Heat Transfer in Metal Foam Heat Exchangers at High ... · Pakeeza Hafeez Doctor of Philosophy...

Heat Transfer in Metal Foam Heat Exchangers at High Temperature

by

Pakeeza Hafeez

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Mechanical and Industrial Engineering Department University of Toronto

© Copyright by Pakeeza Hafeez 2016

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Heat Transfer in Metal Foam Heat Exchangers at High

Temperature

Pakeeza Hafeez

Doctor of Philosophy

Mechanical and Industrial Engineering Department

University of Toronto

2016

Abstract

Heat transfer though open-cell metal foam is experimentally studied for heat exchanger and heat

shield applications at high temperatures (~750°C). Nickel foam sheets with pore densities of 10

and 40 pores per linear inch (PPI), have been used to make the heat exchangers and heat shields

by using thermal spray coating to deposit an Inconel skin on a foam core. Heat transfer

measurements were performed on a test rig capable of generating hot gas up to 1000°C. The heat

exchangers were tested by exposing their outer surface to combustion gases at a temperature of

550°C and 750°C while being cooled by air flowing through them at room temperature at velocities

up to 5 𝑚 𝑠⁄ . The temperature rise of the air, the surface temperature of the heat exchangers and

the air temperature inside the heat exchanger were measured. The volumetric heat transfer

coefficient and Nusselt number were calculated for different velocities. The heat transfer

performance of the 40PPI sample brazed with the foil is found to be the most efficient. Pressure

drop measurements were also performed for 10 and 40PPI metal foam.

Thermographic measurements were done on 40PPI foam heat exchangers using a high temperature

infrared camera. A high power electric heater was used to produce hot air at 300°C that passed

over the foam heat exchanger while the cooling air was blown through it. Heat shields were made

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by depositing porous skins on metal foam and it was observed that a small amount of coolant

leaking through the pores notably reduces the heat transfer from the hot gases. An analytical model

was developed based assuming local thermal non-equilibrium that accounts for the temperature

difference between soild and fluid phase. The experimental results are found to be in good

agreement with the predicted values of the model.

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Acknowledgments

I would like to thank my supervisor Professor S. Chandra who provided me this opportunity to

perform my research at CACT (Center for Advance Coating Technologies) under his supervision

and my co-supervisor J. Mostaghimi for his assistance, and advice throughout this research. Their

guidance and supervision helped me to complete this demanding work.

I am thankful to Professor T. Coyle for his invaluable suggestions during the course of this thesis.

From CACT staff I would like to thanks Dr. V. Pershin and T. Lee for their assistance in laboratory

work.

Next, I would like thank my supervisory committee M. Thomson and J. S. Wallace for providing

their careful attention to the details of the project and their suggestions each year.

To my friends, thank you for offering me advice, and supporting me through this entire process,

especially, I would like to thank J. Esmaeelpanah for his discussions on the topic, his

encouragement in my ups and downs and his support in hands on machine shop work. I would also

like to acknowledge CACT colleagues, Sina, Mehrdad, and Amini for their help.I would like to

say my special thanks to Subramaniam Yugeswaran, and Saeid Salavati for helping me in sample

preparation.

This journey would not have been possible without the support of my family. I am grateful for

their emotional and financial support. I would like to thank my parents; Abdul Hafeez and Anjum

Hafeez, my siblings Ghazanfarah, Farooq and Zoya Hafeez for encouraging me in all of my

pursuits. I would like to say my special thanks to my momy for her unconditional love, continued

support and persistent follow-up on my thesis. Her firm belief in me and my work kept me

motivated to achieve this dream. Finally I would like to thank my husband David Anthony Brown

for all his moral support during this arduous journey. Above all I want to thank my Lord to Whom

I shall return.

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Table of Contents

List of Figures ................................................................................................................................ ix

Nomenclature .................................................................................................................................xv

Chapter 1 Introduction ....................................................................................................................1

Background and Motivation ................................................................................................1

Literature Review.................................................................................................................3

Research Objectives ...........................................................................................................10

Organization of Thesis .......................................................................................................11

2 Chapter 2 Metal Foam Structure and its Properties ..................................................................13

Introduction ........................................................................................................................13

Characterization of Metal Foam Geometric Properties .....................................................13

Unit Cell Representation ....................................................................................................15

Summary ............................................................................................................................18

3 Chapter 3 Fabrication of Metal Foam Heat Exchangers ...........................................................19

Introduction ........................................................................................................................19

