F44
C
110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,
&5X,'F14=',F6.4,/)
120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,
&5X,'F24=',F6.4,/)
130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,
&5X,'F34=',F6.4,/)
140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,
&5X,'F44=',F6.4,//)
C WRITE(7,160)
160 FORMAT(/,20X,'EMISSIVITIES',//)
C WRITE(7,100)(I,E(I),I=1,N)
C WRITE(7,170)
170 FORMAT(/,20X,'TEMPERATURES IN R',//)
C WRITE(7,100)(I,T(I),I=1,N)
A(1,1)=F11-1./(1.-E(1))
A(1,2)=F12
A(1,3)=F13
A(1,4)=F14
C
A(2,1)=F21
A(2,2)=F22-1./(1.-E(2))
A(2,3)=F23
A(2,4)=F24
C
A(3,1)=F31
A(3,2)=F32
A(3,3)=F33-1./(1.-E(3))
A(3,4)=F34
C
A(4,1)=F41
A(4,2)=F42
A(4,3)=F43
A(4,4)=F44-1./(1.-E(4))
C
C WRITE(7,180)
180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)
C WRITE(7,200)((A(I,J),J=1,N),I=1,N)
DO I=1,N
B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))
ENDDO
C WRITE(7,250)
C WRITE(7,100)(I,B(I,1),I=1,N)
200 FORMAT(1X,4E15.6)
143
250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)
C WRITE(7,55)
55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)
CALL EQSOLVE(A,B,N,N,1)
C WRITE(7,50)
C WRITE(7,100)(I,B(I,1),I=1,N)
DO I=1,N
Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))
ENDDO
Frback =Q(1)
Frtop =Q(2)
Frfront=Q(3)
Frnose=Q(4)
C WRITE(7,350)
C WRITE(7,100)(I,Q(I),I=1,N)
100 FORMAT(4(I3,E15.6))
50 FORMAT(/,20X,'RADIOCITIES',/)
350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)
RETURN
END
C**********************************************************************C
C**********************************************************************C
SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,i4,V4,i5,V5,
&Dth,Harea,Tsurf,Tin,Losses,Uncer,IND)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 i1,i2,i4,i5,Losses,M1,M2
PI=4.*ATAN(1.E00)
C FAC=491.3744
FAC1=3.413 ! converts Watts to BTU/hr
C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)
C=0.24*0.5215*3600
C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J
P1=Pven+Pamb
T1=Tven+460.0
TI=Tin
TS=Tsurf
a=Harea
f=0.5
144
ATH=PI*(Dth**2)/4.
DATH=PI*((Dth+0.001)**2)/4. -ATH
h=((FAC1*(V2*i2)/a)-Losses)/
&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+V4*i4+f*V2*i2+f*V5*i5)))/
&(C*P1*ATH))
WRITE(5,*)' '
if(IND.EQ.1)WRITE(5,*)' hSide =',h,' BUT/hr.sqft.F'
if(IND.EQ.2)WRITE(5,*)' hNose =',h,' BUT/hr.sqft.F'
H2=h*h
C
C i2 v2
C ------- - Floss
C a
C ---------------------------------------
C sqrt(T1)(i1v1+i4v4+fi2v2+fi5v5)
C Ts-Ti - -------------------------
C C P1 A_throat
C
DLOSS=0.1*Losses
dv1=0.1
dv2=0.1
dv4=0.1
dv5=0.1
di1=0.01
di2=0.01
di4=0.01
di5=0.01
da=1./(32.*32.*144)
dts=0.5
dti=0.5
dt1=0.5
dp1=0.5
Df=0.1
C1=FAC1*(V2*i2/a)-Losses
Q1=C*P1*Ath
Q2=Q1*sqrt(T1)
M1=(Ts-Ti)*Q1
A=FAC1*(i1*v1+i4*v4)
145
B=FAC1*(i2*v2+i5*v5)
M2=M1-sqrt(T1)*(A+f*B)
DHDF=B*Q1*C1*sqrt(T1)/(M2**2)
DHDTI= C1*(Q1**2)/(M2**2)
DHDTS=-C1*(Q1**2)/(M2**2)
DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))
DHDLOSS=-Q1/M2
DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)
DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)
DHDI4=FAC1*v4*Q1*C1*sqrt(T1)/(M2**2)
DHDV4=FAC1*i4*Q1*C1*sqrt(T1)/(M2**2)
DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDI5=FAC1*v5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV5=FAC1*i5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDATH=C1*C*P1*(M2-M1)/(M2**2)
DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)
DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))
ZF=(DF*DHDF)**2
ZA=(DA*DHDA)**2
ZI1=(DI1*DHDI1)**2
ZV1=(DV1*DHDV1)**2
ZI2=(DI2*DHDI2)**2
ZV2=(DV2*DHDV2)**2
ZI4=(DI4*DHDI4)**2
ZV4=(DV4*DHDV4)**2
ZI5=(DI5*DHDI5)**2
ZV5=(DV5*DHDV5)**2
ZTS=(DTS*DHDTS)**2
ZTI=(DTI*DHDTI)**2
ZATH=(DATH*DHDATH)**2
ZP1=(DP1*DHDP1)**2
ZT1=(DT1*DHDT1)**2
ZLOSS=(DLOSS*DHDLOSS)**2
Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+ZI4+ZI4+ZV5+ZV5+
&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))
146
if(IND.EQ.1) then
WRITE(4,*)' TOTAL UNCER.%:',Uncer
WRITE(4,*)' '
WRITE(4,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(4,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(4,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(4,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(4,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(4,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h
WRITE(4,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h
WRITE(4,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h
WRITE(4,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h
WRITE(4,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(4,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(4,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(4,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(4,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(4,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(4,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
endif
if(IND.EQ.2) then
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(5,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h
WRITE(5,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h
WRITE(5,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h
WRITE(5,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h
WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
endif
RETURN
END
C**********************************************************************C
147
C**********************************************************************C
SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(NDIM,NDIM),B(NDIM,NB)
DO 291 J1=1,NA
C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE
C VALUE IN PIVOTAL COLUMN.
101 TEMP=0.
DO 121 J2=J1,NA
IF(ABS(A(J2,J1))-TEMP) 121,111,111
111 TEMP=ABS(A(J2,J1))
IBIG=J2
121 CONTINUE
IF(IBIG-J1)5001,201,131
C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE
C VALUE IN PIVOT POSITION.
131 DO 141 J2=J1,NA
TEMP=A(J1,J2)
A(J1,J2)=A(IBIG,J2)
141 A(IBIG,J2)=TEMP
DO 161 J2=1,NB
TEMP=B(J1,J2)
B(J1,J2)=B(IBIG,J2)
161 B(IBIG,J2)=TEMP
C COMPUTE COEFFICIENTS IN PIVOTAL ROW.
201 TEMP=A(J1,J1)
DO 221 J2=J1,NA
221 A(J1,J2)=A(J1,J2)/TEMP
DO 231 J2=1,NB
231 B(J1,J2)=B(J1,J2)/TEMP
IF(J1-NA)236,301,5001
C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.
236 N1=J1+1
DO 281 J2=N1,NA
TEMP=A(J2,J1)
DO 241 J3=N1,NA
241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)
DO 251 J3=1,NB
251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)
281 CONTINUE
291 CONTINUE
C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.
301 IF(NA-1)5001,5001,311
311 DO 391 J1=1,NB
N1=NA
321 DO 341 J2=N1,NA
341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)
148
N1=N1-1
IF(N1-1)5001,391,321
391 CONTINUE
5001 CONTINUE
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
149
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
150
Rig2-reduce-friction.f
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,NoseR,NoseL
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1, FILE='input.dat',STATUS='old')
OPEN(UNIT=5, FILE='fric-uncertain.out',STATUS='old')
OPEN(UNIT=7, FILE='friction-details.out',STATUS='old')
OPEN(UNIT=8, FILE='friction-plot.out',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
! T E S T S E C T I O N G E O M E T R Y
NoseR=0.969 ! inches
NoseR=NoseR/12 ! feet
Angle=125. ! degrees
RigL=36. ! inches
Side=3. ! inches
Side=Side/12 ! feet
Side2=3.226 ! inches
Side2=Side2/12 ! feet
C
C CALCULATION
hypo1=sqrt(NoseR**2 + SIDE2**2)
hypo2=sqrt(NoseR**2 + SIDE**2)
151
beta1=atan(NoseR/SIDE2)*180/PI
beta2=atan(NoseR/SIDE)*180/PI
alpha1=90-beta1
alpha2=90-beta2
gamma1=180-65-alpha1
gamma2=180-60-alpha2
theta1=43.28255
theta2=180-gamma1-gamma2-theta1
sigma1=180-gamma1-theta1
Top=sqrt(hypo1**2 + hypo2**2 -
&2*hypo1*hypo2*COS((gamma1+gamma2)*PI/180))
Pitch=2.418 ! inches
nturb=9
RibbedL=nturb*Pitch
Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +
&NoseR*COS(60*PI/180)
Wave=0.5*Top+NoseR*SIN(60*PI/180)
Bot=NoseR*(SIN(60*PI/180)+SIN(65*PI/180)) ! Flat projected bottom for radiation losses only
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side2+Top
Area1=0.5*NoseR*SIDE2
Area2=0.5*NoseR*SIDE
AreaNose=(PI*(NoseR**2)*(Angle/360))
AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)
Across=Area1+Area2+AreaNose+AreaTop
Dh=4*Across/Perim
read(1,*)ntests,TurbH,TurbW,Turbr
DO 333 I=1,10
READ(1,10)TITLE
WRITE(5,10)TITLE
333 WRITE(7,10)TITLE
10 FORMAT(A80,//)
152
Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,
&12.*Top,12.*Bot,12.*Perim,144.*ACross,12*Dh,Pitch,RigL,
&RibbedL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Nose Length=',f8.3,' inches',/,
&2x,'Side 1 (Plexi)=',f8.3,' inches',/,
&2x,'Side 2 (LC)=',f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Bottom Flat Line=',f8.3,' inches',/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/,
&2x,'Ribbed Length=',f8.3,' inches',/)
Poe=Pitch/TurbH
eoDh=TurbH/(12*Dh)
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
401 FORMAT(I4)
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f9.4,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
! R E A D I N D A T A
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,
&SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
153
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
Mv=F(Athroat,Pven+Pamb,Tven+460)
TinR=Tin+460.
CALL AIRPROP(TinR,gamain,CONin,VISin,PRin,CPin)
VISin=VISin/3600.
C REYNOLDS NUMBER
Re=4.*Mv/(Perim*VISin)
C***************************************************
! DARCY FRICTION FACTOR CALCULATIONS
Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb
Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb
Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TinR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/RibbedL)*((Pinlet-Pamb)*144.)/
&(0.5*Rho*(Um**2))
DeltaP=(Pinlet-Pamb)*144.
