Citation
Use of metallic foams for heat-transfer enhancement in the cooling jacket of a rocket propulsion element

Material Information

Title:
Use of metallic foams for heat-transfer enhancement in the cooling jacket of a rocket propulsion element
Creator:
Avenall, Ryan Jeffrey ( Dissertant )
Chung, Jacob N. ( Thesis advisor )
Ingley, Skip ( Reviewer )
Sankar, Bhavani ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
2004
Language:
English
Physical Description:
xiii, 94 p.

Subjects

Subjects / Keywords:
Coolants ( jstor )
Cooling ( jstor )
Foams ( jstor )
Heat flux ( jstor )
Heat transfer ( jstor )
Heaters ( jstor )
Nickel ( jstor )
Pressure reduction ( jstor )
Rocket propulsion ( jstor )
Wall temperature ( jstor )
Mechanical and Aerospace Engineering thesis, M.S
Dissertations, Academic -- UF -- Mechanical and Aerospace Engineering

Notes

Abstract:
Rocket propulsion has been used in many different aspects of space travel and military tasks. Nearly 800 years ago, the Chinese were the first to develop this concept using solid propellants. Since the early 1900's, fuel-cooled thrust chambers have been a concern as well as an ongoing advancement in rocket propulsion. With the higher demand today for longer lasting and farther travel, and the extreme temperatures that these elements experience, a break-through technology is needed in the cooling of these thrust chambers. In this thesis the idea of using a porous metallic foam will be implemented and tested for its heat transfer capabilities inorder to solve this problem. The goal is to cool the hot wall temperatures without creating large pressure drops in the coolant passage. The testing of this idea involves two systems: a large-scale system and a small-scale system. In both these systems the coolant will be nitrogen gas compressed to 300 psig. The nitrogen then flows through an annulus and is exhausted into the atmosphere. Constant heat flux heaters placed inside the inner tube of the annulus will produce the hot wall temperatures. Then using thermocouples, the hot wall temperatures will be read into an Excel spreadsheet. The pressure drop is measured using two digital pressure gauges. For the large system a heat transfer enhancement for the copper foam was found to be 1.5 or 50% and for nickel foam was found to be 1.82 or 82%. This caused the hot wall temperatures to decrease by an average of 71.84⁰ F and 100.74⁰ F for the copper and nickel foams, respectively. The pressure drop through the copper foam and nickel foam remained about the same and was 1 psig for 23 cfm and 3 psig for 45 cfm in comparison to zero pressure drop for the open channel system. For the small system a heat transfer enhancement for the copper foam was found to be 1.14 or 14% and for nickel foam was found to be 1.15 or 15%. The wall temperatures in this system decreased by an average of 29.04⁰ F and 36.04⁰ F for the copper and nickel foams respectively. The pressure drop through the copper foam and nickel foam relative to the open channel is 1.2 psig and 0.8 psig, respectively, for 23 cfm, and for 45 cfm the pressure drop is 2.8 psig and 2.6 psig, respectively.
Subject:
foams, heat, metal, porous, propulsion, transfer
General Note:
Title from title page of source document.
General Note:
Document formatted into pages; contains 107 pages.
General Note:
Includes vita.
Thesis:
Thesis (M.S.)--University of Florida, 2004.
Bibliography:
Includes bibliographical references.
Original Version:
Text (Electronic thesis) in PDF format.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Avenall, Ryan Jeffrey. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
12/18/2004
Resource Identifier:
57722291 ( OCLC )

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Full Text











USE OF METALLIC FOAMS FOR HEAT TRANSFER ENHANCEMENT IN THE
COOLING JACKET OF A ROCKET PROPULSION ELEMENT















By

RYAN JEFFREY AVENALL


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Ryan Jeffrey Avenall

































This document is dedicated to the Lord, the giver of life, my provider, for without Him
none of this would have been possible.















ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Jacob N. Chung, for believing in me and for

giving me the opportunity to embark on this wonderful research topic. I would also like

to thank my committee, Dr. Skip Ingley, and Dr. Bhavani Sankar, for their much needed

help and advice. NASA provided the funding for this project through URETI.

I would also like to thank my parents who have persevered with me through this

campaign and have given me the guidance in every walk of life. Also, I thank my fiancee

Debbie Simonson, who has repeatedly help me through the times when I wanted to quit.

I also would like to thank my roommate Landon Tully for his continued support. He has

helped me prepare my test facility as well as give me motivation to continue pursuing this

degree. I thank the people involved with me at the Rock Church of Gainesville for all

their prayers and support. Finally I would like to thank the One who has given me life

more abundantly, and whose name is above all names.










TABLE OF CONTENTS


page

A C K N O W L E D G M E N T S ...................... .. ..................................................................... iv

LIST OF TABLES ......................... ......... ........................... vii

LIST O F FIG U R E S .... .............................. ....................... ........ .. ............... ix

ABSTRACT ........ .............. ............. .. ...... .......... .......... xii

CHAPTER

1 ROCKET PROPULSION ................................................................... ..................

H isto ry ...................................................... .......... 1
S tru c tu re ................................................................................................................ 2
C cooling Jacket ...................... ............... ......... ....... ............................ 2
Problem s w ith Cooling .............................................................3

2 PREVIOU S W ORK ........................................................5

M etallic Elements ................ .......... ............... .......... ........ .....5
Metallic Porous Materials ..................................... ...............
Metal Foam Processing and Fabrication ................................................
Rocket Com bustion Testing ........................................ ................. 7
H eat Transfer A analysis .............................................................8
Sub critical Fluids................................8.. ..........8
Supercritical Fluids and Rocket Heat Transfer ...................................... 12

3 NUMERICAL AND ANALYTICAL APPROACH ...............................................15

4 LARGE SYSTEM EXPERIMENTAL SIMULATION AND RESULTS.................21

Test Apparatus Setup and Procedure ....................................................................... 21
Experim mental Results and Com prisons ........................................ ............... 25

5 SMALL SYSTEM EXPERIMENTAL SIMULATION AND RESULTS .............43

Test A pparatus Setup and Procedure ................................................. ............... 43
Experim ental Results and Com parison............................................. 44

6 PRACTICAL ROCKET ENGINE APPLICATION .............................................56

7 RECOMMENDATIONS FOR FUTURE WORK ......................................... 58









8 UNCERTAINTY OF RESULTS ........................................... .......................... 62

9 C O N C L U SIO N S ..................... .... .......................... .. .... ........ .... ...... ...... 65

APPENDIX

A N O M E N C L A T U R E .......................................................................... ....................68

B C O O L A N T PR O PER TIE S.......................................... ..........................................70

C LARGE SYSTEM COLLECTED DATA ...............................................72

D LARGE SYSTEM HEAT TRANSFER ENHANCEMENTS ..................................77

E SMALL SYSTEM COLLECTED DATA......................................... ....................82

F SMALL SYSTEM HEAT TRANSFER ENHANCEMENTS ..................................87

L IST O F R E F E R E N C E S .......................................................................... ....................92

B IO G R A PH IC A L SK E TCH ...................................................................... ..................94















LIST OF TABLES


Table page

8-1.U uncertainty of R results .................................................................... ..... ..................64

B-1. Properties for Liquid Nitrogen Referenced from [15]. ...........................................70

B-2. Properties for Nitrogen Vapor Referenced from [15].............................................70

B-3. Properties for Liquid Water Referenced from [11] .............................................71

B-4. Properties for Water Vapor Referenced from [11]. .............................................71

C-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s. .......... .................................. 73

C-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s ....................................................... 74

C-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s. ........... .............. ............... 75

C-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s. ...................................................... 76

D-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s ............................................78

D-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s............................... 78

D-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s. ..................................79

D-4.Heat Transfer Enhancement @ Heat Flux = 5.69 Mbtu/in2-s............................... 79

D-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s.......... ........ ...............80

D-6.Heat Transfer Enhancement @ Heat Flux = 7.58 Mbtu/in2-s ...................................80

D-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s. ...........................................81

D-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s ...................................81

E-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s ......................................................83

E-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s ....................................................84

E-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s............. ..................... .............85









E-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s .....................................................86

F-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s.............................................88

F-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s .................................... 88

F-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s .........................................89

F-4.Heat Transfer Enhancement @ Heat Flux = 5.69 Mbtu/in2-s............... ................ 89

F-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s .........................................90

F-6.Heat Transfer Enhancement @ Heat Flux = 7.58 Mbtu/in2-s............... ................ 90

F-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s...........................................91

F-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s............... ................ 91















LIST OF FIGURES


Figure page

2-1.Plot of the Reynolds Number Factor, F Referenced from Collier [12]. ....................11

2-2.Plot of the Suppression Factor, S Referenced from Collier [12].............................11

2-3.Plot of Sub Critical and Supercritical Coolant Heat Transfer Referenced from [2].... 12

3-1.2-D Geometrical Representation of a Rocket Engine Combustion Chamber for use in
N u m erical C o d e .................................................. ................ 15

4-1.Representation of Large Testing Apparatus and System.................. .............. ....21

4-2.SEM Photograph of Copper Foam Structure......... ......... ....................23

4-3.Photograph Showing the Brazing of the Copper Foam to the Inner Tube ................23

4-4.SEM Photograph of Nickel Foam Structure......... .......... ...................24

4-5.Photograph Showing the Brazing of the Nickel Foam to the Inner Tube. .................24

4-6.O pen C channel C ross-Section ........................................................................... ..... 26

4-7.Copper Foam Cross Sectional View ................................................. ....... ........ 27

4-8.Nickel Foam Cross Sectional View ................................................. ....... ........ 28

4-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm ................29

4-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm ................29

4-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm ................30

4-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm ................30

4-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm ..............31









4-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm ..............31

4-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm ..............32

4-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm ..............32

4-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm ..............33

4-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm ..............33

4-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm ..............34

4-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm ..............34

4-21.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm ..............35

4-22.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm ..............35

4-23.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm ..............36

4-24.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm ..............36

4-25.Representation of Thermal Circuit for Heat Transfer into the Metallic Foam.........41

5-1.Representation of Small Testing Apparatus. ............. ........... ...... ................. 43

5-2.Open Channel Cross-Section for Small System .................................... ........ 44

5-3.Copper Foam Cross-Section for Small System. .......................................................44

5-4.Nickel Foam Cross-Section for Small System ................................ ..................45

5-5.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm ................46

5-6.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm ................46









5-7.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm ................47

5-8.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm ................47

5-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm ...............48

5-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux 5.69 Mbtu/in2-s & 23 cfm ..................48

5-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm ..............49

5-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm ..............49

5-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm ..............50

5-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm ..............50

5-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm ..............51

5-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm ..............51

5-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm ..............52

5-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm ..............52

5-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm ..............53

5-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm ..............53

7-1.Closed Loop Testing Apparatus Proposed Diagram. ............................................... 59















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

USE OF METALLIC FOAMS FOR HEAT TRANSFER ENHANCEMENT IN THE
COOLING JACKET OF A ROCKET PROPULSION ELEMENT

By

Ryan Jeffrey Avenall

December 2004

Chair: Jacob Chung
Major Department: Mechanical and Aerospace Engineering

Rocket propulsion has been used in many different aspects of space travel and

military tasks. Nearly 800 years ago, the Chinese were the first to develop this concept

using solid propellants. Since the early 1900's, fuel-cooled thrust chambers have been a

concern as well as an ongoing advancement in rocket propulsion. With the higher

demand today for longer lasting and farther travel, and the extreme temperatures that

these elements experience, a break-through technology is needed in the cooling of these

thrust chambers. In this thesis the idea of using a porous metallic foam will be

implemented and tested for its heat transfer capabilities inorder to solve this problem.

The goal is to cool the hot wall temperatures without creating large pressure drops in the

coolant passage.

The testing of this idea involves two systems: a large-scale system and a small-

scale system. In both these systems the coolant will be nitrogen gas compressed to 300

psig. The nitrogen then flows through an annulus and is exhausted into the atmosphere.









Constant heat flux heaters placed inside the inner tube of the annulus will produce the hot

wall temperatures. Then using thermocouples, the hot wall temperatures will be read into

an Excel spreadsheet. The pressure drop is measured using two digital pressure gauges.

For the large system a heat transfer enhancement for the copper foam was found to

be 1.5 or 50% and for nickel foam was found to be 1.82 or 82%. This caused the hot wall

temperatures to decrease by an average of 71.840F and 100.740F for the copper and

nickel foams, respectively. The pressure drop through the copper foam and nickel foam

remained about the same and was 1 psig for 23 cfm and 3 psig for 45 cfm in comparison

to zero pressure drop for the open channel system. For the small system a heat transfer

enhancement for the copper foam was found to be 1.14 or 14% and for nickel foam was

found to be 1.15 or 15%. The wall temperatures in this system decreased by an average

of 29.040F and 36.040F for the copper and nickel foams respectively. The pressure drop

through the copper foam and nickel foam relative to the open channel is 1.2 psig and 0.8

psig, respectively, for 23 cfm, and for 45 cfm the pressure drop is 2.8 psig and 2.6 psig,

respectively.















CHAPTER 1
ROCKET PROPULSION

History

Rocket Propulsion is used in many different devices for different purposes.

Propulsion is mainly used for transportation of some kind. Missiles, space aircraft,

military aircraft, satellites, and commercial aircraft are some examples where propulsion

is utilized. The rocket principle is thought to have been founded by Hero of Alexandria

in 67 A.D. He invented many machines that used the reaction principle which is the

theoretical basis for the rocket. Most of his work was successful in the creation of two

opposing jets exhausting steam. Rocket propulsion uses stored matter, or propellants, to

achieve its thrust by combusting and ejecting these propellants. The three main types of

rocket propulsion are solar propulsion, nuclear propulsion, and chemical propulsion.

Two main types of propellants used are solid and liquid propellants. The first inventor of

the rocket is said to be Feng Jishen a Chinese scientist back in 970 A.D. His work dealt

with two experiments using bamboo tubes and gunpowder, which is now similar to what

we use as fireworks. The first time the rocket principle was used as a weapon was back

in 1275. It wasn't until the twentieth century when rocket propulsion design and theory

started growing rapidly. In 1903, Konstantin Tsiolkovsky, who was a mathematics

teacher, discovered most of the theories for the modern rocket. He developed the rocket

flight equation and invented the multi-stage rocket [1]. He also found that liquid oxygen

and hydrogen would be good propellants to achieve the high exhaust velocity necessary

to travel into space. In 1926, Robert H. Goddard, a professor of physics at Clark









University in Massachusetts, designed the liquid-fuelled rocket combustion chambers and

nozzles [1]. He also accomplished the first flight using a liquid propellant rocket engine

[2]. Goddard had over 214 patents for rocket apparati that later in 1960 the U.S. bought

to create their own rocket engines. Fuel-cooled thrust chambers stem all the way back to

the early 1900's, and are in need of new technology to advance rocket propulsion for

centuries to come.

The Russian space program is noted for being the most focused and active program

since rocket engines became a modern mode of transportation. They are credited with

the first artificial satellite, the first man in space, the first spacecraft on the moon, the first

docking of two spacecraft, and the first space station. The main achievement for the

United States space program was having the first man walk on the moon. Now for both

programs the quest continues, and there have been multiple satellites and space travel

since these first accomplishments by both programs.

Structure

The structure of a rocket propulsion element is quite complex and has been studied

for many years. It is in the form of a converging diverging nozzle. This shape provides

for the maximum thrust and performance needed by the element. The design used has

had an ongoing struggle with the amount of cooling necessary for the element. The skin

of the nozzle has to be able to withstand high temperatures, high pressures, as well as

being lightweight. This makes for a complicated task in building a sufficient nozzle for

the system.

Cooling Jacket

In order to achieve very high thrusts, the combustion of the oxidizer and the fuel

must be very powerful. Therefore the gases that escape through the nozzle after









combustion are extremely hot. For many years the idea of a cooling jacket has been used

to surround the outside of this nozzle. The purpose for this cooling jacket is to cool the

inner walls of the combustion chamber and nozzle regions, which can help in many ways.

First, the parts surrounding the outside of this nozzle won't see as much of the heat from

the combustion. Second, the material of the nozzle itself will be at a much cooler

temperature range, increasing its life expectancy. Third, the use of lighter materials will

help with the overall weight requirement of the system.

To use this cooling channel, a fluid of some sort has to be provided to the system

and then recycled through and back around again. The current method, and probably the

most efficient is to have a separate line from the fuel tank deliver a pressurized flow rate

to the cooling jacket. This then will allow for a continuous supply of coolant without

having to attach another tank. Using the fuel is also a good idea because most of the

fuels used are cryogenic. This means that the coolant will enter the jacket at very cold

temperatures allowing cooling of the walls even further. Most of the rocket engines

today have some form of cooling channel or jacket that was just described. However,

further research into these jackets is necessary.

Problems with Cooling

There still exist many problems today with cooling these nozzles even with the

coolant jacket in place. The main problem is that the coolant channel does not have a

large enough heat transfer coefficient to sufficiently decrease the wall temperature. This

is mainly due to the coolant's fluid properties and dynamics.

The properties of the supercritical fluid dictate how well the fluid will transfer heat.

Supercritical fluids are fluids that are at very high pressures or very high temperatures.

The problem with these supercritical fluids is the extreme pressures they supply to the









surrounding apparatus as well as having systems like pumps that can handle these types

of pressures and temperatures. In using a supercritical fluid you also get the benefit of a

much higher heat transfer coefficient when compared to that of a sub-critical fluid. The

use of these fluids provides cooling for the combustion chamber as well as fuel for the

combustion process. By using these fluids for cooling the heat transfer to the fluid helps

heat up the fluid to a much more combustible state.

However, these extreme temperatures are still too high and need to be decreased.

The throat area is the main concern for improved heat transfer through this cooling

jacket. If the heat transfer can be improved then the life expectancy of the nozzle can be

improved which would save money. Therefore, this is an area of great significance, and

research for innovative ideas is an ongoing task. One area being extensively explored is

the use of metallic elements in the cooling channel to increase the heat transfer.















CHAPTER 2
PREVIOUS WORK

Metallic Elements

Metallic Porous Materials

Previous work has been done using the idea that metal's high conductivity will

work well as an agent in increasing the heat transfer coefficient in certain aspects. Koh

and Stevens [3] found that the heat transfer effectiveness could be greatly increased by

using a porous medium. Koh and Stevens [3] filled a stainless steel annulus with peen

shot (steel particles). The results for Koh and Stevens [3] project were for a fixed coolant

flux of 9.65 lb/ft2 s, the heat flux through the wall was increased from 16 to 20

Btu/ft2 s and the maximum wall temperature was reduced from 1450 to 350 F. As

seen here porous metallic materials can be very helpful in increasing the heat transfer

effectiveness.

Koh and Colony [4] as well as Bartlett and Viskanta [5] have done analytical

studies on the enhancement of the heat transfer due to a high thermal conductivity porous

medium. In Bartlett and Viskanta [5], their analytical approach for the heat transfer

effectiveness was compared with already known data for a particular diameter and heat

flux. Their results show very similar results to that of the experimental, and prove that

the effectiveness of heat transfer should be greatly increased with the introduction of a

porous medium with high conductivity. Koh and Colony [4] completed a similar









procedure earlier by using basic models of heat transfer. They discovered that the heat

transfer using a porous medium is increased significantly.

Metallic foams were then looked at as a possibility in enhancement of heat

transfer for rocket engine cooling passages. Brockmeyer et al. [6] showed the benefits of

using metallic foam for heat transfer enhancement. They looked at cooper alloy and

nickel alloy foams. It is stated here that for the heat transfer enhancement to be

beneficial it must be able to enhance the heat transfer, have improved elevated

temperature properties, reduced weight, simplified manufacturing, and lower system cost.

Brockmeyer et al. [6] found that the heat transfer in the foam structure is excellent due to

the enhanced mixing in the flow paths. They discovered that relative to a flat plate the

heat transfer would be enhanced by a factor of 4 for foam packed heat exchangers. The

relatively high void fraction of the foams also helps with the pressure drop criterion

through the cooling chamber.

Another testing of metallic foams for their enhanced heat transfer was conducted

by Boomsma et al. [7]. They used aluminum alloy foams placed in-between two parallel

plates for heat transfer analysis. Boomsma et al. [7] performed experimental tests on

different porosities, flow rates, and even compared their results with the best commercial

heat exchangers available in that size range. The aluminum foam proved to have very

little pressure drop, if any, and an increase in the efficiency of the heat transfer by nearly

two over any commercial product made for the same situation. Metallic foams have been

proven to show that the efficiency of the heat transfer, along with little loss in pressure, is

a viable way to cool processes effectively.









Metal Foam Processing and Fabrication

There are many different ways to make metallic foams. Metallic sintering, electro

deposition or chemical vapor decomposition (CVD), metal deposition through

evaporation, and investment casting are a few of the processes. When creating a metallic

foam using metal sintering, metallic particles are suspended in slurry and then coated on

a polymeric foam substrate [8]. The substrate vaporizes during this process, and the

metallic particle becomes an object which is the foam. The CVD method uses the

chemical decomposition of a reactive gas in a vacuum onto a heated substrate [8].

Molten metal infiltration can also be used to form such foam materials such as aluminum

and copper [8]. In this process, the foam precursor is coated with a casting and then

packed into casting sand. This assembly is then heated to decompose the precursor and

to harden the casting. Then the molten metal is pressure infiltrated filling all the voids.

When it solidifies it forms a product with solid struts. However, this process is very

expensive and time consuming [8].

Rocket Combustion Testing

Some examples of previous projects dealing with only rocket engine combustion

help to give a better understanding of what is taking place inside of a rocket engine.

These papers were also used for verification purposes of a numerical model that will be

talked about later in this thesis. Tamura et al. [9] performed an investigation on staged

combustion with liquid oxygen and methane. In their study they used water as the

coolant for the cooling passage, and had a scaled down rocket engine assembly for their

combustion. Their tests looked at different injection geometries, speeds, temperatures,

and different mixture ratios as well. Tamura et al. [9] had results for characteristic

velocity vs. mixture ratio, pre burner temperature vs. mixture ratio, efficiency vs.









chamber length, heat flux vs. chamber pressure, and heat flux vs. axial distance away

from the throat. Most of the data collected here is insignificant for our purposes other

than the heat flux vs. axial distance. This will provide a good experimental comparison

between the numerical code and their results. Some assumptions had to be made

however, which could have skewed the results slightly in the numerical simulation. The

coolant velocity, the combustion velocity, and some other geometrical constraints such as

exit diameter were not given in their report. Their results showed about a 9:1 or 9:2 ratio

for heat flux at the throat compared to the combustion chamber.

Results from other papers were also helpful in determining the procedure and

design of our test rig. Elam [10] studied rocket combustion using liquid oxygen and

hydrogen. Here results of hot wall temperatures and heat flux with respect to the location

from the throat were helpful in determining ranges for temperatures and fluxes that might

be needed to get an accurate representation of rocket combustion. Also this paper

showed that many of the rocket engines operate under severe pressures (supercritical

fluids) giving rise to pressure drop concerns with the usage of foam materials.

Heat Transfer Analysis

Sub critical Fluids

Heat transfer analysis of sub critical fluids is based on properties and laminar, or

turbulent flow. For single-phase flow, Incropera and DeWitt [11] present a good

description of the heat transfer analysis. In our case turbulent flow will be the ideal

conditions for consideration. Using Incropera and DeWitt's [11] ideals of annulus flow

one can start to analyze how the fluid reacts to different initial conditions. For instance,

the overall heat transfer analysis changes when using a free stream approach, a constant

heat flux approach, or even a constant wall temperature approach. For both liquid and









vapor phases of the coolant turbulent correlations can be used to figure out the heat

transfer coefficient, the heat flux, and the wall temperatures all of which are extremely

important in designing the test rig for experimental analysis.

For conducting a study on the heat transfer analysis, many equations and theories

are involved. The basic models for heat transfer analysis from Incropera and DeWitt [11]

will be shown here and further explained in Chapter 3. For general considerations

dT, q"P P
= = h(T T- ) where P = rD (1)
dx mh mhc

Eq. (1) explains the energy balance across a basic system with P as the perimeter. For

constant heat flux considerations


T(X)=T +q x (2)
mc

Eq. (2) shows the relationship between the fluid temperature and the wall heat flux. For

constant wall temperature considerations

T,- T, (x) Px
T-T- = exp (3)
T, T,, mcP

Eq. (3) provides an explanation of how the fluid temperature changes due to the constant

surface temperature. When dealing with a free stream constraint the following equation

provides detail into how that heat transfer is considered.


A =exp- UA (4)
A, T. T,, mce

where U is the overall heat transfer coefficient given by


U = h+ (5)









For turbulent flow the entrance length and heat transfer analysis differ significantly from

the laminar correlations. Since turbulent flow is our main concern the correlations used

are

L
-= 4.4Re (6)
D D

NuD =0.023Re Pr04 (7)

Next is the consideration of the two-phase boiling characteristics of a sub critical fluid.