Bonding Techniques ..........................................................................................................19

Plasma Sprayed Heat Exchangers ......................................................................................20

Conventional Brazed Heat Exchangers .............................................................................25

Summary ............................................................................................................................27

4 Chapter 4 Fabrication of High Temperature Test Rig and Experimental Methods ..................28

Introduction ........................................................................................................................28

Fabrication of High Temperature Test Rig ........................................................................28

4.2.1 The Combustion Chamber .....................................................................................28

4.2.2 The Igniter ..............................................................................................................29

4.2.3 The Test Section ....................................................................................................29

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4.2.4 The Convergent Section .........................................................................................30

Measurement System for High Temperature Tests ...........................................................31

4.3.1 The Heat Source and Heating System ...................................................................31

4.3.2 The Cooling System ...............................................................................................33

Experimental Procedure for High Temperature Tests .......................................................34

4.4.1 The Leakage Test ...................................................................................................34

4.4.2 The Force Convection Test ....................................................................................35

Pressure Drop Apparatus ...................................................................................................36

Summary ............................................................................................................................37

5 Chapter 5 High Temperature Heat Exchanger Tests.................................................................38

Introduction ........................................................................................................................38

Hydraulic Characteristics ...................................................................................................39

Heat Transfer Characteristics .............................................................................................42

5.3.1 Surface Temperature Behavior and Peclet Number ...............................................42

5.3.2 Heat transferred to the Air and Performance Comparison .....................................47

5.3.3 Contact Resistance and Air Side Resistance ..........................................................53

5.3.4 Volumetric Heat Transfer Coefficient ...................................................................59

5.3.5 Nusselt Number .....................................................................................................63

Analytical Model ...............................................................................................................65

Conclusions ........................................................................................................................76

Chapter 6 ........................................................................................................................................78

Testing of Cross-Flow Heat Exchangers at Low Temperature .................................................78

Introduction ........................................................................................................................78

Sample Description ............................................................................................................79

Experimental Setup and Procedure ....................................................................................80

6.3.1 Uniform Heating ....................................................................................................83

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6.3.2 Measured Parameters and IR Calibration ..............................................................84

6.3.3 Error and Uncertainty ............................................................................................85

Results and Discussion ......................................................................................................86

6.4.1 Surface Temperature Distribution ..........................................................................86

6.4.2 Heat Removed and Performance Evaluation .........................................................93

6.4.3 NTU - Effectiveness of Heat Exchanger ...............................................................94

6.4.4 Nusselt number ......................................................................................................96

6.4.5 Agreement of Model Predictions with Experimental Measurement ......................98

Summary ..........................................................................................................................100

Chapter 7 ......................................................................................................................................101

Fabrication of Heat Shield from Metal Foam .........................................................................101

Introduction ......................................................................................................................101

Background and Motivation ............................................................................................102

Deposition of Porous Skins on Metal Foam ....................................................................104

Results and Discussion ....................................................................................................109

Experimental Errors and Uncertainty Analysis ...............................................................119

Summary ..........................................................................................................................120

Chapter 8 ......................................................................................................................................121

Summary and Conclusions ......................................................................................................121

REFERENCES ............................................................................................................................124

APPENDIX A ..............................................................................................................................131

APPENDIX B ..............................................................................................................................134

APPENDIX C ..............................................................................................................................136

APPENDIX D ..............................................................................................................................139

APPENDIX E ..............................................................................................................................143

List of Tables

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Table 2.1: Cell properties of 𝑵𝒊 Foam Sample ............................................................................. 17

Table 3.1: Plasma spraying parameters ........................................................................................ 21

Table 5.1: Hydraulic properties of Ni Foam Sample and comparison with literature .................. 40

Table 7.1: Selected spraying parameters for co-deposition spraying ........................................ 105

ix

List of Figures

Figure 2-1: (a) Metal Foam Structure, (b) Unit cell representation .............................................. 15

Figure 2-2: A typical metal foam structures of 10 and 40PPI pore density .................................. 17

Figure 3-1: Photographical view of the steps involved in fabrication of heat exchangers (10, 40PPI

foam core) ..................................................................................................................................... 22

Figure 3-2: Morphology of the Alloy 625 powder ....................................................................... 23

Figure 3-3: Cross section image of thermally sprayed skin on Ni foam ...................................... 23

Figure 3-4: EDS elemental mapping of skin-foam interface ........................................................ 24

