An Experimental Study of Heat Transfer Coefficients and

Friction Factors in Airfoil Leading Edge Cooling Cavities

Roughened with Slanted Ribs

A Thesis Presented

By

Benjamin S. Tom

To

The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

In

Mechanical Engineering

Northeastern University

Boston, Massachusetts

June 2014

2

Table of Contents

Nomenclature ......................................................................................................................................... 6

Abstract .................................................................................................................................................. 9

Introduction ............................................................................................................................................ 9

Theory ................................................................................................................................................... 13

Test Environment .................................................................................................................................. 17

Test Section ....................................................................................................................................... 17

Rig 1 .............................................................................................................................................. 18

Rig 2 .............................................................................................................................................. 20

Rig 3A ............................................................................................................................................ 20

Rig 3B ............................................................................................................................................ 21

Turbulator Geometry ......................................................................................................................... 21

Heater Arrangement .......................................................................................................................... 24

Source Pressure Network .................................................................................................................. 26

The Plenum ....................................................................................................................................... 27

Power Source .................................................................................................................................... 28

Test Procedure ...................................................................................................................................... 28

Liquid Crystal Calibration ................................................................................................................... 28

Cold and Heat Transfer Tests ............................................................................................................. 29

Cold Test Procedure .......................................................................................................................... 29

Heat Transfer Test Procedure ............................................................................................................ 30

Data Post-Processing Procedure ............................................................................................................ 30

Image Processing ............................................................................................................................... 30

FORTRAN Code: Determining Average Nusselt Number, Friction Factor, and Enhancement Factor .... 32

Results and Discussion ........................................................................................................................... 32

Test Rig 1 ........................................................................................................................................... 32

Test Rig 2 ........................................................................................................................................... 38

Test Rig 3A......................................................................................................................................... 43

Test Rig 3B ......................................................................................................................................... 48

Comparative Study: Rigs 1, 2, 3A, and 3B ........................................................................................... 52

Conclusions ........................................................................................................................................... 70

References ............................................................................................................................................ 71

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Appendix A.1: FORTRAN Code for Rig 1 ................................................................................................. 73

Check.f File ........................................................................................................................................ 73

Reduce.F File ..................................................................................................................................... 76

Rig1-reduce-friction.f File .................................................................................................................. 97

Appendix A.2: FORTRAN Codes for Rig 2 .............................................................................................. 118

Check.F ............................................................................................................................................ 118

Reduce.F ......................................................................................................................................... 120

Rig2-reduce-friction.f ....................................................................................................................... 150

Appendix A.3: FORTRAN Codes for Rig 3A ............................................................................................ 158

Check.f ............................................................................................................................................ 158

Rig3a-Reduce-Heat-Transfer.f .......................................................................................................... 160

Rig3a-reduce-friction.f ..................................................................................................................... 191

Appendix A.4: FORTRAN Codes for Rig 3B ............................................................................................ 199

Reduce.f .......................................................................................................................................... 199

Rig3b-Reduce-Heat-Transfer.f.......................................................................................................... 201

Rig3b-reduce-friction.f ..................................................................................................................... 232

Appendix B.1: Rig 1 Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal

Performance) ...................................................................................................................................... 240

Appendix B.2: Rig 2 Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal

Performance) ...................................................................................................................................... 242

Appendix B.3: Rig 3A Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal

Performance) ...................................................................................................................................... 244

Appendix B.4: Rig 3B Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal

Performance) ...................................................................................................................................... 246

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Table of Figures

Figure 1: High Bypass Turbofan Jet Engine and Turbine Blade [16], [17] ................................................. 10

Figure 2: Thermal Resistance Network (Rig 1) ........................................................................................ 15

Figure 3: Test Section Experimental Setup ............................................................................................. 18

Figure 4: Cross-Section of Test Section 1 ................................................................................................ 19

Figure 5: Layers of Material on Fiberglass Wall ...................................................................................... 19

Figure 6: Cross Section of Test Section 2 ................................................................................................ 20

Figure 7: Cross Section of Test Section 3A .............................................................................................. 20

Figure 8: Cross Section of Test Section 3B .............................................................................................. 21

Figure 9: Staggered 45° Turbulator Arrangement on Sidewalls............................................................... 22

Figure 10: Heater Arrangement for Test Rig 1 ........................................................................................ 25

Figure 11: Heater Arrangement for Test Rig 2 ........................................................................................ 25

Figure 12: Heater Arrangement for Test Rig 3A ...................................................................................... 26

Figure 13: Heater Arrangement for Test Rig 3B ...................................................................................... 26

Figure 14: Parallel Network of Pressure Pipes in Laboratory .................................................................. 27

Figure 15: Plenum Structure .................................................................................................................. 27

Figure 16: Multi-Channel Power Source ................................................................................................. 28

Figure 17: Liquid Crystal Calibration ....................................................................................................... 29

Figure 18: Example of image taken by camera of the backwall and nose surfaces used for image

processing ............................................................................................................................................. 31

Figure 19: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall) ......................................................... 33

Figure 20: Rig 1 Nusselt Number Vs Reynolds Number (Nose)................................................................ 34

Figure 21: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) ........................................... 35

Figure 22: Rig 1 Enhancement Factor Vs. Reynolds Number (Backwall) .................................................. 36

Figure 23: Rig 1 Enhancement Factor Vs. Reynolds Number (Nose)........................................................ 37

Figure 24: Rig 1 Friction Factor Vs. Reynolds Number ............................................................................ 38

Figure 25: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall) ......................................................... 39

Figure 26: Rig 2 Nusselt Number Vs. Reynolds Number (Nose) ............................................................... 40

Figure 27: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) ........................................... 41

Figure 28: Rig 2 Enhancement Factor Vs. Reynolds Number (Backwall) .................................................. 42

Figure 29: Rig 2 Enhancement Factor Vs. Reynolds Number (Nose)........................................................ 42

Figure 30: Rig 2 Friction Factor Vs. Reynolds Number ............................................................................ 43

Figure 31: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall) ....................................................... 44

Figure 32: Rig 3A Nusselt Number Vs. Reynolds Number (Nose) ............................................................ 45

Figure 33: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) ........................................ 46

Figure 34: Rig 3A Enhancement Factor Vs. Reynolds Number (Backwall) ................................................ 47

Figure 35: Rig 3A Enhancement Factor Vs. Reynolds Number (Nose) ..................................................... 47

Figure 36: Rig 3A Friction Factor Vs. Reynolds Number .......................................................................... 48

Figure 37: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall) ....................................................... 49

Figure 38: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)......................................... 50

Figure 39: Rig 3B Enhancement Vs. Reynolds Number (Backwall) .......................................................... 51

5

Figure 40: Rig 3B Friction Factor Vs. Reynolds Number .......................................................................... 52

Figure 41: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall) ............. 54

Figure 42: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose) ................... 56

Figure 43: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall) ...... 58

Figure 44: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose) ............ 59

Figure 45: Friction Factor Vs Reynolds Number for All Rigs at All Blockage Ratios .................................. 61

Figure 46: Thermal Performance of All Four Test Sections at Backwall at All Blockage Ratios ................. 63

Figure 47: Thermal Performance of All Four Test Sections at Nose at All Blockage Ratios ....................... 65

Figure 48: Rig 1 Thermal Performance Vs. Re (Backwall and Nose) ........................................................ 66

Figure 49: Rig 2 Thermal Performance Vs. Re (Backwall and Nose) ........................................................ 67

Figure 50: Rig 3A Thermal Performance Vs. Re (Backwall and Nose) ...................................................... 68

Figure 51: Rig 3B Thermal Performance vs. Re (Backwall and Nose) ....................................................... 69

6

Nomenclature

������ = Cross-section area of the test section

������ = Heater area

�� = Venturi throat cross-sectional area

� = Specific heat at constant pressure

��= Hydraulic diameter

e = Turbulator height

� � = Blockage ratio

EF = Enhancement factor

� ̅���� = Darcy friction factor

��̅���� = Smooth wall friction factor

�� = Proportionality Constant in Newton’s 2nd Law (32.2 �����������)

h = Heat transfer coefficient

ℎ�= Heat transfer coefficient of air at ambient temperature

!= Current applied to heater “i”

"���,�!� = Thermal conductivity of air at ambient conditions

$����� = Length of the heater

Nu = Nusselt number for roughened surface

%&� = Nusselt number for smooth wall

'(�� = Number of turbulators

P = Perimeter of test section

)��� = Ambient pressure

)!*�� = Inlet pressure to test section

)+�* = Venturi pressure

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Pr = Prandtl number

,-���. = Heat transfer rate from the heater to the ambient air at middle of test section

,-���* = Heat transfer rate from heater to the heated wall surface within leading edge cavity

,-!* = Incoming heat transfer rate from heaters

,-������ = Heat transfer rate of losses

,-�!//�� = Heat transfer rate at middle of test section at camera location

,-*��� = Heat transfer rate at nose

,0! = Heat flux emitted by surface “i”

,0!* = Incoming heat flux

,0������ = Heat flux losses

Re = Reynolds number

1! = Resistance value of material designated by “i”

S = Turbulator pitch (spacing from center of one rib to next)

�� = Turbulator pitch to Turbulator height ratio

23 = Heated wall surface for radiation calculation

24 = Top wall surface for radiation calculation

25 = View wall surface for radiation calculation

26 = Nose projected surface for radiation calculation

7����� = Temperature of the heater

7!* = Average inlet temperature to the test section

7!*3 = Temperature measured by thermocouple #1 at inlet to the test section

7!*4 = Temperature measured by thermocouple #2 at inlet to the test section

7�!8(!/ = Liquid crystal temperature

7���* = Mean temperature at middle of test section (at camera location)

7+�* = Venturi temperature

8

TP = Thermal performance

7�(�� = Surface temperature at surface of heated wall at middle of test section

9! = Voltage applied to heater “i”

9� = Flow mean velocity

μ = Air dynamic viscosity

ρ = Density of air

9

Abstract

In turbine blade design, the use of turbulators in airfoil cavities has been a preferred means to cool the

metal temperatures within the airfoil. Temperatures in the turbine section of a jet engine can easily

reach beyond material temperature capability limits and without any internal cooling, the turbine blades

will begin to creep and eventually lead to engine failure. The introduction of turbulators has provided a

means to increase the heat transfer coefficient within the airfoil cavities and help promote turbulence

and better mixing to facilitate convective cooling. In this study, 4 different test rigs were experimented

upon with each test rig assessing 3 different turbulator blockage ratios (e/Dh). Each test section’s cross

section was based on leading edge cavity geometry scaled up from a “real-life” airfoil. Turbulators were

placed along the backwall and also along the leading edge nose. The backwall turbulators had rounded

corners and staggered, and were placed 45° along the surface of the wall. The nose turbulators also had

rounded corners and staggered, but, unlike the wall turbulators, were placed at 90° along the nose

surface. To determine the reference temperature of the measured wall and nose surfaces, liquid crystals

were used. The liquid crystals were laid on top of the wall and nose surfaces on one wall of the test

section. Electric foil heaters were placed beneath the liquid crystals to simulate a heated wall boundary

condition. The remaining walls were insulated from the environment to simulate adiabatic conditions.

For this study, the heat transfer coefficient, friction factors, enhancement factors, and thermal

performance were calculated based on experimental data collected on the backwall and nose surfaces.

Upon conclusion of this study, it was found that: (a) Rig 1 has the highest thermal performance at the

nose at all blockage ratios. Rig 3A has the highest thermal performance at the backwall at low and high

blockage ratios. (b) Rig 1 had the highest friction factor across the range of Reynolds Numbers. Rig 2 had

the lowest. (c) As the blockage ratio increased, so did the heat transfer coefficient and friction factors. It

was noted, however, in some cases, that as the blockage ratio increased to the maximum blockage the

heat transfer benefit was reduced. (d) The turbulator spacing was suggested to have a potential impact

on the overall heat transfer coefficient as demonstrated by looking at the results between rigs 2 and 3A

and 3B. (e) To validate the test results and trends seen from this experiment, it is recommended that a

CFD analysis be performed on each test section.

Introduction

The use of turbulators in turbine airfoils has been the preferred means of cooling the airfoil metal

temperatures to achieve the design part life. In jet engine design, the leading edge of an airfoil can be

the life limiting location due to high thermal stress. Figure 1 below shows a picture of a high bypass ratio

turbofan jet engine and highlights where in the engine, turbine airfoils are generally located.

10

Figure 1: High Bypass Turbofan Jet Engine and Turbine Blade [16], [17]

As shown in Figure 1, the turbine airfoils are downstream of the combustor module and thus, are

exposed to the extremely high temperatures in the flowpath. To reduce the metal temperature along

the airfoil’s internal walls, it is necessary to provide a means of convectively cooling the internal

passages of an airfoil. This is where the use of turbulators is effective. Turbulators are used to help

facilitate turbulence and enhanced mixing within the internal cavities of the airfoil by “tripping” the

flow. Tripping the flow enhances mixing and the heat transfer coefficient to facilitate heat transfer from

the hot wall to the cooling flow.

Taslim and Lengkong [1] studied the heat transfer coefficient on the surfaces of 45 degree angled ribs

with sharp and rounded corners within a square channel. A comparison was also done to look at the

heat transfer effectiveness of 45 degree vs 90 degree angled turbulators. Taslim and Lengkong

investigated into 3 different blockage ratios (� �) of 0.133, 0.167, and 0.25 and for rib pitch-to-height

ratios (S/e) of 5, 8.5, and 10. The experiment involved measuring the average temperatures on an

electric heated copper rib upstream and midstream location. It was concluded that sharp cornered

turbulators produced higher heat transfer coefficient. In addition, 45° turbulators proved more

beneficial from heat transfer standpoint at smaller blockage ratio. Moreover, Taslim and Lengkong also

showed that small rib pitch to height ratios led to lower thermal performance.

Domaschke et al [2] performed experiments looking at the heat transfer coefficient and pressure drop

measurement for leading edge geometry consisting of both smooth and rib roughened channels.

Staggered 45° angled turbulators were placed on suction and pressure backwalls with constant pitch and

blockage ratio for Reynolds numbers between 20,000 and 50,000. Using the Transient Liquid Crystal

Method, originally developed by Ireland and Jones, Domaschke et al showed that introducing

turbulators increased the local heat transfer at the walls and at the leading edge. The pressure and

suction backwalls showed an increase up to 350%, while the leading edge only showed a 1.5x increase

11

over the smooth wall. The maximum local heat transfer was seen behind the turbulators away from the

leading edge. Overall thermal performance increased with the introduction of the turbulators, but

decreased with increasing Reynolds Numbers.

Rallabandi et al [3] looked at the heat transfer coefficients and frictions factors for a square channel with

45° round-edged ribs at high Reynolds Numbers for land-based gas turbine applications. They looked at

various high blockage ratios and pitch for Reynolds Numbers ranging from 30,000 to 400,000. Using

copper plates and thermocouples, Rallabandi et al found that larger blockage ratios and smaller rib pitch

led to a higher heat transfer coefficient, but also higher pressure drop. Also, increasing the number of

ribs increased the surface area, which enhanced the heat transfer coefficient. In terms of the friction

factor, Rallabandi et al saw that the rounded edge ribs had lower friction factors than that of the sharp

edged ribs.

Lau et al [4] also looked at turbulent heat transfer and friction in a square channel with discrete

turbulator configurations for two rib to pitch ratios and various angles of attack for Reynolds Number of

10,000 to 80,000. Using brass ribs and heated walls, Lau et al determined the Stanton Number and

friction factors for the different rib configurations. Lau et al concluded that the 90° discrete rib case had

about 10-15% higher average Stanton Number than the 90° transverse rib case and that turning the ribs

in the same direction of the core flow increased it further by another 10-20%. Moreover, the thermal

performances of the parallel oblique ribs with 30°, 45°, and 60°angle of attack was about 20% higher

than the 90° discrete rib configuration. The crossed oblique discrete ribs performed the poorest.

Some other works in the field of turbulator heat transfer for 90° ribs included Dees et al [5]. Dees et al

conducted experiments in a closed loop wind tunnel using a “three-vane, two passage cascade” test

section. Rib turbulators were placed within the test airfoil section, which included two different types of

passages; one being of u-bend shape and the other just a straight radial passage. Dees et al concluded

that rib turbulators increased the overall heat transfer effectiveness in both u-bend and radial channels,

with the ribbed radial channel showing between 40-50% increase in effectiveness. Dees et al also

compared the experimental results to their CFD analysis, and concluded that the CFD analysis under

predicted the overall effectiveness, but the trends were similar.

In addition to square channels, there also have been experiments performed on triangular leading edge

shaped channels. Liu et al [6] investigated internal cooling of a triangular channel with 45° angled ribs at

high rotation numbers for P/e = 8 and e/Dh = 0.087. Reynolds numbers ranged from 10,000 to 40,000

and the rotational speeds ranged from 0-400 RPM. They concluded that in a rotational channel, the

trailing edge had higher heat transfer coefficient, while in a stationary channel, the leading edge had a

higher heat transfer coefficient.

Luo et al [7] also investigated into triangular ducts with ribbed internal surfaces for blockage ratios of

0.11 to 0.21, and rib spacing to rib height ratios of 3.41 to 13.93 for Reynolds number range of 4,000 to

23,000. The test section was uniformly heated using electrically heated nichrome wire around the

triangular duct and temperatures and pressures were taken using thermocouples and pressure taps

along the axial length of the test section. Luo et al concluded that blockage ratio of 0.18 provided the

12

maximum forced convection and pressure drop increased with blockage ratio. In addition, a rib to rib

spacing of 7.22 provided the best thermal performance.

Taslim and Bethka [8] looked at impingement on the leading edge of an airfoil with axial cross flow. The

experiment measured the heat transfer impact for a range of axial to jet mass flow rates of 1.4 to 6.4

and jet Reynolds Numbers from 8,000 to 48,000. Two types of inlet flows were tested; one in the same

direction as the crossflow and one in the opposite direction of the crossflow. Using copper plates and

thermocouples to measure the local temperature, Taslim et Bethka concluded that (1) For both inlet

flow configurations, the sidewall showed a higher heat transfer coefficient than the leading edge nose.

(2) The heat transfer coefficient for impinging jets with crossflow is less than that of impinging jets

without crossflow.

Bunker and Metzger [9] also performed some studies looking at local heat transfer at airfoil leading edge

with impingement cooling without film cooling extraction. Thin temperature coating was sprayed at the

leading edge and variations in jet Reynolds Number, airfoil leading edge sharpness, jet pitch-to-diameter

ratios, and jet nozzle –to-apex travel distances were tested. 4 different types of airfoils were used with

radius of curvature of 0 (sharp edge), 0.2, 0.4, and 1.0. Pitch-to-jet diameter ratios of 4.67, 3.33, and 0

were tested. Jet nozzle-to-airfoil apex distance to width of slot jet ratios of 18, 24, 30, 36, and 42 were

also tested. Experimental results showed that (1) as the pitch to jet nozzle diameter ratio decreases, the

leading edge heat transfer increased, but severely degrades at pitch to jet nozzle diameter ratio of 0. (2)

Heat transfer at the leading edge apex is increased as the nose radius is increased from 0 to 1.

Bunker and Metzger [10] as a follow-up experiment looked at the local heat transfer at airfoil leading

edge with impingement cooling and film cooling extraction. Similar, to the setup described in the

experiment without film cooling extraction, the only difference was that two rows of bleed holes were

added at +/-45° from the apex centerline for film cooling extraction. Cases were the bleed holes were

directly in-line and out of phase with the impingement jet hole were assessed to determine any

differences in heat transfer performance. Bunker et Metzger concluded that the level of heat transfer

was mainly affected by the impinging jets and secondarily by the amount of bleed air. When the bleed

holes were in-line with the jet holes, the local heat transfer coefficient increased by as much as 50%.

When the bleed holes were 180° out of phase with the impingement jets, the local heat transfer

coefficient decreased. Thus, observations showed that alignment of the bleed holes relative to the jet

holes played an important factor in the local heat transfer coefficient.

Different shaped turbulators and bumps have also been investigated to see what shape turbulator or

bump will provide the optimal thermal performance. Taslim et al [11] investigated into convective heat

transfer coefficient of impingement for 4 different typed surfaces on the leading edge of a channel. The

four different types of surfaces included smooth wall, finely roughened wall, conical surface bumps, and

longitudinal ribs. One sided and two sided inflow, and two sided outflow, crossflow, and one sided

outflow were considered. Thermocouples were embedded into brass test plates that simulated the

backwalls and the nose to measure the surface temperatures. Conclusions showed that (1) crossflow

had a strong impact on the heat transfer coefficient and reduced the heat transfer at the leading edge.

13

(2) The conical shaped bumps proved to be most beneficial out of all the types of surfaces and improved

the heat transfer by 40 percent.

Moreover, Taslim et al [12] also looked at the heat transfer of 45° angled, V-shaped, and discrete ribs

using the liquid crystal methodology to determine surface temperatures. The conclusions of this study

entailed the following: (1) 45° and discrete ribs of lowest blockage had the best thermal performance,

while the 90° angled ribs performed the worst. (2) Low blockage ratio V-shaped ribs facing downstream

produced the highest heat transfer enhancement and friction factors. For all other blockage ratios, the

45° ribs showed the highest heat transfer enhancements with friction factors less than those of the V-

shaped ribs.

Besides looking at heat transfer for a ribbed surface, there have been also a lot of studies on other types

of cooling configurations. One such configuration is looking at heat transfer in a leading edge channel

with crossflow with jet impingment. A study was done by Andrei et al [13] to look at heat transfer of a

trapezoidal channel with racetrack holes and film cooling extraction. Using the thermochromic liquid

crystal method, Andrei et al determined the Nusselt Number for jet Re range of 10k to 40k along the

span of the leading edge. They concluded that the heat transfer coefficient peaks towards the tip of the

blade, where the ratio of jet to crossflow velocity is highest, and that Reynolds number plays a critical

factor in the heat transfer coefficient.

Building upon the works of those aforementioned, this paper will look at 45° staggered rounded corner

wall turbulators and 90° staggered rounded corner nose turbulators for 4 triangular shaped leading edge

test sections at 3 different blockage ratios. This experiment will only be concerned with measuring and

calculating the heat transfer and friction factor at the middle of the test section. Since, each test section

is slightly different from each other, the blockage ratios will be dependent on the hydraulic diameter of

the test section and will change with each test section, except rigs 3A and 3B. Rigs 3A and 3B are

essentially the same test section, but the measured backwall surface for rig 3A is opposite that of rig 3B.

This study will make observations on how the different test section and turbulator geometries impact

the heat transfer coefficient, friction factor of the channel, the enhancement factors at the backwall and

nose surfaces between the turbulators, and the overall thermal performance of each test section.

Theory

In this study, the four major parameters of interest are the Nusselt Number, friction factor,

enhancement factor, and the thermal performance. The Nusselt Number, enhancement factor, and

thermal performance can be determined by first defining the thermal resistance network within the

given system. In terms of the friction factor, there are two types of friction factors of concern. The first

being the Darcy Friction Factor and the second one being the smooth wall friction factor, which can be

expressed by the Dittus-Boelter correlation. This section will briefly explain the details and the main

equations used to determine the Nusselt Number, friction factor, enhancement factor, and the thermal

performance.

14

Before performing the heat transfer calculations, it is necessary to determine the characteristics of the

flow and the heat input into the system. This includes the mass flow rate, the inlet temperature and

pressure, the ambient temperature and pressure, and the upstream venturi temperature and pressure.

The mass flow rate can be determined by equation 1.1 for critical venturi.

:; = �.=43=>?��@ABC�DEFGH@AB (1.1)

Once the mass flow rate is known, the Reynolds Number can also be determined by equation 1.2 below.

1I = 6J@�K , where μ = viscosity of air and P = Test Section Perimeter (1.2)

The inlet temperature is the average of the measured inlet temperature readings from the two

thermocouples placed at the inlet to the test section in the plenum as denoted by equation 1.3 below

7!* = HLBMCHLB�4 (1.3)

In addition to the flow characteristics, the heat transfer rate generated by the heaters also needs to be

known to determine the heat transfer coefficient. To determine the heat transfer rate at the middle of

the test section, the measured voltage and amperage need to be known. The heat transfer rate at the

middle of the test section can be expressed by equation 1.4.

,-�!//�� = 3.413P93 3 +0.594 4T (1.4)

Now, since the input flow characteristics are known and the amount of heat input is calculated, the next

steps are to determine the heat losses due to the radiation, conduction, and convection.

To determine amount of heat loss to the environment, a thermal resistance network needs to be

constructed. Figure 2 shows the thermal resistance network for rig 1. Note this thermal resistance

system can be modified and applied to any of the four different test sections. For simplicity, test section

1 is chosen here to show the thermal resistance network due to its symmetrical nature.

Figure 2 below shows the thermal resistance network of the given system.

15

Figure 2: Thermal Resistance Network (Rig 1)

The thermal resistance network consists of the three different modes of heat transfer: conduction,

convection, and radiation. Conduction occurs in the layers between the leading edge cavity and outside

ambient air. Convection occurs only on the ambient surfaces of the test section walls. Radiation occurs

within the leading edge cavity.

To determine the rate at which heat is leaving the heater due to conduction, a thermal balance needs to

be performed per figure 2. This results in equation 1.5 and 1.6

,-���. = ,-*��� = PH�AD?AU�HVDEFTWFDXY (1.5)

,-���* = ZH�AD?AU�HV[\U]^W]U_B? (1.6)

Furthermore, the equations below indicate which elements compose the conductive resistance

network.

1�` = 1+!�a =1���b! + 1��*+ (1.7)

1���* = 0.51!*� Q1�/���!+�3 Q 1.�`�* Q 1�/���!+�4 Q 1����. Q 1�!8(!/ (1.8)

16

1���. = 0.51!*� +1�/���!+�3 + 1.�`�* + 1�/���!+�5 + 1�!���c���� + 1��*+ (1.9)

The convective resistance of air can be calculated at room temperature by equation 1.10 below

1��*+ = 3�d, where ℎ� = �.5e.

f (Osisik, 443) (1.10)

Where, k= Thermal conductivity of air at ambient temperature and $����� = Length of heater

The radiative resistance network is constructed under the assumption of a 4 sided enclosure. It is

important to note that for the nose, the wall projected from the actual nose surface is assumed to

absorb all the radiation emitted from the actual nose surface. This projected nose surface is represented

by a dashed line in Figure 2. This assumption helps to simplify the geometry of the test section for the

radiative heat transfer calculations. To calculate the radiation view factors in rig 1, we take advantage of

the symmetrical nature of the test section, and also use the view factor correlation for two

perpendicular rectangles with a common edge. This simplifies the problem and only view factors, F1-2

and F2-1 need to be calculated. The remaining view factors can be determined by assuming symmetry.

Once the fractions of radiation leaving the surface i is determined, equation 1.11 is used to determine

the radiative heat flux leaving surface i and radiated away to surfaces j

,0��/,!�g = hiLjLHk\U],Ll �imjmHk\U],ml n3�iL (1.11)

Then, an iterative scheme is used to guess the heat transfer coefficient and the temperatures at the top,

view wall, and the projected nose surface. This iterative scheme is run 30 times or until thermal

equilibrium is reached at both the top and front view walls (net heat transfer rate < .001). Using this

iterative scheme, the total heat loss from each surface can be determined. Knowing the amount of heat

loss, one can calculate the rate at which heat is lost at through each of the four surfaces (top, bottom,

front, and back). In addition, the mean temperature at the middle of the test section can also be

calculated by reducing the 1st Law of Thermodynamics to equation 1.12 below

P,-!* − ,-������T = :+`P7���* − 7�(��T (1.12)

Where 7�(�� =7�!8(!/ −,-���*1�����

Utilizing the mean temperature and the knowing the total heat loss, one can determine the heat

transfer coefficient at the wall using equation 1.13

ℎ = 80 LB�80 p_[[A[H[\U]�HEADB (1.13)

Then, the Nusselt Number at the roughened wall can be calculated using equation 1.14.

%& = P�TP �T.DLU,DEF (1.14)

17

To calculate the smooth wall Nusselt Number, the Dittus-Boelter correlation is used as expressed by

equation 1.15.

%&� = 0.0231I�.q)r�.6 (1.15)

Once the roughened and smooth wall Nusselt Numbers are known, the enhancement factor (EF) also

can be calculated using equation 1.16.

st = u(u(k (1.16)

To determine the thermal performance of a particular test configuration, it is necessary to know the

friction factor besides the enhancement factor. The Darcy and smooth wall friction factors can be

determined by equations 1.17 and 1.18. Equation 1.18 is called the Blasius Correlation.

� ̅���� = 4v� = �� wh �*?\UF�n h�LBpA?��DEF

�.=x;E� ny (1.17)

��̅���� = �.53eW�d.�z (1.18)

Where v�= Fanning Coefficient of Friction and ��= Proportionality Constant in Newton’s 2nd Law

h32.2 ����������� n.

Lastly, the thermal performance (TP) of the system can be determined using equations 1.16, 1.17, and

1.18 and can be expressed by equation 1.19.

7) = {|w ]}~DUX�]}kE__?�y

M/� (1.19)

The calculations and general equations in this section can be applied for the other test sections as well.

The only differences are in the input flow characteristics and the test section geometry, which are

unique to each test configuration.

Test Environment

Test Section

The experimental setup consisted of multiple parts. Figure 3 below shows the individual parts that

comprise together to make up the entire test section.

18

Figure 3: Test Section Experimental Setup

The flow enters the plenum from the venturi network through a 1 ¼” pipe. Once in the plenum, the flow

goes through a flow straightener, which makes the flow uniform prior to entering the actual test section.

The test section is insulated all around with the exception of the front and top viewing windows, which

are transparent to capture images of the liquid crystal surfaces on the heated backwall and nose. The

flow then finally exits out of the test section into atmospheric conditions. Supports are used to hold up

the test section relieving the bending stress created by hanging it off of the plenum forward face. There

are also two cameras set up to take pictures of the liquid crystal color at the backwall and nose section.

The cameras are focused near the center of the test section at one particular section between two

consecutive backwall turbulators.

Rig 1

The cross sectional area of test section 1 is shown below in Figure 4.

