Post on 03-Aug-2020
________________________________________________________________________
A Thesis Presented
By
_____________________________________________
to
The Department of __________________________
in partial fulfillment of the requirements for the degree of
Master of Science
in the field of
________________________________________
Northeastern University Boston, Massachusetts
___________________________________
i
Abstract
Varieties of cooling methods have been used to protect hot sections in modern gas turbine
engines so as to allow a higher inlet temperature for increasing turbine efficiency. One
such method is to route the air through passages roughened with ribs (turbulators) within
the airfoil to enhance heat transfer. In an effort to investigate the thermal behavior of the
ribs at different Reynolds numbers, a combined numerical and experimental study was
conducted. In the numerical part, a square channel roughened with 90° ribs of three
geometries was modeled. Square as well as Ramped (with decreasing height in the flow
direction, and with increasing height in the flow direction) ribs in a staggered
arrangement were studied. The numerical models contained the smooth entry and exit
regions to simulate exactly the tested geometries. The applied thermal boundary
conditions to the CFD models matched the test boundary conditions. Numerical results
were obtained from a three-dimensional unstructured computational fluid dynamics
model with over 8 million hexahedral elements. For turbulence modeling, the realizable
𝑘 − 𝜀 was employed in combination with enhanced wall treatment approach for the near
wall regions. In the experimental part, all these geometries were built and tested for heat
transfer coefficients at a Reynolds number range from 10,000 to 60,000, using a liquid
crystal technique. Comparisons are made between the test and numerically-obtained
results in order to evaluate the employed turbulence models and validate the numerically
results. The test and numerically-evaluated results showed reasonable agreements
between the two for Ramped cases. Friction factors are also measured, and both heat
transfer and friction factor results for 3 turbulator geometries are compared. The results
show that the heat transfer coefficients are strongly affected by the rib shape and square
ribs provide higher heat transfer enhancement and pressure drop than other shapes.
ii
Acknowledgements
I would like to express my gratitude to my advisor Dr. Mohammad Taslim for the useful
comments, remarks and engagement through the process of this master thesis.
Furthermore I would like to thank Gerard Quinn and Mehdi Abedi for introducing me to
the topic as well for the support on the way. I am thankful to those who supported me
throughout the course of this thesis for their aspiring guidance, constructive criticism and
invaluable advice. I am sincerely grateful to them for sharing their truthful and
illuminating views on a variety of issues related to the project.
A special thanks to my family. No words can express how grateful I am to my mother
and father for all of the sacrifices that they have made on my behalf. I would also like to
thank Qin Junning and all of my friends who supported me and incented me to strive
towards my goal.
iii
Nomenclature
A channel area D hydraulic diameter of test section
e turbulator (rib) height
S turbulator pitch, center-to-center
w turbulator width
f Darcy friction factor fs smooth wall friction factor from Blausis correlation
h heat transfer coefficient
k thermal conductivity
L turbulated length
𝑚 mass flow rate
𝑁𝑢 Nusselt Number
Nus Nusselt number from Dittus-Boelter correlation P channel perimeter
Pr Prandtl number
Q heat energy
q’’ heat flux
Re Reynolds number
ρ air density
U average velocity in channel
iv
Table of Contents
Abstract ............................................................................................................................................. i
Acknowledgements.......................................................................................................................... ii
Nomenclature ................................................................................................................................. iii
Table of Contents ............................................................................................................................ iv
1 Introduction ............................................................................................................................. 1
2 Test Section .............................................................................................................................. 5
2.1 Square Ribs Test Section .................................................................................................. 5
2.2 Ramped Ribs 1 Test Section ............................................................................................. 9
2.3 Ramped Ribs 2 Test Section ........................................................................................... 13
3 Computational Model ............................................................................................................ 15
4 Procedure ............................................................................................................................... 18
4.1 Leak Tests ....................................................................................................................... 18
4.2 Cold Tests ....................................................................................................................... 18
4.3 Heat Transfer Tests ........................................................................................................ 18
5 Data Reduction ...................................................................................................................... 21
5.1 Friction Factor Calculations ............................................................................................ 21
5.2 Heat Transfer Calculations ............................................................................................. 22
5.3 Green Pixel Area Measurements ................................................................................... 23
6 Results and Discussion ........................................................................................................... 24
6.1 Friction Factor ................................................................................................................ 24
6.2 Heat Transfer Test .......................................................................................................... 25
7 Conclusions ............................................................................................................................ 35
References ..................................................................................................................................... 36
Appendix A: Square Ribs Sample input.dat ................................................................................... 38
Appendix B: Ramped Ribs, Flow Direction 1 Sample input.dat ..................................................... 41
Appendix C: Ramped Ribs, Flow Direction 2 Sample input.dat ..................................................... 44
Appendix D: Square Ribs Heat Transfer Data Reduction Code (FORTRAN) ................................... 47
v
Appendix E: Tabulated Results ...................................................................................................... 66
Cold Tests ................................................................................................................................... 66
1
1 Introduction
Gas turbine engines are employed in varieties of power applications, such as helicopters,
commercial airliners and static power plants. In each application, higher performance is
desired for greater power output and lower fuel consumption.
In the power cycle of a gas turbine engine, air at atmospheric temperature and pressure is
compressed into a burner where the high pressure air is mixed with fuel and ignited. The
high temperature gasses are expanded through a turbine, powering the compressor,
providing shaft power and/or exiting the system at high velocity propelling an aircraft
forward. So the turbine entrance temperature in modern gas turbine engines is often much
higher than the melting temperature of the alloy it is made of. This necessitates proper
cooling of the airfoils to have a reasonably long life span.
Various methods have been developed over the years to keep turbine blade temperatures
below critical levels. The main purpose in turbine blade cooling is achieving maximum
heat transfer coefficients while minimizing the coolant air flow rate.
One such method is to route the air through turbulated serpentine passages within the
airfoil and remove heat from the blade by convection. The coolant is then ejected either at
the tip of the blade, through the cooling slots along the trailing edge or cooling holes
along the airfoil surface. The vortices and other secondary flows introduced by
turbulators increase the heat transfer from the turbine blade walls. Additional heat
transfer is gained by increased extended surface area from the roughened surface.
However, roughening the walls increases the pressure requirements of the compressor.
Fig. 1 shows a typical internal cooling arrangement for a multipass turbine blade [1].
2
Fig. 1 Typical internal cooling arrangement for a multipass turbine blade [1].
Geometric parameters such as turbulator height to passage hydraulic diameter or
blockage ratio e/D, angle of attack, the manner in which the turbulators are positioned
relative to one another (in-line, staggered, crisscross, etc.), turbulator pitch-to-height
ratio S/e, and turbulator shape (round vs sharp corners, fillets, skewness towards the
flow direction) have pronounced effects on both local and overall heat transfer
coefficients. Numerous experimental and numerical studies have been performed in
rectangular rib-roughed cooling channels. Taslim and Korotky [2] investigated the heat
transfer coefficient on the surfaces of round-corner, low-aspect-ratio ribs. They tested a
square channel roughened with ribs on two opposite walls in a staggered manner and
perpendicular to the flow direction. Arts et al. [3] compared the computational results
from a three-dimensional Navier–Stokes solver for heat transfer of a steady viscous
compressible flow in a square channel with one rib-roughened wall with detailed
experiments carried out at the von Karman Institute. The three-dimensional computations
captured the correct position of the reattachment point using the k–l turbulence model.
Korotky and Taslim [4] tested three staggered 90° rib geometries for two distinct thermal
boundary conditions of heated and unheated channel walls. They made the comparisons
3
between the area-weighted average heat transfer coefficients and friction factors for ribs
with rounded corners and those with sharp corners. They concluded that for the rounded-
corner ribs, the rib average heat transfer coefficient depended on the level of roundness.
Gupta et al. [5] measured the local heat transfer distributions in a double wall ribbed
square channel with 90° continuous, 90° saw tooth profiled and 60° V-broken ribs.
Taslim and Spring [6] used liquid crystals to study the effects of turbulator profile and
spacing on heat transfer coefficient. They concluded that low aspect ratio turbulators,
especially with round corners, produced lower heat transfer coefficients. They also found
an optimum pitch-to-height ratio for 90° square turbulators was around 8. Gao and
Sunden [7] investigated the thermal and hydraulic performance of three rib-roughened
rectangular ducts. The ribs were arranged staggered on the two wide walls. They
employed liquid crystal thermography in the heat transfer experiment to demonstrate
detailed temperature distribution between a pair of ribs on the ribbed surfaces. They
found that the secondary flows caused by the inclined ribs created a significant spanwise
variation of the heat transfer coefficients on the rib-roughened wall with high heat
transfer coefficient at one end of the rib and low value at the other. In the streamwise
direction between two consecutive ribs, the temperature distribution showed a sawtooth
variation because of flow reattachment. Lu and Jiang [8] experimentally and numerically
investigated forced convection heat transfer of air in a rectangular channel with 45⁰ ribs
on one wall. They compared the experimental and numerical results and showed that the
SST k–ω turbulence model was more suitable for the convection heat transfer in such
channels than the RNG k–ε turbulence model. They found that the average heat transfer
coefficients increased with increasing mass flow rates and decreasing spacings. Peng et
al. [9] experimentally and numerically studied convection heat transfer in a channel with
90⁰ ribs and V-shaped ribs. They found that both the 90⁰ ribs and V-shaped ribs enhanced
the convection heat transfer compared with a flat wall without ribs, but the pressure drop
also increased. They also compared continuous ribs and interrupted ribs and concluded
that the heat transfer with the 90⁰ interrupted ribs is more than with the 90⁰ continuous
ribs. Promvonge and Thianpong [10] conducted experiments to assess turbulent forced
convection heat transfer and friction loss behaviors for air flow through a constant heat
flux channel fitted with different shaped ribs. The rib cross-sections used in this study
were triangular (isosceles), wedge (right-triangular) and rectangular shapes. They
introduced two rib arrangements, namely, in-line and staggered arrays. The experimental
results showed a significant effect of the presence of the ribs on the heat transfer rate and
friction loss over the smooth wall channel. They found that the in-line rib arrangement
provided higher heat transfer and friction loss than the staggered one for a similar mass
flow rate. Kamali and Binesh [11] developed a computer code to study the turbulent heat
transfer and friction in a square duct with various-shaped ribs mounted on one wall. The
simulations were performed for four rib shapes, i.e., square, triangular, trapezoidal with
decreasing height in the flow direction, and trapezoidal with increasing height in the flow
4
direction. The prepared algorithm and the computer code were applied to demonstrate
distribution of the heat transfer coefficient between a pair of ribs. The results showed that
features of the inter-rib distribution of the heat transfer coefficient are strongly affected
by the rib shape and trapezoidal ribs with decreasing height in the flow direction provide
higher heat transfer enhancement and pressure drop than other shapes. Taslim and Liu
[12] showed that CFD could be considered as a viable tool for the prediction of heat
transfer coefficients in a rib-roughened test section. In the numerical part, a square
channel roughened with 45° ribs of four blockage ratios (e/Dh) of 0.10, 0.15, 0.20, and
0.25, each for a fixed pitch-to-height ratio (P/e) of 10, was modeled. Sharp as well as
round-corner ribs (r/e = 0 and 0.25) in a staggered arrangement were studied. In the
experimental part, a selected number of these geometries were built and tested for heat
transfer coefficients at elevated Reynolds numbers up to 150 000, using a liquid crystal
technique.
5
2 Test Section
Figure 2 depicts the general flowchart of the experiment. The coolant air came from a
100 psi JB #A10053 shop compressor, was sent through an air filter to a pressure
regulator, and then passed through a critical venturi from which the mass flow rate could
be calculated. The flow then went into a 20in by 20in by 21in plenum equipped with a
honeycomb flow straightener. A pressure tap is mounted on the top of the plenum to
measure the static pressure. Two thermocouples are mounted on the front wall for the
average temperature of the inlet air flow, as well as eight 0.25in threaded studs to connect
the test sections.
Fig. 2 Experimental Rig General Flowchart.
2.1 Square Ribs Test Section
6
a)
b)
Fig. 3. Square Ribs (From SolidWorks) a) Side view; b) Top view.
Fig. 4 Square turbulator geometry. All units inches.
7
Fig. 5 Layout and compositions of liquid crystal and heater for Square Ribs.
All test sections were 2in by 2in rectangular channels with a length of 36in, three walls of
which were made of 0.5in-thick Plexiglas. For the square turbulator test section, the
fourth wall was made of a 5in-thick and 4in-width polyurethane slab in order to mitigate
heat loss from the heaters, on which the liquid crystal sheets were also attached and all
pictures were taken. The polyurethane block was combined to the test section side-walls
8
using 6in-length 10-24 threaded rods with nuts and washers. A 0.125in thick plywood
back plate was made to protect the foam from the pressure generated by the washers
when tightened the nuts. The fourth wall included a 3in by 2in unheated “small part”,
manufactured from Plexiglas, to facilitate the connection of the polyurethane block to the
test section entrance. The Plexiglas walls were secured using 10-24 socket cap machine
screws. Three counter bored holes were drilled into the side-walls and the front plate 3in
from the inlet to accommodate copper tubing for reading the air static pressures to
measure the pressure drop across the test section. The experimental apparatus is shown in
Fig. 3. The turbulated length for all test sections was about 11in, so approximately 12.5in
walls at the inlet and the exit were all smooth, respectively. This simulates the
unturbulated cooling passage in the dovetail region of an airfoil. Heat transfer
measurements were performed for the location between the third and fourth turbulators
from the test section inlet. A total of 10 turbulators were machined out of Plexiglas for
this study, and placed onto two opposite walls in a staggered arrangement with an attack
angle of 90⁰ to the flow. Fig. 4 shows the geometry of the turbulator. In each test the ribs
were staggered at half the pitch. All turbulators were buffed using Novus polish to
improve the transparency of the material. Three 2in by 11.125in custom-made etched-foil
heaters with a thickness of 0.006in were glued on the insulation wall where pictures were
taken using heat resistant adhesive to minimize temperature deformation. Fig. 5 shows
the layout and compositions of the liquid crystal sheet and the heaters. The heaters
covered the whole test section including the nonturbulated entry and exit lengths. Three
3in by 12in 0.005in-thick liquid crystal sheets were then cut and glued on the heaters.
The entire test section was connected with the plenum by a custom bell mouth plate with
a 0.5in radius curvature to guide the airflow into the channel and to make the flow
uniform. The bell mouth plate was attached to the channel side-walls with two 8-32
machine screws. These screw heads were counter bored, covered in wood putty and
sanded to form a smooth entrance surface. The bell mouth plate was then bonded using
SciGrip bonding agent.
The test sections were covered on all Plexiglas sides by 2-in-thick insulation foams to
reduce the heat loss to the environment, except for a small window at the location where
the pictures needed to be taken. The heat losses of radiation from the heated wall to the
unheated walls, as well as the losses to the ambient air, were taken into consideration
when calculate the heat transfer coefficients. Heat flux in the test section wall was
provided by the heaters through a custom designed power supply unit. Each heater was
separately controlled by a variable transformer.
To prevent leaks at components interfaces, silicone was employed along the edges as well
as around the screws and the counter bored holes before testing. Aluminum tape was used
at the polyurethane-Plexiglas interfaces. Further caulking and tape were applied if more
leakages were found after the leak test.