Figure 3-5: (a) Ni foil brazed to foam (b) Thermally sprayed foil (c ) result after pull-off test (d)

The foam chunk attached to the aluminum dolly after pull-off test ............................................. 25

Figure 3-6: (a) 40PPI foam heat exchanger (b) The core of 40PPI heat exchanger (d)

Microstructure of 40PPI foam ...................................................................................................... 26

Figure 3-7: (a) Side view of conventional brazed 40PPI fin heat exchanger with the foam core (b)

Front view of the conventional brazed 40PPI fin heat exchanger ................................................ 27

A diagram of the test rig is shown in Figure 4-1. It consisted of four main components: a

combustion chamber; ignition system; test section; and a convergent exhaust duct .................... 28

Figure 4-2: SOLIDWORKS model of the test rig ....................................................................... 30

Figure 4-3: Photograph of the test rig ........................................................................................... 31

Figure 4-4: (a) Schematic of the measurement system (b) Schematic of the wall and air

measurement locations .................................................................................................................. 32

Figure 4-5: Schematic of the leakage test setup............................................................................ 35

Figure 4-6: Flow direction of the gases in hot section and air in cold section ............................. 36

Figure 4-7: Apparatus for pressure drop measurement................................................................. 37

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Figure 5-1: Length normalized pressure drop curves based on 200mm length of 10 and 40PPI

nickel foam heat exchanger versus velocity ................................................................................. 40

Figure 5-2: Friction factor versus Reynolds number for Ni foam from Beavers and Sparrow [69]

and Al foam from Kim et al. [21] from literature is also presented ............................................. 42

Figure 5-3: Local wall temperature of 40PPI plasma sprayed and conventional brazed heat

exchangers at 5 and 10SLPM (Pe<1) ........................................................................................... 45


exchangers at 20(Pe~1), 60 and 200SLPM (Pe>1) ....................................................................... 45

Figure 5-5: Local air temperature of 40PPI plasma sprayed and conventional brazed heat

exchangers at 5 and 10SLPM (Pe<1) ........................................................................................... 46


exchangers at 20(Pe~1), 60 and 200SLPM (Pe>1) ....................................................................... 46

Figure 5-7: Air temperature difference of 10 and 40PPI plasma sprayed and conventional brazed

heat exchangers at different Pe number ........................................................................................ 47

Figure 5-8: Heat transferred to air through 10 and 40PPI plasma sprayed and conventional brazed

heat exchangers at different flow rate ........................................................................................... 49

Figure 5-9: Comparison between 10 and 40PPI thermally sprayed and conventional brazed heat

exchangers..................................................................................................................................... 50

Figure 5-10: Comparison between 40 and 10PPI thermally sprayed heat exchangers and empty

channel .......................................................................................................................................... 50

Figure 5-11: Comparison between 40PPI conventional braze heat exchangers with fin and without

fin .................................................................................................................................................. 51

Figure 5-12: Performance comparison between 10 and 40PPI plasma sprayed heat exchangers 52

Figure 5-13: (a) Plasma sprayed (b) conventional brazed (c) conventional brazed with fin heat

exchangers..................................................................................................................................... 52

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Figure 5-14: Overall heat transfer coefficient for 40PPI heat exchangers ................................... 54

Figure 5-15: Overall heat transfer coefficient for 10PPI heat exchangers ................................... 54

Figure 5-16: Resistance network from coating to foam ............................................................... 55

Figure 5-17: Air side resistance of brazed foam heat exchanger ................................................. 56

Figure 5-18: Air side resistance of plasma sprayed foam heat exchanger ................................... 57

Figure 5-19: Variation of contact resistance with air velocity for 10 and 40PPI heat exchangers

....................................................................................................................................................... 58

Figure 5-20: Variation of interstitial ( hsf) heat transfer coefficient with air velocity for 10 and

40PPI heat exchangers .................................................................................................................. 60

Figure 5-21: Ratio of interstitial ( hsf) heat transfer coefficient of 10PPI and 40PPI. Comparison

with literature (Tsolas and Chandra [40] and Mancin et al.[38]) is also shown ........................... 60

Figure 5-22: Variation of volumetric heat transfer coefficient with air velocity for 10 and 40PPI

foams ............................................................................................................................................. 61

Figure 5-23: Comparison of volumetric heat transfer coefficient for 10PPI heat exchangers with

literature [40] ................................................................................................................................ 62