19

Figure 4: Cross-Section of Test Section 1

Test section 1 is composed of two “see-through” plexi-glass wall and a fiberglass wall. One of the plexi-

glass walls is positioned directly facing the backwall with the liquid crystal and the other one is

positioned at the top wall directly over the nose. They are “see-through”, so pictures of the liquid crystal

can be taken with a camera normal to the surface of the nose and sidewall. The sidewall and nose

sections, where the liquid crystal, are located are made of fiberglass. On the backside of the fiberglass,

polyurethane foam is sprayed to provide insulation and prevent heat loss to the environment from the

backside. Figure 5 below shows, in general, the different layers that compose the fiberglass backwall and

nose sections.

Figure 5: Layers of Material on Fiberglass Wall

On the front side of the fiberglass wall sits the heaters. They span across the length of the test section.

On top of the heaters is the layer of liquid crystal. It also spans across the entire length of the channel. It

is important to keep the temperature of the heater below the melting temperature of the liquid crystal,

otherwise, the liquid crystal will be damaged. Thus, whenever the heaters are on, cooling air should

always be flowing through the channel.

20

Rig 2

Figure 6 below shows the general composition of test section 2. Unlike test section 1, test section 2 is

slightly asymmetric, however, the composition of test section 2 is same as test section 1.

Figure 6: Cross Section of Test Section 2

Rig 3A

Figure 7 below shows the composition of test section 3A. Only notable difference between test sections

1,2, and 3A is the cross sectional area.

Figure 7: Cross Section of Test Section 3A

21

Rig 3B

Figure 8 below shows the composition of test section 3B. In terms of geometry, test sections 3A and 3B

are exactly the same. Test Section 3B is different from 3A in that 3B examines the heat transfer in what

is 3A’s plexiglass sidewall and fiberglass nose.

Figure 8: Cross Section of Test Section 3B

Turbulator Geometry

The wall turbulator geometry for all four test sections are staggered one after the other on opposing

walls with an angle of attack of 45° and pointing away from inflow as shown in Figure 9 below. The nose

turbulators, however, are staggered and 90° to the flow.

22

Figure 9: Staggered 45° Turbulator Arrangement on Sidewalls

This study investigated into four different test sections. In this paper, they are designated as rigs 1,2, 3A,

and 3B. All the rigs had different cross sectional areas, except for 3A and 3B, which had the same cross

sectional areas and were basically mirror images of each other. Table 1 below outlines the test points

and turbulator geometry for rig 1.

Test Re Rib Angle (°) S/e e/Dh

1 6000 45 14.588 0.114

23

2 10000 45 14.588 0.114

3 15000 45 14.588 0.114

4 20000 45 14.588 0.114

5 30000 45 14.588 0.114

6 40000 45 14.588 0.114

7 6000 45 11.698 0.142

8 10000 45 11.698 0.142

9 15000 45 11.698 0.142

10 20000 45 11.698 0.142

11 30000 45 11.698 0.142

12 40000 45 11.698 0.142

13 6000 45 9.738 0.171

14 10000 45 9.738 0.171

15 15000 45 9.738 0.171

16 20000 45 9.738 0.171

17 30000 45 9.738 0.171

18 40000 45 9.738 0.171

Table 1: Test Points and Turbulator Specifications for Rig 1

Likewise, Table 2 below outlines the test points and turbulator geometry for rig 2.

Test Re Rib Angle (°) S/e e/Dh

1 6000 45 12.400 0.067

2 10000 45 12.400 0.067

3 15000 45 12.400 0.067

4 20000 45 12.400 0.067

5 30000 45 12.400 0.067

6 40000 45 12.400 0.067

7 6000 45 9.951 0.084

8 10000 45 9.951 0.084

9 15000 45 9.951 0.084

10 20000 45 9.951 0.084

11 30000 45 9.951 0.084

12 40000 45 9.951 0.084

13 6000 45 8.281 0.101

14 10000 45 8.281 0.101

15 15000 45 8.281 0.101

16 20000 45 8.281 0.101

17 30000 45 8.281 0.101

18 40000 45 8.281 0.101

Table 2: Test Points and Turbulator Specifications for Rig 2

24

Lastly, Table 3 outlines the test points and turbulator geometries for rig 3A and 3B.

Test Re Rib Angle (°) S/e e/Dh

1 6000 45 12.400 0.051

2 10000 45 12.400 0.051

3 15000 45 12.400 0.051

4 20000 45 12.400 0.051

5 30000 45 12.400 0.051

6 40000 45 12.400 0.051

7 6000 45 9.920 0.063

8 10000 45 9.920 0.063

9 15000 45 9.920 0.063

10 20000 45 9.920 0.063

11 30000 45 9.920 0.063

12 40000 45 9.920 0.063

13 6000 45 8.267 0.076

14 10000 45 8.267 0.076

15 15000 45 8.267 0.076

16 20000 45 8.267 0.076

17 30000 45 8.267 0.076

18 40000 45 8.267 0.076

Table 3: Test Points and Turbulator Specifications for Rig 3A and 3B

For all the test sections, it can be seen from tables 1, 2, and 3 that the non-variable elements of the

experiments are the Reynolds Number and the rib angle. The variable elements between each test

section are the pitch or turbulator spacing, rib height, and the cross sectional areas of the test sections

themselves. By carefully observing and comparing the turbulator specifications in tables 1, 2, and 3, it

can be deduced that rig 1 will have the highest blockage ratio (e/Dh) and pitch to rib height ratio (S/e)

out of all the test sections. Rig 2 has the next highest blockage ratio and pitch to rib height ratios and

Rigs 3A and 3B have the lowest. Higher blockage ratios usually result in higher heat transfer coefficients,

however, from previous studies by Taslim and Lengkong (1999), it can be shown that too high of a

blockage ratio can also lead to a decrease in thermal performance due to higher pressure drop.

Heater Arrangement

For each of the 4 test rigs, the heater sizes are chosen based on the sidewall and nose geometries.

Figure 10 below depicts the heater arrangement and sizes for test rig 1:

25

Figure 10: Heater Arrangement for Test Rig 1

For test rig 1, the test section is broken up into 3 equal parts, an inlet, middle, and exit section. A

separate heater is used for each section, and each heater is large enough in width to cover both the

sidewall and nose segments. The use of a single heater for each section is recommended to facilitate in

the amount of heat flux applied to both the sidewalls and nose segments. If 2 separate heaters were

used, the amount of voltage applied to each heater would need to be adjusted to account for the

different heater areas.

Figure 11 below depicts the heater arrangement for test rig 2:

Figure 11: Heater Arrangement for Test Rig 2

The heater arrangement for test rig 2 is different than test rig 1. The most apparent difference is in the

number of heaters used. Unlike test rig 1, test rig 2 has a separate heater for the wall and the nose. The

main reason for using 2 separate heaters is that the heaters only come in certain standard sizes, which

would not be large enough to cover both the wall and nose segments alone. Thus, to facilitate the

application of a constant heat flux across the wall and nose heaters, respectively, three 3”x11” size

heaters were chosen for the wall sections and three 2”x11” heaters were chosen for the nose sections.

It is important to note that since the wall and nose heaters are of different areas, the power applied to

the nose heaters must be a certain amount less than that of the wall heaters in order to output the

same heat flux as the wall heaters.

26

Figure 12 below depicts the heater arrangement for test rig 3A:

Figure 12: Heater Arrangement for Test Rig 3A

For test rig 3A, the heater arrangement is similar to rig 2. Separate heaters are used for each of the wall

and nose sections. They are of equal areas in order to facilitate the application of constant heat across

all the wall and nose sections.

Figure 13 below depicts the heater arrangement for test rig 3B:

Figure 13: Heater Arrangement for Test Rig 3B

The heater arrangement for test rig 3B is similar to rigs 2 and 3A. Some of the notable difference is in

the outlet wall and nose sections of the test section. In the outlet section, there is no nose heater. The

reason for no nose heater in the outlet section is that at the time of the experiment, a 2”x11” heater

was not available. In the absence of a 2”x11” heater, a 3”x11” heater was used to replace it.

Source Pressure Network

The source pressure is generated by a compressor in the mechanical room outside the laboratory. It is

then fed through an air tank which acts as a temporary air storage unit for excess air as it is discharged

and routed to the laboratory for usage. Once the air reaches the laboratory, it enters through a

regulator valve, which controls the amount of air entering the downstream pipe. In the lab, there is a

parallel network of pipes, but only one circuit is used at a time to feed the air downstream towards the

test rig as depicted in Figure 14 below:

27

Figure 14: Parallel Network of Pressure Pipes in Laboratory

Before the air enters the test rig, it is further regulated by a nozzle venturi of a specific diameter. For this

experiment, the two venturi nozzle diameters used were Ø.225” and Ø.320. These specific diameter

venturis were used mainly because they covered the range of Reynolds Number in concern for this

experiment. There are also drain valves at the bottom right and left of the pressure network as depicted

in Figure 14 to facilitate the draining of any additional moisture and condensation. In addition, there is

also a cold water cooling system in place to help cool the passing air during hot and humid days. It is

recommended the air temperature in the system remain relatively cool to the ambient temperature in

the room, because the temperature affects the pressure measured in the system, which in turns impacts

the friction factor calculations.

The Plenum

Figure 15 below shows the general setup of the plenum.

Figure 15: Plenum Structure

28

The plenum is the section of the test rig in between the pressure source and the actual test section. The

plenum is a six-sided enclosure composed of 6 plexi-glass see-thru walls. It is tightened down by bolts at

all interfaces and is sealed up using silicon. The air is supplied to the plenum equally from the left and

right sidewalls of the plenum as shown in Figure 3 by PVC tubes. Once in the plenum, the air is then

straightened and filtered through a honeycomb “diffuser” or “straightener”. After the air has been

filtered and straightened, it then enters the inlet of the test section.

Power Source

A multi-channel power source was used to provide current to the foil heaters within the test sections.

Each heater was connected to a separate channel and two voltmeters were used to measure the voltage

and current through each channel. There were two different types of dials on the power source. One

was the master dial, which controlled all the channels. The second was the “fine tuning” dial, which

varied the voltage at much finer resolution, and only controlled a particular channel. In cases, where the

flux needed to be controlled individually for each heater, the “fine tuning” dial was used. Figure 16

below shows a picture of the multi-channel power source that was used for this experiment.

Figure 16: Multi-Channel Power Source

Test Procedure

Liquid Crystal Calibration

A liquid crystal calibration was performed to determine the reference temperature and color prior to

the start of any testing on any test section. The liquid crystal calibration is important, because the

reference temperature of the liquid crystal will be used to determine the surface temperature. Figure 17

below shows a still-image of liquid crystal calibration video. In the image, one can see that the

calibration is performed in a hot-water bath, and using a thermocouple probe, the temperature is

measured as the bath is cooled naturally by ambient air and “induced stirring”. The calibration is done

until the liquid crystal has turned from black to dark blue (very hot) and to black again (cool). During the

entire calibration, it is important to record the reference temperature at the reference color, which in

this case is green. Note there are different shades of green, so the color “green” is subjective to the

29

experimenter, but it is essential that the experimenter be consistent in determining the color “green”

throughout the image processing step for each test section.

Figure 17: Liquid Crystal Calibration

Cold and Heat Transfer Tests

Two different types of tests were performed for this experiment, heat transfer and cold tests. The cold

tests were done to determine the friction factor at ambient conditions without any effect from heated

wall conditions. Heat transfer tests were done to determine the heat transfer coefficient, enhancement

factors, and also the friction factor at heated wall condition.

Cold Test Procedure

For the cold test, venturi pressure, plenum pressure and temperature, and inlet and exit pressures of

the test sections were measured. The venturi pressures that were decided on encompassed the range of

Reynolds Numbers from the heat transfer tests, and data was taken at increments of 5 psi. In some

cases, two different venturis (Ø 0.225” and Ø 0.32”) needed to be used to cover the range of Reynolds

Numbers of interest. Below outlines the steps in performing the cold test to determine the cold friction

factor at ambient conditions:

1. Turn on the air compressor and wait 2 minutes for the air in the channel to come to equilibrium

2. Set the first test venturi pressure

3. Record the ambient temperature and pressure, venturi pressure and temperature, plenum

temperature, and inlet and exit pressures of the test section.

4. Go to next higher venturi pressure.

5. Repeat steps 3 and 4 until all Reynolds Numbers have been tested. Switch out venturi diameters

if necessary.

30

Heat Transfer Test Procedure

For the heat transfer tests, a range of Reynolds Numbers (Re~6000, 10000, 15000, 20000, 30000, 40000)

were covered. Venturi pressures were determined based on the Reynolds Numbers of concern and the

geometry of the test section. Below outlines the steps in performing the heat transfer tests to

determine the heat transfer coefficient:

1. Turn on the air compressor and set the first test venturi pressure.

2. Turn on the multi-channel power source to turn on the heaters.

3. Wait 5-10 min for thermal equilibrium to be reached within the test section

4. Set the minimum voltage to each heater until a hint of color is seen on liquid crystal at the

midstream wall and nose sections. Note the wall and nose sections liquid crystal may not start

to show color at the same time. If color is seen at either the backwall or nose section, set that as

the minimum voltage.

5. Run the voltage up to the maximum voltage until the nose and backwall liquid crystals are all

blue colored. Wait 1-2 min for the liquid crystal color to stabilize. Record this as your maximum

voltage.

6. Go back to the minimum voltage and wait for 5 minutes until thermal equilibrium is reached.

7. Record voltage and amperage for each heater, ambient temperature and pressure, venturi

pressure, plenum temperature and pressure, and inlet and exit pressure of the test section

8. Take a picture using a digital camera of the liquid crystal of the backwall and nose surfaces.

9. Increment the voltage to each heater using following rule of thumb:

a. Voltage increment = (max voltage – min voltage)/20

i. The voltage increment can be adjusted depending on how quickly the liquid

crystal seems to heat up

10. Repeat steps 7-9 until the liquid crystal on both the backwall and nose sections are all blue

colored.

11. Repeat steps 1-10 for all other venturi test pressures.

Data Post-Processing Procedure

Image Processing

Following the data collection, the next step is to process the data. One of the data processing steps is to

digitize the images collected during the test. Previously, it was noted that to determine the reference

temperature of the liquid crystal, a liquid crystal calibration needs to be done. This calibration

determines the reference temperature and color of the liquid crystal, which will be used for digitizing

the pictures. In this experiment, the color green is chosen as the reference color. Using an image

digitizing software tool called Sigma Scan, the image is processed to calculate the number of pixels that

31

the reference color green takes up in the area of the red box defined in

Figure 18 below. The red box defines one repeated segment of the entire test section or equivalent to

the pitch from the center of one turbulator to the next. The number of pixels is used to determine the

“weighted-average” Nusselt Number and heat transfer coefficient. This image digitization is repeated for

the nose as well as shown in the second picture in Figure 18.

Figure 18: Example of image taken by camera of the backwall and nose surfaces used for image processing

32

FORTRAN Code: Determining Average Nusselt Number, Friction Factor, and

Enhancement Factor

Three FORTRAN codes were used in the data processing. One was called the “Check.f” file, which read

the data input file and searched for any typos or errors. The second code was called the “Reduce.f” file.

The “Reduce.f” file processed the input file and calculated the heat transfer coefficient, Nusselt Number,

Enhancement Factors, and the friction factor at heated wall condition. The last code used was called

“Reduce-Friction.F”, which determined the cold friction factor at ambient conditions. Once all the

results were processed, the output was inputted into Microsoft Excel, which calculated a “weighted-

average” Nusselt Number, Friction Factor, and Enhancement Factor using the number of pixels

determined from the image processing.

Results and Discussion

The following results will be presented for rigs 1, 2, 3A, and 3B.

• Nusselt Number Vs. Reynolds Number (sidewall and nose sections) – Midstream location

• Enhancement Factor Vs. Reynolds Number (sidewall and nose sections) – Midstream location

• Friction Factor Vs. Reynolds Number

Test Rig 1

For test rig 1, there were 3 heaters; one for the inlet, the midsection, and the exit. Each heater spanned

across the wall and nose sections. The results that follow for all test sections are representative of the

midstream section backwall and nose sections. Figure 19 below shows a plot of Nusselt Number Vs.

Reynolds Number for the backwall for all three blockage ratios. The three blockage ratios are 0.114,

0.142, and 0.171.

33

Figure 19: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall)

Figure 19 shows that the Nusselt Number trends upwards with blockage ratio. There is some slight

variation in the data as indicated at the higher Reynolds Number cases, where the medium blockage

data point is nearly the same as the maximum blockage data point. The two Reynolds Numbers, where

this occurrence is seen is at Re ~20,000 and 30,000. Overall the data shows that as the height and width

of the turbulator increases, so does the Nusselt Number, which is as expected. The taller and wider the

turbulator, flow turbulence increases and thus, improving mixing and cooling due to convection at the

backwall.

Figure 20 below shows the Nusselt Number vs. Re plot at the nose for the 3 different blockages.

50.00

80.00

110.00

140.00

170.00

200.00

230.00

260.00

290.00

320.00

350.00

380.00

0 10000 20000 30000 40000 50000

Nu

Re

Rig 1 Nusselt Number Vs. Re (Backwall)

e/Dh = 0.114

e/Dh = 0.142

e/Dh = 0.171

34

Figure 20: Rig 1 Nusselt Number Vs Reynolds Number (Nose)

Similar to Figure 19, the Nusselt Number trends upwards with blockage ratio. The variation in Nusselt

Number between the different blockage ratios is very small. It can be seen that the medium blockage

data point is very close or in some cases exceeds the maximum blockage data point, as indicated at Re

~20000 and 30000. This may be due to some experimental variation at the higher Reynolds Number or

because, at higher Reynolds Number, the positive impact of higher turbulator blockage on Nusselt

Number is diminished. Overall, the Nusselt Number trends as expected, with the maximum blockage

ratio resulting in the most heat transfer benefit.

50.00

80.00

110.00

140.00

170.00

200.00

230.00

260.00

290.00

320.00

350.00

380.00

0 10000 20000 30000 40000 50000

Nu

Re

Rig 1 Nusselt Number Vs. Re (Nose)

e/Dh = 0.114

e/Dh = 0.142

e/Dh = 0.171

35

Figure 21: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)

Figure 21 plots rig 1 backwall and nose Nusselt Numbers together for all three blockage ratios and

shows the differences between the backwall and nose more clearly. The Nusselt Numbers for the nose

for all blockages are substantially higher than that of the backwall. At the lowest Reynolds Number of

approximately 6000, the nose Nusselt Number is about 38% to 43% higher than that of the backwall

depending on the blockage ratio. At the highest Reynolds Number of approximately 40,000, the nose

Nusselt Number is about 24% to 31% higher than that of the backwall depending on the blockage ratio.

Rig 1 turbulator configuration will be best suited for an airfoil design, where the leading edge is the life

limiting location and hottest area as determined by heat transfer analysis.

Figure 22 below shows the trend between the enhancement factor and the Reynolds Number at the

backwall.

50.00

80.00

110.00

140.00

170.00

200.00

230.00

260.00

290.00

320.00

350.00

380.00

0 10000 20000 30000 40000 50000

Nu

Re

Rig 1 Nusselt Number Vs. Re (Backwall Vs. Nose)

e/Dh = 0.114(backwall)

e/Dh = 0.142(backwall)

e/Dh = 0.171(backwall)

e/Dh = 0.114 (nose)

e/Dh = 0.142 (nose)

e/Dh = 0.171 (nose)

36

Figure 22: Rig 1 Enhancement Factor Vs. Reynolds Number (Backwall)

The enhancement factor is defined by eq. 1.16. The ratio of Nu to %&� indicates how much heat transfer

benefit the ribbed wall has over the smooth wall case. If EF > 1, then the test condition has a positive

heat transfer benefit and, if EF < 1, the test condition has a negative heat transfer benefit. In the case of

Rig #1, the EF on average will provide 3-3.5x benefit over a smooth wall channel, depending on the Re of

the flow. This conclusion further proves that the introduction of turbulators in a smooth channel

improves the heat transfer due to convection.

2.50

2.80

3.10

3.40

3.70

4.00

4.30

4.60

4.90

5.20

5.50

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

EF

Re

Rig 1 Enhancement Factor Vs. Re (Backwall)

e/Dh = 0.114

e/Dh = 0.142

e/Dh = 0.171

37

Figure 23 below shows the EF at the nose location for the 3 different blockage ratios at various Reynolds

Numbers.

Figure 23: Rig 1 Enhancement Factor Vs. Reynolds Number (Nose)

The EF trends as expected at the nose location. It can be seen that the nose has a higher EF than the

backwall. This results in a higher heat transfer benefit at the nose than the sidewall. On average the

nose will provide roughly 3.5 to 5 times higher heat transfer cooling over the smooth wall case,

depending on the Re of the flow. Thus, if a turbine airfoil design requires more cooling at the leading

edge nose than the sidewall, rig #1 configuration will be the ideal design to provide higher heat transfer

coefficient at the nose.

The experiment also looked at the Cold Friction Factor vs. Reynolds Number for test rig 1. Figure 24

below shows how the friction factor trends with Reynolds Number for the three different blockage

ratios.

2.50

2.80

3.10

3.40

3.70

4.00

4.30

4.60

4.90

5.20

5.50

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

EF

Re

Rig 1 Enhancement Factor Vs. Re (Nose)

e/Dh = 0.114

e/Dh = 0.142

e/Dh = 0.171

38

Figure 24: Rig 1 Friction Factor Vs. Reynolds Number

Figure 24 shows that the Darcy friction factor trends upwards with increasing turbulator size. Darcy

friction factor increases with blockage ratio, because pressure drop across the channel increases with

higher blockage. In addition, there seems to be linear relationship between blockage ratio and Darcy

Friction Factor. This is demonstrated by the fact that the friction factor increases by approximately the

same amount with each incremental change in the blockage ratio.

Test Rig 2

The next series of plots measure the heat transfer coefficient, friction factor, and enhancement

factors of test section 2. For rig 2, the 3 different blockage ratios considered are 0.067, 0.084, and 0.101.

Figure 25 below shows the backwall Nusselt Number for the 3 blockage ratios for a range of Reynolds

Numbers. Figure 20 highlights that the heat transfer coefficient increases with blockage ratio, however,

it can be seen that as the blockage ratio increases, the benefit of increasing the rib height does not

provide much more heat transfer benefit. Going from a blockage ratio of 0.067 to 0.084, the heat

transfer benefit is on average 11%, while going from a blockage ratio of 0.084 to 0.101, the benefit is

only on average 3%. This demonstrates that there is an optimal blockage ratio that provides the best

heat transfer coefficient and if the blockage ratio is too high, it will provide a detrimental or neutral

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10000 20000 30000 40000 50000

f

Re

Rig 1 Cold Friction Factor Vs. Re

e/Dh = .171 (Darcy)

e/Dh = .142 (Darcy)

e/Dh = .114 (Darcy)

e/Dh = .171 (Smooth)

e/Dh = .142 (Smooth)

e/Dh = .114 (Smooth)

39

effect. The detrimental or neutral effect to the heat transfer coefficient can be attributed to most likely

large recirculation or dead zones that develop at the bottom of the turbulators at higher blockage ratios.

These dead zones prevent the core flow from reattaching to the backwall thus, reducing the heat

transfer benefit due to convection in those areas.

Figure 25: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall)

Figure 26 below shows the Nusselt Number for the nose section at the 3 different blockage ratios for a

range of Reynolds Numbers. The trend for the nose section is similar to the backwall in that the Nusselt

Number trends upwards with blockage ratio. It can be deduced, similar to the backwall, that the benefit

of going from a blockage ratio of 0.067 to 0.084, there is greater heat transfer benefit than going from a

blockage ratio of 0.084 to 0.101. Once again, this suggests that if the blockage ratio increases too high, it

is possible that the heat transfer benefit will be reduced or neutralized.

25

50

75

100

125

150

175

200

225

250

0 5000 10000 15000 20000 25000 30000 35000 40000

Nu

Re

Rig 2 Nusselt Number Vs. Re (Backwall)

e/Dh = 0.067

e/Dh = 0.084

e/Dh = 0.101

40

Figure 26: Rig 2 Nusselt Number Vs. Reynolds Number (Nose)

Figure 27 below plots Rig 2 Nusselt Number Vs. Reynolds Number for both the backwall and the nose. By

observing the figure below, it can be seen that the backwall and nose Nusselt Numbers are very similar

across the range of Reynolds Numbers when comparing the same blockage ratio. When comparing the

backwall and the nose at the same blockage ratio, the differences in Nusselt Number across the range of

Reynolds Numbers are for a majority less than 10%. It is only at the highest blockage ratio does one see

a slightly higher Nusselt Number on the nose than on the backwall on average. The fact that the

backwall and nose have similar heat transfer across all blockage ratios, in reality, is beneficial to an

airfoil engineer. This is because, the casting die used to form the leading edge cavity will have a longer

usable life, since the engineer can now tolerate some minimal wear of the casting tooling without having

it impact aero and thermal performance of the airfoil significantly.

25

50

75

100

125

150

175

200

225

250

0 5000 10000 15000 20000 25000 30000 35000 40000

Nu

Re

Rig 2 Nusselt Number Vs Re (Nose)

e/Dh = 0.067

e/Dh = 0.084

e/Dh = 0.101

41

Figure 27: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)

Figure 28 and Figure 29 below highlight the enhancement factors for the backwall and nose sections. As

the blockage ratio increases, so does the enhancement factor. When comparing the backwall and nose

sections, the enhancement factor for the nose is higher than the backwall. At higher Re, however, it can

be seen that the difference in enhancement factor between the nose and the backwall is minimal,

whereas, at lower Re, the difference is more significant, anywhere from 3-10%. This can be attributed to

the tendency of eddies forming at higher Re directly underneath the turbulators leading to a reduction

in heat transfer enhancement.

25

50

75

100

125

150

175

200

225

250

0 5000 10000 15000 20000 25000 30000 35000 40000

Nu

Re

Rig 2 Nusselt Number Vs. Re (Backwall vs. Nose)

e/Dh = 0.067 (backwall)

e/Dh = 0.084 (backwall)

e/Dh = 0.101 (backwall)

e/Dh = 0.067 (nose)

e/Dh = 0.084 (nose)

e/Dh = 0.101 (nose)

42

Figure 28: Rig 2 Enhancement Factor Vs. Reynolds Number (Backwall)

Figure 29: Rig 2 Enhancement Factor Vs. Reynolds Number (Nose)

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

0 5000 10000 15000 20000 25000 30000 35000 40000

EF

Re

Rig 2 Enhancement Factor Vs. Re (Backwall)

e/Dh = 0.067

e/Dh = 0.084

e/Dh = 0.101

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

0 5000 10000 15000 20000 25000 30000 35000 40000

EF

Re

Rig 2 Enhancement Factor Vs. Re (Nose)

e/Dh = 0.067

e/Dh = 0.084

e/Dh = 0.101

43

Figure 30 is a plot of Cold Friction Factor vs. Re for the 3 different blockage ratios. Once again, similar to

rig 1, the Darcy friction factor trends upwards with blockage ratios. The Darcy friction factor for rig 2 is

less than that of rig 1, indicating the pressure loss across the channel is less for rig 2.

Figure 30: Rig 2 Friction Factor Vs. Reynolds Number

Test Rig 3A

The next series of plots measure the heat transfer coefficient, friction factor, and enhancement factors

of test section 3A. For rig 3A, the 3 different blockage ratios considered are 0.051, 0.063, and 0.076.

Figure 31 below shows the backwall Nusselt Number for the 3 blockage ratios for a range of Reynolds

Numbers. In general, an increase in blockage ratio would result in an increase in heat transfer

coefficient. As shown in figure 22, the Nusselt Number along the backwall does not vary much for

blockage ratios 0.051 and 0.063, but for blockage of 0.076, there is a much larger increase in heat

transfer coefficient. On average, the difference in Nusselt Number between blockage of 0.051 and 0.063

is 3.5%, whereas the average difference in Nusselt Number between blockage of 0.063 and 0.076 is

around 11%. It is suggested that the large blockage increases the heat transfer coefficient by creating

turbulence and enhancing mixing.

0

0.1

0.2

0.3

0.4

0.5

0 10000 20000 30000 40000 50000

f

Re

Rig 2 Cold Friction Factor Vs. Re

e/Dh = .101 (Darcy)

e/Dh = .084 (Darcy)

e/Dh = .067 (Darcy)

e/Dh = .101 (Smooth)

e/Dh = .084 (Smooth)

e/Dh = .067 (Smooth)

44

Figure 31: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall)

Figure 32 plots the Nusselt Number Vs. Reynolds Number for the nose section for rig 3A. Similar to the

backwall Nusselt Number trend, the nose exhibits a similar trend. Comparing blockage ratios of 0.051

and 0.063, the difference in Nusselt Number is minimal, whereas between a blockage of 0.051 and

0.063, the Nusselt Number is slightly more distinct. Between blockage of 0.051 and 0.063, there is only a

difference of about 3.5%, and between a blockage of 0.063 and 0.076, there is a difference of 11.2%.

This indicates, like the case with the backwall heat transfer, the large blockage helps to promote a

higher Nusselt Number or heat transfer coefficient.

50

75

100

125

150

175

200

225

250

275

300

0 10000 20000 30000 40000 50000

Nu

Re

Rig 3A Nusselt Number Vs. Re (Backwall)

e/Dh = 0.051

e/Dh = 0.063

e/Dh = 0.076

45

Figure 32: Rig 3A Nusselt Number Vs. Reynolds Number (Nose)

Figure 33 plots rig 3A Nusselt Number vs. Reynolds Number for both the backwall and nose. The nose,

similar to rig 1, is significantly much higher than that of the backwall, anywhere from 7%-30% higher

depending on the Reynolds Number and blockage ratio. Figure 33 also indicates that at the minimum

and medium blockage ratios, the Nusselt Numbers are very similar to each other. The Nusselt Number at

the maximum blockage ratio is substantially higher than that of at the minimum and medium blockage

ratio. This trend will not be beneficial from a manufacturing viewpoint, because it shows that as the

casting die wears from maximum to medium dimension, the thermal performance of the airfoil will

degrade significantly. Nevertheless, similar to rig 1, rig 3A will be an ideal design that has the leading

edge as the hottest area during turbine operation, since the nose has a higher heat transfer than at the

backwall.

50

75

100

125

150

175

200

225

250

275

300

0 10000 20000 30000 40000 50000

Nu

Re

Rig 3A Nusselt Number Vs. Re (Nose)

e/Dh = 0.051

e/Dh = 0.063

e/Dh = 0.076

46

Figure 33: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)

Figure 34 and Figure 35 highlight the enhancement factors for both the backwall and nose sections for

rig 3A. Comparing the backwall and nose sections, the nose has a higher enhancement factor than the

backwall by on average 17.7% across the span of Reynolds Numbers. Usually for turbine blade design,

the leading edge of a blade is the life limiting area due to high thermal stress. Rig 3A exhibits a

turbulator and cavity design that will help improve the heat transfer in the leading edge due to the

higher enhancement factor at the nose.