9
All turbulators mounted on the front plate were placed with respect to the center of heater
2, with two turbulators on either side of the area of investigation. The centerline of
turbulator 3 on the liquid crystal side was mounted in line with half pitch upstream of the
center of heater 2, with two turbulators mounted upstream and downstream, respectively.
2.2 Ramped Ribs 1 Test Section
a)
b)
Fig. 6 Ramped Ribs, flow direction 1 (From SolidWorks) a) Side view; b) Top view.
10
Fig.7 Ramped turbulator geometry. All units inches.
For the ramped turbulators test section, a back plate of Plexiglas with an identical hole
pattern as the polyurethane was used to replace the insulation wall in Square Ribs test
section because the heaters and liquid crystal sheets could not extend over the actual
turbulator surface. The 4in by 34in plate, made of 0.5in thick clear Plexiglas, was
transparent and allowed for the photo taking of the green area showed on the liquid
crystals on a digital camera. On the plate surface facing the air flow, five Inconel heaters
were mounted. Each heater was a wire wound that was sandwiched between two low-
conductivity Kapton foils in a shape of maze. The heating element had a thickness of
0.0005in and the Kapton foil had a thickness of 0.001in. The central heater, which is
measured 2in by 11.125in, was surrounded by four 1in by 8.25in guard heaters abutting
the upstream and downstream, respectively. The central heater was the only one that
directly involved in measuring the heat transfer coefficients. The guard heaters were
installed to minimize the influences of any cross-conduction within the back plate. The
foil heaters were glued to three 3in by 12in liquid crystal sheets which were in turn glued
to the clear Plexiglas plate to measure and record the surface temperature for the
calculation of Nusselt numbers.
11
Fig. 8 Layout and compositions of liquid crystal and heater for Ramped Ribs.
The technique of the steady state liquid crystal thermography was employed to measure
the heat transfer coefficients in these test sections. The liquid crystal sheet’s color
changes depending on a specific range of temperatures; in these experiments the green
color was calibrated as a reference color. Using thin Minco heaters, one wall of the test
section is heated at a known heat flux. It is noted that in a stationary channel, the heal
transfer coefficient is not sensitive to the number of heated walls [13]. The reference
color is then moved from one location to another such that the whole area of investigation
is eventually covered with the reference color at one time or another by carefully
adjusting the currents and voltages supplied by the custom voltage regulator box. This
process results in a series of photos each corresponding to a certain covered area of the
reference color. Knowing the heat flux, the surface temperature, and the air mixed mean
temperature, the heat transfer coefficient can be calculated with each picture. The air
mixed mean temperature is calculated through an energy balance between the test section
entrance and the position of investigation.
12
Before testing, the liquid crystal sheet was calibrated as follows. A water bath was used
to obtain uniform isochromes on a sample piece of the liquid crystal sheets used
throughout these studies. The temperature corresponding to each color was measured
using a precision thermocouple and videos were taken at laboratory conditions
simultaneously so as to simulate closely the actual experiment environment. Distilled
water was heated to 100°F in a glass beaker using a hot plate and poured into an insulated
cup where the test sample was secured. Along with the water cooled down, the test
sample went through its color bandwidth changing. The water was periodically stirred
with a glass stick to make the temperature uniform in the cup. When the test sample
turned green, the temperature showed on the data acquisition unit was assigned to this
color. These videos could be played back to verify the temperature assignments.
Reference colors along with their measured temperatures of 95.7⁰F and 93.0⁰F were then
chosen to be used throughout the experiments for the Square Ribs test section and the
Ramped Ribs one, respectively. It should be noted that all possible shades of the selected
reference color showed a temperature difference of no more than 0.5⁰F.
Fig. 9 Liquid crystal calibration for Ramped Ribs test section.
13
Fig. 10 Liquid crystal calibration for Square Ribs test section.
For pressures 0-2in H20, a Dywer 1430 Micromanometer with a specific gravity of 1.000
was used. For pressures 2-30in H20, a Dynatech single column standing manometer with
a specific gravity of 0.827 was used. Ambient pressures were assumed to be the same as
the ambient pressures at Logan International Airport in Boston, Massachusetts. For the
calculation of the local heat transfer coefficient, the small heat loss through the Plexiglas
plate to the lab was taken into account. For a typical test run, the Reynolds number was
set by precisely fixing the mass flow rate through adjusting the pressure of venturi. The
heat flux was then induced by turning on the main power supply and adjusting each
heater's power separately until the first band of reference color was showed on the liquid
crystal sheet in the location of interest. 30 minutes were allowed so that the systems came
to thermal equilibrium at which time a photograph was taken and data recorded. The
power to the heaters was then increased such that the reference color was moved to a
location next to the previous one and another picture was taken. The process was
repeated for all Reynolds numbers. Each photograph was digitized in order to measure
the area covered by the reference color. This was done by using a commercial software
package installed on a PC. Once the areas were measured, the local area-weighted
average heat transfer coefficients were calculated. Additionally, the non-dimensional
friction factors were measured to quantify the pressure drop across the turbulated region.
2.3 Ramped Ribs 2 Test Section
a)
14
b)
Fig. 11 Ramped Ribs, flow direction 2 a) Side view; b) Top view. Flow from left to right.
For the ramped ribs, two flow directions were tested. Flow direction 1, showed in Fig. 6,
corresponds to the case in which the air encounter the front of the ramped rib first, then
moved over the ramp.
Flow direction 2, showed in Fig. 11, corresponds to the case in which the air encounter
the ramp first, the moved up on the rib roof and tripped over the rib.
15
3 Computational Model
a)
b)
Fig. 12 A typical mesh for the two kinds of geometries a) Square; b) Ramped
16
a)
b)
Fig. 13 Details of the mesh distribution around the turbulators a) Square; b)
Ramped.
17
The computational models were constructed for a 90° rib-roughened channel with five
ribs on each side in a staggered arrangement. The domain included the entry and exit
regions exactly simulating the test setup. Numerical models were meshed and run for
Square Ribs as well as Ramped Ribs of both directions. Figure 12 shows a typical mesh
for the two kinds of geometries while Fig. 13 shows the details of the mesh distribution
around the turbulators. These meshes are made coarser so the details will be visible in
these graphs. It is seen that there are regions of high mesh concentration close to the rib
surfaces in order to capture the viscous effects in the recirculating zones. This
arrangement continues on both sides to cover the entire channel length with a total of ten
ribs. The CFD analyses were performed using Fluent/UNS solver by Ansys, Inc., a
pressure-correction based, multi-block, multi-grid, unstructured/adaptive solver.
Realizable k−ε turbulence model in combination with enhanced wall treatment approach
for the near wall regions was used. The equation of state for an ideal gas was turned on to
take the compressibility effects into consideration. For boundary conditions, the mass
flow rate was employed at the test section entrance and atmospheric conditions were
applied at the exit. Mesh independence was achieved at about 8000 000 cells for a typical
model. Meshes in all models were totally hexagonal, a preferred choice for CFD analysis,
and were varied in size bi-geometrically from the boundaries to the center of the
computational realm in order to have smaller cells close to the walls.
18
4 Procedure
4.1 Leak Tests When the test section was attached to the plenum or turbulators were changed for another
experiment, a leak test should be performed to ensure all compressed air is going through
the test section to outlet. The leak test was done as follows. First, turn on the compressor
and set the venturi to the highest pressure that would be used in the experiments; Next,
suds made from a mixture of soap and water were applied to any space where an air leak
could probably occur: Plexiglas and Plexiglas seams, Plexiglas and polyurethane seams,
areas around pressures taps, etc. If there were leaks, the bubbles of the suds would
enlarge. If no leaks, the bubbles would disappear slowly. When all the leaks were located,
more silicone caulking applied around leaked areas after the compressor was shut down.
In addition, a leak test was conducted around the plastic tubing connections on the
venturi to ensure a correct pressure reading. This process was repeated whenever a
venturi was manipulated, or any change was conducted on the pipes.
4.2 Cold Tests Cold tests were aimed to measure the pressure drop in the channel. First, the manometers
were placed on the experiment table and zeroed. The compressor was started. A
preliminary pressure reading was taken at the plenum and inlet pressure taps with the
30in manometer. If the pressure was below 2in H20, the micromanometer was used; if it
was over 2in H20, the tall manometer was used.
All data readings were recorded by hand into a log sheet. Temperatures at the venturi and
the inlet of the test section, as well as ambient temperature were read from the data
acquisition unit. Venturi pressure was read from the round pressure gage mounted near
the venturi. Then, the liquid manometers were used to measure the plenum and inlet
pressures.
4.3 Heat Transfer Tests To start the heat transfer test, a specific venturi pressure should be set up to get the
wanted air flow rate. Then the multimeters were switched on to read voltages and
currents. The individual rheostats were adjusted such that a uniform heat flux would be
maintained through all the heaters. In the Square Ribs test section, with three identical
heaters, voltages would be uniform. In the Ramped Ribs test section, the voltages were
different because the center heater and the guard heaters are of different areas.
19
For a uniform heat flux:
𝑞"𝑐𝑒𝑛𝑡𝑒𝑟 = 𝑞"𝑔𝑢𝑎𝑟𝑑 (1)
(𝑄 𝐴⁄ )𝑐𝑒𝑛𝑡𝑒𝑟 = (𝑄 𝐴⁄ )𝑔𝑢𝑎𝑟𝑑 (2)
Power is calculated from the heater voltage and resistance.
𝑄 = 𝐼 × 𝑉 (3)
𝐼 = 𝑉 𝑅⁄ (4)
𝑄 =𝑉2
𝑅 (5)
This yields:
𝑉𝑐𝑒𝑛𝑡𝑒𝑟2
𝐴𝑐𝑒𝑛𝑡𝑒𝑟𝑅𝑐𝑒𝑛𝑡𝑒𝑟=
𝑉𝑔𝑢𝑎𝑟𝑑2
𝐴𝑔𝑢𝑎𝑟𝑑𝑅𝑔𝑢𝑎𝑟𝑑 (6)
𝑉𝑔𝑢𝑎𝑟𝑑 = 𝑉𝑐𝑒𝑛𝑡𝑒𝑟 √𝑅𝑔𝑢𝑎𝑟𝑑𝐴𝑔𝑢𝑎𝑟𝑑
𝑅𝑐𝑒𝑛𝑡𝑒𝑟𝐴𝑐𝑒𝑛𝑡𝑒𝑟
2 (7)
In a typical data recording process, the thermocouple temperatures were recorded first,
and then the multimeter readings. Pressures readings were taken for every tenth photos.
At last, the pictures were taken. The BBA light bulb was used for illumination during
photographing instead of the room light. The experiment concluded when the green color
was no longer visible in the area of interest, or further increase in voltage produced no
movement for the green color band, especially around the side walls. A set of
photographs is provided in appendix A, depicting the color progression in a Square Ribs
test.
Fig. 14 shows a typical measurement for Square Ribs. The No fill symbols show the Nu
of each picture while the Solid fill ones show the area-weighted average Nusselt number
for the corresponding Reynolds number.
20
Fig. 14 A typical test result of Square Ribs.
0
50
100
150
200
250
300
350
400
450
5000 15000 25000 35000 45000 55000 65000
Nu
Re
Square Ribs
21
5 Data Reduction
5.1 Friction Factor Calculations Darcy friction factor, f, is a non-dimensional number describing the pressure drop in a
channel.
𝑓 =Δ𝑝
4(𝐿
𝐷)
𝜌𝑈2
2
(8)
where Δp is the pressure drop across the turbulated length L.
Δ𝑝 = 𝑝𝑖𝑛𝑙𝑒𝑡 − 𝑝𝑜𝑢𝑡𝑙𝑒𝑡 (9)
The hydraulic diameter is defined as:
𝐷 =4𝐴
𝑃 (10)
where A is the channel cross-section area and P is the channel perimeter.
The air density ρ is calculated from the ideal gas equation, with R the ideal gas constant:
𝜌 =𝑝𝑖𝑛𝑙𝑒𝑡
𝑇𝑖𝑛𝑙𝑒𝑡𝑅 (11)
where 𝑇𝑖𝑛𝑙𝑒𝑡 is the average inlet temperature from the two inlet thermocouples 𝑇1 and 𝑇2:
𝑇𝑖𝑛𝑙𝑒𝑡 =𝑇1+𝑇2
2 (12)
The average velocity of the flow, U, is calculated from:
𝑈 =�̇�
𝜌𝐴 (13)
The mass flow rate is calculated from relations provided by the venturi manufacturers.
For the 0.15in diameter venturi manufactured by FlowMaxx Engineering:
�̇� = [𝑎 + 𝑏(𝑝𝑣𝑒𝑛𝑡 + 𝑝𝑎𝑚𝑏) +𝑐
√𝑝𝑣𝑒𝑛𝑡+𝑝𝑎𝑚𝑏2 ]
𝑝𝑣𝑒𝑛𝑡+𝑝𝑎𝑚𝑏
𝑇𝑣𝑒𝑛𝑡+460 (14)
with the constants:
22
{𝑎 = 0.0093357474
𝑏 = 3.2726956 × 10−7
𝑐 = −0.00024626555 (15)
Reynolds number Re is a non-dimensional number describing the ratio of momentum to
vicious forces.
𝑅𝑒 =4�̇�
𝑃𝜇 (16)
Dynamic viscosity μ is interpolated from standard air tables using the inlet temperature.
The friction factor for the turbulated test section can be compared to the smooth wall
friction factor from Blausis correlation:
𝑓𝑠 =0.316
𝑅𝑒0.25 (17)
5.2 Heat Transfer Calculations Reduction of the heat transfer data was completed by a program written in FORTRAN.
The first step in the data reduction program was to define the test section geometry. This
included the areas and thicknesses of the Plexiglas and polyurethane walls, or Plexiglas
back plate for Ramped Ribs cases, as well as the heater areas. Next, the raw data is read
into the program. Starting with the data from the first photograph, the heat transfer into
the system from the first heater upstream to the area of investigation is calculated. A
thermal circuit is then defined based on the thickness and thermal conductivity of
materials that form the test section. An initial guess is made of the heat transfer
coefficient and temperatures on the test section walls. Using this guess, a system of
equations describing the radiational loss is defined and solved using Gaussian
elimination. Total heat flux losses from each test section wall could then be calculated.
If the net heat flux out of the unheated walls was greater than or equal to 0.001, the
updated heat flux and temperature values were used as the new initial guesses and
subsequent iterations performed until convergence.
On the other hand, the smooth wall Nusselt number was estimated from the Dittus-
Boelter correlation:
𝑁𝑢𝑠 = 0.023𝑅𝑒0.8𝑃𝑟0.4 (18)
23
The uncertainty of the reduced values were calculated using Kline and McClintock
uncertainty analysis (19), where Δ𝐹 is the uncertainty of a linear function F (𝑥𝑖), and Δ𝑥𝑖
is the uncertainty of the independent variable 𝑥𝑖.
Δ𝐹 = [∑ (𝜕𝐹
𝜕𝑥𝑖)
2𝑛𝑖=1 ]
1/2
(19)
With the Nusselt number of a single data point calculated, the data reduction program
advanced to subsequent data entries until a data point was calculated for each photograph
taken. Ramped Ribs tests produced two Nu values: one for the ramp with decreasing
height in the flow direction and one for the opposite.