In Collier [12] the two-phase region is described by many correlations. The two-phase

region occurs when the liquid at the surface starts nucleate boiling. Nucleate boiling is

the formation of vapor bubbles by nucleation on the surface and causes the liquid to

change phase. According to Collier [12] there are seven steps to accomplish in order to

calculate the heat transfer coefficient in this region. These steps are listed below.

(a) Calculate 1/Xtt (Martinelli parameter)

09 05 0 1
X =(1- quality 9 Pg P f5( (8)
X,, = ) (8)
Quality ) pPf g)

(b) Evaluate F from figure

(c) Calculate he


0.023 4(I- ali)] kf D(F) (9)
7D)Pf kf D

(d) Calculate Re,

S41i(1 quality)
Re =
zDpf (10)
Re = F1 25 Ref

(e) Evaluate S from figure


























10 1


Figure 2-1.Plot of the Reynolds Number Factor, F Referenced from Collier [12].


C

KL~
ci
4Z1


Rerp= Re x F vs2


Figure 2-2.Plot of the Suppression Factor, S Referenced from Collier [12].

(f) Calculate hncb

k 079 045 049
hb -0.00122 f pfPf AT024A 075 (s
S0 5 0 29h0 24 024 sat sat


(g) Calculate hP


(11)


ht = hcb + h


(12)









These equations are used to evaluate the overall heat transfer coefficient in the two-

phase region. Properties should be taken at the average temperature of the fluid.

Supercritical Fluids and Rocket Heat Transfer

For supercritical fluids the question is whether or not the heat transfer trends are

similar to that of sub critical fluids. This would help in an overall analysis of the fluids

used. The properties of the fluid will be different as well as the way the fluid reacts

chemically at such high pressures and temperatures. Some articles that can be helpful in

better understanding the phenomenon of supercritical fluids are Watts and Chou [13] as

well as Labuntsov [14]. Additional information on supercritical fluids is found in Sutton

and Ross [2]. The detail is limited about the supercritical region other than a graph that

shows that supercritical fluids follow the same pattern of heat transfer as sub critical

fluids except the nucleate boiling region. This graph is shown in the figure below.


,E

/ /





,f .Supercritical
coolant









T,1 T, (log scale)

Figure 2-3.Plot of Sub Critical and Supercritical Coolant Heat Transfer Referenced from
[2].









In Sutton and Ross [2] their contribution is the explanation of how heat transfer

analysis is carried out for regeneratively cooled rocket engines. They discuss everything

from the heat transfer coefficients to the method of calculating individual heat fluxes at

different areas of the engine. Some of these ideas or examples are listed below.

q = h(T T)= = (13)

T -T
q hg /k+ (14)
S+W I
/hg + k +h,

q = hg(To Tg) (15)


q = )(Tg T1), (16)


q = h (T7, T1) (17)

These explain the heat flux through different regions as well as the overall heat flux

through the regeneratively cooled thrust chamber.

k
hg = 0.026Re' Pr04 (18)
gd 2R


h, =0.023c Red02 Pr 3 (19)
A

These correlations explain the heat transfer coefficient for the hot gases as well as that for

the coolant side during its forced convection as a liquid. These models can be used to get

an overall idea of how the heat transfer throughout the chamber is occurring, and where

problem situations will and can occur.






14


In Barron [15], it discusses how supercritical fluids follow the same pattern of heat

transfer as those of near critical fluids. They discuss in further detail the correlations

used to study the heat transfer for the near critical fluid.


h, =0.0208 kRe8 Pr04 1+0.01457 b (20)
D /PbPw

Where the subscript 'w' stands for wall temperature, and 'b' stands for bulk temperature.

All the other correlations are identical and can be calculated using the non-near

critical correlations.















CHAPTER 3
NUMERICAL AND ANALYTICAL APPROACH

By using all the correlations stated in chapter 2 the numerical analysis can begin.

The analysis is based on a very crude 2-D model of a rocket combustion system, which is

shown below.









-1'--- ?Ro'
Combustion
Gas @ To




I IL
-- L1 --- L2

X=O
XL XV


Figure 3-1.2-D Geometrical Representation of a Rocket Engine Combustion Chamber for
use in Numerical Code.

As seen in this figure the wall thickness will be neglected, therefore neglecting the

conduction heat transfer due to the wall thickness. From this model two different

assumptions are made which change the overall process. First, there is uniform constant

free stream combustion gas temperatures in the combustion chamber, and second, that a









uniform heat flux on the surface is prevalent. These two models will be built in order to

show real life simulation as well as experimental simulation. Starting with the free

stream combustion gases, the simulation is built on the basis of changing area with

respect to the distance x down the chamber. The analysis is also carried out for sub

critical fluids. The first step is to study the liquid phase of the coolant. Shown below are

the steps taken in order to figure out the wall temperatures, coolant temperatures, and the

distance down the chamber until the bulk starts to boil.

R, = (L x)tana, +R (21)
(21)
R2 = (x L )tan a2 + R

T- Tm(x) ex LA, (22)



ST(x)= exp 2 UL Rl (x)Cx (23)
To T, pl


,(x) = T T- (T ,,)exp- 2 L Lx tan a 2 tan a + Rox (24)


Using these equations and knowing that the temperature of the coolant at the boiling

point will be the boiling temperature of the coolant, thus solving for the boiling point.


in(T Tb 2~U, (L XL tan a Xa 2 tan a, + RXL (25)


R, R 2 c, lTo Tb
XL t-- o- + L -- L~ I---n T (26)
tan a, tan a, UL tan a, T, -T

This shows the important aspects of the liquid phase and how to apply them to a nozzle

geometry system. Next is the two-phase region, which is characterized by the nucleate

boiling as well as forced convection. In this region the assumption that the coolant









temperature remains constant at the boiling temperature is used. This changes when it

completely vaporizes.
Hg XV
jf MH = 22U-2ATbR(x)Ox (27)
Hf XL

This distance however is based on whether or not it occurs before the throat or after the

throat. Since it is unknown both cases must be considered.

for (X(L1 )

R R 2h, 2RoX
X, +LI + +2LXL X+ L (28)
tan al tan al ) U2ATb tan a, tan a

for (X )L )

Ro
R L tan aO
X, =L,- t (29)
tan a2 ihfg + tan a (L +X -2LX)+ L 2ROXL
LTrU2 ATb tan a2 tan 2 L tan a

Next the vapor phase must be analyzed. Here only the temperatures need to be

determined, and they follow a similar analysis as the liquid phase. This is also going to

be affected by whether or not the distance to full vaporization takes place before the

throat or after the throat.

for (X (L1) and x = Xv : L,


T(X) T (T0 7 p 2z1J7,, tan a, zx x -L, X, + (X30
()= To -(To- Tb)exp -- tan 2v 2 V (30)
Cp,v + Ro (x-XV)


for (X<(LI) and x = L,: L










S, tana x -Lx+ L2
,(x) = To (TO (L,))exp (31)
mc1,V +R,(x-L,)

for (X )L,) and x= X, : L


2zU, tan a x 1x + L X
T() = T (T T)exp V (32)
c ,v + R,(x X,)

Then in order to solve for the wall temperatures, a specific equation that works for all

three regions is shown below.

h To + h
T, = where i = ,20, v (33)
h, +h,

These are the main important characteristics needed in order to study what is occurring in

the chambers. The wall temperature being the most important shows how the foam will

affect the overall heat transfer throughout the chamber.

Similarly a constant heat flux simulation is generated to compare with the free

stream simulation. This is used to simulate how the test rig reacts for comparison with

the experimental results as well as what takes place in real simulations with the free

stream gases. Again the first step is to calculate the liquid phase of the coolant.

OT. q P
Tm q where P = 2TR, (x) (34)
cx he ,


(x) = Tm, + 2.qs [Lx tan al x2 tan al + Rox (35)


Rx (R Roi (T _- c
XL = L, + (3 )
Stan aL tan a, ;rq, tan a,









The next step to consider is the two-phase region. It is again important to note that the

analysis is dependent upon whether or not the distance to be fully vaporized occurs

before the throat or after the throat.

i2dH = q"Pdx (37)

for (X, (L)

SL+ + + XL 2L + 2R X2] (38)
tan a, l tan a1) !, tan al tan a1

for (X,)L,)


Ro L, +
R tan a2 2
LX, a (39)
X 1 tana'2 hg tana L(2LX+-RXL +L
t nq2, tan a2 tan a, tana2

The final aspect to consider is the vapor phase for constant heat flux. However the

temperatures during the vapor phase are again a function of where the distance to full

vaporization occurs.

for (X, (L1) and x = X : L,


T(X)= Tb+ 2 [(L x- L2x2 LX + )tana, +R( -Xv) (40)
mC P,v

for (X, (,L) and x = L : L


Tm(X)= T(L1)+ 2q (x2 -Lx+ L)tan2 + Ro(x- L)] (41)
r ( ) ad x pa ,v

for (X,)L,) and x = Xv : L










T(x) =T + 2,[(x2 -Lx /X2 -LXv)tan2 + Ro(x Xv)] (42)
P,v

The wall temperatures are again calculated by one simple equation. This equation is

dependent on what phase the coolant is in. This equation is shown below.

T, = + Tm () (43)
h

The same type of analysis is carried out for a cylindrical geometry. These equations are

then used to formulate a simulation for both the free stream combustion gas consideration

and the constant heat flux consideration.

For supercritical fluids the numerical model is different. There is not a two-phase

flow to deal with. The only difference between the calculations for this flow and for the

two-phase flow is how the heat transfer coefficients are calculated. These calculations

are shown in chapter 2.















CHAPTER 4
LARGE SYSTEM EXPERIMENTAL SIMULATION AND RESULTS

Test Apparatus Setup and Procedure

The large test rig for this project is a stainless steel cylindrical annulus which is

set up to test high-pressure gaseous nitrogen. It will operate under the constant heat flux

consideration discussed earlier in chapter 3. The setup and equipment for the testing


procedure is listed below.


Figure 4-1.Representation of Large Testing Apparatus and System.

1. Test Apparatus

2. Band Heaters

3. Power Switching Units

4. Temperature Control Units









5. Thermocouples

6. Pressure Gauges

7. Piping, valves and parts

8. Nitrogen Tanks

9. Metallic Foam

10. Data Acquisition Board and Computer

The first step is to power up everything starting with the data acquisition unit and ending

with the band heaters. When the band heaters are powered up they will be given enough

time to heat up to an assumed temperature. The system is then charged with 300 psig of

nitrogen, and the exhaust valve is opened enough to obtain the desired flow rate reading.

Eight cases will be run with three tests each completed without any metallic foams

present. These tests include heat fluxes of 1.9 MBtu/in2-s, 5.69 Mbtu/in2-s, 7.58

Mbtu/in2-s and 9.48 Mbtu/in2-s. At each individual heat flux there will be three tests

completed at a flow rate of 45 cfm or 1.16 lb/s @ a pressure of 250 psig and three tests

also completed at a flow rate of 23 cfm or 567 lb/s @ a pressure of 225 psig. The same

process will also be completed for the copper based foam. Figures below show the

structure of this foam and how it is brazed to the outside of the inner tube.
































Figure 4-2.SEM Photograph of Copper Foam Structure.


Figure 4-3.Photograph Showing the Brazing of the Copper Foam to the Inner Tube.

This same process will be completed for the nickel-based foam. Figures below show

photographs of the structure of this foam as well as how it is brazed.
































Figure 4-4.SEM Photograph of Nickel Foam Structure.


Figure 4-5.Photograph Showing the Brazing of the Nickel Foam to the Inner Tube.









Experimental Results and Comparisons

Some preliminary tests were done to see how the system functioned. The tests

were confusing at first as the temperature profiles were scattered and inconsistent unlike

the conclusions from the theoretical analysis. The temperature profiles were decreasing

in nature at one instant and increasing at another. The first correction attempted was to

check the calibration of the thermocouples. This was done by taking all the

thermocouples and placing them in a glass of cold water. All the results came out almost

identical with a few varying but within the expected limit of the thermocouple reader.

However when the thermocouples were moved around or shaken it was noticed that the

values of some altered. The next step was to change the frequency that the thermocouple

reader responded at from 50 Hz to 400 Hz. This made the difference and now all the

thermocouples seem to be working properly. Just for completion the thermocouples were

also placed in a heated glass of water to make sure that they still read identical

temperatures.

This did not correct the problem with the incorrect and varying temperature

profiles. The next step was to look at the heaters and how they functioned. First the

controllers that supply the power to the heaters are set up to run on a percent power basis.

The max power or heat flux that the heaters can provide is 37 MBtu/in2-s. The

controllers where set up at 2% power or heat flux to check how the heaters worked. It

was determined immediately that the heaters do not heat up uniformly like expected. The

heaters had a cold side (side that heated up slower) and a hot side (side that heated up

faster). The next step then was to see if the hot side of one heater being up against the

cold side of the next heater would produce the same temperature reading. This

functioned best and produced good results when the cold side of the heater was on the









inside of the hot side of the other heater. This then gave an almost perfect contact

between the two heaters when heated up because the heaters expand. However this

would not work inside the tubes because it was impractical to push them down the tube

and keep the heater just on the inside of the other. So instead the heaters are pushed

together as they are slid down the tube, which provided good results as well.

The temperature readings appear linear, but that is from a combination of two

things. First it should be linear by theoretical understanding because of the convective

heat transfer across these. Second the heaters having a cold side and a hot side do not

provide the same heat flux uniformly across their surface providing a linear response to

the control. This type of temperature profile however was very consistent over multiple

tests at different heat fluxes and coolant flow rates, and will be used to check the percent

enhancement of the foam to the overall heat transfer. The figure below shows the open

channel cross-section.


Figure 4-6.Open Channel Cross-Section.









The test results for the open channel flow cannot be shown in comparison with

that of the numerical model. The reason for this is that the heaters that are used do not

provide a uniform heat flux. Therefore the data will not exactly portray that of a

theoretical constant heat flux at the surface.

The metallic foam is brazed to the outside of the inner tube and fills the gap

between the inner tube and the outer tube of the annulus. The figure below shows the

cross section with the copper foam.









INi











Figure 4-7.Copper Foam Cross Sectional View.

Just like the copper foam, the nickel foam is brazed to the outside of the inner tube and

fills the gap between the inner tube and the outer tube of the annulus. The figure below

shows the cross section with the foam.































Figure 4-8.Nickel Foam Cross Sectional View.

The copper foam data as well as the nickel foam data is shown below with the

open channel data for comparison. All 8 test cases are shown below providing the hot

wall temperature, bulk fluid temperature, and the pressure drop.

From these figures, the trend of increasing heat flux provides an increase in the

hot wall temperature which is expected. It is also shown predominantly that with three

tests at each individual test case the temperature profiles remain the same which means

that the system is functioning properly and is calibrated well. From these profiles it is

also determined that a linear increase in temperature over each heated area, and a linear

increase for the coolant temperature is predominant. This is expected with theoretical

analyses explaining this linear dependence.

When looking at the data collected in Appendix D for the copper and nickel

foams some interesting characteristics are found. First of all our notion that the foam












Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature
Comparison (@1.9 Mbtulin2-s & 23 cfm)


240
230
220 -*- Open Test #1
210
200 -W- Open Test #2
200
190 Open Test #3
S180 Copper Test #1
S170 --- Copper Test #2
160 -- Copper Test #3
E 150
150 -1-Nickel Test #1
S140
130 Nickel Test #2
120 Nickel Test #3
110
100
0 5 10 15 20 25
Length (in)



Figure 4-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm.



Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 1.9 Mbtulin2-s & 23 cfm)

88

86
-*-Open Test #1
84 -- Open Test #2

E 82 Open Test #3
S80 Copper Test #1
80
-K-Copper Test #2
78 -
78 --e-Copper Test #3
76 iNickel Test#1
74 Nickel Test #2
Nickel Test #3
72

70
0 0.5 1 1.5 2 2.5



Figure 4-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23
cfm.











Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 1.9 M btulin2-s & 45 cfm)


-*-Open Test #1
-- Open Test #2
Open Test #3
Copper Test #1
-- Copper Test #2
--Copper Test #3
--Nickel Test #1
-- Nickel Test #2
Nickel Test #3


Length (in)



Figure 4-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 1.9 Mbtulin2-s & 45 cfm)


-*-Open Test#1
-- Open Test #2
Open Test #3
Copper Test #1
-K-Copper Test #2
-Copper Test #3
-Nickel Test #1
Nickel Test #2
Nickel Test #3


Figure 4-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45
cfm.











Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 5.69 Mbtulin2-s & 23 cfm)

460 -
440
420 -*- Open Test #1
400 --Open Test #2
380
E- 360 Open Test #3
2 340 Copper Test #1
320
S300 ---- Copper Test #2
S280 -- Copper Test #3
S20 --Nickel Test#1
240
220 --Nickel Test #2
200 Nickel Test#3
180
160
0 5 10 15 20 25
Length (in)



Figure 4-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 5.69 Mbtulin2-s & 23 cfm)

94
92
90 --- Open Test #1
88 -- Open Test #2
86 Open Test #3
S84 -Copper Test #1
82 -
S8 -K- Copper Test #2
a"80
-E 78 -*- Copper Test #3
E 78
76 Nickel Test#1
74- -- Nickel Test#2
72- Nickel Test#3
70 -
68
0 0.5 1 1.5 2 2.5



Figure 4-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23
cfm.











Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature
Comparison (@ 5.69 Mbtulin2-s & 45 cfm)

440
420
400 -*- Open Test #1
380
S380 -- Open Test #2
360
340 Open Test #3
320 Copper Test #1
300 --- Copper Test #2
280 --- Copper Test #3
2 260 -- Nickel Test #1
240
220 Nickel Test #2
220
200 Nickel Test #3
180
160
0 5 10 15 20 25
Length (in)



Figure 4-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 5.69 Mbtulin2-s & 45 cfm)

100

95
-*-Open Test #1
90 --- Open Test #2

S85 Open Test #3
SCopper Test #1
0 80

75
-e--Copper Test #3
70 -- Nickel Test #1

65- -- Nickel Test#2
Nickel Test #3
60

55
0 0.5 1 1.5 2 2.5



Figure 4-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45
cfm.












Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 7.58 Mbtulin2-s & 23 cfm)

540 -
520
500 --Open Test#1
480
460 -m --Open Test #2
440
S420 Open Test #3
3 400 Copper Test #1
380
S360 --- Copper Test #2
340
S320 --CopperTest#3
300
280 ---Nickel Test#1
260 --Nickel Test#2
240
220 Nickel Test #3
200
180
0 5 10 15 20 25
Length (in)



Figure 4-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 7.58 Mbtulin2-s & 23 cfm)

100

95*- Open Test #1

90 -- Open Test #2
SOpen Test #3
S85 Copper Test #1
S-- Copper Test #2
80 -- Copper Test #3

-75 Nickel Test #1
SNickel Test #2

70 Nickel Test #3

65
0 0.5 1 1.5 2 2.5



Figure 4-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23
cfm.











Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature
Comparison (@ 7.58 Mbtulin2-s & 45 cfm)

520
500 r
480
460 -- Open Test #1
440 -W- Open Test #2
^ 420
E 400 Open Test #3
2 380 Copper Test #1
360
340 -u- Copper Test #2
340
320 --- Copper Test #3
300 -1- Nickel Test #1
280
260 Nickel Test #2
240 Nickel Test #3
220
200
180 -
0 5 10 15 20 25
Length (in)



Figure 4-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant Temperature
Comparison (@ 7.58 Mbtulin2-s & 45 cfm)

100

95
-*- Open Test #1
90 -I Open Test #2
SOpen Test #3
85 Copper Test #1
S-- Copper Test #2
0. 80 -0- Copper Test #3
-1- Nickel Test #1
75 Nickel Test #2
Nickel Test #3
70

65
0 0.5 1 1.5 2 2.5



Figure 4-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45
cfm.











Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 9.48 Mbtulin2-s & 23 cfm)

620 -
600
580
560 --Open Test #1
540
520 --- Open Test #2
500
480 Open Test#3
460 Copper Test #1
420
400 -)- Copper Test #2
380
E 360 -e--Copper Test #3
320 -e Nickel Test#1
300
280 -- Nickel Test#2
260
240 Nickel Test#3
220
200
0 5 10 15 20 25
Length (in)



Figure 4-21.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 9.48 Mbtulin2-s & 23 cfm)

105 -

100 -*-Open Test #1

95- --- Open Test #2
L Open Test #3
90 -
Copper Test #1
85 Copper Test #2
80 o -e-Copper Test #3
E 80
S-I- Nickel Test #1
75 Nickel Test #2

70 / Nickel Test #3

65
0 0.5 1 1.5 2 2.5



Figure 4-22.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23
cfm.












Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature
Comparison (@ 9.48 Mbtulin2-s & 45 cfm)


600
580 "
560
540
520 -- Open Test #1
500 -W- Open Test #2
480
L 460 Open Test #3
440
420 Copper Test #1
400
380 -- Copper Test #2
360 -0- Copper Test #3
E 340
320 -1- Nickel Test #1
S300
280 -Nickel Test #2
260
240 Nickel Test #3
220
200
180 T
0 5 10 15 20 25
Length (in)



Figure 4-23.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 9.48 Mbtulin2-s & 45 cfm)

98
96
94
92 -*- Open Test #1
90 -m- Open Test #2
88 -
S86 Open Test #3
84 -CopperTest#1
8 82
80 ---)- Copper Test #2
S78 ---CopperTest#3
S76 --Nickel Test#1
74-
72 -- Nickel Test#2
70 Nicke Test#3
68
66
64
0 0.5 1 1.5 2 2.5



Figure 4-24.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45
cfm.









would enhance the heat transfer is true. We did not get the enhancement we thought

were possible, but that is mainly due to the open system parameters and the fact that the

heaters did not function as intended. If the system had been closed loop then the tests

could have been run for hours until a true equilibrium had been accomplished. This then

might have described the true form of the foam enhancement. The average percent

enhancement is based on the average overall temperatures recorded experimentally and

the supposed heat flux. Using these parameters we can come up with an estimate of the

heat transfer coefficient at each position down the tube and compare the values with and

without foam.

T + T (44)
h '

Ts = surface temperature (hot wall temperature)

Tf = fluid bulk temperature

The results for the foam filled channels in comparison to that of the open channel are now

considered. As can be determined from these tables shown in Appendix E, the average

heat transfer enhancement remains relatively the same for the particular foams. However

with increasing heat flux the temperature differential increases. The overall systems

average heat transfer enhancement is 50.22% for the copper foam and 81.58% for the

nickel foam. From analytical reviews a higher enhancement is expected. Particularly

from Kuzay et al. [16] it is shown how liquid nitrogen interacts with metallic foams.

From this paper the Nusselt number and the friction factor can be calculated for our

particular situation. The friction factor is calculated as shown below.

f = 26.8CRe -023 -629 (45)









Here the constant C is equal to 1.0 for brazed foams, the Reynolds number will be

replaced with our Reynolds number based on the hydraulic diameter, and 6 is the

porosity of the metallic foam. The friction factor will then be used to calculate the

pressure drop. This pressure drop uses the normal horizontal cylinder calculation.

LV2
Ap = p f (46)
2Dh

The Nusselt number is calculated as shown below.

Nud = 0.606Pe056 E52 (47)

The Nusselt number here is based on the diameter and for our purposes it will be based

on the hydraulic diameter. Pe is the Peclet number, which is equivalent to the Reynolds

number times the Prandtl number. Again we will use the Reynolds number based on the

hydraulic diameter to determine the Peclet number. In order to calculate the porosity it

either had to be provided to me from the manufacturer, or it can be calculated with a few

known parameters. A study done by Zhao et al. [8] shows the particular details needed

for my foam purchased from Porvair Fuel Cell Company. Their study shows an average

cell size and the ligament size of a copper foam from Porvair. Their average cell size is

.104 in and the ligament size is .0104 in. Then it explains how to use these two

parameters to calculate the porosity of the foam. Shown below are the steps in order to

calculate the porosity.


df 1 1 (48)
= 1.18 C
-dp 3;r 1 exp( 1 (48)
Sexp^ U/0.04jJ

Here df is the ligament diameter and dp is the pore size diameter or cell size diameter.

From here the porosity can be calculated and used to solve for the Nusselt number as well









as the friction factor. By using the before mentioned diameters of the copper foam (they

will also be used to estimate the porosity of the nickel foam) the porosity used in the

experiments was found to be .955.

