A Thesis Presented to - Northeastern University349748/fulltext.pdf · ribs. Promvonge and Thianpong...

________________________________________________________________________

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


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


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.


Ramped Rib from the

channel inlet on the bottom surface, flow direction 1, Re = 30000.

33


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

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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,

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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

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[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



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)


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)


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)


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)


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,/)


&5X,'F24=',F6.4,/)


&5X,'F34=',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)


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

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