Figure 5-24: Comparison of volumetric heat transfer coefficient for 40PPI heat exchangers with

literature [40] ................................................................................................................................ 63

Figure 5-25: Comparison with literature. Nusselt number based on pore diameter vs Reynold

number based on pore diameter .................................................................................................... 64

Figure 5-26: Schematic of the analytical model for foam heat exchanger .................................. 66

Figure 5-27: Predicted and measured solid and fluid temperatures for 10PPI foam at 90SLPM 75

Figure 5-28: Predicted and measured solid and fluid temperatures for 10PPI foam at 120SLPM

....................................................................................................................................................... 76

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Figure 6-1: Schematic of the cross flow heat exchanger showing the air and gas flow directions

across the test sample .................................................................................................................... 79

Figure 6-2: Photographs of (a) 40PPI test sample (b) Hollow sample ......................................... 80

Figure 6-3: Schematic of the experimental setup for low temperature test .................................. 81

Figure 6-4: Photograph of the experimental setup for low temperature test ................................ 82

Figure 6-5: Outlet temperature of the heater when foam was inserted in outlet duct as a flow

straightener, and when there was no foam. ................................................................................... 83

Figure 6-6: temperature measurement at the exit of the heater outlet duct outlet (a) with foam as a

flow straightener (b) without any flow straightener ..................................................................... 84

Figure 6-7: The calibration curve between thermocouple and IR temperature ............................ 85

Figure 6-8: IR thermographs for foam heat exchanger and hollow channel for case 1 where hot air

flow rate was kept constant to 90SLPM and coolant flowrate was varied to (a),(b) 20SLPM

(c),(d)40SLPM and (e),(f)120SLPM. The average temperature measured from FLIR infrared

camera is also mentioned on each thermograph ........................................................................... 89

Figure 6-9: IR temperature distribution of 40PPI foam heat exchanger and hollow channel for case

2 i.e. when the hot air and coolant flow rate were varied in a ratio such that 𝑪𝒓 = 𝑪𝒎𝒊𝒏𝑪𝒎𝒂𝒙 =

𝟎. 𝟓 .The hot air and coolant flowrates are (a),(b) 20 ,10SLPM (c),(d) 60,30SLPM, and(e),(f)

140,70SLPM. The average temperature measured from FLIR infrared camera is also mentioned

on each thermograph ..................................................................................................................... 90

Figure 6-10: IR temperature distribution of 40PPI foam heat exchanger and hollow channel for

case 3 i.e. when the hot air and coolant flow rate were varied in a ratio such that 𝑪𝒓 =

𝑪𝒎𝒊𝒏𝑪𝒎𝒂𝒙 = 𝟏 .The hot air and coolant flowrates are (a),(b) 35,35SLPM and (c),(d)

75,75SLPM. The average temperature measured from FLIR infrared camera is also mentioned on

each thermograph .......................................................................................................................... 91

Figure 6-11: Average temperature taken from IR thermographs (FLIR ThermoVision LabView)

for 40PPI foam heat exchanger and hollow channel for case 1 .................................................... 92

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Figure 6-14: Heat transferred to the air flowing through the foam heat exchanger for case 1 ..... 94

Figure 6-15: The effectiveness NTU graph. Theoretical values are taken from[75] .................... 96

Figure 6-16: Nusselt versus Reynold for 40PPI heat exchanger tested in cross flow arrangement in

IR test set-up ................................................................................................................................. 97

Figure 6-17: Experimentally measured and analytically predicted non-dimensionalized

temperatures for 40PPI heat exchanger tested in cross flow arrangement in IR test set-up ......... 99

Figure 6-18: Experimentally measured and analytically predicted non-dimensionalized

temperatures for 40PPI heat exchanger tested in cross flow arrangement in IR test set-up ....... 100

Figure 7-1: (a) Sample A: 40PPI Ni foam, (b) Foam with temporary skin (c) Foam with metallic

skin .............................................................................................................................................. 106

Figure 7-2: SEM microstructure of pore former (polyester) ...................................................... 107

Figure 7-3: SEM microstructure of Co-deposition sprayed porous Alloy-625 coating .............. 107

Figure 7-4: (a) surface after pull-off test (b) Alloy-625 coating attached to the aluminum dolly

after the test ................................................................................................................................. 108

Figure 7-5: Test apparatus to visually inspect the uniform porosity of the sample .................... 108

Figure 7-6: The amount of air effused from the porous surface for the amount of air supplied in to

the sample ................................................................................................................................... 109