The fluid properties were then calculated at two different state points 225 psig &

90 F and 250 psig & 85 F. The density at the two given points is 1.07 lb/ft3 and 1.2 lb/ft3

respectively. The viscosity is 3.84e-7 lb-s/ft2 and 3.82e-7 lb-s/ft2 respectively. The

conductivity is 0.0034 lb/s-R for both states. Then the Prandtl number is .717 and .718

respectively. The Reynolds and Peclet numbers can now be calculated and used to

calculate the Nusselt number and friction factor for our system. The first friction factor is

2.59 and the second is 2.94. These factors lead to the expected pressure drops of 0.18 psi

and 0.06 psi respectively. The corresponding pressure drops experimentally were 4 psi

and 2 psi for the copper foam respectively, and 3 psi and 1 psig respectively for the nickel

foam, which are much higher than the expected pressure drops. This could be due to

many different aspects. First, the correlations being used for liquid nitrogen might not be

a good assumption for gaseous nitrogen. However, being that liquids usually have a

higher viscosity than gases this does not seem to be a basis reason for error. Second, the

foam could not be completely open in all pore areas. With closer inspection of the foam

it is evident that some of the pores are closed off and not completely open. In the making

of the foam it is possible that not all the pores become open of its metallic substance,

therefore causing a higher pressure drop in the system. Third, there is a possible flaw in

the design of the system's apparatus. Inside the outer tube there is an inner tube that

connects together immediately after the foam to provide a method to insert the

thermocouples and heaters for testing. The two flanges that are bolted together form this









connection. These flanges create a disturbance in the flow's path, which can also be

shown in these results.

Using the traditional internal flow calculation for the open channel Nusselt

number, the new Nusselt number which is based on the foam properties can now be

compared. The internal flow calculation is shown below.

NuDh = 0.023 Re" Pr04 (49)

Using this equation for the experimental system, the Nusselt number for the two different

Reynolds number cases is 187.49 @ 45 cfm and 120.83 @ 23 cfm. The Nusselt numbers

based on the foam properties are 384.56 @ 45 cfm and 282.78 @ 23 cfm. This shows

that there should be a great enhancement by using the foam over the open channel flow.

The conductivities for each case with the foam and with the open channel change. Using

this information the overall expected heat transfer ratio or enhancement could be

calculated. For the open channel case, all that is needed is the conductivity of the fluid.

In order to calculate the heat transfer coefficient the Nusselt number definition as

described below is used.

hD
NuDh h (50)
k

For the foam case the effective conductivity must be calculated in order to find the

effective heat transfer coefficient. This conductivity is calculated using the equation

below from Calmidi and Mahajan [17].

kf = ( )k + k, (51)

where ks is the conductivity of the solid

kf is the conductivity of the fluid









The conductivity of the solid is found by using the given data sheet from Porvair for the

various foams, and calculating the relative density based on the porosity mentioned

earlier. The conductivities where found to be 0.219 lb/s-R for copper foam and 0.05 lb/s-

R for the nickel foam. Using these properties the calculated effective conductivities are

0.0131 lb/s-R for the copper foam and 0.0055 lb/s-R for the nickel foam. The typical

heat transfer coefficient ratios were then found to be 7.97 for copper foam and 3.34 for

nickel foam at 45 cfm, and 8.87 for copper foam and 3.81 for nickel foam at 23 cfm.

In experiments it was shown that the average heat transfer was increased by a

factor of 1.5 for the copper foam and 1.82 for the nickel foam. This could be low for a

couple of reasons. First, the heaters that were supplied do not act as constant heat flux

heaters. Therefore, not providing the right amount of heat flux specified. The second

reason is how well the foam is brazed to the tube. If there is space between many of the

ligaments and the tube then the heat transfer will not be greatly increased. In light of this

an analytical review of the gap being a contact resistance was undertaken. A simple

thermal circuit was constructed describing the path for the heat transfer through the wall

and is shown below.


La/Ka Lb/Kb Lc/Kc 1/heff

Tsl Ts2 Ts3 Ts4 Tn


Figure 4-25.Representation of Thermal Circuit for Heat Transfer into the Metallic Foam.

T -T
q L (52)
S /K /K, + h,









Here the subscript 's' stands for surface, 'N' stands for nitrogen, 'A' stands for the

stainless steel wall, 'B' stands for the brazing foil, 'C' stands for the nitrogen gap, and

he, is calculated from the above equations for the heat transfer with metallic foam

inserts. The wall temperature used was 192.92 F and the nitrogen temperature used was

82.87 F. The calculated heff was 23.733 lb/ft-s-R for 23 cfm. The thickness and

conductivity of the stainless steel wall is 0.12 in and 2.07 lb/s-R respectively. The

thickness and conductivity of the foil is 0.079 in and 53.1 lb/s-R respectively, and the

conductivity of the nitrogen gap is 0.0034 lb/s-R. With the known heat flux for the

particular flow rate and wall temperatures collected the length of the gap can now be

solved for. The result is 0.019 in in length for the gap of nitrogen between the foil and

the foam. After talking with engineers at Porvair it is difficult for them to get a good

braze on this large of a system. This is most likely the reason for the lower numbers in

heat transfer enhancement.















CHAPTER 5
SMALL SYSTEM EXPERIMENTAL SIMULATION AND RESULTS

Test Apparatus Setup and Procedure

The small test rig for this project will again be an annulus made from stainless

steel, but all the parts are off the shelf parts that screw together. It will also operate under

the constant heat flux consideration talked about earlier in chapter 3. The setup and

equipment for the testing procedure is listed below.

ax...iii~iiiiiii IP


Figure 5-1.Representation of Small Testing Apparatus.

This system contains all the same components as the large system except for the

size of the test apparatus and instead of using band heaters, a cable heater is used for the

small system. The procedure for startup is the same process. The heat fluxes tested will









also remain the same as well as the flow rates. By using the same flow rates, the velocity

of the nitrogen will be much quicker in the smaller system than in the larger system

providing faster cooling.

Experimental Results and Comparison

Like the large system, the small system will test open channel heat transfer, heat

transfer with copper foam inserts, and heat transfer with nickel foam inserts. The system

has a hydraulic diameter of 0.56 inches, and contains a foam testing section of 5 inches in

length. The foam will be the same 10 ppi foam that was used in the larger system. The

cross-sectional views of each testing situation are shown below.


Figure 5-2.Open Channel Cross-Section for Small System.


Figure 5-3.Copper Foam Cross-Section for Small System.
























Figure 5-4.Nickel Foam Cross-Section for Small System.

All 8 test cases for the three testing situations are combined below for comparison

purposes, providing the hot wall temperature, bulk fluid temperature, and the pressure

drop. The test results are also compared to the large system to determine the validity of

the large system results.

These figures show that the trend of increasing the heat flux provides an increase in

the hot wall temperature which is expected. It is also shown predominantly that with

multiple tests of each individual test case the temperature profiles remain the same, which

means that the system is running properly and is calibrated. From these profiles it is also

shown that a linear increase in temperature over each heated area, and a linear increase

for the coolant temperature is predominant. This is expected with theoretical analyses

that explain this linear dependence.

When looking at the data collected for the copper and nickel foams, some

interesting characteristics are found. First of all our notion that the foam would enhance

the heat transfer is true. However, the results that are obtained are not what was

expected. The heat transfer enhancement is much lower than anticipated, and is much







46



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@1.9 Mbtulin2-s & 23 cfm)

240
230
220 -- Open Test #1
210 --Open Test #2
200
190 Open Test #3
S180 Copper Test #1
? 170 ,I --Copper Test #2
S160 -*-Copper Test #3
E 150
S150 Nickel Test #1
140
130 ) Nickel Test #2
120 Nickel Test #3
110
100
0 1 2 3 4 5
Length (in)



Figure 5-5.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@1.9 Mbtulin2-s & 23 cfm)

88

86

84 -e--Open Test #1
---Open Test #2
S82 Open Test #3

S80 Copper Test #1
78 --- Copper Test #2
S78 -*Copper Test #3
i- 76 -Nickel Test #1
Nickel Test #2
74 -Nickel Test #3
72

70
0 0.5 1 1.5 2 2.5



Figure 5-6.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm.







47



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 1.9 Mbtulin2-s & 45 cfm)


-- Open Test #1
-W- Open Test #2
Open Test #3
Copper Test #1
-- Copper Test #2
--- Copper Test #3
-- Nickel Test #1
S Nickel Test #2
Nickel Test #3


Length (in)


Figure 5-7.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@1.9 Mbtulin2-s & 45 cfm)


-*- Open Test #1
-W- Open Test #2
Open Test #3
Copper Test #1
-- Copper Test #2
-*- Copper Test #3
-I- Nickel Test #1
- Nickel Test #2
Nickel Test #3


Figure 5-8.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant
Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm.







48



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 5.69 Mbtulin2-s & 23 cfm)


460
440
420
400 -- Open Test #1
380 -W- Open Test #2
S360 Open Test #3
340 Copper Test #1
320
30 -- Copper Test #2
300
E 280 -*-Copper Test #3
260 -I-Nickel Test #1
240 Nickel Test #2
220 Nickel Test #3
200
180
160
0 1 2 3 4 5
Length (in)



Figure 5-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 5.69 Mbtulin2-s & 23 cfm)


94
92
90
88 --Open Test #1
86 ----Open Test #2
84 Open Test #3
SCopper Test #1
2 )K- Copper Test #2
< 80
S-4-- Copper Test #3
E 78
7 6- Nickel Test #1
76
74 Nickel Test #2
Nickel Test #3
72
70
68
0 0.5 1 1.5 2 2.5



Figure 5-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux 5.69 Mbtu/in2-s & 23 cfm.







49



Nickel Foam, Copper Foam & Open Channel Hot Wall
Te mpe rature Comparison (@ 5.69 M btulin2-s & 45 cfm)

440 -
420
400
380 ---Open Test #1
360
S360 --Open Test#2
340
320 Open Test#3
300 CopperTest#1
a. 280 --- Copper Test #2
E 260
240 --Nickel Test#1
220 Nickel Test #2
200
180
160
0 1 2 3 4 5
Length (in)



Figure 5-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 5.69 Mbtulin2-s & 45 cfm)

100

95

90 -*--Open Test#1

E 85- -m-- Open Test#2
Sv I" Open Test #3
75 80 Copper Test #1
75 -
-- Copper Test #2
S70 -Nickel Test#1

65 Nickel Test #2

60

55
0 0.5 1 1.5 2 2.5



Figure 5-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45
cfm.







50



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 7.58 Mbtulin2-s & 23 cfm)

540
520
500
480
440 --Open Test#1
S420 ----Open Test #2
380 Open Test #3
2 360 Copper Test #1
340
320 -- Copper Test #2
S300 -I Nickel Test #1
280
260 Nickel Test #2
240
220
200
180
0 1 2 3 4 5
Length (in)



Figure 5-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 7.58 Mbtulin2-s & 23 cfm)

100

95


--Open Test #1
-n-Open Test #2
Open Test #3
Copper Test #1
--Copper Test #2
--Nickel Test #1
--Nickel Test #2


Figure 5-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23
cfm.







51



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 7.58 Mbtulin2-s & 45 cfm)


-*- Open Test #1
-W- Open Test #2
Open Test #3
Copper Test #1
-- Copper Test #2
-I- Nickel Test #1
- Nickel Test #2


0 1 2 3 4 5
Length (in)



Figure 5-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 7.58 Mbtulin2-s & 45 cfm)


-*- Open Test #1
-W- Open Test #2
Open Test #3
Copper Test #1
-- Copper Test #2
-I- Nickel Test #1
- Nickel Test #2


0.5 1 1.5 2


Figure 5-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45
cfm.


85



80



2 75

E
I-

70



65







52



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 9.48 Mbtulin2-s & 23 cfm)

620
600
580
560
520 --Open Test #1
500 -- -Open Test #2
480
460 Open Test #3
440
S400 CopperTest#1
380
E 360 --- Copper Test #2
340
S320 Nickel Test#1
300
280 --Nickel Test#2
260
240
220
200
0 1 2 3 4 5
Length (in)



Figure 5-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 9.48 Mbtulin2-s & 23 cfm)


-- Open Test #1
-- Open Test #2
Open Test #3
Copper Test #1
Copper Test #2
- Nickel Test #1
SNickel Test #2


Figure 5-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23
cfm.







53



Nickel Foam, Copper Foam & Open Channel Hot Wall
Temperature Comparison (@ 9.48 Mbutlin2-s & 45 cfm)


600
560
540
520
500 --- Open Test #1
480
460 Open Test #2
420 Open Test #3
380 Copper Test#1
$ 360
E 340 CopperTest#2
S320 -- Nickel Test#1
280
260 --Nickel Test#2
240
220
200
180
0 1 2 3 4 5
Length (in)



Figure 5-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot
Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm.


Nickel Foam, Copper Foam & Open Channel Coolant
Temperature Comparison (@ 9.48 Mbtulin2-s & 45 cfm)


82


80

U-
S78


76
E


74-


72


-- Open Test #1
-- Open Test #2
Open Test #3
Copper Test #1
Copper Test #2
-- Nickel Test #1
Nickel Test #2


0.5 1 1.5 2


Figure 5-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel
Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45
cfm.









lower then the results shown with the larger system. With a smaller system better

controllability was expected as well as quicker response to the heat transfer, but based on

the results this was not achieved. Many characteristics could have caused this

unfavorable result with the most obvious being the process of installing the heaters and

thermocouples. The thermocouples were placed on the inside of the coil heater for the

smaller system because of clearance issues, but in the larger system the thermocouples

were located between the outside of the band heater and the inner wall. Also in the small

system the thermocouples were connected to the heater using a product called JB Weld

that is widely used in the automobile industry, but not knowing it's conductivity

properties creates difficulty in determining the heat transfer characteristics.

A positive result is the small magnitude of pressure drop that is associated with the

foam. In comparing both the larger system and smaller system the pressure drops

through the foams stayed relatively constant from one system to the next. The pressure

drop that occurred with the copper foam at 23 cfm for the larger system was 1 psi and for

the smaller system was 1.2 psi. These pressures are taken relative to the pressure drop

that occurred with open channel flow and proves that the foam induces low pressure

drops. This was expected since the length and diameter ratio stayed the same between

the two systems. The pressure drop plays an important role in how effective the heat

transfer is, but more importantly how feasible it is to use foam in a high-pressure minimal

loss system. For the nickel the pressure drop produced similar results with 1 psi for the

larger system and 0.8 psi for the smaller system.

The average heat transfer enhancement although not favorable still proved the

theory. For the copper foam the enhancement is 14% in comparison to 50% for the larger






55


system, and for the nickel foam 15% in comparison to 82% for the larger system. These

numbers are far from what is desired, but proved that a better process is needed to

determine the feasibility of the foams for use in rocket propulsion elements. The pressure

drop and enhancement show that this is a viable technology for propulsion elements and

needs to be considered further.















CHAPTER 6
PRACTICAL ROCKET ENGINE APPLICATION

For scaling purposes these experimental results for the copper foam and nickel

foam were used to determine what could possibly happen at rocket engine specifications.

The properties that were used to determine the heat transfer enhancement and pressure

drop are a combination of specifications known as well as some from page 333 of Rocket

Propulsion Elements [2]. The specifications used are as follows: wall thickness is 0.02

in, total flow area for the coolant is .566 in2, max heat flux is 60 Btu/in2s, and a max wall

temperature of 1400 R. Assumed properties were as follows: Reynolds number is

1,000,000, the pressure of the coolant is 1500 psi, and the temperature of the coolant at

the highest heat flux is 90 R. The coolant temperature provides us with a Prandtl number

of 1.22 and a conductivity of 0.0104 lb/s-R. Using the Nusselt number and the effective

conductivity correlations in chapter 4 the Nusselt number with foam is 2025.37 with a

porosity of 95%, and the effective conductivity is 0.024 lb/s-R with the foam

conductivity being .287 lb/s-R. By using these correlations an effective heat transfer

coefficient can be calculated, and is found to be 691.54 lb/ft-s-R. Using the Nusselt

correlation in chapter 4 for internal flow without foam the Nusselt number is 1570.91.

The heat transfer coefficient for the internal flow without foam is 228.99 lb/ft-s-R. We

also know that the heat flux is equal to the heat transfer coefficient multiplied by the

temperature difference between the wall and the coolant. Since the heat flux is going to

stay the same whether or not there is foam in the cooling channel we can then set the two









equations equal to each other and solve for the new surface temperature. The new

surface temperature would be 523.79 R compared to the original temperature of 1400 R.

By using my experimental results where there is an average of 1.5 times the enhancement

in heat transfer then the new surface temperature would be 963.33 R compared to 1400

R. For the pressure drop calculation an average temperature of the coolant which is

194.508 R will be used to calculate the properties and determine the pressure drop over a

2-foot length. The properties are as follows: Prandtl number is 0.785, the conductivity is

0.0116 lb/s-R, the density is 1.36 lb/ft3, and the viscosity is 1.13e-7 lb-s/ft2. Using the

definition of the Reynolds number the velocity is calculated to be 37.75 ft/s for a

Reynolds number of 1,000,000. Using the correlations for friction factor and pressure

drop as outlined in chapter 4 the expected pressure drop can be determined. This

expected pressure drop comes out to be 9.11 psi with a friction factor of 1.54. With my

experimental results of 3 psi at an expected 0.18 psi, then the pressure drop for this

system would be 151.78 psi with an expected of 9.11 psi. These numbers depict a

positive heat transfer enhancement even with my experimental results as well as minimal

pressure drop. However, these correlations and scaling based on my experimental results

need to be performed on exact dimensions of a cooling channel and with exact

specifications for that rocket engine that the cooling channel in question resides. When

this is completed a more accurate representation of what can be achieved with this idea of

metallic foam inserts used in the cooling channels will be shown. Also a more accurate

representation of how much pressure drop through these cooling passages can be

achieved.















CHAPTER 7
RECOMMENDATIONS FOR FUTURE WORK

This experimental project can be improved especially in the heating elements that

are used in the test rig. These heating elements do not provide a uniform constant heat

flux which is desired. Results that could compare with the numerical code would be

more favorable in this situation. Also with these heating elements it might be more

beneficial to use some kind of combustion process to simulate activity that is closer to the

actual function of a rocket engine. I believe that this would give more insight into the

enhancement due to the foam, and be directly applicable to the rocket engines in use

today. However, using a constant heat flux model can still be beneficial where the

enhancement of the foam can be scaled to the largest heat flux in a rocket engine. This

would then provide an estimate of how well the foam improves the most critical point on

a rocket engine.

The next improvement would be to make the system a closed loop system unlike

it's current state of an open loop system. The open loop system uses the nitrogen directly

from the tanks at a relatively constant pressure, and the system exhausts the nitrogen into

the atmosphere. This causes many problems with the system with the most important

being the time frame that the nitrogen can be used. As the nitrogen exhausts into the

atmosphere less nitrogen is available from the tanks. After a certain time the pressure in

the system starts to decreases at a given volumetric flow rate. When using the larger heat

fluxes it takes an excessive amount of time to come to an equilibrium state. Even then










with any of the heat fluxes it is not a guarantee that the system is able to reach

equilibrium. With a closed loop system the testing could continue for hours with out a

huge loss in nitrogen which would provide a better estimate of the equilibrium state.

The closed loop system would have a pump that cycles the nitrogen and

overcomes any small pressure drop in the system. When the nitrogen exits the test rig it

will enter into a heat exchanger in order to cool it back down to its original starting

temperature. This system is shown below.


Apparatus Flow
Control Valve






NlPressure trogen Tank
Relief Valve +-Water In

J__-e ~ /-'VnQter Out

Rotameer / Conpressor

Heat Exchanger




Control Valve

Figure 7-1.Closed Loop Testing Apparatus Proposed Diagram.

Using a closed loop system will improve the measurements for flow rate and pressure. In

the closed loop system both the flow rate and pressure would remain constant which

would provide more accurate results for the overall system parameters. There also could

be some temperature control instituted at the inlet of the apparatus to make sure the

temperature remains constant at the inlet to the system.









Another problem that could have skewed some of the data was the placement of

the thermocouples which were placed on top of the heaters between the heaters and the

inner wall of the inner tube. Because of the expanding nature of the heaters the

thermocouples could then be held tightly in place. A better solution is needed to imbed

the thermocouples in the wall of the inner tube from the inside of the tube. This would

provide a better understanding of what is taking place in the wall itself without having the

heaters dictate the results. Also imbedding some thermocouples into the foam in

different areas would have been beneficial to see how the foam was reacting to the wall

heat flux.

Another ongoing problem is how to perfectly braze or connect the foam to the

surface. When inspecting the foam not every single ligament that wraps around the pipe

is actually sintered to the pipe. This is extremely necessary in order to achieve maximum

enhancement of the heat transfer. If there is any space at all between the ligament and the

surface the contact resistance of that gap is extremely high, and is incapable of achieving

good conduction at that particular point. As shown in chapter 4 the length of the gap only

has to be one half of a millimeter to achieve the skewed data that was taken. The idea of

compressing the foam into the foil before brazing seems like a very plausible technique

as long as the compression does not deform the foam. If too much deformation is caused

then the void percentage or porosity decreases and the pressure drop will increase.

The pressure drop of the foam could also be improved by constructing the foam

so that some pores are not blocked. This will then provide the most efficient flow

through the foam that can be achieved. Another consideration is designing a better inner

tube for the apparatus. With the connection flanges at the end of the inner tube the









pressure drop is skewed, and is not an accurate representation of the pressure drop

through the foam. The foams can also be created with a 5 ppi (pores per linear inch)

instead of ours which was 10 ppi which will allow more flow to pass through and

therefore decreasing the pressure drop.

Finally a concentrated model of the nozzle throat region would be ideal. If

building a converging-diverging shape a more accurate representation of the rocket

engine can be tested and simulated. The foam would then be reacting similar to the most

critical point on a rocket engine. The overall enhancement could then determine how the

critical point could be better cooled and protected.















CHAPTER 8
UNCERTAINTY OF RESULTS

The uncertainty of results is how precise I believe the conclusions are. For these

results the uncertainty will be calculated based on the design of the apparatus, the

different systems resolution, as well as the repeatability of the results in question.

Typical uncertainties will include the design-stage uncertainty and the standard deviation

for scatter in the data [18]. The measurements of consideration will be temperature,

pressure, and flow which will affect the heat transfer coefficient and also the Nusselt

number. For temperature the error of the larger system comes from the thermocouple

reader itself and the repeatability of the results. However for the smaller system, the

thermocouples are not against the wall, but are connected to the inside of the heater so

that there is a conduction error relative to those results as well. For the thermocouple

reader the instrument uncertainty is 1.80F and has a resolution of 1.8e-60F. The

following equation can then be used to determine the design-stage uncertainty [18].

Pid = /i,+/o+
1 (53)
o, = Re solution
2

The standard deviation is the error from the mean to calculate the overall temperature,

and can now be calculated. The following equations will detail steps in order to calculate

the standard deviation [18].









T = T +t,, S
1 N
T=-YT
N-
(54)
t = 4.303

S1N
S2 1(T T)2
N-1

By using these two error calculations the uncertainty can be determined in the

temperature measurements for the larger system. For the smaller system the conduction

error also must be calculated. This error will be based on the conductivity of the heater,

the length of the heater, as well as the heat flux that is provided by the heater. This error

is 1.80F for 1.9 Mbtu/in2-s, 5.5980F for 5.69 Mbtu/in2-s, 7.4520F for 7.58 Mbtu/in2-

s, and 9.3240F for 9.48 Mbtu/in2-s. These are calculated using the conductivity of the

lb
heater which is 2.37 Using these equations the uncertainty of the temperature
s-R

data for the larger system is + 27.828 F, and is + 28.566 F for the smaller system.

For pressure calculations a digital pressure gage is used to measure the static

pressure at the inlet to the apparatus and at the exit. The resolution for these pressure

gages is 0.1 psi and the instrument uncertainty is +1 psi. Using the same process for the

temperature the uncertainty in pressure is 1.479 psi. For the flow measurement the

same process is followed with a resolution of 2 scfm, and instrument uncertainty of +1

scfm which provides a total uncertainty of +1.414 scfm. Using this information the

lb
uncertainty of the heat transfer coefficient is 2.46e-5 for the larger system
ft-s-R

lb
and 2.4e-5 for the smaller system.
ft-s-R










The data in the appendices reflects the values that have the uncertainties explained

in this chapter. There may be other uncertainties that may have occurred from instrument

malfunction or other undeterminable quantities. These uncertainties are the best

description for the data recorded in these experiments using the values that would

influence them the most.

Table 8-1.Uncertainty of Results

Apparatus Temperature Pressure Flow Rate Heat Transfer Enhancement
F Psi Cfm %
Large +27.828 +1.479 +1.414 +0.0646
Small +28.566 +1.479 +1.414 +0.063















CHAPTER 9
CONCLUSIONS

In conclusion the engineering modeling and overall experimentation was a success.

For the large system even though the results did not meet expectations they did prove that

the theory of using a metallic medium will increase the heat transfer enhancement. The

results for pressure drop were also positive, but the pressure drop did not meet

expectations. The heat transfer enhancement can be explained by defective brazing of the

foam to the outside of the hot wall. When looking at the test section it is clear that there

is space between the ligaments of the foam and the hot wall. The connection of these

ligaments to the hot wall is vital to the transfer of heat from one medium to the next.