50

75

100

125

150

175

200

225

250

275

300

0 10000 20000 30000 40000 50000

Nu

Re

Rig 3A Nusselt Number Vs. Re (Backwall Vs. Nose)

e/Dh = 0.051 (backwall)

e/Dh = 0.063 (backwall)

e/Dh = 0.076 (backwall)

e/Dh = 0.051 (nose)

e/Dh = 0.063 (nose)

e/Dh = 0.076 (nose)

47

Figure 34: Rig 3A Enhancement Factor Vs. Reynolds Number (Backwall)

Figure 35: Rig 3A Enhancement Factor Vs. Reynolds Number (Nose)

2.000

2.250

2.500

2.750

3.000

3.250

3.500

3.750

4.000

0 10000 20000 30000 40000 50000

EF

Re

Rig 3A Enhancement Factor Vs. Re (Backwall)

e/Dh = 0.051

e/Dh = 0.063

e/Dh = 0.076

2.000

2.250

2.500

2.750

3.000

3.250

3.500

3.750

4.000

0 10000 20000 30000 40000 50000

EF

Re

Rig 3A Enhancement Factor Vs. Re (Nose)

e/Dh = 0.051

e/Dh = 0.063

e/Dh = 0.076

48

Figure 36 shows the Cold Friction Factor for the 3 blockage ratios for a range of Reynolds Numbers. As

the blockage increases, so does the Cold Darcy friction factor. This trend is similar to the Darcy friction

factor trends for rigs 1 and 2. It is also important to note that the difference in Darcy friction factors

between the medium and lowest blockage is not as high as the difference between the highest and

medium blockage. This can be due to minor experimental variation or if the trend is indeed real, a

significant increase in Darcy friction factor at higher blockage ratios.

Figure 36: Rig 3A Friction Factor Vs. Reynolds Number

Test Rig 3B

For test rig 3B, the same blockage ratios were analyzed as test rig 3A. Test rigs 3A and 3B essentially

have the same geometric cross sections. The only difference is that for test rig 3B, the wall opposite of

the measured wall for rig 3A, is now being measured. The nose section in rig 3B is the same as 3A and

the heat transfer is assumed the same as rig 3A, and will not be assessed for rig 3B.

Figure 37 demonstrates the heat transfer capability of the backwall for rig 3B. The trend is similar to the

other test rigs in that as the blockage ratio increases, so does the heat transfer coefficient. However,

once again, as the highest blockage is approached, the difference in heat transfer capability between the

highest and medium blockage is minimal and is on the average of around 2%. The difference in Nusselt

0

0.1

0.2

0.3

0.4

0.5

0 10000 20000 30000 40000 50000

f

Re

Rig 3A Cold Friction Factor Vs. Re

e/Dh = .076 (Darcy)

e/Dh = .063 (Darcy)

e/Dh = .051 (Darcy)

e/Dh = .076 (Smooth)

e/Dh = .063 (Smooth)

e/Dh = .051 (Smooth)

49

Number between the medium and smallest blockage is much higher in the order of around 8%. This

suggests that the higher blockage ratio does not necessarily lead to higher heat transfer coefficient and

in some cases the higher rib height may produce recirculation zones underneath the ribs that reduce the

heat transfer benefit.

Figure 37: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall)

Figure 38 shows Rig 3B Nusselt Number Vs. Reynolds Number for both the backwall and the nose

surfaces. The nose has a higher Nusselt Number than that of the backwall for mostly across the entire

range of Reynolds Numbers and blockage ratios, ranging anywhere from 0% to 16%. At the medium and

maximum blockage ratios, the backwall Nusselt Numbers are very similar, and at the minimum and

medium blockage ratios, the nose Nusselt Numbers are not much different from each other. This

indicates that if the wall turbulators are designed to max tolerance and the nose turbulators are

designed to nominal tolerance, any minimal wear to the casting die over time will not have a significant

heat transfer impact within the leading edge airfoil cavity.

50

75

100

125

150

175

200

225

250

275

300

0 10000 20000 30000 40000 50000

Nu

Re

Rig 3B Nusselt Number Vs. Re (Backwall)

e/Dh = 0.051

e/Dh = 0.063

e/Dh = 0.076

50

Figure 38: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose)

Figure 39 shows the enhancement factor for the 3 different blockage ratio over a range of Reynolds

Numbers for rig 3B. It can be seen that as the blockage ratio increases, so does the enhancement factor.

However, as demonstrated by figure 30 for rig 3A, the enhancement at higher blockage ratios is not as

much as it is at lower blockage ratios. Going from the medium blockage to the highest blockage, the

enhancement in heat transfer performance is only about 2.7%, where going from the smallest blockage

to the medium blockage, the enhancement is greater at roughly 8%. This is indicative that there is an

optimum blockage that provides the best heat transfer benefit.

50

75

100

125

150

175

200

225

250

275

300

325

0 10000 20000 30000 40000 50000

Nu

Re

Rig 3B Nusselt Number Vs. Re (Backwall Vs. Nose)

e/Dh = 0.051 (backwall)

e/Dh = 0.063 (backwall)

e/Dh = 0.076 (backwall)

e/Dh = 0.051 (nose)

e/Dh = 0.063 (nose)

e/Dh = 0.076 (nose)

51

Figure 39: Rig 3B Enhancement Vs. Reynolds Number (Backwall)

Lastly, Figure 40 highlights the friction factor of rig 3B. Essentially, since rigs 3A and 3B share the same

geometric area and cross sectional area, the friction factor for both rigs should be the same. When

comparing Figure 36 and Figure 40, the friction factors are similar, which is to be expected.

2.000

2.250

2.500

2.750

3.000

3.250

3.500

3.750

4.000

0 10000 20000 30000 40000 50000

EF

Re

Rig 3B Enhancement Factor Vs. Re (Backwall)

e/Dh = 0.051

e/Dh = 0.063

e/Dh = 0.076

52

Figure 40: Rig 3B Friction Factor Vs. Reynolds Number

Comparative Study: Rigs 1, 2, 3A, and 3B

In this study, it is essential to compare the heat transfer, friction factors, and thermal performance

between all the rigs. Each rig provides a different performance due to their geometric differences in the

channel and turbulator geometries. This comparative study assesses the Nusselt Number, friction

factors, and thermal performance over a Reynolds’ Number range of 6000 to 40,000 at all blockage

ratios for all four rigs.

In analyzing the backwall for all the rigs, Figure 41 shows that rig 1 demonstrates the highest heat

transfer coefficient based on the Nusselt Number Vs. Reynolds Number relationship. After rig 1, rig 3B,

then, rig 2, and lastly rig 3A have the next highest heat transfer coefficient. This is mostly likely due to

the higher blockage ratios (e/Dh) of rig 1, which helps to promote more turbulence. In terms of blockage

ratios, rig 1 has the highest blockage ratio, followed by rig 2 and then rigs 3A and 3B. If it is safe to

assume that blockage ratio has a large effect on the heat transfer coefficient, one would question why

rig 2 performed similar to rig 3B on the sidewall. It can be suggested that blockage is not the only factor

that impacts the heat transfer coefficient, but also perhaps the pitch or spacing between turbulators.

0

0.1

0.2

0.3

0.4

0.5

0 10000 20000 30000 40000 50000

f

Re

Rig 3B Cold Friction Factor Vs. Re

e/Dh = .076 (Darcy)

e/Dh = .063 (Darcy)

e/Dh = .051 (Darcy)

e/Dh = .076 (Smooth)

e/Dh = .063 (Smooth)

e/Dh = .051 (Smooth)

53

Looking at Table 2 and Table 3, it can be seen that rig 2 turbulator pitch to rib height ratio is slightly

higher than rigs 3A and 3B, however, the actual turbulator spacing from the test geometry indicates that

rig 2 has a slightly smaller turbulator spacing than rigs 3A and 3B by about .070”. This slight difference in

turbulator spacing between rigs 2 and 3B may influence the heat transfer capability. As indicated in

Taslim and Lengkong (1999), one of the findings was that if the turbulator spacing was too close it

actually reduced the heat transfer coefficient due to the introduction of wakes behind the turbulators.

This prevents the flow from reattaching to the backwall easily and reduces the local heat transfer

coefficient.

0

50

100

150

200

250

300

350

400

0 10000 20000 30000 40000 50000

Nu

Re

Nusselt Number Vs. Re (Backwall, Min e/Dh)

Rig 1 Wall Min e/Dh

Rig 2 Wall Min e/Dh

Rig 3A Wall Min e/Dh

Rig 3B Wall Min e/Dh

54

Figure 41: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall)

0

50

100

150

200

250

300

350

400

0 10000 20000 30000 40000 50000

Nu

Re

Nusselt Number Vs. Re (Backwall, Med e/Dh)

Rig 1 Wall Med e/Dh

Rig 2 Wall Med e/Dh

Rig 3A Wall Med e/Dh

Rig 3B Wall Med e/Dh

0

50

100

150

200

250

300

350

400

0 10000 20000 30000 40000 50000

Nu

Re

Nusselt Number Vs. Re (Backwall, Max e/Dh)

Rig 1 Wall Max e/Dh

Rig 2 Wall Max e/Dh

Rig 3A Wall Max e/Dh

Rig 3B Wall Max e/Dh

55

Figure 42 compares the heat transfer capability at the nose sections for all the rigs. Similar to the trend

seen in Figure 41 on the backwall, rig 1 nose possesses the highest heat transfer coefficient. Rig 3A and

3B nose is slightly higher than rig 2 nose. It is important to note again that since rigs 3A and 3B have the

same channel and turbulator geometry, the results at the nose apply to both rigs 3A and 3B. The reason

why rigs 3A and 3B nose has slightly higher heat transfer coefficient than rig 2, can be attributed to

possibly the smaller pitch or turbulator spacing in rig 2. As mentioned previously, though rig 2 has a

higher blockage, the slightly smaller pitch, may actually reduce the heat transfer coefficient overall,

because it may not allow the flow to reattach to the nose surface after going over the turbulators.

0

50

100

150

200

250

300

350

400

0 10000 20000 30000 40000 50000

Nu

Re

Nusselt Number Vs. Re (Nose, Min e/Dh)

Rig 1 Nose Min e/Dh

Rig 2 Nose Min e/Dh

Rig 3A/3B Nose Min e/Dh

56

Figure 42: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose)

0

50

100

150

200

250

300

350

400

0 10000 20000 30000 40000 50000

Nu

Re

Nusselt Number Vs. Re (Nose, Med e/Dh)

Rig 1 Nose Med e/Dh

Rig 2 Nose Med e/Dh

Rig 3A/3B Nose Med e/Dh

0

50

100

150

200

250

300

350

400

0 10000 20000 30000 40000 50000

Nu

Re

Nusselt Number Vs. Re (Nose, Max e/Dh)

Rig 1 Nose Max e/Dh

Rig 2 Nose Max e/Dh

Rig 3A/3B Nose Max e/Dh

57

Figure 43 and Figure 44 show the enhancement factor for all the rigs at the backwall and nose sections.

The enhancement factor is greatest for rig 1 at both the backwall and nose sections. After rig 1, at the

backwall, rig 3B has the next highest enhancement factor, and then, followed by rig 2 and rig 3A, which

have similar enhancement factors at the backwall. At the nose location, rig 1 has the highest

enhancement factor, followed by rigs 3A and 3B, and lastly rig 2. Rigs 3A and 3B have a slightly higher

enhancement factor than rig 2 due to once again the minimal difference in turbulator spacing.

2

2.5

3

3.5

4

4.5

5

5.5

0 10000 20000 30000 40000 50000

EF

Re

Enhancement Factor Vs. Re (Backwall, Min e/Dh)

Rig 1 Wall Min e/Dh

Rig 2 Wall Min e/Dh

Rig 3A Wall Min e/Dh

Rig 3B Wall Min e/Dh

2

2.5

3

3.5

4

4.5

5

5.5

0 10000 20000 30000 40000 50000

EF

Re

Enhancement Factor Vs. Re (Backwall, Med e/Dh)

Rig 1 Wall Med e/Dh

Rig 2 Wall Med e/Dh

Rig 3A Wall Med e/Dh

Rig 3B Wall Med e/Dh

58

Figure 43: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall)

2

2.5

3

3.5

4

4.5

5

5.5

0 10000 20000 30000 40000 50000

EF

Re

Enhancement Factor Vs. Re (Backwall, Max e/Dh)

Rig 1 Wall Max e/Dh

Rig 2 Wall Max e/Dh

Rig 3A Wall Max e/Dh

Rig 3B Wall Max e/Dh

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 10000 20000 30000 40000 50000

EF

Re

Enhancement Factor Vs. Re (Nose, Min e/Dh)

Rig 1 Nose Min e/Dh

Rig 2 Nose Min e/Dh

Rig 3A/3B Nose Min e/Dh

59

Figure 44: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose)

In Figure 45, the cold friction factors are plotted up against the Reynolds Number for all four test rigs at

the minimum, medium, and maximum blockage ratios. In general, the Darcy Friction Factor increases

with increasing blockage ratio as expected. At medium and maximum blockage ratios, Rig 1 has the

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 10000 20000 30000 40000 50000

EF

Re

Enhancement Factor Vs. Re (Nose, Med e/Dh)

Rig 1 Nose Med e/Dh

Rig 2 Nose Med e/Dh

Rig 3A/3B Nose Med e/Dh

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 10000 20000 30000 40000 50000

EF

Re

Enhancement Factor Vs. Re (Nose, Max e/Dh)

Rig 1 Nose Max e/Dh

Rig 2 Nose Max e/Dh

Rig 3A/3B Nose Max e/Dh

60

highest Darcy friction factor, followed by rig 3A and 3B, and lastly, rig 2. The reason why Rig 1’s friction

factor is the highest is because, it has the highest rib height to hydraulic diameter ratio out of all the rigs.

A higher e/Dh usually increases the friction factor. One interesting results is why rigs 3A/3B have a

higher friction factor than rig 2. According to tables 2 and 3, rig 2 has a higher e/Dh than rigs 3A/3B, so

as a result, the assumption is that rig 2 should have a higher friction factor. Though, rigs 2 and 3 may

have slightly rib-to-rib spacing, the differences are not great enough to show why rig 2 friction factor is

less than that of rigs 3A and 3B. The reason is most likely to the geometric differences in the cross

sectional areas between rigs 2 and 3A/3B. Rig 2 has a more asymmetrical cross sectional area and has

the turbulators lying at angle to the incoming flow, while rigs 3A/3B has the wall and nose turbulators

lying more perpendicular to the incoming flow, which may lead to higher pressure drop. The higher

pressure drop in rigs 3A/3B is the most likely reason why it has a higher friction factor than that of rig 2.

In turbine blade design, a high pressure drop is usually not recommended, because it usually requires

more cooling flow to cool the entire cavity. This takes away precious cooling from other turbine

hardware downstream of the jet engine, and thus, not recommended.

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0 10000 20000 30000 40000 50000 60000

f

Re

Friction Factor Vs. Re (Min e/Dh)

Rig 1 Min e/Dh (Darcy)

Rig 1 Min e/Dh (smooth)

Rig 2 Min e/Dh (Darcy)

Rig 2 Min e/Dh (Smooth)

Rig 3A Min e/Dh (Darcy)

Rig 3A Min e/Dh (Smooth)

Rig 3B Min e/Dh (Darcy)

Rig 3B Min e/Dh (Smooth)

61

Figure 45: Friction Factor Vs Reynolds Number for All Rigs at All Blockage Ratios

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0 10000 20000 30000 40000 50000 60000

f

Re

Friction Factor Vs. Re (Med e/Dh)

Rig 1 Med e/Dh (Darcy)

Rig 1 Med e/Dh (smooth)

Rig 2 Med e/Dh (Darcy)

Rig 2 Med e/Dh (Smooth)

Rig 3A Med e/Dh (Darcy)

Rig 3A Med e/Dh (Smooth)

Rig 3B Med e/Dh (Darcy)

Rig 3B Med e/Dh (Smooth)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0 10000 20000 30000 40000 50000 60000

f

Re

Friction Factor Vs. Re (Max e/Dh)

Rig 1 Max e/Dh (Darcy)

Rig 1 Max e/Dh (smooth)

Rig 2 Max e/Dh (Darcy)

Rig 2 Max e/Dh (Smooth)

Rig 3A Max e/Dh (Darcy)

Rig 3A Max e/Dh (Smooth)

Rig 3B Max e/Dh (Darcy)

Rig 3B Max e/Dh (Smooth)

62

The thermal performance of each test section is also calculated. The thermal performance takes into

account not only the heat transfer enhancement, but also the pressure drop across the test section

length. Thermal performance can be calculated using eq. 1.19. Figure 46 shows the thermal

performance at the heated wall for all four test rigs for minimum, nominal, and maximum blockage

ratios. It is important to note for this comparison, the blockage ratios are specific to each test section as

specified in tables 1-3.

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10000 20000 30000 40000 50000

TP

Re

Thermal Performance Vs. Re (Backwall, Min e/Dh)

Rig 1 Min Wall e/Dh

Rig 2 Min Wall e/Dh

Rig 3A Min Wall e/Dh

Rig 3B Min Wall e/Dh

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10000 20000 30000 40000 50000

TP

Re

Thermal Performance Vs. Re (Backwall, Med e/Dh)

Rig 1 Med Wall e/Dh

Rig 2 Med Wall e/Dh

Rig 3A Med Wall e/Dh

Rig 3B Med Wall e/Dh

63

Figure 46: Thermal Performance of All Four Test Sections at Backwall at All Blockage Ratios

Figure 46 shows that rigs 2 has the highest thermal performance at the wall out of all the test sections at

all blockage ratios. Rig 1 has the second highest thermal performance, Rig 3B has the 3rd highest, and rig

3A has the lowest thermal performance at the wall. Rig 2 has the highest thermal performance, because

it has a very low friction factor. Rig 1 has the next highest thermal performance, because of its blockage

ratio is much higher than that of the other rigs, which increases the enhancement factor. However, the

higher blockage ratio induces a higher pressure drop across the test channel, which slightly reduces the

overall thermal performance of rig 1. It is important to note that though rigs 3A and 3B share the same

blockage ratio, rig 3B has a higher thermal performance than rig 3A, because rig 3B has a smaller

backwall surface area for convection. Smaller surface area results in a higher heat transfer coefficient,

which means higher Nusselt Number and higher thermal performance.

The thermal performance at the nose is also determined for all four test sections for minimum, nominal,

and maximum blockage ratios. Figure 47 below compares the thermal performance for each test

section.

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10000 20000 30000 40000 50000

TP

Re

Thermal Performance Vs. Re (Backwall, Max e/Dh)

Rig 1 Max Wall e/Dh

Rig 2 Max Wall e/Dh

Rig 3A Max Wall e/Dh

Rig 3B Max Wall e/Dh

64

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Thermal Performance Vs. Re (Nose, Min e/Dh)

Rig 1 Min Nose e/Dh

Rig 2 Min Nose e/Dh

Rig 3A/3B Min Nose e/Dh

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Thermal Performance Vs. Re (Nose, Med e/Dh)

Rig 1 Med Nose e/Dh

Rig 2 Med Nose e/Dh

Rig 3A/3B Med Nose e/Dh

65

Figure 47: Thermal Performance of All Four Test Sections at Nose at All Blockage Ratios

Figure 47 shows that the thermal performance at the nose is highest for rig 1 for all blockage ratios and

at all Reynolds numbers at the nose. Rig 2 has the next highest thermal performance. Rigs 3A and 3B

follow closely behind rig 2. At higher Reynolds Numbers, rigs 3A and 3B have equivalent or slightly

higher thermal performance than rig 2. The thermal performance trends slightly downwards with higher

blockage ratio for all test sections. This is due to the higher pressure drop across the test channel with

larger blockage ratios.

Another interesting comparison to observe is the thermal performance between backwall and nose for

each rig for minimum, nominal, and maximum blockage ratios.

Figure 48 looks at the thermal performance for rig 1 backwall and nose at the three blockage ratios.

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Thermal Performance Vs. Re (Nose, Max e/Dh)

Rig 1 Max Nose e/Dh

Rig 2 Max Nose e/Dh

Rig 3A/3B Max Nose e/Dh

66

Figure 48: Rig 1 Thermal Performance Vs. Re (Backwall and Nose)

Figure 48 shows that the thermal performance of the nose is higher than that of the backwall. On

average, at minimum e/Dh, the nose is 37% higher than that of the backwall; at nominal e/Dh, the nose

is 34.6% higher than that of the backwall; at maximum e/Dh, the nose is 31.2% higher than that of the

backwall. This trend indicates that as the blockage increases, the thermal performance decreases. This is

due to the increase in pressure drop due to the higher blockage. In addition, as the blockage increases,

the nose’s thermal performance seems to decrease relatively more than that of the backwall. This

behavior would not be beneficial to die wear, as it indicates that as the die wears overtime, the

performance of subsequent cast airfoils would decrease. Regardless, rig 1 would still be an ideal design,

where the nose needs more cooling than that of the backwall, to meet life requirements.

Figure 49 highlights the thermal performance of rig 2 backwall and nose.

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Rig 1 Thermal Performance Vs. Re

Rig 1 Min Wall e/Dh

Rig 1 Nom Wall e/Dh

Rig 1 Max Wall e/Dh

Rig 1 Nose Min e/Dh

Rig 1 Nom Nose e/Dh

Rig 1 Max Nose e/Dh

67

Figure 49: Rig 2 Thermal Performance Vs. Re (Backwall and Nose)

Figure 49 shows that, unlike rig 1, the wall and nose thermal performance are relatively similar. On

average across the range of Reynolds Number, at minimum e/Dh, the nose is 1% higher than that of the

backwall; at nominal e/Dh, the nose is 1.1% higher than that of the backwall; at maximum e/Dh, the

nose is 2.3% higher than that of the backwall. One thing to note is that at the lower Reynolds Number,

the nose is higher than that of the backwall, but as the Reynolds Number crosses beyond around 15,000,

the backwall thermal performance seems to exceed that of the nose. Rig 2 would be the optimal design

for balance in thermal performance on both the backwall and nose.

Figure 50 below plots the thermal performance vs. Reynolds Number for Rig 3 backwall and nose.

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Rig 2 Thermal Performance Vs. Re

Rig 2 Min Wall e/Dh

Rig 2 Nom Wall e/Dh

Rig 2 Max Wall e/Dh

Rig 2 Nose Min e/Dh

Rig 2 Nom Nose e/Dh

Rig 2 Max Nose e/Dh

68

Figure 50: Rig 3A Thermal Performance Vs. Re (Backwall and Nose)

Figure 50 shows that the nose has a higher thermal performance than that of the backwall. On average

across the range of Reynolds Numbers, at the minimum e/Dh, the nose’s thermal performance is 18.2%

higher than that of the backwall; at the nominal e/Dh, the nose is 21.8% higher than that of the

backwall; at the maximum e/Dh, the nose is 22.2% higher than that of the backwall. One interesting

finding to note is that, compared to rig 1 nose, the thermal performance for rig 3A nose does not

decrease as much with increasing Reynolds’ Number. This is beneficial to an airfoil engineer, because it

means that the airfoil’s thermal performance will not degrade much with increasing flow velocity or

engine operation.

Figure 51 shows the thermal performance of rig 3B’s backwall and nose.

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Rig 3A Thermal Performance Vs. Re

Rig 3A Min Wall e/Dh

Rig 3A Nom Wall e/Dh

Rig 3A Max Wall e/Dh

Rig 3A Nose Min e/Dh

Rig 3A Nom Nose e/Dh

Rig 3A Max Nose e/Dh

69

Figure 51: Rig 3B Thermal Performance vs. Re (Backwall and Nose)

Figure 51 depicts, similar to rig 2, the thermal performance of rig 3B backwall and nose are similar to

each other across the range of Reynolds Numbers. On average across the range of Reynolds Numbers, at

the minimum e/Dh, the nose is 7.2% higher than that of the backwall; at the nominal e/Dh, the nose is

1.6% higher than that of the backwall; at the maximum e/Dh, the nose is 10.4% higher than that of the

backwall. This type of design is a very well balanced configuration, which provides almost equivalent

thermal performance to both the backwall and the nose areas.

In conclusion, rig 1 has the highest potential thermal performance at the leading edge nose, while rig 2

has the highest thermal performance at the backwall. Rigs 2 and 3B have a relatively well balanced

configuration in that in provides almost equivalent thermal performance on both the backwall and nose

areas. Rigs 1 and 3A, on the other hand, provide better thermal performance at the nose surfaces. One

key learning from these results is that though, higher Nusselt Number is indicative of high heat transfer

capability, it is also important to observe the pressure drop as well. Thus, the reason why thermal

performance is examined in this study. In turbine blade design, there exists a tradeoff between heat

transfer coefficient and pressure drop. Higher pressure drop requires more cooling flow to be able to

drive the cooling air from the inlet to the exit of the cooling channels. As a result, this reduces the

overall engine performance and more bleed air needs to be taken from the compressor to cool the

turbine section. A good design is where the heat transfer enhancement is high, but the pressure drop

across the channel is minimized.

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 10000 20000 30000 40000 50000

TP

Re

Rig 3B Thermal Performance vs. Re

Rig 3B Min Wall e/Dh

Rig 3B Nom Wall e/Dh

Rig 3B Max Wall e/Dh

Rig 3B Nose Min e/Dh

Rig 3B Nom Nose e/Dh

Rig 3B Max Nose e/Dh

70

Conclusions

In this study, 45° wall turbulators and 90° nose turbulators at various blockage ratios for 4 different test

sections were assessed. It looked at how the blockage ratio and the pitch to turbulator height ratio

affected the heat transfer coefficient, friction factor, and the enhancement factors of the wall and nose

sections between turbulators. The following are the conclusions from this study:

1. Rig 1 has the highest thermal performance at the nose at all blockage ratios. Rig 2 has the

highest thermal performance at the backwall at all blockage ratios.

2. Rig 1 had the highest friction factor across the range of Reynolds Numbers. Rig 2 had the lowest.

3. As the blockage ratio increased, so did the heat transfer coefficient and friction factors. It was

noted, however, that as the blockage ratio increased to the maximum blockage the heat

transfer benefit was reduced.

4. The turbulator spacing was suggested to have a potential impact on the overall heat transfer

coefficient as demonstrated by looking at the results between rigs 2 and 3A and 3B. Though, rigs

3A and 3B possessed smaller blockage ratios than rig 2, the fact that the turbulator spacing of rig

3 was slightly larger may have increased the heat transfer coefficient slightly beyond that of rig

2.

5. To validate the test results and trends seen from this experiment, it is recommended that a

future effort be conducted to model each test section and perform a CFD analysis.

71

References

[1] Taslim, M.E., and Lengkong A., 1999, “ 45 deg Round-Corner Rib Heat Transfer Coefficient

Measurements in a Square Channel”, ASME Journal of Turbomachinery, Vol. 121.

[2] Domaschke, Norbert, Wolfersdorf, Jens von, and Semmler, Klaus, 2012, “Heat Transfer and Pressure

Drop Measurements in a Rib Roughened Leading Edge Cooling Channel”, Vol. 134.

[3] Rallabandi Akhilesh P., Alkhamis, Nawaf, and Han, Je-Chin, 2011, “Heat Transfer and Pressure Drop

Measurements for a Square With 45 deg Round-Edged Ribs at High Reynolds Numbers”, Vol. 133

[4] Lau, S.C., McMillin, R.D., Han, J.C., 1991, “Turbulent Heat Transfer and Friction in a Square Channel

With Discrete Rib Turbulators”, Vol. 113.

[5] Dees, Jason E., Bogard, David G., Ledezma, Gustavo A., Laskowski, Gregory M., and Tolpadi, Anil K.,

2012, “Experimental Measurements and Computational Predictions for an Internally Cooled Simulated

Turbine Vane With 90 Degree Rib Turbulators”, Vol 124.

[6] Liu, Yao-Hsien, Huh, Michael, Rhee, Dong-Ho, Han, Je-Chin, and Moon, Hee-Koo, 2009, “Heat

Transfer in Leading Edge, Triangular Shaped Cooling Channels With Angled Ribs Under High Rotation

Numbers”, Vol. 131.

[7] Luo, D.D, Leung, C.W., and Chan T.L., 2004, “Forced convection and flow friction characteristics of air-

cooled horizontal equilateral triangular ducts with ribbed internal surfaces”, Int. J. Heat and Mass

Transfer, 47, pp. 5439-5450

[8] Taslim, M.E., and Bethka, D., 2009, “Experimental and Numerical Impingement Heat Transfer in an

Airfoil Leading-Edge cooling Channel With Cross-Flow”, Vol. 131.

[9] Metzger, D.E., Bunker, R.S., 1990, “Local Heat Transfer in Internally Cooled Turbine Airfoil Leading

Edge Regions: Part I – Impingement Cooling Without Film Coolant Extraction”, ASME Journal of

Turbomachinery, Vol. 112, pp. 451-458

[10] Metzger, D.E., Bunker, R.S., 1990, “Local Heat Transfer in Internally Cooled Turbine Airfoil Leading

Edge Regions: Part II – Impingement Cooling With Film Coolant Extraction”, ASME Journal of

Turbomachinery, Vol. 112, pp. 459-466

[11] Taslim, M.E, Setayeshgar, L., and Spring, S.D., 2001, “An Experimental Evaluation of Advanced

Leading Edge Impingement Coolilng Concepts”, Vol. 123.

[12] Taslim, M.E., Li, T., and Kercher, D.M., 1996. “Experimental Heat Transfer and Friction in Channels

Roughened With Angled, V-Shaped, and Discrete Ribs on Two Opposite Walls”, Vol. 118.

72

[13] Luca, Andrei, Carcasci, Carlo, Soghe, Riccardo Da, Facchini, Bruno, Maiuolo, Francesco, Tarchi,

Lorenzo, and Zecchi, Stefano, 2013, “Heat Transfer Measurements in a Leading Edge Geometry With

Racetrack Holes and Film Cooling Extraction”, Vol. 135.

[14] Kaminski, Deborah A., and Jensen, Michael K. Introduction to Thermal and Fluids Engineering. John

Wiley & Sons, INC. Hoboken, NJ, 2005.