CALL UNCERTAIN(Dh,RibbedL,DeltaP,Rho,Um,Uncer)
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,DeltaP,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
154
WRITE(8,304)Re,fDarcy,fsmooth,fDarcy/fsmooth
304 format(f8.1,2(4x,E13.7),F8.3)
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Pressure Drop =',f9.4,' inches of water',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)
STOP
END
C**********************************************************************C
SUBROUTINE UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)
IMPLICIT REAL*8(A-H,O-Z)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
dDh =0.05/12. ! feet
dRigL =0.05 ! inches
dDeltaP=0.001*H2Otopsi*144 ! psf (0.002 inches of water)
dRho =0.02*Rho ! 2% error
dUm =0.02*Um ! 2% error
fDarcy=gc*((12.*Dh)/RigL)*(DeltaP)/
&(0.5*Rho*(Um**2))
f2=fDarcy**2
155
WRITE(5,*)' '
WRITE(5,*)' fDarcy =',fDarcy
WRITE(5,*)' '
C=24*gc
dfdDh=C*DeltaP/(RigL*Rho*(Um**2))
dfdDeltaP=C*Dh/(RigL*Rho*(Um**2))
dfdRigL=-C*Dh*DeltaP/(RigL*RigL*Rho*(Um**2))
dfdRho=-C*Dh*DeltaP/(RigL*Rho*Rho*(Um**2))
dfdUm=-2*C*Dh*DeltaP/(RigL*Rho*(Um**3))
ZDh=(dfdDh*dDh)**2
ZRigL=(dfdRigL*dRigL)**2
ZDeltaP=(dfdDeltaP*dDeltaP)**2
ZRho=(dfdRho*dRho)**2
ZUm=(dfdUm*dUm)**2
Uncer=100*SQRT((ZDh+ZRigL+ZDeltaP+ZRho+ZUm)/(f2))
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with Dh',100.*sqrt(ZDh)/fDarcy
WRITE(5,*)' % Uncer. assoc. with RigL',100.*sqrt(ZRigL)/fDarcy
WRITE(5,*)' % Uncer. assoc. with DeltaP',100.*sqrt(ZDeltaP)/fDarcy
WRITE(5,*)' % Uncer. assoc. with Rho',100.*sqrt(ZRho)/fDarcy
WRITE(5,*)' % Uncer. assoc. with Um',100.*sqrt(ZUm)/fDarcy
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
156
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
157
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C*******************************************************************
158
Appendix A.3: FORTRAN Codes for Rig 3A
Author: Professor Mohammad Taslim
Check.f
character*25 filename
character*80 title
write(6,*)'enter the name of the data file that you',
* ' want to check'
read(5,10)filename
10 format(a25)
open(unit=1,file=filename,status='old')
open(unit=2,file='output.dat',status='old')
write(6,*)'is there a title for this file? enter 1=yes, 0=no'
read(5,*)ans
if(ans.eq.0)goto 30
read(1,*)NTESTS
do i=1,11
read(1,20)title
20 FORMAT(A80,//)
enddo
30 do i=1,NTESTS
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,V4,A4,
&V5,A5,V6,A6,SG,Pplen,DP,Pamb,Dthroat
if(Tven.lt.45.or.Tven.gt.90)write(6,*)
&' ** CHECK Tven IN TEST ',i
if(Tin1.lt.50.or.Tin1.gt.90)write(6,*)' ** CHECK Tin1 IN TEST '
if(Tin2.lt.50.or.Tin2.gt.90)write(6,*)' ** CHECK Tin2 IN TEST '
if(Tamb.lt.60.or.Tamb.gt.80)write(6,*)' ** CHECK Tamb IN TEST '
if(Pamb.lt.28.or.Pamb.gt.31)write(6,*)' ** CHECK Pamb IN TEST '
if(old1.eq.0)goto 31
err1=abs((v1/a1)-old1)/old1
err2=abs((v2/a2)-old2)/old2
err3=abs((v3/a3)-old3)/old3
err4=abs((v4/a4)-old4)/old4
err5=abs((v5/a5)-old5)/old5
err6=abs((v6/a6)-old6)/old6
if(err1.gt..0125)write(6,*)'error in heater 1 entry, test #'
*,testno
if(err2.gt..0125)write(6,*)'error in heater 2 entry, test #'
159
*,testno
if(err3.gt..0125)write(6,*)'error in heater 3 entry, test #'
*,testno
if(err4.gt..0125)write(6,*)'error in heater 4 entry, test #'
*,testno
if(err5.gt..0125)write(6,*)'error in heater 5 entry, test #'
*,testno
if(err6.gt..0125)write(6,*)'error in heater 6 entry, test #'
*,testno
31 write(6,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5,v6/a6
write(2,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5,v6/a6
C if(flag.eq.1)goto 32
old1=v1/a1
old2=v2/a2
old3=v3/a3
old4=v4/a4
old5=v5/a5
old6=v6/a6
flag=1.
32 continue
enddo
35 format(1x,f4.0,2x,6(1x,f10.6))
write(6,*)' '
write(6,*)' '
write(6,*)' Resistances are in file : output.dat'
stop
end
160
Rig3a-Reduce-Heat-Transfer.f
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,NuS,NuN,NoseR,NoseL,LossesS,LossesN,l1,l2
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
FAC1=3.413 ! converts Watts to BTU/hr
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1,FILE='input.dat',STATUS='old')
OPEN(UNIT=2,FILE='nu-plots-side.dat',STATUS='old')
OPEN(UNIT=3,FILE='nu-plots-nose.dat',STATUS='old')
OPEN(UNIT=4,FILE='uncertain-side.out',STATUS='old')
OPEN(UNIT=5,FILE='uncertain-nose.out',STATUS='old')
OPEN(UNIT=7,FILE='output.dat',STATUS='old')
OPEN(UNIT=8,FILE='friction.out',STATUS='old')
OPEN(UNIT=9,FILE='nu-pictures-side.dat',STATUS='old')
OPEN(UNIT=10,FILE='nu-pictures-nose.dat',STATUS='old')
OPEN(UNIT=11,FILE='convergence.dat',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
NoseR=1.281 ! inches
NoseR=NoseR/12 ! feet
Angle=138. ! degrees
RigL=36. ! inches
Side=3. ! inches
Side=Side/12 ! feet
161
Side2=1.372 ! inches
Side2=Side2/12 ! feet
C
C CALCULATION
hypo1=sqrt(NoseR**2 + SIDE**2)
hypo2=sqrt(NoseR**2 + SIDE2**2)
beta1=atan(NoseR/SIDE)*180/PI
beta2=atan(NoseR/SIDE2)*180/PI
alpha1=90-beta1
alpha2=90-beta2
gamma1=180-0.5*Angle-alpha1
gamma2=180-0.5*Angle-alpha2
l1=NoseR*tan(0.5*Angle*PI/180)
l2=NoseR*tan(0.5*Angle*PI/180)
a=SIDE +l1
b=SIDE2+l2
Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))
stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)
stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)
theta1=Asin(stheta1)*180/PI
theta2=Asin(stheta2)*180/PI
sigma1=180-gamma1-theta1
sigma2=180-gamma2-theta2
Pitch=2.48 ! inches
nturb=9
Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +
&NoseR*COS(0.5*Angle*PI/180)
Wave=0.5*Top+NoseR*SIN(0.5*Angle*PI/180)
Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side2+Top
Area1=0.5*NoseR*SIDE
162
Area2=0.5*NoseR*SIDE2
AreaNose=(PI*(NoseR**2)*(Angle/360))
AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)
Across=Area1+Area2+AreaNose+AreaTop
Dh=4*Across/Perim
C NOTE: At the camera location, Side and Nose heaters were exactly 3" by 11" (4 mils, MINCO)
C Beginning and end sections were covered with (1.935" x 10.8" nose) and (4.09" x 10.8" side) (6
mils,BIRK)
! HEATER AT CAMERA LOCATION:
HlengthS=11.
HlengthS=HlengthS/12.
HwidthS=3.
HwidthS=HwidthS/12.
HareaS=HlengthS*HwidthS
HlengthN=11.
HlengthN=HlengthN/12.
HwidthN=3.0
HwidthN=HwidthN/12.
HareaN=HlengthN*HwidthN
Write(7,101)12*NoseR,Angle,12*Side,12*Side2,12*l1,12*l2,
&12*Top,12*HlengthS,12*HwidthS,144*HareaS,12*HlengthN,
&12*HwidthN,144*HareaN,alpha1,alpha2,beta1,beta2,sigma1,
&sigma2,gamma1,gamma2,theta1,theta2,12*Perim,144*ACross,12*Dh,
&Pitch,12*Have,12*Wave,12*Bot,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Side 1 (LC)=',f8.3,' inches',/,
&2x,'Side 2 (Plexi)=',f8.3,' inches',/,
&2x,'l1 and l2=',f8.3,5x,f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Side Heater Length=',f8.3,' inches',/,
&2x,'Side Heater Width=',f8.3,' inches',/,
&2x,'Side Heater area=',f8.3,' Sq.in',/,
&2x,'Nose Heater Length=',f8.3,' inches',/,
&2x,'Nose Heater Width=',f8.3,' inches',/,
&2x,'Nose Heater area=',f8.3,' Sq.in',/,
&2x,'alpha1 and alpha2=',f8.3,5x,f8.3,/,
&2x,'beta1 and beta2=',f8.3,5x,f8.3,/,
&2x,'sigma1 and sigma2=',f8.3,5x,f8.3,/,
&2x,'gamma1 and gamma2=',f8.3,5x,f8.3,/,
&2x,'theta1 and theta2=',f8.3,5x,f8.3,/,
163
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Average Test Section Height=',f8.3,' inches',/,
&2x,'Average Test Section Width=',f8.3,' inches',/,
&2x,'Flat projection bottom for rad losses=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
! R E A D I N D A T A
read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid
Poe=Pitch/TurbH
eoDh=TurbH/(12*Dh)
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
WRITE(10,401)ntests
401 FORMAT(I4)
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
DO 333 I=1,11
READ(1,10)TITLE
WRITE(5,10)TITLE
WRITE(7,10)TITLE
333 WRITE(10,10)TITLE
10 FORMAT(A80,//)
WRITE(9,451)
WRITE(10,451)
451 FORMAT(' no. Re Nu h uncer',
&' Nu_smooth EF',/)
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,
&V4,A4,V5,A5,V6,A6,SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
WRITE(7,*)' '
164
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' V1,A1,V2,A2,V3,A3'
WRITE(7,*)' V4,A4,V5,A5,V6,A6'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,201)V1,A1,V2,A2,V3,A3
WRITE(7,201)V4,A4,V5,A5,V6,A6
201 FORMAT(5X,3(' ',F5.2,' ',F6.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
Mv=F(Athroat,Pven+Pamb,Tven+460)
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
C HEAT FLUX, BTU/(sqft.hr)
FluxS=V2*A2*FAC1/HareaS
FluxN=V5*A5*FAC1/HareaN
C TOTAL HEAT GENERATED FROMINLET TO CAMERA LOCATION , BTU/hr
Q=(A1*V1+A4*V4+0.5*A2*V2+0.5*A5*V5)*FAC1
CALL HTCSIDE(Q,FluxS,TmS,TsurfS,hS,LossesS)
CALL HTCNOSE(Q,FluxN,TmN,TsurfN,hN,LossesN)
TmRS=TmS+460.
CALL AIRPROP(TmRS,gammS,CONmS,VISmS,PRmS,CPmS)
VISmS=VISmS/3600.
TmRN=TmN+460.
CALL AIRPROP(TmRN,gammN,CONmN,VISmN,PRmN,CPmN)
165
VISmN=VISmN/3600.