When analyzing a thermal circuit to predict the amount of space between the wall and the

foam that would provide the desired enhancement it was found that a distance of only 0.5

0.02 in would work. This then corresponds to the fact that if I can see the gap then this

gap is the main reason for our lack of heat transfer enhancement. When discussing with

the engineers that built and brazed our foam they stated that it is very difficult for them to

get good contact on such a large piece. With the smaller system the engineers advised

that the contact would be much better and that there should be improved performance.

For the small system the results were not what was expected as the results were

much lower than the larger system. However, the system still produced results of

increasing heat transfer and minimal pressure drop which is favorable. The

thermocouples that were used to measure the wall temperature were attached to the inside









of the heater using a product called JB Weld. The problem with using this product is the

conductivity is not known which doesn't allow for the calculation of the heat transfer

through the material. I believe that this is the main reason for the unfavorable results

obtained from this system. The temperature differential across the heater itself also has a

major effect on the heat transfer read by the thermocouples.

The results for these systems provide heat transfer enhancements for the copper

foam of 50% for the larger system and 14% for the smaller system. The nickel foam

provided heat transfer enhancements of 82% for the larger system and 15% for the

smaller system. The pressure drops are 1 psi at 23 cfm and 3 psi at 45 cfm for copper in

the larger system and 1.2 psi at 23 cfm and 2.8 psi at 45 cfm for copper in the smaller

system. For nickel foam the pressure drops were about the same in all cases.

When scaling these results to rocket engine specifications it is calculated that the

expected heat transfer enhancement would be 1.55 or 55% and the expected pressure

drop would be 151.78 psi. These results are all based on assumptions, and need to be

scaled to an exact system with current coolant properties for that particular rocket engine.

By analyzing these results new technology for the brazing technique is needed in

order to achieve the full potential of the porous metallic medium or foams. Some ideas

are already being tested while others are still in the development stage. One possibility is

to have one side of the system under vacuum, and the other side under pressure in order

to press the ligaments into the brazing foil so that when they are heated everything sinters

together.

For the future a combustion test rig would be the best scenario to predict heat

transfer enhancements from the metallic foams. Some theories for this are also in the






67


development stage such as creating a half converging-diverging nozzle where the bottom

side is flat and the top side is the converging-diverging shape. On the flat side the

material will be clear in order to see the hot wall which will be covered with a

temperature sensitive paint. This then could be photographed to get a complete picture of

how the hot wall temperature profiles appear. The foam would then conform to the

outside of the converging-diverging shape, and hot air will be passed through the

chamber to simulate hot combustion gases.















APPENDIX A
NOMENCLATURE

R inside radius of the outer skin
Ro inside radius of the inner skin or the radius of the nozzle throat
XL distance where the liquid begins to boil
XV distance where the liquid becomes completely vaporized
A cross sectional flow area of the coolant
thk wall thickness
D hydraulic diameter
hg heat transfer coefficient of the combustion gases
hi heat transfer coefficient of the coolant in its liquid phase
h2o heat transfer coefficient of the coolant in its two phase region
h heat transfer coefficient of the coolant in its vapor phase
UL overall heat transfer during the liquid phase
U20 overall heat transfer during the two phase region
U, overall heat transfer during the vapor phase
kf thermal conductivity of the combustion gases
ki thermal conductivity of the coolant in its liquid phase
Red Reynolds number based on diameter
Pr Prandtls number for combustion gases
Pr, Prandtls number for the coolant in liquid phase
Pr, Prandtls number for the coolant in vapor phase
TO combustion gas temperature in degree F
Tb boiling temperature of the coolant in degree F
T,,, coolant inlet temperature in degree F
T4 coolant temperature at L1 in degree F
T wall surface temperature in degree F
rh coolant mass flow rate
cp,l specific heat of the coolant during its liquid phase
Cp, specific heat of the coolant during its vapor phase
Reg Reynolds number based on the gaseous form of the coolant
quality quality of the coolant
P/u kinematic viscosity of the coolant in liquid phase









Ug kinematic viscosity of the coolant in vapor phase
f friction factor
Fro, Froude number with all flow as liquid
NuLT Nusselt number for laminar-turbulent flow
p1 density of the coolant in liquid phase
pg density of the coolant in vapor phase
h heat of vaporization of the coolant
q, heat flux
Ri inside radius of the inner skin upstream of the nozzle throat
R2 inside radius of the inner skin downstream of the nozzle throat
Li length from entrance of nozzle to the throat
L2 length from throat to exit of nozzle
L total length of nozzle
al angle of inclination upstream of throat
a2 angle of inclination downstream of throat
As surface area
d coolant channel width

















APPENDIX B
COOLANT PROPERTIES

Table B-1. Properties for Liquid Nitrogen Referenced from [15].
Temp. psat rhof Cp mu k hfg Pr sigmaL Betat

(K) (kPa) (kg/m3) (kJ/kg- mua- (mW/m- (kJ/kg) (mN/m) (K-1)
K) s) K)
65 17.4 860.9 2.008 278 158.7 214 3.52 11.66 0.0047
70 38.5 840 2.024 220 149.9 208.3 2.97 10.48 0.00504
75 76 818.1 2.042 173 143 202.3 2.47 9.3 0.00544
77.36 101.3 807.3 2.051 158 139.6 199.3 2.32 8.75 0.00566
80 136.7 795.1 2.063 141 136.2 195.8 2.14 8.22 0.00592
85 228.4 771 2.088 119 129.3 188.7 1.922 7.18 0.0065
90 359.8 745.6 2.122 104 122.4 180.9 1.803 6.12 0.00723
95 539.8 718.6 2.17 93 115.5 172 1.747 5.08 0.00816
100 777.8 689.6 2.24 85 108.5 161.6 1.755 4.04 0.00942
105 1083.6 657.7 2.35 78 101.1 149.4 1.813 0.01119
110 1467.2 621.7 2.533 73 93.6 135 1.976 0.01394
115 1939.4 579.3 2.723 68 84.7 117.3 2.19 0.01884
120 2512.9 524.9 2.92 65 74.6 94.3 2.54 0.0305
125 3204.4 436.8 3.124 62 61.5 54.9 3.14

Table B-2. Properties for Nitrogen Vapor Referenced from [15].
Temp. rhog Cp mu k Pr
(mW/m-
(K) (kg/m3) (kJ/kg-K) (muPa-s) ( /m-
K)
65 0.911 1.056 4.62 6.12 0.797
70 1.893 1.064 4.95 6.58 0.8
75 3.532 1.076 5.29 7.03 0.81
77.36 4.604 1.084 5.41 7.23 0.811
80 6.071 1.095 5.62 7.49 0.822
85 9.789 1.13 5.94 7.95 0.844
90 15.027 1.185 6.27 8.4 0.885
95 22.21 1.279 6.6 8.86 0.953
100 31.9 1.407 6.98 9.33 1.053
105 44.93 1.593 7.54 10.16 1.182
110 62.57 1.88 8.26 11.14 1.394
115 87.21 2.36 9.32 12.59 1.75
120 124.44 3.29 10.27 13.91 2.43
125 197.08 5.86 12.86 16.69 4.51










Table B-3. Properties for Liquid Water Referenced from


Temp. p


vf *
10(^3


hfg cp,f


mu,f*
10^6


kf


(mW/m-
(K) (bars) (m3/kg) (kJ/kg) (kJ/kg-K) (Ns/m2) ()/-
K)
300 0.03531 1.003 2438 4.179 855 613
310 0.06221 1.007 2414 4.178 695 628
320 0.1053 1.011 2390 4.18 577 640
330 0.1719 1.016 2366 4.184 489 650
340 0.2713 1.021 2342 4.188 420 660
350 0.4163 1.027 2317 4.195 365 668
360 0.6209 1.034 2291 4.203 324 674
370 0.904 1.041 2265 4.214 289 679
373.15 1.0133 1.044 2257 4.217 279 680
380 1.2869 1.049 2239 4.226 260 683
390 1.794 1.058 2212 4.239 237 686
400 2.455 1.067 2183 4.256 217 688
410 3.302 1.077 2153 4.278 200 688
420 4.37 1.088 2123 4.302 185 688
430 5.699 1.099 2091 4.331 173 685
440 7.333 1.11 2059 4.36 162 682
450 9.319 1.123 2024 4.4 152 678
460 11.71 1.137 1989 4.44 143 673
470 14.55 1.152 1951 4.48 136 667


sim *


sigma *
Prf 10^3

(N/m)

5.83 71.7
4.62 70
3.77 68.3
3.15 66.6
2.66 64.9
2.29 63.2
2.02 61.4
1.8 59.5
1.76 58.9
1.61 57.6
1.47 55.6
1.34 53.6
1.24 51.5
1.16 49.4
1.09 47.2
1.04 45.1
0.99 42.9
0.95 40.7
0.92 38.5


Table B-4. Properties for Water Vapor Referenced from [1


Temp. p


(K)
300
310
320
330
340
350
360
370
373.15
380
390
400
410
420
430
440
450
460
470


(bars)

0.03531
0.06221
0.1053
0.1719
0.2713
0.4163
0.6209
0.904
1.0133
1.2869
1.794
2.455
3.302
4.37
5.699
7.333
9.319
11.71
14.55


Vg
(m3/kg)

39.13
22.93
13.98
8.82
5.74
3.846
2.645
1.861
1.679
1.337
0.98
0.731
0.553
0.425
0.331
0.261
0.208
0.167
0.136


cp,g
(kJ/kg-
K)
1.872
1.882
1.895
1.911
1.93
1.954
1.983
2.017
2.029
2.057
2.104
2.158
2.221
2.291
2.369
2.46
2.56
2.68
2.79


mu,g *
10^6
(Ns/m2)

9.09
9.49
9.89
10.29
10.69
11.09
11.49
11.89
12.02
12.29
12.69
13.05
13.42
13.79
14.14
14.5
14.85
15.19
15.54


kg
(mW/m-
K)
19.6
20.4
21
21.7
22.3
23
23.7
24.5
24.8
25.4
26.3
27.2
28.2
29.8
30.4
31.7
33.1
34.6
36.3


beta *
10^6
(K-1)

276.1
361.9
436.7
504
566
624.2
697.9
728.7
750.1
788
841
896
952
1010


1].
Prg



0.857
0.873
0.894
0.908
0.925
0.942
0.96
0.978
0.984
0.999
1.013
1.033
1.054
1.075
1.1
1.12
1.14
1.17
1.2


[11].















APPENDIX C
LARGE SYSTEM COLLECTED DATA











Table C-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi)


75.78 75.7755


73.72 75.2967


75.34 76.4629


79.76 82.6727


76.27 83.8909

78.46 82.0455


77.44 84.3848


72.54 85.9833

71.66 86.6705


250 250


250 250


250 250


250- 248


250-248

250-248


250-249


250-249

250-249


134.283


146.755


147.809


113.455


113.635

113.351


103.183


100.981

97.6681


201.44489


212.85109


208.27061


177.94101


181.2204

181.34206


146.55618


148.1098

145.12112


203.39474


213.71793


212.60477


187.47365


189.2365

191.74677


179.05389


182.774

181.95186


73.92 78.1767 225-225


69.10 76.2695 225-225


69.29 76.2389 225 -225


78.96 82.9950 225-221


73.17 84.8174 225-221

71.44 85.5640 225-221


78.99 83.9215 225-222


75.67 85.5276 225-222

70.56 86.9174 225-222


Open 1


Open 2


Open 3


Copper 1


Copper 2

Copper 3


Nickel 1


Nickel 2

Nickel 3


159.278


167.050


162.328


116.277


118.831

117.881


104.318


102.781

101.901


227.3252


229.8974


221.49


182.42126


190.07349

189.5883


153.28725


153.31686

151.81512


227.9768


229.8974


227.558


187.40555


195.48978

195.87119


182.75182


186.46452

185.17941











Table C-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi)


250.161 411.75292 413.64544 71.18


271.904 424.10916 426.84283 64.86


274.225 424.10198 429.98986 59.47


168.423 342.30212 381.86007 73.82


173.517 343.25683 381.12249 77.74

170.246 342.43515 385.81216 71.43


169.478 280.11035 388.23553 80.26


164.486 276.47708 386.47784 77.14

161.692 274.17184 387.13412 77.39


75.2201 225 -225


78.0789 225-225


81.4317 225-225


89.5055 225-221


90.7403 225-221

95.4023 225-221


85.6463 225-222


84.0919 225-222

84.7868 225-222


Open 1


Open 2


Open 3


Copper 1


Copper 2

Copper


Nickel 1


Nickel 2

Nickel 3


270.29


284.87


295.86


184.492


185.344

187.756


176.461


173.756

164.880


429.4525


438.8863


443.2950


376.81930


376.59332

377.25683


302.76589


299.48980

291.88162


433.2375


444.3536


455.2811


391.83865


397.53579

402.63143


394.15112


402.07992

399.13226


69.88


69.17


68.72


79.91


79.44

73.88


80.34


81.13

78.00


77.0507


81.0526


86.4217


86.6322


86.1689

93.1427


84.6011


90.9873

93.2346


250 -250


250 -250


250 -250


250- 248


250- 248

250- 248


250- 249


250- 249

250- 249











Table C-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi)


516.68865 525.94104


524.05572 525.10717


520.48193 527.83984


439.59527 472.60073


450.25210 481.36550

441.24813 485.19686


352.23730 481.19842


353.72534 478.89318

353.75427 485.01846


250 -250


250 -250


250 -250


250 248


250 248

250 248


250 249


250 249

250 249


307.078


315.739


315.561


199.158


197.252

195.347


190.708


191.814

190.954


498.96701 503.59198


503.20904 507.83523


503.40328 508.65893


427.77948 464.56900


417.31130 458.09515

420.29760 468.85986


330.63854 471.92694


335.52566 475.52236

327.07125 464.38754


74.60


67.58


67.01


77.82


77.20

69.85


76.93


76.50

78.08


82.2235 225 -225


86.8526 225-225


92.1013 225-225


85.2194 225-221


87.7290 225-221

95.1661 225-221


86.7872 225-222


85.0184 225-222

85.2500 225 -222


Open 1


Open 2


Open 3


Copper 1


Copper 2

Copper


Nickel 1


Nickel 2

Nickel 3


328.033


334.812


335.708


208.951


211.918

206.692


198.530


196.587

188.818


66.93


68.87


73.56


79.44


77.58

72.81


78.74


78.75

76.09


89.3400


89.2662


88.5713


87.7290


85.6444

95.8905


86.1383


86.1459

88.8643











Table C-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi)


597.07354 606.11560


597.71154 603.59942


583.60125 590.11993


482.07531 546.82489


482.64846 534.57421

483.52532 537.55334


388.66555 558.18426


368.97787 531.26098

389.31463 547.05664


250 -250


250 -250


250 -250


250 248


250 248

250 248


250 249


250 249

250 249


339.472


358.313


364.457


215.219


215.480

210.438


193.114


209.631

198.059


559.33056 572.41320


572.01416 577.90197


573.28295 584.00732


473.84771 519.88720


466.11245 525.60638

464.16293 515.45806


349.69885 523.45385


368.36495 539.06091

343.10491 522.36676


77.46


70.09


66.07


77.41


71.40

76.49


76.95


78.80

76.46


83.0671 225-225


87.7947 225-225


91.8349 225-225


87.2658 225 -221


96.2706 225 -221

88.5943 225-221


86.5862 225-222


88.4316 225-222

85.6520 225 -222


Open 1


Open 2


Open 3


Copper 1


Copper 2

Copper


Nickel 1


Nickel 2

Nickel 3


382.471


383.537


368.068


224.565


224.289

220.426


206.374


202.676

214.405


71.70


71.93


73.47


68.70


75.14

68.23


76.77


78.32

76.12


92.3136


93.6655


88.9379


104.990


90.1468

102.951


94.4712


87.2888

88.6632















APPENDIX D
LARGE SYSTEM HEAT TRANSFER ENHANCEMENTS










Table D-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s
23 cfm 45 cfm
Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T
(in) (F) (F) (F) (F)
Open Channel X=0 162.8865814 74.9489619 142.9490407 70.77190908
Open Channel X=10 226.2375895 75.39702352 207.5221965 73.83348973
Open Channel X=20 229.0490519 75.84508515 209.9058126 76.89507039
Copper Foam X=0 117.6630986 78.16603343 113.4805324 74.5269165
Copper Foam X=10 187.3610178 80.51787567 180.1678212 79.49287923
Copper Foam X=20 192.92217 82.86971792 189.4856364 84.45884196
Nickel Foam X=0 103.0001271 73.883667 100.6110509 75.07815297
Nickel Foam X=10 152.8064117 79.78161621 146.595703 80.26685587
Nickel Foam X=20 184.7985839 85.67956543 181.259918 85.4555587


Table D-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s.
23 cfm 45 cfm
Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F)
Copper X=0 2.22643427 122.64 45.2234828 1.852899414 85.29 29.4685
Copper X=10 1.411794552 41.18 38.8765717 1.3279243 32.79 27.35437523
Copper X=20 1.392099529 39.21 36.1268819 1.266445795 26.64 20.42017616
Copper Avg. 1.676776117 67.68 40.07564546 1.482423169 48.24 25.7476838
Nickel X=0 3.020202978 202.02 59.8864543 2.826828815 182.68 42.3379898
Nickel X=10 2.06560751 106.56 73.4311778 2.015543953 101.55 60.9264935
Nickel X=20 1.545656616 54.57 44.250468 1.388357933 38.84 28.6458946
Nickel Avg. 2.210489035 121.05 59.1893667 2.076910233 107.69 43.97012596










Table D-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s.
23 cfm 45 cfm
Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T
(in) (F) (F) (F) (F)
Open Channel X=0 283.6784058 69.26132202 265.4305623 65.17510732
Open Channel X=10 437.2113139 75.38485082 419.9880269 71.70937782
Open Channel X=20 444.2907918 81.50837962 423.4927165 78.2436142
Copper Foam X=0 185.8645325 77.74797058 170.7290802 74.33611552
Copper Foam X=10 376.8898214 83.19547516 342.664703 83.10943349
Copper Foam X=20 397.3352966 88.64797974 382.9315796 91.88275147
Nickel Foam X=0 171.6995341 79.82757568 165.218867 78.27136231
Nickel Foam X=10 298.0457763 84.71764628 276.9197591 81.55653254
Nickel Foam X=20 398.4544377 89.60771688 387.2825012 84.84170278


Table D-4.Heat Transfer Enhancement @ Heat Flux = 5.69 Mbtu/in2-s.
23 cfm 45 cfm
Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F)
Copper X= 0 1.983202944 98.32 97.813873 2.07749036 107.75 94.7014821
Copper X= 10 1.231983073 23.2 60.3214925 1.34182846 34.18 77.32332393
Copper X=20 1.175242364 17.52 46.95549517 1.18622399 18.62 40.5611369
Copper Avg. 1.463476127 46.35 68.36362022 1.535180937 53.52 70.86198098
Nickel X = 0 2.333868652 133.39 111.9788717 2.303176563 130.32 100.2116953
Nickel X= 10 1.696102915 69.61 139.1655376 1.782723674 78.27 143.0682679
Nickel X = 20 1.174635791 17.46 45.8363541 1.141542755 14.15 36.2102153
Nickel Avg. 1.734869119 73.49 98.9935878 1.742480997 74.25 93.163392833










Table D-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s.
23 cfm 45 cfm
Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T
(in) (F) (F) (F) (F)
Open Channel X=0 332.8514709 69.79203542 312.7929891 69.7369105
Open Channel X=10 520.4087728 79.42562739 501.8597819 78.39803314
Open Channel X=20 526.2960205 89.05921936 506.6953837 87.05915578
Copper Foam X=0 209.1875204 76.6129303 197.2526092 74.9626592
Copper Foam X=10 443.6985067 83.1838061 421.7961324 82.1671168
Copper Foam X=20 479.7210388 89.75468191 463.8413391 89.3715744
Nickel Foam X=0 194.645401 77.86675852 191.1592153 77.1743036
Nickel Foam X=10 353.238973 82.45815191 331.0784912 81.42978790
Nickel Foam X=20 481.7033589 87.04954529 470.6122843 85.68527221


Table D-6.Heat Transfer Enhancement @ Heat Flux = 7.58 Mbtu/in2-s.
23 cfm 45 cfm
Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F)
Copper X= 0 1.984237216 98.42 123.6631506 1.987539275 98.75 115.5403798
Copper X= 10 1.223204337 22.32 76.71026613 1.246838195 24.68 80.0636495
Copper X=20 1.121216724 12.12 46.5749817 1.120614446 12.06 42.8540446
Copper Avg. 1.442886092 44.29 82.31639947 1.451663972 45.16 79.48602464
Nickel X= 0 2.25263310 125.26 138.2060699 2.132353089 113.24 121.6337738
Nickel X= 10 1.62856122 62.86 167.1697998 1.696230515 69.62 170.7812907
Nickel X = 20 1.107899597 10.79 44.5926616 1.090170902 9.02 36.0830994
Nickel Avg. 1.663031305 66.30 116.6561771 1.639584835 63.96 109.4993879










Table D-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s.
23 cfm 45 cfm
Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T
(in) (F) (F) (F) (F)
Open Channel X=0 378.0259298 72.37232971 354.0811971 71.2113088
Open Channel X=10 592.7954509 82.00568517 568.2092285 79.38845952
Open Channel X=20 599.944987 91.63904063 578.1075032 87.56561025
Copper Foam X=0 223.0940094 70.69442749 213.7131653 75.10685221
Copper Foam X=10 482.749705 85.02868779 468.041036 82.90857188
Copper Foam X=20 539.6508179 99.3629481 520.31722 90.71029154
Nickel Foam X=0 207.8185475 77.07605235 200.2684326 77.40847015
Nickel Foam X=10 382.3193563 83.60859172 353.7229105 82.14922968
Nickel Foam X=20 545.5006307 90.14113108 528.2938436 86.88998922


Table D-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s.
23 cfm 45 cfm
Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F)
Copper X = 0 2.005606553 100.56 154.9319204 2.040815328 104.08 140.3680318
Copper X= 10 1.28429161 28.43 110.0457459 1.269227641 26.92 100.1681926
Copper X=20 1.154485466 15.45 60.29416913 1.141838877 14.18 57.7902832
Copper Avg. 1.48146121 48.15 108.4239451 1.483960616 48.39 99.4421692
Nickel X = 0 2.337829025 133.78 170.2073823 2.302376483 130.24 153.8127645
Nickel X= 10 1.709981113 71.00 210.4760946 1.799956342 80.00 214.486318
Nickel X=20 1.116273948 11.63 54.4443563 1.111322178 11.13 49.8136596
Nickel Avg. 1.721361362 72.14 145.042611067 1.737885001 73.79 139.370914033















APPENDIX E
SMALL SYSTEM COLLECTED DATA











Table E-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi)


Open 1

Open 2

Open 3

Copper 1

Copper 2

Copper3

Nickel 1

Nickel 2

Nickel 3


165.52

163.60

174.29

139.90

136.15

N/A


145.66

140.30

N/A


192.1659

193.0621

203.3263

166.9825

164.1066

N/A


175.1364

169.7693

N/A


213.1811

215.3773

222.1749

196.8803

192.7121

N/A


199.1910

192.0843

N/A


78.44

76.45

80.12

75.92

75.61

N/A


75.81

75.89

N/A


80.454

80.485

82.361

77.713

77.405

N/A


76.038

77.010

N/A


250 -
249.2
250 -
249.2
250 -
249.2

250 248

250 248

N/A

250 -
248.4
250 -
248.4

N/A


165.37

164.11

169.66

136.89

139.35

N/A


135.37

135.14

N/A


190.2827

192.0604

195.0120

163.7549

166.8621

N/A


164.1809

163.9568

N/A


209.9980

212.8589

214.9440

190.6197

195.6767

N/A


186.0627

183.0221

N/A


80.52

80.12

79.59

75.50

76.25

N/A


74.82

73.67

N/A


82.315

83.033

81.157

77.064

79.605

N/A


76.609

75.481

N/A


225 -224

225 -224

225 -224
225 -
221.2
225-
221.2

N/A

225-
221.4
225-
221.4

N/A











Table E-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi)


Open 1

Open 2

Open 3

Copper 1

Copper 2

Copper3

Nickel 1

Nickel 2

Nickel 3


325.16

310.10

308.04

279.23

278.61

N/A


270.66

274.05

N/A


399.6222

394.0860

396.0406

349.6771

352.8575

N/A


349.3570

351.0493

N/A


453.2384

439.5377

440.2188

426.3079

425.2640

N/A


420.5239

421.7853

N/A


78.97

78.04

76.30

74.24

75.37

N/A


72.11

73.23

N/A


83.002

82.068

82.122

77.604

78.508

N/A


74.578

75.698

N/A


250 -
249.2
250 -
249.2
250 -
249.2

250 248

250 248

N/A

250 -
248.4
250 -
248.4

N/A


271.55

278.56

274.57

263.75

267.78

N/A


263.07

260.55

N/A


353.2010

359.1530

356.8550

335.8836

338.8597

N/A


333.5133

331.8354

N/A


400.7974

402.0888

400.8553

405.4524

407.1486

N/A


399.0906

395.7205

N/A


73.05

77.11

75.35

72.18

73.54

N/A


75.94

73.27

N/A


78.872

80.470

80.501

78.678

77.798

N/A


78.408

77.080

N/A


225 -224

225 -224

225 -224
225 -
221.2
225-
221.2

N/A

225-
221.4
225-
221.4

N/A











Table E-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi)


Open 1

Open 2

Open 3

Copper 1

Copper 2

Copper3

Nickel 1

Nickel 2

Nickel 3


360.40

357.05

357.08

327.25

332.13

N/A


313.23

317.47

N/A


478.3792

477.1538

480.5461

414.5352

418.5368

N/A


401.8642

407.1270

N/A


528.6232

529.5001

532.8924

502.1995

507.0419

N/A


486.3750

491.2174

N/A


78.88

78.02

76.71

74.92

75.82

N/A


72.39

75.54

N/A


80.447

81.157

80.964

78.724

79.852

N/A


76.199

77.551

N/A


250 -
249.2
250 -
249.2
250 -
249.2

250 248

250 248

N/A

250 -
248.4
250 -
248.4

N/A


332.48

336.52

329.90

323.81

316.85

N/A


307.30

304.12

N/A


443.0685

450.0203

433.9856

406.4892

399.1341

N/A


391.2782

389.5859

N/A


498.3579

501.5257

490.3261

490.9999

483.0258

N/A


477.3210

473.9573

N/A


78.21

78.23

75.26

77.77

73.30

N/A


75.51

71.70

N/A


80.231

80.246

77.945

79.783

78.230

N/A


77.976

76.184

N/A


225 -224

225 -224

225 -224
225 -
221.2
225-
221.2

N/A

225-
221.4
225-
221.4

N/A














Table E-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s.
23 cfm 45 cfm
Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P
X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi)


Open 1

Open 2

Open 3

Copper 1

Copper 2

Copper3

Nickel 1

Nickel 2

Nickel 3


420.76

437.41

423.91

372.71

379.04

N/A


360.82

363.56

N/A


536.5902

552.1902

540.7947

472.7391

477.1610

N/A


465.7585

469.7456

N/A


596.7148

611.6840

600.9194

575.7499

581.4331

N/A


571.5021

576.7506

N/A


72.81

77.56

75.72

75.78

76.69

N/A


74.17

73.94

N/A


77.736

81.142

79.080

78.022

80.269

N/A


76.408

77.296

N/A


250 -
249.2
250 -
249.2
250 -
249.2

250 248

250 248

N/A

250 -
248.4
250 -
248.4

N/A


406.05

416.36

385.11

370.15

368.25

N/A


345.77

347.46

N/A


513.6828

522.7652

501.8813

460.7346

459.6907

N/A


454.3775

456.9002

N/A


575.2790

576.1766

565.7901

564.3760

562.9117

N/A


558.8598

558.4393

N/A


74.61

75.65

75.92

76.43

74.87

N/A


74.36

73.24

N/A


78.864

77.667

78.833

79.790

78.454

N/A


76.825

76.153

N/A


225 -224

225 -224

225 -224
225 -
221.2
225 -
221.2

N/A

225-
221.4
225-
221.4

N/A















APPENDIX F
SMALL SYSTEM HEAT TRANSFER ENHANCEMENTS




Full Text

PAGE 1

USE OF METALLIC FOAMS FOR HEAT TRANSFER ENHANCEMENT IN THE COOLING JACKET OF A ROCKET PROPULSION ELEMENT By RYAN JEFFREY AVENALL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Ryan Jeffrey Avenall

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This document is dedicated to the Lord, the giver of life, my provider, for without Him none of this would have been possible.