Figure 7-7: (a) Surface temperature measured by thermocouples in burner test rig at 750ºC gas

inlet temperature (b) Schematic of the sample A under experimental condition for understanding

of the temperature measurements ............................................................................................... 111

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Figure 7-8 Convection heat transfer and convection loss due to transpiration cooling at different

blowing ratios.............................................................................................................................. 112

Figure 7-9: Surface temperature and cooling efficiency as a function of distance at M=0.016 . 114

Figure 7-10: Surface temperature and cooling efficiency as a function of distance at M=2 ...... 114

Figure 7-11: Cooling efficiency as a function of distance at different blowing ratios ............... 115

Figure 7-12: Average cooling efficiency as a function of blowing ratios .................................. 115

Figure 7-13: Average cooling efficiency as a function of blowing ratios comparison with literature

..................................................................................................................................................... 116

Figure 7-14: Stanton number ratio of porous to non-porous surface as a function of Reynolds

number ........................................................................................................................................ 117

Figure 7-15: IR image of surface temperature of 40 PPI thermally sprayed foam at different

blowing ratios.............................................................................................................................. 118

Figure 7-16: Calibration curve between thermocouple measurements and IR measurements ... 119


exchangers at 5 and 10SLPM (Pe<1) ......................................................................................... 134


exchangers at 20(Pe~1), 60 and 200SLPM (Pe>1) ..................................................................... 135


exchangers at 5 and 10SLPM (Pe<1) ......................................................................................... 135


exchangers at 20(Pe~1), 60 and 200SLPM (Pe>1) ..................................................................... 135

xv

Nomenclature

𝐴 Area (𝑚2)

Asf Surface area of foam (𝑚2)

𝐶𝐹 Inertial Coefficient

𝐶𝑝 Specific Heat Capacity (𝐽 𝑘𝑔𝐾)⁄

𝐶𝑚𝑖𝑛 Heat capacity rate of cold fluid (𝐽 𝑠𝐾)⁄

𝐶𝑚𝑎𝑥 Heat capacity rate of hot fluid (𝐽 𝑠𝐾)⁄

𝐶𝑟 Thermal heat capacity ratio

𝐷𝑎 Darcy number

𝑑𝑓 Fiber diameter (𝑚)

𝑑ℎ Hydraulic diameter (𝑚)

𝑑𝑝 Pore diameter (𝑚)

𝑓 Friction factor

𝐻 Height of the channel (𝑚)

ℎc Heat transfer coefficient of air side (𝑊/𝑚2𝑘)

ℎ𝑠𝑓 Interstitial heat transfer coefficient of air side (𝑊/𝑚2𝑘)

𝑘 Thermal conductivity (𝑊 𝑚 𝐾⁄ )

𝑘𝑠𝑒 Effective thermal conductivity of solid (𝑊 𝑚 𝐾⁄ )

𝑘𝑓𝑒 Effective thermal conductivity of fluid (𝑊 𝑚 𝐾⁄ )

𝐾 Permeability (𝑚2)

L Length of the channel (m)

LTE Local thermal equilibrium

LTNE Local thermal non equilibrium

mair Mass flow rate of air (𝑘𝑔 𝑠⁄ )

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𝑀 Blowing ratio

NTU Number of transfer unit

𝑁𝑢 Nusselt number

𝑁𝑢𝑑𝑝 Nusselt number based on pore diameter

∆𝑃 Pressure drop (𝑁/𝑚2)

𝑃𝑒 Peclet number

�� Heat transfer between hot and cold section (𝑊)

𝑞″ Heat flux (𝑊/𝑚2)

𝑅"𝑐𝑜𝑛𝑡 Resistance of the interface (𝑚2𝑘 𝑤⁄ )

𝑅"𝑐𝑜𝑛𝑣 Air side resistance (𝑚2𝑘 𝑤⁄ )

𝑅"𝑐𝑜𝑛𝑑 Resistance of the material (𝑚2𝑘 𝑤⁄

𝑅𝑒 Reynolds number

𝑅𝑒𝑑𝑝 Reynolds number based on pore diameter

𝑅𝑒𝑘 Reynolds number based on permeability

𝑆 Total surface area (𝑚2)

𝑆𝑡 Stanton number

𝑇 Temperature (𝐾)

𝑈𝑜 Overall heat transfer coefficient (𝑊/𝑚2𝑘)