C REYNOLDS NUMBER
ReS=4.*Mv/(Perim*VISmS)
ReN=4.*Mv/(Perim*VISmN)
! NUSSELT NUMBER
NuS=hS*Dh/CONmS
NuN=hN*Dh/CONmN
RatioNu=NuN/NuS
SmoothNuS=0.023*(ReS**0.8)*(PrmS**0.4)
SmoothNuN=0.023*(ReN**0.8)*(PrmN**0.4)
! ENHACEMENT
EFS=NuS/SmoothNuS
EFN=NuN/SmoothNuN
! UNCERTAINTY ANALYSIS
IND=1
CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,A4,V4,A5,V5,
&Dthroat,HareaS,TsurfS,Tin,LossesS,UncerS,IND)
IND=2
CALL UNCERTAIN(Pamb,Pven,Tven,A4,V4,A5,V5,A1,V1,A2,V2,
&Dthroat,HareaN,TsurfN,Tin,LossesN,UncerN,IND)
WRITE( 9,305)testno,ReS,NuS,hS,uncerS,SmoothNuS,EFS
WRITE(10,305)testno,ReN,NuN,hN,uncerN,SmoothNuN,EFN
305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)
WRITE(2,*)ReS,NuS
WRITE(3,*)ReN,NuN
WRITE(7,300)TmS,MV,ReS
WRITE(7,301)TmN,MV,ReN
WRITE(7,302)RatioNu
302 format(5x,'Nu_Nose/Nu_Side=',f8.3)
C**********************************************************************************
C**********************************************************************************
! DARCY FRICTION FACTOR CALCULATIONS
166
Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb
Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb
TmR=0.5*(TmRS+TmRN)
Re=0.5*(ReS+ReN)
Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*TmR)
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/
&(0.5*Rho*(Um**2))
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth
C**********************************************************************************
C**********************************************************************************
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Inlet Pressure=',f9.4,' psia',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm_Side=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReS=',F8.2)
301 FORMAT(30X,'Tm_Nose=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReN=',F8.2)
STOP
END
C************************************************************************************
**************C
C********************************** ON THE SIDE WALL
**********************************************C
167
C************************************************************************************
**************C
SUBROUTINE HTCSIDE(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
168
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! MINCO
tinc = 0.5e-03/12. ! MINCO
tadh1= 0.75e-03/12. ! MINCO
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
169
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Top*HlengthS ! Top surface
Afront=1.5*Side2*HlengthS ! Front surface
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
170
C THE POINT IN QUESTION
Aback=1.5*Side*HlengthS ! Back surface
Abot =1.5*PI*NoseR*(Angle/360)*HlengthN ! Bottom surface
C write(6,*)Atop,Afront,Abot,Aback
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=h
htop=0.8*h ! Guess
hbot=1.2*h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Top,Bot,Have,HlengthN,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)Frtop,Frfront,Frbot,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
171
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fbot=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frbot
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
172
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=h
htop=0.8*h
hbot=1.2*h
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' ON THE SIDE WALL',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
173
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,htop,hfront,hbot
120 FORMAT(5x,'hside=',F8.3,1X,'htop=',F8.3,1X,'hfront=',F8.3,1X,
&'hnose=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C****************************************************************************C
C****************************ON THE NOSE ************************************C
C****************************************************************************C
SUBROUTINE HTCNOSE(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
174
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
175
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! MINCO
tinc = 0.5e-03/12. ! MINCO
tadh1= 0.75e-03/12. ! MINCO
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
176
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Side2*HlengthS ! Top surface (since NOSE is now the back surface)
Afront=1.5*Top*HlengthS ! Front surface (since NOSE is now the back surface)
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Abot =1.5*Side*HlengthS ! Bottom surface
Aback=1.5*PI*NoseR*(Angle/360)*HlengthN ! Back surface
C write(6,*)Aback,Atop,Afront,Abot
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
177
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=(0.8/1.2)*h
htop=(1/1.2)*h ! Guess
hbot=(1/1.2)*h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Side2,Side,Wave,HlengthS,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)Frtop,Frfront,Frbot,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
178
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fbot=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frbot
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
179
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=(0.8/1.2)*h ! Guess
htop=(1/1.2)*h ! Guess
hbot=(1/1.2)*h ! Guess
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' ON THE NOSE',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
180
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Nose, Top, Front and Back Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,hbot,hfront,htop
120 FORMAT(5x,'hnose=',F8.3,1X,'hback=',F8.3,1X,'htop=',F8.3,1X,
&'hfront=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from Nose, Front, Ftop and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C****************************************************************************
C****************************************************************************
C**********************************************************************C
SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)
PI=4.*ATAN(1.E00)
W=H1
H=0.5*(Bot+Top)
T(1)=Tsurf + 460.
T(2)=Ttop + 460.
T(3)=Tfront+ 460.
T(4)=Tbot + 460.
W=W/(3.*Hlength)
H=H/(3.*Hlength)
C Emissivities
E(1)=.85 ! Liquid Crystal Foil, Back Wall
E(2)=.9 ! Plexiglas, Top Wall
181
E(3)=.9 ! Plexiglas, Front Wall
E(4)=.85 ! Liquid Crystal Foil, Nose Wall
C
N=4
SIGMA=0.1712E-08
C WRITE(7,150)
150 FORMAT(//,20X,'SHAPE FACTORS',//)
C
F11=0.
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F12=Z1*(Z2+Z3+Z4+Z5)
F14=F12
F13=1.-F11-F12-F14
C
F31=F13
F32=F12
F33=0.
F34=F14
C
DUM=W
W=H
H=DUM
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
182
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F21=Z1*(Z2+Z3+Z4+Z5)
F22=0.
F23=F21
F24=1.-F21-F22-F23
C
F41=F21
F42=F24
F43=F23
F44=0.
C
C WRITE(7,110)F11,F12,F13,F14
C WRITE(7,120)F21,F22,F23,F24
C WRITE(7,130)F31,F32,F33,F34
C WRITE(7,140)F41,F42,F43,F44
C
110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,
&5X,'F14=',F6.4,/)
120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,
&5X,'F24=',F6.4,/)
130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,
&5X,'F34=',F6.4,/)
140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,
&5X,'F44=',F6.4,//)
C WRITE(7,160)
160 FORMAT(/,20X,'EMISSIVITIES',//)
C WRITE(7,100)(I,E(I),I=1,N)
C WRITE(7,170)
170 FORMAT(/,20X,'TEMPERATURES IN R',//)
C WRITE(7,100)(I,T(I),I=1,N)
A(1,1)=F11-1./(1.-E(1))
A(1,2)=F12
A(1,3)=F13
A(1,4)=F14
C
A(2,1)=F21
A(2,2)=F22-1./(1.-E(2))
A(2,3)=F23
A(2,4)=F24
C
A(3,1)=F31
A(3,2)=F32
183
A(3,3)=F33-1./(1.-E(3))
A(3,4)=F34
C
A(4,1)=F41
A(4,2)=F42
A(4,3)=F43
A(4,4)=F44-1./(1.-E(4))
C
C WRITE(7,180)
180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)
C WRITE(7,200)((A(I,J),J=1,N),I=1,N)
DO I=1,N
B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))
ENDDO
C WRITE(7,250)
C WRITE(7,100)(I,B(I,1),I=1,N)
200 FORMAT(1X,4E15.6)
250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)
C WRITE(7,55)
55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)
CALL EQSOLVE(A,B,N,N,1)
C WRITE(7,50)
C WRITE(7,100)(I,B(I,1),I=1,N)
DO I=1,N
Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))
ENDDO
Frback =Q(1)
Frtop =Q(2)
Frfront=Q(3)
Frnose=Q(4)
C WRITE(7,350)
C WRITE(7,100)(I,Q(I),I=1,N)
100 FORMAT(4(I3,E15.6))
50 FORMAT(/,20X,'RADIOCITIES',/)
350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)
RETURN
END
C**********************************************************************C
C**********************************************************************C
SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,i4,V4,i5,V5,
&Dth,Harea,Tsurf,Tin,Losses,Uncer,IND)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 i1,i2,i4,i5,Losses,M1,M2
PI=4.*ATAN(1.E00)
184
C FAC=491.3744
FAC1=3.413 ! converts Watts to BTU/hr
C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)
C=0.24*0.5215*3600
C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J
P1=Pven+Pamb
T1=Tven+460.0
TI=Tin
TS=Tsurf
a=Harea
f=0.5
ATH=PI*(Dth**2)/4.
DATH=PI*((Dth+0.001)**2)/4. -ATH
h=((FAC1*(V2*i2)/a)-Losses)/
&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+V4*i4+f*V2*i2+f*V5*i5)))/
&(C*P1*ATH))
WRITE(5,*)' '
if(IND.EQ.1)WRITE(5,*)' hSide =',h,' BUT/hr.sqft.F'
if(IND.EQ.2)WRITE(5,*)' hNose =',h,' BUT/hr.sqft.F'
H2=h*h
C
C i2 v2
C ------- - Floss
C a
C ---------------------------------------
C sqrt(T1)(i1v1+i4v4+fi2v2+fi5v5)
C Ts-Ti - -------------------------
C C P1 A_throat
C
DLOSS=0.1*Losses
dv1=0.1
dv2=0.1
dv4=0.1
dv5=0.1
di1=0.01
185
di2=0.01
di4=0.01
di5=0.01
da=1./(32.*32.*144)
dts=0.5
dti=0.5
dt1=0.5
dp1=0.5
Df=0.1
C1=FAC1*(V2*i2/a)-Losses
Q1=C*P1*Ath
Q2=Q1*sqrt(T1)
M1=(Ts-Ti)*Q1
A=FAC1*(i1*v1+i4*v4)
B=FAC1*(i2*v2+i5*v5)
M2=M1-sqrt(T1)*(A+f*B)
DHDF=B*Q1*C1*sqrt(T1)/(M2**2)
DHDTI= C1*(Q1**2)/(M2**2)
DHDTS=-C1*(Q1**2)/(M2**2)
DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))
DHDLOSS=-Q1/M2
DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)
DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)
DHDI4=FAC1*v4*Q1*C1*sqrt(T1)/(M2**2)
DHDV4=FAC1*i4*Q1*C1*sqrt(T1)/(M2**2)
DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDI5=FAC1*v5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV5=FAC1*i5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDATH=C1*C*P1*(M2-M1)/(M2**2)
DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)
DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))
ZF=(DF*DHDF)**2
ZA=(DA*DHDA)**2
ZI1=(DI1*DHDI1)**2
186
ZV1=(DV1*DHDV1)**2
ZI2=(DI2*DHDI2)**2
ZV2=(DV2*DHDV2)**2
ZI4=(DI4*DHDI4)**2
ZV4=(DV4*DHDV4)**2
ZI5=(DI5*DHDI5)**2
ZV5=(DV5*DHDV5)**2
ZTS=(DTS*DHDTS)**2
ZTI=(DTI*DHDTI)**2
ZATH=(DATH*DHDATH)**2
ZP1=(DP1*DHDP1)**2
ZT1=(DT1*DHDT1)**2
ZLOSS=(DLOSS*DHDLOSS)**2
Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+ZI4+ZI4+ZV5+ZV5+
&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/H2)
if(IND.EQ.1) then
WRITE(4,*)' TOTAL UNCER.%:',Uncer
WRITE(4,*)' '
WRITE(4,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(4,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(4,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(4,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(4,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(4,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h
WRITE(4,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h
WRITE(4,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h
WRITE(4,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h
WRITE(4,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(4,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(4,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(4,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(4,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(4,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(4,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
endif
if(IND.EQ.2) then
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(5,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h
187
WRITE(5,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h
WRITE(5,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h
WRITE(5,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h
WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
endif
RETURN
END
C**********************************************************************C
C**********************************************************************C
SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(NDIM,NDIM),B(NDIM,NB)
DO 291 J1=1,NA
C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE
C VALUE IN PIVOTAL COLUMN.
101 TEMP=0.
DO 121 J2=J1,NA
IF(ABS(A(J2,J1))-TEMP) 121,111,111
111 TEMP=ABS(A(J2,J1))
IBIG=J2
121 CONTINUE
IF(IBIG-J1)5001,201,131
C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE
C VALUE IN PIVOT POSITION.
131 DO 141 J2=J1,NA
TEMP=A(J1,J2)
A(J1,J2)=A(IBIG,J2)
141 A(IBIG,J2)=TEMP
DO 161 J2=1,NB
TEMP=B(J1,J2)
B(J1,J2)=B(IBIG,J2)
161 B(IBIG,J2)=TEMP
C COMPUTE COEFFICIENTS IN PIVOTAL ROW.
201 TEMP=A(J1,J1)
DO 221 J2=J1,NA
221 A(J1,J2)=A(J1,J2)/TEMP
DO 231 J2=1,NB
231 B(J1,J2)=B(J1,J2)/TEMP
188
IF(J1-NA)236,301,5001
C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.
236 N1=J1+1
DO 281 J2=N1,NA
TEMP=A(J2,J1)
DO 241 J3=N1,NA
241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)
DO 251 J3=1,NB
251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)
281 CONTINUE
291 CONTINUE
C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.