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ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Jacob N. Chung, for believing in me and for giving me the opportunity to embark on this wonderful research topic. I would also like to thank my committee, Dr. Skip Ingley, and Dr. Bhavani Sankar, for their much needed help and advice. NASA provided the funding for this project through URETI. I would also like to thank my parents who have persevered with me through this campaign and have given me the guidance in every walk of life. Also, I thank my fiance Debbie Simonson, who has repeatedly help me through the times when I wanted to quit. I also would like to thank my roommate Landon Tully for his continued support. He has helped me prepare my test facility as well as give me motivation to continue pursuing this degree. I thank the people involved with me at the Rock Church of Gainesville for all their prayers and support. Finally I would like to thank the One who has given me life more abundantly, and whose name is above all names. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................iv LIST OF TABLES ............................................................................................................vii LIST OF FIGURES ...........................................................................................................ix ABSTRACT ......................................................................................................................xii CHAPTER 1 ROCKET PROPULSION.............................................................................................1 History..........................................................................................................................1 Structure................................................................................................................2 Cooling Jacket.......................................................................................................2 Problems with Cooling.................................................................................................3 2 PREVIOUS WORK......................................................................................................5 Metallic Elements.........................................................................................................5 Metallic Porous Materials......................................................................................5 Metal Foam Processing and Fabrication...............................................................7 Rocket Combustion Testing.........................................................................................7 Heat Transfer Analysis.................................................................................................8 Sub critical Fluids..................................................................................................8 Supercritical Fluids and Rocket Heat Transfer...................................................12 3 NUMERICAL AND ANALYTICAL APPROACH..................................................15 4 LARGE SYSTEM EXPERIMENTAL SIMULATION AND RESULTS.................21 Test Apparatus Setup and Procedure..........................................................................21 Experimental Results and Comparisons.....................................................................25 5 SMALL SYSTEM EXPERIMENTAL SIMULATION AND RESULTS................43 Test Apparatus Setup and Procedure..........................................................................43 Experimental Results and Comparison.......................................................................44 6 PRACTICAL ROCKET ENGINE APPLICATION..................................................56 7 RECOMMENDATIONS FOR FUTURE WORK.....................................................58 v

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8 UNCERTAINTY OF RESULTS...............................................................................62 9 CONCLUSIONS........................................................................................................65 APPENDIX A NOMENCLATURE...................................................................................................68 B COOLANT PROPERTIES.........................................................................................70 C LARGE SYSTEM COLLECTED DATA..................................................................72 D LARGE SYSTEM HEAT TRANSFER ENHANCEMENTS...................................77 E SMALL SYSTEM COLLECTED DATA..................................................................82 F SMALL SYSTEM HEAT TRANSFER ENHANCEMENTS...................................87 LIST OF REFERENCES...................................................................................................92 BIOGRAPHICAL SKETCH.............................................................................................94 vi

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LIST OF TABLES Table page 8-1.Uncertainty of Results.................................................................................................64 B-1. Properties for Liquid Nitrogen Referenced from [15]..............................................70 B-2. Properties for Nitrogen Vapor Referenced from [15]...............................................70 B-3. Properties for Liquid Water Referenced from [11]...................................................71 B-4. Properties for Water Vapor Referenced from [11]...................................................71 C-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s..........................................................73 C-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s........................................................74 C-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s........................................................75 C-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s........................................................76 D-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s..............................................78 D-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s......................................78 D-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s............................................79 D-4.Heat Transfer Enhancement @ Heat Flux = 5.69 Mbtu/in2-s....................................79 D-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s............................................80 D-6.Heat Transfer Enhancement @ Heat Flux = 7.58 Mbtu/in2-s....................................80 D-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s............................................81 D-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s....................................81 E-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s...........................................................83 E-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s.........................................................84 E-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s.........................................................85 vii

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E-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s.........................................................86 F-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s...............................................88 F-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s.......................................88 F-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s.............................................89 F-4.Heat Transfer Enhancement @ Heat Flux = 5.69 Mbtu/in2-s.....................................89 F-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s.............................................90 F-6.Heat Transfer Enhancement @ Heat Flux = 7.58 Mbtu/in2-s.....................................90 F-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s.............................................91 F-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s.....................................91 viii

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LIST OF FIGURES Figure page 2-1.Plot of the Reynolds Number Factor, F Referenced from Collier [12].......................11 2-2.Plot of the Suppression Factor, S Referenced from Collier [12].................................11 2-3.Plot of Sub Critical and Supercritical Coolant Heat Transfer Referenced from [2]....12 3-1.2-D Geometrical Representation of a Rocket Engine Combustion Chamber for use in Numerical Code........................................................................................................15 4-1.Representation of Large Testing Apparatus and System.............................................21 4-2.SEM Photograph of Copper Foam Structure...............................................................23 4-3.Photograph Showing the Brazing of the Copper Foam to the Inner Tube..................23 4-4.SEM Photograph of Nickel Foam Structure................................................................24 4-5.Photograph Showing the Brazing of the Nickel Foam to the Inner Tube...................24 4-6.Open Channel Cross-Section.......................................................................................26 4-7.Copper Foam Cross Sectional View............................................................................27 4-8.Nickel Foam Cross Sectional View.............................................................................28 4-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm..................29 4-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm..................29 4-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm..................30 4-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm..................30 4-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm................31 ix

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4-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm................31 4-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm................32 4-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm................32 4-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm................33 4-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm................33 4-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm................34 4-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm................34 4-21.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm................35 4-22.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm................35 4-23.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm................36 4-24.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm................36 4-25.Representation of Thermal Circuit for Heat Transfer into the Metallic Foam..........41 5-1.Representation of Small Testing Apparatus................................................................43 5-2.Open Channel Cross-Section for Small System..........................................................44 5-3.Copper Foam Cross-Section for Small System...........................................................44 5-4.Nickel Foam Cross-Section for Small System............................................................45 5-5.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm..................46 5-6.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm..................46 x

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5-7.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm..................47 5-8.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm..................47 5-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm................48 5-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux 5.69 Mbtu/in2-s & 23 cfm....................48 5-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm................49 5-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm................49 5-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm................50 5-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm................50 5-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm................51 5-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm................51 5-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm................52 5-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm................52 5-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm................53 5-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm................53 7-1.Closed Loop Testing Apparatus Proposed Diagram...................................................59 xi

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science USE OF METALLIC FOAMS FOR HEAT TRANSFER ENHANCEMENT IN THE COOLING JACKET OF A ROCKET PROPULSION ELEMENT By Ryan Jeffrey Avenall December 2004 Chair: Jacob Chung Major Department: Mechanical and Aerospace Engineering Rocket propulsion has been used in many different aspects of space travel and military tasks. Nearly 800 years ago, the Chinese were the first to develop this concept using solid propellants. Since the early 1900s, fuel-cooled thrust chambers have been a concern as well as an ongoing advancement in rocket propulsion. With the higher demand today for longer lasting and farther travel, and the extreme temperatures that these elements experience, a break-through technology is needed in the cooling of these thrust chambers. In this thesis the idea of using a porous metallic foam will be implemented and tested for its heat transfer capabilities inorder to solve this problem. The goal is to cool the hot wall temperatures without creating large pressure drops in the coolant passage. The testing of this idea involves two systems: a large-scale system and a small-scale system. In both these systems the coolant will be nitrogen gas compressed to 300 psig. The nitrogen then flows through an annulus and is exhausted into the atmosphere. xii

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Constant heat flux heaters placed inside the inner tube of the annulus will produce the hot wall temperatures. Then using thermocouples, the hot wall temperatures will be read into an Excel spreadsheet. The pressure drop is measured using two digital pressure gauges. For the large system a heat transfer enhancement for the copper foam was found to be 1.5 or 50% and for nickel foam was found to be 1.82 or 82%. This caused the hot wall temperatures to decrease by an average of 71.84F and 100.74F for the copper and nickel foams, respectively. The pressure drop through the copper foam and nickel foam remained about the same and was 1 psig for 23 cfm and 3 psig for 45 cfm in comparison to zero pressure drop for the open channel system. For the small system a heat transfer enhancement for the copper foam was found to be 1.14 or 14% and for nickel foam was found to be 1.15 or 15%. The wall temperatures in this system decreased by an average of 29.04F and 36.04F for the copper and nickel foams respectively. The pressure drop through the copper foam and nickel foam relative to the open channel is 1.2 psig and 0.8 psig, respectively, for 23 cfm, and for 45 cfm the pressure drop is 2.8 psig and 2.6 psig, respectively. xiii

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CHAPTER 1 ROCKET PROPULSION History Rocket Propulsion is used in many different devices for different purposes. Propulsion is mainly used for transportation of some kind. Missiles, space aircraft, military aircraft, satellites, and commercial aircraft are some examples where propulsion is utilized. The rocket principle is thought to have been founded by Hero of Alexandria in 67 A.D. He invented many machines that used the reaction principle which is the theoretical basis for the rocket. Most of his work was successful in the creation of two opposing jets exhausting steam. Rocket propulsion uses stored matter, or propellants, to achieve its thrust by combusting and ejecting these propellants. The three main types of rocket propulsion are solar propulsion, nuclear propulsion, and chemical propulsion. Two main types of propellants used are solid and liquid propellants. The first inventor of the rocket is said to be Feng Jishen a Chinese scientist back in 970 A.D. His work dealt with two experiments using bamboo tubes and gunpowder, which is now similar to what we use as fireworks. The first time the rocket principle was used as a weapon was back in 1275. It wasnt until the twentieth century when rocket propulsion design and theory started growing rapidly. In 1903, Konstantin Tsiolkovsky, who was a mathematics teacher, discovered most of the theories for the modern rocket. He developed the rocket flight equation and invented the multi-stage rocket [1]. He also found that liquid oxygen and hydrogen would be good propellants to achieve the high exhaust velocity necessary to travel into space. In 1926, Robert H. Goddard, a professor of physics at Clark 1

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2 University in Massachusetts, designed the li quid-fuelled rocket combustion chambers and nozzles [1]. He also accomplished the first flight using a liquid pr opellant rocket engine [2]. Goddard had over 214 patents for rocket apparati that later in 1960 the U.S. bought to create their own rocket engines. Fuel-coo led thrust chambers stem all the way back to the early 1900s, and are in need of new technology to advance rocket propulsion for centuries to come. The Russian space program is noted for be ing the most focused and active program since rocket engines became a modern mode of transportation. They are credited with the first artificial satellite, the first man in space, the first spacecraft on the moon, the first docking of two spacecraft, and the first spa ce station. The main achievement for the United States space program was having the fi rst man walk on the moon. Now for both programs the quest continues, and there have been multiple satellites and space travel since these first accomplishments by both programs. Structure The structure of a rocket propulsion elemen t is quite complex and has been studied for many years. It is in the form of a converging diverging nozzle. This shape provides for the maximum thrust and performance needed by the element. The design used has had an ongoing struggle with the amount of cool ing necessary for the element. The skin of the nozzle has to be able to withstand high temperatures, high pr essures, as well as being lightweight. This makes for a complicated task in building a sufficient nozzle for the system. Cooling Jacket In order to achieve very high thrusts, th e combustion of the oxidizer and the fuel must be very powerful. Therefore the gases that escape through the nozzle after

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3 combustion are extremely hot. For many years the idea of a cooling jacket has been used to surround the outside of this nozzle. The purpose for this cooling jacket is to cool the inner walls of the combustion chamber and nozzle regions, which can help in many ways. First, the parts surrounding the outside of this nozzle wont see as much of the heat from the combustion. Second, the material of the nozzle itself will be at a much cooler temperature range, increasing its life expectancy. Third, the use of lighter materials will help with the overall weight requirement of the system. To use this cooling channel, a fluid of some sort has to be provided to the system and then recycled through and back around again. The current method, and probably the most efficient is to have a separate line from the fuel tank deliver a pressurized flow rate to the cooling jacket. This then will allow for a continuous supply of coolant without having to attach another tank. Using the fuel is also a good idea because most of the fuels used are cryogenic. This means that the coolant will enter the jacket at very cold temperatures allowing cooling of the walls even further. Most of the rocket engines today have some form of cooling channel or jacket that was just described. However, further research into these jackets is necessary. Problems with Cooling There still exist many problems today with cooling these nozzles even with the coolant jacket in place. The main problem is that the coolant channel does not have a large enough heat transfer coefficient to sufficiently decrease the wall temperature. This is mainly due to the coolants fluid properties and dynamics. The properties of the supercritical fluid dictate how well the fluid will transfer heat. Supercritical fluids are fluids that are at very high pressures or very high temperatures. The problem with these supercritical fluids is the extreme pressures they supply to the

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4 surrounding apparatus as well as having systems like pumps that can handle these types of pressures and temperatures. In using a supercritical fluid you also get the benefit of a much higher heat transfer coefficient when compared to that of a sub-critical fluid. The use of these fluids provides cooling for the combustion chamber as well as fuel for the combustion process. By using these fluids for cooling the heat transfer to the fluid helps heat up the fluid to a much more combustible state. However, these extreme temperatures are still too high and need to be decreased. The throat area is the main concern for improved heat transfer through this cooling jacket. If the heat transfer can be improved then the life expectancy of the nozzle can be improved which would save money. Therefore, this is an area of great significance, and research for innovative ideas is an ongoing task. One area being extensively explored is the use of metallic elements in the cooling channel to increase the heat transfer.

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CHAPTER 2 PREVIOUS WORK Metallic Elements Metallic Porous Materials Previous work has been done using the idea that metals high conductivity will work well as an agent in increasing the heat transfer coefficient in certain aspects. Koh and Stevens [3] found that the heat transfer effectiveness could be greatly increased by using a porous medium. Koh and Stevens [3] filled a stainless steel annulus with peen shot (steel particles). The results for Koh and Stevens [3] project were for a fixed coolant flux of 9.65 sftlb2 the heat flux through the wall was increased from 16 to 20 sftBtu2 and the maximum wall temperature was reduced from 1450 to 350. As seen here porous metallic materials can be very helpful in increasing the heat transfer effectiveness. F Koh and Colony [4] as well as Bartlett and Viskanta [5] have done analytical studies on the enhancement of the heat transfer due to a high thermal conductivity porous medium. In Bartlett and Viskanta [5], their analytical approach for the heat transfer effectiveness was compared with already known data for a particular diameter and heat flux. Their results show very similar results to that of the experimental, and prove that the effectiveness of heat transfer should be greatly increased with the introduction of a porous medium with high conductivity. Koh and Colony [4] completed a similar 5

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6 procedure earlier by using basic models of heat transfer. They discovered that the heat transfer using a porous medium is increased significantly. Metallic foams were then looked at as a possibility in enhancement of heat transfer for rocket engine cooling passages. Brockmeyer et al. [6] showed the benefits of using metallic foam for heat transfer enhancement. They looked at cooper alloy and nickel alloy foams. It is stated here that for the heat transfer enhancement to be beneficial it must be able to enhance the heat transfer, have improved elevated temperature properties, reduced weight, simplified manufacturing, and lower system cost. Brockmeyer et al. [6] found that the heat transfer in the foam structure is excellent due to the enhanced mixing in the flow paths. They discovered that relative to a flat plate the heat transfer would be enhanced by a factor of 4 for foam packed heat exchangers. The relatively high void fraction of the foams also helps with the pressure drop criterion through the cooling chamber. Another testing of metallic foams for their enhanced heat transfer was conducted by Boomsma et al. [7]. They used aluminum alloy foams placed in-between two parallel plates for heat transfer analysis. Boomsma et al. [7] performed experimental tests on different porosities, flow rates, and even compared their results with the best commercial heat exchangers available in that size range. The aluminum foam proved to have very little pressure drop, if any, and an increase in the efficiency of the heat transfer by nearly two over any commercial product made for the same situation. Metallic foams have been proven to show that the efficiency of the heat transfer, along with little loss in pressure, is a viable way to cool processes effectively.

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7 Metal Foam Processing and Fabrication There are many different ways to make metallic foams. Metallic sintering, electro deposition or chemical vapor decomposition (CVD), metal deposition through evaporation, and investment casting are a few of the processes. When creating a metallic foam using metal sintering, metallic particles are suspended in slurry and then coated on a polymeric foam substrate [8]. The substrate vaporizes during this process, and the metallic particle becomes an object which is the foam. The CVD method uses the chemical decomposition of a reactive gas in a vacuum onto a heated substrate [8]. Molten metal infiltration can also be used to form such foam materials such as aluminum and copper [8]. In this process, the foam precursor is coated with a casting and then packed into casting sand. This assembly is then heated to decompose the precursor and to harden the casting. Then the molten metal is pressure infiltrated filling all the voids. When it solidifies it forms a product with solid struts. However, this process is very expensive and time consuming [8]. Rocket Combustion Testing Some examples of previous projects dealing with only rocket engine combustion help to give a better understanding of what is taking place inside of a rocket engine. These papers were also used for verification purposes of a numerical model that will be talked about later in this thesis. Tamura et al. [9] performed an investigation on staged combustion with liquid oxygen and methane. In their study they used water as the coolant for the cooling passage, and had a scaled down rocket engine assembly for their combustion. Their tests looked at different injection geometries, speeds, temperatures, and different mixture ratios as well. Tamura et al. [9] had results for characteristic velocity vs. mixture ratio, pre burner temperature vs. mixture ratio, efficiency vs.

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8 chamber length, heat flux vs. chamber pressure, and heat flux vs. axial distance away from the throat. Most of the data collected here is insignificant for our purposes other than the heat flux vs. axial distance. This will provide a good experimental comparison between the numerical code and their results. Some assumptions had to be made however, which could have skewed the results slightly in the numerical simulation. The coolant velocity, the combustion velocity, and some other geometrical constraints such as exit diameter were not given in their report. Their results showed about a 9:1 or 9:2 ratio for heat flux at the throat compared to the combustion chamber. Results from other papers were also helpful in determining the procedure and design of our test rig. Elam [10] studied rocket combustion using liquid oxygen and hydrogen. Here results of hot wall temperatures and heat flux with respect to the location from the throat were helpful in determining ranges for temperatures and fluxes that might be needed to get an accurate representation of rocket combustion. Also this paper showed that many of the rocket engines operate under severe pressures (supercritical fluids) giving rise to pressure drop concerns with the usage of foam materials. Heat Transfer Analysis Sub critical Fluids Heat transfer analysis of sub critical fluids is based on properties and laminar, or turbulent flow. For single-phase flow, Incropera and DeWitt [11] present a good description of the heat transfer analysis. In our case turbulent flow will be the ideal conditions for consideration. Using Incropera and DeWitts [11] ideals of annulus flow one can start to analyze how the fluid reacts to different initial conditions. For instance, the overall heat transfer analysis changes when using a free stream approach, a constant heat flux approach, or even a constant wall temperature approach. For both liquid and

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9 vapor phases of the coolant turbulent correlations can be used to figure out the heat transfer coefficient, the heat flux, and the wall temperatures all of which are extremely important in designing the test rig for experimental analysis. For conducting a study on the heat transfer analysis, many equations and theories are involved. The basic models for heat transfer analysis from Incropera and DeWitt [11] will be shown here and further explained in Chapter 3. For general considerations msppsmTThcmPcmPqdxdT" where DP (1) Eq. (1) explains the energy balance across a basic system with P as the perimeter. For constant heat flux considerations xcmPqTxTpsimm",)( (2) Eq. (2) shows the relationship between the fluid temperature and the wall heat flux. For constant wall temperature considerations hcmPxTTxTTpimsmsexp)(, (3) Eq. (3) provides an explanation of how the fluid temperature changes due to the constant surface temperature. When dealing with a free stream constraint the following equation provides detail into how that heat transfer is considered. psimomiocmAUTTTTTTexp,, (4) where U is the overall heat transfer coefficient given by 111oihhU (5)

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10 For turbulent flow the entrance length and heat transfer analysis differ significantly from the laminar correlations. Since turbulent flow is our main concern the correlations used are 61Re4.4DeDL (6) 4.054PrRe023.0DDNu (7) Next is the consideration of the two-phase boiling characteristics of a sub critical fluid. In Collier [12] the two-phase region is described by many correlations. The two-phase region occurs when the liquid at the surface starts nucleate boiling. Nucleate boiling is the formation of vapor bubbles by nucleation on the surface and causes the liquid to change phase. According to Collier [12] there are seven steps to accomplish in order to calculate the heat transfer coefficient in this region. These steps are listed below. (a) Calculate 1/Xtt (Martinelli parameter) 1.05.09.01gffgttqualityqualityX (8) (b) Evaluate F from figure (c) Calculate ch FDkkcDqualitymfffpff4.0,8.014023.0 (9) (d) Calculate tpRe ftpffFDqualitymReRe14Re25.1 (10) (e) Evaluate S from figure

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11 Figure 2-1.Plot of the Reynolds Number Factor, F Referenced from Collier [12]. Figure 2-2.Plot of the Suppression Factor, S Referenced from Collier [12]. (f) Calculate ncbh SpThckhsatsatgfgfffpfncb75.024.024.024.029.05.049.045.0,79.000122.0 (11) (g) Calculate tph cncbtphhh (12)

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12 These equations are used to evaluate the overall heat transfer coefficient in the two-phase region. Properties should be taken at the average temperature of the fluid. Supercritical Fluids and Rocket Heat Transfer For supercritical fluids the question is whether or not the heat transfer trends are similar to that of sub critical fluids. This would help in an overall analysis of the fluids used. The properties of the fluid will be different as well as the way the fluid reacts chemically at such high pressures and temperatures. Some articles that can be helpful in better understanding the phenomenon of supercritical fluids are Watts and Chou [13] as well as Labuntsov [14]. Additional information on supercritical fluids is found in Sutton and Ross [2]. The detail is limited about the supercritical region other than a graph that shows that supercritical fluids follow the same pattern of heat transfer as sub critical fluids except the nucleate boiling region. This graph is shown in the figure below. Figure 2-3.Plot of Sub Critical and Supercritical Coolant Heat Transfer Referenced from [2].