𝑢 Velocity (𝑚 𝑠⁄ )

𝑢𝑝 Pore velocity (𝑚 𝑠⁄ )

𝑊 Width of the channel (m)

Subscripts

𝑎 Air

𝑏 Base plate

𝑐 Cross section

𝑑𝑝 Pore diameter

xvii

𝑒 Effective

𝑓 Fluid

𝑖 Inlet

𝑜 Outlet

𝑠 Surface

𝑣 Volumetric

𝑡 Total

∞ Main stream condition

Greek Symbols

𝛼𝑠𝑓 Surface area density (𝑚2/𝑚3)

∆𝑇 𝑙𝑚 Log mean temperature difference (𝐾)

∀ Volume (𝑚3)

𝜖 Porosity (%)

∈ Effectiveness

𝜂 Cooling efficiency

𝑟𝑓 Hollowness ratio

𝜇 Dynamic Viscosity (𝑘𝑔/𝑚𝑠)

𝜌 Density (𝑘𝑔/𝑚3)

𝜈 Kinematic Viscosity (𝑚2 𝑠⁄ )

𝛿 Uncertainty

1

Chapter 1

Introduction

Background and Motivation

Heat exchangers play an important role in a variety of industrial applications where they have a

significant impact on the energy efficiency, cost, size, and weight of energy conversion systems.

Since the 1970s heat exchanger technology has been improved to overcome issues such as low

thermal efficiency, performance degradation due to fouling and failures caused by thermal stress,

and also to reduce the size of heat exchangers [1] . Another problem encountered by early heat

exchangers was that bulky units were difficult to fit into existing installations of large power plants.

For example, the entire layout of a gas turbine power plant has had to be reversed to accommodate

a simplified flow path for recuperated gas [2]. Building compact heat exchangers, therefore, offers

a great opportunity to minimize heat exchanger weight and volume and reduce the cost of energy

conversion system.

Increased compactness can be achieved by reducing the size of heat exchanger passages or by

adding secondary surfaces (fins) within the passage. Compact heat exchangers with extended

surfaces, such as wavy fins, offset strip fins, and louvered fin, are often utilized to increase the

heat transfer area. The louvered fin is considered one of the most efficient geometries to enhance

the heat transfer rate and is widely used in automotive and aircraft air-cooled heat exchangers [3,

4]. However, the manufacturing process of louvered fins requires heavy investment in tooling and

maintenance. They have relatively low structural strength since they are made from very thin

aluminum sheet and manufacturing them is complicated. Consequently, there is a demand for

compact heat exchangers that have a high heat transfer rate, good structural strength and are simple

to manufacture.

The cost of energy and environmental degradation caused by energy conversion processes, have

become topics of great concern in the past few decades. With growing awareness of the limits to

2

use of fossil fuels resources there has been a greater focus around the world on energy usage and

consumption. Increasing the efficiency of thermal systems is vital for reducing the problems

associated with energy consumption. The U.S. industrial sector accounts for about one-third of

the total energy consumed in the United States and 20 to 50% of industrial energy input is lost as

waste heat in the form of hot exhaust gases, cooling water, and heat lost from hot equipment

surfaces and heated products [5]. Waste heat recovery systems are frequently implemented, but

constrained by factors such as temperature limits and the costs associated with the recovery

equipment. Another barrier is the lack of suitable materials that can withstand corrosion and heat

while being exposed to exhaust gases. Carbon steel begins to oxidize at 425ºC and stainless steel

at 650ºC and therefore advanced alloys or composite materials must be used for heat exchangers

used to recover heat at higher temperatures [3]. Therefore, development of an efficient, compact

heat exchanger that can withstand high temperature is desirable for energy conversion applications.

Metal foams offer a possible solution to developing compact, high efficiency heat exchangers. Due

their unique characteristics (i.e. high strength, low weight, high surface area density, and noise

attenuation) they can be used in a broad range of applications such compact heat exchangers,

electronic cooling, and noise control system. The Centre for Advanced Coatings Technology

(CACT) at the University of Toronto has developed a unique technology to fabricate lightweight,

complex shaped, high temperature heat exchangers out of metal foams. Foams of nickel and

aluminum, now widely commercially available, make very efficient heat exchangers since they

have very large internal surface area for heat transfer. Heat exchangers are made from sandwich

structures in which surface skins made of metals, ceramics, or a mixture of the two, are deposited

on a metal foam core. Skins are deposited by thermal spraying, a process in which metal or ceramic

wires or powders are fed into a high temperature gas jet where they melt while being sprayed onto

a surface. The molten droplets coalesce and freeze upon impact, forming a dense, solid layer. The

spraying process eliminates most machining and forming and significantly reduces manufacturing

costs. Sprayed skins can be made from high-temperature alloys or ceramics, which are otherwise

very difficult to shape. Cooling gas circulates through the open cell foam, eliminating the need to

drill complex cooling channels.