5.3 Green Pixel Area Measurements The area weight averaged Nusselt number for a single Reynolds number was calculated
as follows:
𝑁𝑢̅̅ ̅̅ =∑ (𝑁𝑢𝑖𝐴𝑖)𝑛
𝑖=1
∑ 𝐴𝑖𝑛𝑖=1
(20)
where n is the number of the data points for a single Reynolds number, 𝑁𝑢𝑖 is a single
Nusselt number, and 𝐴𝑖 is the calibrated green area of the area of interest. The green area
was calculated by manually counting the pixels in the image analysis program ImageJ.
Using the “polygon” tool in ImageJ, the green area is outlined in a closed path. Next, the
“measurement” tool was set to measure the area enclosed by the path and a measurement
taken. The Reynolds numbers were averaged for a given venturi pressure setting.
The thermal performance was calculated to compare the area weight averaged Nusselt
number and friction factor of the turbulated channel to the smooth wall:
𝑇𝑃 =(𝑁𝑢̅̅ ̅̅ 𝑁𝑢̅̅ ̅̅ 𝑠⁄ )
(𝑓 𝑓𝑠⁄ )1/3 (21)
24
6 Results and Discussion
6.1 Friction Factor
Fig. 15 Cold test friction factor results.
Overall, all geometries tested exhibited a more or less stable friction factor as the
Reynolds number increased. However, the Square Ribs test section has a higher friction
factor than the Ramped Ribs. The physical explanation for this behavior is that, for
square geometry, there is very little transition zone from the top of turbulator to the floor
of channel. The flow is forced to quickly expand after a confined space, interacts with the
recirculation caused by the sharp drop of the rib as it moves towards the channel exit. The
shear stresses are the main cause of increased flow resistance and, consequently,
increased friction factor coefficients. For slower changing geometry, flow moves down
the ramp without separating from the surface before approaching the next turbulator. As a
result, the flow experiences less resistance and friction factor coefficients are lower.
0.0
0.1
0.2
0.3
0.4
0.5
0 10000 20000 30000 40000 50000 60000
f
Re
RAMPED RIBS, FLOW
DIRECTION 2
SQUARE RIBS
RAMPED RIBS, FLOW
DIRECTION 1
25
6.2 Heat Transfer Test It has been established both experimentally and analytically that, given enough space
between a pair of turbulators for the flow to reattach, the heat transfer coefficient reaches
its maximum in the reattachment zone and decreases monotonically in the flow direction
until it approaches the next turbulator where it starts to increase again due to a stagnation
point type of flow.
The heat transfer coefficient corresponding to each picture was calculated from:
ℎ =�̇�"−�̇�"𝑡−�̇�"𝑟
𝑇𝑠−𝑇𝑚 (22)
where 𝑇𝑠 is the surface temperature and 𝑇𝑚 is the mean air temperature at the area of
interest. �̇�" is the heat flux generated by the foil heater, �̇�"𝑡 is the total heat loss from the
heaters to ambient and �̇�"𝑟 is the radiational loss from the heated wall to the surrounding
unheated walls. Air properties were evaluated at the mean air temperature, 𝑇𝑚. Heat
transfer results were gathered for air Reynolds numbers from about 10,000 to 60,000.
Figures 15, 16, 17, 18 and 19 show the measured average Nusselt number on the area of
interest in each test section for different air Reynolds numbers. It should be mentioned
that, in these figures, the symbols represent the measured data while the lines represent
the numerically-obtained results.
26
Fig. 16 Nusselt number variation along the channel on the bottom and top walls,
Square Ribs.
27
Fig. 17 Nusselt number variation along the channel on the bottom and top walls,
Ramped Ribs, flow direction 1. (Copper Rib)
28
Fig. 18 Nusselt number variation along the channel on the bottom wall, Ramped
Ribs, flow direction 1. (Plexiglas Rib)
29
Fig. 19 Nusselt number variation along the channel on the bottom and top walls,
Ramped Ribs, flow direction 2. (Copper Rib)
30
Fig. 20 Nusselt number variation along the channel on the bottom wall, Ramped
Ribs, flow direction 2. (Plexiglas Rib)
As the air Reynolds number increases, there is stronger interaction between the flow and
turbulators. These interactions increase the heat transfer coefficients on the area in
between the two ribs where the pictures were taken as is seen in those figures. In general,
Nusselt numbers on the roof of turbulators are much higher than those on the other
surfaces. However, the first rib of Square-Rib Test Section does not benefit from the
diversion of the air on the opposite wall which produces lower heat transfer coefficients
on the roof surface. This behavior is due to the bypassing of the air flow caused by the
corner of the first rib, which results in more recirculation on the roof of the turbulators.
On the other hand, the heat transfer coefficients of Ramped Ribs for both flow directions
are lower than those of the Square-Rib Test Section. Tests confirm this behavior while
numerical results show the opposite trend. A possible explanation is that for Ramped
Ribs, the air after tripping over these long ribs will not reattach to the channel surface
between the ribs as effectively as it would when the ribs are shorter with the flow
direction. For square geometry, vortices shed from the relatively sharp corners enhance
the mixing of the near-wall warm air with the cooler core air thus increasing the heat
transfer coefficients compared to those of Ramped Ribs which are streamlined. However,
for a Ramped Rib geometry, the results of which are shown in Figures 16, 17, 18 and 19,
ribs with flow direction 2 produced lower heat transfer coefficients than ribs with flow
direction 1. For these ribs with flow direction 1, air flow sees a sudden blockage that
causes the flow to trip over the rib. This will cause a lot of mixing thus increasing the
31
heat transfer coefficients. For ribs with flow direction 2, air moves up the ramp with not
much resistance thus less mixing occurs and, as a result, heat transfer coefficients will be
less. At the same time, although stronger vortices may shed from the end edges, they are
dissipated to the core flow and do not get a chance to scrub against the surface area
between the ribs. The end result is a lower heat transfer coefficient for the flow direction
2 ribs.
Rib 1 shows a lower heat transfer coefficient because this region does not benefit from
the secondary flows created by any upstream rib. There is a remarkable increase in heat
transfer coefficient from rib 1 to rib 5 for Ramped Ribs, flow direction 1. Secondary
flows caused by the presence of ribs swirl along the wall surface and create a number of
recirculation. These vortices have an additive effect along the channel and, as a result,
Nusselt number increases along the channel from rib 1 to rib 5.A similar behavior is
observed for square geometry except that the Nusselt number variation in the flow
direction is only pronounced from rib 1 to 2. For other ribs, the Nusselt number shows a
slight increase. It is speculated that stronger secondary flows created by these sharper ribs
establish the flow domain faster than the previous case of smoother ribs, thus only a
slight variation in Nusselt number is seen. However, for the Ramped Ribs flow direction
2, the Nusselt number slightly decreases along the test section from rib2 onward. It is
speculated that the secondary flows and shed vortices from the rib corners additively
reduce the flow reattachment strength in the flow direction thus causing a continuous
reduction in the heat transfer coefficient along the flow direction.
Figures 20, 21 and 22 show the iso-Nu contours, extracted from the numerical solutions,
for a typical region between a pair of ribs in the middle of the channel. It can be seen that
the roof region corresponds to the highest Nusselt number region.
32
Fig. 21 CFD Contours of Nusselt numbers for the 3rd
Square Rib from the channel
inlet on the bottom surface, Re = 30000.
Fig. 22 CFD Contours of Nusselt numbers for the 3rd
Ramped Rib from the
channel inlet on the bottom surface, flow direction 1, Re = 30000.
33
Fig. 23 CFD Contours of Nusselt numbers for the 3rd
Ramped Rib from the
channel inlet on the bottom surface, flow direction 2, Re = 30000.
Figure 22 shows the test results only.
Fig. 24 Test results for three geometries.
34
Nu
Square Ribs
Ramped Ribs, Flow
Direction 1
Ramped Ribs, Flow
Direction 2
Re Tests CFD Tests CFD Tests CFD
10000 79.32 42.21 78.17 59.80 68.64 58.33
20000 125.82 62.92 110.80 98.01 94.83 96.49
30000 170.33 83.27 138.23 126.19 114.93 125.68
40000 226.27 105.56 160.16 149.89 140.26 151.36
50000 268.76 128.46 175.93 171.85 150.15 175.27
60000 301.85 148.31 198.63 196.55 173.13 198.34
Table. 1 Comparison between tests results and CFD
Table.1 shows the comparison between tests and CFD results. Of the three cases, the flow
over the Square Ribs appears to be the most complex; since the rib face is perpendicular
to the flow direction, sizable primary and secondary recirculation regions form near the
front and rear corners at the rib bottom. The agreements between the numerical and test
results for the Ramped Ribs are very encouraging given that realizable 𝑘 − 𝜀 turbulence
model in combination with enhanced wall treatment approach for the near wall regions
was used with a reasonable convergence time on a typical PC. The Square Ribs,
especially when they are with elevated air flow Reynolds numbers as was the case in this
investigation, create such a complex flow field that capturing all effects may require other
models for turbulence.
35
7 Conclusions
A parametric investigation was performed to experimentally and numerically determine
what effects turbulator profile has on friction factors and heat transfer coefficients in
turbine airfoils. The experiments and simulations were performed for two rib geometries
and three flow directions. It is found that features of the inter-rib distribution of the heat
transfer coefficient are strongly affected by the rib shape. Thus, a better understanding of
its effect will facilitate more efficient cooled airfoil designs. Major conclusions of this
study were:
a) Friction factors for the Square Ribs were higher than those for the Ramped Ribs.
b) The two flow directions on the Ramped Ribs produced the same friction factors.
c) At Reynolds number beyond 20,000, the friction factors stayed constant with
values of about 0.17 and 0.26 for the Ramped and Square Ribs, respectively.
d) The Square Ribs provide higher heat transfer enhancement and pressure drop than
the Ramped Ribs.
e) For the same amount of cooling air, the heat transfer performance for the Ramped
Ribs with flow direction 1 was found to be superior to that for flow direction 2.
36
References
[1] P. Ligrani, "Heat Transfer Augmentation Technologies for Internal Cooling of Turbine
Components of Gas Turbine Engines," International Journal of Rotating Machinery, pp. 138-
169, 2013.
[2] M. E. Taslim and G. J. Korotky, "Low-Aspect-Ratio Rib Heat Transfer Coefficient
Measurements in a Square Channel," Journal of Turbomachinery, vol. 120, pp. 831-838,
1998.
[3] T. Arts, G. Rau, M. Cakan, J. Vialonga, D. Fernandez, F. Tarnowski and E. Laroche,
"Experimental and numerical investigation on flow and heat transfer in large-scale, turbine
cooling, representative, rib-roughened channels," Journal of Power and Energy, vol. 211,
pp. 263-272, 1997.
[4] G. J. Korotky and M. E. Taslim, "Rib Heat Trasfer Coefficient Measurements in a Rib-
Roughened Square Passage," Journal of Turbomachinery, vol. 120, pp. 376-385, 1998.
[5] A. Gupta, V. SriHarsha, S. Prabhu and R. Vedula, "Local heat transfer distribution in a square
channel with 90⁰ continuous, 90⁰ saw tooth profiled and 60⁰ broken ribs," Experimental
Thermal and Fluid Science, vol. 32, pp. 997-1010, 2008.
[6] M. E. Taslim and S. D. Spring, "Effects of Turbulator Profile and Spacing on Heat Transfer
and Friction in a Channel," Journal of Thermophysics and Heat Transfer, vol. 8, no. 3, pp.
555-562, 1994.
[7] X. Gao and B. Sunden, "Heat trasfer and pressure drop measurements in rib-roughened
rectangular ducts," Experimental Thermal and Fluid Science, vol. 24, pp. 25-34, 2001.
[8] B. Lu and P.-X. Jiang, "Experimental and numerical investigation of convection heat transfer
in a rectangular channel with angled ribs," Experimental Thermal and Fluid Science, vol. 30,
p. 513–521, 2006.
[9] W. Peng, P.-X. Jiang, Y.-P. Wang and B.-Y. Wei, "Experimental and numerical investigation of
convection heat transfer in channels," Applied Thermal Engineering, vol. 31, pp. 2702-2708,
2011.
37
[10] P. Promvonge and C. Thianpong, "Thermal performance assessment of turbulent channel
flows over different shaped ribs," International Communications in Heat and Mass Transfer,
vol. 35, p. 1327–1334, 2008.
[11] R. Kamali and A. Binesh, "The importance of rib shape effects on the local heat transfer and
flow friction characteristics of square ducts with ribbed internal surfaces," International
Communications in Heat and Mass Transfer, vol. 35, p. 1032–1040, 2008.
[12] M. E. Taslim and H. Liu, "A Combined Numerical and Experimental Study of Heat Transfer in
a Roughened Square Channel with 45⁰ Ribs," International Journal of Rotating Machinery,
vol. 1, pp. 60-66, 2005.
[13] M. E. Taslim, T. Li and S. D. Spring, "Measurements of Heat Transfer Coefficients and
Friction Factors in Rib-Roughened Channels Simulating Leading-Edge Cavities of a Modern
Turbine Blade," Journal of turbomachinery, vol. 119, no. 3, pp. 601-609, 1997.