301 IF(NA-1)5001,5001,311
311 DO 391 J1=1,NB
N1=NA
321 DO 341 J2=N1,NA
341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)
N1=N1-1
IF(N1-1)5001,391,321
391 CONTINUE
5001 CONTINUE
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
189
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
190
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
191
Rig3a-reduce-friction.f
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,NoseR,NoseL
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1, FILE='input.dat',STATUS='old')
OPEN(UNIT=5, FILE='fric-uncertain.out',STATUS='old')
OPEN(UNIT=7, FILE='friction.out',STATUS='old')
OPEN(UNIT=8, FILE='friction-plot.out',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
! T E S T S E C T I O N G E O M E T R Y
NoseR=1.281 ! inches
NoseR=NoseR/12 ! feet
Angle=138. ! degrees
RigL=36. ! inches
Side=3. ! inches
Side=Side/12 ! feet
Side2=1.372 ! inches
Side2=Side2/12 ! feet
C
C CALCULATION
hypo1=sqrt(NoseR**2 + SIDE**2)
hypo2=sqrt(NoseR**2 + SIDE2**2)
192
beta1=atan(NoseR/SIDE)*180/PI
beta2=atan(NoseR/SIDE2)*180/PI
alpha1=90-beta1
alpha2=90-beta2
gamma1=180-0.5*Angle-alpha1
gamma2=180-0.5*Angle-alpha2
l1=NoseR*tan(0.5*Angle*PI/180)
l2=NoseR*tan(0.5*Angle*PI/180)
a=SIDE +l1
b=SIDE2+l2
Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))
stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)
stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)
theta1=Asin(stheta1)*180/PI
theta2=Asin(stheta2)*180/PI
sigma1=180-gamma1-theta1
sigma2=180-gamma2-theta2
Pitch=2.48 ! inches
nturb=9
Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +
&NoseR*COS(0.5*Angle*PI/180)
Wave=0.5*Top+NoseR*SIN(0.5*Angle*PI/180)
Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side2+Top
Area1=0.5*NoseR*SIDE
Area2=0.5*NoseR*SIDE2
AreaNose=(PI*(NoseR**2)*(Angle/360))
AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)
Across=Area1+Area2+AreaNose+AreaTop
Dh=4*Across/Perim
193
read(1,*)ntests,TurbH,TurbW,Turbr
DO 333 I=1,10
READ(1,10)TITLE
WRITE(5,10)TITLE
333 WRITE(7,10)TITLE
10 FORMAT(A80,//)
Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,
&12.*Top,12.*Bot,12.*Perim,144.*ACross,12*Dh,Pitch,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Nose Length=',f8.3,' inches',/,
&2x,'Side 1 (Plexi)=',f8.3,' inches',/,
&2x,'Side 2 (LC)=',f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Bottom Flat Line=',f8.3,' inches',/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
Poe=Pitch/TurbH
eoDh=TurbH/(12*Dh)
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
401 FORMAT(I4)
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f9.4,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
! R E A D I N D A T A
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,
&SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
194
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
Mv=F(Athroat,Pven+Pamb,Tven+460)
TinR=Tin+460.
CALL AIRPROP(TinR,gamain,CONin,VISin,PRin,CPin)
VISin=VISin/3600.
C REYNOLDS NUMBER
Re=4.*Mv/(Perim*VISin)
C***************************************************
! DARCY FRICTION FACTOR CALCULATIONS
Pplen=2*Pplen*H2Otopsi+Pamb
DeltaP=2*Pinlet ! inches of water using Micromanometer
Rho=(Pamb+0.5*DeltaP*H2Otopsi)*144./(Rgas*(TinR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*(DeltaP*H2Otopsi*144.)/
&(0.5*Rho*(Um**2))
CALL UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)
195
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,DeltaP,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,304)Re,fDarcy,fsmooth,fDarcy/fsmooth
304 format(f8.1,2(4x,E13.7),F8.3)
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Pressure Drop =',f9.4,' inches of water',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)
STOP
END
C**********************************************************************C
SUBROUTINE UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)
IMPLICIT REAL*8(A-H,O-Z)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
C=24*144*gc*H2Otopsi
dDh =0.05/12.
dRigL =0.1 ! inches
dDeltaP=0.002*H2Otopsi ! 0.002 inches of water
dRho =0.02*Rho ! 2% error
dUm =0.02*Um ! 2% error
196
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*(DeltaP*H2Otopsi*144.)/
&(0.5*Rho*(Um**2))
f2=fDarcy**2
WRITE(5,*)' '
WRITE(5,*)' fDarcy =',fDarcy
WRITE(5,*)' '
dfdDh=C*DeltaP/(RigL*Rho*(Um**2))
dfdDeltaP=C*Dh/(RigL*Rho*(Um**2))
dfdRigL=-C*Dh*DeltaP/(RigL*RigL*Rho*(Um**2))
dfdRho=-C*Dh*DeltaP/(RigL*Rho*Rho*(Um**2))
dfdUm=-2*C*Dh*DeltaP/(RigL*Rho*(Um**3))
ZDh=(dfdDh*dDh)**2
ZRigL=(dfdRigL*dRigL)**2
ZDeltaP=(dfdDeltaP*dDeltaP)**2
ZRho=(dfdRho*dRho)**2
ZUm=(dfdUm*dUm)**2
Uncer=100*SQRT((ZDh+ZRigL+ZDeltaP+ZRho+ZUm)/(f2))
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with Dh',100.*sqrt(ZDh)/fDarcy
WRITE(5,*)' % Uncer. assoc. with RigL',100.*sqrt(ZRigL)/fDarcy
WRITE(5,*)' % Uncer. assoc. with DeltaP',100.*sqrt(ZDeltaP)/fDarcy
WRITE(5,*)' % Uncer. assoc. with Rho',100.*sqrt(ZRho)/fDarcy
WRITE(5,*)' % Uncer. assoc. with Um',100.*sqrt(ZUm)/fDarcy
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
197
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
198
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
199
Appendix A.4: FORTRAN Codes for Rig 3B
Author: Professor Mohammad Taslim
Reduce.f
character*25 filename
character*80 title
write(6,*)'enter the name of the data file that u',
* ' want to check'
read(5,10)filename
10 format(a25)
open(unit=1,file=filename,status='old')
open(unit=2,file='output.dat',status='old')
write(6,*)'is there a title for this file? enter 1=yes, 0=no'
read(5,*)ans
if(ans.eq.0)goto 30
read(1,*)NTESTS
do i=1,11
read(1,20)title
20 FORMAT(A80,//)
enddo
30 do i=1,NTESTS
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,V4,A4,
&V5,A5,V6,A6,SG,Pplen,DP,Pamb,Dthroat
if(Tven.lt.45.or.Tven.gt.90)write(6,*)
&' ** CHECK Tven IN TEST ',i
if(Tin1.lt.50.or.Tin1.gt.90)write(6,*)' ** CHECK Tin1 IN TEST '
if(Tin2.lt.50.or.Tin2.gt.90)write(6,*)' ** CHECK Tin2 IN TEST '
if(Tamb.lt.60.or.Tamb.gt.80)write(6,*)' ** CHECK Tamb IN TEST '
if(Pamb.lt.28.or.Pamb.gt.31)write(6,*)' ** CHECK Pamb IN TEST '
if(old1.eq.0)goto 31
err1=abs((v1/a1)-old1)/old1
err2=abs((v2/a2)-old2)/old2
err3=abs((v3/a3)-old3)/old3
err4=abs((v4/a4)-old4)/old4
err5=abs((v5/a5)-old5)/old5
if(err1.gt..0125)write(6,*)'error in heater 1 entry, test #'
*,testno
if(err2.gt..0125)write(6,*)'error in heater 2 entry, test #'
*,testno
200
if(err3.gt..0125)write(6,*)'error in heater 3 entry, test #'
*,testno
if(err4.gt..0125)write(6,*)'error in heater 4 entry, test #'
*,testno
if(err5.gt..0125)write(6,*)'error in heater 5 entry, test #'
*,testno
31 write(6,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5
write(2,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5
C if(flag.eq.1)goto 32
old1=v1/a1
old2=v2/a2
old3=v3/a3
old4=v4/a4
old5=v5/a5
flag=1.
32 continue
enddo
35 format(1x,f4.0,2x,5(1x,f10.6))
write(6,*)' '
write(6,*)' '
write(6,*)' Resistances are in file : output.dat'
stop
end
201
Rig3b-Reduce-Heat-Transfer.f
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,NuS,NuN,NoseR,NoseL,LossesS,LossesN,l1,l2
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
FAC1=3.413 ! converts Watts to BTU/hr
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1,FILE='input.dat',STATUS='old')
OPEN(UNIT=2,FILE='nu-plots-side.dat',STATUS='old')
OPEN(UNIT=3,FILE='nu-plots-nose.dat',STATUS='old')
OPEN(UNIT=4,FILE='uncertain-side.out',STATUS='old')
OPEN(UNIT=5,FILE='uncertain-nose.out',STATUS='old')
OPEN(UNIT=7,FILE='output.dat',STATUS='old')
OPEN(UNIT=8,FILE='friction.out',STATUS='old')
OPEN(UNIT=9,FILE='nu-pictures-side.dat',STATUS='old')
OPEN(UNIT=10,FILE='nu-pictures-nose.dat',STATUS='old')
OPEN(UNIT=11,FILE='convergence.dat',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
NoseR=1.281 ! inches
NoseR=NoseR/12 ! feet
Angle=138. ! degrees
RigL=36. ! inches
Side=3. ! inches
Side=Side/12 ! feet
202
Side2=1.372 ! inches
Side2=Side2/12 ! feet
C
C CALCULATION
hypo1=sqrt(NoseR**2 + SIDE**2)
hypo2=sqrt(NoseR**2 + SIDE2**2)
beta1=atan(NoseR/SIDE)*180/PI
beta2=atan(NoseR/SIDE2)*180/PI
alpha1=90-beta1
alpha2=90-beta2
gamma1=180-0.5*Angle-alpha1
gamma2=180-0.5*Angle-alpha2
l1=NoseR*tan(0.5*Angle*PI/180)
l2=NoseR*tan(0.5*Angle*PI/180)
a=SIDE +l1
b=SIDE2+l2
Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))
stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)
stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)
theta1=Asin(stheta1)*180/PI
theta2=Asin(stheta2)*180/PI
sigma1=180-gamma1-theta1
sigma2=180-gamma2-theta2
Pitch=2.48 ! inches
nturb=9
Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +
&NoseR*COS(0.5*Angle*PI/180)
Wave=0.5*Top+NoseR*SIN(0.5*Abgle*PI/180)
Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side2+Top
Area1=0.5*NoseR*SIDE
203
Area2=0.5*NoseR*SIDE2
AreaNose=(PI*(NoseR**2)*(Angle/360))
AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)
Across=Area1+Area2+AreaNose+AreaTop
Dh=4*Across/Perim
C NOTE: At the camera location, Side and Nose heaters were exactly 2" by 11"
C End section was covered with (3" x 11" nose)
! HEATER AT CAMERA LOCATION:
HlengthS=11.
HlengthS=HlengthS/12.
HwidthS=2.
HwidthS=HwidthS/12.
HareaS=HlengthS*HwidthS
HlengthN=11.
HlengthN=HlengthN/12.
HwidthN=2.
HwidthN=HwidthN/12.