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13 In Sutton and Ross [2] their contribution is the explanation of how heat transfer analysis is carried out for regeneratively cooled rocket engines. They discuss everything from the heat transfer coefficients to the method of calculating individual heat fluxes at different areas of the engine. Some of these ideas or examples are listed below. AQTThqlo (13) lwglghkthTTq11 (14) wgogTThq (15) wlwgwTTtkq (16) lwllTThq (17) These explain the heat flux through different regions as well as the overall heat flux through the regeneratively cooled thrust chamber. odgRkh2PrRe026.04.08.0 (18) 322.0PrRe023.0dl A mch (19) These correlations explain the heat transfer coefficient for the hot gases as well as that for the coolant side during its forced convection as a liquid. These models can be used to get an overall idea of how the heat transfer throughout the chamber is occurring, and where problem situations will and can occur.

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14 In Barron [15], it discusses how supercritical fluids follow the same pattern of heat transfer as those of near critical fluids. They discuss in further detail the correlations used to study the heat transfer for the near critical fluid. wbbwDflDkh01457.01PrRe0208.04.08.0 (20) Where the subscript w stands for wall temperature, and b stands for bulk temperature. All the other correlations are identical and can be calculated using the non-near critical correlations.

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CHAPTER 3 NUMERICAL AND ANALYTICAL APPROACH By using all the correlations stated in chapter 2 the numerical analysis can begin. The analysis is based on a very crude 2-D model of a rocket combustion system, which is shown below. Figure 3-1.2-D Geometrical Representation of a Rocket Engine Combustion Chamber for use in Numerical Code. As seen in this figure the wall thickness will be neglected, therefore neglecting the conduction heat transfer due to the wall thickness. From this model two different assumptions are made which change the overall process. First, there is uniform constant free stream combustion gas temperatures in the combustion chamber, and second, that a 15

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16 uniform heat flux on the surface is prevalent. These two models will be built in order to show real life simulation as well as experimental simulation. Starting with the free stream combustion gases, the simulation is built on the basis of changing area with respect to the distance x down the chamber. The analysis is also carried out for sub critical fluids. The first step is to study the liquid phase of the coolant. Shown below are the steps taken in order to figure out the wall temperatures, coolant temperatures, and the distance down the chamber until the bulk starts to boil. ooRLxRRxLR 212111tantan (21) lpsLimomocmAUTTxTT,,exp)( (22) xlpLimomoxxRcmUTTxTT01,,)(2exp)( (23) xRxxLcmUTTTxTolpLimoom1211,,tan2tan2exp)( (24) Using these equations and knowing that the temperature of the coolant at the boiling point will be the boiling temperature of the coolant, thus solving for the boiling point. LoLLlpLimoboXRXXLcmUTTTT1211,,tan2tan2ln (25) imoboLlpooLTTTTUcmLRLRX,1,21111lntantantan (26) This shows the important aspects of the liquid phase and how to apply them to a nozzle geometry system. Next is the two-phase region, which is characterized by the nucleate boiling as well as forced convection. In this region the assumption that the coolant

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17 temperature remains constant at the boiling temperature is used. This changes when it completely vaporizes. VLgfXXbHHxxRTUHm)(22 (27) This distance however is based on whether or not it occurs before the throat or after the throat. Since it is unknown both cases must be considered. for 1LXv 1211221111tan22tantantanLoLLbfgooVXRXXLTUhmLRLRX (28) for 1LXV 2211221212222121tan22tantantantantanLoLLbfgooVXRLXLXLTUhmRLRLX (29) Next the vapor phase must be analyzed. Here only the temperatures need to be determined, and they follow a similar analysis as the liquid phase. This is also going to be affected by whether or not the distance to full vaporization takes place before the throat or after the throat. for 1LXv and 1:LXxV VoVVvpVboomXxRXXLxxLcmUTTTxT21211,2121tan2exp)( (30) for 1LXv and LLx:1

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18 121122,12121tan2exp)()(LxRLxLxcmULTTTxTovpVmoom (31) for 1LXv and LXxV: VoVVvpVboomXxRXLXxLxcmUTTTxT12122,2121tan2exp)( (32) Then in order to solve for the wall temperatures, a specific equation that works for all three regions is shown below. igmiogshhThThT where vli,2, (33) These are the main important characteristics needed in order to study what is occurring in the chambers. The wall temperature being the most important shows how the foam will affect the overall heat transfer throughout the chamber. Similarly a constant heat flux simulation is generated to compare with the free stream simulation. This is used to simulate how the test rig reacts for comparison with the experimental results as well as what takes place in real simulations with the free stream gases. Again the first step is to calculate the liquid phase of the coolant. lpsmcmPqxT," where )(21xRP (34) xRxxLcmqTxTolpsimm1211,",tan21tan2)( (35) 1",,21111tantantanslpimbooLqcmTTLRRLX (36)

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19 The next step to consider is the two-phase region. It is again important to note that the analysis is dependent upon whether or not the distance to be fully vaporized occurs before the throat or after the throat. PdxqdHms" (37) for 1LXV 2111"21111tan22tantantanLoLsfgooVXRLXqhmRLRLX (38) for 1LXV 2122121212"21221tan22tantantantantanLXRLXXLqhmLRRLXLoLLsfgooV (39) The final aspect to consider is the vapor phase for constant heat flux. However the temperatures during the vapor phase are again a function of where the distance to full vaporization occurs. for 1LXV and 1:LXxV VoVVvpsbmXxRXXLxxLcmqTxT12121,"tan21212)( (40) for 1LXV and LLx:1 122112,"1tan21212)()(LxRLxLxcmqLTxTovpsm (41) for 1LXV and LXxV:

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20 VoVVvpsbmXxRXLXxLxcmqTxT21212,"tan21212)( (42) The wall temperatures are again calculated by one simple equation. This equation is dependent on what phase the coolant is in. This equation is shown below. )("xThqTmiss (43) The same type of analysis is carried out for a cylindrical geometry. These equations are then used to formulate a simulation for both the free stream combustion gas consideration and the constant heat flux consideration. For supercritical fluids the numerical model is different. There is not a two-phase flow to deal with. The only difference between the calculations for this flow and for the two-phase flow is how the heat transfer coefficients are calculated. These calculations are shown in chapter 2.

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CHAPTER 4 LARGE SYSTEM EXPERIMENTAL SIMULATION AND RESULTS Test Apparatus Setup and Procedure The large test rig for this project is a stainless steel cylindrical annulus which is set up to test high-pressure gaseous nitrogen. It will operate under the constant heat flux consideration discussed earlier in chapter 3. The setup and equipment for the testing procedure is listed below. Figure 4-1.Representation of Large Testing Apparatus and System. 1. Test Apparatus 2. Band Heaters 3. Power Switching Units 4. Temperature Control Units 21

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22 5. Thermocouples 6. Pressure Gauges 7. Piping, valves and parts 8. Nitrogen Tanks 9. Metallic Foam 10. Data Acquisition Board and Computer The first step is to power up everything starting with the data acquisition unit and ending with the band heaters. When the band heaters are powered up they will be given enough time to heat up to an assumed temperature. The system is then charged with 300 psig of nitrogen, and the exhaust valve is opened enough to obtain the desired flow rate reading. Eight cases will be run with three tests each completed without any metallic foams present. These tests include heat fluxes of 1.9 MBtu/in2-s, 5.69 Mbtu/in2-s, 7.58 Mbtu/in2-s and 9.48 Mbtu/in2-s. At each individual heat flux there will be three tests completed at a flow rate of 45 cfm or 1.16 lb/s @ a pressure of 250 psig and three tests also completed at a flow rate of 23 cfm or 567 lb/s @ a pressure of 225 psig. The same process will also be completed for the copper based foam. Figures below show the structure of this foam and how it is brazed to the outside of the inner tube.

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23 Figure 4-2.SEM Photograph of Copper Foam Structure. Figure 4-3.Photograph Showing the Brazing of the Copper Foam to the Inner Tube. This same process will be completed for the nickel-based foam. Figures below show photographs of the structure of this foam as well as how it is brazed.

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24 Figure 4-4.SEM Photograph of Nickel Foam Structure. Figure 4-5.Photograph Showing the Brazing of the Nickel Foam to the Inner Tube.

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25 Experimental Results and Comparisons Some preliminary tests were done to see how the system functioned. The tests were confusing at first as the temperature profiles were scattered and inconsistent unlike the conclusions from the theoretical analysis. The temperature profiles were decreasing in nature at one instant and increasing at another. The first correction attempted was to check the calibration of the thermocouples. This was done by taking all the thermocouples and placing them in a glass of cold water. All the results came out almost identical with a few varying but within the expected limit of the thermocouple reader. However when the thermocouples were moved around or shaken it was noticed that the values of some altered. The next step was to change the frequency that the thermocouple reader responded at from 50 Hz to 400 Hz. This made the difference and now all the thermocouples seem to be working properly. Just for completion the thermocouples were also placed in a heated glass of water to make sure that they still read identical temperatures. This did not correct the problem with the incorrect and varying temperature profiles. The next step was to look at the heaters and how they functioned. First the controllers that supply the power to the heaters are set up to run on a percent power basis. The max power or heat flux that the heaters can provide is 37 MBtu/in2-s. The controllers where set up at 2% power or heat flux to check how the heaters worked. It was determined immediately that the heaters do not heat up uniformly like expected. The heaters had a cold side (side that heated up slower) and a hot side (side that heated up faster). The next step then was to see if the hot side of one heater being up against the cold side of the next heater would produce the same temperature reading. This functioned best and produced good results when the cold side of the heater was on the

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26 inside of the hot side of the other heater. This then gave an almost perfect contact between the two heaters when heated up because the heaters expand. However this would not work inside the tubes because it was impractical to push them down the tube and keep the heater just on the inside of the other. So instead the heaters are pushed together as they are slid down the tube, which provided good results as well. The temperature readings appear linear, but that is from a combination of two things. First it should be linear by theoretical understanding because of the convective heat transfer across these. Second the heaters having a cold side and a hot side do not provide the same heat flux uniformly across their surface providing a linear response to the control. This type of temperature profile however was very consistent over multiple tests at different heat fluxes and coolant flow rates, and will be used to check the percent enhancement of the foam to the overall heat transfer. The figure below shows the open channel cross-section. Figure 4-6.Open Channel Cross-Section.

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27 The test results for the open channel flow cannot be shown in comparison with that of the numerical model. The reason for this is that the heaters that are used do not provide a uniform heat flux. Therefore the data will not exactly portray that of a theoretical constant heat flux at the surface. The metallic foam is brazed to the outside of the inner tube and fills the gap between the inner tube and the outer tube of the annulus. The figure below shows the cross section with the copper foam. Figure 4-7.Copper Foam Cross Sectional View. Just like the copper foam, the nickel foam is brazed to the outside of the inner tube and fills the gap between the inner tube and the outer tube of the annulus. The figure below shows the cross section with the foam.

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28 Figure 4-8.Nickel Foam Cross Sectional View. The copper foam data as well as the nickel foam data is shown below with the open channel data for comparison. All 8 test cases are shown below providing the hot wall temperature, bulk fluid temperature, and the pressure drop. From these figures, the trend of increasing heat flux provides an increase in the hot wall temperature which is expected. It is also shown predominantly that with three tests at each individual test case the temperature profiles remain the same which means that the system is functioning properly and is calibrated well. From these profiles it is also determined that a linear increase in temperature over each heated area, and a linear increase for the coolant temperature is predominant. This is expected with theoretical analyses explaining this linear dependence. When looking at the data collected in Appendix D for the copper and nickel foams some interesting characteristics are found. First of all our notion that the foam

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29 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 1.9 Mbtu/in2-s & 23 cfm)1001101201301401501601701801902002102202302400510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 1.9 Mbtu/in2-s & 23 cfm)7072747678808284868800.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm.

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30 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 1.9 Mbtu/in2-s & 45 cfm)901001101201301401501601701801902002102200510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 1.9 Mbtu/in2-s & 45 cfm)687072747678808284868800.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm.

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31 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 5.69 Mbtu/in2-s & 23 cfm)1601802002202402602803003203403603804004204404600510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 5.69 Mbtu/in2-s & 23 cfm)687072747678808284868890929400.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm.

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32 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 5.69 Mbtu/in2-s & 45 cfm)1601802002202402602803003203403603804004204400510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 5.69 Mbtu/in2-s & 45 cfm)55606570758085909510000.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm.

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33 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 7.58 Mbtu/in2-s & 23 cfm)1802002202402602803003203403603804004204404604805005205400510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 7.58 Mbtu/in2-s & 23 cfm)6570758085909510000.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm.

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34 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 7.58 Mbtu/in2-s & 45 cfm)1802002202402602803003203403603804004204404604805005200510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 7.58 Mbtu/in2-s & 45 cfm)6570758085909510000.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm.

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35 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 9.48 Mbtu/in2-s & 23 cfm)2002202402602803003203403603804004204404604805005205405605806006200510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-21.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 9.48 Mbtu/in2-s & 23 cfm)6570758085909510010500.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-22.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm.

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36 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 9.48 Mbtu/in2-s & 45 cfm)1802002202402602803003203403603804004204404604805005205405605806000510152025Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 4-23.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 9.48 Mbtu/in2-s & 45 cfm)64666870727476788082848688909294969800.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nicke Test #3 Figure 4-24.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm.

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37 would enhance the heat transfer is true. We did not get the enhancement we thought were possible, but that is mainly due to the open system parameters and the fact that the heaters did not function as intended. If the system had been closed loop then the tests could have been run for hours until a true equilibrium had been accomplished. This then might have described the true form of the foam enhancement. The average percent enhancement is based on the average overall temperatures recorded experimentally and the supposed heat flux. Using these parameters we can come up with an estimate of the heat transfer coefficient at each position down the tube and compare the values with and without foam. fssThqT" (44) Ts = surface temperature (hot wall temperature) Tf = fluid bulk temperature The results for the foam filled channels in comparison to that of the open channel are now considered. As can be determined from these tables shown in Appendix E, the average heat transfer enhancement remains relatively the same for the particular foams. However with increasing heat flux the temperature differential increases. The overall systems average heat transfer enhancement is 50.22% for the copper foam and 81.58% for the nickel foam. From analytical reviews a higher enhancement is expected. Particularly from Kuzay et al. [16] it is shown how liquid nitrogen interacts with metallic foams. From this paper the Nusselt number and the friction factor can be calculated for our particular situation. The friction factor is calculated as shown below. 29.623.0Re8.26Cf (45)

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38 Here the constant C is equal to 1.0 for brazed foams, the Reynolds number will be replaced with our Reynolds number based on the hydraulic diameter, and is the porosity of the metallic foam. The friction factor will then be used to calculate the pressure drop. This pressure drop uses the normal horizontal cylinder calculation. fDLVph22 (46) The Nusselt number is calculated as shown below. 2.556.0606.0PeNud (47) The Nusselt number here is based on the diameter and for our purposes it will be based on the hydraulic diameter. is the Peclet number, which is equivalent to the Reynolds number times the Prandtl number. Again we will use the Reynolds number based on the hydraulic diameter to determine the Peclet number. In order to calculate the porosity it either had to be provided to me from the manufacturer, or it can be calculated with a few known parameters. A study done by Zhao et al. [8] shows the particular details needed for my foam purchased from Porvair Fuel Cell Company. Their study shows an average cell size and the ligament size of a copper foam from Porvair. Their average cell size is .104 in and the ligament size is .0104 in. Then it explains how to use these two parameters to calculate the porosity of the foam. Shown below are the steps in order to calculate the porosity. Pe 04.01exp113118.1pfdd (48) Here df is the ligament diameter and dp is the pore size diameter or cell size diameter. From here the porosity can be calculated and used to solve for the Nusselt number as well

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39 as the friction factor. By using the before mentioned diameters of the copper foam (they will also be used to estimate the porosity of the nickel foam) the porosity used in the experiments was found to be .955. The fluid properties were then calculated at two different state points 225 psig & 90 F and 250 psig & 85 F. The density at the two given points is 1.07 lb/ft3 and 1.2 lb/ft3 respectively. The viscosity is 3.84e-7 lb-s/ft2 and 3.82e-7 lb-s/ft2 respectively. The conductivity is 0.0034 lb/s-R for both states. Then the Prandtl number is .717 and .718 respectively. The Reynolds and Peclet numbers can now be calculated and used to calculate the Nusselt number and friction factor for our system. The first friction factor is 2.59 and the second is 2.94. These factors lead to the expected pressure drops of 0.18 psi and 0.06 psi respectively. The corresponding pressure drops experimentally were 4 psi and 2 psi for the copper foam respectively, and 3 psi and 1 psig respectively for the nickel foam, which are much higher than the expected pressure drops. This could be due to many different aspects. First, the correlations being used for liquid nitrogen might not be a good assumption for gaseous nitrogen. However, being that liquids usually have a higher viscosity than gases this does not seem to be a basis reason for error. Second, the foam could not be completely open in all pore areas. With closer inspection of the foam it is evident that some of the pores are closed off and not completely open. In the making of the foam it is possible that not all the pores become open of its metallic substance, therefore causing a higher pressure drop in the system. Third, there is a possible flaw in the design of the systems apparatus. Inside the outer tube there is an inner tube that connects together immediately after the foam to provide a method to insert the thermocouples and heaters for testing. The two flanges that are bolted together form this

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40 connection. These flanges create a disturbance in the flows path, which can also be shown in these results. Using the traditional internal flow calculation for the open channel Nusselt number, the new Nusselt number which is based on the foam properties can now be compared. The internal flow calculation is shown below. 4.08.0PrRe023.0DhDhNu (49) Using this equation for the experimental system, the Nusselt number for the two different Reynolds number cases is 187.49 @ 45 cfm and 120.83 @ 23 cfm. The Nusselt numbers based on the foam properties are 384.56 @ 45 cfm and 282.78 @ 23 cfm. This shows that there should be a great enhancement by using the foam over the open channel flow. The conductivities for each case with the foam and with the open channel change. Using this information the overall expected heat transfer ratio or enhancement could be calculated. For the open channel case, all that is needed is the conductivity of the fluid. In order to calculate the heat transfer coefficient the Nusselt number definition as described below is used. khDNuhDh (50) For the foam case the effective conductivity must be calculated in order to find the effective heat transfer coefficient. This conductivity is calculated using the equation below from Calmidi and Mahajan [17]. fseffkkk 1 (51) where ks is the conductivity of the solid kf is the conductivity of the fluid

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41 The conductivity of the solid is found by using the given data sheet from Porvair for the various foams, and calculating the relative density based on the porosity mentioned earlier. The conductivities where found to be 0.219 lb/s-R for copper foam and 0.05 lb/s-R for the nickel foam. Using these properties the calculated effective conductivities are 0.0131 lb/s-R for the copper foam and 0.0055 lb/s-R for the nickel foam. The typical heat transfer coefficient ratios were then found to be 7.97 for copper foam and 3.34 for nickel foam at 45 cfm, and 8.87 for copper foam and 3.81 for nickel foam at 23 cfm. In experiments it was shown that the average heat transfer was increased by a factor of 1.5 for the copper foam and 1.82 for the nickel foam. This could be low for a couple of reasons. First, the heaters that were supplied do not act as constant heat flux heaters. Therefore, not providing the right amount of heat flux specified. The second reason is how well the foam is brazed to the tube. If there is space between many of the ligaments and the tube then the heat transfer will not be greatly increased. In light of this an analytical review of the gap being a contact resistance was undertaken. A simple thermal circuit was constructed describing the path for the heat transfer through the wall and is shown below. Figure 4-25.Representation of Thermal Circuit for Heat Transfer into the Metallic Foam. effCCBBAANsxhKLKLKLTTq11," (52)

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42 Here the subscript s stands for surface, N stands for nitrogen, A stands for the stainless steel wall, B stands for the brazing foil, C stands for the nitrogen gap, and is calculated from the above equations for the heat transfer with metallic foam inserts. The wall temperature used was 192.92 F and the nitrogen temperature used was 82.87 F. The calculated heff was 23.733 lb/ft-s-R for 23 cfm. The thickness and conductivity of the stainless steel wall is 0.12 in and 2.07 lb/s-R respectively. The thickness and conductivity of the foil is 0.079 in and 53.1 lb/s-R respectively, and the conductivity of the nitrogen gap is 0.0034 lb/s-R. With the known heat flux for the particular flow rate and wall temperatures collected the length of the gap can now be solved for. The result is 0.019 in in length for the gap of nitrogen between the foil and the foam. After talking with engineers at Porvair it is difficult for them to get a good braze on this large of a system. This is most likely the reason for the lower numbers in heat transfer enhancement. effh

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CHAPTER 5 SMALL SYSTEM EXPERIMENTAL SIMULATION AND RESULTS Test Apparatus Setup and Procedure The small test rig for this project will again be an annulus made from stainless steel, but all the parts are off the shelf parts that screw together. It will also operate under the constant heat flux consideration talked about earlier in chapter 3. The setup and equipment for the testing procedure is listed below. Figure 5-1.Representation of Small Testing Apparatus. This system contains all the same components as the large system except for the size of the test apparatus and instead of using band heaters, a cable heater is used for the small system. The procedure for startup is the same process. The heat fluxes tested will 43

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44 also remain the same as well as the flow rates. By using the same flow rates, the velocity of the nitrogen will be much quicker in the smaller system than in the larger system providing faster cooling. Experimental Results and Comparison Like the large system, the small system will test open channel heat transfer, heat transfer with copper foam inserts, and heat transfer with nickel foam inserts. The system has a hydraulic diameter of 0.56 inches, and contains a foam testing section of 5 inches in length. The foam will be the same 10 ppi foam that was used in the larger system. The cross-sectional views of each testing situation are shown below. Figure 5-2.Open Channel Cross-Section for Small System. Figure 5-3.Copper Foam Cross-Section for Small System.

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45 Figure 5-4.Nickel Foam Cross-Section for Small System. All 8 test cases for the three testing situations are combined below for comparison purposes, providing the hot wall temperature, bulk fluid temperature, and the pressure drop. The test results are also compared to the large system to determine the validity of the large system results. These figures show that the trend of increasing the heat flux provides an increase in the hot wall temperature which is expected. It is also shown predominantly that with multiple tests of each individual test case the temperature profiles remain the same, which means that the system is running properly and is calibrated. From these profiles it is also shown that a linear increase in temperature over each heated area, and a linear increase for the coolant temperature is predominant. This is expected with theoretical analyses that explain this linear dependence. When looking at the data collected for the copper and nickel foams, some interesting characteristics are found. First of all our notion that the foam would enhance the heat transfer is true. However, the results that are obtained are not what was expected. The heat transfer enhancement is much lower than anticipated, and is much

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46 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 1.9 Mbtu/in2-s & 23 cfm)100110120130140150160170180190200210220230240012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 5-5.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 1.9 Mbtu/in2-s & 23 cfm)7072747678808284868800.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 5-6.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 23 cfm.

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47 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 1.9 Mbtu/in2-s & 45 cfm)90100110120130140150160170180190200210220012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 5-7.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 1.9 Mbtu/in2-s & 45 cfm)687072747678808284868800.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 5-8.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 1.9 Mbtu/in2-s & 45 cfm.

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48 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 5.69 Mbtu/in2-s & 23 cfm)160180200220240260280300320340360380400420440460012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 5-9.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 5.69 Mbtu/in2-s & 23 cfm)687072747678808284868890929400.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Copper Test #3 Nickel Test #1 Nickel Test #2 Nickel Test #3 Figure 5-10.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux 5.69 Mbtu/in2-s & 23 cfm.

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49 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 5.69 Mbtu/in2-s & 45 cfm)160180200220240260280300320340360380400420440012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-11.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 5.69 Mbtu/in2-s & 45 cfm)55606570758085909510000.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-12.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 5.69 Mbtu/in2-s & 45 cfm.

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50 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 7.58 Mbtu/in2-s & 23 cfm)180200220240260280300320340360380400420440460480500520540012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-13.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 7.58 Mbtu/in2-s & 23 cfm)6570758085909510000.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-14.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 23 cfm.

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51 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 7.58 Mbtu/in2-s & 45 cfm)180200220240260280300320340360380400420440460480500520012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-15.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 7.58 Mbtu/in2-s & 45 cfm)657075808500.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-16.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 7.58 Mbtu/in2-s & 45 cfm.

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52 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 9.48 Mbtu/in2-s & 23 cfm)200220240260280300320340360380400420440460480500520540560580600620012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-17.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 9.48 Mbtu/in2-s & 23 cfm)6570758085909510010500.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-18.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 23 cfm.