38
Appendix A: Square Ribs Sample input.dat
SQUARE RIBS
Pic# Pven Tven Tin1 Tin2 Tamb V1 A1 V2 A2 V3 A3 S.G. Pplen Pinlet Pamb Dthroat
1 36 64.6 69.8 69.8 71.6 14.57 0.334 14.81 0.334 14.70 0.348 1.000 0.0305 0.017 30.14 0.15
2 36 64.0 69.4 69.5 69.8 14.95 0.343 15.20 0.353 15.10 0.357 1.000 0.0305 0.017 30.14 0.15
3 36 64.1 69.4 69.5 71.3 15.34 0.352 15.59 0.362 15.50 0.367 1.000 0.0305 0.017 30.14 0.15
4 36 64.1 69.5 69.5 70.8 15.82 0.363 16.09 0.374 16.01 0.379 1.000 0.0305 0.017 30.14 0.15
5 36 64.0 69.4 69.2 70.6 16.40 0.376 16.68 0.388 16.60 0.393 1.000 0.0305 0.017 30.14 0.15
6 36 64.3 69.2 69.3 71.6 17.01 0.389 17.31 0.401 17.23 0.407 1.000 0.0305 0.017 30.12 0.15
7 36 64.3 69.4 69.4 70.2 17.43 0.400 17.90 0.415 17.83 0.421 1.000 0.0305 0.017 30.10 0.15
8 36 64.4 69.4 69.3 71.6 17.97 0.412 18.42 0.428 18.38 0.434 1.000 0.0305 0.017 30.10 0.15
9 36 64.2 69.4 69.4 71.3 18.51 0.424 18.97 0.440 18.91 0.447 1.000 0.0305 0.017 30.10 0.15
10 36 64.0 69.2 69.2 71.3 19.13 0.438 19.61 0.455 19.55 0.462 1.000 0.032 0.018 30.05 0.15
11 36 64.0 69.2 69.3 70.1 19.63 0.450 20.12 0.467 20.07 0.474 1.000 0.032 0.018 30.05 0.15
12 36 64.1 69.1 69.2 71.4 20.16 0.462 20.67 0.479 20.63 0.487 1.000 0.032 0.018 30.03 0.15
13 36 64.4 69.3 69.4 71.1 20.55 0.471 21.03 0.488 21.01 0.496 1.000 0.032 0.018 30.03 0.15
14 36 64.0 69.3 69.3 70.7 21.18 0.485 21.66 0.502 21.64 0.510 1.000 0.032 0.018 30.03 0.15
15 36 64.0 69.2 69.3 71.2 21.80 0.499 22.22 0.515 22.21 0.524 1.000 0.032 0.018 30.03 0.15
16 36 64.0 69.1 69.2 70.0 23.53 0.537 23.62 0.547 23.64 0.557 1.000 0.031 0.018 30.03 0.15
1 8 69.7 67.1 66.9 71.3 18.89 0.434 18.86 0.438 18.84 0.445 1.000 0.117 0.065 29.91 0.32
2 8 71.1 67.3 67.2 72.0 19.35 0.443 19.31 0.448 19.29 0.456 1.000 0.117 0.065 29.91 0.32
3 8 71.4 67.4 67.3 72.1 19.91 0.456 19.86 0.461 19.86 0.470 1.000 0.117 0.065 29.90 0.32
4 8 71.8 67.7 67.6 72.6 20.53 0.471 20.49 0.476 20.49 0.485 1.000 0.117 0.065 29.90 0.32
5 8 70.5 67.6 67.5 70.7 21.11 0.484 21.09 0.489 21.08 0.498 1.000 0.117 0.065 29.90 0.32
6 8 69.9 67.4 67.3 71.0 21.78 0.499 21.74 0.504 21.75 0.514 1.000 0.117 0.065 29.90 0.32
7 8 70.8 67.6 67.5 71.8 22.34 0.512 22.29 0.517 22.32 0.527 1.000 0.117 0.065 29.90 0.32
8 8 70.2 67.5 67.4 70.6 22.96 0.526 22.92 0.531 22.92 0.541 1.000 0.117 0.065 29.90 0.32
9 8 69.8 67.4 67.3 70.4 23.67 0.542 23.60 0.547 23.67 0.559 1.000 0.117 0.065 29.89 0.32
10 8 70.4 67.3 67.2 71.6 24.11 0.552 24.05 0.558 24.09 0.569 1.000 0.1155 0.066 29.89 0.32
11 8 70.6 67.4 67.3 71.1 24.67 0.565 24.62 0.571 24.67 0.582 1.000 0.1155 0.066 29.89 0.32
12 8 69.9 67.4 67.3 70.6 25.10 0.575 25.04 0.580 25.10 0.592 1.000 0.1155 0.066 29.89 0.32
13 8 70.5 67.3 67.2 71.4 25.84 0.591 25.74 0.597 25.81 0.609 1.000 0.1155 0.066 29.89 0.32
14 8 71.0 67.5 67.4 71.8 26.33 0.603 26.23 0.608 26.33 0.621 1.000 0.1155 0.066 29.89 0.32
15 8 70.2 67.5 67.4 70.4 27.04 0.618 26.94 0.624 27.06 0.638 1.000 0.1155 0.066 29.89 0.32
16 8 70.2 67.2 67.2 71.3 28.10 0.643 28.00 0.648 28.12 0.663 1.000 0.1155 0.066 29.89 0.32
17 8 71.1 67.4 67.3 72.2 29.00 0.663 28.90 0.669 29.06 0.685 1.000 0.119 0.066 29.89 0.32
1 19 71.1 66.6 66.6 72.4 21.06 0.483 20.98 0.487 21.00 0.497 1.000 0.2525 0.1395 29.88 0.32
2 19 70.5 66.5 66.5 71.3 21.61 0.495 21.51 0.499 21.55 0.509 1.000 0.2525 0.1395 29.89 0.32
39
3 19 71.4 66.7 66.7 72.5 22.21 0.509 22.12 0.513 22.16 0.524 1.000 0.2525 0.1395 29.90 0.32
4 19 71.1 66.8 66.8 71.4 22.89 0.525 22.80 0.529 22.85 0.540 1.000 0.2525 0.1395 29.90 0.32
5 19 70.3 66.7 66.7 70.7 23.60 0.541 23.50 0.545 23.57 0.557 1.000 0.2525 0.1395 29.90 0.32
6 19 70.8 66.6 66.5 72.1 24.40 0.559 24.31 0.564 24.36 0.576 1.000 0.2525 0.1395 29.90 0.32
7 19 71.3 66.6 66.6 71.9 25.10 0.575 24.99 0.580 25.07 0.592 1.000 0.2525 0.1395 29.90 0.32
8 19 70.4 66.4 66.5 70.6 25.87 0.593 25.74 0.597 25.85 0.610 1.000 0.2525 0.1395 29.90 0.32
9 19 69.9 66.4 66.4 71.0 26.65 0.610 26.55 0.615 26.65 0.629 1.000 0.2525 0.1395 29.90 0.32
10 19 71.1 66.6 66.6 72.0 27.26 0.624 27.15 0.629 27.28 0.644 1.000 0.250 0.138 29.92 0.32
11 19 70.6 66.7 66.6 70.9 27.87 0.638 27.74 0.643 27.88 0.657 1.000 0.250 0.138 29.92 0.32
12 19 70.8 66.5 66.5 71.8 28.62 0.654 28.49 0.660 28.64 0.675 1.000 0.250 0.138 29.92 0.32
13 19 71.5 66.6 66.7 72.1 29.27 0.670 29.09 0.674 29.25 0.690 1.000 0.250 0.138 29.92 0.32
14 19 70.5 66.6 66.5 70.9 29.85 0.683 29.67 0.688 29.87 0.704 1.000 0.250 0.138 29.92 0.32
15 19 70.2 66.6 66.5 71.3 30.59 0.700 30.44 0.705 30.62 0.722 1.000 0.250 0.138 29.94 0.32
16 19 69.9 66.2 66.1 70.5 31.37 0.717 31.19 0.722 31.40 0.740 1.000 0.250 0.138 29.94 0.32
17 19 69.4 66.0 66.1 69.6 32.42 0.741 32.20 0.745 32.44 0.764 1.000 0.252 0.1365 29.94 0.32
1 31 70.9 67.1 67.2 71.1 22.99 0.527 22.73 0.528 22.71 0.537 1.000 0.466 0.2585 29.92 0.32
2 31 71.9 67.0 67.0 72.2 23.82 0.546 23.56 0.547 23.55 0.556 1.000 0.466 0.2585 29.85 0.32
3 31 70.2 66.5 66.5 70.9 24.62 0.565 24.35 0.566 24.39 0.576 1.000 0.466 0.2585 29.85 0.32
4 31 71.2 66.5 66.4 71.8 25.26 0.579 24.97 0.580 25.01 0.591 1.000 0.466 0.2585 29.85 0.32
5 31 71.8 66.7 66.6 72.2 25.97 0.595 25.68 0.596 25.70 0.607 1.000 0.466 0.2585 29.85 0.32
6 31 71.2 66.4 66.4 71.5 26.82 0.614 26.49 0.615 26.56 0.628 1.000 0.466 0.2585 29.85 0.32
7 31 70.3 66.2 66.3 71.1 27.60 0.632 27.24 0.632 27.30 0.645 1.000 0.466 0.2585 29.85 0.32
8 31 71.3 66.6 66.5 72.1 28.34 0.649 28.02 0.650 28.09 0.663 1.000 0.466 0.2585 29.85 0.32
9 31 71.5 66.4 66.4 71.8 29.17 0.667 28.84 0.668 28.91 0.683 1.000 0.466 0.2585 29.85 0.32
10 31 70.7 66.1 66.0 71.5 29.77 0.681 29.41 0.682 29.49 0.696 1.000 0.462 0.258 29.85 0.32
11 31 71.7 66.2 66.2 72.3 30.76 0.704 30.46 0.706 30.60 0.721 1.000 0.462 0.258 29.85 0.32
12 31 71.6 66.2 66.3 71.8 31.84 0.720 31.31 0.726 31.43 0.742 1.000 0.462 0.258 29.83 0.32
13 31 70.5 65.7 65.7 71.6 32.40 0.741 32.21 0.746 32.30 0.762 1.000 0.462 0.258 29.83 0.32
14 31 71.6 65.8 65.8 72.2 33.04 0.754 32.82 0.761 33.03 0.779 1.000 0.462 0.258 29.83 0.32
15 31 71.2 65.9 65.9 71.8 33.82 0.774 33.66 0.780 33.83 0.797 1.000 0.462 0.258 29.83 0.32
16 31 70.0 65.6 65.5 70.9 34.69 0.793 34.49 0.799 34.67 0.816 1.000 0.462 0.258 29.79 0.32
17 31 71.1 65.6 65.5 71.9 35.58 0.812 35.36 0.818 35.56 0.837 1.000 0.462 0.258 29.78 0.32
18 31 71.4 65.8 65.7 71.8 36.47 0.833 36.24 0.838 36.47 0.859 1.000 0.462 0.258 29.77 0.32
19 31 70.3 65.4 65.5 70.5 37.39 0.853 37.11 0.858 37.38 0.880 1.000 0.462 0.258 29.77 0.32
20 31 70.9 65.5 65.5 71.8 38.61 0.881 38.21 0.884 38.55 0.907 1.000 0.463 0.2555 29.77 0.32
21 31 71.1 65.9 65.9 71.6 39.62 0.904 39.15 0.905 39.50 0.929 1.000 0.463 0.2555 29.77 0.32
22 31 70.1 65.4 65.3 70.6 41.08 0.936 40.61 0.939 40.91 0.961 1.000 0.463 0.2555 29.77 0.32
1 42 70.7 64.6 64.6 71.8 25.83 0.591 25.46 0.591 25.54 0.604 1.000 0.7385 0.4085 29.75 0.32
2 42 71.0 65.1 65.1 71.3 26.58 0.610 26.18 0.608 26.26 0.621 1.000 0.7385 0.4085 29.75 0.32
3 42 70.6 65.2 65.2 71.4 27.17 0.622 26.71 0.620 26.86 0.635 1.000 0.7385 0.4085 29.75 0.32
4 42 71.3 65.3 65.2 71.9 28.03 0.641 27.53 0.638 27.73 0.655 1.000 0.7385 0.4085 29.75 0.32
5 42 71.7 65.5 65.4 72.0 28.68 0.657 28.21 0.655 28.39 0.670 1.000 0.7385 0.4085 29.75 0.32
6 42 70.7 65.1 65.1 70.8 29.34 0.673 28.86 0.670 29.06 0.685 1.000 0.7385 0.4085 29.72 0.32
40
7 42 71.4 65.5 65.6 71.6 30.18 0.689 29.70 0.688 29.81 0.704 1.000 0.7385 0.4085 29.72 0.32
8 42 70.7 65.3 65.3 70.8 31.13 0.712 30.58 0.708 30.73 0.726 1.000 0.7385 0.4085 29.72 0.32
9 42 71.3 65.4 65.4 72.0 32.05 0.733 31.48 0.730 31.63 0.746 1.000 0.7385 0.4085 29.72 0.32
10 42 71.7 65.7 65.6 72.1 32.79 0.751 32.22 0.747 32.45 0.765 1.000 0.7265 0.4035 29.72 0.32
11 42 70.7 65.4 65.3 71.6 33.71 0.769 33.12 0.767 33.31 0.785 1.000 0.7265 0.4035 29.72 0.32
12 42 71.4 65.5 65.4 72.0 34.33 0.785 33.92 0.786 34.26 0.807 1.000 0.7265 0.4035 29.72 0.32
13 42 71.3 65.5 65.5 72.0 34.98 0.800 34.53 0.800 34.84 0.820 1.000 0.7265 0.4035 29.72 0.32
14 42 70.5 65.4 65.3 71.4 35.59 0.814 35.14 0.814 35.40 0.834 1.000 0.7265 0.4035 29.72 0.32
15 42 71.5 65.6 65.6 71.9 36.20 0.827 35.78 0.828 36.06 0.850 1.000 0.7265 0.4035 29.73 0.32
16 42 71.6 65.7 65.7 72.0 36.89 0.843 36.42 0.842 36.72 0.866 1.000 0.7265 0.4035 29.73 0.32
17 42 70.7 65.5 65.4 71.3 37.65 0.860 37.17 0.860 37.49 0.883 1.000 0.7265 0.4035 29.73 0.32
18 42 70.4 65.3 65.2 71.2 38.57 0.881 38.05 0.879 38.36 0.903 1.000 0.7265 0.4035 29.73 0.32
19 42 71.0 65.4 65.5 72.1 39.44 0.900 38.91 0.900 39.29 0.925 1.000 0.7265 0.4035 29.73 0.32
20 42 71.5 65.6 65.6 72.1 40.60 0.927 40.04 0.926 40.51 0.953 1.000 0.726 0.402 29.73 0.32
21 42 70.6 65.2 65.3 70.8 41.96 0.958 41.49 0.960 41.82 0.985 1.000 0.726 0.402 29.73 0.32
22 42 70.7 65.3 65.3 71.6 43.30 0.987 42.79 0.989 43.21 1.015 1.000 0.726 0.402 29.73 0.32
1 53 70.9 65.4 65.4 71.2 27.47 0.629 26.96 0.625 27.12 0.641 0.827 2.35 1.25 29.73 0.32
2 53 71.1 65.6 65.6 71.7 28.40 0.651 27.89 0.647 28.06 0.663 0.827 2.35 1.25 29.74 0.32
3 53 71.6 65.6 65.5 72.3 29.25 0.670 28.65 0.664 28.83 0.681 0.827 2.35 1.25 29.74 0.32