Few studies have been carried out on the thermal behavior of metal foams at high temperatures

(~750ºC). This thesis focuses on the testing of lightweight, efficient, compact heat exchangers for

high temperature applications.

3

Literature Review

Flow through porous media has been studied in detail for the past 150 years. Darcy [6] was the

first in 1856 to model flow through porous media, deriving the now well-known Darcy’s law. Later

Dupuit [7] and then Forchheimer [8] made modifications to add the effect of inertial drag effect at

higher velocities to Darcy’s law producing the so-called Dupuit-Forchheimer extension of Darcy’s

law. Hazen [9] was the first who observed effect of temperature on the hydraulic conductivity

coefficient in Darcy’s law, and finally Krüger [10] connected those modifications to a dynamic

viscosity term.

Porous structures in the form of packed beds, sintered materials, textile structures and foam

materials have been widely used as thermal energy absorbers, for electronic cooling, geothermal

systems and in many others industrial applications. The high thermal conductivity of porous metal

structures works well to increase heat transfer. Koh and Stevens [11] filled a stainless steel annulus

with peen shot (steel particles) and found that the heat transfer effectiveness could be greatly

increased and the maximum wall temperature reduced. Koh and Colony [12] did analytical studies

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

Renken and Poulikakos [13] did an experimental investigation of forced convective heat transport

in a packed bed of spheres filling a heated channel. They measured the wall and the fluid/porous

matrix composite temperatures and reported the local heat flux at the channel wall. The Nusselt

number measurements showed a significant increase in the local heat transfer at the channel wall

and they concluded that the porous medium was a viable alternative for heat transfer augmentation

during forced convection in channels.

Golombok and Jariwala [14] measured the heat transfer coefficient for gas-to-solid convective heat

exchange in a metal fiber burner using the matrix as a heat regenerator.

Metallic foams have a large surface area to volume ratio and the tortuous paths through the metal

foam structure enhance heat transfer significantly. They are commercially available and already

used in a wide range of applications [15]. Metal foam can be used in both low temperature

(compact heat exchangers and electronic cooling) and high temperature (combustors and burners)

applications.

4

Younis and Viskanta [16] experimentally determined the volumetric heat transfer coefficient for a

gas flowing through ceramic foams and found it to be significantly different from the previous

available data for packed beds. They numerically investigated local thermal non-equilibrium

(LTNE) and developed a correlation for finding the Nusselt number.

Bastarows et al. [17] studied the single-sided heating of a foam-filled channel for electronics

cooling applications. Their experimental method used both conductive thermal epoxy bonding and

brazing of the metal foam to a heated plate. The test results revealed that brazed foam materials

were much more effective at heat removal than epoxy-bonded samples and that the heat exchange

performance was three times more efficient compared to a conventional fin-pin array.

Calmidi and Mahajan and Calmidi [18-20] studied experimentally and numerically the

characteristics of aluminum foam. They conducted forced convection experiments on the

aluminum foam that was heated at the base while air passed through it as a coolant. They suggested

two models for pore diameter estimation, based on cubic unit cell and dodecahedron unit cell

structure. They proposed a semi-empirical correlation for determination of effective thermal

conductivity and interstitial heat transfer coefficient.

Kim et al. [21] conducted experiments on forced convection through aluminum foam with pore

density ranging from 10 to 40 pores per inch (PPI) and constant porosity of 0.92. The aluminum

foam was placed inside a channel in which the upper wall was maintained at constant temperature

while the lower wall is thermally insulated. They found improvement in heat transfer performance

with increase in pore density. In another study Kim et al. [22] compared the performance of porous

fins made of aluminum foam with conventional louvered fins and concluded that porous fins with

high pore density and low porosity are preferable to reduce heat exchanger size.

Bhattacharya et al. [23] conducted experiments on forced convection through 5 and 20PPI

aluminum foam fins. The results show that heat transfer was enhanced when the air gap between

two longitudinal metal fins was filled with foam. The heat transfer coefficient was increased by

increasing the number of fins which in turn increased the heat transfer area.