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53 Nickel Foam, Copper Foam & Open Channel Hot Wall Temperature Comparison (@ 9.48 Mbut/in2-s & 45 cfm)180200220240260280300320340360380400420440460480500520540560580600012345Length (in)Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-19.Comparison Between Nickel Foam, Copper Foam, and Open Channel Hot Wall Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm. Nickel Foam, Copper Foam & Open Channel Coolant Temperature Comparison (@ 9.48 Mbtu/in2-s & 45 cfm)72747678808200.511.522.5Temperature (F) Open Test #1 Open Test #2 Open Test #3 Copper Test #1 Copper Test #2 Nickel Test #1 Nickel Test #2 Figure 5-20.Comparison Between Nickel Foam, Copper Foam, and Open Channel Coolant Temperature Readings Using a Heat Flux of 9.48 Mbtu/in2-s & 45 cfm.

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54 lower then the results shown with the larger system. With a smaller system better controllability was expected as well as quicker response to the heat transfer, but based on the results this was not achieved. Many characteristics could have caused this unfavorable result with the most obvious being the process of installing the heaters and thermocouples. The thermocouples were placed on the inside of the coil heater for the smaller system because of clearance issues, but in the larger system the thermocouples were located between the outside of the band heater and the inner wall. Also in the small system the thermocouples were connected to the heater using a product called JB Weld that is widely used in the automobile industry, but not knowing its conductivity properties creates difficulty in determining the heat transfer characteristics. A positive result is the small magnitude of pressure drop that is associated with the foam. In comparing both the larger system and smaller system the pressure drops through the foams stayed relatively constant from one system to the next. The pressure drop that occurred with the copper foam at 23 cfm for the larger system was 1 psi and for the smaller system was 1.2 psi. These pressures are taken relative to the pressure drop that occurred with open channel flow and proves that the foam induces low pressure drops. This was expected since the length and diameter ratio stayed the same between the two systems. The pressure drop plays an important role in how effective the heat transfer is, but more importantly how feasible it is to use foam in a high-pressure minimal loss system. For the nickel the pressure drop produced similar results with 1 psi for the larger system and 0.8 psi for the smaller system. The average heat transfer enhancement although not favorable still proved the theory. For the copper foam the enhancement is 14% in comparison to 50% for the larger

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55 system, and for the nickel foam 15% in comparison to 82% for the larger system. These numbers are far from what is desired, but proved that a better process is needed to determine the feasibility of the foams for use in rocket propulsion elements. The pressure drop and enhancement show that this is a viable technology for propulsion elements and needs to be considered further.

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CHAPTER 6 PRACTICAL ROCKET ENGINE APPLICATION For scaling purposes these experimental results for the copper foam and nickel foam were used to determine what could possibly happen at rocket engine specifications. The properties that were used to determine the heat transfer enhancement and pressure drop are a combination of specifications known as well as some from page 333 of Rocket Propulsion Elements [2]. The specifications used are as follows: wall thickness is 0.02 in, total flow area for the coolant is .566 in2, max heat flux is 60 Btu/in2s, and a max wall temperature of 1400 R. Assumed properties were as follows: Reynolds number is 1,000,000, the pressure of the coolant is 1500 psi, and the temperature of the coolant at the highest heat flux is 90 R. The coolant temperature provides us with a Prandtl number of 1.22 and a conductivity of 0.0104 lb/s-R. Using the Nusselt number and the effective conductivity correlations in chapter 4 the Nusselt number with foam is 2025.37 with a porosity of 95%, and the effective conductivity is 0.024 lb/s-R with the foam conductivity being .287 lb/s-R. By using these correlations an effective heat transfer coefficient can be calculated, and is found to be 691.54 lb/ft-s-R. Using the Nusselt correlation in chapter 4 for internal flow without foam the Nusselt number is 1570.91. The heat transfer coefficient for the internal flow without foam is 228.99 lb/ft-s-R. We also know that the heat flux is equal to the heat transfer coefficient multiplied by the temperature difference between the wall and the coolant. Since the heat flux is going to stay the same whether or not there is foam in the cooling channel we can then set the two 56

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57 equations equal to each other and solve for the new surface temperature. The new surface temperature would be 523.79 R compared to the original temperature of 1400 R. By using my experimental results where there is an average of 1.5 times the enhancement in heat transfer then the new surface temperature would be 963.33 R compared to 1400 R. For the pressure drop calculation an average temperature of the coolant which is 194.508 R will be used to calculate the properties and determine the pressure drop over a 2-foot length. The properties are as follows: Prandtl number is 0.785, the conductivity is 0.0116 lb/s-R, the density is 1.36 lb/ft3, and the viscosity is 1.13e-7 lb-s/ft2. Using the definition of the Reynolds number the velocity is calculated to be 37.75 ft/s for a Reynolds number of 1,000,000. Using the correlations for friction factor and pressure drop as outlined in chapter 4 the expected pressure drop can be determined. This expected pressure drop comes out to be 9.11 psi with a friction factor of 1.54. With my experimental results of 3 psi at an expected 0.18 psi, then the pressure drop for this system would be 151.78 psi with an expected of 9.11 psi. These numbers depict a positive heat transfer enhancement even with my experimental results as well as minimal pressure drop. However, these correlations and scaling based on my experimental results need to be performed on exact dimensions of a cooling channel and with exact specifications for that rocket engine that the cooling channel in question resides. When this is completed a more accurate representation of what can be achieved with this idea of metallic foam inserts used in the cooling channels will be shown. Also a more accurate representation of how much pressure drop through these cooling passages can be achieved.

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CHAPTER 7 RECOMMENDATIONS FOR FUTURE WORK This experimental project can be improved especially in the heating elements that are used in the test rig. These heating elements do not provide a uniform constant heat flux which is desired. Results that could compare with the numerical code would be more favorable in this situation. Also with these heating elements it might be more beneficial to use some kind of combustion process to simulate activity that is closer to the actual function of a rocket engine. I believe that this would give more insight into the enhancement due to the foam, and be directly applicable to the rocket engines in use today. However, using a constant heat flux model can still be beneficial where the enhancement of the foam can be scaled to the largest heat flux in a rocket engine. This would then provide an estimate of how well the foam improves the most critical point on a rocket engine. The next improvement would be to make the system a closed loop system unlike its current state of an open loop system. The open loop system uses the nitrogen directly from the tanks at a relatively constant pressure, and the system exhausts the nitrogen into the atmosphere. This causes many problems with the system with the most important being the time frame that the nitrogen can be used. As the nitrogen exhausts into the atmosphere less nitrogen is available from the tanks. After a certain time the pressure in the system starts to decreases at a given volumetric flow rate. When using the larger heat fluxes it takes an excessive amount of time to come to an equilibrium state. Even then 58

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59 with any of the heat fluxes it is not a guarantee that the system is able to reach equilibrium. With a closed loop system the testing could continue for hours with out a huge loss in nitrogen which would provide a better estimate of the equilibrium state. The closed loop system would have a pump that cycles the nitrogen and overcomes any small pressure drop in the system. When the nitrogen exits the test rig it will enter into a heat exchanger in order to cool it back down to its original starting temperature. This system is shown below. Figure 7-1.Closed Loop Testing Apparatus Proposed Diagram. Using a closed loop system will improve the measurements for flow rate and pressure. In the closed loop system both the flow rate and pressure would remain constant which would provide more accurate results for the overall system parameters. There also could be some temperature control instituted at the inlet of the apparatus to make sure the temperature remains constant at the inlet to the system.

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60 Another problem that could have skewed some of the data was the placement of the thermocouples which were placed on top of the heaters between the heaters and the inner wall of the inner tube. Because of the expanding nature of the heaters the thermocouples could then be held tightly in place. A better solution is needed to imbed the thermocouples in the wall of the inner tube from the inside of the tube. This would provide a better understanding of what is taking place in the wall itself without having the heaters dictate the results. Also imbedding some thermocouples into the foam in different areas would have been beneficial to see how the foam was reacting to the wall heat flux. Another ongoing problem is how to perfectly braze or connect the foam to the surface. When inspecting the foam not every single ligament that wraps around the pipe is actually sintered to the pipe. This is extremely necessary in order to achieve maximum enhancement of the heat transfer. If there is any space at all between the ligament and the surface the contact resistance of that gap is extremely high, and is incapable of achieving good conduction at that particular point. As shown in chapter 4 the length of the gap only has to be one half of a millimeter to achieve the skewed data that was taken. The idea of compressing the foam into the foil before brazing seems like a very plausible technique as long as the compression does not deform the foam. If too much deformation is caused then the void percentage or porosity decreases and the pressure drop will increase. The pressure drop of the foam could also be improved by constructing the foam so that some pores are not blocked. This will then provide the most efficient flow through the foam that can be achieved. Another consideration is designing a better inner tube for the apparatus. With the connection flanges at the end of the inner tube the

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61 pressure drop is skewed, and is not an accurate representation of the pressure drop through the foam. The foams can also be created with a 5 ppi (pores per linear inch) instead of ours which was 10 ppi which will allow more flow to pass through and therefore decreasing the pressure drop. Finally a concentrated model of the nozzle throat region would be ideal. If building a converging-diverging shape a more accurate representation of the rocket engine can be tested and simulated. The foam would then be reacting similar to the most critical point on a rocket engine. The overall enhancement could then determine how the critical point could be better cooled and protected.

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CHAPTER 8 UNCERTAINTY OF RESULTS The uncertainty of results is how precise I believe the conclusions are. For these results the uncertainty will be calculated based on the design of the apparatus, the different systems resolution, as well as the repeatability of the results in question. Typical uncertainties will include the design-stage uncertainty and the standard deviation for scatter in the data [18]. The measurements of consideration will be temperature, pressure, and flow which will affect the heat transfer coefficient and also the Nusselt number. For temperature the error of the larger system comes from the thermocouple reader itself and the repeatability of the results. However for the smaller system, the thermocouples are not against the wall, but are connected to the inside of the heater so that there is a conduction error relative to those results as well. For the thermocouple reader the instrument uncertainty is 1.8F and has a resolution of 1.8e-6F. The following equation can then be used to determine the design-stage uncertainty [18]. solutionocodRe2122 (53) The standard deviation is the error from the mean to calculate the overall temperature, and can now be calculated. The following equations will detail steps in order to calculate the standard deviation [18]. 62

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63 NiiTpvNiiTpviTTNStTNTStTT122,1,11303.41 (54) By using these two error calculations the uncertainty can be determined in the temperature measurements for the larger system. For the smaller system the conduction error also must be calculated. This error will be based on the conductivity of the heater, the length of the heater, as well as the heat flux that is provided by the heater. This error is 1.8F for 1.9 Mbtu/in2-s, 5.598F for 5.69 Mbtu/in2-s, 7.452F for 7.58 Mbtu/in2-s, and 9.324F for 9.48 Mbtu/in2-s. These are calculated using the conductivity of the heater which is 2.37 R slb Using these equations the uncertainty of the temperature data for the larger system is and is for the smaller system. Fo828.27 Fo566.28 For pressure calculations a digital pressure gage is used to measure the static pressure at the inlet to the apparatus and at the exit. The resolution for these pressure gages is 0.1 psi and the instrument uncertainty is 1 psi. Using the same process for the temperature the uncertainty in pressure is 1.479 psi. For the flow measurement the same process is followed with a resolution of 2 scfm, and instrument uncertainty of 1 scfm which provides a total uncertainty of 1.414 scfm. Using this information the uncertainty of the heat transfer coefficient is 2.46e-5 Rsftlb for the larger system and 2.4e-5 Rsftlb for the smaller system.

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64 The data in the appendices reflects the values that have the uncertainties explained in this chapter. There may be other uncertainties that may have occurred from instrument malfunction or other undeterminable quantities. These uncertainties are the best description for the data recorded in these experiments using the values that would influence them the most. Table 8-1.Uncertainty of Results Apparatus Temperature Pressure Flow Rate Heat Transfer Enhancement F Psi Cfm % Large 27.828 1.479 1.414 0.0646 Small 28.566 1.479 1.414 0.063

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CHAPTER 9 CONCLUSIONS In conclusion the engineering modeling and overall experimentation was a success. For the large system even though the results did not meet expectations they did prove that the theory of using a metallic medium will increase the heat transfer enhancement. The results for pressure drop were also positive, but the pressure drop did not meet expectations. The heat transfer enhancement can be explained by defective brazing of the foam to the outside of the hot wall. When looking at the test section it is clear that there is space between the ligaments of the foam and the hot wall. The connection of these ligaments to the hot wall is vital to the transfer of heat from one medium to the next. When analyzing a thermal circuit to predict the amount of space between the wall and the foam that would provide the desired enhancement it was found that a distance of only 0.5 0.02 in would work. This then corresponds to the fact that if I can see the gap then this gap is the main reason for our lack of heat transfer enhancement. When discussing with the engineers that built and brazed our foam they stated that it is very difficult for them to get good contact on such a large piece. With the smaller system the engineers advised that the contact would be much better and that there should be improved performance. For the small system the results were not what was expected as the results were much lower than the larger system. However, the system still produced results of increasing heat transfer and minimal pressure drop which is favorable. The thermocouples that were used to measure the wall temperature were attached to the inside 65

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66 of the heater using a product called JB Weld. The problem with using this product is the conductivity is not known which doesnt allow for the calculation of the heat transfer through the material. I believe that this is the main reason for the unfavorable results obtained from this system. The temperature differential across the heater itself also has a major effect on the heat transfer read by the thermocouples. The results for these systems provide heat transfer enhancements for the copper foam of 50% for the larger system and 14% for the smaller system. The nickel foam provided heat transfer enhancements of 82% for the larger system and 15% for the smaller system. The pressure drops are 1 psi at 23 cfm and 3 psi at 45 cfm for copper in the larger system and 1.2 psi at 23 cfm and 2.8 psi at 45 cfm for copper in the smaller system. For nickel foam the pressure drops were about the same in all cases. When scaling these results to rocket engine specifications it is calculated that the expected heat transfer enhancement would be 1.55 or 55% and the expected pressure drop would be 151.78 psi. These results are all based on assumptions, and need to be scaled to an exact system with current coolant properties for that particular rocket engine. By analyzing these results new technology for the brazing technique is needed in order to achieve the full potential of the porous metallic medium or foams. Some ideas are already being tested while others are still in the development stage. One possibility is to have one side of the system under vacuum, and the other side under pressure in order to press the ligaments into the brazing foil so that when they are heated everything sinters together. For the future a combustion test rig would be the best scenario to predict heat transfer enhancements from the metallic foams. Some theories for this are also in the

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67 development stage such as creating a half converging-diverging nozzle where the bottom side is flat and the top side is the converging-diverging shape. On the flat side the material will be clear in order to see the hot wall which will be covered with a temperature sensitive paint. This then could be photographed to get a complete picture of how the hot wall temperature profiles appear. The foam would then conform to the outside of the converging-diverging shape, and hot air will be passed through the chamber to simulate hot combustion gases.

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APPENDIX A NOMENCLATURE R inside radius of the outer skin Ro inside radius of the inner skin or the radius of the nozzle throat X L distance where the liquid begins to boil XV distance where the liquid becomes completely vaporized A cross sectional flow area of the coolant thk wall thickness D hydraulic diameter gh heat transfer coefficient of the combustion gases lh heat transfer coefficient of the coolant in its liquid phase 2h heat transfer coefficient of the coolant in its two phase region vh heat transfer coefficient of the coolant in its vapor phase LU overall heat transfer during the liquid phase 2U overall heat transfer during the two phase region vU overall heat transfer during the vapor phase fk thermal conductivity of the combustion gases lk thermal conductivity of the coolant in its liquid phase dRe Reynolds number based on diameter P r Prandtls number for combustion gases lPr Prandtls number for the coolant in liquid phase vPr Prandtls number for the coolant in vapor phase oT combustion gas temperature in degree F bT boiling temperature of the coolant in degree F imT, coolant inlet temperature in degree F 1LT coolant temperature at L1 in degree F sT wall surface temperature in degree F m coolant mass flow rate lpc, specific heat of the coolant during its liquid phase vpc, specific heat of the coolant during its vapor phase gRe Reynolds number based on the gaseous form of the coolant quality quality of the coolant l kinematic viscosity of the coolant in liquid phase 68

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69 g kinematic viscosity of the coolant in vapor phase f friction factor loFr Froude number with all flow as liquid LTNu Nusselt number for laminar-turbulent flow l density of the coolant in liquid phase g density of the coolant in vapor phase fgh heat of vaporization of the coolant "sq heat flux 1R inside radius of the inner skin upstream of the nozzle throat 2R inside radius of the inner skin downstream of the nozzle throat 1L length from entrance of nozzle to the throat 2L length from throat to exit of nozzle L total length of nozzle 1 angle of inclination upstream of throat 2 angle of inclination downstream of throat As surface area d coolant channel width

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APPENDIX B COOLANT PROPERTIES Table B-1. Properties for Liquid Nitrogen Referenced from [15]. Temp. psat rhof Cp mu k hfg Pr sigmaL Betat (K) (kPa) (kg/m3) (kJ/kg-K) (muPa-s) (mW/m-K) (kJ/kg) (mN/m) (K-1) 65 17.4 860.9 2.008 278 158.7 214 3.52 11.66 0.0047 70 38.5 840 2.024 220 149.9 208.3 2.97 10.48 0.00504 75 76 818.1 2.042 173 143 202.3 2.47 9.3 0.00544 77.36 101.3 807.3 2.051 158 139.6 199.3 2.32 8.75 0.00566 80 136.7 795.1 2.063 141 136.2 195.8 2.14 8.22 0.00592 85 228.4 771 2.088 119 129.3 188.7 1.922 7.18 0.0065 90 359.8 745.6 2.122 104 122.4 180.9 1.803 6.12 0.00723 95 539.8 718.6 2.17 93 115.5 172 1.747 5.08 0.00816 100 777.8 689.6 2.24 85 108.5 161.6 1.755 4.04 0.00942 105 1083.6 657.7 2.35 78 101.1 149.4 1.813 0.01119 110 1467.2 621.7 2.533 73 93.6 135 1.976 0.01394 115 1939.4 579.3 2.723 68 84.7 117.3 2.19 0.01884 120 2512.9 524.9 2.92 65 74.6 94.3 2.54 0.0305 125 3204.4 436.8 3.124 62 61.5 54.9 3.14 Table B-2. Properties for Nitrogen Vapor Referenced from [15]. Temp. rhog Cp mu k Pr (K) (kg/m3) (kJ/kg-K) (muPa-s) (mW/m-K) 65 0.911 1.056 4.62 6.12 0.797 70 1.893 1.064 4.95 6.58 0.8 75 3.532 1.076 5.29 7.03 0.81 77.36 4.604 1.084 5.41 7.23 0.811 80 6.071 1.095 5.62 7.49 0.822 85 9.789 1.13 5.94 7.95 0.844 90 15.027 1.185 6.27 8.4 0.885 95 22.21 1.279 6.6 8.86 0.953 100 31.9 1.407 6.98 9.33 1.053 105 44.93 1.593 7.54 10.16 1.182 110 62.57 1.88 8.26 11.14 1.394 115 87.21 2.36 9.32 12.59 1.75 120 124.44 3.29 10.27 13.91 2.43 125 197.08 5.86 12.86 16.69 4.51 70

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71 Table B-3. Properties for Liquid Water Referenced from [11]. Temp. p vf 10^3 hfg cp,f mu,f 10^6 kf Prf sigma 10^3 beta 10^6 (K) (bars) (m3/kg) (kJ/kg) (kJ/kg-K) (Ns/m2) (mW/m-K) (N/m) (K-1) 300 0.03531 1.003 2438 4.179 855 613 5.83 71.7 276.1 310 0.06221 1.007 2414 4.178 695 628 4.62 70 361.9 320 0.1053 1.011 2390 4.18 577 640 3.77 68.3 436.7 330 0.1719 1.016 2366 4.184 489 650 3.15 66.6 504 340 0.2713 1.021 2342 4.188 420 660 2.66 64.9 566 350 0.4163 1.027 2317 4.195 365 668 2.29 63.2 624.2 360 0.6209 1.034 2291 4.203 324 674 2.02 61.4 697.9 370 0.904 1.041 2265 4.214 289 679 1.8 59.5 728.7 373.15 1.0133 1.044 2257 4.217 279 680 1.76 58.9 750.1 380 1.2869 1.049 2239 4.226 260 683 1.61 57.6 788 390 1.794 1.058 2212 4.239 237 686 1.47 55.6 841 400 2.455 1.067 2183 4.256 217 688 1.34 53.6 896 410 3.302 1.077 2153 4.278 200 688 1.24 51.5 952 420 4.37 1.088 2123 4.302 185 688 1.16 49.4 1010 430 5.699 1.099 2091 4.331 173 685 1.09 47.2 440 7.333 1.11 2059 4.36 162 682 1.04 45.1 450 9.319 1.123 2024 4.4 152 678 0.99 42.9 460 11.71 1.137 1989 4.44 143 673 0.95 40.7 470 14.55 1.152 1951 4.48 136 667 0.92 38.5 Table B-4. Properties for Water Vapor Referenced from [11]. Temp. p Vg cp,g mu,g 10^6 kg Prg (K) (bars) (m3/kg) (kJ/kg-K) (Ns/m2) (mW/m-K) 300 0.03531 39.13 1.872 9.09 19.6 0.857 310 0.06221 22.93 1.882 9.49 20.4 0.873 320 0.1053 13.98 1.895 9.89 21 0.894 330 0.1719 8.82 1.911 10.29 21.7 0.908 340 0.2713 5.74 1.93 10.69 22.3 0.925 350 0.4163 3.846 1.954 11.09 23 0.942 360 0.6209 2.645 1.983 11.49 23.7 0.96 370 0.904 1.861 2.017 11.89 24.5 0.978 373.15 1.0133 1.679 2.029 12.02 24.8 0.984 380 1.2869 1.337 2.057 12.29 25.4 0.999 390 1.794 0.98 2.104 12.69 26.3 1.013 400 2.455 0.731 2.158 13.05 27.2 1.033 410 3.302 0.553 2.221 13.42 28.2 1.054 420 4.37 0.425 2.291 13.79 29.8 1.075 430 5.699 0.331 2.369 14.14 30.4 1.1 440 7.333 0.261 2.46 14.5 31.7 1.12 450 9.319 0.208 2.56 14.85 33.1 1.14 460 11.71 0.167 2.68 15.19 34.6 1.17 470 14.55 0.136 2.79 15.54 36.3 1.2

PAGE 85

APPENDIX C LARGE SYSTEM COLLECTED DATA

PAGE 86

73 Table C-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Ou t P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi) Open 1 159.278 227.3252 227.9768 75.78 75. 7755 250 250 134.283 201.44489 203.39474 73.92 78.1767 225 225 Open 2 167.050 229.8974 229.8974 73.72 75. 2967 250 250 146.755 212.85109 213.71793 69.10 76.2695 225 225 Open 3 162.328 221.49 227.558 75. 34 76.4629 250 250 147.809 208.270 61 212.60477 69.29 76.2389 225 225 Copper 1 116.277 182.42126 187.40555 79.76 82. 6727 250 248 113.455 177.94101 187.47365 78.96 82.9950 225 221 Copper 2 118.831 190.07349 195.489 78 76.27 83.8909 250 248 113.635 181.2204 189.2365 73.17 84.8174 225 221 Copper 3 117.881 189.5883 195.871 19 78.46 82.0455 250 248 113.351 181.34206 191.746 77 71.44 85.5640 225 221 Nickel 1 104.318 153.28725 182.751 82 77.44 84.3848 250 249 103.183 146.55618 179.053 89 78.99 83.9215 225 222 Nickel 2 102.781 153.31686 186.464 52 72.54 85.9833 250 249 100.981 148.1098 182.774 75.67 85.5276 225 222 Nickel 3 101.901 151.81512 185.179 41 71.66 86.6705 250 249 97.6681 145.12112 181.951 86 70.56 86.9174 225 222

PAGE 87

74 Table C-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Ou t P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi) Open 1 270.29 429.4525 433.2375 69.88 77. 0507 250 250 250.161 411.75292 413.64544 71.18 75.2201 225 225 Open 2 284.87 438.8863 444.3536 69.17 81. 0526 250 250 271.904 424.10916 426.84283 64.86 78.0789 225 225 Open 3 295.86 443.2950 455.2811 68.72 86. 4217 250 250 274.225 424.10198 429.98986 59.47 81.4317 225 225 Copper 1 184.492 376.81930 391.838 65 79.91 86.6322 250 248 168.423 342.30212 381.860 07 73.82 89.5055 225 221 Copper 2 185.344 376.59332 397.535 79 79.44 86.1689 250 248 173.517 343.25683 381.122 49 77.74 90.7403 225 221 Copper 3 187.756 377.25683 402.631 43 73.88 93.1427 250 248 170.246 342.43515 385.812 16 71.43 95.4023 225 221 Nickel 1 176.461 302.76589 394.151 12 80.34 84.6011 250 249 169.478 280.11035 388.235 53 80.26 85.6463 225 222 Nickel 2 173.756 299.48980 402.079 92 81.13 90.9873 250 249 164.486 276.47708 386.477 84 77.14 84.0919 225 222 Nickel 3 164.880 291.88162 399.132 26 78.00 93.2346 250 249 161.692 274.17184 387.134 12 77.39 84.7868 225 222