4 53 71.5 65.6 65.5 70.9 29.97 0.685 29.34 0.680 29.61 0.699 0.827 2.35 1.25 29.74 0.32
5 53 71.5 66.0 65.9 71.9 30.99 0.710 30.39 0.705 30.62 0.723 0.827 2.35 1.25 29.74 0.32
6 53 71.9 66.1 66.1 72.5 31.98 0.732 31.33 0.727 31.63 0.746 0.827 2.35 1.25 29.74 0.32
7 53 71.7 66.1 66.1 71.9 33.05 0.757 32.41 0.751 32.69 0.771 0.827 2.35 1.25 29.77 0.32
8 53 71.2 66.1 66.1 71.0 34.15 0.781 33.45 0.775 33.71 0.795 0.827 2.35 1.25 29.77 0.32
9 53 71.0 65.9 65.9 71.3 35.03 0.800 34.30 0.795 34.63 0.816 0.827 2.35 1.25 29.77 0.32
10 53 71.8 65.7 65.7 72.4 36.12 0.825 35.36 0.819 35.71 0.841 0.827 2.3 1.25 29.77 0.32
11 53 71.5 65.8 65.7 71.4 37.03 0.847 36.26 0.840 36.57 0.862 0.827 2.3 1.25 29.77 0.32
12 53 71.2 65.8 65.8 71.0 38.39 0.877 37.57 0.870 37.95 0.894 0.827 2.3 1.25 29.77 0.32
13 53 71.0 65.9 65.9 71.2 39.38 0.899 38.58 0.893 38.95 0.916 0.827 2.3 1.25 29.77 0.32
14 53 71.2 66.0 66.0 71.8 40.50 0.923 39.69 0.918 40.04 0.943 0.827 2.3 1.25 29.77 0.32
15 53 71.5 65.9 65.9 71.8 41.64 0.949 40.73 0.942 40.99 0.965 0.827 2.3 1.25 29.77 0.32
16 53 71.7 65.9 65.9 72.4 42.74 0.975 41.85 0.967 42.28 0.995 0.827 2.3 1.25 29.77 0.32
17 53 71.8 65.8 65.9 72.2 44.15 1.007 43.34 1.001 43.78 1.029 0.827 2.3 1.25 29.77 0.32
41
Appendix B: Ramped Ribs, Flow Direction 1 Sample input.dat
Pic# Pven Tven Tin1 Tin2 Tamb V1 A1 V2 A2 V3 A3 S. G. Pplen Pinlet Pamb Dthroat
1 36 64.8 69.3 69.3 71.9 21.23 0.163 13.72 0.323 21.17 0.166 1.000 0.0275 0.0135 29.83 0.15
2 36 64.8 69.6 69.5 71.9 21.94 0.169 14.17 0.334 21.87 0.171 1.000 0.0275 0.0135 29.83 0.15
3 36 64.5 69.5 69.4 70.7 22.53 0.174 14.55 0.343 22.48 0.176 1.000 0.0275 0.0135 29.83 0.15
4 36 64.4 69.4 69.4 70.7 23.15 0.179 14.94 0.352 23.08 0.181 1.000 0.0275 0.0135 29.83 0.15
5 36 64.5 69.5 69.4 72.0 23.81 0.183 15.38 0.362 23.74 0.186 1.000 0.0275 0.0135 29.83 0.15
6 36 64.8 69.5 69.5 72.5 24.43 0.189 15.78 0.372 24.38 0.191 1.000 0.0275 0.0135 29.83 0.15
7 36 64.7 69.6 69.5 71.6 25.08 0.194 16.20 0.382 25.02 0.196 1.000 0.0275 0.0135 29.83 0.15
8 36 64.9 69.6 69.5 70.5 25.69 0.198 16.60 0.391 25.64 0.201 1.000 0.0275 0.0135 29.83 0.15
9 36 64.3 69.3 69.3 70.1 26.30 0.202 16.99 0.400 26.25 0.205 1.000 0.0275 0.0135 29.83 0.15
10 36 64.6 69.4 69.3 69.9 26.81 0.207 17.30 0.408 26.72 0.209 1.000 0.0275 0.013 29.83 0.15
11 36 64.0 69.1 69.1 70.8 27.60 0.213 17.82 0.420 27.52 0.216 1.000 0.0275 0.013 29.83 0.15
12 36 64.3 69.3 69.2 71.7 28.21 0.217 18.21 0.429 28.14 0.220 1.000 0.0275 0.013 29.85 0.15
13 36 64.8 69.3 69.3 72.2 28.80 0.222 18.59 0.438 28.75 0.225 1.000 0.0275 0.013 29.85 0.15
14 36 64.8 69.6 69.5 72.4 29.46 0.227 19.02 0.448 29.38 0.230 1.000 0.0275 0.013 29.85 0.15
15 36 65.0 69.7 69.6 72.7 30.14 0.232 19.44 0.458 30.05 0.235 1.000 0.0275 0.013 29.85 0.15
16 36 65.0 69.7 69.6 72.2 30.69 0.236 19.82 0.467 30.64 0.240 1.000 0.0275 0.013 29.85 0.15
17 36 64.9 69.8 69.7 71.0 31.60 0.243 20.39 0.480 31.54 0.246 1.000 0.027 0.0125 29.85 0.15
1 8 64.0 68.3 68.3 72.1 24.99 0.192 16.11 0.379 24.93 0.195 1.000 0.097 0.0445 29.81 0.32
2 8 63.5 67.9 67.9 71.0 25.80 0.199 16.62 0.392 25.71 0.201 1.000 0.097 0.0445 29.81 0.32
3 8 63.9 68.0 68.0 72.3 26.70 0.206 17.20 0.406 26.63 0.209 1.000 0.097 0.0445 29.81 0.32
4 8 64.4 68.1 68.1 72.3 27.61 0.213 17.79 0.419 27.53 0.216 1.000 0.097 0.0445 29.81 0.32
5 8 63.6 67.9 67.9 71.0 28.33 0.218 18.25 0.430 28.24 0.221 1.000 0.097 0.0445 29.81 0.32
6 8 63.3 67.8 67.8 71.2 28.90 0.223 18.63 0.439 28.83 0.226 1.000 0.097 0.0445 29.81 0.32
7 8 63.8 67.9 67.9 72.0 29.77 0.230 19.19 0.452 29.70 0.233 1.000 0.097 0.0445 29.81 0.32
8 8 63.5 67.9 67.9 71.3 30.52 0.235 19.68 0.464 30.44 0.238 1.000 0.097 0.0445 29.81 0.32
9 8 63.4 67.8 67.8 70.7 31.38 0.242 20.21 0.477 31.29 0.245 1.000 0.097 0.0445 29.81 0.32
10 8 63.8 67.7 67.8 71.9 32.45 0.250 20.90 0.492 32.37 0.253 1.000 0.097 0.0445 29.81 0.32
11 8 63.4 67.8 67.8 70.9 33.24 0.256 21.42 0.505 33.17 0.260 1.000 0.097 0.0445 29.82 0.32
12 8 63.6 67.7 67.7 70.3 34.06 0.261 21.93 0.516 33.96 0.266 1.000 0.097 0.0445 29.82 0.32
13 8 63.5 67.6 67.6 70.0 34.90 0.269 27.50 0.530 34.86 0.273 1.000 0.097 0.0445 29.82 0.32
14 8 63.5 67.6 67.6 70.1 35.74 0.275 23.03 0.542 35.69 0.279 1.000 0.097 0.0445 29.82 0.32
15 8 63.4 67.5 67.4 69.8 36.58 0.282 23.58 0.555 36.55 0.286 1.000 0.097 0.0445 29.82 0.32
16 8 63.3 67.3 67.3 70.3 37.54 0.288 24.17 0.569 37.60 0.294 1.000 0.097 0.0445 29.82 0.32
17 8 63.4 67.4 67.4 71.2 38.41 0.296 24.73 0.582 38.32 0.300 1.000 0.097 0.0445 29.82 0.32
18 8 63.7 67.7 67.6 72.1 39.02 0.301 25.12 0.592 38.99 0.3050 1.000 0.097 0.0445 29.82 0.32
19 8 63.6 67.6 67.6 72.0 39.92 0.307 25.70 0.604 39.85 0.3110 1.000 0.0965 0.0445 29.82 0.32
1 19 63.7 67.1 67.1 71.2 26.29 0.202 16.83 0.397 25.99 0.203 1.000 0.209 0.0935 29.81 0.32
2 19 64.0 67.2 67.2 72.6 27.32 0.211 17.61 0.415 27.21 0.213 1.000 0.209 0.0935 29.81 0.32
3 19 64.0 67.1 67.1 70.9 28.25 0.218 18.22 0.430 28.12 0.220 1.000 0.209 0.0935 29.81 0.32
4 19 64.1 67.0 67.0 71.7 29.41 0.227 18.96 0.447 29.28 0.230 1.000 0.209 0.0935 29.81 0.32
5 19 64.4 67.3 67.3 72.7 30.31 0.234 19.53 0.460 30.19 0.236 1.000 0.209 0.0935 29.81 0.32
6 19 64.3 67.2 67.2 71.5 31.23 0.241 20.14 0.475 31.12 0.244 1.000 0.209 0.0935 29.81 0.32
42
7 19 64.2 67.1 67.2 70.6 32.23 0.248 20.76 0.489 32.10 0.251 1.000 0.209 0.0935 29.81 0.32
8 19 64.2 67.0 67.0 70.4 32.96 0.254 21.26 0.501 32.89 0.257 1.000 0.209 0.0935 29.81 0.32
9 19 64.1 66.9 66.9 69.9 34.10 0.263 22.00 0.518 34.03 0.266 1.000 0.209 0.0935 29.81 0.32
10 19 64.4 66.9 66.8 69.8 35.22 0.272 27.70 0.534 35.12 0.275 1.000 0.2105 0.0935 29.81 0.32
11 19 64.0 66.8 66.7 70.8 36.31 0.279 23.39 0.551 36.21 0.283 1.000 0.2105 0.0935 29.81 0.32
12 19 65.1 67.0 67.0 71.9 37.45 0.289 24.13 0.569 37.38 0.292 1.000 0.2105 0.0935 29.81 0.32
13 19 64.7 67.3 67.3 72.3 38.63 0.298 24.87 0.585 38.51 0.301 1.000 0.2105 0.0935 29.81 0.32
14 19 64.6 67.3 67.4 72.5 39.47 0.303 25.42 0.598 39.38 0.308 1.000 0.2105 0.0935 29.81 0.32
15 19 64.5 67.4 67.4 71.6 40.57 0.312 26.09 0.614 40.47 0.317 1.000 0.2105 0.0935 29.81 0.32
16 19 64.3 67.2 67.2 70.5 41.63 0.320 26.78 0.630 41.55 0.325 1.000 0.2105 0.0935 29.81 0.32
17 19 64.4 67.0 67.0 70.0 42.68 0.329 27.49 0.647 42.63 0.333 1.000 0.2105 0.0935 29.81 0.32
18 19 64.2 66.9 66.9 70.0 43.71 0.336 28.12 0.661 43.65 0.341 1.000 0.2105 0.0935 29.80 0.32
19 19 64.2 66.8 66.8 69.7 44.53 0.343 28.67 0.674 44.44 0.347 1.000 0.2105 0.0935 29.80 0.32
20 19 64.0 66.7 66.7 69.5 45.59 0.351 29.32 0.690 45.57 0.356 1.000 0.210 0.0935 29.80 0.32
1 31 71.3 67.7 67.8 71.7 26.96 0.208 17.37 0.410 26.92 0.210 1.000 0.372 0.1605 29.79 0.32
2 31 71.9 68.0 68.0 71.7 28.14 0.217 18.12 0.428 28.05 0.220 1.000 0.372 0.1605 29.79 0.32
3 31 71.2 67.7 67.7 71.5 29.03 0.224 18.72 0.442 29.04 0.227 1.000 0.372 0.1605 29.79 0.32
4 31 71.8 68.0 67.9 72.2 30.35 0.233 19.54 0.460 30.28 0.237 1.000 0.372 0.1605 29.79 0.32
5 31 72.0 67.6 67.7 72.2 31.43 0.242 20.23 0.477 31.37 0.246 1.000 0.372 0.1605 29.79 0.32
6 31 71.2 67.5 67.5 70.9 32.56 0.251 20.96 0.494 32.48 0.254 1.000 0.372 0.1605 29.79 0.32
7 31 71.2 67.6 67.7 71.5 33.84 0.261 21.79 0.513 33.75 0.264 1.000 0.372 0.1605 29.79 0.32
8 31 71.8 67.8 67.8 72.1 34.75 0.268 22.38 0.527 34.68 0.272 1.000 0.372 0.1605 29.84 0.32
9 31 71.7 67.9 67.9 71.8 35.81 0.275 23.07 0.543 35.78 0.280 1.000 0.372 0.1605 29.84 0.32
10 31 71.0 67.8 67.9 71.1 36.93 0.284 23.78 0.560 36.85 0.288 1.000 0.3725 0.161 29.84 0.32
11 31 71.8 67.9 67.9 72.2 38.02 0.293 24.51 0.577 38.01 0.297 1.000 0.3725 0.161 29.84 0.32
12 31 71.6 67.9 68.0 71.5 39.28 0.303 25.30 0.596 39.24 0.307 1.000 0.3725 0.161 29.84 0.32
13 31 71.0 67.8 67.8 71.2 40.68 0.312 26.18 0.616 40.67 0.318 1.000 0.3725 0.161 29.84 0.32
14 31 71.7 68.0 68.0 72.1 41.83 0.322 26.93 0.634 41.78 0.326 1.000 0.3725 0.161 29.84 0.32
15 31 71.8 68.0 68.0 71.9 43.09 0.332 27.76 0.653 43.09 0.337 1.000 0.3725 0.161 29.84 0.32
16 31 71.4 67.9 67.9 71.6 44.31 0.341 28.50 0.670 44.28 0.346 1.000 0.3725 0.161 29.84 0.32
17 31 71.6 67.8 67.9 71.3 45.52 0.349 29.27 0.688 45.44 0.355 1.000 0.3725 0.161 29.87 0.32
18 31 71.1 67.6 67.7 71.6 46.62 0.358 29.98 0.705 46.53 0.363 1.000 0.3725 0.161 29.87 0.32
19 31 71.9 68.0 68.0 72.5 47.90 0.368 30.78 0.724 47.68 0.374 1.000 0.3725 0.161 29.87 0.32
20 31 71.4 67.7 67.7 71.2 49.02 0.377 31.52 0.741 49.03 0.382 1.000 0.372 0.163 29.87 0.32
1 42 71.8 66.0 66.0 71.8 27.73 0.213 17.79 0.419 27.66 0.216 1.000 0.594 0.2545 29.68 0.32
2 42 71.4 66.2 66.2 72.0 29.12 0.225 18.71 0.441 29.08 0.228 1.000 0.594 0.2545 29.68 0.32
3 42 71.6 66.1 66.1 72.0 30.66 0.236 19.71 0.464 30.62 0.240 1.000 0.594 0.2545 29.68 0.32
4 42 71.8 66.4 66.5 71.5 32.18 0.248 20.68 0.487 32.14 0.251 1.000 0.594 0.2545 29.68 0.32
5 42 71.5 66.3 66.3 71.8 33.63 0.260 21.63 0.510 33.63 0.263 1.000 0.594 0.2545 29.69 0.32
6 42 71.8 66.3 66.3 72.2 35.25 0.272 22.67 0.534 35.24 0.276 1.000 0.594 0.2545 29.69 0.32