[15] Ozisik M. Necati. Heat Transfer A Basic Approach. McGraw-Hill. New York, NY, 1985.

[16] “CF6-6_engine_cutaway.jpg” . 8 Jan 2007. Photograph. Wikipedia. Web. 18 Mar 2014.

http://en.wikipedia.org/wiki/File:CF6-6_engine_cutaway.jpg

[17] “Turbine blade with a thermal barrier coating”. 11 July 1979. Photograph. Wikipedia. Web. 18 Mar

2014. http://en.wikipedia.org/wiki/File:ThermalBarrierCoating.JPG

73

Appendix A.1: FORTRAN Code for Rig 1

Author: Professor Mohammad Taslim

Check.f File

implicit real*8(a-h,o-z)

real*8 i1,i2,i3,i4,new1,new2,new3,new4

character*25 filename

character*80 title

open(2, file='output.dat', status='old') ! output file

write(6,*)'enter the name of the data file that u',

&' want to check'

read(5,10)filename

10 format(a25)

open(unit=4,file=filename,status='old')

read(4,*)n

do i=1,11

read(4,20)title

20 format(a80,/,/)

enddo

DO I=1,n

read(4,*)Ph1,Pven,Tven,Tin1,Tin2,Tamb,

&V1,i1,V2,i2,V3,i3,SG,Pplen,DP,Pamb,Dthroat

if(Tamb.lt.40.or.Tamb.gt.80)

&write(2,9)Pven,ph1

9 format(' Check Tamb for Pven=',f6.1,' ph1',f6.1)

if(Pamb.lt.29.or.Pamb.gt.32)

&write(2,19)Pven,ph1

19 format(' Check Pamb for Pven=',f6.1,' ph1',f6.1)

if(Tin1.lt.40.or.Pamb.gt.80)

&write(2,29)Pven,ph1

29 format(' Check Tin1 for Pv=',f6.1,' ph1',f6.1)

if(Tin2.lt.40.or.Pamb.gt.80)

&write(2,28)Pven,ph1

28 format(' Check Tin2 for Pv=',f6.1,' ph1',f6.1)

if(old1.eq.0)goto 43

74

new1=V1/i1

new2=V2/i2

new3=V3/i3

err1=abs((new1-old1)/old1)

err2=abs((new2-old2)/old2)

err3=abs((new3-old3)/old3)

if(err1.gt..01)then

write(6,37)pven,ph1

new1=old1

endif

37 format('error in heater 1 entry,Pv,Ph1 #',F4.1,f5.0)

if(err2.gt..01)then

write(6,38)pven,ph1

new2=old2

endif

38 format('error in heater 2 entry,Pv,Ph1 #',F4.1,f5.0)

if(err3.gt..01)then

write(6,39)pven,ph1

new3=old3

endif

39 format('error in heater 3 entry,Pv,Ph1 #',F4.1,f5.0)

43 write(2,41)ph1,v1/i1,v2/i2,v3/i3

write(6,41)ph1,v1/i1,v2/i2,v3/i3

if(flag.eq.1)goto 32

old1=V1/i1

old2=V2/i2

old3=V3/i3

flag=1.

go to 30

32 old1=new1

old2=new2

old3=new3

75

30 continue

ENDDO

41 format(1x,f4.1,4(1x,f7.3))

write(6,*)

write(6,*)' NOTE : THE RESISTANCES FOR ALL HEATERS ARE',

&' IN FILE output.dat'

stop

end

76

Reduce.F File

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,Nu,NoseR,NoseL,Losses

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,

&Side,Top,BOt,NoseR,Perim,Dh

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

FAC1=3.413 ! converts Watts to BTU/hr

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1, FILE='input.dat',STATUS='old')

OPEN(UNIT=4,FILE='nu-plots.dat',STATUS='old')

OPEN(UNIT=5, FILE='uncertain.out',STATUS='old')

OPEN(UNIT=7, FILE='output.dat',STATUS='old')

OPEN(UNIT=8, FILE='friction.out',STATUS='old')

OPEN(UNIT=10,FILE='nu-pictures.dat',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

NoseR=0.504 ! inches

NoseR=NoseR/12. ! feet

Angle=144. ! degrees

RigL=36. ! inches

C

C FIBERGLAS

C

Side=3. ! inches

Side=Side/12. ! feet

C

C PLEXI

C

77

Top=2.813 ! inches

Top=Top/12. ! feet

Pitch=3.72 ! inches

nturb=9

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side+Top

Bot=SQRT(2*(NoseR**2)*(1-COS(Angle*PI/180)))

H1=SQRT((SIDE**2)-(0.5*(Top-Bot))**2)

Area1=0.5*(Top+Bot)*H1

Area2=(PI*(NoseR**2)*(Angle/360))-

&(0.5*Bot*NoseR*COS(0.5*Angle*PI/180))

Across=Area1+Area2

Dh=4*Across/Perim

! EACH HEATER

Hlength=11.

Hlength=Hlength/12.

Hwidth=4.26

Hwidth=Hwidth/12.

Harea=Hlength*Hwidth

Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,

&12.*Top,12.*Bot,12.*Hlength,12.*Hwidth,

&144.*Harea,12.*Perim,144.*ACross,12*Dh,Pitch,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Nose Length=',f8.3,' inches',/,

&2x,'Side 1 (Plexi)=',f8.3,' inches',/,

&2x,'Side 2 (LC)=',f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Bottom Flat Line=',f8.3,' inches',/,

&2x,'Heater Length=',f8.3,' inches',/,

&2x,'Heater Width=',f8.3,' inches',/,

&2x,'Heater area=',f8.3,' Sq.in',/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

! R E A D I N D A T A

78

read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid

Poe=Pitch/TurbH

eoDh=(TurbH/12)/Dh

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

DO 333 I=1,11

READ(1,10)TITLE

WRITE(5,10)TITLE

WRITE(7,10)TITLE

333 WRITE(10,10)TITLE

10 FORMAT(A80,//)

WRITE(10,451)

451 FORMAT(' no. Re Nu h uncer',

&' Nu_smooth EF',/)

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3

&,SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' V1,A1,V2,A2,V3,A3'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,201)V1,A1,V2,A2,V3,A3

201 FORMAT(5X,3(' ',F5.2,' ',F6.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

79

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

Mv=F(Athroat,Pven+Pamb,Tven+460)

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

C HEAT FLUX, BTU/(sqft.hr)

Flux=V2*A2*FAC1/(Harea)

C TOTAL HEAT GENERATED FROMINLET TO cAMERA LOCATION , BTU/hr

Q=(A1*V1+0.5*A2*V2)*FAC1

CALL HTC(Q,Flux,Tm,Tsurf,h,Losses)

TmR=Tm+460.

CALL AIRPROP(TmR,gamm,CONm,VISm,PRm,CPm)

VISm=VISm/3600.

C REYNOLDS NUMBER

Re=4.*Mv/(Perim*VISm)

! NUSSELT NUMBER

Nu=h*Dh/CONm

SmoothNu=0.023*(Re**0.8)*(Prm**0.4)

! ENHACEMENT

EF=Nu/SmoothNu

! NUSSELT NUMBER UNCERTAINTY ANALYSIS

CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,Dthroat,Harea,

&Tsurf,Tin,Losses,Uncer)

WRITE(10,305)testno,Re,Nu,h,uncer,SmoothNu,EF

80

305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)

WRITE(4,*)Re,Nu

WRITE(7,300)Tm,MV,Re

C***************************************************

! DARCY FRICTION FACTOR CALCULATIONS

Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb

Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb

Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/

&(0.5*Rho*(Um**2))

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Inlet Pressure=',f9.4,' psia',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)

STOP

END

81

C**********************************************************************C

SUBROUTINE HTC(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,

&Side,Top,BOt,NoseR,Perim,Dh

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

82

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! BIRK

tinc = 1.0e-03/12. ! BIRK

tadh1= 1.0e-03/12. ! BIRK

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

83

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Top*Hlength ! Top surface

Afront=1.5*Side*Hlength ! Front surface

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

84

C THE POINT IN QUESTION

Anose=1.5*PI*NoseR*(Angle/360)*Hlength ! Nose surface

Aback=1.5*Side*Hlength ! Side surface

C write(6,*)Atop,Afront,Anose,Aback

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=h

htop=0.8*h ! Guess

hnose=h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

C write(6,*)Frtop,Frfront,Frnose,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

85

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fnose=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Ftop*Atop+Fnose*Anose+Ffront*Afront+Fback*Aback

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frnose

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

86

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=h

htop=0.8*h

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' LEADING-EDGE CHANNEL',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

87

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,h,hfront,htop

120 FORMAT(5x,'hside=',F8.3,1X,'hnose=',F8.3,1X,'hfront=',F8.3,1X,

&'htop=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)Fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frnose

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C***************************************************************

SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)

PI=4.*ATAN(1.E00)

W=H1

H=0.5*(Bot+Top)

T(1)=Tsurf + 460.

T(2)=Ttop + 460.

T(3)=Tfront+ 460.

88

T(4)=Tbot + 460.

W=W/(3.*Hlength)

H=H/(3.*Hlength)

C Emissivities

E(1)=.85 ! Liquid Crystal Foil, Back Wall

E(2)=.9 ! Plexiglas, Top Wall

E(3)=.9 ! Plexiglas, Front Wall

E(4)=.85 ! Liquid Crystal Foil, Nose Wall

C

N=4

SIGMA=0.1712E-08

C WRITE(7,150)

150 FORMAT(//,20X,'SHAPE FACTORS',//)

C

F11=0.

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F12=Z1*(Z2+Z3+Z4+Z5)

F14=F12

F13=1.-F11-F12-F14

C

F31=F13

F32=F12

F33=0.

F34=F14

C

DUM=W

W=H

H=DUM

W2=W*W

89

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F21=Z1*(Z2+Z3+Z4+Z5)

F22=0.

F23=F21

F24=1.-F21-F22-F23

C

F41=F21

F42=F24

F43=F23

F44=0.

C

C WRITE(7,110)F11,F12,F13,F14

C WRITE(7,120)F21,F22,F23,F24

C WRITE(7,130)F31,F32,F33,F34

C WRITE(7,140)F41,F42,F43,F44

C

110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,

&5X,'F14=',F6.4,/)

120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,

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

130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,

&5X,'F34=',F6.4,/)

140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,

&5X,'F44=',F6.4,//)

C WRITE(7,160)

160 FORMAT(/,20X,'EMISSIVITIES',//)

C WRITE(7,100)(I,E(I),I=1,N)

C WRITE(7,170)

170 FORMAT(/,20X,'TEMPERATURES IN R',//)

C WRITE(7,100)(I,T(I),I=1,N)

A(1,1)=F11-1./(1.-E(1))

A(1,2)=F12

A(1,3)=F13

90

A(1,4)=F14

C

A(2,1)=F21

A(2,2)=F22-1./(1.-E(2))

A(2,3)=F23

A(2,4)=F24

C

A(3,1)=F31

A(3,2)=F32

A(3,3)=F33-1./(1.-E(3))

A(3,4)=F34

C

A(4,1)=F41

A(4,2)=F42

A(4,3)=F43

A(4,4)=F44-1./(1.-E(4))

C

C WRITE(7,180)

180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)

C WRITE(7,200)((A(I,J),J=1,N),I=1,N)

DO I=1,N

B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))

ENDDO

C WRITE(7,250)

C WRITE(7,100)(I,B(I,1),I=1,N)

200 FORMAT(1X,4E15.6)

250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)

C WRITE(7,55)

55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)

CALL EQSOLVE(A,B,N,N,1)

C WRITE(7,50)

C WRITE(7,100)(I,B(I,1),I=1,N)

DO I=1,N

Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))

ENDDO

Frback =Q(1)

Frtop =Q(2)

Frfront=Q(3)

Frnose=Q(4)

C WRITE(7,350)

C WRITE(7,100)(I,Q(I),I=1,N)

100 FORMAT(4(I3,E15.6))

50 FORMAT(/,20X,'RADIOCITIES',/)

350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)

RETURN

END

C**********************************************************************C

91

SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,Dth,Harea,Tsurf,

&Tin,Losses,Uncer)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 i1,i2,Losses,M1,M2

PI=4.*ATAN(1.E00)

C FAC=491.3744

FAC1=3.413 ! converts Watts to BTU/hr

C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)

C=0.24*0.5215*3600

C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J

P1=Pven+Pamb

T1=Tven+460.0

TI=Tin

TS=Tsurf

a=Harea

f=0.5

ATH=PI*(Dth**2)/4.

DATH=PI*((Dth+0.001)**2)/4. -ATH

h=((FAC1*(V2*i2)/a)-Losses)/

&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+f*V2*i2)))/(C*P1*ATH))

WRITE(5,*)' '

WRITE(5,*)' h =',h,' BUT/hr.sqft.F'

H2=h*h

C

C i2 v2

C ------- - Floss

C a

C -------------------------------------

C sqrt(T1)(i1 v1 + f i2 v2)

C Ts-Ti - -------------------------

C C P1 A_throat

C

DLOSS=0.1*Losses

92

dv1=0.1

dv2=0.1

di1=0.01

di2=0.01

da=1./(32.*32.*144)

dts=0.5

dti=0.5

dt1=0.5

dp1=0.5

Df=0.1

C1=FAC1*(V2*i2/a)-Losses

Q1=C*P1*Ath

Q2=Q1*sqrt(T1)

M1=(Ts-Ti)*Q1

A=FAC1*(i1*v1)

B=FAC1*(i2*v2)

M2=M1-sqrt(T1)*(A+f*B)

DHDF=B*Q1*C1*sqrt(T1)/(M2**2)

DHDTI= C1*(Q1**2)/(M2**2)

DHDTS=-C1*(Q1**2)/(M2**2)

DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))

DHDLOSS=-Q1/M2

DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)

DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)

DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDATH=C1*C*P1*(M2-M1)/(M2**2)

DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)

DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))

ZF=(DF*DHDF)**2

ZA=(DA*DHDA)**2

ZI1=(DI1*DHDI1)**2

ZV1=(DV1*DHDV1)**2

ZI2=(DI2*DHDI2)**2

ZV2=(DV2*DHDV2)**2

ZTS=(DTS*DHDTS)**2

ZTI=(DTI*DHDTI)**2

ZATH=(DATH*DHDATH)**2

93

ZP1=(DP1*DHDP1)**2

ZT1=(DT1*DHDT1)**2

ZLOSS=(DLOSS*DHDLOSS)**2

Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+

&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

RETURN

END

C**********************************************************************C

SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(NDIM,NDIM),B(NDIM,NB)

DO 291 J1=1,NA

C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE

C VALUE IN PIVOTAL COLUMN.

101 TEMP=0.

DO 121 J2=J1,NA

IF(ABS(A(J2,J1))-TEMP) 121,111,111

111 TEMP=ABS(A(J2,J1))

IBIG=J2

121 CONTINUE

IF(IBIG-J1)5001,201,131

C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE

C VALUE IN PIVOT POSITION.

131 DO 141 J2=J1,NA

TEMP=A(J1,J2)

A(J1,J2)=A(IBIG,J2)

141 A(IBIG,J2)=TEMP

DO 161 J2=1,NB

TEMP=B(J1,J2)

94

B(J1,J2)=B(IBIG,J2)

161 B(IBIG,J2)=TEMP

C COMPUTE COEFFICIENTS IN PIVOTAL ROW.

201 TEMP=A(J1,J1)

DO 221 J2=J1,NA

221 A(J1,J2)=A(J1,J2)/TEMP

DO 231 J2=1,NB

231 B(J1,J2)=B(J1,J2)/TEMP

IF(J1-NA)236,301,5001

C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.

236 N1=J1+1

DO 281 J2=N1,NA

TEMP=A(J2,J1)

DO 241 J3=N1,NA

241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)

DO 251 J3=1,NB

251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)

281 CONTINUE

291 CONTINUE

C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.

301 IF(NA-1)5001,5001,311

311 DO 391 J1=1,NB

N1=NA

321 DO 341 J2=N1,NA

341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)

N1=N1-1

IF(N1-1)5001,391,321

391 CONTINUE

5001 CONTINUE

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

95

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

96

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

97

Rig1-reduce-friction.f File

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,Nu,NoseR,NoseL,Losses

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,

&Side,Top,BOt,NoseR,Perim,Dh

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

FAC1=3.413 ! converts Watts to BTU/hr

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1, FILE='input.dat',STATUS='old')

OPEN(UNIT=4,FILE='nu-plots.dat',STATUS='old')

OPEN(UNIT=5, FILE='uncertain.out',STATUS='old')

OPEN(UNIT=7, FILE='output.dat',STATUS='old')

OPEN(UNIT=8, FILE='friction.out',STATUS='old')

OPEN(UNIT=10,FILE='nu-pictures.dat',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

NoseR=0.504 ! inches

NoseR=NoseR/12. ! feet

Angle=144. ! degrees

RigL=36. ! inches

C

C FIBERGLAS

C

Side=3. ! inches

Side=Side/12. ! feet

C

C PLEXI

C

98

Top=2.813 ! inches

Top=Top/12. ! feet

Pitch=3.72 ! inches

nturb=9

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side+Top

Bot=SQRT(2*(NoseR**2)*(1-COS(Angle*PI/180)))

H1=SQRT((SIDE**2)-(0.5*(Top-Bot))**2)

Area1=0.5*(Top+Bot)*H1

Area2=(PI*(NoseR**2)*(Angle/360))-

&(0.5*Bot*NoseR*COS(0.5*Angle*PI/180))

Across=Area1+Area2

Dh=4*Across/Perim

! EACH HEATER

Hlength=11.

Hlength=Hlength/12.

Hwidth=4.26

Hwidth=Hwidth/12.

Harea=Hlength*Hwidth

Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,

&12.*Top,12.*Bot,12.*Hlength,12.*Hwidth,

&144.*Harea,12.*Perim,144.*ACross,12*Dh,Pitch,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Nose Length=',f8.3,' inches',/,

&2x,'Side 1 (Plexi)=',f8.3,' inches',/,

&2x,'Side 2 (LC)=',f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Bottom Flat Line=',f8.3,' inches',/,

&2x,'Heater Length=',f8.3,' inches',/,

&2x,'Heater Width=',f8.3,' inches',/,

&2x,'Heater area=',f8.3,' Sq.in',/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

! R E A D I N D A T A

99

read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid

Poe=Pitch/TurbH

eoDh=(TurbH/12)/Dh

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

DO 333 I=1,11

READ(1,10)TITLE

WRITE(5,10)TITLE

WRITE(7,10)TITLE

333 WRITE(10,10)TITLE

10 FORMAT(A80,//)

WRITE(10,451)

451 FORMAT(' no. Re Nu h uncer',

&' Nu_smooth EF',/)

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3

&,SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' V1,A1,V2,A2,V3,A3'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,201)V1,A1,V2,A2,V3,A3

201 FORMAT(5X,3(' ',F5.2,' ',F6.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

100

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

Mv=F(Athroat,Pven+Pamb,Tven+460)

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

C HEAT FLUX, BTU/(sqft.hr)

Flux=V2*A2*FAC1/(Harea)

C TOTAL HEAT GENERATED FROMINLET TO cAMERA LOCATION , BTU/hr

Q=(A1*V1+0.5*A2*V2)*FAC1

CALL HTC(Q,Flux,Tm,Tsurf,h,Losses)

TmR=Tm+460.

CALL AIRPROP(TmR,gamm,CONm,VISm,PRm,CPm)

VISm=VISm/3600.

C REYNOLDS NUMBER

Re=4.*Mv/(Perim*VISm)

! NUSSELT NUMBER

Nu=h*Dh/CONm

SmoothNu=0.023*(Re**0.8)*(Prm**0.4)

! ENHACEMENT

EF=Nu/SmoothNu

! NUSSELT NUMBER UNCERTAINTY ANALYSIS

CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,Dthroat,Harea,

&Tsurf,Tin,Losses,Uncer)

WRITE(10,305)testno,Re,Nu,h,uncer,SmoothNu,EF

101

305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)

WRITE(4,*)Re,Nu

WRITE(7,300)Tm,MV,Re

C***************************************************

! DARCY FRICTION FACTOR CALCULATIONS

Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb

Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb

Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/

&(0.5*Rho*(Um**2))

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Inlet Pressure=',f9.4,' psia',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)

STOP

END

102

C**********************************************************************C

SUBROUTINE HTC(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,Hlength,H1,Angle,

&Side,Top,BOt,NoseR,Perim,Dh

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

103

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! BIRK

tinc = 1.0e-03/12. ! BIRK

tadh1= 1.0e-03/12. ! BIRK

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

104

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Top*Hlength ! Top surface

Afront=1.5*Side*Hlength ! Front surface

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

105

C THE POINT IN QUESTION

Anose=1.5*PI*NoseR*(Angle/360)*Hlength ! Nose surface

Aback=1.5*Side*Hlength ! Side surface

C write(6,*)Atop,Afront,Anose,Aback

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=h

htop=0.8*h ! Guess

hnose=h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

C write(6,*)Frtop,Frfront,Frnose,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

106

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fnose=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Ftop*Atop+Fnose*Anose+Ffront*Afront+Fback*Aback

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frnose

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

107

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=h

htop=0.8*h

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' LEADING-EDGE CHANNEL',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

108

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,h,hfront,htop

120 FORMAT(5x,'hside=',F8.3,1X,'hnose=',F8.3,1X,'hfront=',F8.3,1X,

&'htop=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)Fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frnose

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C***************************************************************

SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)

PI=4.*ATAN(1.E00)

W=H1

H=0.5*(Bot+Top)

T(1)=Tsurf + 460.

T(2)=Ttop + 460.

T(3)=Tfront+ 460.

109

T(4)=Tbot + 460.

W=W/(3.*Hlength)

H=H/(3.*Hlength)

C Emissivities

E(1)=.85 ! Liquid Crystal Foil, Back Wall

E(2)=.9 ! Plexiglas, Top Wall

E(3)=.9 ! Plexiglas, Front Wall

E(4)=.85 ! Liquid Crystal Foil, Nose Wall

C

N=4

SIGMA=0.1712E-08

C WRITE(7,150)

150 FORMAT(//,20X,'SHAPE FACTORS',//)

C

F11=0.

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F12=Z1*(Z2+Z3+Z4+Z5)

F14=F12

F13=1.-F11-F12-F14

C

F31=F13

F32=F12

F33=0.

F34=F14

C

DUM=W

W=H

H=DUM

W2=W*W

110

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F21=Z1*(Z2+Z3+Z4+Z5)

F22=0.

F23=F21

F24=1.-F21-F22-F23

C

F41=F21

F42=F24

F43=F23

F44=0.

C

C WRITE(7,110)F11,F12,F13,F14

C WRITE(7,120)F21,F22,F23,F24

C WRITE(7,130)F31,F32,F33,F34

C WRITE(7,140)F41,F42,F43,F44

C

110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,

&5X,'F14=',F6.4,/)

120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,

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

130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,

&5X,'F34=',F6.4,/)

140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,

&5X,'F44=',F6.4,//)

C WRITE(7,160)

160 FORMAT(/,20X,'EMISSIVITIES',//)

C WRITE(7,100)(I,E(I),I=1,N)

C WRITE(7,170)

170 FORMAT(/,20X,'TEMPERATURES IN R',//)

C WRITE(7,100)(I,T(I),I=1,N)

A(1,1)=F11-1./(1.-E(1))

A(1,2)=F12

A(1,3)=F13

111

A(1,4)=F14

C

A(2,1)=F21

A(2,2)=F22-1./(1.-E(2))

A(2,3)=F23

A(2,4)=F24

C

A(3,1)=F31

A(3,2)=F32

A(3,3)=F33-1./(1.-E(3))

A(3,4)=F34

C

A(4,1)=F41

A(4,2)=F42

A(4,3)=F43

A(4,4)=F44-1./(1.-E(4))

C

C WRITE(7,180)

180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)

C WRITE(7,200)((A(I,J),J=1,N),I=1,N)

DO I=1,N

B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))

ENDDO

C WRITE(7,250)

C WRITE(7,100)(I,B(I,1),I=1,N)

200 FORMAT(1X,4E15.6)

250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)

C WRITE(7,55)

55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)

CALL EQSOLVE(A,B,N,N,1)

C WRITE(7,50)

C WRITE(7,100)(I,B(I,1),I=1,N)

DO I=1,N

Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))

ENDDO

Frback =Q(1)

Frtop =Q(2)

Frfront=Q(3)

Frnose=Q(4)

C WRITE(7,350)

C WRITE(7,100)(I,Q(I),I=1,N)

100 FORMAT(4(I3,E15.6))

50 FORMAT(/,20X,'RADIOCITIES',/)

350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)

RETURN

END

C**********************************************************************C

112

SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,Dth,Harea,Tsurf,

&Tin,Losses,Uncer)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 i1,i2,Losses,M1,M2

PI=4.*ATAN(1.E00)

C FAC=491.3744

FAC1=3.413 ! converts Watts to BTU/hr

C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)

C=0.24*0.5215*3600

C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J

P1=Pven+Pamb

T1=Tven+460.0

TI=Tin

TS=Tsurf

a=Harea

f=0.5

ATH=PI*(Dth**2)/4.

DATH=PI*((Dth+0.001)**2)/4. -ATH

h=((FAC1*(V2*i2)/a)-Losses)/

&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+f*V2*i2)))/(C*P1*ATH))

WRITE(5,*)' '

WRITE(5,*)' h =',h,' BUT/hr.sqft.F'

H2=h*h

C

C i2 v2

C ------- - Floss

C a

C -------------------------------------

C sqrt(T1)(i1 v1 + f i2 v2)

C Ts-Ti - -------------------------

C C P1 A_throat

C

DLOSS=0.1*Losses

113

dv1=0.1

dv2=0.1

di1=0.01

di2=0.01

da=1./(32.*32.*144)

dts=0.5

dti=0.5

dt1=0.5

dp1=0.5

Df=0.1

C1=FAC1*(V2*i2/a)-Losses

Q1=C*P1*Ath

Q2=Q1*sqrt(T1)

M1=(Ts-Ti)*Q1

A=FAC1*(i1*v1)

B=FAC1*(i2*v2)

M2=M1-sqrt(T1)*(A+f*B)

DHDF=B*Q1*C1*sqrt(T1)/(M2**2)

DHDTI= C1*(Q1**2)/(M2**2)

DHDTS=-C1*(Q1**2)/(M2**2)

DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))

DHDLOSS=-Q1/M2

DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)

DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)

DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDATH=C1*C*P1*(M2-M1)/(M2**2)

DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)

DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))

ZF=(DF*DHDF)**2

ZA=(DA*DHDA)**2

ZI1=(DI1*DHDI1)**2

ZV1=(DV1*DHDV1)**2

ZI2=(DI2*DHDI2)**2

ZV2=(DV2*DHDV2)**2

ZTS=(DTS*DHDTS)**2

ZTI=(DTI*DHDTI)**2

ZATH=(DATH*DHDATH)**2

114

ZP1=(DP1*DHDP1)**2

ZT1=(DT1*DHDT1)**2

ZLOSS=(DLOSS*DHDLOSS)**2

Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+

&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

RETURN

END

C**********************************************************************C

SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(NDIM,NDIM),B(NDIM,NB)

DO 291 J1=1,NA

C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE

C VALUE IN PIVOTAL COLUMN.

101 TEMP=0.

DO 121 J2=J1,NA

IF(ABS(A(J2,J1))-TEMP) 121,111,111

111 TEMP=ABS(A(J2,J1))

IBIG=J2

121 CONTINUE

IF(IBIG-J1)5001,201,131

C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE

C VALUE IN PIVOT POSITION.

131 DO 141 J2=J1,NA

TEMP=A(J1,J2)

A(J1,J2)=A(IBIG,J2)

141 A(IBIG,J2)=TEMP

DO 161 J2=1,NB

TEMP=B(J1,J2)

115

B(J1,J2)=B(IBIG,J2)

161 B(IBIG,J2)=TEMP

C COMPUTE COEFFICIENTS IN PIVOTAL ROW.

201 TEMP=A(J1,J1)

DO 221 J2=J1,NA

221 A(J1,J2)=A(J1,J2)/TEMP

DO 231 J2=1,NB

231 B(J1,J2)=B(J1,J2)/TEMP

IF(J1-NA)236,301,5001

C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.

236 N1=J1+1

DO 281 J2=N1,NA

TEMP=A(J2,J1)

DO 241 J3=N1,NA

241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)

DO 251 J3=1,NB

251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)

281 CONTINUE

291 CONTINUE

C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.

301 IF(NA-1)5001,5001,311

311 DO 391 J1=1,NB

N1=NA

321 DO 341 J2=N1,NA

341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)

N1=N1-1

IF(N1-1)5001,391,321

391 CONTINUE

5001 CONTINUE

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

116

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

117

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

118

Appendix A.2: FORTRAN Codes for Rig 2

Author: Professor Mohammad Taslim

Check.F

character*25 filename

character*80 title

write(6,*)'enter the name of the data file that u',

* ' want to check'

read(5,10)filename

10 format(a25)

open(unit=1,file=filename,status='old')

open(unit=2,file='output.dat',status='old')

write(6,*)'is there a title for this file? enter 1=yes, 0=no'

read(5,*)ans

if(ans.eq.0)goto 30

read(1,*)NTESTS

do i=1,11

read(1,20)title

20 FORMAT(A80,//)

enddo

30 do i=1,NTESTS

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3

&,SG,Pplen,Pinlet,Pamb,Dthroat

if(Tven.lt.45.or.Tven.gt.90)write(6,*)

&' ** CHECK Tven IN TEST ',i

if(Tin1.lt.50.or.Tin1.gt.90)write(6,*)' ** CHECK Tin1 IN TEST '

if(Tin2.lt.50.or.Tin2.gt.90)write(6,*)' ** CHECK Tin2 IN TEST '

if(Tamb.lt.60.or.Tamb.gt.80)write(6,*)' ** CHECK Tamb IN TEST '

if(Pamb.lt.28.or.Pamb.gt.31)write(6,*)' ** CHECK Pamb IN TEST '

if(old1.eq.0)goto 31

err1=abs((v1/a1)-old1)/old1

err2=abs((v2/a2)-old2)/old2

err3=abs((v3/a3)-old3)/old3

if(err1.gt..0125)write(6,*)'error in heater 1 entry, test #'

*,testno

if(err2.gt..0125)write(6,*)'error in heater 2 entry, test #'

*,testno

if(err3.gt..0125)write(6,*)'error in heater 3 entry, test #'

119

*,testno

31 write(6,35)testno,v1/a1,v2/a2,v3/a3

write(2,35)testno,v1/a1,v2/a2,v3/a3

C if(flag.eq.1)goto 32

old1=v1/a1

old2=v2/a2

old3=v3/a3

flag=1.