PAGE 88

75 Table C-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Ou t P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi) Open 1 328.033 516.68865 525.94104 66.93 89. 3400 250 250 307.078 498.96701 503.59198 74.60 82.2235 225 225 Open 2 334.812 524.05572 525.10717 68.87 89. 2662 250 250 315.739 503.20904 507.83523 67.58 86.8526 225 225 Open 3 335.708 520.48193 527.83984 73.56 88. 5713 250 250 315.561 503.40328 508.65893 67.01 92.1013 225 225 Copper 1 208.951 439.59527 472.600 73 79.44 87.7290 250 248 199.158 427.77948 464.569 00 77.82 85.2194 225 221 Copper 2 211.918 450.25210 481.365 50 77.58 85.6444 250 248 197.252 417.31130 458.095 15 77.20 87.7290 225 221 Copper 3 206.692 441.24813 485.196 86 72.81 95.8905 250 248 195.347 420.29760 468.859 86 69.85 95.1661 225 221 Nickel 1 198.530 352.23730 481.198 42 78.74 86.1383 250 249 190.708 330.63854 471.926 94 76.93 86.7872 225 222 Nickel 2 196.587 353.72534 478.893 18 78.75 86.1459 250 249 191.814 335.52566 475.522 36 76.50 85.0184 225 222 Nickel 3 188.818 353.75427 485.018 46 76.09 88.8643 250 249 190.954 327.07125 464.387 54 78.08 85.2500 225 222

PAGE 89

Table C-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=10 in X=20 in (F) (F) (Psi) X=0 in X=10 in X=20 in (F) (F) (Psi) Open 1 382.471 597.07354 606.11560 71.70 92.3136 250 250 339.472 559.33056 572.41320 77.46 83.0671 225 225 Open 2 383.537 597.71154 603.59942 71.93 93.6655 250 250 358.313 572.01416 577.90197 70.09 87.7947 225 225 Open 3 368.068 583.60125 590.11993 73.47 88.9379 250 250 364.457 573.28295 584.00732 66.07 91.8349 225 225 Copper 1 224.565 482.07531 546.82489 68.70 104.990 250 248 215.219 473.84771 519.88720 77.41 87.2658 225 221 Copper 2 224.289 482.64846 534.57421 75.14 90.1468 250 248 215.480 466.11245 525.60638 71.40 96.2706 225 221 Copper 3 220.426 483.52532 537.55334 68.23 102.951 250 248 210.438 464.16293 515.45806 76.49 88.5943 225 221 Nickel 1 206.374 388.66555 558.18426 76.77 94.4712 250 249 193.114 349.69885 523.45385 76.95 86.5862 225 222 Nickel 2 202.676 368.97787 531.26098 78.32 87.2888 250 249 209.631 368.36495 539.06091 78.80 88.4316 225 222 Nickel 3 214.405 389.31463 547.05664 76.12 88.6632 250 249 198.059 343.10491 522.36676 76.46 85.6520 225 222 76

PAGE 90

APPENDIX D LARGE SYSTEM HEAT TRANSFER ENHANCEMENTS

PAGE 91

Table D-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 162.8865814 74.9489619 142.9490407 70.77190908 Open Channel X=10 226.2375895 75.39702352 207.5221965 73.83348973 Open Channel X=20 229.0490519 75.84508515 209.9058126 76.89507039 Copper Foam X=0 117.6630986 78.16603343 113.4805324 74.5269165 Copper Foam X=10 187.3610178 80.51787567 180.1678212 79.49287923 Copper Foam X=20 192.92217 82.86971792 189.4856364 84.45884196 Nickel Foam X=0 103.0001271 73.883667 100.6110509 75.07815297 Nickel Foam X=10 152.8064117 79.78161621 146.595703 80.26685587 Nickel Foam X=20 184.7985839 85.67956543 181.259918 85.4555587 78 Table D-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F) Copper X=0 2.22643427 122.64 45.2234828 1.852899414 85.29 29.4685 Copper X=10 1.411794552 41.18 38.8765717 1.3279243 32.79 27.35437523 Copper X=20 1.392099529 39.21 36.1268819 1.266445795 26.64 20.42017616 Copper Avg. 1.676776117 67.68 40.07564546 1.482423169 48.24 25.7476838 Nickel X=0 3.020202978 202.02 59.8864543 2.826828815 182.68 42.3379898 Nickel X=10 2.06560751 106.56 73.4311778 2.015543953 101.55 60.9264935 Nickel X=20 1.545656616 54.57 44.250468 1.388357933 38.84 28.6458946 Nickel Avg. 2.210489035 121.05 59.1893667 2.076910233 107.69 43.97012596

PAGE 92

Table D-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 283.6784058 69.26132202 265.4305623 65.17510732 Open Channel X=10 437.2113139 75.38485082 419.9880269 71.70937782 Open Channel X=20 444.2907918 81.50837962 423.4927165 78.2436142 Copper Foam X=0 185.8645325 77.74797058 170.7290802 74.33611552 Copper Foam X=10 376.8898214 83.19547516 342.664703 83.10943349 Copper Foam X=20 397.3352966 88.64797974 382.9315796 91.88275147 Nickel Foam X=0 171.6995341 79.82757568 165.218867 78.27136231 Nickel Foam X=10 298.0457763 84.71764628 276.9197591 81.55653254 Nickel Foam X=20 398.4544377 89.60771688 387.2825012 84.84170278 79 Table D-4.Heat Transfer Enhancement @ Heat Flux = 5.69 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 1.983202944 98.32 97.813873 2.07749036 107.75 94.7014821 Copper X = 10 1.231983073 23.2 60.3214925 1.34182846 34.18 77.32332393 Copper X = 20 1.175242364 17.52 46.95549517 1.18622399 18.62 40.5611369 Copper Avg. 1.463476127 46.35 68.36362022 1.535180937 53.52 70.86198098 Nickel X = 0 2.333868652 133.39 111.9788717 2.303176563 130.32 100.2116953 Nickel X = 10 1.696102915 69.61 139.1655376 1.782723674 78.27 143.0682679 Nickel X = 20 1.174635791 17.46 45.8363541 1.141542755 14.15 36.2102153 Nickel Avg. 1.734869119 73.49 98.9935878 1.742480997 74.25 93.163392833

PAGE 93

80 Table D-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 332.8514709 69.79203542 312.7929891 69.7369105 Open Channel X=10 520.4087728 79.42562739 501.8597819 78.39803314 Open Channel X=20 526.2960205 89.05921936 506.6953837 87.05915578 Copper Foam X=0 209.1875204 76.6129303 197.2526092 74.9626592 Copper Foam X=10 443.6985067 83.1838061 421.7961324 82.1671168 Copper Foam X=20 479.7210388 89.75468191 463.8413391 89.3715744 Nickel Foam X=0 194.645401 77.86675852 191.1592153 77.1743036 Nickel Foam X=10 353.238973 82.45815191 331.0784912 81.42978790 Nickel Foam X=20 481.7033589 87.04954529 470.6122843 85.68527221 Table D-6.Heat Transfer Enhancem ent @ Heat Flux = 7.58 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differentia l (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 1.984237216 98.42 123.6631506 1.987539275 98.75 115.5403798 Copper X = 10 1.223204337 22.32 76.71026613 1.246838195 24.68 80.0636495 Copper X = 20 1.121216724 12.12 46.5749817 1.120614446 12.06 42.8540446 Copper 1.451663972 Avg. 1.442886092 44.29 82.316 39947 45.16 79.48602464 Nickel X = 0 2.25263310 125.26 138.2060699 2.132353089 113.24 121.6337738 Nickel X = 10 1.62856122 62.86 167.1697998 1.696230515 69.62 170.7812907 Nickel X = 20 1.107899597 10.79 44.5926616 1.090170902 9.02 36.0830994 Nickel Avg. 1.663031305 66.30 116.65 61771 1.639584835 63.96 109.4993879

PAGE 94

Table D-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 378.0259298 72.37232971 354.0811971 71.2113088 Open Channel X=10 592.7954509 82.00568517 568.2092285 79.38845952 Open Channel X=20 599.944987 91.63904063 578.1075032 87.56561025 Copper Foam X=0 223.0940094 70.69442749 213.7131653 75.10685221 Copper Foam X=10 482.749705 85.02868779 468.041036 82.90857188 Copper Foam X=20 539.6508179 99.3629481 520.31722 90.71029154 Nickel Foam X=0 207.8185475 77.07605235 200.2684326 77.40847015 Nickel Foam X=10 382.3193563 83.60859172 353.7229105 82.14922968 Nickel Foam X=20 545.5006307 90.14113108 528.2938436 86.88998922 81 Table D-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 2.005606553 100.56 154.9319204 2.040815328 104.08 140.3680318 Copper X = 10 1.28429161 28.43 110.0457459 1.269227641 26.92 100.1681926 Copper X = 20 1.154485466 15.45 60.29416913 1.141838877 14.18 57.7902832 Copper Avg. 1.48146121 48.15 108.4239451 1.483960616 48.39 99.4421692 Nickel X = 0 2.337829025 133.78 170.2073823 2.302376483 130.24 153.8127645 Nickel X = 10 1.709981113 71.00 210.4760946 1.799956342 80.00 214.486318 Nickel X = 20 1.116273948 11.63 54.4443563 1.111322178 11.13 49.8136596 Nickel Avg. 1.721361362 72.14 145.042611067 1.737885001 73.79 139.370914033

PAGE 95

APPENDIX E SMALL SYSTEM COLLECTED DATA

PAGE 96

Table E-1.Test Results for a Heat Flux of 1.9 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) Open 1 165.52 192.1659 213.1811 78.44 80.454 250 249.2 165.37 190.2827 209.9980 80.52 82.315 225 224 Open 2 163.60 193.0621 215.3773 76.45 80.485 250 249.2 164.11 192.0604 212.8589 80.12 83.033 225 224 Open 3 174.29 203.3263 222.1749 80.12 82.361 250 249.2 169.66 195.0120 214.9440 79.59 81.157 225 224 Copper 1 139.90 166.9825 196.8803 75.92 77.713 250 248 136.89 163.7549 190.6197 75.50 77.064 225 221.2 Copper 2 136.15 164.1066 192.7121 75.61 77.405 250 248 139.35 166.8621 195.6767 76.25 79.605 225 221.2 Copper 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Nickel 1 145.66 175.1364 199.1910 75.81 76.038 250 248.4 135.37 164.1809 186.0627 74.82 76.609 225 221.4 Nickel 2 140.30 169.7693 192.0843 75.89 77.010 250 248.4 135.14 163.9568 183.0221 73.67 75.481 225 221.4 Nickel 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 83

PAGE 97

84 Table E-2.Test Results for a Heat Flux of 5.69 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Ou t P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=2.00 in X=3.94 in (F) (F) (Psi ) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) Open 1 325.16 399.6222 453.2384 78.97 83.002 250 249.2 271.55 353.2010 400.7974 73.05 78.872 225 224 Open 2 310.10 394.0860 439.5377 78.04 82.068 250 249.2 278.56 359.1530 402.0888 77.11 80.470 225 224 Open 3 308.04 396.0406 440.2188 76.30 82.122 250 249.2 274.57 356.8550 400.8553 75.35 80.501 225 224 Copper 1 279.23 349.6771 426.3079 74.24 77.604 250 248 263.75 335.8836 405.4524 72.18 78.678 225 221.2 Copper 2 278.61 352.8575 425.2640 75.37 78.508 250 248 267.78 338.8597 407.1486 73.54 77.798 225 221.2 Copper 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Nickel 1 270.66 349.3570 420.5239 72.11 74.578 250 248.4 263.07 333.5133 399.0906 75.94 78.408 225 221.4 Nickel 2 274.05 351.0493 421.7853 73.23 75.698 250 248.4 260.55 331.8354 395.7205 73.27 77.080 225 221.4 Nickel 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

PAGE 98

Table E-3.Test Results for a Heat Flux of 7.58 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) Open 1 360.40 478.3792 528.6232 78.88 80.447 250 249.2 332.48 443.0685 498.3579 78.21 80.231 225 224 Open 2 357.05 477.1538 529.5001 78.02 81.157 250 249.2 336.52 450.0203 501.5257 78.23 80.246 225 224 Open 3 357.08 480.5461 532.8924 76.71 80.964 250 249.2 329.90 433.9856 490.3261 75.26 77.945 225 224 Copper 1 327.25 414.5352 502.1995 74.92 78.724 250 248 323.81 406.4892 490.9999 77.77 79.783 225 221.2 Copper 2 332.13 418.5368 507.0419 75.82 79.852 250 248 316.85 399.1341 483.0258 73.30 78.230 225 221.2 Copper 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Nickel 1 313.23 401.8642 486.3750 72.39 76.199 250 248.4 307.30 391.2782 477.3210 75.51 77.976 225 221.4 Nickel 2 317.47 407.1270 491.2174 75.54 77.551 250 248.4 304.12 389.5859 473.9573 71.70 76.184 225 221.4 Nickel 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 85

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Table E-4.Test Results for a Heat Flux of 9.48 Mbtu/in2-s. 23 cfm 45 cfm Test # T (F) @ T (F) @ T (F) @ N2 In N2 Out P T (F) @ T (F) @ T (F) @ N2 In N2 Out P X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) X=0 in X=2.00 in X=3.94 in (F) (F) (Psi) Open 1 420.76 536.5902 596.7148 72.81 77.736 250 249.2 406.05 513.6828 575.2790 74.61 78.864 225 224 Open 2 437.41 552.1902 611.6840 77.56 81.142 250 249.2 416.36 522.7652 576.1766 75.65 77.667 225 224 Open 3 423.91 540.7947 600.9194 75.72 79.080 250 249.2 385.11 501.8813 565.7901 75.92 78.833 225 224 Copper 1 372.71 472.7391 575.7499 75.78 78.022 250 248 370.15 460.7346 564.3760 76.43 79.790 225 221.2 Copper 2 379.04 477.1610 581.4331 76.69 80.269 250 248 368.25 459.6907 562.9117 74.87 78.454 225 221.2 Copper 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Nickel 1 360.82 465.7585 571.5021 74.17 76.408 250 248.4 345.77 454.3775 558.8598 74.36 76.825 225 221.4 Nickel 2 363.56 469.7456 576.7506 73.94 77.296 250 248.4 347.46 456.9002 558.4393 73.24 76.153 225 221.4 Nickel 3 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 86

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APPENDIX F SMALL SYSTEM HEAT TRANSFER ENHANCEMENTS

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Table F-1.Average Temperatures @ Heat Flux = 1.9 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 167.80333 78.3367 166.38 80.07666 Open Channel X=2.00 196.18477 79.71835 192.4517 81.1225 Open Channel X=3.94 216.91111 81.1 212.6003 82.16833 Copper Foam X=0 138.025 75.765 138.12 75.875 Copper Foam X=2.00 165.54455 76.662 165.3085 77.10475 Copper Foam X=3.94 194.7962 77.559 193.1482 78.3345 Nickel Foam X=0 142.98 75.85 135.255 74.245 Nickel Foam X=2.00 172.45285 76.187 164.06885 75.145 Nickel Foam X=3.94 195.63765 76.524 184.5424 76.045 88 Table F-2.Heat Transfer Enhancement @ Heat Flux = 1.9 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 1.437 43.6984 29.77833 1.3865 38.6510 28.26 Copper X = 2.00 1.3103 31.034 30.64022 1.2622 26.2182 27.1432 Copper X = 3.94 1.1584 15.843 22.11491 1.136 13.6031 19.4521 Copper Avg. 1.3019 30.19 27.511153 1.2616 26.15667 24.951767 Nickel X = 0 1.3327 33.2736 24.82333 1.4146 41.4577 31.125 Nickel X = 2.00 1.2098 20.9841 23.73192 1.252 25.1961 28.38285 Nickel X = 3.94 1.1402 14.0181 21.27346 1.2022 20.216678 28.0579 Nickel Avg. 1.2276 22.7567 23.276237 1.2896 28.96 29.188583

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89 Table F-3.Average Temperatures @ Heat Flux = 5.69 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 314.43333 77.77 274.89333 75.17 Open Channel X=2.00 396.58293 80.08367 356.403 77.5588 Open Channel X=3.94 444.33163 82.3973 401.24717 79.9477 Copper Foam X=0 278.92 74.805 265.765 72.86 Copper Foam X=2.00 351.2673 76.4305 337.37165 75.549 Copper Foam X=3.94 425.78595 78.056 406.3005 78.238 Nickel Foam X=0 272.355 72.67 261.81 74.605 Nickel Foam X=2.00 350.20315 73.904 332.67435 76.1745 Nickel Foam X=3.94 421.1546 75.138 397.40555 77.744 Table F-4.Heat Transfer Enhancem ent @ Heat Flux = 5.69 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differentia l (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 1.1595 15.9461 35.51333 1.0353 3.53456 9.12833 Copper X = 2.00 1.1516 15.1589 45.31563 1.065 6.5018 19.03135 Copper X = 3.94 1.0408 4.08489 18.54568 .9793 0 -5.05333 Copper Avg. 1.1173 11.73 33.12488 1.0265 2.65333 7.70212 Nickel X = 0 1.1852 18.51833 42.07833 1.0669 6.68696 13.08333 Nickel X = 2.00 1.1455 14.549 48 46.37978 1.0871 8.71125 23.72865 Nickel X = 3.94 1.046 4.6002 8 23.17703 1.0051 .51239 3.84162 Nickel Avg. 1.1256 12.55667 37.2117133 1.0530 5.30333 13.5512

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Table F-5.Average Temperatures @ Heat Flux = 7.58 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 358.17667 77.87 332.96667 77.2333 Open Channel X=2.00 478.69303 79.363 442.35813 78.35365 Open Channel X=3.94 530.33857 80.856 496.73657 79.474 Copper Foam X=0 329.69 75.37 320.33 75.535 Copper Foam X=2.00 416.536 77.329 402.81165 77.27075 Copper Foam X=3.94 504.6207 79.288 487.01285 79.0065 Nickel Foam X=0 315.35 73.965 305.71 73.605 Nickel Foam X=2.00 404.4956 75.42 390.43205 75.3425 Nickel Foam X=3.94 488.7962 76.875 475.63915 77.08 90 Table F-6.Heat Transfer Enhancement @ Heat Flux = 7.58 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 1.1022 10.2181 28.48667 1.0447 4.46838 12.63667 Copper X = 2.00 1.1772 17.72458 62.15703 1.1182 11.81528 39.54648 Copper X = 3.94 1.0568 5.67788 25.71787 1.0227 2.26865 9.72372 Copper Avg. 1.1121 11.20667 38.78719 1.0619 6.18667 20.635623 Nickel X = 0 1.1612 16.12431 42.82667 1.1018 10.18003 27.25667 Nickel X = 2.00 1.2135 21.3490 74.19743 1.1552 15.52413 51.92608 Nickel X = 3.94 1.0912 9.11858 41.54237 1.0469 4.69276 21.09742 Nickel Avg. 1.1553 15.53 52.85549 1.1013 10.13 33.426723

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Table F-7.Average Temperatures @ Heat Flux = 9.48 Mbtu/in2-s. 23 cfm 45 cfm Type Position Avg. Wall T Avg. N2 T Avg. Wall T Avg. N2 T (in) (F) (F) (F) (F) Open Channel X=0 427.36 75.3633 402.50667 75.3933 Open Channel X=2.00 543.1917 77.3413 512.77643 76.92398 Open Channel X=3.94 603.1061 79.31933 572.41523 78.45467 Copper Foam X=0 375.875 76.235 369.2 75.65 Copper Foam X=2.00 474.95005 77.69025 460.21265 77.386 Copper Foam X=3.94 578.5915 79.1455 563.64385 79.122 Nickel Foam X=0 362.19 74.055 346.615 73.8 Nickel Foam X=2.00 467.75205 75.4535 455.63885 75.1445 Nickel Foam X=3.94 574.12635 76.852 558.64955 76.489 91 Table F-8.Heat Transfer Enhancement @ Heat Flux = 9.48 Mbtu/in2-s. 23 cfm 45 cfm Type Position h Ratio % Enhancement Temp. Differential (F) h Ratio % Enhancement Temp. Differential (F) Copper X = 0 1.1747 17.4732 51.485 1.1143 11.43361 33.30667 Copper X = 2.00 1.1727 17.26593 68.24165 1.1385 13.85113 52.56378 Copper X = 3.94 1.0487 4.873554 24.5146 1.0195 1.948046 8.77138 Copper Avg. 1.1320 13.2033 48.0804167 1.0907 9.07667 31.547277 Nickel X = 0 1.2216 22.163812 65.17 1.1990 19.90300 55.89167 Nickel X = 2.00 1.1875 18.748948 75.43965 1.1455 14.54899 57.13758 Nickel X = 3.94 1.0533 5.331548 28.97975 1.0244 2.44732 13.76568 Nickel Avg. 1.1541 15.41333 56.5298 1.1230 12.29667 42.2649767

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LIST OF REFERENCES [1] M.J.L. Turner, Rocket and Spacecraft Propul sion, Praxis Publishing, Chichester, UK, 2000. [2] G.P. Sutton, D.M. Ross, Rocket Propul sion Elements, 7ed., John Wiley & Sons, Inc., Toronto, Canada, 1998. [3] J.C.Y. Koh, R.L. Stevens, Enhancemen t of Cooling Effectiveness by Porous Materials in Coolant Passage, Journal of Heat Transfer V.97, May 1975 309-311. [4] J.C.Y. Koh, R. Colony, Analysis of Cooli ng Effectiveness for Porous Material in a Coolant Passage, Journal of H eat Transfer, August 1974 324-330. [5] R.F. Bartlett, R. Viskanta, Enhancement of Forced Convection in an Asymmetrically Heated Duct Filled with High Thermal Conductivity Porous Media, Journal of Enhanced Heat Transfer V.6, January 1996 1-9. [6] J.W. Brockmeyer, A.J. Fortini, B.E. Willia ms, R.H. Tuffias, High-Efficiency OpenCell Foam Heat Exchangers For Activel y Cooled Propulsion Components, AIAA98-3441, Pacoima, CA, 1998. [7] K. Boomsma, D. Poulikakos, F. Zwick, Metal Foams as Compact High Performance Heat Exchangers, Mechanics of Materials V.35, 2003 1161-1176. [8] C.Y. Zhao, T. Kim, T.J. Lu, H.P. Hodson, Thermal Transport Phenomena in Porvair Metal Foams and Sintered Beds, University of Cambridge, England, August 2001. [9] H. Tamura, F. Ono, A. Kumakawa, N. Yatsuyanagi, LOX/Methane Staged Combustion Rocket Combustor Investigation, AIAA-87-1856 23 rd Propulsion Conference, San Diego,CA, July 1987. [10] S.K. Elam, Subscale LOX/Hydrogen Testi ng with a Modular Chamber and a Swirl Coaxial Injector, AIAA-91-1874 27 th Joint Propulsion Conference, Sacramento,CA, June 1991. [11] F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, 5ed., John Wiley & Sons, Inc., Toronto, Canada, 2002. [12] J.G. Collier, Convective Boiling and Condensation, 2ed., McGraw-Hill Book Company, New York, 1981.

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93 [13] M.J. Watts, C.T. Chou, Mixed Convection He at Transfer to Supercritical Pressure Water, Proceedings of the Internationa l Heat Transfer Conference V.16, 1982 495500. [14] D.A. Labuntsov, Some Questions of Convec tive Heat Transfer in the Supercritical Region, Thermal Engineer ing V.19, March 1972 101-104. [15] R.F. Barron, Cryogenic Heat Transfer, Ta ylor & Francis, Philadelphia, 1999. [16] T.M. Kuzay, J.T. Collins, J. Koons, Boiling Liquid Nitrogen Heat Transfer in Channels with Porous Copper Inserts, International Journa l of Heat and Mass Transfer V.42, 1999 1189-1204. [17] V.V. Calmidi, R.L. Mahajan, The Effective Thermal Conductivity of High Porosity Fibrous Metal Foams, Journal of Heat Transfer V.121, May 1999 466-471. [18] R.S. Figliola, D.E. Beasley, Theory and Design for Mechanical Measurements, 2 ed., John Wiley and Sons, Inc., Toronto, Canada, 1995.

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BIOGRAPHICAL SKETCH Ryan Jeffrey Avenall was born April 15, 1980, in Ann Arbor, Michigan. He graduated from Leon High School in May 1998. He attended the University of Florida and received a B.S. with honors in mechanical engineering in December, 2002. He received a graduate assistantship from the University of Florida where a Master of Science was awarded in December 2004. 94