7 42 71.5 66.4 66.4 71.2 36.53 0.281 23.47 0.553 36.49 0.285 1.000 0.594 0.2545 29.69 0.32
8 42 71.8 66.8 66.8 72.0 38.05 0.293 24.47 0.576 38.08 0.298 1.000 0.594 0.2545 29.69 0.32
9 42 72.0 67.2 67.2 72.1 39.49 0.304 25.38 0.598 39.48 0.308 1.000 0.594 0.2545 29.69 0.32
10 42 71.2 66.7 66.7 71.8 40.84 0.315 26.26 0.618 40.84 0.319 1.000 0.5725 0.2455 29.69 0.32
11 42 71.5 66.1 66.1 71.1 42.48 0.327 27.27 0.642 42.43 0.332 1.000 0.5725 0.2455 29.69 0.32
12 42 71.5 66.2 66.2 71.7 43.28 0.338 28.13 0.662 43.80 0.342 1.000 0.5725 0.2455 29.69 0.32
13 42 72.0 66.4 66.4 72.3 45.20 0.348 29.05 0.683 45.10 0.352 1.000 0.5725 0.2455 29.69 0.32
14 42 71.5 66.4 66.4 71.3 46.63 0.359 29.94 0.704 46.55 0.364 1.000 0.5725 0.2455 29.71 0.32
15 42 71.6 66.5 66.5 71.9 48.32 0.372 31.03 0.730 48.29 0.377 1.000 0.5725 0.2455 29.71 0.32
16 42 72.0 66.4 66.4 72.4 49.60 0.382 31.86 0.749 49.54 0.387 1.000 0.5725 0.2455 29.71 0.32
43
17 42 71.1 66.3 66.3 71.5 50.81 0.391 32.67 0.767 50.82 0.396 1.000 0.5725 0.2455 29.71 0.32
18 42 72.0 66.5 66.5 72.1 52.21 0.401 33.52 0.788 52.19 0.407 1.000 0.5725 0.2455 29.71 0.32
19 42 71.2 66.6 66.7 71.2 53.28 0.410 34.18 0.803 53.36 0.416 1.000 0.5735 0.2465 29.71 0.32
1 53 73.0 66.1 66.2 73.5 30.14 0.231 19.43 0.458 30.23 0.236 1.000 0.8065 0.3445 29.69 0.32
2 53 72.0 65.5 65.5 72.3 31.76 0.245 20.48 0.483 31.86 0.249 1.000 0.8065 0.3445 29.68 0.32
3 53 72.2 65.3 65.3 72.3 33.13 0.256 21.35 0.503 33.21 0.260 1.000 0.8065 0.3445 29.68 0.32
4 53 71.8 65.3 65.2 71.0 34.67 0.267 22.33 0.526 34.74 0.272 1.000 0.8065 0.3445 29.68 0.32
5 53 71.7 65.3 65.3 71.8 36.27 0.280 23.34 0.550 36.18 0.283 1.000 0.8065 0.3445 29.68 0.32
6 53 72.0 65.3 65.2 72.0 37.71 0.291 24.35 0.573 37.72 0.295 1.000 0.8065 0.3445 29.68 0.32
7 53 71.7 65.2 65.2 71.2 39.30 0.303 25.28 0.595 39.21 0.306 1.000 0.8065 0.3445 29.68 0.32
8 53 71.6 65.2 65.2 71.7 40.82 0.315 26.31 0.619 40.79 0.319 1.000 0.8065 0.3445 29.68 0.32
9 53 71.2 65.2 65.2 71.4 42.21 0.324 27.16 0.639 42.14 0.329 1.000 0.8065 0.3445 29.68 0.32
10 53 71.8 65.5 65.5 71.9 43.30 0.333 27.84 0.655 43.26 0.337 1.000 0.808 0.3445 29.68 0.32
11 53 71.7 65.5 65.6 72.2 45.09 0.347 28.99 0.682 45.03 0.351 1.000 0.808 0.3445 29.68 0.32
12 53 71.1 65.4 65.4 71.3 46.59 0.359 29.94 0.704 46.46 0.362 1.000 0.808 0.3445 29.68 0.32
13 53 71.7 65.5 65.5 72.2 47.82 0.369 30.78 0.724 47.86 0.374 1.000 0.808 0.3445 29.68 0.32
14 53 71.3 65.5 65.5 70.8 49.60 0.381 31.53 0.743 49.14 0.384 1.000 0.808 0.3445 29.68 0.32
15 53 71.6 65.6 65.6 72.1 50.57 0.389 32.37 0.761 50.54 0.394 1.000 0.808 0.3445 29.68 0.32
16 53 71.7 65.8 65.8 71.2 51.98 0.400 33.39 0.784 51.87 0.405 1.000 0.808 0.3445 29.68 0.32
17 53 71.7 65.7 65.8 71.8 53.28 0.409 34.14 0.802 53.26 0.415 1.000 0.808 0.3445 29.68 0.32
18 53 71.6 65.7 65.7 71.1 54.65 0.420 35.04 0.8240 54.61 0.426 1.000 0.808 0.3445 29.68 0.32
19 53 71.8 65.9 65.9 72.0 56.26 0.433 36.09 0.8480 56.36 0.440 1.000 0.808 0.3445 29.68 0.32
20 53 71.6 65.8 65.8 71.0 57.89 0.444 37.11 0.8700 57.91 0.451 1.000 0.809 0.3455 29.68 0.32
44
Appendix C: Ramped Ribs, Flow Direction 2 Sample input.dat
Pic# Pven Tven Tin1 Tin2 Tamb V1 A1 V2 A2 V3 A3 S. G. Pplen Pinlet Pamb Dthroat
1 36 70.6 69.5 69.5 70.5 19.86 0.153 12.84 0.303 19.60 0.154 1.000 0.0275 0.012 29.94 0.15
2 36 70.0 69.2 69.3 70.4 20.43 0.158 13.20 0.312 20.17 0.159 1.000 0.0275 0.012 29.94 0.15
3 36 70.4 69.3 69.3 71.2 21.07 0.163 13.62 0.322 20.81 0.164 1.000 0.0275 0.012 29.94 0.15
4 36 71.3 69.3 69.4 71.5 21.68 0.168 14.01 0.331 21.41 0.168 1.000 0.0275 0.012 29.94 0.15
5 36 71.4 69.4 69.5 71.4 22.27 0.172 14.39 0.339 21.97 0.173 1.000 0.0275 0.012 29.94 0.15
6 36 70.6 69.4 69.4 70.4 22.91 0.177 14.71 0.347 22.58 0.177 1.000 0.0275 0.012 29.94 0.15
7 36 70.2 69.3 69.3 70.6 23.05 0.182 15.17 0.358 23.30 0.183 1.000 0.0275 0.012 29.92 0.15
8 36 70.4 69.3 69.3 71.1 24.14 0.186 15.52 0.367 23.86 0.187 1.000 0.0275 0.012 29.92 0.15
9 36 71.2 69.4 69.4 71.5 24.83 0.192 15.99 0.377 24.55 0.193 1.000 0.0275 0.012 29.92 0.15
10 36 71.6 69.4 69.4 71.5 25.41 0.196 16.35 0.386 25.13 0.197 1.000 0.027 0.012 29.92 0.15
11 36 70.5 69.4 69.4 70.4 26.07 0.201 16.76 0.395 25.77 0.202 1.000 0.027 0.012 29.92 0.15
12 36 70.1 69.3 69.3 70.7 26.74 0.207 17.20 0.406 26.44 0.207 1.000 0.027 0.012 29.92 0.15
13 36 70.7 69.3 69.4 71.3 27.81 0.215 17.89 0.422 27.52 0.216 1.000 0.027 0.012 29.92 0.15
14 36 71.5 69.5 69.5 71.6 28.61 0.221 18.40 0.434 28.27 0.222 1.000 0.027 0.012 29.92 0.15
15 36 71.2 69.5 69.6 71.2 29.24 0.224 18.81 0.443 28.90 0.226 1.000 0.027 0.012 29.92 0.15
16 36 70.5 69.5 69.5 70.4 29.81 0.230 19.19 0.452 29.74 0.231 1.000 0.027 0.012 29.92 0.15
17 36 70.2 69.4 69.4 70.9 30.42 0.235 19.61 0.462 30.10 0.236 1.000 0.027 0.012 29.92 0.15
18 36 70.9 69.4 69.5 71.4 31.23 0.241 20.11 0.474 30.88 0.242 1.000 0.027 0.012 29.92 0.15
19 36 71.5 69.5 69.5 71.6 31.98 0.247 20.56 0.484 31.61 0.248 1.000 0.027 0.013 29.92 0.15
1 8 71.4 68.0 68.0 71.7 22.96 0.176 14.79 0.349 22.71 0.178 1.000 0.0975 0.0425 29.97 0.32
2 8 71.1 68.0 68.0 71.1 23.58 0.182 15.20 0.359 23.28 0.183 1.000 0.0975 0.0425 29.97 0.32
3 8 70.6 67.8 67.9 71.2 24.21 0.187 15.60 0.368 23.92 0.188 1.000 0.0975 0.0425 29.97 0.32
4 8 71.1 67.8 67.8 71.5 25.01 0.193 16.12 0.380 24.70 0.194 1.000 0.0975 0.0425 29.97 0.32
5 8 71.7 68.0 68.0 71.7 25.82 0.199 16.68 0.393 25.51 0.200 1.000 0.0975 0.0425 29.97 0.32
6 8 71.0 68.0 67.9 70.8 26.64 0.206 17.23 0.406 26.32 0.207 1.000 0.0975 0.0425 29.97 0.32
7 8 70.4 67.9 67.9 70.5 27.28 0.211 17.63 0.416 26.94 0.212 1.000 0.0975 0.0425 29.97 0.32
8 8 70.6 67.7 67.7 71.3 28.16 0.218 18.20 0.430 27.86 0.219 1.000 0.0975 0.0425 29.97 0.32
9 8 71.4 67.8 67.9 71.6 28.92 0.223 18.68 0.440 28.55 0.224 1.000 0.0975 0.0425 29.97 0.32
10 8 71.4 67.9 67.9 71.6 29.73 0.229 19.20 0.453 29.37 0.230 1.000 0.0975 0.045 29.97 0.32
11 8 70.5 67.9 67.9 70.5 30.43 0.235 19.66 0.464 30.10 0.236 1.000 0.0975 0.045 29.97 0.32
12 8 70.4 67.9 67.9 71.2 31.35 0.242 20.25 0.477 30.98 0.243 1.000 0.0975 0.045 29.95 0.32
13 8 71.2 67.9 67.9 71.5 32.32 0.249 20.86 0.492 31.93 0.250 1.000 0.0975 0.045 29.95 0.32
14 8 71.1 67.8 67.9 71.2 33.00 0.254 21.30 0.502 32.62 0.256 1.000 0.0975 0.045 29.95 0.32
15 8 70.5 67.9 67.9 70.5 33.67 0.260 21.75 0.513 33.31 0.261 1.000 0.0975 0.045 29.95 0.32
16 8 70.2 67.8 67.9 70.9 34.51 0.266 22.29 0.525 34.15 0.268 1.000 0.0975 0.045 29.95 0.32
17 8 70.8 67.7 67.8 71.4 35.45 0.273 22.88 0.539 35.06 0.275 1.000 0.0975 0.045 29.95 0.32
18 8 71.5 67.9 68.0 71.7 35.91 0.276 23.21 0.546 35.56 0.278 1.000 0.0975 0.045 29.95 0.32
19 8 70.8 67.8 67.9 71.0 37.01 0.285 23.89 0.563 36.65 0.287 1.000 0.0975 0.045 29.95 0.32
20 8 70.2 67.9 67.9 71.0 37.83 0.291 24.39 0.574 37.43 0.293 1.000 0.097 0.044 29.95 0.32
1 19 71.8 67.8 67.8 71.8 24.17 0.186 15.63 0.369 23.69 0.188 1.000 0.21 0.089 29.86 0.32
2 19 70.5 67.6 67.5 71.1 25.35 0.196 16.26 0.384 25.08 0.197 1.000 0.21 0.089 29.86 0.32
3 19 71.3 67.5 67.5 71.5 26.09 0.202 16.77 0.396 25.83 0.203 1.000 0.21 0.089 29.86 0.32
4 19 71.7 67.6 67.5 71.7 26.90 0.207 17.30 0.408 26.65 0.209 1.000 0.21 0.089 29.86 0.32
5 19 70.9 67.5 67.5 70.6 27.84 0.215 17.88 0.422 27.52 0.216 1.000 0.21 0.089 29.86 0.32
6 19 70.5 67.4 67.4 70.7 28.98 0.224 18.63 0.439 28.68 0.225 1.000 0.21 0.089 29.86 0.32
7 19 70.9 67.3 67.3 71.3 30.11 0.232 19.35 0.456 29.82 0.234 1.000 0.21 0.089 29.86 0.32
8 19 71.5 67.4 67.4 71.6 30.97 0.239 19.90 0.470 30.71 0.253 1.000 0.21 0.089 29.86 0.32
9 19 71.7 67.5 67.5 71.7 31.89 0.246 20.50 0.483 31.56 0.248 1.000 0.21 0.089 29.87 0.32
45
10 19 71.0 67.5 67.5 71.0 32.80 0.253 21.09 0.497 32.52 0.255 1.000 0.21 0.091 29.87 0.32
11 19 70.5 67.3 67.3 71.3 33.88 0.261 21.78 0.513 33.54 0.263 1.000 0.21 0.091 29.87 0.32
12 19 71.4 67.5 67.5 71.7 34.85 0.269 22.38 0.527 34.50 0.270 1.000 0.21 0.091 29.87 0.32
13 19 71.7 67.6 67.5 71.6 35.89 0.276 23.07 0.543 35.58 0.279 1.000 0.21 0.091 29.87 0.32
14 19 70.5 67.3 67.3 70.7 36.68 0.283 23.59 0.556 36.38 0.285 1.000 0.21 0.091 29.87 0.32
15 19 71.6 67.5 67.5 71.5 37.64 0.290 24.16 0.569 37.29 0.292 1.000 0.21 0.091 29.87 0.32
16 19 71.4 67.5 67.5 71.4 38.38 0.296 24.67 0.581 38.11 0.298 1.000 0.21 0.091 29.87 0.32
17 19 70.6 67.4 67.4 70.6 39.49 0.304 25.35 0.597 39.10 0.306 1.000 0.21 0.091 29.87 0.32
18 19 70.2 67.3 67.3 71.1 40.16 0.309 25.79 0.607 39.85 0.312 1.000 0.21 0.091 29.87 0.32
19 19 71.5 67.5 67.5 71.8 41.27 0.318 26.54 0.625 40.98 0.320 1.000 0.21 0.091 29.87 0.32
20 19 71.5 67.5 67.5 71.5 42.38 0.326 27.22 0.640 47.00 0.329 1.000 0.209 0.0905 29.87 0.32
1 31 70.8 67.7 67.7 71.2 24.82 0.191 16.03 0.378 24.55 0.192 1.000 0.3785 0.1655 29.78 0.32
2 31 71.2 67.9 67.9 70.8 26.04 0.201 16.80 0.397 25.75 0.202 1.000 0.3785 0.1655 29.78 0.32
3 31 70.5 67.7 67.6 70.3 27.26 0.210 17.61 0.416 26.97 0.212 1.000 0.3785 0.1655 29.78 0.32
4 31 70.4 67.6 67.6 71.1 28.20 0.217 18.23 0.430 27.94 0.219 1.000 0.3785 0.1655 29.78 0.32
5 31 71.2 67.6 67.7 71.5 29.11 0.225 18.83 0.444 28.83 0.226 1.000 0.3785 0.1655 29.78 0.32