32 continue

enddo

35 format(2x,f4.0,2x,3(1x,f10.6))

write(6,*)' '

write(6,*)' '

write(6,*)' Resistances are in file : output.dat'

stop

end

120

Reduce.F

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,NuS,NuN,NoseR,NoseL,LossesS,LossesN

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

FAC1=3.413 ! converts Watts to BTU/hr

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1,FILE='input.dat',STATUS='old')

OPEN(UNIT=2,FILE='nu-plots-side.dat',STATUS='old')

OPEN(UNIT=3,FILE='nu-plots-nose.dat',STATUS='old')

OPEN(UNIT=4,FILE='uncertain-side.out',STATUS='old')

OPEN(UNIT=5,FILE='uncertain-nose.out',STATUS='old')

OPEN(UNIT=7,FILE='output.dat',STATUS='old')

OPEN(UNIT=8,FILE='friction.out',STATUS='old')

OPEN(UNIT=9,FILE='nu-pictures-side.dat',STATUS='old')

OPEN(UNIT=10,FILE='nu-pictures-nose.dat',STATUS='old')

OPEN(UNIT=11,FILE='convergence.dat',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

NoseR=0.969 ! inches

NoseR=NoseR/12 ! feet

Angle=125. ! degrees

RigL=36. ! inches

Side=3. ! inches

Side=Side/12 ! feet

121

Side2=3.226 ! inches

Side2=Side2/12 ! feet

C

C CALCULATION

hypo1=sqrt(NoseR**2 + SIDE2**2)

hypo2=sqrt(NoseR**2 + SIDE**2)

beta1=atan(NoseR/SIDE2)*180/PI

beta2=atan(NoseR/SIDE)*180/PI

alpha1=90-beta1

alpha2=90-beta2

gamma1=180-65-alpha1

gamma2=180-60-alpha2

theta1=43.28255

theta2=180-gamma1-gamma2-theta1

sigma1=180-gamma1-theta1

Top=sqrt(hypo1**2 + hypo2**2 -

&2*hypo1*hypo2*COS((gamma1+gamma2)*PI/180))

Pitch=2.418 ! inches

nturb=9

Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +

&NoseR*COS(60*PI/180)

Wave=0.5*Top+NoseR*SIN(60*PI/180)

Bot=NoseR*(SIN(60*PI/180)+SIN(65*PI/180)) ! Flat projected bottom for radiation losses only

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side2+Top

Area1=0.5*NoseR*SIDE2

Area2=0.5*NoseR*SIDE

AreaNose=(PI*(NoseR**2)*(Angle/360))

AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)

Across=Area1+Area2+AreaNose+AreaTop

Dh=4*Across/Perim

! EACH HEATER

122

HlengthS=11.

HlengthS=HlengthS/12.

HwidthS=3.

HwidthS=HwidthS/12.

HareaS=HlengthS*HwidthS

HlengthN=10.9

HlengthN=HlengthN/12.

HwidthN=1.95

HwidthN=HwidthN/12.

HareaN=HlengthN*HwidthN

Write(7,101)12*NoseR,Angle,12*Side,12*Side2,

&12*Top,12*HlengthS,12*HwidthS,144*HareaS,12*HlengthN,

&12*HwidthN,144*HareaN,alpha1,alpha2,beta1,beta2,sigma1,

&gamma1,gamma2,theta1,theta2,12*Perim,144*ACross,12*Dh,

&Pitch,12*Have,12*Wave,12*Bot,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Side 1 (LC)=',f8.3,' inches',/,

&2x,'Side 2 (Plexi)=',f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Side Heater Length=',f8.3,' inches',/,

&2x,'Side Heater Width=',f8.3,' inches',/,

&2x,'Side Heater area=',f8.3,' Sq.in',/,

&2x,'Nose Heater Length=',f8.3,' inches',/,

&2x,'Nose Heater Width=',f8.3,' inches',/,

&2x,'Nose Heater area=',f8.3,' Sq.in',/,

&2x,'alpha1 and alpha2=',f8.3,5x,f8.3,/,

&2x,'beta1 and beta2=',f8.3,5x,f8.3,/,

&2x,'sigma1=',f8.3,/,

&2x,'gamma1 and gamma2=',f8.3,5x,f8.3,/,

&2x,'theta1 and theta2=',f8.3,5x,f8.3,/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Average Test Section Height=',f8.3,' inches',/,

&2x,'Average Test Section Width=',f8.3,' inches',/,

&2x,'Flat projection bottom for rad losses=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

! R E A D I N D A T A

read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid

Poe=Pitch/TurbH

123

eoDh=(TurbH/12)/Dh

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

WRITE(10,401)ntests

401 FORMAT(I4)

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

DO 333 I=1,11

READ(1,10)TITLE

WRITE(5,10)TITLE

WRITE(7,10)TITLE

333 WRITE(10,10)TITLE

10 FORMAT(A80,//)

WRITE(10,451)

451 FORMAT(' no. Re Nu h uncer',

&' Nu_smooth EF',/)

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,

&V4,A4,V5,A5,V6,A6

&,SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' V1,A1,V2,A2,V3,A3'

WRITE(7,*)' V4,A4,V5,A5,V6,A6'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,201)V1,A1,V2,A2,V3,A3

WRITE(7,201)V4,A4,V5,A5,V6,A6

201 FORMAT(5X,3(' ',F5.2,' ',F6.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

124

Athroat=PI*(Dthroat**2)/4. ! square inches

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

Mv=F(Athroat,Pven+Pamb,Tven+460)

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

C HEAT FLUX, BTU/(sqft.hr)

FluxS=V2*A2*FAC1/(HareaS)

FluxN=V5*A5*FAC1/(HareaN)

C TOTAL HEAT GENERATED FROMINLET TO CAMERA LOCATION , BTU/hr

Q=(A1*V1+A4*V4+0.5*A2*V2+0.5*A5*V5)*FAC1

CALL HTCSIDE(Q,FluxS,TmS,TsurfS,hS,LossesS)

CALL HTCNOSE(Q,FluxN,TmN,TsurfN,hN,LossesN)

TmRS=TmS+460.

CALL AIRPROP(TmRS,gammS,CONmS,VISmS,PRmS,CPmS)

VISmS=VISmS/3600.

TmRN=TmN+460.

CALL AIRPROP(TmRN,gammN,CONmN,VISmN,PRmN,CPmN)

VISmN=VISmN/3600.

C REYNOLDS NUMBER

ReS=4.*Mv/(Perim*VISmS)

ReN=4.*Mv/(Perim*VISmN)

! NUSSELT NUMBER

NuS=hS*Dh/CONmS

NuN=hN*Dh/CONmN

RatioNu=NuN/NuS

125

SmoothNuS=0.023*(ReS**0.8)*(PrmS**0.4)

SmoothNuN=0.023*(ReN**0.8)*(PrmN**0.4)

! ENHACEMENT

EFS=NuS/SmoothNuS

EFN=NuN/SmoothNuN

! UNCERTAINTY ANALYSIS

IND=1

CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,A4,V4,A5,V5,

&Dthroat,HareaS,TsurfS,Tin,LossesS,UncerS,IND)

IND=2

CALL UNCERTAIN(Pamb,Pven,Tven,A4,V4,A5,V5,A1,V1,A2,V2,

&Dthroat,HareaN,TsurfN,Tin,LossesN,UncerN,IND)

WRITE( 9,305)testno,ReS,NuS,hS,uncerS,SmoothNuS,EFS

WRITE(10,305)testno,ReN,NuN,hN,uncerN,SmoothNuN,EFN

305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)

WRITE(2,*)ReS,NuS

WRITE(3,*)ReN,NuN

WRITE(7,300)TmS,MV,ReS

WRITE(7,301)TmN,MV,ReN

WRITE(7,302)RatioNu

302 format(5x,'Nu_Nose/Nu_Side=',f8.3)

C***************************************************

! DARCY FRICTION FACTOR CALCULATIONS

Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb

Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb

TmR=0.5*(TmRS+TmRN)

Re=0.5*(ReS+ReN)

Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/

&(0.5*Rho*(Um**2))

fsmooth=0.316/(Re**0.25) ! Blasius correlation

126

write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Inlet Pressure=',f9.4,' psia',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm_Side=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReS=',F8.2)

301 FORMAT(30X,'Tm_Nose=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReN=',F8.2)

STOP

END

C************************************************************************************

**************C

C********************************** ON THE SIDE WALL

**********************************************C

C************************************************************************************

**************C

SUBROUTINE HTCSIDE(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

127

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

128

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! BIRK

tinc = 1.0e-03/12. ! BIRK

tadh1= 1.0e-03/12. ! BIRK

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

129

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Top*HlengthS ! Top surface

Afront=1.5*Side2*HlengthS ! Front surface

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Aback=1.5*Side*HlengthS ! Back surface

Abot =1.5*PI*NoseR*(Angle/360)*HlengthN ! Bottom surface

C write(6,*)Atop,Afront,Abot,Aback

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

130

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=h

htop=0.8*h ! Guess

hbot=1.2*h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Top,Bot,Have,HlengthN,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frbot)

C write(6,*)Frtop,Frfront,Frbot,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

131

Fbot=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frbot

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

132

hfront=h

htop=0.8*h

hbot=1.2*h

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' ON THE SIDE WALL',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',

&/,10x,4F10.2,' F')

133

write(7,120)h,htop,hfront,hbot

120 FORMAT(5x,'hside=',F8.3,1X,'htop=',F8.3,1X,'hfront=',F8.3,1X,

&'hnose=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frbot

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C****************************************************************************C

C****************************ON THE NOSE ************************************C

C****************************************************************************C

SUBROUTINE HTCNOSE(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

134

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

135

tkap = 1.0e-03/12. ! BIRK

tinc = 1.0e-03/12. ! BIRK

tadh1= 1.0e-03/12. ! BIRK

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

136

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Side2*HlengthS ! Top surface (since NOSE is now the back surface)

Afront=1.5*Top*HlengthS ! Front surface (since NOSE is now the back surface)

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Abot =1.5*Side*HlengthS ! Bottom surface

Aback=1.5*PI*NoseR*(Angle/360)*HlengthN ! Back surface

C write(6,*)Aback,Atop,Afront,Abot

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=(0.8/1.2)*h

htop=(1/1.2)*h ! Guess

hbot=(1/1.2)*h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

137

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Side2,Side,Wave,HlengthS,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frbot)

C write(6,*)Frtop,Frfront,Frbot,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fbot=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

138

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frbot

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=(0.8/1.2)*h ! Guess

htop=(1/1.2)*h ! Guess

hbot=(1/1.2)*h ! Guess

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

139

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' ON THE NOSE',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Nose, Top, Front and Back Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,hbot,hfront,htop

120 FORMAT(5x,'hnose=',F8.3,1X,'hback=',F8.3,1X,'htop=',F8.3,1X,

&'hfront=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from Nose, Front, Ftop and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frbot

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

140

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C****************************************************************************

C****************************************************************************

C**********************************************************************C

SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)

PI=4.*ATAN(1.E00)

W=H1

H=0.5*(Bot+Top)

T(1)=Tsurf + 460.

T(2)=Ttop + 460.

T(3)=Tfront+ 460.

T(4)=Tbot + 460.

W=W/(3.*Hlength)

H=H/(3.*Hlength)

C Emissivities

E(1)=.85 ! Liquid Crystal Foil, Back Wall

E(2)=.9 ! Plexiglas, Top Wall

E(3)=.9 ! Plexiglas, Front Wall

E(4)=.85 ! Liquid Crystal Foil, Nose Wall

C

N=4

SIGMA=0.1712E-08

C WRITE(7,150)

150 FORMAT(//,20X,'SHAPE FACTORS',//)

C

F11=0.

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

141

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F12=Z1*(Z2+Z3+Z4+Z5)

F14=F12

F13=1.-F11-F12-F14

C

F31=F13

F32=F12

F33=0.

F34=F14

C

DUM=W

W=H

H=DUM

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F21=Z1*(Z2+Z3+Z4+Z5)

F22=0.

F23=F21

F24=1.-F21-F22-F23

C

F41=F21

F42=F24

F43=F23

F44=0.

C

142

C WRITE(7,110)F11,F12,F13,F14

C WRITE(7,120)F21,F22,F23,F24

C WRITE(7,130)F31,F32,F33,F34

C WRITE(7,140)F41,F42,F43,F44

C

110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,

&5X,'F14=',F6.4,/)

120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,

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

130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,

&5X,'F34=',F6.4,/)

140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,

&5X,'F44=',F6.4,//)

C WRITE(7,160)

160 FORMAT(/,20X,'EMISSIVITIES',//)

C WRITE(7,100)(I,E(I),I=1,N)

C WRITE(7,170)

170 FORMAT(/,20X,'TEMPERATURES IN R',//)

C WRITE(7,100)(I,T(I),I=1,N)

A(1,1)=F11-1./(1.-E(1))

A(1,2)=F12

A(1,3)=F13

A(1,4)=F14

C

A(2,1)=F21

A(2,2)=F22-1./(1.-E(2))

A(2,3)=F23

A(2,4)=F24

C

A(3,1)=F31

A(3,2)=F32

A(3,3)=F33-1./(1.-E(3))

A(3,4)=F34

C

A(4,1)=F41

A(4,2)=F42

A(4,3)=F43

A(4,4)=F44-1./(1.-E(4))

C

C WRITE(7,180)

180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)

C WRITE(7,200)((A(I,J),J=1,N),I=1,N)

DO I=1,N

B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))

ENDDO

C WRITE(7,250)

C WRITE(7,100)(I,B(I,1),I=1,N)

200 FORMAT(1X,4E15.6)

143

250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)

C WRITE(7,55)

55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)

CALL EQSOLVE(A,B,N,N,1)

C WRITE(7,50)

C WRITE(7,100)(I,B(I,1),I=1,N)

DO I=1,N

Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))

ENDDO

Frback =Q(1)

Frtop =Q(2)

Frfront=Q(3)

Frnose=Q(4)

C WRITE(7,350)

C WRITE(7,100)(I,Q(I),I=1,N)

100 FORMAT(4(I3,E15.6))

50 FORMAT(/,20X,'RADIOCITIES',/)

350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)

RETURN

END

C**********************************************************************C

C**********************************************************************C

SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,i4,V4,i5,V5,

&Dth,Harea,Tsurf,Tin,Losses,Uncer,IND)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 i1,i2,i4,i5,Losses,M1,M2

PI=4.*ATAN(1.E00)

C FAC=491.3744

FAC1=3.413 ! converts Watts to BTU/hr

C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)

C=0.24*0.5215*3600

C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J

P1=Pven+Pamb

T1=Tven+460.0

TI=Tin

TS=Tsurf

a=Harea

f=0.5

144

ATH=PI*(Dth**2)/4.

DATH=PI*((Dth+0.001)**2)/4. -ATH

h=((FAC1*(V2*i2)/a)-Losses)/

&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+V4*i4+f*V2*i2+f*V5*i5)))/

&(C*P1*ATH))

WRITE(5,*)' '

if(IND.EQ.1)WRITE(5,*)' hSide =',h,' BUT/hr.sqft.F'

if(IND.EQ.2)WRITE(5,*)' hNose =',h,' BUT/hr.sqft.F'

H2=h*h

C

C i2 v2

C ------- - Floss

C a

C ---------------------------------------

C sqrt(T1)(i1v1+i4v4+fi2v2+fi5v5)

C Ts-Ti - -------------------------

C C P1 A_throat

C

DLOSS=0.1*Losses

dv1=0.1

dv2=0.1

dv4=0.1

dv5=0.1

di1=0.01

di2=0.01

di4=0.01

di5=0.01

da=1./(32.*32.*144)

dts=0.5

dti=0.5

dt1=0.5

dp1=0.5

Df=0.1

C1=FAC1*(V2*i2/a)-Losses

Q1=C*P1*Ath

Q2=Q1*sqrt(T1)

M1=(Ts-Ti)*Q1

A=FAC1*(i1*v1+i4*v4)

145

B=FAC1*(i2*v2+i5*v5)

M2=M1-sqrt(T1)*(A+f*B)

DHDF=B*Q1*C1*sqrt(T1)/(M2**2)

DHDTI= C1*(Q1**2)/(M2**2)

DHDTS=-C1*(Q1**2)/(M2**2)

DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))

DHDLOSS=-Q1/M2

DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)

DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)

DHDI4=FAC1*v4*Q1*C1*sqrt(T1)/(M2**2)

DHDV4=FAC1*i4*Q1*C1*sqrt(T1)/(M2**2)

DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDI5=FAC1*v5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV5=FAC1*i5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDATH=C1*C*P1*(M2-M1)/(M2**2)

DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)

DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))

ZF=(DF*DHDF)**2

ZA=(DA*DHDA)**2

ZI1=(DI1*DHDI1)**2

ZV1=(DV1*DHDV1)**2

ZI2=(DI2*DHDI2)**2

ZV2=(DV2*DHDV2)**2

ZI4=(DI4*DHDI4)**2

ZV4=(DV4*DHDV4)**2

ZI5=(DI5*DHDI5)**2

ZV5=(DV5*DHDV5)**2

ZTS=(DTS*DHDTS)**2

ZTI=(DTI*DHDTI)**2

ZATH=(DATH*DHDATH)**2

ZP1=(DP1*DHDP1)**2

ZT1=(DT1*DHDT1)**2

ZLOSS=(DLOSS*DHDLOSS)**2

Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+ZI4+ZI4+ZV5+ZV5+

&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))

146

if(IND.EQ.1) then

WRITE(4,*)' TOTAL UNCER.%:',Uncer

WRITE(4,*)' '

WRITE(4,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(4,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(4,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(4,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(4,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(4,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h

WRITE(4,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h

WRITE(4,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h

WRITE(4,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h

WRITE(4,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(4,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(4,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(4,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(4,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(4,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(4,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

endif

if(IND.EQ.2) then

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(5,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h

WRITE(5,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h

WRITE(5,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h

WRITE(5,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h

WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

endif

RETURN

END

C**********************************************************************C

147

C**********************************************************************C

SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(NDIM,NDIM),B(NDIM,NB)

DO 291 J1=1,NA

C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE

C VALUE IN PIVOTAL COLUMN.

101 TEMP=0.

DO 121 J2=J1,NA

IF(ABS(A(J2,J1))-TEMP) 121,111,111

111 TEMP=ABS(A(J2,J1))

IBIG=J2

121 CONTINUE

IF(IBIG-J1)5001,201,131

C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE

C VALUE IN PIVOT POSITION.

131 DO 141 J2=J1,NA

TEMP=A(J1,J2)

A(J1,J2)=A(IBIG,J2)

141 A(IBIG,J2)=TEMP

DO 161 J2=1,NB

TEMP=B(J1,J2)

B(J1,J2)=B(IBIG,J2)

161 B(IBIG,J2)=TEMP

C COMPUTE COEFFICIENTS IN PIVOTAL ROW.

201 TEMP=A(J1,J1)

DO 221 J2=J1,NA

221 A(J1,J2)=A(J1,J2)/TEMP

DO 231 J2=1,NB

231 B(J1,J2)=B(J1,J2)/TEMP

IF(J1-NA)236,301,5001

C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.

236 N1=J1+1

DO 281 J2=N1,NA

TEMP=A(J2,J1)

DO 241 J3=N1,NA

241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)

DO 251 J3=1,NB

251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)

281 CONTINUE

291 CONTINUE

C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.

301 IF(NA-1)5001,5001,311

311 DO 391 J1=1,NB

N1=NA

321 DO 341 J2=N1,NA

341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)

148

N1=N1-1

IF(N1-1)5001,391,321

391 CONTINUE

5001 CONTINUE

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

149

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

150

Rig2-reduce-friction.f

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,NoseR,NoseL

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1, FILE='input.dat',STATUS='old')

OPEN(UNIT=5, FILE='fric-uncertain.out',STATUS='old')

OPEN(UNIT=7, FILE='friction-details.out',STATUS='old')

OPEN(UNIT=8, FILE='friction-plot.out',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

! T E S T S E C T I O N G E O M E T R Y

NoseR=0.969 ! inches

NoseR=NoseR/12 ! feet

Angle=125. ! degrees

RigL=36. ! inches

Side=3. ! inches

Side=Side/12 ! feet

Side2=3.226 ! inches

Side2=Side2/12 ! feet

C

C CALCULATION

hypo1=sqrt(NoseR**2 + SIDE2**2)

hypo2=sqrt(NoseR**2 + SIDE**2)

151

beta1=atan(NoseR/SIDE2)*180/PI

beta2=atan(NoseR/SIDE)*180/PI

alpha1=90-beta1

alpha2=90-beta2

gamma1=180-65-alpha1

gamma2=180-60-alpha2

theta1=43.28255

theta2=180-gamma1-gamma2-theta1

sigma1=180-gamma1-theta1

Top=sqrt(hypo1**2 + hypo2**2 -

&2*hypo1*hypo2*COS((gamma1+gamma2)*PI/180))

Pitch=2.418 ! inches

nturb=9

RibbedL=nturb*Pitch

Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +

&NoseR*COS(60*PI/180)

Wave=0.5*Top+NoseR*SIN(60*PI/180)

Bot=NoseR*(SIN(60*PI/180)+SIN(65*PI/180)) ! Flat projected bottom for radiation losses only

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side2+Top

Area1=0.5*NoseR*SIDE2

Area2=0.5*NoseR*SIDE

AreaNose=(PI*(NoseR**2)*(Angle/360))

AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)

Across=Area1+Area2+AreaNose+AreaTop

Dh=4*Across/Perim

read(1,*)ntests,TurbH,TurbW,Turbr

DO 333 I=1,10

READ(1,10)TITLE

WRITE(5,10)TITLE

333 WRITE(7,10)TITLE

10 FORMAT(A80,//)

152

Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,

&12.*Top,12.*Bot,12.*Perim,144.*ACross,12*Dh,Pitch,RigL,

&RibbedL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Nose Length=',f8.3,' inches',/,

&2x,'Side 1 (Plexi)=',f8.3,' inches',/,

&2x,'Side 2 (LC)=',f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Bottom Flat Line=',f8.3,' inches',/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/,

&2x,'Ribbed Length=',f8.3,' inches',/)

Poe=Pitch/TurbH

eoDh=TurbH/(12*Dh)

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

401 FORMAT(I4)

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f9.4,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

! R E A D I N D A T A

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,

&SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

153

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

Mv=F(Athroat,Pven+Pamb,Tven+460)

TinR=Tin+460.

CALL AIRPROP(TinR,gamain,CONin,VISin,PRin,CPin)

VISin=VISin/3600.

C REYNOLDS NUMBER

Re=4.*Mv/(Perim*VISin)

C***************************************************

! DARCY FRICTION FACTOR CALCULATIONS

Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb

Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb

Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TinR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/RibbedL)*((Pinlet-Pamb)*144.)/

&(0.5*Rho*(Um**2))

DeltaP=(Pinlet-Pamb)*144.

CALL UNCERTAIN(Dh,RibbedL,DeltaP,Rho,Um,Uncer)

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,DeltaP,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

154

WRITE(8,304)Re,fDarcy,fsmooth,fDarcy/fsmooth

304 format(f8.1,2(4x,E13.7),F8.3)

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Pressure Drop =',f9.4,' inches of water',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)

STOP

END

C**********************************************************************C

SUBROUTINE UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)

IMPLICIT REAL*8(A-H,O-Z)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

dDh =0.05/12. ! feet

dRigL =0.05 ! inches

dDeltaP=0.001*H2Otopsi*144 ! psf (0.002 inches of water)

dRho =0.02*Rho ! 2% error

dUm =0.02*Um ! 2% error

fDarcy=gc*((12.*Dh)/RigL)*(DeltaP)/

&(0.5*Rho*(Um**2))

f2=fDarcy**2

155

WRITE(5,*)' '

WRITE(5,*)' fDarcy =',fDarcy

WRITE(5,*)' '

C=24*gc

dfdDh=C*DeltaP/(RigL*Rho*(Um**2))

dfdDeltaP=C*Dh/(RigL*Rho*(Um**2))

dfdRigL=-C*Dh*DeltaP/(RigL*RigL*Rho*(Um**2))

dfdRho=-C*Dh*DeltaP/(RigL*Rho*Rho*(Um**2))

dfdUm=-2*C*Dh*DeltaP/(RigL*Rho*(Um**3))

ZDh=(dfdDh*dDh)**2

ZRigL=(dfdRigL*dRigL)**2

ZDeltaP=(dfdDeltaP*dDeltaP)**2

ZRho=(dfdRho*dRho)**2

ZUm=(dfdUm*dUm)**2

Uncer=100*SQRT((ZDh+ZRigL+ZDeltaP+ZRho+ZUm)/(f2))

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with Dh',100.*sqrt(ZDh)/fDarcy

WRITE(5,*)' % Uncer. assoc. with RigL',100.*sqrt(ZRigL)/fDarcy

WRITE(5,*)' % Uncer. assoc. with DeltaP',100.*sqrt(ZDeltaP)/fDarcy

WRITE(5,*)' % Uncer. assoc. with Rho',100.*sqrt(ZRho)/fDarcy

WRITE(5,*)' % Uncer. assoc. with Um',100.*sqrt(ZUm)/fDarcy

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

156

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

157

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C*******************************************************************

158

Appendix A.3: FORTRAN Codes for Rig 3A

Author: Professor Mohammad Taslim

Check.f

character*25 filename

character*80 title

write(6,*)'enter the name of the data file that you',

* ' want to check'

read(5,10)filename

10 format(a25)

open(unit=1,file=filename,status='old')

open(unit=2,file='output.dat',status='old')

write(6,*)'is there a title for this file? enter 1=yes, 0=no'

read(5,*)ans

if(ans.eq.0)goto 30

read(1,*)NTESTS

do i=1,11

read(1,20)title

20 FORMAT(A80,//)

enddo

30 do i=1,NTESTS

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,V4,A4,

&V5,A5,V6,A6,SG,Pplen,DP,Pamb,Dthroat

if(Tven.lt.45.or.Tven.gt.90)write(6,*)

&' ** CHECK Tven IN TEST ',i

if(Tin1.lt.50.or.Tin1.gt.90)write(6,*)' ** CHECK Tin1 IN TEST '

if(Tin2.lt.50.or.Tin2.gt.90)write(6,*)' ** CHECK Tin2 IN TEST '

if(Tamb.lt.60.or.Tamb.gt.80)write(6,*)' ** CHECK Tamb IN TEST '

if(Pamb.lt.28.or.Pamb.gt.31)write(6,*)' ** CHECK Pamb IN TEST '

if(old1.eq.0)goto 31

err1=abs((v1/a1)-old1)/old1

err2=abs((v2/a2)-old2)/old2

err3=abs((v3/a3)-old3)/old3

err4=abs((v4/a4)-old4)/old4

err5=abs((v5/a5)-old5)/old5

err6=abs((v6/a6)-old6)/old6

if(err1.gt..0125)write(6,*)'error in heater 1 entry, test #'

*,testno

if(err2.gt..0125)write(6,*)'error in heater 2 entry, test #'

159

*,testno

if(err3.gt..0125)write(6,*)'error in heater 3 entry, test #'

*,testno

if(err4.gt..0125)write(6,*)'error in heater 4 entry, test #'

*,testno

if(err5.gt..0125)write(6,*)'error in heater 5 entry, test #'

*,testno

if(err6.gt..0125)write(6,*)'error in heater 6 entry, test #'

*,testno

31 write(6,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5,v6/a6

write(2,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5,v6/a6

C if(flag.eq.1)goto 32

old1=v1/a1

old2=v2/a2

old3=v3/a3

old4=v4/a4

old5=v5/a5

old6=v6/a6

flag=1.

32 continue

enddo

35 format(1x,f4.0,2x,6(1x,f10.6))

write(6,*)' '

write(6,*)' '

write(6,*)' Resistances are in file : output.dat'

stop

end

160

Rig3a-Reduce-Heat-Transfer.f

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,NuS,NuN,NoseR,NoseL,LossesS,LossesN,l1,l2

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

FAC1=3.413 ! converts Watts to BTU/hr

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1,FILE='input.dat',STATUS='old')

OPEN(UNIT=2,FILE='nu-plots-side.dat',STATUS='old')

OPEN(UNIT=3,FILE='nu-plots-nose.dat',STATUS='old')

OPEN(UNIT=4,FILE='uncertain-side.out',STATUS='old')

OPEN(UNIT=5,FILE='uncertain-nose.out',STATUS='old')

OPEN(UNIT=7,FILE='output.dat',STATUS='old')

OPEN(UNIT=8,FILE='friction.out',STATUS='old')

OPEN(UNIT=9,FILE='nu-pictures-side.dat',STATUS='old')

OPEN(UNIT=10,FILE='nu-pictures-nose.dat',STATUS='old')

OPEN(UNIT=11,FILE='convergence.dat',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

NoseR=1.281 ! inches

NoseR=NoseR/12 ! feet

Angle=138. ! degrees

RigL=36. ! inches

Side=3. ! inches

Side=Side/12 ! feet

161

Side2=1.372 ! inches

Side2=Side2/12 ! feet

C

C CALCULATION

hypo1=sqrt(NoseR**2 + SIDE**2)

hypo2=sqrt(NoseR**2 + SIDE2**2)

beta1=atan(NoseR/SIDE)*180/PI

beta2=atan(NoseR/SIDE2)*180/PI

alpha1=90-beta1

alpha2=90-beta2

gamma1=180-0.5*Angle-alpha1

gamma2=180-0.5*Angle-alpha2

l1=NoseR*tan(0.5*Angle*PI/180)

l2=NoseR*tan(0.5*Angle*PI/180)

a=SIDE +l1

b=SIDE2+l2

Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))

stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)

stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)

theta1=Asin(stheta1)*180/PI

theta2=Asin(stheta2)*180/PI

sigma1=180-gamma1-theta1

sigma2=180-gamma2-theta2

Pitch=2.48 ! inches

nturb=9

Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +

&NoseR*COS(0.5*Angle*PI/180)

Wave=0.5*Top+NoseR*SIN(0.5*Angle*PI/180)

Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side2+Top

Area1=0.5*NoseR*SIDE

162

Area2=0.5*NoseR*SIDE2

AreaNose=(PI*(NoseR**2)*(Angle/360))

AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)

Across=Area1+Area2+AreaNose+AreaTop

Dh=4*Across/Perim

C NOTE: At the camera location, Side and Nose heaters were exactly 3" by 11" (4 mils, MINCO)

C Beginning and end sections were covered with (1.935" x 10.8" nose) and (4.09" x 10.8" side) (6

mils,BIRK)

! HEATER AT CAMERA LOCATION:

HlengthS=11.