HareaN=HlengthN*HwidthN
Write(7,101)12*NoseR,Angle,12*Side,12*Side2,12*l1,12*l2,
&12*Top,12*HlengthS,12*HwidthS,144*HareaS,12*HlengthN,
&12*HwidthN,144*HareaN,alpha1,alpha2,beta1,beta2,sigma1,
&sigma2,gamma1,gamma2,theta1,theta2,12*Perim,144*ACross,12*Dh,
&Pitch,12*Have,12*Wave,12*Bot,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Side 1 (LC)=',f8.3,' inches',/,
&2x,'Side 2 (Plexi)=',f8.3,' inches',/,
&2x,'l1 and l2=',f8.3,5x,f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Side Heater Length=',f8.3,' inches',/,
&2x,'Side Heater Width=',f8.3,' inches',/,
&2x,'Side Heater area=',f8.3,' Sq.in',/,
&2x,'Nose Heater Length=',f8.3,' inches',/,
&2x,'Nose Heater Width=',f8.3,' inches',/,
&2x,'Nose Heater area=',f8.3,' Sq.in',/,
&2x,'alpha1 and alpha2=',f8.3,5x,f8.3,/,
&2x,'beta1 and beta2=',f8.3,5x,f8.3,/,
&2x,'sigma1 and sigma2=',f8.3,5x,f8.3,/,
&2x,'gamma1 and gamma2=',f8.3,5x,f8.3,/,
&2x,'theta1 and theta2=',f8.3,5x,f8.3,/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
204
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Average Test Section Height=',f8.3,' inches',/,
&2x,'Average Test Section Width=',f8.3,' inches',/,
&2x,'Flat projection bottom for rad losses=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
! R E A D I N D A T A
read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid
Poe=Pitch/TurbH
eoDh=TurbH/(12*Dh)
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
WRITE(10,401)ntests
401 FORMAT(I4)
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
DO 333 I=1,11
READ(1,10)TITLE
WRITE(5,10)TITLE
WRITE(7,10)TITLE
333 WRITE(10,10)TITLE
10 FORMAT(A80,//)
WRITE(9,451)
WRITE(10,451)
451 FORMAT(' no. Re Nu h uncer',
&' Nu_smooth EF',/)
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,
&V4,A4,V5,A5,V6,A6,SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,100) i
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
205
WRITE(7,*)' V1,A1,V2,A2,V3,A3'
WRITE(7,*)' V4,A4,V5,A5,V6,A6'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,201)V1,A1,V2,A2,V3,A3
WRITE(7,201)V4,A4,V5,A5,V6,A6
201 FORMAT(5X,3(' ',F5.2,' ',F6.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
Mv=F(Athroat,Pven+Pamb,Tven+460)
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
C HEAT FLUX, BTU/(sqft.hr)
FluxS=V2*A2*FAC1/(HareaS)
FluxN=V5*A5*FAC1/(HareaN)
C TOTAL HEAT GENERATED FROMINLET TO CAMERA LOCATION , BTU/hr
Q=(A1*V1+A4*V4+0.5*A2*V2+0.5*A5*V5)*FAC1
CALL HTCSIDE(Q,FluxS,TmS,TsurfS,hS,LossesS)
CALL HTCNOSE(Q,FluxN,TmN,TsurfN,hN,LossesN)
TmRS=TmS+460.
CALL AIRPROP(TmRS,gammS,CONmS,VISmS,PRmS,CPmS)
VISmS=VISmS/3600.
TmRN=TmN+460.
CALL AIRPROP(TmRN,gammN,CONmN,VISmN,PRmN,CPmN)
VISmN=VISmN/3600.
206
C REYNOLDS NUMBER
ReS=4.*Mv/(Perim*VISmS)
ReN=4.*Mv/(Perim*VISmN)
! NUSSELT NUMBER
NuS=hS*Dh/CONmS
NuN=hN*Dh/CONmN
RatioNu=NuN/NuS
SmoothNuS=0.023*(ReS**0.8)*(PrmS**0.4)
SmoothNuN=0.023*(ReN**0.8)*(PrmN**0.4)
! ENHACEMENT
EFS=NuS/SmoothNuS
EFN=NuN/SmoothNuN
! UNCERTAINTY ANALYSIS
IND=1
CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,A4,V4,A5,V5,
&Dthroat,HareaS,TsurfS,Tin,LossesS,UncerS,IND)
IND=2
CALL UNCERTAIN(Pamb,Pven,Tven,A4,V4,A5,V5,A1,V1,A2,V2,
&Dthroat,HareaN,TsurfN,Tin,LossesN,UncerN,IND)
WRITE( 9,305)testno,ReS,NuS,hS,uncerS,SmoothNuS,EFS
WRITE(10,305)testno,ReN,NuN,hN,uncerN,SmoothNuN,EFN
305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)
WRITE(2,*)ReS,NuS
WRITE(3,*)ReN,NuN
WRITE(7,300)TmS,MV,ReS
WRITE(7,301)TmN,MV,ReN
WRITE(7,302)RatioNu
302 format(5x,'Nu_Nose/Nu_Side=',f8.3)
C**********************************************************************************
C**********************************************************************************
! DARCY FRICTION FACTOR CALCULATIONS
207
Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb
Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb
TmR=0.5*(TmRS+TmRN)
Re=0.5*(ReS+ReN)
Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/
&(0.5*Rho*(Um**2))
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth
C**********************************************************************************
C**********************************************************************************
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Inlet Pressure=',f9.4,' psia',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm_Side=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReS=',F8.2)
301 FORMAT(30X,'Tm_Nose=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReN=',F8.2)
STOP
END
C************************************************************************************
**************C
C********************************** ON THE SIDE WALL
**********************************************C
208
C************************************************************************************
**************C
SUBROUTINE HTCSIDE(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
209
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! MINCO
tinc = 0.5e-03/12. ! MINCO
tadh1= 0.75e-03/12. ! MINCO
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
210
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Top*HlengthS ! Top surface
Afront=1.5*Side2*HlengthS ! Front surface
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
211
C THE POINT IN QUESTION
Aback=1.5*Side*HlengthS ! Back surface
Abot =1.5*PI*NoseR*(Angle/360)*HlengthN ! Bottom surface
C write(6,*)Atop,Afront,Abot,Aback
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=h
htop=0.8*h ! Guess
hbot=1.2*h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Top,Bot,Have,HlengthN,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)Frtop,Frfront,Frbot,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
212
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fbot=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frbot
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
213
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=h
htop=0.8*h
hbot=1.2*h
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' ON THE SIDE WALL',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
214
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,htop,hfront,hbot
120 FORMAT(5x,'hside=',F8.3,1X,'htop=',F8.3,1X,'hfront=',F8.3,1X,
&'hnose=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C****************************************************************************C
C****************************ON THE NOSE ************************************C
C****************************************************************************C
SUBROUTINE HTCNOSE(Q,Flux,Tm,Tsurf,h,Losses)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,
&RigL,Mv,Losses,kfiber,NoseR
COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,
&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave
C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)
215
C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON
C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil
C LIQUID CRYSTAL
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --
C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq
C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON
C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches
C SPRAYFOAM ---- AMBIENT AIR
C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber
C -- tspray/ksty -- 1/ho
C T O P W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C F R O N T W A L L
C FROM THE INSIDE TO THE AMBIENT AIR
C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches
C STYROFOAM ---- AMBIENT
C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho
C*******************************************************************C
C Natural Convection Heat transfer coefficient on the outer surface
De=6./12. ! ft, test section side with insulation
TambR=Tamb+460.
CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)
ho=0.36*con/De ! Ozisik, Page 443
C write(6,*)' ho ',ho
216
C*******************************************************************C
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)
ksty = 0.02 ! BTU/hr.ft.F
kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)
kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19
kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)
kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)
kblack = 0.165 ! BTU/hr.ft.F Glycerin
kliq = 0.165 ! BTU/hr.ft.F Glycerin
kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)
tplexi = 0.5/12. ! United Industries
tfiber = 0.187/12. ! United Industries
tsty = 0.
tspray = 2./12. ! United Industries
tkap = 1.0e-03/12. ! MINCO
tinc = 0.5e-03/12. ! MINCO
tadh1= 0.75e-03/12. ! MINCO
tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)
tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE
tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)
tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)
tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)
Rplexi= tplexi/kplexi
Rfiber= tfiber/kfiber
Rsty = tsty/ksty
Rspray= tspray/ksty
Rconv = 1./ho
Rinc = tinc/kinc
Rkap = tkap/kkap
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
217
C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap
C write(6,*)' Radh2',Radh2,' Rblack',Rblack
C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl
C write(6,*)' Rplexi ',Rplexi
C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv
C Resistance from mid heater to the Liquid Crystals (Reference Temperature)
Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq
C Resistance from mid heater to ambient
Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv
C write(6,*)' Rfront',Rfront,' Rback',Rback
C**************************************************C
C H E A T E D W A L L
Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
Fback = (Theater-Tamb)/Rback
Ffront = (Theater-Tliquid)/Rfront
Tsurf= Tliquid -Ffront*Rmyl
Perloss=100.*(Fback/Flux)
C**************************************************C
C write(6,*)' Tsurf', Tsurf
C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Atop =1.5*Side2*HlengthS ! Top surface (since NOSE is now the back surface)
Afront=1.5*Top*HlengthS ! Front surface (since NOSE is now the back surface)
C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO
C THE POINT IN QUESTION
Abot =1.5*Side*HlengthS ! Bottom surface
Aback=1.5*PI*NoseR*(Angle/360)*HlengthN ! Back surface
C write(6,*)Aback,Atop,Afront,Abot
C AIR INLET PROPERTIES
TinR=Tin+460.
CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)
218
C INITIAL GUESSES
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Fback)/(Tsurf-Tm)
hfront=(0.8/1.2)*h
htop=(1/1.2)*h ! Guess
hbot=(1/1.2)*h ! Guess
Ttop=Tm ! Guess
Tfront=Tm ! Guess
Tbot=Tsurf
C ITERATIONS STARTS HERE
DO I=1,30
C EVALUATING FNET
C RADIATIONAL LOSSES
CALL RADIATION(Side2,Side,Wave,HlengthS,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)Frtop,Frfront,Frbot,Frback
C FLUX LOSSES FROM TOP AND FRONT WALLS
R1= Rplexi+Rconv !from surface to ambient
C T O P W A L L
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Ftop=(Ttop-Tamb)/R1
C F R O N T W A L L
R1= Rplexi+Rconv !from surface to ambient
219
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Ffront=(Tfront-Tamb)/R1
Fbot=Fback
C TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot
C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION
Qadd = Q-Qwaste
C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER
C COEFFICIENT IS BEING MEASURED
Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance
C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)
Losses=Fback+Frback+Frbot
C write(6,*)' Losses',Losses
C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
h=(Flux-Losses)/(Tsurf-Tm)
C FILM TEMPERATURE
Tf=(Tsurf+Tm)/2.
C DENSITY AT FILM TEMPERATURE
Rho=Pamb/(Rgas*(Tf+460.))
C OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)
Vis=Vis/3600.
220
Re=4.*Mv/(Perim*Vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
hfront=(0.8/1.2)*h ! Guess
htop=(1/1.2)*h ! Guess
hbot=(1/1.2)*h ! Guess
FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop
FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront
IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)
&go to 34
enddo
write(7,400)
400 FORMAT(/,20x,'***** Did not converge after 30 iterations',
&' *****',/)
WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,
&'FNETTOP,FNETFRONT=',2E15.5,/)
GO TO 503
34 WRITE(7,500)I,FNETTOP,FNETFRONT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT =',2E15.5,/)
503 continue
C**************************************
write(7,101)
101 FORMAT(//,10x,' ON THE NOSE',/)
WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater
102 FORMAT(/,
&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F',/ ,
&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,
&5X,'Ambient Temperature = ',F8.3,' F',/,
&5X,'Air Inlet Temperature = ',F8.3,' F',/,
&5X,'Air Mixed Mean Temperature',F8.3,' F',/,
&5X,'Heater Temperature= ',F8.3,' F')
write(7,115)Tf
115 FORMAT(5X,'Film Temperatures',F9.3,' F')
221
write(7,110)Tsurf,Ttop,Tfront,Tsurf
110 FORMAT(5x,'Nose, Top, Front and Back Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,120)h,hbot,hfront,htop
120 FORMAT(5x,'hnose=',F8.3,1X,'hback=',F8.3,1X,'htop=',F8.3,1X,
&'hfront=',F8.3,' BTU/hr.sqft.F')
write(7,170)Q
170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')
write(7,116)Qwaste
116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')
write(7,180)fback,ftop,ffront,fback
180 FORMAT(5X,'Flux Losses from Nose, Front, Ftop and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
C****************************************************************************
C****************************************************************************
C**********************************************************************C
SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frnose)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)
PI=4.*ATAN(1.E00)
W=H1
H=0.5*(Bot+Top)
T(1)=Tsurf + 460.