6 31 71.0 67.7 67.7 71.3 30.39 0.235 19.64 0.463 30.09 0.236 1.000 0.3785 0.1655 29.78 0.32
7 31 70.8 67.6 67.6 70.8 31.57 0.244 20.42 0.482 31.25 0.245 1.000 0.3785 0.1655 29.78 0.32
8 31 70.5 67.6 67.6 70.7 32.84 0.253 21.22 0.500 32.51 0.255 1.000 0.3785 0.1655 29.78 0.32
9 31 70.9 67.8 67.8 71.4 34.06 0.262 22.02 0.519 33.74 0.264 1.000 0.3785 0.1655 29.78 0.32
10 31 71.5 67.8 67.9 71.7 35.21 0.272 22.75 0.536 34.86 0.272 1.000 0.3795 0.1645 29.78 0.32
11 31 71.4 67.9 68.0 71.5 36.48 0.282 23.58 0.556 36.14 0.283 1.000 0.3795 0.1645 29.78 0.32
12 31 70.9 68.1 68.0 70.6 37.68 0.291 24.34 0.574 37.30 0.292 1.000 0.3795 0.1645 29.78 0.32
13 31 70.7 67.7 67.7 71.3 38.88 0.299 25.10 0.592 38.54 0.302 1.000 0.3795 0.1645 29.78 0.32
14 31 71.4 67.6 67.6 71.7 40.22 0.310 25.97 0.612 39.83 0.312 1.000 0.3795 0.1645 29.78 0.32
15 31 71.7 67.6 67.6 71.5 41.09 0.317 26.56 0.625 40.65 0.319 1.000 0.3795 0.1645 29.78 0.32
16 31 71.4 67.8 67.8 70.8 42.20 0.325 27.17 0.640 41.79 0.327 1.000 0.3795 0.1645 29.78 0.32
17 31 71.3 67.7 67.7 71.3 43.25 0.333 27.84 0.655 42.85 0.335 1.000 0.3795 0.1645 29.78 0.32
18 31 71.8 67.7 67.8 71.7 44.58 0.343 28.68 0.675 44.15 0.345 1.000 0.3795 0.1645 29.78 0.32
19 31 71.8 68.0 68.0 71.6 45.62 0.351 29.38 0.691 45.24 0.354 1.000 0.3795 0.1645 29.78 0.32
20 31 71.0 67.8 67.9 70.6 46.36 0.357 29.83 0.702 45.95 0.359 1.000 0.3785 0.168 29.78 0.32
1 42 71.4 66.1 66.1 71.2 26.57 0.204 17.19 0.405 26.22 0.206 1.000 0.5755 0.2485 29.77 0.32
2 42 71.3 66.1 66.1 71.1 27.91 0.215 18.05 0.426 27.54 0.216 1.000 0.5755 0.2485 29.77 0.32
3 42 70.6 66.1 66.1 71.0 29.15 0.225 18.83 0.445 28.78 0.226 1.000 0.5755 0.2485 29.77 0.32
4 42 71.6 66.3 66.3 71.6 30.15 0.233 19.50 0.460 29.81 0.234 1.000 0.5755 0.2485 29.77 0.32
5 42 71.7 66.4 66.4 71.6 31.30 0.242 20.24 0.478 30.93 0.243 1.000 0.5755 0.2485 29.77 0.32
6 42 71.2 66.4 66.4 70.8 32.55 0.250 21.01 0.495 32.18 0.252 1.000 0.5755 0.2485 29.77 0.32
7 42 70.9 66.3 66.3 71.3 33.51 0.259 21.67 0.511 33.13 0.260 1.000 0.5755 0.2485 29.77 0.32
8 42 71.5 66.4 66.4 71.7 34.47 0.266 22.26 0.525 34.11 0.268 1.000 0.5755 0.2485 29.77 0.32
9 42 71.1 66.4 66.4 70.9 35.74 0.275 23.08 0.544 35.34 0.277 1.000 0.5755 0.2485 29.77 0.32
10 42 70.7 66.2 66.2 70.6 36.91 0.284 23.87 0.562 36.57 0.287 1.000 0.5745 0.2505 29.77 0.32
11 42 70.9 66.3 66.3 71.4 37.92 0.292 24.50 0.577 37.51 0.294 1.000 0.5745 0.2505 29.77 0.32
12 42 71.6 66.3 66.2 71.7 39.16 0.302 25.30 0.596 38.75 0.304 1.000 0.5745 0.2505 29.77 0.32
13 42 71.1 66.3 66.3 71.0 40.34 0.311 26.09 0.614 39.96 0.313 1.000 0.5745 0.2505 29.77 0.32
14 42 71.3 66.5 66.5 71.0 41.29 0.317 26.67 0.628 40.91 0.320 1.000 0.5745 0.2505 29.77 0.32
15 42 70.7 66.6 66.5 70.4 42.53 0.328 27.48 0.647 42.18 0.330 1.000 0.5745 0.2505 29.77 0.32
16 42 70.2 66.4 66.4 70.5 43.66 0.336 28.19 0.664 43.23 0.339 1.000 0.5745 0.2505 29.77 0.32
17 42 70.6 66.4 66.4 71.2 44.69 0.345 28.88 0.680 44.38 0.347 1.000 0.5745 0.2505 29.77 0.32
18 42 71.5 66.4 66.4 71.6 45.62 0.351 29.45 0.693 45.26 0.355 1.000 0.5745 0.2505 29.77 0.32
19 42 71.2 66.4 66.4 71.4 46.92 0.361 30.20 0.712 46.53 0.364 1.000 0.5745 0.2505 29.77 0.32
20 42 70.6 66.4 66.4 70.7 48.19 0.371 31.06 0.731 47.82 0.374 1.000 0.5745 0.2505 29.77 0.32
21 42 70.5 66.5 66.5 71.1 49.55 0.381 31.93 0.751 49.11 0.384 1.000 0.5745 0.2505 29.77 0.32
1 53 71.8 66.0 65.9 71.8 28.29 0.218 18.33 0.433 28.01 0.220 1.000 0.8065 0.345 29.80 0.32
2 53 70.8 65.8 65.8 71.3 29.63 0.229 19.19 0.453 29.34 0.230 1.000 0.8065 0.345 29.79 0.32
3 53 71.6 65.8 65.8 71.7 30.72 0.237 19.89 0.470 30.21 0.237 1.000 0.8065 0.345 29.79 0.32
4 53 71.1 65.8 65.7 71.2 32.01 0.247 20.73 0.489 31.48 0.247 1.000 0.8065 0.345 29.78 0.32
5 53 70.7 65.8 65.7 71.2 33.34 0.258 21.60 0.509 32.85 0.258 1.000 0.8065 0.345 29.77 0.32
46
6 53 71.4 66.0 66.0 71.7 34.50 0.266 22.34 0.527 34.02 0.267 1.000 0.8065 0.345 29.77 0.32
7 53 71.7 65.9 65.9 71.7 35.72 0.276 23.15 0.546 35.25 0.277 1.000 0.8065 0.345 29.77 0.32
8 53 71.7 66.0 65.9 71.3 37.03 0.286 23.96 0.565 36.54 0.287 1.000 0.8065 0.345 29.77 0.32
9 53 70.7 65.9 65.8 71.2 38.15 0.293 24.69 0.582 37.61 0.295 1.000 0.8065 0.345 29.77 0.32
10 53 71.1 65.9 65.9 71.8 39.29 0.303 25.42 0.599 38.75 0.304 1.000 0.8065 0.3465 29.77 0.32
11 53 71.4 66.0 65.9 71.6 40.65 0.314 26.33 0.620 40.11 0.314 1.000 0.8065 0.3465 29.76 0.32
12 53 70.8 65.9 65.9 71.1 42.03 0.323 27.20 0.640 41.44 0.325 1.000 0.8065 0.3465 29.75 0.32
13 53 71.5 66.1 66.0 71.7 43.30 0.334 28.04 0.661 42.77 0.335 1.000 0.8065 0.3465 29.75 0.32
14 53 71.3 66.1 66.1 71.3 44.59 0.344 28.86 0.680 44.09 0.345 1.000 0.8065 0.3465 29.75 0.32
15 53 70.8 66.0 66.0 71.4 45.93 0.354 29.77 0.701 45.44 0.356 1.000 0.8065 0.3465 29.75 0.32
16 53 71.5 66.1 66.0 71.8 47.33 0.364 30.64 0.721 46.72 0.366 1.000 0.8065 0.3465 29.73 0.32
17 53 71.5 66.3 66.3 71.5 48.55 0.374 31.34 0.738 47.99 0.376 1.000 0.8065 0.3465 29.72 0.32
18 53 70.7 66.2 66.2 71.2 49.92 0.384 32.23 0.758 49.31 0.386 1.000 0.8065 0.3465 29.72 0.32
19 53 71.1 66.2 66.2 72.0 51.03 0.393 32.96 0.775 50.46 0.395 1.000 0.8065 0.3465 29.72 0.32
20 53 71.6 66.2 66.2 71.4 52.37 0.403 33.88 0.797 51.85 0.406 1.000 0.8075 0.348 29.72 0.32
21 53 70.9 66.2 66.1 71.5 53.64 0.413 34.65 0.815 53.11 0.415 1.000 0.8075 0.348 29.70 0.32
47
Appendix D: Square Ribs Heat Transfer Data Reduction Code (FORTRAN)
C THIS PROGRAM WAS USED FOR SQUARE TEST SECTION WITH SQUARE RIBS
IN THE BASEMENT OF EGAN
C BUILDING. TEST SECTION WAS 36" LONG WITH 3 HEATERS
C CONTROL PANEL ARANGEMENT FOR ONE HEATED WALL CASE
C CHANNEL 1 Back Heater # 1
C CHANNEL 2 Back Heater # 2
C CHANNEL 3 Back Heater # 3
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*80 TITLE
REAL*8 Mv,Nut,Nus,Length
COMMON Dh,AR,Width,Length,Hlength,P,Distance,Rgas,Mv,
&Tin,Tamb,Pamb,Tliquid
F(A,P,T)=0.5215*A*P/SQRT(T)
Rgas=53.34
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
PI=4.*ATAN(1.E00)
FAC1=3.413 ! converts Watts to BTU/hr
gc=32.2 ! lbm.ft/(lbf.s^2)
C
C Rectangular Cross Sectional Area
C
height=2. ! inches
height=height/12. ! ft
width=2. ! inches
width=width/12. ! ft
P=2.*height+2.*width ! ft
Across=height*width ! ft^2
Dh=4.*Across/P ! ft
C AR : defined as top/side
AR=width/height
48
OPEN(UNIT=1,FILE='input.dat',STATUS='old')
OPEN(UNIT=2,FILE='fric-plot.out',STATUS='old')
OPEN(UNIT=3,FILE='uncertainties.out',STATUS='old')
OPEN(UNIT=7,FILE='output.dat',STATUS='old')
OPEN(UNIT=8,FILE='nu-picture.out',STATUS='old')
C
READ(1,*)NP,Pitch,NRibs,Ribh,alpha,Tliquid
WRITE(7,402)NP
402 FORMAT(/,20x,'A total of',I5,2x,'pictures were taken',/)
DPLength=NRibs*Pitch/12. ! ft
poe=Pitch/Ribh
eoDh=Ribh/(12*Dh)
C HEAT TRANSFER AREA
Hlength=11.0
Hlength=Hlength/12.
Length=3*Hlength ! Total heated length for radiation
losses
Hwidth=2.0
Hwidth=Hwidth/12.
Area=Hwidth*Hlength ! sq.ft
C
Distance=1.5*Hlength ! ft
DO I=1,10
READ(1,10)TITLE
WRITE(7,10)TITLE
WRITE(3,10)TITLE
enddo
10 FORMAT(A80,//)
WRITE(7,100)12*Height,12*Width,12*Dh,AR,Pitch,
&NRibs,Ribh,poe,eoDh,Alpha,12*DPLength,12*Hlength,
&12*Hwidth
100 FORMAT(/,
&3x,'Channel Height=',f6.2,' inches',/,
&3x,'Channel Width=',f6.2,' inches',/,
&3x,'Channel Hydraulic Diameter=',f8.3,' inches',/,
&3x,'Channel Aspect Ratio=',f7.3,/,
&3x,'Rib Pitch=',f7.3,' inches',/,
&3x,'No. of Ribs=',i2,/,
&3x,'Rib Height=',f7.3,' inches',/,
&3x,'Rib Pitch to Height=',f7.3,/,
&3x,'Rib Height to Channel Dh=',f7.3,/,
&3x,'Rib Angle to Flow direction=',f6.2,/,
&3x,'Rib-Roughened Langth=',f7.3,' inches',/,
49
&3x,'Heater Length=',f7.3,' inches',/,
&3x,'Heater Width=',f7.3,' inches',/)
WRITE(8,450)
450 FORMAT(' PHOTO RE NUT EF UNCER ',//)
DO 1 I=1,NP
READ(1,*)PHOTO,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,
&SG,Pplen,Pinlet,Pamb,Dthroat
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,101)PHOTO
101 FORMAT(/,' PHOTO #',f3.0)
WRITE(7,*)' '
WRITE(7,*)' '
WRITE(7,*)' Collected Data: V1,I1,V2,I2,V3,I3'
WRITE(7,*)' Pven,Tven,Tin1,Tin2,Tamb,Pplen,Pinlet,Pamb',
&'Dthroat'
WRITE(7,*)' '
WRITE(7,200)V1,A1,V2,A2,V3,A3,Pven,Tven,Tin1,Tin2,Tamb,
&Pplen,Pinlet,Pamb,Dthroat
Tin=0.5*(Tin1+Tin2)
Pamb=Pamb*Hgtopsi ! psi
IF(SG.EQ.1.)DeltaP=2*Pinlet*H2Otopsi
IF(SG.NE.1.)DeltaP=SG*Pinlet*H2Otopsi
! AIR MASS FLOW RATE FROM THE CRITICAL VENTURI
Athroat=PI*(Dthroat**2)/4.
Mv=F(Athroat,Pven+Pamb,T1+460)
! TOTAL HEAT ADDED TO THE AIR BY THE HEATERS FRON THE
! INLET TO THE POINT IN QUESTION
Q=V1*A1+0.5*V2*A2
Q=Q*FAC1
! HEAT FLUX, BTU/(sqft.Sec)
Flux=V2*A2*FAC1/(Area)
CALL COEFFICIENT(Q,Flux,Tm,Tback,hturb,Floss)
! FILM TEMPERATURE
TF=(Tback+Tm)/2.
! DENSITY AT FILM TEMPERATURE
50
RHO=((Pamb+0.5*DeltaP)*144)/(Rgas*(TF+460.))
! OTHER PROPERTIES AT FILM TEMPERATURE
TfR=TF+460.
CALL AIRPROP(TfR,GAMMA,CON,VIS,PR,CP)
VIS=VIS/3600
! REYNOLDS NUMBER
Re=4.*Mv/(P*VIS)
! SMOOTH CHANNEL NUSSELT NUMBER FROM DITTUS-BOELTER
CORRELATION
Nus=.023*(RE**.8)*(PR**.4)
! NUSSELT NUMBER
Nut=Hturb*Dh/Con
! ENHANCEMENT FACTOR = NUt/NUs
EF=Nut/Nus
! AVERAGE VELOCITY, Um, ft/Sec.