HlengthS=HlengthS/12.

HwidthS=3.

HwidthS=HwidthS/12.

HareaS=HlengthS*HwidthS

HlengthN=11.

HlengthN=HlengthN/12.

HwidthN=3.0

HwidthN=HwidthN/12.

HareaN=HlengthN*HwidthN

Write(7,101)12*NoseR,Angle,12*Side,12*Side2,12*l1,12*l2,

&12*Top,12*HlengthS,12*HwidthS,144*HareaS,12*HlengthN,

&12*HwidthN,144*HareaN,alpha1,alpha2,beta1,beta2,sigma1,

&sigma2,gamma1,gamma2,theta1,theta2,12*Perim,144*ACross,12*Dh,

&Pitch,12*Have,12*Wave,12*Bot,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Side 1 (LC)=',f8.3,' inches',/,

&2x,'Side 2 (Plexi)=',f8.3,' inches',/,

&2x,'l1 and l2=',f8.3,5x,f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Side Heater Length=',f8.3,' inches',/,

&2x,'Side Heater Width=',f8.3,' inches',/,

&2x,'Side Heater area=',f8.3,' Sq.in',/,

&2x,'Nose Heater Length=',f8.3,' inches',/,

&2x,'Nose Heater Width=',f8.3,' inches',/,

&2x,'Nose Heater area=',f8.3,' Sq.in',/,

&2x,'alpha1 and alpha2=',f8.3,5x,f8.3,/,

&2x,'beta1 and beta2=',f8.3,5x,f8.3,/,

&2x,'sigma1 and sigma2=',f8.3,5x,f8.3,/,

&2x,'gamma1 and gamma2=',f8.3,5x,f8.3,/,

&2x,'theta1 and theta2=',f8.3,5x,f8.3,/,

163

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Average Test Section Height=',f8.3,' inches',/,

&2x,'Average Test Section Width=',f8.3,' inches',/,

&2x,'Flat projection bottom for rad losses=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

! R E A D I N D A T A

read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid

Poe=Pitch/TurbH

eoDh=TurbH/(12*Dh)

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

WRITE(10,401)ntests

401 FORMAT(I4)

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

DO 333 I=1,11

READ(1,10)TITLE

WRITE(5,10)TITLE

WRITE(7,10)TITLE

333 WRITE(10,10)TITLE

10 FORMAT(A80,//)

WRITE(9,451)

WRITE(10,451)

451 FORMAT(' no. Re Nu h uncer',

&' Nu_smooth EF',/)

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,

&V4,A4,V5,A5,V6,A6,SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

WRITE(7,*)' '

164

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' V1,A1,V2,A2,V3,A3'

WRITE(7,*)' V4,A4,V5,A5,V6,A6'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,201)V1,A1,V2,A2,V3,A3

WRITE(7,201)V4,A4,V5,A5,V6,A6

201 FORMAT(5X,3(' ',F5.2,' ',F6.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

Mv=F(Athroat,Pven+Pamb,Tven+460)

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

C HEAT FLUX, BTU/(sqft.hr)

FluxS=V2*A2*FAC1/HareaS

FluxN=V5*A5*FAC1/HareaN

C TOTAL HEAT GENERATED FROMINLET TO CAMERA LOCATION , BTU/hr

Q=(A1*V1+A4*V4+0.5*A2*V2+0.5*A5*V5)*FAC1

CALL HTCSIDE(Q,FluxS,TmS,TsurfS,hS,LossesS)

CALL HTCNOSE(Q,FluxN,TmN,TsurfN,hN,LossesN)

TmRS=TmS+460.

CALL AIRPROP(TmRS,gammS,CONmS,VISmS,PRmS,CPmS)

VISmS=VISmS/3600.

TmRN=TmN+460.

CALL AIRPROP(TmRN,gammN,CONmN,VISmN,PRmN,CPmN)

165

VISmN=VISmN/3600.

C REYNOLDS NUMBER

ReS=4.*Mv/(Perim*VISmS)

ReN=4.*Mv/(Perim*VISmN)

! NUSSELT NUMBER

NuS=hS*Dh/CONmS

NuN=hN*Dh/CONmN

RatioNu=NuN/NuS

SmoothNuS=0.023*(ReS**0.8)*(PrmS**0.4)

SmoothNuN=0.023*(ReN**0.8)*(PrmN**0.4)

! ENHACEMENT

EFS=NuS/SmoothNuS

EFN=NuN/SmoothNuN

! UNCERTAINTY ANALYSIS

IND=1

CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,A4,V4,A5,V5,

&Dthroat,HareaS,TsurfS,Tin,LossesS,UncerS,IND)

IND=2

CALL UNCERTAIN(Pamb,Pven,Tven,A4,V4,A5,V5,A1,V1,A2,V2,

&Dthroat,HareaN,TsurfN,Tin,LossesN,UncerN,IND)

WRITE( 9,305)testno,ReS,NuS,hS,uncerS,SmoothNuS,EFS

WRITE(10,305)testno,ReN,NuN,hN,uncerN,SmoothNuN,EFN

305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)

WRITE(2,*)ReS,NuS

WRITE(3,*)ReN,NuN

WRITE(7,300)TmS,MV,ReS

WRITE(7,301)TmN,MV,ReN

WRITE(7,302)RatioNu

302 format(5x,'Nu_Nose/Nu_Side=',f8.3)

C**********************************************************************************

C**********************************************************************************

! DARCY FRICTION FACTOR CALCULATIONS

166

Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb

Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb

TmR=0.5*(TmRS+TmRN)

Re=0.5*(ReS+ReN)

Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*TmR)

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/

&(0.5*Rho*(Um**2))

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth

C**********************************************************************************

C**********************************************************************************

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Inlet Pressure=',f9.4,' psia',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm_Side=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReS=',F8.2)

301 FORMAT(30X,'Tm_Nose=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReN=',F8.2)

STOP

END

C************************************************************************************

**************C

C********************************** ON THE SIDE WALL

**********************************************C

167

C************************************************************************************

**************C

SUBROUTINE HTCSIDE(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

168

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! MINCO

tinc = 0.5e-03/12. ! MINCO

tadh1= 0.75e-03/12. ! MINCO

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

169

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Top*HlengthS ! Top surface

Afront=1.5*Side2*HlengthS ! Front surface

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

170

C THE POINT IN QUESTION

Aback=1.5*Side*HlengthS ! Back surface

Abot =1.5*PI*NoseR*(Angle/360)*HlengthN ! Bottom surface

C write(6,*)Atop,Afront,Abot,Aback

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=h

htop=0.8*h ! Guess

hbot=1.2*h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Top,Bot,Have,HlengthN,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frbot)

C write(6,*)Frtop,Frfront,Frbot,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

171

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fbot=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frbot

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

172

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=h

htop=0.8*h

hbot=1.2*h

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' ON THE SIDE WALL',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

173

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,htop,hfront,hbot

120 FORMAT(5x,'hside=',F8.3,1X,'htop=',F8.3,1X,'hfront=',F8.3,1X,

&'hnose=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frbot

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C****************************************************************************C

C****************************ON THE NOSE ************************************C

C****************************************************************************C

SUBROUTINE HTCNOSE(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

174

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

175

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! MINCO

tinc = 0.5e-03/12. ! MINCO

tadh1= 0.75e-03/12. ! MINCO

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

176

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Side2*HlengthS ! Top surface (since NOSE is now the back surface)

Afront=1.5*Top*HlengthS ! Front surface (since NOSE is now the back surface)

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Abot =1.5*Side*HlengthS ! Bottom surface

Aback=1.5*PI*NoseR*(Angle/360)*HlengthN ! Back surface

C write(6,*)Aback,Atop,Afront,Abot

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

177

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=(0.8/1.2)*h

htop=(1/1.2)*h ! Guess

hbot=(1/1.2)*h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Side2,Side,Wave,HlengthS,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frbot)

C write(6,*)Frtop,Frfront,Frbot,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

178

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fbot=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frbot

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

179

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=(0.8/1.2)*h ! Guess

htop=(1/1.2)*h ! Guess

hbot=(1/1.2)*h ! Guess

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' ON THE NOSE',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

180

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Nose, Top, Front and Back Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,hbot,hfront,htop

120 FORMAT(5x,'hnose=',F8.3,1X,'hback=',F8.3,1X,'htop=',F8.3,1X,

&'hfront=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from Nose, Front, Ftop and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frbot

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C****************************************************************************

C****************************************************************************

C**********************************************************************C

SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)

PI=4.*ATAN(1.E00)

W=H1

H=0.5*(Bot+Top)

T(1)=Tsurf + 460.

T(2)=Ttop + 460.

T(3)=Tfront+ 460.

T(4)=Tbot + 460.

W=W/(3.*Hlength)

H=H/(3.*Hlength)

C Emissivities

E(1)=.85 ! Liquid Crystal Foil, Back Wall

E(2)=.9 ! Plexiglas, Top Wall

181

E(3)=.9 ! Plexiglas, Front Wall

E(4)=.85 ! Liquid Crystal Foil, Nose Wall

C

N=4

SIGMA=0.1712E-08

C WRITE(7,150)

150 FORMAT(//,20X,'SHAPE FACTORS',//)

C

F11=0.

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F12=Z1*(Z2+Z3+Z4+Z5)

F14=F12

F13=1.-F11-F12-F14

C

F31=F13

F32=F12

F33=0.

F34=F14

C

DUM=W

W=H

H=DUM

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

182

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F21=Z1*(Z2+Z3+Z4+Z5)

F22=0.

F23=F21

F24=1.-F21-F22-F23

C

F41=F21

F42=F24

F43=F23

F44=0.

C

C WRITE(7,110)F11,F12,F13,F14

C WRITE(7,120)F21,F22,F23,F24

C WRITE(7,130)F31,F32,F33,F34

C WRITE(7,140)F41,F42,F43,F44

C

110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,

&5X,'F14=',F6.4,/)

120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,

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

130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,

&5X,'F34=',F6.4,/)

140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,

&5X,'F44=',F6.4,//)

C WRITE(7,160)

160 FORMAT(/,20X,'EMISSIVITIES',//)

C WRITE(7,100)(I,E(I),I=1,N)

C WRITE(7,170)

170 FORMAT(/,20X,'TEMPERATURES IN R',//)

C WRITE(7,100)(I,T(I),I=1,N)

A(1,1)=F11-1./(1.-E(1))

A(1,2)=F12

A(1,3)=F13

A(1,4)=F14

C

A(2,1)=F21

A(2,2)=F22-1./(1.-E(2))

A(2,3)=F23

A(2,4)=F24

C

A(3,1)=F31

A(3,2)=F32

183

A(3,3)=F33-1./(1.-E(3))

A(3,4)=F34

C

A(4,1)=F41

A(4,2)=F42

A(4,3)=F43

A(4,4)=F44-1./(1.-E(4))

C

C WRITE(7,180)

180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)

C WRITE(7,200)((A(I,J),J=1,N),I=1,N)

DO I=1,N

B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))

ENDDO

C WRITE(7,250)

C WRITE(7,100)(I,B(I,1),I=1,N)

200 FORMAT(1X,4E15.6)

250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)

C WRITE(7,55)

55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)

CALL EQSOLVE(A,B,N,N,1)

C WRITE(7,50)

C WRITE(7,100)(I,B(I,1),I=1,N)

DO I=1,N

Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))

ENDDO

Frback =Q(1)

Frtop =Q(2)

Frfront=Q(3)

Frnose=Q(4)

C WRITE(7,350)

C WRITE(7,100)(I,Q(I),I=1,N)

100 FORMAT(4(I3,E15.6))

50 FORMAT(/,20X,'RADIOCITIES',/)

350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)

RETURN

END

C**********************************************************************C

C**********************************************************************C

SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,i4,V4,i5,V5,

&Dth,Harea,Tsurf,Tin,Losses,Uncer,IND)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 i1,i2,i4,i5,Losses,M1,M2

PI=4.*ATAN(1.E00)

184

C FAC=491.3744

FAC1=3.413 ! converts Watts to BTU/hr

C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)

C=0.24*0.5215*3600

C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J

P1=Pven+Pamb

T1=Tven+460.0

TI=Tin

TS=Tsurf

a=Harea

f=0.5

ATH=PI*(Dth**2)/4.

DATH=PI*((Dth+0.001)**2)/4. -ATH

h=((FAC1*(V2*i2)/a)-Losses)/

&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+V4*i4+f*V2*i2+f*V5*i5)))/

&(C*P1*ATH))

WRITE(5,*)' '

if(IND.EQ.1)WRITE(5,*)' hSide =',h,' BUT/hr.sqft.F'

if(IND.EQ.2)WRITE(5,*)' hNose =',h,' BUT/hr.sqft.F'

H2=h*h

C

C i2 v2

C ------- - Floss

C a

C ---------------------------------------

C sqrt(T1)(i1v1+i4v4+fi2v2+fi5v5)

C Ts-Ti - -------------------------

C C P1 A_throat

C

DLOSS=0.1*Losses

dv1=0.1

dv2=0.1

dv4=0.1

dv5=0.1

di1=0.01

185

di2=0.01

di4=0.01

di5=0.01

da=1./(32.*32.*144)

dts=0.5

dti=0.5

dt1=0.5

dp1=0.5

Df=0.1

C1=FAC1*(V2*i2/a)-Losses

Q1=C*P1*Ath

Q2=Q1*sqrt(T1)

M1=(Ts-Ti)*Q1

A=FAC1*(i1*v1+i4*v4)

B=FAC1*(i2*v2+i5*v5)

M2=M1-sqrt(T1)*(A+f*B)

DHDF=B*Q1*C1*sqrt(T1)/(M2**2)

DHDTI= C1*(Q1**2)/(M2**2)

DHDTS=-C1*(Q1**2)/(M2**2)

DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))

DHDLOSS=-Q1/M2

DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)

DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)

DHDI4=FAC1*v4*Q1*C1*sqrt(T1)/(M2**2)

DHDV4=FAC1*i4*Q1*C1*sqrt(T1)/(M2**2)

DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDI5=FAC1*v5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV5=FAC1*i5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDATH=C1*C*P1*(M2-M1)/(M2**2)

DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)

DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))

ZF=(DF*DHDF)**2

ZA=(DA*DHDA)**2

ZI1=(DI1*DHDI1)**2

186

ZV1=(DV1*DHDV1)**2

ZI2=(DI2*DHDI2)**2

ZV2=(DV2*DHDV2)**2

ZI4=(DI4*DHDI4)**2

ZV4=(DV4*DHDV4)**2

ZI5=(DI5*DHDI5)**2

ZV5=(DV5*DHDV5)**2

ZTS=(DTS*DHDTS)**2

ZTI=(DTI*DHDTI)**2

ZATH=(DATH*DHDATH)**2

ZP1=(DP1*DHDP1)**2

ZT1=(DT1*DHDT1)**2

ZLOSS=(DLOSS*DHDLOSS)**2

Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+ZI4+ZI4+ZV5+ZV5+

&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/H2)

if(IND.EQ.1) then

WRITE(4,*)' TOTAL UNCER.%:',Uncer

WRITE(4,*)' '

WRITE(4,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(4,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(4,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(4,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(4,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(4,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h

WRITE(4,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h

WRITE(4,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h

WRITE(4,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h

WRITE(4,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(4,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(4,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(4,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(4,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(4,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(4,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

endif

if(IND.EQ.2) then

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(5,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h

187

WRITE(5,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h

WRITE(5,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h

WRITE(5,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h

WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

endif

RETURN

END

C**********************************************************************C

C**********************************************************************C

SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(NDIM,NDIM),B(NDIM,NB)

DO 291 J1=1,NA

C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE

C VALUE IN PIVOTAL COLUMN.

101 TEMP=0.

DO 121 J2=J1,NA

IF(ABS(A(J2,J1))-TEMP) 121,111,111

111 TEMP=ABS(A(J2,J1))

IBIG=J2

121 CONTINUE

IF(IBIG-J1)5001,201,131

C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE

C VALUE IN PIVOT POSITION.

131 DO 141 J2=J1,NA

TEMP=A(J1,J2)

A(J1,J2)=A(IBIG,J2)

141 A(IBIG,J2)=TEMP

DO 161 J2=1,NB

TEMP=B(J1,J2)

B(J1,J2)=B(IBIG,J2)

161 B(IBIG,J2)=TEMP

C COMPUTE COEFFICIENTS IN PIVOTAL ROW.

201 TEMP=A(J1,J1)

DO 221 J2=J1,NA

221 A(J1,J2)=A(J1,J2)/TEMP

DO 231 J2=1,NB

231 B(J1,J2)=B(J1,J2)/TEMP

188

IF(J1-NA)236,301,5001

C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.

236 N1=J1+1

DO 281 J2=N1,NA

TEMP=A(J2,J1)

DO 241 J3=N1,NA

241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)

DO 251 J3=1,NB

251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)

281 CONTINUE

291 CONTINUE

C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.

301 IF(NA-1)5001,5001,311

311 DO 391 J1=1,NB

N1=NA

321 DO 341 J2=N1,NA

341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)

N1=N1-1

IF(N1-1)5001,391,321

391 CONTINUE

5001 CONTINUE

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

189

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

190

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

191

Rig3a-reduce-friction.f

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,NoseR,NoseL

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1, FILE='input.dat',STATUS='old')

OPEN(UNIT=5, FILE='fric-uncertain.out',STATUS='old')

OPEN(UNIT=7, FILE='friction.out',STATUS='old')

OPEN(UNIT=8, FILE='friction-plot.out',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

! T E S T S E C T I O N G E O M E T R Y

NoseR=1.281 ! inches

NoseR=NoseR/12 ! feet

Angle=138. ! degrees

RigL=36. ! inches

Side=3. ! inches

Side=Side/12 ! feet

Side2=1.372 ! inches

Side2=Side2/12 ! feet

C

C CALCULATION

hypo1=sqrt(NoseR**2 + SIDE**2)

hypo2=sqrt(NoseR**2 + SIDE2**2)

192

beta1=atan(NoseR/SIDE)*180/PI

beta2=atan(NoseR/SIDE2)*180/PI

alpha1=90-beta1

alpha2=90-beta2

gamma1=180-0.5*Angle-alpha1

gamma2=180-0.5*Angle-alpha2

l1=NoseR*tan(0.5*Angle*PI/180)

l2=NoseR*tan(0.5*Angle*PI/180)

a=SIDE +l1

b=SIDE2+l2

Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))

stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)

stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)

theta1=Asin(stheta1)*180/PI

theta2=Asin(stheta2)*180/PI

sigma1=180-gamma1-theta1

sigma2=180-gamma2-theta2

Pitch=2.48 ! inches

nturb=9

Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +

&NoseR*COS(0.5*Angle*PI/180)

Wave=0.5*Top+NoseR*SIN(0.5*Angle*PI/180)

Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side2+Top

Area1=0.5*NoseR*SIDE

Area2=0.5*NoseR*SIDE2

AreaNose=(PI*(NoseR**2)*(Angle/360))

AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)

Across=Area1+Area2+AreaNose+AreaTop

Dh=4*Across/Perim

193

read(1,*)ntests,TurbH,TurbW,Turbr

DO 333 I=1,10

READ(1,10)TITLE

WRITE(5,10)TITLE

333 WRITE(7,10)TITLE

10 FORMAT(A80,//)

Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,

&12.*Top,12.*Bot,12.*Perim,144.*ACross,12*Dh,Pitch,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Nose Length=',f8.3,' inches',/,

&2x,'Side 1 (Plexi)=',f8.3,' inches',/,

&2x,'Side 2 (LC)=',f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Bottom Flat Line=',f8.3,' inches',/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

Poe=Pitch/TurbH

eoDh=TurbH/(12*Dh)

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

401 FORMAT(I4)

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f9.4,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

! R E A D I N D A T A

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,

&SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

194

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

Mv=F(Athroat,Pven+Pamb,Tven+460)

TinR=Tin+460.

CALL AIRPROP(TinR,gamain,CONin,VISin,PRin,CPin)

VISin=VISin/3600.

C REYNOLDS NUMBER

Re=4.*Mv/(Perim*VISin)

C***************************************************

! DARCY FRICTION FACTOR CALCULATIONS

Pplen=2*Pplen*H2Otopsi+Pamb

DeltaP=2*Pinlet ! inches of water using Micromanometer

Rho=(Pamb+0.5*DeltaP*H2Otopsi)*144./(Rgas*(TinR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*(DeltaP*H2Otopsi*144.)/

&(0.5*Rho*(Um**2))

CALL UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)

195

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,DeltaP,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,304)Re,fDarcy,fsmooth,fDarcy/fsmooth

304 format(f8.1,2(4x,E13.7),F8.3)

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Pressure Drop =',f9.4,' inches of water',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)

STOP

END

C**********************************************************************C

SUBROUTINE UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)

IMPLICIT REAL*8(A-H,O-Z)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

C=24*144*gc*H2Otopsi

dDh =0.05/12.

dRigL =0.1 ! inches

dDeltaP=0.002*H2Otopsi ! 0.002 inches of water

dRho =0.02*Rho ! 2% error

dUm =0.02*Um ! 2% error

196

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*(DeltaP*H2Otopsi*144.)/

&(0.5*Rho*(Um**2))

f2=fDarcy**2

WRITE(5,*)' '

WRITE(5,*)' fDarcy =',fDarcy

WRITE(5,*)' '

dfdDh=C*DeltaP/(RigL*Rho*(Um**2))

dfdDeltaP=C*Dh/(RigL*Rho*(Um**2))

dfdRigL=-C*Dh*DeltaP/(RigL*RigL*Rho*(Um**2))

dfdRho=-C*Dh*DeltaP/(RigL*Rho*Rho*(Um**2))

dfdUm=-2*C*Dh*DeltaP/(RigL*Rho*(Um**3))

ZDh=(dfdDh*dDh)**2

ZRigL=(dfdRigL*dRigL)**2

ZDeltaP=(dfdDeltaP*dDeltaP)**2

ZRho=(dfdRho*dRho)**2

ZUm=(dfdUm*dUm)**2

Uncer=100*SQRT((ZDh+ZRigL+ZDeltaP+ZRho+ZUm)/(f2))

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with Dh',100.*sqrt(ZDh)/fDarcy

WRITE(5,*)' % Uncer. assoc. with RigL',100.*sqrt(ZRigL)/fDarcy

WRITE(5,*)' % Uncer. assoc. with DeltaP',100.*sqrt(ZDeltaP)/fDarcy

WRITE(5,*)' % Uncer. assoc. with Rho',100.*sqrt(ZRho)/fDarcy

WRITE(5,*)' % Uncer. assoc. with Um',100.*sqrt(ZUm)/fDarcy

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

197

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

198

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

199

Appendix A.4: FORTRAN Codes for Rig 3B

Author: Professor Mohammad Taslim

Reduce.f

character*25 filename

character*80 title

write(6,*)'enter the name of the data file that u',

* ' want to check'

read(5,10)filename

10 format(a25)

open(unit=1,file=filename,status='old')

open(unit=2,file='output.dat',status='old')

write(6,*)'is there a title for this file? enter 1=yes, 0=no'

read(5,*)ans

if(ans.eq.0)goto 30

read(1,*)NTESTS

do i=1,11

read(1,20)title

20 FORMAT(A80,//)

enddo

30 do i=1,NTESTS

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,V4,A4,

&V5,A5,V6,A6,SG,Pplen,DP,Pamb,Dthroat

if(Tven.lt.45.or.Tven.gt.90)write(6,*)

&' ** CHECK Tven IN TEST ',i

if(Tin1.lt.50.or.Tin1.gt.90)write(6,*)' ** CHECK Tin1 IN TEST '

if(Tin2.lt.50.or.Tin2.gt.90)write(6,*)' ** CHECK Tin2 IN TEST '

if(Tamb.lt.60.or.Tamb.gt.80)write(6,*)' ** CHECK Tamb IN TEST '

if(Pamb.lt.28.or.Pamb.gt.31)write(6,*)' ** CHECK Pamb IN TEST '

if(old1.eq.0)goto 31

err1=abs((v1/a1)-old1)/old1

err2=abs((v2/a2)-old2)/old2

err3=abs((v3/a3)-old3)/old3

err4=abs((v4/a4)-old4)/old4

err5=abs((v5/a5)-old5)/old5

if(err1.gt..0125)write(6,*)'error in heater 1 entry, test #'

*,testno

if(err2.gt..0125)write(6,*)'error in heater 2 entry, test #'

*,testno

200

if(err3.gt..0125)write(6,*)'error in heater 3 entry, test #'

*,testno

if(err4.gt..0125)write(6,*)'error in heater 4 entry, test #'

*,testno

if(err5.gt..0125)write(6,*)'error in heater 5 entry, test #'

*,testno

31 write(6,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5

write(2,35)testno,v1/a1,v2/a2,v3/a3,v4/a4,v5/a5

C if(flag.eq.1)goto 32

old1=v1/a1

old2=v2/a2

old3=v3/a3

old4=v4/a4

old5=v5/a5

flag=1.

32 continue

enddo

35 format(1x,f4.0,2x,5(1x,f10.6))

write(6,*)' '

write(6,*)' '

write(6,*)' Resistances are in file : output.dat'

stop

end

201

Rig3b-Reduce-Heat-Transfer.f

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,NuS,NuN,NoseR,NoseL,LossesS,LossesN,l1,l2

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

FAC1=3.413 ! converts Watts to BTU/hr

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1,FILE='input.dat',STATUS='old')

OPEN(UNIT=2,FILE='nu-plots-side.dat',STATUS='old')

OPEN(UNIT=3,FILE='nu-plots-nose.dat',STATUS='old')

OPEN(UNIT=4,FILE='uncertain-side.out',STATUS='old')

OPEN(UNIT=5,FILE='uncertain-nose.out',STATUS='old')

OPEN(UNIT=7,FILE='output.dat',STATUS='old')

OPEN(UNIT=8,FILE='friction.out',STATUS='old')

OPEN(UNIT=9,FILE='nu-pictures-side.dat',STATUS='old')

OPEN(UNIT=10,FILE='nu-pictures-nose.dat',STATUS='old')

OPEN(UNIT=11,FILE='convergence.dat',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

NoseR=1.281 ! inches

NoseR=NoseR/12 ! feet

Angle=138. ! degrees

RigL=36. ! inches

Side=3. ! inches

Side=Side/12 ! feet

202

Side2=1.372 ! inches

Side2=Side2/12 ! feet

C

C CALCULATION

hypo1=sqrt(NoseR**2 + SIDE**2)

hypo2=sqrt(NoseR**2 + SIDE2**2)

beta1=atan(NoseR/SIDE)*180/PI

beta2=atan(NoseR/SIDE2)*180/PI

alpha1=90-beta1

alpha2=90-beta2

gamma1=180-0.5*Angle-alpha1

gamma2=180-0.5*Angle-alpha2

l1=NoseR*tan(0.5*Angle*PI/180)

l2=NoseR*tan(0.5*Angle*PI/180)

a=SIDE +l1

b=SIDE2+l2

Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))

stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)

stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)

theta1=Asin(stheta1)*180/PI

theta2=Asin(stheta2)*180/PI

sigma1=180-gamma1-theta1

sigma2=180-gamma2-theta2

Pitch=2.48 ! inches

nturb=9

Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +

&NoseR*COS(0.5*Angle*PI/180)

Wave=0.5*Top+NoseR*SIN(0.5*Abgle*PI/180)

Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side2+Top

Area1=0.5*NoseR*SIDE

203

Area2=0.5*NoseR*SIDE2

AreaNose=(PI*(NoseR**2)*(Angle/360))

AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)

Across=Area1+Area2+AreaNose+AreaTop

Dh=4*Across/Perim

C NOTE: At the camera location, Side and Nose heaters were exactly 2" by 11"

C End section was covered with (3" x 11" nose)

! HEATER AT CAMERA LOCATION:

HlengthS=11.

HlengthS=HlengthS/12.

HwidthS=2.

HwidthS=HwidthS/12.

HareaS=HlengthS*HwidthS

HlengthN=11.

HlengthN=HlengthN/12.

HwidthN=2.

HwidthN=HwidthN/12.

HareaN=HlengthN*HwidthN

Write(7,101)12*NoseR,Angle,12*Side,12*Side2,12*l1,12*l2,

&12*Top,12*HlengthS,12*HwidthS,144*HareaS,12*HlengthN,

&12*HwidthN,144*HareaN,alpha1,alpha2,beta1,beta2,sigma1,

&sigma2,gamma1,gamma2,theta1,theta2,12*Perim,144*ACross,12*Dh,

&Pitch,12*Have,12*Wave,12*Bot,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Side 1 (LC)=',f8.3,' inches',/,

&2x,'Side 2 (Plexi)=',f8.3,' inches',/,

&2x,'l1 and l2=',f8.3,5x,f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Side Heater Length=',f8.3,' inches',/,

&2x,'Side Heater Width=',f8.3,' inches',/,

&2x,'Side Heater area=',f8.3,' Sq.in',/,

&2x,'Nose Heater Length=',f8.3,' inches',/,

&2x,'Nose Heater Width=',f8.3,' inches',/,

&2x,'Nose Heater area=',f8.3,' Sq.in',/,

&2x,'alpha1 and alpha2=',f8.3,5x,f8.3,/,

&2x,'beta1 and beta2=',f8.3,5x,f8.3,/,

&2x,'sigma1 and sigma2=',f8.3,5x,f8.3,/,

&2x,'gamma1 and gamma2=',f8.3,5x,f8.3,/,

&2x,'theta1 and theta2=',f8.3,5x,f8.3,/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

204

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Average Test Section Height=',f8.3,' inches',/,

&2x,'Average Test Section Width=',f8.3,' inches',/,

&2x,'Flat projection bottom for rad losses=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

! R E A D I N D A T A

read(1,*)ntests,TurbH,TurbW,Turbr,Tliquid

Poe=Pitch/TurbH

eoDh=TurbH/(12*Dh)

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

WRITE(10,401)ntests

401 FORMAT(I4)

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f8.3,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

DO 333 I=1,11

READ(1,10)TITLE

WRITE(5,10)TITLE

WRITE(7,10)TITLE

333 WRITE(10,10)TITLE

10 FORMAT(A80,//)

WRITE(9,451)

WRITE(10,451)

451 FORMAT(' no. Re Nu h uncer',

&' Nu_smooth EF',/)

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,V1,A1,V2,A2,V3,A3,

&V4,A4,V5,A5,V6,A6,SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

WRITE(7,100) i

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

205

WRITE(7,*)' V1,A1,V2,A2,V3,A3'

WRITE(7,*)' V4,A4,V5,A5,V6,A6'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,201)V1,A1,V2,A2,V3,A3

WRITE(7,201)V4,A4,V5,A5,V6,A6

201 FORMAT(5X,3(' ',F5.2,' ',F6.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

Mv=F(Athroat,Pven+Pamb,Tven+460)

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

C HEAT FLUX, BTU/(sqft.hr)

FluxS=V2*A2*FAC1/(HareaS)

FluxN=V5*A5*FAC1/(HareaN)

C TOTAL HEAT GENERATED FROMINLET TO CAMERA LOCATION , BTU/hr

Q=(A1*V1+A4*V4+0.5*A2*V2+0.5*A5*V5)*FAC1

CALL HTCSIDE(Q,FluxS,TmS,TsurfS,hS,LossesS)

CALL HTCNOSE(Q,FluxN,TmN,TsurfN,hN,LossesN)

TmRS=TmS+460.