T(2)=Ttop + 460.
T(3)=Tfront+ 460.
T(4)=Tbot + 460.
W=W/(3.*Hlength)
H=H/(3.*Hlength)
C Emissivities
E(1)=.85 ! Liquid Crystal Foil, Back Wall
E(2)=.9 ! Plexiglas, Top Wall
222
E(3)=.9 ! Plexiglas, Front Wall
E(4)=.85 ! Liquid Crystal Foil, Nose Wall
C
N=4
SIGMA=0.1712E-08
C WRITE(7,150)
150 FORMAT(//,20X,'SHAPE FACTORS',//)
C
F11=0.
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F12=Z1*(Z2+Z3+Z4+Z5)
F14=F12
F13=1.-F11-F12-F14
C
F31=F13
F32=F12
F33=0.
F34=F14
C
DUM=W
W=H
H=DUM
W2=W*W
H2=H*H
Z1=1./(PI*W)
Z2=W*ATAN(1./W)
Z3=H*ATAN(1./H)
Z=SQRT(H2+W2)
Z4=-Z*ATAN(1./Z)
Z=(1.+W2)*(1.+H2)
ZZ=1.+W2+H2
ZZZ=Z/ZZ
223
Z=W2*ZZ/((1.+W2)*(W2+H2))
Z=Z**W2
ZZZ=ZZZ*Z
Z=H2*ZZ/((1.+H2)*(W2+H2))
Z=Z**H2
ZZZ=ZZZ*Z
Z5=.25*LOG(ZZZ)
F21=Z1*(Z2+Z3+Z4+Z5)
F22=0.
F23=F21
F24=1.-F21-F22-F23
C
F41=F21
F42=F24
F43=F23
F44=0.
C
C WRITE(7,110)F11,F12,F13,F14
C WRITE(7,120)F21,F22,F23,F24
C WRITE(7,130)F31,F32,F33,F34
C WRITE(7,140)F41,F42,F43,F44
C
110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,
&5X,'F14=',F6.4,/)
120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,
&5X,'F24=',F6.4,/)
130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,
&5X,'F34=',F6.4,/)
140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,
&5X,'F44=',F6.4,//)
C WRITE(7,160)
160 FORMAT(/,20X,'EMISSIVITIES',//)
C WRITE(7,100)(I,E(I),I=1,N)
C WRITE(7,170)
170 FORMAT(/,20X,'TEMPERATURES IN R',//)
C WRITE(7,100)(I,T(I),I=1,N)
A(1,1)=F11-1./(1.-E(1))
A(1,2)=F12
A(1,3)=F13
A(1,4)=F14
C
A(2,1)=F21
A(2,2)=F22-1./(1.-E(2))
A(2,3)=F23
A(2,4)=F24
C
A(3,1)=F31
A(3,2)=F32
224
A(3,3)=F33-1./(1.-E(3))
A(3,4)=F34
C
A(4,1)=F41
A(4,2)=F42
A(4,3)=F43
A(4,4)=F44-1./(1.-E(4))
C
C WRITE(7,180)
180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)
C WRITE(7,200)((A(I,J),J=1,N),I=1,N)
DO I=1,N
B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))
ENDDO
C WRITE(7,250)
C WRITE(7,100)(I,B(I,1),I=1,N)
200 FORMAT(1X,4E15.6)
250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)
C WRITE(7,55)
55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)
CALL EQSOLVE(A,B,N,N,1)
C WRITE(7,50)
C WRITE(7,100)(I,B(I,1),I=1,N)
DO I=1,N
Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))
ENDDO
Frback =Q(1)
Frtop =Q(2)
Frfront=Q(3)
Frnose=Q(4)
C WRITE(7,350)
C WRITE(7,100)(I,Q(I),I=1,N)
100 FORMAT(4(I3,E15.6))
50 FORMAT(/,20X,'RADIOCITIES',/)
350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)
RETURN
END
C**********************************************************************C
C**********************************************************************C
SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,i4,V4,i5,V5,
&Dth,Harea,Tsurf,Tin,Losses,Uncer,IND)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 i1,i2,i4,i5,Losses,M1,M2
PI=4.*ATAN(1.E00)
225
C FAC=491.3744
FAC1=3.413 ! converts Watts to BTU/hr
C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)
C=0.24*0.5215*3600
C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J
P1=Pven+Pamb
T1=Tven+460.0
TI=Tin
TS=Tsurf
a=Harea
f=0.5
ATH=PI*(Dth**2)/4.
DATH=PI*((Dth+0.001)**2)/4. -ATH
h=((FAC1*(V2*i2)/a)-Losses)/
&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+V4*i4+f*V2*i2+f*V5*i5)))/
&(C*P1*ATH))
WRITE(5,*)' '
if(IND.EQ.1)WRITE(5,*)' hSide =',h,' BUT/hr.sqft.F'
if(IND.EQ.2)WRITE(5,*)' hNose =',h,' BUT/hr.sqft.F'
H2=h*h
C
C i2 v2
C ------- - Floss
C a
C ---------------------------------------
C sqrt(T1)(i1v1+i4v4+fi2v2+fi5v5)
C Ts-Ti - -------------------------
C C P1 A_throat
C
DLOSS=0.1*Losses
dv1=0.1
dv2=0.1
dv4=0.1
dv5=0.1
di1=0.01
226
di2=0.01
di4=0.01
di5=0.01
da=1./(32.*32.*144)
dts=0.5
dti=0.5
dt1=0.5
dp1=0.5
Df=0.1
C1=FAC1*(V2*i2/a)-Losses
Q1=C*P1*Ath
Q2=Q1*sqrt(T1)
M1=(Ts-Ti)*Q1
A=FAC1*(i1*v1+i4*v4)
B=FAC1*(i2*v2+i5*v5)
M2=M1-sqrt(T1)*(A+f*B)
DHDF=B*Q1*C1*sqrt(T1)/(M2**2)
DHDTI= C1*(Q1**2)/(M2**2)
DHDTS=-C1*(Q1**2)/(M2**2)
DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))
DHDLOSS=-Q1/M2
DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)
DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)
DHDI4=FAC1*v4*Q1*C1*sqrt(T1)/(M2**2)
DHDV4=FAC1*i4*Q1*C1*sqrt(T1)/(M2**2)
DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDI5=FAC1*v5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDV5=FAC1*i5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))
DHDATH=C1*C*P1*(M2-M1)/(M2**2)
DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)
DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))
ZF=(DF*DHDF)**2
ZA=(DA*DHDA)**2
ZI1=(DI1*DHDI1)**2
227
ZV1=(DV1*DHDV1)**2
ZI2=(DI2*DHDI2)**2
ZV2=(DV2*DHDV2)**2
ZI4=(DI4*DHDI4)**2
ZV4=(DV4*DHDV4)**2
ZI5=(DI5*DHDI5)**2
ZV5=(DV5*DHDV5)**2
ZTS=(DTS*DHDTS)**2
ZTI=(DTI*DHDTI)**2
ZATH=(DATH*DHDATH)**2
ZP1=(DP1*DHDP1)**2
ZT1=(DT1*DHDT1)**2
ZLOSS=(DLOSS*DHDLOSS)**2
Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+ZI4+ZI4+ZV5+ZV5+
&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))
if(IND.EQ.1) then
WRITE(4,*)' TOTAL UNCER.%:',Uncer
WRITE(4,*)' '
WRITE(4,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(4,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(4,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(4,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(4,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(4,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h
WRITE(4,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h
WRITE(4,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h
WRITE(4,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h
WRITE(4,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(4,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(4,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(4,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(4,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(4,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(4,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
endif
if(IND.EQ.2) then
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(5,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h
228
WRITE(5,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h
WRITE(5,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h
WRITE(5,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h
WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
endif
RETURN
END
C**********************************************************************C
C**********************************************************************C
SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION A(NDIM,NDIM),B(NDIM,NB)
DO 291 J1=1,NA
C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE
C VALUE IN PIVOTAL COLUMN.
101 TEMP=0.
DO 121 J2=J1,NA
IF(ABS(A(J2,J1))-TEMP) 121,111,111
111 TEMP=ABS(A(J2,J1))
IBIG=J2
121 CONTINUE
IF(IBIG-J1)5001,201,131
C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE
C VALUE IN PIVOT POSITION.
131 DO 141 J2=J1,NA
TEMP=A(J1,J2)
A(J1,J2)=A(IBIG,J2)
141 A(IBIG,J2)=TEMP
DO 161 J2=1,NB
TEMP=B(J1,J2)
B(J1,J2)=B(IBIG,J2)
161 B(IBIG,J2)=TEMP
C COMPUTE COEFFICIENTS IN PIVOTAL ROW.
201 TEMP=A(J1,J1)
DO 221 J2=J1,NA
221 A(J1,J2)=A(J1,J2)/TEMP
DO 231 J2=1,NB
231 B(J1,J2)=B(J1,J2)/TEMP
229
IF(J1-NA)236,301,5001
C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.
236 N1=J1+1
DO 281 J2=N1,NA
TEMP=A(J2,J1)
DO 241 J3=N1,NA
241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)
DO 251 J3=1,NB
251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)
281 CONTINUE
291 CONTINUE
C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.