UM=MV/(Across*RHO)
! FRICTION FACTOR
FRIC=2.*gc*DeltaP*144*(Dh/DPlength)/(RHO*Um*Um)
Write(2,405)Re,FRIC
! UNCERTAINTY ANALYSIS
CALL UNCERTAIN(Pamb,Pven,Tven,a1,V1,a2,V2,Dthroat,Area,Tback,
&Tin,Floss,Uncer)
WRITE(7,300)TM,MV,UM,RE,FRIC
WRITE(7,401)NUS,NUT,EF,UNCER
WRITE(8,403)PHOTO,RE,NUT,EF,UNCER
1 CONTINUE
405 FORMAT(10X,E12.5,10X,E12.5)
406 FORMAT(10X,'Friction Factor= ',E10.4)
403 FORMAT(1X,F3.0,1X,E11.6,1X,E11.6,1X,E11.6,1X,E9.3)
200 FORMAT(4X,F5.1,' ',F4.3,' ',F5.1,' ',F4.3,' ',
&F5.1,' ',F4.3,
&/,4X,' ',F5.1,' ',F4.1,' ',F4.1,' ',F4.1,
&' ',F4.1,' ',F7.4,' ',F7.4,' ',F7.4,' ',F7.3)
51
300 FORMAT(/,X,'Tm=',F6.2,1X,' Mv=',E9.3,1X,
&' Um=',F6.2,1X,'Re=',F8.2,1X,'f (darcy)=',F8.4)
401 FORMAT(X,'NUs=',F8.3,2X,'NUt=',F8.3,2X,' EF=',F7.4,2X,
&'% UNCER (in h) =',F7.2)
REWIND 1
READ(1,*)dum
DO I=1,10
READ(1,10)TITLE
WRITE(2,10)TITLE
WRITE(8,10)TITLE
enddo
STOP
END
C*******************************************************************
***C
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)
FAC1=3.413 ! converts Watts to BTU/hr
C=0.24*0.5215*3600
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(3,*)' '
WRITE(3,*)' h =',h,' BUT/hr.sqft.F'
H2=h*h
C
C i2 v2
C ------- - Floss
C a2
52
C -------------------------------------
C sqrt(T1)(i1 v1 + f i2 v2)
C Ts-Ti - -------------------------
C C P1 A_throat
C
DLOSS=0.1*Losses
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
53
ZATH=(DATH*DHDATH)**2
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(3,*)' TOTAL UNCER.%:',Uncer
WRITE(3,*)' '
WRITE(3,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h
WRITE(3,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h
WRITE(3,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h
WRITE(3,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h
WRITE(3,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h
WRITE(3,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h
WRITE(3,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h
WRITE(3,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h
WRITE(3,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h
WRITE(3,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h
WRITE(3,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h
WRITE(3,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h
WRITE(3,*)' ******************************************'
WRITE(3,*)' '
WRITE(3,*)' '
RETURN
END
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)
54
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
SUBROUTINE COEFFICIENT(Q,Fluxb,Tm,Tback,hback,Floss)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 kinc,kadh,kkap,kmyl,kpoly,ksty,kblack,kliq,kplex,
&Length,Mv
COMMON Dh,AR,Width,Length,Hlength,P,Distance,Rgas,Mv,
&Tin,Tamb,Pamb,Tliquid
C B A C K W A L L (LIQUID CRYSTAL WALL)
C FROM THE CENTER OF HEATING ELEMENT TO THE AMBIENT AIR
C 0.25 mil INCONEL HEATING ELEMENT ----- 0.5 mil ADHESIVE -----
0.5 mil
C KAPTON ---- 2 mil ADHESIVE ----- 4 inches POLYURETHANE ----
AMBIENT
C tinc1/kinc -- tadh1/kadh -- tkap/kkap -- tadh2/kadh --
tpoly/kpoly -- 1/ho
C FROM THE CENTER OF HEATING ELEMENT TO THE AIR INSIDE THE TEST
SECTION
55
C 0.25 mil INCONEL HEATING ELEMENT ----- 1.0 mil ADHESIVE -----
2.0 mil
C KAPTON ---- 3.5 mil ADHESIVE ---- 3.0 mil ABSORPTIVE BLACK
BACKGROUND
C ---- 2.0 mil LIQUID CRYSTAL ---- 5.0 mil MYLAR ---- AIR INSIDE
THE TEST SECTION
C tinc/kinc -- tadh1/kadh -- tkap/kkap -- tadh3/kadh
C -- tblack/kblack -- tliq/kliq -- tmyl/kmyl -- 1/hi
C T O P , F R O N T A N D B O T T O M W A L L S
C FROM THE INSIDE AIR TO THE AMBIENT AIR
C AIR INSIDE ---- 0.45 inches PLEXIGLAS ---- 2.0 inches
STYROFOAM ----
C AMBIENT AIR
C 1/hi -- tplex/kplex -- tsty/ksty -- 1/ho
C Heat transfer coefficient on the outer surface
De=7./12. ! ft, test section side with insulation
TambR=Tamb+460
CALL AIRPROP(TambR,GAMMA,CON,VIS,PR,CP)
VIS=VIS/3600
ho=0.36*con/De ! Ozisik, Page 443
c
tinc = 0.50e-03/12. ! MINCO's fact sheet
tadh1 = 0.5e-03/12. ! MINCO's fact sheet
tadh2 = 2.0e-03/12.
tadh3 = 3.5e-03/12. ! double-stck tape used on back of
L.C.
tkap = 1.0e-03/12. ! MINCO's fact sheet
tpoly = 4./12.
tplex = 0.45/12.
tsty = 1.375/12.
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)
56
kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K)
ksty = 0.02 ! BTU/hr.ft.F
kpoly= 0.543 ! BTU/hr.ft.F from GOLDENWEST INC.
BTU/(ft.hr.F)
kplex= 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3
BTU/hr.F.sqft/in,
! same given by 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
Rinc = tinc/kinc
Radh1 = tadh1/kadh
Radh2 = tadh2/kadh
Radh3 = tadh3/kadh
Rkap = tkap/kkap
Rpoly = tpoly/kpoly
Rsty = tsty/ksty
Rplex= tplex/kplex
Rblack = tblack/kblack
Rliq = tliq/kliq
Rmyl = tmyl/kmyl
Rconv = 1./ho
Rback = 0.5*Rinc + Radh1 + Rkap + Radh2 + Rpoly + Rconv
Rfront =0.5*Rinc + Radh1 + Rkap + Radh3 + Rblack + Rliq
C WRITE(6,*)' Rinc,Radh1,Radh2,Radh3',Rinc,Radh1,Radh2,Radh3
C WRITE(6,*)' Rkap,Rpoly,Rsty,Rplex,Rblack',Rkap,Rpoly,Rsty,
C &Rplex,Rblack
C WRITE(6,*)' Rliq,Rmyl,Rconv,Rback,Rfront',Rliq,Rmyl,Rconv,
C &Rback,Rfront
Theater = (fluxb+Tamb/Rback+Tliquid/Rfront)/
&(1./Rback+1./Rfront)
flback = (Theater-Tamb)/Rback ! loss from the back side
ffront = (Theater-Tliquid)/Rfront
Tback= Tliquid -ffront*Rmyl ! Surface temperature, Ts
57
perloss=100.*(flback/fluxb)
WRITE(7,*)' '
WRITE(7,*)' LIQUID CRYTAL SIDE'
WRITE(7,*)' '
WRITE(7,101)Theater, fluxb, flback, ffront,
& perloss,Tliquid,Tback,Tamb,ho
100 FORMAT(/,5X,'HEATER TEMPERATURE = ',F8.3,' F',/,
&5X,'TOTAL HEAT FLUX = ',F8.3,' BTU/hr.sqft',/,
&5X,'HEAT FLUX TO THE BACK = ',F8.3,' BTU/hr.sqft',/,
&5X,'HEAT FLUX TO THE FRONT = ',F8.3,' BTU/hr.sqft',/,
&5X,'% OF HEAT LOST FROM THE BACK SIDE = ',F8.3,/,
&5X,'LIQUID CRYSTAL TEMPERATURE = ',F8.3,' F',/,
&5X,'SURFACE TEMPERATURE = ',F8.3,' F',/,
&5X,'AMBIENT TEMPERATURE = ',F8.3,' F',/,
&5X,'Uinf where camera is located= ',F8.3,' ft/s',/,
&5X,'Re based on the test section outer dimension= ',E13.6,/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F')
101 FORMAT(/,5X,'HEATER TEMPERATURE = ',F8.3,' F',/,
&5X,'TOTAL HEAT FLUX = ',F8.3,' BTU/hr.sqft',/,
&5X,'HEAT FLUX TO THE BACK = ',F8.3,' BTU/hr.sqft',/,
&5X,'HEAT FLUX TO THE FRONT = ',F8.3,' BTU/hr.sqft',/,
&5X,'% OF HEAT LOST FROM THE BACK SIDE = ',F8.3,/,
&5X,'LIQUID CRYSTAL TEMPERATURE = ',F8.3,' F',/,
&5X,'SURFACE TEMPERATURE = ',F8.3,' F',/,
&5X,'AMBIENT TEMPERATURE = ',F8.3,' F',/,
&5X,'Outer heat transfer coefficient= ',F8.3,
&' BTU/hr.sqft.F')
Atop=(AR*Width)*Hlength*(1.+distance/Hlength)
Abot=Atop
Aback= (Width)*Hlength*(1.+distance/Hlength)
Afront=Aback
! AIR INLET ENTHALPY
TinR=Tin+460
CALL AIRPROP(TinR,GAMMA,CON,VIS,PR,CP)
VIS=VIS/3600
Hin=CP*TinR
! ITERATIONS STARTS HERE
! INITIAL GUESSES
Hout=Hin + (Q/(3600.*Mv))
TmR=Hout/CP
Tm=TmR-460
hback=(Fluxb-Flback)/(Tback-Tm)
hfront=hback
htop=0.8*hback
hbot=htop
58
Ttop=Tm
Tfront=Tm
Tbot=Tm
DO I=1,20
! RADIATIONAL LOSSES
call rad(AR,Width,Length,Tback,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
C write(6,*)'Frback',Frback
C write(6,*)'Frtop',Frtop
C write(6,*)'Frfront',Frfront
C write(6,*)'Frbot',Frbot
C FLUX LOSSES FROM TOP, BOTTOM AND FRONT WALLS
R1= Rplex+Rsty+Rconv !from surface to ambient
! TOP WALL
R3=1./htop
Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))
Fltop=(Ttop-Tamb)/R1
! BOTTOM WALL
R3=1./hbot
Tbot=((1./R3)*Tm+(1./R1)*Tamb-Frbot)/((1./R1)+(1./R3))
Flbot=(Tbot-Tamb)/R1
! FRONT WALL
R3=1./hfront
Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))
Flfront=(Tfront-Tamb)/R1
! TOTAL HEAT LOSS TO THE AMBIENT
Qwaste=Fltop*Atop+Flbot*Abot+Flfront*Afront+Flback*Aback
! NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN
QUESTION
Qadd = Q-Qwaste
! AIR MIXED MEAN ENTHALPY AT THE POINT WHERE THE HEAT
TRANSFER
! COEFFICIENT IS BEING MEASURED
Hout=Hin + Qadd/(3600.*Mv)
59
! AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT
TRANSFER
! COEFFICIENT IS BEING MEASURED
TmR=Hout/CP
Tm=TmR-460.
CALL AIRPROP(TmR,GAMMA,CON,VIS,PR,CP)
VIS=VIS/3600
! HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING
Floss=Flback+Frback
hback=(Fluxb-Flback-Frback)/(Tback-Tm)
hfront=hback
! FILM TEMPERATURE
Tf=(Tback+Tm)/2.
! DENSITY AT FILM TEMPERATURE
RHO=Pamb/(Rgas*(Tf+460.))
! OTHER PROPERTIES AT FILM TEMPERATURE
TfR=Tf+460.
CALL AIRPROP(TfR,GAMMA,CON,VIS,PR,CP)
VIS=VIS/3600
Re=4.*Mv/(P*vis)
! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL
htop=0.8*hback
hbot=htop
FNETTOP=htop*(Ttop-Tm)+Fltop+Frtop
FNETBOT=hbot*(Tbot-Tm)+Flbot+Frbot
FNETFRONT=hfront*(Tfront-Tm)+Flfront+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 20 iterations',
&' *****',/)
WRITE(9,410)Re,PHOTO,FNETTOP,FNETFRONT,FNETBOT
410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',F3.0,5X,
&'FNETTOP,FNETFRONT & FNETBOT=',3E15.5,/)
GO TO 503
60
34 WRITE(7,500)I,FNETTOP,FNETFRONT,FNETBOT
500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,
&'FNETTOP,FNETFRONT & FNETBOT =',3E15.5,/)
503 continue
write(7,110)Tback,Ttop,Tfront,Tbot
110 FORMAT(5x,'Back, Top, Front and Botom Wall Temperatures: ',
&/,10x,4F10.2,' F')
write(7,115)Tm,Tf
115 FORMAT(5X,'Air Mixed Mean and Film Temperatures',2F9.3,' F')
write(7,120)hback,htop
120 FORMAT(5x,'hturb=',F8.3,5X,'hunt=',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(7,190)Fluxb,Fluxtop,Fluxf,Fluxbot
190 FORMAT(5X,'Heat Fluxes Generated by Back, Top, Front and'
&,' Bottom Heaters:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,180)Flback,Fltop,Fl front,Flbot
180 FORMAT(5X,'Flux Losses from Back, Top, Front and'
&,' Bottom Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
write(7,150)Frback,Frtop,Frfront,Frbot
150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'
&,' Bottom Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')
RETURN
END
SUBROUTINE RAD(AR,Width,Length,Tback,Ttop,Tfront,Tbot,
&Frback,Frtop,Frfront,Frbot)
IMPLICIT REAL*8(A-H,O-Z)
REAL*8 Length
DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)
W=Width
H=AR*Width
H=H/Length
W=W/Length
T(1)=Tback + 460.
T(2)=Ttop + 460.
T(3)=Tfront+ 460.
T(4)=Tbot + 460.
C Emissivities
E(1)=.85 ! Liquid Crystal Foil
E(2)=.9 ! PLEXIGLAS
E(3)=.9 ! PLEXIGLAS
E(4)=.9 ! PLEXIGLAS
N=4
PI=4.*ATAN(1.E00)
SIGMA=0.1712E-08
C WRITE(7,150)
61
150 FORMAT(//,20X,'SHAPE FACTORS',//)
C Shape Factors
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
F31=F13
F32=F12
F33=0.
F34=F14
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
62
F24=1.-F21-F22-F23
F41=F21
F42=F24
F43=F23
F44=0.
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
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
A(2,1)=F21
A(2,2)=F22-1./(1.-E(2))
A(2,3)=F23
A(2,4)=F24
A(3,1)=F31
A(3,2)=F32
A(3,3)=F33-1./(1.-E(3))
A(3,4)=F34
A(4,1)=F41
A(4,2)=F42
A(4,3)=F43
A(4,4)=F44-1./(1.-E(4))
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)
63
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)
Frbot= 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
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,
64
& 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
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)
65
cpx=cp(j)
kx=k(j)
gamx=gam(j)
190 return
end
C*******************************************************************
***C
66
Appendix E: Tabulated Results
Cold Tests
SQUARE RIBS
Re f
19983 0.27
25419 0.27
29996 0.26
35373 0.29
40828 0.25
45294 0.25
50747 0.25
56345 0.25
60874 0.23
5065 0.35
9982 0.31
15123 0.26
RAMPED RIBS, FLOW DIRECTION 2
Re f
5105 0.22
10088 0.22
15287 0.20
20301 0.18
25661 0.17
30145 0.17
35511 0.17
40905 0.16
45431 0.16
50828 0.17
56274 0.16
60789 0.16
RAMPED RIBS, FLOW DIRECTION 1
Re f
20356 0.18
25734 0.18
30277 0.18
35719 0.17
41131 0.17
45643 0.17
51254 0.16
56625 0.16
61184 0.16
5150 0.22
10065 0.19
15210 0.19