CALL AIRPROP(TmRS,gammS,CONmS,VISmS,PRmS,CPmS)

VISmS=VISmS/3600.

TmRN=TmN+460.

CALL AIRPROP(TmRN,gammN,CONmN,VISmN,PRmN,CPmN)

VISmN=VISmN/3600.

206

C REYNOLDS NUMBER

ReS=4.*Mv/(Perim*VISmS)

ReN=4.*Mv/(Perim*VISmN)

! NUSSELT NUMBER

NuS=hS*Dh/CONmS

NuN=hN*Dh/CONmN

RatioNu=NuN/NuS

SmoothNuS=0.023*(ReS**0.8)*(PrmS**0.4)

SmoothNuN=0.023*(ReN**0.8)*(PrmN**0.4)

! ENHACEMENT

EFS=NuS/SmoothNuS

EFN=NuN/SmoothNuN

! UNCERTAINTY ANALYSIS

IND=1

CALL UNCERTAIN(Pamb,Pven,Tven,A1,V1,A2,V2,A4,V4,A5,V5,

&Dthroat,HareaS,TsurfS,Tin,LossesS,UncerS,IND)

IND=2

CALL UNCERTAIN(Pamb,Pven,Tven,A4,V4,A5,V5,A1,V1,A2,V2,

&Dthroat,HareaN,TsurfN,Tin,LossesN,UncerN,IND)

WRITE( 9,305)testno,ReS,NuS,hS,uncerS,SmoothNuS,EFS

WRITE(10,305)testno,ReN,NuN,hN,uncerN,SmoothNuN,EFN

305 FORMAT(2X,F3.0,2X,F10.1,2X,F10.3,2X,F10.3,2X,F6.2,2X,2F10.3)

WRITE(2,*)ReS,NuS

WRITE(3,*)ReN,NuN

WRITE(7,300)TmS,MV,ReS

WRITE(7,301)TmN,MV,ReN

WRITE(7,302)RatioNu

302 format(5x,'Nu_Nose/Nu_Side=',f8.3)

C**********************************************************************************

C**********************************************************************************

! DARCY FRICTION FACTOR CALCULATIONS

207

Pplen=(2.*Pplen*SG)*H2Otopsi + Pamb

Pinlet=(2.*Pinlet*SG)*H2Otopsi + Pamb

TmR=0.5*(TmRS+TmRN)

Re=0.5*(ReS+ReN)

Rho=(Pamb+0.5*(Pinlet-Pamb))*144./(Rgas*(TmR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*((Pinlet-Pamb)*144.)/

&(0.5*Rho*(Um**2))

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,Pinlet,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,*)Re,fDarcy,fsmooth,fDarcy/fsmooth

C**********************************************************************************

C**********************************************************************************

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Inlet Pressure=',f9.4,' psia',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm_Side=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReS=',F8.2)

301 FORMAT(30X,'Tm_Nose=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'ReN=',F8.2)

STOP

END

C************************************************************************************

**************C

C********************************** ON THE SIDE WALL

**********************************************C

208

C************************************************************************************

**************C

SUBROUTINE HTCSIDE(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

209

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! MINCO

tinc = 0.5e-03/12. ! MINCO

tadh1= 0.75e-03/12. ! MINCO

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

210

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Top*HlengthS ! Top surface

Afront=1.5*Side2*HlengthS ! Front surface

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

211

C THE POINT IN QUESTION

Aback=1.5*Side*HlengthS ! Back surface

Abot =1.5*PI*NoseR*(Angle/360)*HlengthN ! Bottom surface

C write(6,*)Atop,Afront,Abot,Aback

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=h

htop=0.8*h ! Guess

hbot=1.2*h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Top,Bot,Have,HlengthN,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frbot)

C write(6,*)Frtop,Frfront,Frbot,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

212

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fbot=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frbot

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

213

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=h

htop=0.8*h

hbot=1.2*h

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' ON THE SIDE WALL',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

214

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Back, Top, Front and Nose Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,htop,hfront,hbot

120 FORMAT(5x,'hside=',F8.3,1X,'htop=',F8.3,1X,'hfront=',F8.3,1X,

&'hnose=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from LC Side wall, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frbot

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C****************************************************************************C

C****************************ON THE NOSE ************************************C

C****************************************************************************C

SUBROUTINE HTCNOSE(Q,Flux,Tm,Tsurf,h,Losses)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 kinc,kadh,kkap,kmyl,ksty,kblack,kliq,kplexi,

&RigL,Mv,Losses,kfiber,NoseR

COMMON Rgas,Mv,Tin,Tamb,Pamb,Tliquid,PI,HlengthS,HlengthN,Angle,

&Side,Side2,Top,Bot,NoseR,Perim,Dh,Have,Wave

C HEATED SIDE AND NOSE WALL (LIQUID CRYSTALS)

215

C FROM THE CENTER OF HEATING ELEMENT TO THE Liquid Crystal Layer

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 2 mil KAPTON

C 1.5 mil ADHESIVE ---- 3 mil ABSORPTIVE BLACK BACKGROUND ---- 2.0 mil

C LIQUID CRYSTAL

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh1/kadh --

C -- tkap2/kkap -- tadh2/kadh -- tblack/kblack -- tliq/kliq

C FROM THE CENTER OF HEATING ELEMENT TO THE AIRAMBIENT AIR

C 0.25 mil INCONEL HEATING ELEMENT ---- 1 mil ADHESIVE ---- 1 mil KAPTON

C 2 mil ADHESIVE ---- 0.187 inches FIBERGLASS ---- 2.0 inches

C SPRAYFOAM ---- AMBIENT AIR

C tinc1/kinc -- tadh1/kadh -- tkap1/kkap -- tadh3/kadh -- tfiber/kfiber

C -- tspray/ksty -- 1/ho

C T O P W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C F R O N T W A L L

C FROM THE INSIDE TO THE AMBIENT AIR

C AIR INSIDE THE TEST SECTION ---- 0.5 inches PLEXIGLAS ---- 2.0 inches

C STYROFOAM ---- AMBIENT

C 1/hi -- tplexi/kplex -- tsty/ksty -- 1/ho

C*******************************************************************C

C Natural Convection Heat transfer coefficient on the outer surface

De=6./12. ! ft, test section side with insulation

TambR=Tamb+460.

CALL AIRPROP(TambR,gamx,con,visx,prx,cpx)

ho=0.36*con/De ! Ozisik, Page 443

C write(6,*)' ho ',ho

216

C*******************************************************************C

kkap = 0.0942 ! BTU/hr.ft.F MINCO (0.163 W/m.K) agrees with(0.095 BTU/hr.ft.F)

ksty = 0.02 ! BTU/hr.ft.F

kplexi = 0.11 ! BTU/hr.ft.F AIN Plastics k=1.3 BTU/hr.F.sqft/in(1-800-523-7500)

kmyl = 0.085 ! BTU/hr.ft.F Abauf's serpentine report, page 19

kadh = 0.1272 ! BTU/hr.ft.F MINCO (0.220 W/m.K)

kinc = 9.0152 ! BTU/hr.ft.F MINCO (inconel 600 K=15.6 W/m.K)

kblack = 0.165 ! BTU/hr.ft.F Glycerin

kliq = 0.165 ! BTU/hr.ft.F Glycerin

kfiber =0.02 ! BTU/hr.ft.F Mark's Handbook (Fiberglass)

tplexi = 0.5/12. ! United Industries

tfiber = 0.187/12. ! United Industries

tsty = 0.

tspray = 2./12. ! United Industries

tkap = 1.0e-03/12. ! MINCO

tinc = 0.5e-03/12. ! MINCO

tadh1= 0.75e-03/12. ! MINCO

tadh2 = 1.5e-03/12. ! adhesive thickness (from DAVIS)

tadh3 = 2.0e-03/12. ! DOUBLE-STICK TAPE

tblack = 3.0e-03/12. ! absorptive black background (from DAVIS)

tliq = 2.0e-03/12. ! liquid crystal thickness (from DAVIS)

tmyl = 5.0e-03/12. ! MYLAR thickness (from DAVIS)

Rplexi= tplexi/kplexi

Rfiber= tfiber/kfiber

Rsty = tsty/ksty

Rspray= tspray/ksty

Rconv = 1./ho

Rinc = tinc/kinc

Rkap = tkap/kkap

Radh1 = tadh1/kadh

Radh2 = tadh2/kadh

Radh3 = tadh3/kadh

Rblack = tblack/kblack

Rliq = tliq/kliq

Rmyl = tmyl/kmyl

217

C write(6,*)' Rinc',Rinc,' Radh1',Radh1,' Rkap ',Rkap

C write(6,*)' Radh2',Radh2,' Rblack',Rblack

C write(6,*)' Radh3',Radh3,' Rliq ',Rliq,' Rmyl ',Rmyl

C write(6,*)' Rplexi ',Rplexi

C write(6,*)' Rfiber',Rfiber,' Rconv',Rconv

C Resistance from mid heater to the Liquid Crystals (Reference Temperature)

Rfront=0.5*Rinc + Radh1 + Rkap + Radh2 + Rblack + Rliq

C Resistance from mid heater to ambient

Rback=0.5*Rinc+Radh1+Rkap+Radh3+Rfiber+Rspray+Rconv

C write(6,*)' Rfront',Rfront,' Rback',Rback

C**************************************************C

C H E A T E D W A L L

Theater = (Flux+Tamb/Rback+Tliquid/Rfront)/

&(1./Rback+1./Rfront)

Fback = (Theater-Tamb)/Rback

Ffront = (Theater-Tliquid)/Rfront

Tsurf= Tliquid -Ffront*Rmyl

Perloss=100.*(Fback/Flux)

C**************************************************C

C write(6,*)' Tsurf', Tsurf

C TOTAL UNHEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Atop =1.5*Side2*HlengthS ! Top surface (since NOSE is now the back surface)

Afront=1.5*Top*HlengthS ! Front surface (since NOSE is now the back surface)

C TOTAL HEATED WALL SURFACES FROM THE BEGINNING OF THE FIRST HEATER TO

C THE POINT IN QUESTION

Abot =1.5*Side*HlengthS ! Bottom surface

Aback=1.5*PI*NoseR*(Angle/360)*HlengthN ! Back surface

C write(6,*)Aback,Atop,Afront,Abot

C AIR INLET PROPERTIES

TinR=Tin+460.

CALL AIRPROP(TinR,gamin,CONin,VISin,PRin,CPin)

218

C INITIAL GUESSES

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Q/(3600.*Mv*CPin) ! Energy balance

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Fback)/(Tsurf-Tm)

hfront=(0.8/1.2)*h

htop=(1/1.2)*h ! Guess

hbot=(1/1.2)*h ! Guess

Ttop=Tm ! Guess

Tfront=Tm ! Guess

Tbot=Tsurf

C ITERATIONS STARTS HERE

DO I=1,30

C EVALUATING FNET

C RADIATIONAL LOSSES

CALL RADIATION(Side2,Side,Wave,HlengthS,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frbot)

C write(6,*)Frtop,Frfront,Frbot,Frback

C FLUX LOSSES FROM TOP AND FRONT WALLS

R1= Rplexi+Rconv !from surface to ambient

C T O P W A L L

R3=1./htop

Ttop=((1./R3)*Tm+(1./R1)*Tamb-Frtop)/((1./R1)+(1./R3))

Ftop=(Ttop-Tamb)/R1

C F R O N T W A L L

R1= Rplexi+Rconv !from surface to ambient

219

R3=1./hfront

Tfront=((1./R3)*Tm+(1./R1)*Tamb-Frfront)/((1./R1)+(1./R3))

Ffront=(Tfront-Tamb)/R1

Fbot=Fback

C TOTAL HEAT LOSS TO THE AMBIENT

Qwaste=Fback*Aback+Ftop*Atop+Ffront*Afront+Fbot*Abot

C NET HEAT ADDED TO THE AIR FROM THE INLET TO THE POINT IN QUESTION

Qadd = Q-Qwaste

C AIR MIXED MEAN TEMPERATURE AT THE POINT WHERE THE HEAT TRANSFER

C COEFFICIENT IS BEING MEASURED

Tm=Tin+Qadd/(3600.*Mv*CPin) ! Energy balance

C FLUX LOSSES OF THE HEATED SUEFACES (TO THE AMBIENT AND RADIATIONAL)

Losses=Fback+Frback+Frbot

C write(6,*)' Losses',Losses

C HEAT TRANSFER COEFFICIENT FROM THE NEWTON LAW OF COOLING

h=(Flux-Losses)/(Tsurf-Tm)

C FILM TEMPERATURE

Tf=(Tsurf+Tm)/2.

C DENSITY AT FILM TEMPERATURE

Rho=Pamb/(Rgas*(Tf+460.))

C OTHER PROPERTIES AT FILM TEMPERATURE

TfR=Tf+460.

CALL AIRPROP(TfR,gam,Con,Vis,Pr,Cp)

Vis=Vis/3600.

220

Re=4.*Mv/(Perim*Vis)

! HEAT TRANSFER COEFFICIENT ON THE NON-TURBULATED WALL

hfront=(0.8/1.2)*h ! Guess

htop=(1/1.2)*h ! Guess

hbot=(1/1.2)*h ! Guess

FNETTOP=htop*(Ttop-Tm)+Ftop+Frtop

FNETFRONT=hfront*(Tfront-Tm)+Ffront+Frfront

IF(abs(FNETTOP).le.0.001.AND.abs(FNETFRONT).le.0.001)

&go to 34

enddo

write(7,400)

400 FORMAT(/,20x,'***** Did not converge after 30 iterations',

&' *****',/)

WRITE(9,410)Re,Ph,FNETTOP,FNETFRONT

410 FORMAT(5X,'Re=',E12.5,5X,'PHOTO # ',I3,5X,

&'FNETTOP,FNETFRONT=',2E15.5,/)

GO TO 503

34 WRITE(7,500)I,FNETTOP,FNETFRONT

500 FORMAT(/,5x,'Convergence after',i4,' iterations ',/,5X,

&'FNETTOP,FNETFRONT =',2E15.5,/)

503 continue

C**************************************

write(7,101)

101 FORMAT(//,10x,' ON THE NOSE',/)

WRITE(7,102)Flux,ho,Tliquid,Tamb,Tin,Tm,Theater

102 FORMAT(/,

&5X,'Total Heat Flux= ',F8.3,' BTU/hr.sqft',/,

&5X,'Outer heat transfer coefficient= ',F8.3,

&' BTU/hr.sqft.F',/ ,

&5X,'Liquid Crystal Temperature = ',F8.3,' F',/,

&5X,'Ambient Temperature = ',F8.3,' F',/,

&5X,'Air Inlet Temperature = ',F8.3,' F',/,

&5X,'Air Mixed Mean Temperature',F8.3,' F',/,

&5X,'Heater Temperature= ',F8.3,' F')

write(7,115)Tf

115 FORMAT(5X,'Film Temperatures',F9.3,' F')

221

write(7,110)Tsurf,Ttop,Tfront,Tsurf

110 FORMAT(5x,'Nose, Top, Front and Back Wall Temperatures: ',

&/,10x,4F10.2,' F')

write(7,120)h,hbot,hfront,htop

120 FORMAT(5x,'hnose=',F8.3,1X,'hback=',F8.3,1X,'htop=',F8.3,1X,

&'hfront=',F8.3,' BTU/hr.sqft.F')

write(7,170)Q

170 format(5x,'Total Elect. Power=',F8.3,' BTU/hr')

write(7,116)Qwaste

116 FORMAT(5X,'Total Heat Loss to Ambient=',F8.3,' BTU/hr')

write(7,180)fback,ftop,ffront,fback

180 FORMAT(5X,'Flux Losses from Nose, Front, Ftop and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

write(7,150)Frback,Frtop,Frfront,Frbot

150 FORMAT(5X,'Radiative Fluxes from Back, Top, Front and'

&,' Nose Surfaces:',/,10x,4F10.3,' BTU/sqft.hr')

RETURN

END

C****************************************************************************

C****************************************************************************

C**********************************************************************C

SUBROUTINE RADIATION(Top,Bot,H1,Hlength,Tsurf,Ttop,Tfront,Tbot,

&Frback,Frtop,Frfront,Frnose)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(4,4),B(4,1),E(4),T(4),Q(4)

PI=4.*ATAN(1.E00)

W=H1

H=0.5*(Bot+Top)

T(1)=Tsurf + 460.

T(2)=Ttop + 460.

T(3)=Tfront+ 460.

T(4)=Tbot + 460.

W=W/(3.*Hlength)

H=H/(3.*Hlength)

C Emissivities

E(1)=.85 ! Liquid Crystal Foil, Back Wall

E(2)=.9 ! Plexiglas, Top Wall

222

E(3)=.9 ! Plexiglas, Front Wall

E(4)=.85 ! Liquid Crystal Foil, Nose Wall

C

N=4

SIGMA=0.1712E-08

C WRITE(7,150)

150 FORMAT(//,20X,'SHAPE FACTORS',//)

C

F11=0.

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F12=Z1*(Z2+Z3+Z4+Z5)

F14=F12

F13=1.-F11-F12-F14

C

F31=F13

F32=F12

F33=0.

F34=F14

C

DUM=W

W=H

H=DUM

W2=W*W

H2=H*H

Z1=1./(PI*W)

Z2=W*ATAN(1./W)

Z3=H*ATAN(1./H)

Z=SQRT(H2+W2)

Z4=-Z*ATAN(1./Z)

Z=(1.+W2)*(1.+H2)

ZZ=1.+W2+H2

ZZZ=Z/ZZ

223

Z=W2*ZZ/((1.+W2)*(W2+H2))

Z=Z**W2

ZZZ=ZZZ*Z

Z=H2*ZZ/((1.+H2)*(W2+H2))

Z=Z**H2

ZZZ=ZZZ*Z

Z5=.25*LOG(ZZZ)

F21=Z1*(Z2+Z3+Z4+Z5)

F22=0.

F23=F21

F24=1.-F21-F22-F23

C

F41=F21

F42=F24

F43=F23

F44=0.

C

C WRITE(7,110)F11,F12,F13,F14

C WRITE(7,120)F21,F22,F23,F24

C WRITE(7,130)F31,F32,F33,F34

C WRITE(7,140)F41,F42,F43,F44

C

110 FORMAT(5X,'F11=',F6.4,5X,'F12=',F6.4,5X,'F13=',F6.4,

&5X,'F14=',F6.4,/)

120 FORMAT(5X,'F21=',F6.4,5X,'F22=',F6.4,5X,'F23=',F6.4,

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

130 FORMAT(5X,'F31=',F6.4,5X,'F32=',F6.4,5X,'F33=',F6.4,

&5X,'F34=',F6.4,/)

140 FORMAT(5X,'F41=',F6.4,5X,'F42=',F6.4,5X,'F43=',F6.4,

&5X,'F44=',F6.4,//)

C WRITE(7,160)

160 FORMAT(/,20X,'EMISSIVITIES',//)

C WRITE(7,100)(I,E(I),I=1,N)

C WRITE(7,170)

170 FORMAT(/,20X,'TEMPERATURES IN R',//)

C WRITE(7,100)(I,T(I),I=1,N)

A(1,1)=F11-1./(1.-E(1))

A(1,2)=F12

A(1,3)=F13

A(1,4)=F14

C

A(2,1)=F21

A(2,2)=F22-1./(1.-E(2))

A(2,3)=F23

A(2,4)=F24

C

A(3,1)=F31

A(3,2)=F32

224

A(3,3)=F33-1./(1.-E(3))

A(3,4)=F34

C

A(4,1)=F41

A(4,2)=F42

A(4,3)=F43

A(4,4)=F44-1./(1.-E(4))

C

C WRITE(7,180)

180 FORMAT(//,20X,'COEFFICIENT MATRIX',/)

C WRITE(7,200)((A(I,J),J=1,N),I=1,N)

DO I=1,N

B(I,1)=-E(I)*SIGMA*(T(I)**2.)*(T(I)**2.)/(1.-E(I))

ENDDO

C WRITE(7,250)

C WRITE(7,100)(I,B(I,1),I=1,N)

200 FORMAT(1X,4E15.6)

250 FORMAT(/,20X,'RIGHT HAND SIDE ',/)

C WRITE(7,55)

55 FORMAT(//,20X,'GAUSSIAN ELIMINATION METHOD',/)

CALL EQSOLVE(A,B,N,N,1)

C WRITE(7,50)

C WRITE(7,100)(I,B(I,1),I=1,N)

DO I=1,N

Q(I)=E(I)*(SIGMA*(T(I)**2.)*(T(I)**2.)-B(I,1))/(1.-E(I))

ENDDO

Frback =Q(1)

Frtop =Q(2)

Frfront=Q(3)

Frnose=Q(4)

C WRITE(7,350)

C WRITE(7,100)(I,Q(I),I=1,N)

100 FORMAT(4(I3,E15.6))

50 FORMAT(/,20X,'RADIOCITIES',/)

350 FORMAT(/,20X,'HEAT FLUXES IN BTU/hr.sqft',/)

RETURN

END

C**********************************************************************C

C**********************************************************************C

SUBROUTINE UNCERTAIN(Pamb,Pven,Tven,i1,V1,i2,V2,i4,V4,i5,V5,

&Dth,Harea,Tsurf,Tin,Losses,Uncer,IND)

IMPLICIT REAL*8(A-H,O-Z)

REAL*8 i1,i2,i4,i5,Losses,M1,M2

PI=4.*ATAN(1.E00)

225

C FAC=491.3744

FAC1=3.413 ! converts Watts to BTU/hr

C (3600 s/hr)(144 sqin/sqft)/(1055 J/BTU)

C=0.24*0.5215*3600

C 0.5215 given by Fox, Cp=0.24 BTU/(lbm.R) and 1 BTU=1055 J

P1=Pven+Pamb

T1=Tven+460.0

TI=Tin

TS=Tsurf

a=Harea

f=0.5

ATH=PI*(Dth**2)/4.

DATH=PI*((Dth+0.001)**2)/4. -ATH

h=((FAC1*(V2*i2)/a)-Losses)/

&(TS-TI-(SQRT(T1)*(FAC1*(V1*i1+V4*i4+f*V2*i2+f*V5*i5)))/

&(C*P1*ATH))

WRITE(5,*)' '

if(IND.EQ.1)WRITE(5,*)' hSide =',h,' BUT/hr.sqft.F'

if(IND.EQ.2)WRITE(5,*)' hNose =',h,' BUT/hr.sqft.F'

H2=h*h

C

C i2 v2

C ------- - Floss

C a

C ---------------------------------------

C sqrt(T1)(i1v1+i4v4+fi2v2+fi5v5)

C Ts-Ti - -------------------------

C C P1 A_throat

C

DLOSS=0.1*Losses

dv1=0.1

dv2=0.1

dv4=0.1

dv5=0.1

di1=0.01

226

di2=0.01

di4=0.01

di5=0.01

da=1./(32.*32.*144)

dts=0.5

dti=0.5

dt1=0.5

dp1=0.5

Df=0.1

C1=FAC1*(V2*i2/a)-Losses

Q1=C*P1*Ath

Q2=Q1*sqrt(T1)

M1=(Ts-Ti)*Q1

A=FAC1*(i1*v1+i4*v4)

B=FAC1*(i2*v2+i5*v5)

M2=M1-sqrt(T1)*(A+f*B)

DHDF=B*Q1*C1*sqrt(T1)/(M2**2)

DHDTI= C1*(Q1**2)/(M2**2)

DHDTS=-C1*(Q1**2)/(M2**2)

DHDA=-(FAC1*i2*v2)*Q1/(M2*(a**2))

DHDLOSS=-Q1/M2

DHDI1=FAC1*v1*Q1*C1*sqrt(T1)/(M2**2)

DHDV1=FAC1*i1*Q1*C1*sqrt(T1)/(M2**2)

DHDI4=FAC1*v4*Q1*C1*sqrt(T1)/(M2**2)

DHDV4=FAC1*i4*Q1*C1*sqrt(T1)/(M2**2)

DHDI2=FAC1*v2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV2=FAC1*i2*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDI5=FAC1*v5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDV5=FAC1*i5*Q1*(M2+C1*f*a*sqrt(T1))/(a*(M2**2))

DHDATH=C1*C*P1*(M2-M1)/(M2**2)

DHDP1 =C1*C*Ath*(M2-M1)/(M2**2)

DHDT1=0.5*C1*Q1/(T1*(sqrt(T1)*(A+f*B)))

ZF=(DF*DHDF)**2

ZA=(DA*DHDA)**2

ZI1=(DI1*DHDI1)**2

227

ZV1=(DV1*DHDV1)**2

ZI2=(DI2*DHDI2)**2

ZV2=(DV2*DHDV2)**2

ZI4=(DI4*DHDI4)**2

ZV4=(DV4*DHDV4)**2

ZI5=(DI5*DHDI5)**2

ZV5=(DV5*DHDV5)**2

ZTS=(DTS*DHDTS)**2

ZTI=(DTI*DHDTI)**2

ZATH=(DATH*DHDATH)**2

ZP1=(DP1*DHDP1)**2

ZT1=(DT1*DHDT1)**2

ZLOSS=(DLOSS*DHDLOSS)**2

Uncer=100*SQRT((ZI1+ZI2+ZV1+ZV2+ZI4+ZI4+ZV5+ZV5+

&ZA+ZTS+ZTI+ZATH+ZP1+ZT1+ZLOSS+ZF)/(H2))

if(IND.EQ.1) then

WRITE(4,*)' TOTAL UNCER.%:',Uncer

WRITE(4,*)' '

WRITE(4,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(4,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(4,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(4,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(4,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(4,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h

WRITE(4,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h

WRITE(4,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h

WRITE(4,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h

WRITE(4,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(4,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(4,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(4,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(4,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(4,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(4,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

endif

if(IND.EQ.2) then

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with f',100.*sqrt(ZF)/h

WRITE(5,*)' % Uncer. assoc. with I1',100.*sqrt(ZI1)/h

WRITE(5,*)' % Uncer. assoc. with V1',100.*sqrt(ZV1)/h

WRITE(5,*)' % Uncer. assoc. with I2',100.*sqrt(ZI2)/h

WRITE(5,*)' % Uncer. assoc. with V2',100.*sqrt(ZV2)/h

WRITE(5,*)' % Uncer. assoc. with I4',100.*sqrt(ZI4)/h

228

WRITE(5,*)' % Uncer. assoc. with V4',100.*sqrt(ZV4)/h

WRITE(5,*)' % Uncer. assoc. with I5',100.*sqrt(ZI5)/h

WRITE(5,*)' % Uncer. assoc. with V5',100.*sqrt(ZV5)/h

WRITE(5,*)' % Uncer. assoc. with Tin',100.*sqrt(ZTI)/h

WRITE(5,*)' % Uncer. assoc. with Ts',100.*sqrt(ZTS)/h

WRITE(5,*)' % Uncer. assoc. with Tven',100.*sqrt(ZT1)/h

WRITE(5,*)' % Uncer. assoc. with Pven',100.*sqrt(ZP1)/h

WRITE(5,*)' % Uncer. assoc. with Aheater',100.*sqrt(ZA)/h

WRITE(5,*)' % Uncer. assoc. with Floss',100.*sqrt(ZLOSS)/h

WRITE(5,*)' % Uncer. assoc. with Athroat',100.*sqrt(ZATH)/h

endif

RETURN

END

C**********************************************************************C

C**********************************************************************C

SUBROUTINE EQSOLVE(A,B,NA,NDIM,NB)

IMPLICIT REAL*8(A-H,O-Z)

DIMENSION A(NDIM,NDIM),B(NDIM,NB)

DO 291 J1=1,NA

C FIND REMAINING ROW CONTAINING LARGEST ABSOLUTE

C VALUE IN PIVOTAL COLUMN.

101 TEMP=0.

DO 121 J2=J1,NA

IF(ABS(A(J2,J1))-TEMP) 121,111,111

111 TEMP=ABS(A(J2,J1))

IBIG=J2

121 CONTINUE

IF(IBIG-J1)5001,201,131

C REARRANGING ROWS TO PLACE LARGEST ABSOLUTE

C VALUE IN PIVOT POSITION.

131 DO 141 J2=J1,NA

TEMP=A(J1,J2)

A(J1,J2)=A(IBIG,J2)

141 A(IBIG,J2)=TEMP

DO 161 J2=1,NB

TEMP=B(J1,J2)

B(J1,J2)=B(IBIG,J2)

161 B(IBIG,J2)=TEMP

C COMPUTE COEFFICIENTS IN PIVOTAL ROW.

201 TEMP=A(J1,J1)

DO 221 J2=J1,NA

221 A(J1,J2)=A(J1,J2)/TEMP

DO 231 J2=1,NB

231 B(J1,J2)=B(J1,J2)/TEMP

229

IF(J1-NA)236,301,5001

C COMPUTE NEW COEFFICIENTS IN REMAINING ROWS.

236 N1=J1+1

DO 281 J2=N1,NA

TEMP=A(J2,J1)

DO 241 J3=N1,NA

241 A(J2,J3)=A(J2,J3)-TEMP*A(J1,J3)

DO 251 J3=1,NB

251 B(J2,J3)=B(J2,J3)-TEMP*B(J1,J3)

281 CONTINUE

291 CONTINUE

C OBTAINING SOLUTIONS BY BACK SUBSTITUTION.