301 IF(NA-1)5001,5001,311
311 DO 391 J1=1,NB
N1=NA
321 DO 341 J2=N1,NA
341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)
N1=N1-1
IF(N1-1)5001,391,321
391 CONTINUE
5001 CONTINUE
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
230
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
231
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
232
Rig3b-reduce-friction.f
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,NoseR,NoseL
F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi
! provided by the manufacturer (Fox Valves)
PI=4.*ATAN(1.E00)
! C O N V E R S I O N F A C T O R S
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi
PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf
Rgas=53.34 ! gas constant for air
! I N P U T / O U T P U T F I L E S
OPEN(UNIT=1, FILE='input.dat',STATUS='old')
OPEN(UNIT=5, FILE='fric-uncertain.out',STATUS='old')
OPEN(UNIT=7, FILE='friction.out',STATUS='old')
OPEN(UNIT=8, FILE='friction-plot.out',STATUS='old')
! T E S T S E C T I O N G E O M E T R Y
! T E S T S E C T I O N G E O M E T R Y
NoseR=1.281 ! inches
NoseR=NoseR/12 ! feet
Angle=138. ! degrees
RigL=36. ! inches
Side=3. ! inches
Side=Side/12 ! feet
Side2=1.372 ! inches
Side2=Side2/12 ! feet
C
C CALCULATION
hypo1=sqrt(NoseR**2 + SIDE**2)
hypo2=sqrt(NoseR**2 + SIDE2**2)
233
beta1=atan(NoseR/SIDE)*180/PI
beta2=atan(NoseR/SIDE2)*180/PI
alpha1=90-beta1
alpha2=90-beta2
gamma1=180-0.5*Angle-alpha1
gamma2=180-0.5*Angle-alpha2
l1=NoseR*tan(0.5*Angle*PI/180)
l2=NoseR*tan(0.5*Angle*PI/180)
a=SIDE +l1
b=SIDE2+l2
Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))
stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)
stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)
theta1=Asin(stheta1)*180/PI
theta2=Asin(stheta2)*180/PI
sigma1=180-gamma1-theta1
sigma2=180-gamma2-theta2
Pitch=2.48 ! inches
nturb=9
Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +
&NoseR*COS(0.5*Angle*PI/180)
Wave=0.5*Top+NoseR*SIN(0.5*Angle*PI/180)
Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only
NoseL=2*PI*NoseR*(Angle/360)
Perim=NoseL+Side+side2+Top
Area1=0.5*NoseR*SIDE
Area2=0.5*NoseR*SIDE2
AreaNose=(PI*(NoseR**2)*(Angle/360))
AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)
Across=Area1+Area2+AreaNose+AreaTop
Dh=4*Across/Perim
234
read(1,*)ntests,TurbH,TurbW,Turbr
DO 333 I=1,10
READ(1,10)TITLE
WRITE(5,10)TITLE
333 WRITE(7,10)TITLE
10 FORMAT(A80,//)
Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,
&12.*Top,12.*Bot,12.*Perim,144.*ACross,12*Dh,Pitch,RigL
101 format(/,
&2x,'Nose Radius=',f8.3,' inches',/,
&2x,'Nose Angle=',f8.3,' degrees',/,
&2x,'Nose Length=',f8.3,' inches',/,
&2x,'Side 1 (Plexi)=',f8.3,' inches',/,
&2x,'Side 2 (LC)=',f8.3,' inches',/,
&2x,'Top=',f8.3,' inches',/,
&2x,'Bottom Flat Line=',f8.3,' inches',/,
&2x,'Cross Section Perimter=',f8.3,' inches',/,
&2x,'Cross Section Area=',f8.3,' sq. in',/,
&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,
&2x,'Turbulator Pitch=',f8.3,' inches',/,
&2x,'Test Section Length=',f8.3,' inches',/)
Poe=Pitch/TurbH
eoDh=TurbH/(12*Dh)
WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe
401 FORMAT(I4)
402 FORMAT(10x,'********************',/,
&2x,'NUMBER OF TESTS : ',I5,/,
&2x,'Turbulator Height=',f8.3,' inches',/,
&2x,'Turbulator Width=',f8.3,' inches',/,
&2x,'Turbulator Corner Radius=',f8.3,' inches',/,
&2x,'Turb Height over Channel Hydraulic diameter=',f9.4,/,
&2x,'Turb Pith over Height=',f8.3,/,
&10x,'********************',/)
! R E A D I N D A T A
DO i=1,ntests
READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,
&SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
235
WRITE(7,100) i
WRITE(7,*)' '
WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'
WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'
WRITE(7,*)' '
WRITE(7,200)testno,Pven,Pplen,Pinlet
200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))
WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb
202 FORMAT(5X,4(' ',F5.1),2X,F5.2)
Athroat=PI*(Dthroat**2)/4. ! square inches
WRITE(7,403)Dthroat
403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)
Pamb=Pamb*Hgtopsi ! psi
Tin=(Tin1+Tin2)/2.
C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
Mv=F(Athroat,Pven+Pamb,Tven+460)
TinR=Tin+460.
CALL AIRPROP(TinR,gamain,CONin,VISin,PRin,CPin)
VISin=VISin/3600.
C REYNOLDS NUMBER
Re=4.*Mv/(Perim*VISin)
C***************************************************
! DARCY FRICTION FACTOR CALCULATIONS
Pplen=2*Pplen*H2Otopsi+Pamb
DeltaP=2*Pinlet ! inches of water using Micromanometer
Rho=(Pamb+0.5*DeltaP*H2Otopsi)*144./(Rgas*(TinR))
Um=Mv/(Across*Rho)
fDarcy=gc*((12.*Dh)/(nturb*Pitch))*(DeltaP*H2Otopsi*144.)/
&(0.5*Rho*(Um**2))
236
CALL UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)
fsmooth=0.316/(Re**0.25) ! Blasius correlation
write(7,303)Pamb,Pplen,DeltaP,Rho,Um,fDarcy,fsmooth,
&fDarcy/fsmooth
WRITE(8,304)Re,fDarcy,fsmooth,fDarcy/fsmooth
304 format(f8.1,2(4x,E13.7),F8.3)
303 format(/,
&5x,'Ambient Pressure=',f9.4,' psia',/,
&5x,'Plenum Pressure=',f9.4,' psia',/,
&5x,'Pressure Drop =',f9.4,' inches of water',/,
&5x,'Air Density=',f9.4,' lbm/cu.ft',/,
&5x,'Air Average Velocity=',f9.4,' ft/s',/,
&5x,'Darcy Friction Factor=',f9.4,/,
&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,
&5x,'f_turb/f_Smooth=',f9.4,/)
C **********************************************************
ENDDO
100 FORMAT(30X,'TEST # ',I2)
300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)
STOP
END
C**********************************************************************C
SUBROUTINE UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)
IMPLICIT REAL*8(A-H,O-Z)
Hgtopsi= 0.49083935 ! converts inches of Hg to psi
H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi
gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)
C=24*144*gc*H2Otopsi
dDh =0.05/12.
dRigL =0.1 ! inches
dDeltaP=0.002*H2Otopsi ! 0.002 inches of water
dRho =0.02*Rho ! 2% error
dUm =0.02*Um ! 2% error
237
fDarcy=gc*((12.*Dh)/RigL)*(DeltaP*H2Otopsi*144.)/
&(0.5*Rho*(Um**2))
f2=fDarcy**2
WRITE(5,*)' '
WRITE(5,*)' fDarcy =',fDarcy
WRITE(5,*)' '
dfdDh=C*DeltaP/(RigL*Rho*(Um**2))
dfdDeltaP=C*Dh/(RigL*Rho*(Um**2))
dfdRigL=-C*Dh*DeltaP/(RigL*RigL*Rho*(Um**2))
dfdRho=-C*Dh*DeltaP/(RigL*Rho*Rho*(Um**2))
dfdUm=-2*C*Dh*DeltaP/(RigL*Rho*(Um**3))
ZDh=(dfdDh*dDh)**2
ZRigL=(dfdRigL*dRigL)**2
ZDeltaP=(dfdDeltaP*dDeltaP)**2
ZRho=(dfdRho*dRho)**2
ZUm=(dfdUm*dUm)**2
Uncer=100*SQRT((ZDh+ZRigL+ZDeltaP+ZRho+ZUm)/(f2))
WRITE(5,*)' TOTAL UNCER.%:',Uncer
WRITE(5,*)' '
WRITE(5,*)' % Uncer. assoc. with Dh',100.*sqrt(ZDh)/fDarcy
WRITE(5,*)' % Uncer. assoc. with RigL',100.*sqrt(ZRigL)/fDarcy
WRITE(5,*)' % Uncer. assoc. with DeltaP',100.*sqrt(ZDeltaP)/fDarcy
WRITE(5,*)' % Uncer. assoc. with Rho',100.*sqrt(ZRho)/fDarcy
WRITE(5,*)' % Uncer. assoc. with Um',100.*sqrt(ZUm)/fDarcy
RETURN
END
C**********************************************************************C
SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)
IMPLICIT REAL*8(A-H,O-Z)
c physical properties of dry air at one atmosphere
c ref: ge heat transfer handbook
c
c temperature range: 160 to 3960 deg. rankine
238
c -300 to 3500 deg. fahreinheit
c
c t - temperature, R
c gamx - ratios of specific heats
c kx - thermal conductivity, BTU/hr.ft.R
c mux - viscosity, lbm/hr.ft
c prx - prandtl no.
c cpx - specific heat, BTU/lbm.R
c
c
dimension tab(34),gam(34),pr(34),cp(34)
real*8 k(34),mu(34),kx,mux
data nent/34/
data tab/ 160., 260.,
& 360., 460., 560., 660., 760., 860., 960., 1060.,
& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,
& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,
& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./
data gam/ 1.417, 1.411,
& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,
& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,
& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,
& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/
data k/ 0.0063,0.0086,
& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,
& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,
& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,
& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/
data mu/ 0.0130,0.0240,
& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,
& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,
& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,
& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/
data pr/ 0.7710,0.7590,
& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,
& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,
& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,
& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/
data cp/ 0.247, 0.242,
& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,
& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,
& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,
& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/
c
c
if(t.lt.tab(1)) print 510,t,tab(1)
510 format(" in airprop --- temp=",f8.1," is less than min temp",
&" of ",f8.1)
239
if(t.gt.tab(nent)) print 520, t,tab(nent)
520 format(" in airprop --- temp=",f8.1," is greater than max",
&" temp of ",f8.1)
if(t-tab(1))120,120,100
100 if(tab(nent)-t)130,130,110
110 m=2
go to 140
120 j=1
go to 180
130 j=nent
go to 180
140 if(t-tab(m))160,170,150
150 m=m+1
go to 140
c
c -- Linear Interpolation ---
c
160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))
mux= mu(m-1)+(mu(m)-mu(m-1))*slp
prx= pr(m-1)+(pr(m)-pr(m-1))*slp
cpx=cp(m-1)+(cp(m)-cp(m-1))*slp
kx=k(m-1)+(k(m)-k(m-1))*slp
gamx=gam(m-1)+(gam(m)-gam(m-1))*slp
go to 190
170 j=m
go to 180
180 mux=mu(j)
prx=pr(j)
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C**********************************************************************C
240
Appendix B.1: Rig 1 Results (Nusselt Number, Enhancement Factor,
Friction Factor, and Thermal Performance)
Rig1 Min Turbulator
Avg Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6893.07 3.21 4.60 75.67 108.19 1.56 2.24
10411.57 3.05 4.29 100.14 140.36 1.43 2.01
15340.89 2.91 3.98 130.18 177.73 1.33 1.82
21109.06 2.70 3.73 155.71 214.92 1.23 1.70
30821.30 2.65 3.57 207.27 278.80 1.18 1.59
40624.05 2.64 3.42 257.41 332.56 1.15 1.49