301 IF(NA-1)5001,5001,311

311 DO 391 J1=1,NB

N1=NA

321 DO 341 J2=N1,NA

341 B(N1-1,J1)=B(N1-1,J1)-B(J2,J1)*A(N1-1,J2)

N1=N1-1

IF(N1-1)5001,391,321

391 CONTINUE

5001 CONTINUE

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

230

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

231

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

232

Rig3b-reduce-friction.f

IMPLICIT REAL*8(A-H,O-Z)

CHARACTER*80 TITLE

REAL*8 Mv,NoseR,NoseL

F(A,P,T)=0.5215*A*P/SQRT(T) ! Correlation for the critical venturi

! provided by the manufacturer (Fox Valves)

PI=4.*ATAN(1.E00)

! C O N V E R S I O N F A C T O R S

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

Oiltopsi=0.827*Hgtopsi/13.6 ! converts inches of Oil to psi

PFAC=248.8*1.4504E-04*144 ! converts inches of H2O to psf

Rgas=53.34 ! gas constant for air

! I N P U T / O U T P U T F I L E S

OPEN(UNIT=1, FILE='input.dat',STATUS='old')

OPEN(UNIT=5, FILE='fric-uncertain.out',STATUS='old')

OPEN(UNIT=7, FILE='friction.out',STATUS='old')

OPEN(UNIT=8, FILE='friction-plot.out',STATUS='old')

! T E S T S E C T I O N G E O M E T R Y

! T E S T S E C T I O N G E O M E T R Y

NoseR=1.281 ! inches

NoseR=NoseR/12 ! feet

Angle=138. ! degrees

RigL=36. ! inches

Side=3. ! inches

Side=Side/12 ! feet

Side2=1.372 ! inches

Side2=Side2/12 ! feet

C

C CALCULATION

hypo1=sqrt(NoseR**2 + SIDE**2)

hypo2=sqrt(NoseR**2 + SIDE2**2)

233

beta1=atan(NoseR/SIDE)*180/PI

beta2=atan(NoseR/SIDE2)*180/PI

alpha1=90-beta1

alpha2=90-beta2

gamma1=180-0.5*Angle-alpha1

gamma2=180-0.5*Angle-alpha2

l1=NoseR*tan(0.5*Angle*PI/180)

l2=NoseR*tan(0.5*Angle*PI/180)

a=SIDE +l1

b=SIDE2+l2

Top=sqrt(a**2 + b**2 - 2*a*b*COS((180-Angle)*PI/180))

stheta1=(hypo2/Top)*SIN((gamma1+gamma2)*PI/180)

stheta2=(hypo1/Top)*SIN((gamma1+gamma2)*PI/180)

theta1=Asin(stheta1)*180/PI

theta2=Asin(stheta2)*180/PI

sigma1=180-gamma1-theta1

sigma2=180-gamma2-theta2

Pitch=2.48 ! inches

nturb=9

Have=hypo1*(SIN(theta1*PI/180)/SIN(sigma1*PI/180)) +

&NoseR*COS(0.5*Angle*PI/180)

Wave=0.5*Top+NoseR*SIN(0.5*Angle*PI/180)

Bot=2*NoseR*(SIN(0.5*Angle*PI/180)) ! Flat projected bottom for radiation losses only

NoseL=2*PI*NoseR*(Angle/360)

Perim=NoseL+Side+side2+Top

Area1=0.5*NoseR*SIDE

Area2=0.5*NoseR*SIDE2

AreaNose=(PI*(NoseR**2)*(Angle/360))

AreaTop=0.5*hypo1*hypo2*sin((gamma1+gamma2)*PI/180)

Across=Area1+Area2+AreaNose+AreaTop

Dh=4*Across/Perim

234

read(1,*)ntests,TurbH,TurbW,Turbr

DO 333 I=1,10

READ(1,10)TITLE

WRITE(5,10)TITLE

333 WRITE(7,10)TITLE

10 FORMAT(A80,//)

Write(7,101)12.*NoseR,Angle,12.*NoseL,12.*Side,12.*Side,

&12.*Top,12.*Bot,12.*Perim,144.*ACross,12*Dh,Pitch,RigL

101 format(/,

&2x,'Nose Radius=',f8.3,' inches',/,

&2x,'Nose Angle=',f8.3,' degrees',/,

&2x,'Nose Length=',f8.3,' inches',/,

&2x,'Side 1 (Plexi)=',f8.3,' inches',/,

&2x,'Side 2 (LC)=',f8.3,' inches',/,

&2x,'Top=',f8.3,' inches',/,

&2x,'Bottom Flat Line=',f8.3,' inches',/,

&2x,'Cross Section Perimter=',f8.3,' inches',/,

&2x,'Cross Section Area=',f8.3,' sq. in',/,

&2x,'Test Section Hydraulic Diameter=',f8.3,' inches',/,

&2x,'Turbulator Pitch=',f8.3,' inches',/,

&2x,'Test Section Length=',f8.3,' inches',/)

Poe=Pitch/TurbH

eoDh=TurbH/(12*Dh)

WRITE(7,402)ntests,TurbH,TurbW,Turbr,eoDh,Poe

401 FORMAT(I4)

402 FORMAT(10x,'********************',/,

&2x,'NUMBER OF TESTS : ',I5,/,

&2x,'Turbulator Height=',f8.3,' inches',/,

&2x,'Turbulator Width=',f8.3,' inches',/,

&2x,'Turbulator Corner Radius=',f8.3,' inches',/,

&2x,'Turb Height over Channel Hydraulic diameter=',f9.4,/,

&2x,'Turb Pith over Height=',f8.3,/,

&10x,'********************',/)

! R E A D I N D A T A

DO i=1,ntests

READ(1,*)testno,Pven,Tven,Tin1,Tin2,Tamb,

&SG,Pplen,Pinlet,Pamb,Dthroat

WRITE(7,*)' '

WRITE(7,*)' '

235

WRITE(7,100) i

WRITE(7,*)' '

WRITE(7,*)' Collected Data: testno,Pven,Pplen,Pinlet'

WRITE(7,*)' Tven,Tin1,Tin2,Tamb,Pamb'

WRITE(7,*)' '

WRITE(7,200)testno,Pven,Pplen,Pinlet

200 FORMAT(5X,F3.0,' ',F5.1,2(' ',F7.4))

WRITE(7,202)Tven,Tin1,Tin2,Tamb,Pamb

202 FORMAT(5X,4(' ',F5.1),2X,F5.2)

Athroat=PI*(Dthroat**2)/4. ! square inches

WRITE(7,403)Dthroat

403 Format(2x,'Venturi Throat Diameter=',f8.3,' inches',/)

Pamb=Pamb*Hgtopsi ! psi

Tin=(Tin1+Tin2)/2.

C AIR MASS FLOW RATE FROM THE CRITICAL VENTURI

Mv=F(Athroat,Pven+Pamb,Tven+460)

TinR=Tin+460.

CALL AIRPROP(TinR,gamain,CONin,VISin,PRin,CPin)

VISin=VISin/3600.

C REYNOLDS NUMBER

Re=4.*Mv/(Perim*VISin)

C***************************************************

! DARCY FRICTION FACTOR CALCULATIONS

Pplen=2*Pplen*H2Otopsi+Pamb

DeltaP=2*Pinlet ! inches of water using Micromanometer

Rho=(Pamb+0.5*DeltaP*H2Otopsi)*144./(Rgas*(TinR))

Um=Mv/(Across*Rho)

fDarcy=gc*((12.*Dh)/(nturb*Pitch))*(DeltaP*H2Otopsi*144.)/

&(0.5*Rho*(Um**2))

236

CALL UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)

fsmooth=0.316/(Re**0.25) ! Blasius correlation

write(7,303)Pamb,Pplen,DeltaP,Rho,Um,fDarcy,fsmooth,

&fDarcy/fsmooth

WRITE(8,304)Re,fDarcy,fsmooth,fDarcy/fsmooth

304 format(f8.1,2(4x,E13.7),F8.3)

303 format(/,

&5x,'Ambient Pressure=',f9.4,' psia',/,

&5x,'Plenum Pressure=',f9.4,' psia',/,

&5x,'Pressure Drop =',f9.4,' inches of water',/,

&5x,'Air Density=',f9.4,' lbm/cu.ft',/,

&5x,'Air Average Velocity=',f9.4,' ft/s',/,

&5x,'Darcy Friction Factor=',f9.4,/,

&5x,'Smooth Channel Darcy Friction Factor=',f9.4,/,

&5x,'f_turb/f_Smooth=',f9.4,/)

C **********************************************************

ENDDO

100 FORMAT(30X,'TEST # ',I2)

300 FORMAT(/,30X,'Tm=',F6.2,' Mv=',E9.3,'lbs/sec',1X,'Re=',F8.2)

STOP

END

C**********************************************************************C

SUBROUTINE UNCERTAIN(Dh,RigL,DeltaP,Rho,Um,Uncer)

IMPLICIT REAL*8(A-H,O-Z)

Hgtopsi= 0.49083935 ! converts inches of Hg to psi

H2Otopsi=Hgtopsi/13.6 ! converts inches of H2O to psi

gc=32.2 ! proportionality constant in Newton's 2nd law, lbm.ft/(lbf.s2)

C=24*144*gc*H2Otopsi

dDh =0.05/12.

dRigL =0.1 ! inches

dDeltaP=0.002*H2Otopsi ! 0.002 inches of water

dRho =0.02*Rho ! 2% error

dUm =0.02*Um ! 2% error

237

fDarcy=gc*((12.*Dh)/RigL)*(DeltaP*H2Otopsi*144.)/

&(0.5*Rho*(Um**2))

f2=fDarcy**2

WRITE(5,*)' '

WRITE(5,*)' fDarcy =',fDarcy

WRITE(5,*)' '

dfdDh=C*DeltaP/(RigL*Rho*(Um**2))

dfdDeltaP=C*Dh/(RigL*Rho*(Um**2))

dfdRigL=-C*Dh*DeltaP/(RigL*RigL*Rho*(Um**2))

dfdRho=-C*Dh*DeltaP/(RigL*Rho*Rho*(Um**2))

dfdUm=-2*C*Dh*DeltaP/(RigL*Rho*(Um**3))

ZDh=(dfdDh*dDh)**2

ZRigL=(dfdRigL*dRigL)**2

ZDeltaP=(dfdDeltaP*dDeltaP)**2

ZRho=(dfdRho*dRho)**2

ZUm=(dfdUm*dUm)**2

Uncer=100*SQRT((ZDh+ZRigL+ZDeltaP+ZRho+ZUm)/(f2))

WRITE(5,*)' TOTAL UNCER.%:',Uncer

WRITE(5,*)' '

WRITE(5,*)' % Uncer. assoc. with Dh',100.*sqrt(ZDh)/fDarcy

WRITE(5,*)' % Uncer. assoc. with RigL',100.*sqrt(ZRigL)/fDarcy

WRITE(5,*)' % Uncer. assoc. with DeltaP',100.*sqrt(ZDeltaP)/fDarcy

WRITE(5,*)' % Uncer. assoc. with Rho',100.*sqrt(ZRho)/fDarcy

WRITE(5,*)' % Uncer. assoc. with Um',100.*sqrt(ZUm)/fDarcy

RETURN

END

C**********************************************************************C

SUBROUTINE AIRPROP(t,gamx,kx,mux,prx,cpx)

IMPLICIT REAL*8(A-H,O-Z)

c physical properties of dry air at one atmosphere

c ref: ge heat transfer handbook

c

c temperature range: 160 to 3960 deg. rankine

238

c -300 to 3500 deg. fahreinheit

c

c t - temperature, R

c gamx - ratios of specific heats

c kx - thermal conductivity, BTU/hr.ft.R

c mux - viscosity, lbm/hr.ft

c prx - prandtl no.

c cpx - specific heat, BTU/lbm.R

c

c

dimension tab(34),gam(34),pr(34),cp(34)

real*8 k(34),mu(34),kx,mux

data nent/34/

data tab/ 160., 260.,

& 360., 460., 560., 660., 760., 860., 960., 1060.,

& 1160., 1260., 1360., 1460., 1560., 1660., 1760., 1860.,

& 1960., 2060., 2160., 2260., 2360., 2460., 2560., 2660.,

& 2760., 2860., 2960., 3160., 3360., 3560., 3760., 3960./

data gam/ 1.417, 1.411,

& 1.406, 1.403, 1.401, 1.398, 1.395, 1.390, 1.385, 1.378,

& 1.372, 1.366, 1.360, 1.355, 1.350, 1.345, 1.340, 1.336,

& 1.332, 1.328, 1.325, 1.321, 1.318, 1.315, 1.312, 1.309,

& 1.306, 1.303, 1.299, 1.293, 1.287, 1.281, 1.275, 1.269/

data k/ 0.0063,0.0086,

& 0.0108,0.0130,0.0154,0.0176,0.0198,0.0220,0.0243,0.0265,

& 0.0282,0.0301,0.0320,0.0338,0.0355,0.0370,0.0386,0.0405,

& 0.0422,0.0439,0.0455,0.0473,0.0490,0.0507,0.0525,0.0542,

& 0.0560,0.0578,0.0595,0.0632,0.0666,0.0702,0.0740,0.0780/

data mu/ 0.0130,0.0240,

& 0.0326,0.0394,0.0461,0.0519,0.0576,0.0627,0.0679,0.0721,

& 0.0766,0.0807,0.0847,0.0882,0.0920,0.0950,0.0980,0.1015,

& 0.1045,0.1075,0.1101,0.1110,0.1170,0.1200,0.1230,0.1265,

& 0.1300,0.1330,0.1360,0.1420,0.1480,0.1535,0.1595,0.1655/

data pr/ 0.7710,0.7590,

& 0.7390,0.7180,0.7030,0.6940,0.6860,0.6820,0.6790,0.6788,

& 0.6793,0.6811,0.6865,0.6880,0.6882,0.6885,0.6887,0.6890,

& 0.6891,0.6893,0.6895,0.6897,0.6899,0.6900,0.6902,0.6905,

& 0.6907,0.6909,0.6910,0.6913,0.6917,0.6921,0.6925,0.6929/

data cp/ 0.247, 0.242,

& 0.241, 0.240, 0.241, 0.242, 0.244, 0.246, 0.248, 0.251,

& 0.254, 0.257, 0.260, 0.264, 0.267, 0.270, 0.272, 0.275,

& 0.277, 0.279, 0.282, 0.284, 0.286, 0.288, 0.291, 0.293,

& 0.296, 0.298, 0.300, 0.305, 0.311, 0.318, 0.326, 0.338/

c

c

if(t.lt.tab(1)) print 510,t,tab(1)

510 format(" in airprop --- temp=",f8.1," is less than min temp",

&" of ",f8.1)

239

if(t.gt.tab(nent)) print 520, t,tab(nent)

520 format(" in airprop --- temp=",f8.1," is greater than max",

&" temp of ",f8.1)

if(t-tab(1))120,120,100

100 if(tab(nent)-t)130,130,110

110 m=2

go to 140

120 j=1

go to 180

130 j=nent

go to 180

140 if(t-tab(m))160,170,150

150 m=m+1

go to 140

c

c -- Linear Interpolation ---

c

160 slp=(t-tab(m-1))/(tab(m)-tab(m-1))

mux= mu(m-1)+(mu(m)-mu(m-1))*slp

prx= pr(m-1)+(pr(m)-pr(m-1))*slp

cpx=cp(m-1)+(cp(m)-cp(m-1))*slp

kx=k(m-1)+(k(m)-k(m-1))*slp

gamx=gam(m-1)+(gam(m)-gam(m-1))*slp

go to 190

170 j=m

go to 180

180 mux=mu(j)

prx=pr(j)

cpx=cp(j)

kx=k(j)

gamx=gam(j)

190 return

end

C**********************************************************************C

240

Appendix B.1: Rig 1 Results (Nusselt Number, Enhancement Factor,

Friction Factor, and Thermal Performance)

Rig1 Min Turbulator

Avg Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6893.07 3.21 4.60 75.67 108.19 1.56 2.24

10411.57 3.05 4.29 100.14 140.36 1.43 2.01

15340.89 2.91 3.98 130.18 177.73 1.33 1.82

21109.06 2.70 3.73 155.71 214.92 1.23 1.70

30821.30 2.65 3.57 207.27 278.80 1.18 1.59

40624.05 2.64 3.42 257.41 332.56 1.15 1.49

Rig1 Nominal Turbulator

Avg Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6890.38 3.53 5.00 83.29 117.58 1.47 2.07

10411.54 3.29 4.53 107.97 148.31 1.33 1.82

15344.07 3.04 4.19 140.11 187.28 1.20 1.66

21171.73 3.06 4.03 176.84 233.00 1.20 1.58

31166.21 2.91 3.72 229.39 292.77 1.11 1.42

41161.35 2.73 3.58 269.12 352.74 1.02 1.34

Rig1 Max Turbulator

Avg Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6916.61 3.84 5.33 90.66 125.81 1.42 1.97

10435.14 3.51 4.71 115.16 154.51 1.27 1.70

15360.82 3.13 4.17 140.16 186.63 1.11 1.48

21170.30 3.08 3.92 178.32 226.35 1.09 1.38

31177.92 2.91 3.75 229.50 295.64 1.00 1.28

41188.24 2.88 3.58 283.39 352.88 0.99 1.23

241

Rig 1 Min Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

6942.26 0.297 0.035 8.579

8708.73 0.306 0.033 9.364

10475.87 0.304 0.031 9.719

12236.06 0.298 0.030 9.908

14004.98 0.297 0.029 10.217

15757.82 0.294 0.028 10.413

17702.30 0.276 0.027 10.079

21290.16 0.279 0.026 10.657

24870.15 0.274 0.025 10.881

28419.48 0.271 0.024 11.124

31948.93 0.269 0.024 11.363

35658.60 0.267 0.023 11.607

39295.53 0.266 0.022 11.868

42903.34 0.266 0.022 12.118

Rig 1 Nominal Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

6906.82 0.491 0.035 14.159

8672.85 0.485 0.033 14.826

10435.90 0.480 0.031 15.365

12199.98 0.466 0.030 15.493

13972.63 0.465 0.029 16.008

15738.36 0.455 0.028 16.125

17643.91 0.439 0.027 16.022

21229.98 0.434 0.026 16.573

24787.91 0.430 0.025 17.084

28381.49 0.430 0.024 17.657

31973.11 0.426 0.024 18.009

35559.22 0.428 0.023 18.596

39169.58 0.427 0.022 19.022

42751.52 0.428 0.022 19.492

Rig 1 Max Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

6989.91 0.691 0.035 19.981

8750.26 0.675 0.033 20.646

10507.61 0.673 0.031 21.554

12274.80 0.651 0.030 21.693

14042.80 0.637 0.029 21.935

15808.69 0.627 0.028 22.235

17642.03 0.613 0.027 22.367

21216.50 0.605 0.026 23.104

24794.71 0.597 0.025 23.714

28385.40 0.595 0.024 24.452

31982.14 0.591 0.024 25.015

35588.60 0.552 0.023 23.990

39210.76 0.569 0.022 25.347

42797.99 0.562 0.022 25.579

242

Appendix B.2: Rig 2 Results (Nusselt Number, Enhancement Factor,

Friction Factor, and Thermal Performance)

Rig2 Min Turbulator

Avg Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6220.73 2.578 2.604 55.96 56.50 1.63 1.64

9493.66 2.609 2.602 79.42 79.21 1.54 1.54

13916.84 2.449 2.658 101.24 109.89 1.38 1.50

18668.34 2.310 2.311 120.80 120.79 1.31 1.31

28066.29 2.223 2.202 161.13 159.62 1.22 1.21

37674.07 2.242 2.192 205.55 201.18 1.21 1.18

Rig2 Nominal Turbulator

Avg Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6213.23 2.938 3.209 63.72 69.60 1.66 1.81

9488.07 2.870 3.014 87.32 91.71 1.55 1.63

13911.05 2.760 2.873 114.09 118.76 1.41 1.47

18546.96 2.721 2.561 141.60 133.23 1.37 1.29

28155.52 2.486 2.423 180.65 176.14 1.24 1.21

37461.78 2.433 2.352 222.10 214.82 1.20 1.16

Rig 2 Max Turbulator

Avg Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6152.94 3.027 3.567 65.13 76.73 1.51 1.78

9459.86 2.995 3.212 90.90 97.52 1.45 1.55

13850.38 2.868 3.117 118.08 128.26 1.35 1.47

18650.01 2.493 2.755 130.36 144.16 1.17 1.29

28103.61 2.493 2.652 180.91 192.36 1.15 1.22

37299.56 2.556 2.570 232.48 233.95 1.16 1.16

243

Rig 2 Minimum Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

5394.5 0.089 0.037 2.4

6762 0.141 0.035 4.038

8136.8 0.155 0.033 4.67

9507.1 0.171 0.032 5.337

10885.7 0.174 0.031 5.627

12263.7 0.172 0.030 5.719

13641.7 0.167 0.029 5.711

15023.3 0.167 0.029 5.845

16225.4 0.149 0.028 5.321

19015.1 0.154 0.027 5.727

21802.6 0.150 0.026 5.76

24586.8 0.150 0.025 5.938

27510.5 0.145 0.025 5.893

30258.7 0.147 0.024 6.127

33010.2 0.146 0.023 6.236

35765.3 0.145 0.023 6.309

38491.5 0.143 0.023 6.337

Rig 2 Nominal Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

5415.7 0.176 0.037 4.791

6781.3 0.225 0.035 6.463

8156.2 0.214 0.033 6.434

9531.6 0.214 0.032 6.682

10907.7 0.218 0.031 7.049

12278.2 0.215 0.030 7.173

13654.5 0.216 0.029 7.404

15039.8 0.219 0.029 7.691

16382.7 0.215 0.028 7.712

19140.2 0.214 0.027 7.953

21904.4 0.209 0.026 8.039

24680.9 0.205 0.025 8.129

27458.2 0.203 0.025 8.29

30218.4 0.199 0.024 8.309

32994.3 0.194 0.023 8.295

35808.1 0.193 0.023 8.405

38642.6 0.189 0.023 8.405

Rig 2 Maximum Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

5371.7 0.267 0.037 7.223

6748.3 0.282 0.035 8.086

8124.6 0.292 0.033 8.763

9493.9 0.285 0.032 8.892

10864.8 0.283 0.031 9.138

12236.3 0.284 0.030 9.439

13617.5 0.285 0.029 9.742

14998.4 0.281 0.029 9.847

16457.1 0.276 0.028 9.904

19227.3 0.265 0.027 9.89

21998.7 0.259 0.026 9.997

24850.3 0.257 0.025 10.212

27734.7 0.253 0.024 10.35

30420.5 0.250 0.024 10.467

33160.7 0.249 0.023 10.619

35875.5 0.244 0.023 10.622

38573.6 0.245 0.023 10.859

244

Appendix B.3: Rig 3A Results (Nusselt Number, Enhancement Factor,

Friction Factor, and Thermal Performance)

Rig3A Minimum Turbulator

Avg

Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6892 2.701 2.913 63.653 68.632 1.515 1.633

10201 2.686 3.078 86.588 99.205 1.453 1.666

15344 2.463 2.902 110.084 129.682 1.279 1.508

20504 2.399 2.776 135.225 156.405 1.240 1.434

31313 2.186 2.845 172.934 224.944 1.105 1.438

41169 2.165 2.672 213.234 263.011 1.078 1.330

Rig3A Nominal Turbulator

Avg

Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6850 2.771 3.413 64.978 79.986 1.423 1.753

10200 2.460 3.097 79.350 99.808 1.216 1.531

15358 2.339 2.741 104.698 122.612 1.115 1.306

20427 2.397 2.834 134.780 159.250 1.136 1.344

31154 2.231 2.908 176.297 228.936 1.035 1.349

41022 2.234 2.592 219.432 254.454 1.023 1.187

Rig3A Maximum Turbulator

Avg

Re

Avg EF

Wall

Avg EF

Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

Avg TP

Nose

6795 3.002 3.613 69.923 84.136 1.382 1.664

10152 2.790 3.495 89.621 112.194 1.229 1.540

15316 2.680 3.423 119.662 152.682 1.153 1.472

20494 2.698 3.297 152.039 185.619 1.141 1.395

31126 2.552 3.068 201.000 241.539 1.073 1.290

40911 2.530 2.971 247.888 291.036 1.046 1.228

245

Rig 3A Minimum Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

7338 0.287 0.034 8.397

9184.2 0.244 0.032 7.568

11027.6 0.254 0.031 8.251

12867.7 0.249 0.030 8.398

14709.8 0.247 0.029 8.592

16560.8 0.245 0.028 8.801

18410.6 0.245 0.027 9.02

20260.3 0.240 0.026 9.08

22117.4 0.238 0.026 9.177

23968.7 0.236 0.025 9.288

25798.6 0.235 0.025 9.42

37151.5 0.220 0.023 9.667

41004.7 0.219 0.022 9.877

44892.6 0.218 0.022 10.052

48649.7 0.217 0.021 10.195

52366.6 0.214 0.021 10.227

Rig 3A Nominal Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

7261.8 0.321 0.034 9.375

9109.3 0.326 0.032 10.093

10953.1 0.310 0.031 10.049

12799.1 0.311 0.030 10.46

14651.7 0.333 0.029 11.585

16502.1 0.325 0.028 11.671

18344.2 0.324 0.027 11.936

20199.1 0.314 0.027 11.833

22037.3 0.309 0.026 11.933

23986 0.305 0.025 12.026

25876.1 0.300 0.025 12.025

37119.1 0.288 0.023 12.654

40868.1 0.283 0.022 12.747

44634.2 0.279 0.022 12.823

48320.6 0.274 0.021 12.837

52128.8 0.273 0.021 13.048

Rig 3A Maximum Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

7275.9 0.450 0.034 13.145

9117.9 0.450 0.032 13.911

10967.7 0.438 0.031 14.198

12807.7 0.446 0.030 15.02

14658.6 0.452 0.029 15.737

16499.1 0.438 0.028 15.725

18345.3 0.436 0.027 16.063

20199.2 0.431 0.027 16.275

22041.9 0.429 0.026 16.551

23883.2 0.423 0.025 16.635

25790.7 0.418 0.025 16.779

37253.2 0.389 0.023 17.096

41076 0.386 0.022 17.41

44910.9 0.381 0.022 17.564

48653.8 0.382 0.021 17.932

52401.8 0.380 0.021 18.187

246

Appendix B.4: Rig 3B Results (Nusselt Number, Enhancement Factor,

Friction Factor, and Thermal Performance)

Rig3B Min Turb

Avg

Re

Avg EF

Wall Avg EF Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

6878 3.030 Same as Rig 3A 71.269 68.632 1.696

10206 2.896 Same as Rig 3A 93.409 99.205 1.592

15384 2.751 Same as Rig 3A 123.256 129.682 1.427

20540 2.654 Same as Rig 3A 149.871 156.405 1.350

31145 2.446 Same as Rig 3A 192.644 224.944 1.226

41030 2.337 Same as Rig 3A 229.500 263.011 1.163

Rig3B Nom Turb

Avg

Re

Avg EF

Wall Avg EF Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

6898 3.191 Same as Rig 3A 75.260 79.986 1.639

10238 3.084 Same as Rig 3A 99.730 99.808 1.499

15381 2.957 Same as Rig 3A 132.446 122.612 1.368

20543 2.895 Same as Rig 3A 163.458 159.250 1.332

31232 2.768 Same as Rig 3A 218.596 228.936 1.261

41143 2.589 Same as Rig 3A 254.864 254.454 1.160

Rig3B Nom Turb

Avg

Re

Avg EF

Wall Avg EF Nose

Avg Nu

Wall

Avg Nu

Nose

Avg TP

Wall

6898 3.191 Same as Rig 3A 75.260 79.986 1.639

10238 3.084 Same as Rig 3A 99.730 99.808 1.499

15381 2.957 Same as Rig 3A 132.446 122.612 1.368

20543 2.895 Same as Rig 3A 163.458 159.250 1.332

31232 2.768 Same as Rig 3A 218.596 228.936 1.261

41143 2.589 Same as Rig 3A 254.864 254.454 1.160

247

Rig 3B Minimum Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

7270.7 0.225 0.034 6.575

9106.8 0.225 0.032 6.962

10953.6 0.241 0.031 7.789

12798.3 0.239 0.030 8.029

14640.4 0.238 0.029 8.277

16485.8 0.244 0.028 8.75

18322.3 0.243 0.027 8.956

20164.1 0.247 0.027 9.322

22004.7 0.236 0.026 9.092

23863.2 0.246 0.025 9.663

25714 0.240 0.025 9.626

37266.3 0.227 0.023 9.977

40958.3 0.227 0.022 10.228

44751.8 0.225 0.022 10.363

48381.7 0.221 0.021 10.376

52250.1 0.219 0.021 10.482

Rig 3B Nominal Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

7277.9 0.320 0.034 9.366

9109.2 0.327 0.032 10.108

10947.2 0.326 0.031 10.539

12798.7 0.332 0.030 11.174

14654.4 0.341 0.029 11.885

16496.1 0.339 0.028 12.148

18333.6 0.331 0.027 12.17

20168.1 0.320 0.027 12.052

22015.4 0.322 0.026 12.413

23866.1 0.323 0.025 12.694

25768.8 0.319 0.025 12.807

37184.2 0.296 0.023 13.014

41009.8 0.297 0.022 13.365

44785.1 0.291 0.022 13.399

48527.7 0.288 0.021 13.533

52228.6 0.285 0.021 13.643

Rig 3B Maximum Turbulator Cold Friction Factor

Re Fdarcy Fsmooth Fdarcy/Fsmooth

7237.2 0.418 0.034 12.211

9073.1 0.450 0.032 13.902

10917.9 0.424 0.031 13.729

12763.9 0.446 0.030 14.998

14610 0.444 0.029 15.442

16453.3 0.432 0.028 15.493

18308.8 0.426 0.027 15.684

20155.9 0.428 0.027 16.144

22011.7 0.423 0.026 16.321

23851.3 0.421 0.025 16.554

25679.6 0.415 0.025 16.626

37202.6 0.396 0.023 17.401

41071.6 0.394 0.022 17.742

44954.8 0.390 0.022 17.988

48708.1 0.387 0.021 18.21

52377.6 0.386 0.021 18.459

248