Rig1 Nominal Turbulator
Avg Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6890.38 3.53 5.00 83.29 117.58 1.47 2.07
10411.54 3.29 4.53 107.97 148.31 1.33 1.82
15344.07 3.04 4.19 140.11 187.28 1.20 1.66
21171.73 3.06 4.03 176.84 233.00 1.20 1.58
31166.21 2.91 3.72 229.39 292.77 1.11 1.42
41161.35 2.73 3.58 269.12 352.74 1.02 1.34
Rig1 Max Turbulator
Avg Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6916.61 3.84 5.33 90.66 125.81 1.42 1.97
10435.14 3.51 4.71 115.16 154.51 1.27 1.70
15360.82 3.13 4.17 140.16 186.63 1.11 1.48
21170.30 3.08 3.92 178.32 226.35 1.09 1.38
31177.92 2.91 3.75 229.50 295.64 1.00 1.28
41188.24 2.88 3.58 283.39 352.88 0.99 1.23
241
Rig 1 Min Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
6942.26 0.297 0.035 8.579
8708.73 0.306 0.033 9.364
10475.87 0.304 0.031 9.719
12236.06 0.298 0.030 9.908
14004.98 0.297 0.029 10.217
15757.82 0.294 0.028 10.413
17702.30 0.276 0.027 10.079
21290.16 0.279 0.026 10.657
24870.15 0.274 0.025 10.881
28419.48 0.271 0.024 11.124
31948.93 0.269 0.024 11.363
35658.60 0.267 0.023 11.607
39295.53 0.266 0.022 11.868
42903.34 0.266 0.022 12.118
Rig 1 Nominal Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
6906.82 0.491 0.035 14.159
8672.85 0.485 0.033 14.826
10435.90 0.480 0.031 15.365
12199.98 0.466 0.030 15.493
13972.63 0.465 0.029 16.008
15738.36 0.455 0.028 16.125
17643.91 0.439 0.027 16.022
21229.98 0.434 0.026 16.573
24787.91 0.430 0.025 17.084
28381.49 0.430 0.024 17.657
31973.11 0.426 0.024 18.009
35559.22 0.428 0.023 18.596
39169.58 0.427 0.022 19.022
42751.52 0.428 0.022 19.492
Rig 1 Max Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
6989.91 0.691 0.035 19.981
8750.26 0.675 0.033 20.646
10507.61 0.673 0.031 21.554
12274.80 0.651 0.030 21.693
14042.80 0.637 0.029 21.935
15808.69 0.627 0.028 22.235
17642.03 0.613 0.027 22.367
21216.50 0.605 0.026 23.104
24794.71 0.597 0.025 23.714
28385.40 0.595 0.024 24.452
31982.14 0.591 0.024 25.015
35588.60 0.552 0.023 23.990
39210.76 0.569 0.022 25.347
42797.99 0.562 0.022 25.579
242
Appendix B.2: Rig 2 Results (Nusselt Number, Enhancement Factor,
Friction Factor, and Thermal Performance)
Rig2 Min Turbulator
Avg Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6220.73 2.578 2.604 55.96 56.50 1.63 1.64
9493.66 2.609 2.602 79.42 79.21 1.54 1.54
13916.84 2.449 2.658 101.24 109.89 1.38 1.50
18668.34 2.310 2.311 120.80 120.79 1.31 1.31
28066.29 2.223 2.202 161.13 159.62 1.22 1.21
37674.07 2.242 2.192 205.55 201.18 1.21 1.18
Rig2 Nominal Turbulator
Avg Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6213.23 2.938 3.209 63.72 69.60 1.66 1.81
9488.07 2.870 3.014 87.32 91.71 1.55 1.63
13911.05 2.760 2.873 114.09 118.76 1.41 1.47
18546.96 2.721 2.561 141.60 133.23 1.37 1.29
28155.52 2.486 2.423 180.65 176.14 1.24 1.21
37461.78 2.433 2.352 222.10 214.82 1.20 1.16
Rig 2 Max Turbulator
Avg Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6152.94 3.027 3.567 65.13 76.73 1.51 1.78
9459.86 2.995 3.212 90.90 97.52 1.45 1.55
13850.38 2.868 3.117 118.08 128.26 1.35 1.47
18650.01 2.493 2.755 130.36 144.16 1.17 1.29
28103.61 2.493 2.652 180.91 192.36 1.15 1.22
37299.56 2.556 2.570 232.48 233.95 1.16 1.16
243
Rig 2 Minimum Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
5394.5 0.089 0.037 2.4
6762 0.141 0.035 4.038
8136.8 0.155 0.033 4.67
9507.1 0.171 0.032 5.337
10885.7 0.174 0.031 5.627
12263.7 0.172 0.030 5.719
13641.7 0.167 0.029 5.711
15023.3 0.167 0.029 5.845
16225.4 0.149 0.028 5.321
19015.1 0.154 0.027 5.727
21802.6 0.150 0.026 5.76
24586.8 0.150 0.025 5.938
27510.5 0.145 0.025 5.893
30258.7 0.147 0.024 6.127
33010.2 0.146 0.023 6.236
35765.3 0.145 0.023 6.309
38491.5 0.143 0.023 6.337
Rig 2 Nominal Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
5415.7 0.176 0.037 4.791
6781.3 0.225 0.035 6.463
8156.2 0.214 0.033 6.434
9531.6 0.214 0.032 6.682
10907.7 0.218 0.031 7.049
12278.2 0.215 0.030 7.173
13654.5 0.216 0.029 7.404
15039.8 0.219 0.029 7.691
16382.7 0.215 0.028 7.712
19140.2 0.214 0.027 7.953
21904.4 0.209 0.026 8.039
24680.9 0.205 0.025 8.129
27458.2 0.203 0.025 8.29
30218.4 0.199 0.024 8.309
32994.3 0.194 0.023 8.295
35808.1 0.193 0.023 8.405
38642.6 0.189 0.023 8.405
Rig 2 Maximum Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
5371.7 0.267 0.037 7.223
6748.3 0.282 0.035 8.086
8124.6 0.292 0.033 8.763
9493.9 0.285 0.032 8.892
10864.8 0.283 0.031 9.138
12236.3 0.284 0.030 9.439
13617.5 0.285 0.029 9.742
14998.4 0.281 0.029 9.847
16457.1 0.276 0.028 9.904
19227.3 0.265 0.027 9.89
21998.7 0.259 0.026 9.997
24850.3 0.257 0.025 10.212
27734.7 0.253 0.024 10.35
30420.5 0.250 0.024 10.467
33160.7 0.249 0.023 10.619
35875.5 0.244 0.023 10.622
38573.6 0.245 0.023 10.859
244
Appendix B.3: Rig 3A Results (Nusselt Number, Enhancement Factor,
Friction Factor, and Thermal Performance)
Rig3A Minimum Turbulator
Avg
Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6892 2.701 2.913 63.653 68.632 1.515 1.633
10201 2.686 3.078 86.588 99.205 1.453 1.666
15344 2.463 2.902 110.084 129.682 1.279 1.508
20504 2.399 2.776 135.225 156.405 1.240 1.434
31313 2.186 2.845 172.934 224.944 1.105 1.438
41169 2.165 2.672 213.234 263.011 1.078 1.330
Rig3A Nominal Turbulator
Avg
Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6850 2.771 3.413 64.978 79.986 1.423 1.753
10200 2.460 3.097 79.350 99.808 1.216 1.531
15358 2.339 2.741 104.698 122.612 1.115 1.306
20427 2.397 2.834 134.780 159.250 1.136 1.344
31154 2.231 2.908 176.297 228.936 1.035 1.349
41022 2.234 2.592 219.432 254.454 1.023 1.187
Rig3A Maximum Turbulator
Avg
Re
Avg EF
Wall
Avg EF
Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
Avg TP
Nose
6795 3.002 3.613 69.923 84.136 1.382 1.664
10152 2.790 3.495 89.621 112.194 1.229 1.540
15316 2.680 3.423 119.662 152.682 1.153 1.472
20494 2.698 3.297 152.039 185.619 1.141 1.395
31126 2.552 3.068 201.000 241.539 1.073 1.290
40911 2.530 2.971 247.888 291.036 1.046 1.228
245
Rig 3A Minimum Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
7338 0.287 0.034 8.397
9184.2 0.244 0.032 7.568
11027.6 0.254 0.031 8.251
12867.7 0.249 0.030 8.398
14709.8 0.247 0.029 8.592
16560.8 0.245 0.028 8.801
18410.6 0.245 0.027 9.02
20260.3 0.240 0.026 9.08
22117.4 0.238 0.026 9.177
23968.7 0.236 0.025 9.288
25798.6 0.235 0.025 9.42
37151.5 0.220 0.023 9.667
41004.7 0.219 0.022 9.877
44892.6 0.218 0.022 10.052
48649.7 0.217 0.021 10.195
52366.6 0.214 0.021 10.227
Rig 3A Nominal Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
7261.8 0.321 0.034 9.375
9109.3 0.326 0.032 10.093
10953.1 0.310 0.031 10.049
12799.1 0.311 0.030 10.46
14651.7 0.333 0.029 11.585
16502.1 0.325 0.028 11.671
18344.2 0.324 0.027 11.936
20199.1 0.314 0.027 11.833
22037.3 0.309 0.026 11.933
23986 0.305 0.025 12.026
25876.1 0.300 0.025 12.025
37119.1 0.288 0.023 12.654
40868.1 0.283 0.022 12.747
44634.2 0.279 0.022 12.823
48320.6 0.274 0.021 12.837
52128.8 0.273 0.021 13.048
Rig 3A Maximum Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
7275.9 0.450 0.034 13.145
9117.9 0.450 0.032 13.911
10967.7 0.438 0.031 14.198
12807.7 0.446 0.030 15.02
14658.6 0.452 0.029 15.737
16499.1 0.438 0.028 15.725
18345.3 0.436 0.027 16.063
20199.2 0.431 0.027 16.275
22041.9 0.429 0.026 16.551
23883.2 0.423 0.025 16.635
25790.7 0.418 0.025 16.779
37253.2 0.389 0.023 17.096
41076 0.386 0.022 17.41
44910.9 0.381 0.022 17.564
48653.8 0.382 0.021 17.932
52401.8 0.380 0.021 18.187
246
Appendix B.4: Rig 3B Results (Nusselt Number, Enhancement Factor,
Friction Factor, and Thermal Performance)
Rig3B Min Turb
Avg
Re
Avg EF
Wall Avg EF Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
6878 3.030 Same as Rig 3A 71.269 68.632 1.696
10206 2.896 Same as Rig 3A 93.409 99.205 1.592
15384 2.751 Same as Rig 3A 123.256 129.682 1.427
20540 2.654 Same as Rig 3A 149.871 156.405 1.350
31145 2.446 Same as Rig 3A 192.644 224.944 1.226
41030 2.337 Same as Rig 3A 229.500 263.011 1.163
Rig3B Nom Turb
Avg
Re
Avg EF
Wall Avg EF Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
6898 3.191 Same as Rig 3A 75.260 79.986 1.639
10238 3.084 Same as Rig 3A 99.730 99.808 1.499
15381 2.957 Same as Rig 3A 132.446 122.612 1.368
20543 2.895 Same as Rig 3A 163.458 159.250 1.332
31232 2.768 Same as Rig 3A 218.596 228.936 1.261
41143 2.589 Same as Rig 3A 254.864 254.454 1.160
Rig3B Nom Turb
Avg
Re
Avg EF
Wall Avg EF Nose
Avg Nu
Wall
Avg Nu
Nose
Avg TP
Wall
6898 3.191 Same as Rig 3A 75.260 79.986 1.639
10238 3.084 Same as Rig 3A 99.730 99.808 1.499
15381 2.957 Same as Rig 3A 132.446 122.612 1.368
20543 2.895 Same as Rig 3A 163.458 159.250 1.332
31232 2.768 Same as Rig 3A 218.596 228.936 1.261
41143 2.589 Same as Rig 3A 254.864 254.454 1.160
247
Rig 3B Minimum Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
7270.7 0.225 0.034 6.575
9106.8 0.225 0.032 6.962
10953.6 0.241 0.031 7.789
12798.3 0.239 0.030 8.029
14640.4 0.238 0.029 8.277
16485.8 0.244 0.028 8.75
18322.3 0.243 0.027 8.956
20164.1 0.247 0.027 9.322
22004.7 0.236 0.026 9.092
23863.2 0.246 0.025 9.663
25714 0.240 0.025 9.626
37266.3 0.227 0.023 9.977
40958.3 0.227 0.022 10.228
44751.8 0.225 0.022 10.363
48381.7 0.221 0.021 10.376
52250.1 0.219 0.021 10.482
Rig 3B Nominal Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
7277.9 0.320 0.034 9.366
9109.2 0.327 0.032 10.108
10947.2 0.326 0.031 10.539
12798.7 0.332 0.030 11.174
14654.4 0.341 0.029 11.885
16496.1 0.339 0.028 12.148
18333.6 0.331 0.027 12.17
20168.1 0.320 0.027 12.052
22015.4 0.322 0.026 12.413
23866.1 0.323 0.025 12.694
25768.8 0.319 0.025 12.807
37184.2 0.296 0.023 13.014
41009.8 0.297 0.022 13.365
44785.1 0.291 0.022 13.399
48527.7 0.288 0.021 13.533
52228.6 0.285 0.021 13.643
Rig 3B Maximum Turbulator Cold Friction Factor
Re Fdarcy Fsmooth Fdarcy/Fsmooth
7237.2 0.418 0.034 12.211
9073.1 0.450 0.032 13.902
10917.9 0.424 0.031 13.729
12763.9 0.446 0.030 14.998
14610 0.444 0.029 15.442
16453.3 0.432 0.028 15.493
18308.8 0.426 0.027 15.684
20155.9 0.428 0.027 16.144
22011.7 0.423 0.026 16.321
23851.3 0.421 0.025 16.554
25679.6 0.415 0.025 16.626
37202.6 0.396 0.023 17.401
41071.6 0.394 0.022 17.742
44954.8 0.390 0.022 17.988
48708.1 0.387 0.021 18.21
52377.6 0.386 0.021 18.459
248
top related