Hwang et al. [24] calculated the interstitial heat transfer coefficient and friction factor

characteristics for flow across a channel filled with aluminum foam. They found that both friction

factor and interstitial heat transfer coefficient increase with decreasing foam porosity at fixed

5

Reynolds number. They developed a two-equation, non-equilibrium model of heat transfer and

found agreement with experimental results.

Boomsma et al. [25] measured the hydraulic and thermal performance of open cell aluminum foam

used as a heat exchanger in forced convection flow. They compared the drag coefficient and

permeability of brazed foam and un-brazed foam. They directed the coolant through a rectangular

channel containing the aluminum foam and found that these heat exchangers had significantly

higher efficiency when compared with commercially available heat exchangers. They also studied

the effect of compression on hydraulic characteristics.

Pavel and Mohammad [26] performed an experimental and numerical study to investigate the heat

transfer behavior of a pipe filled with porous insert subjected to constant heat flux condition. They

concluded that the heat transfer can be improved by using a porous insert with approximately the

same diameter as that of the pipe with reasonable pressure drop.

Zhao et al. [27] have done experimental and numerical study of air cooled forced convection in

FeCrA1Y foams and copper foam. Their experimental work concluded that cell size has a more

significant effect on overall heat transfer than porosity. Their results further indicated that the heat

transfer in copper foam was more sensitive to cell size than relative density and the reverse was

true for FeCrA1Y foam, which was due to the difference in thermal conductivities of the two

different materials. They determined an optimal porosity by considering a balance between the

pressure drop and heat transfer and found that it decreases as the Reynolds number increases. They

used the model of Calmidi and Mahajan [18] and found a numerical solution for the equations

assuming local thermal non-equilibrium (LTNE). Lu et al. [28] and Zhao et al. [29] performed an

analytical study on forced convection through a foam encased pipe for a constant heat flux

condition.

Hsieh et al. [30] experimentally investigated the heat transfer characteristics of aluminum foam

heat sinks to determine the effect of porosity and pore density of aluminum foam and the effect of

air velocity on Nusselt number. They showed that Nusselt number increases and the difference

between solid and gas phase decreases with increase in porosity and pore density.

Fuller et al. [31] experimentally investigated the heat transfer between FeCrAIY and copper foam.

They concluded that volumetric heat transfer coefficient was found to be strongly dependent on

6

porosity in case of FeCrAIY foam while it was a function of porosity and pore size in case of

copper foam since the effect of pore size becomes more significant as the thermal conductivity of

the solid increases. They found that the volumetric heat transfer coefficient of copper foam was

about 2 to 3 times as high as in FeCrAIY foam.

Tzeng [32] experimentally and numerically investigated the heat transfer in

compressed/uncompressed aluminum foam filled in a rectangular channel. It was found that the

uncompressed sample has a larger Nusselt number than their compressed counterparts. They

presented a numerical model for flow and heat transfer characteristics in compressed metal foam

and empirically determined the interstitial heat transfer coefficient and dispersion conductivity.

Salas and Waas [33] experimentally investigated the effect of foam thickness on convective heat

transfer of a metal foam sandwich panel, which they modelled using a finite element method. They

found that by increasing the foam thickness heat transfer increases but this effect weakens as the

foam height increases. Their numerical predictions indicated that orientation of foam strut is of

secondary importance while the foam thickness and strut size are the important properties on

convective heat transfer.

Bonnet et al. [34] performed an experimental study on compressibility effects on permeability

and inertia coefficient. They found that for Reynolds number ranging from 10 to 5000 the

Forchheimer law describes the flow behavior.

Kurtbas and Celik [35] performed an experimental study on foam filled horizontal rectangular

channel under mixed convection flow. They worked on aluminum foams of 10, 20 and 30PPI. A

uniform heat flux was applied to top and bottom of the channel. They found that average Nusselt

number increases proportional to pore density. They found that for different pore densities forced

convection was dominant for Richardson number < 0.1 while mixed convection was observed for

Richardson number > 10.

Hetsroni et al. [36] studied natural convection in metal foam strips with internal heat generation

for two different pore densities of metal foam i.e. 20 and 40PPI. They found from thermal maps

that heat transfer is increased dramatically for 20PPI metal foam comparatively flat plate. They

[37] also studies forced convection of liquid using IR technique. They investigated the heat transfer

7

in a window for transmission of a high-energy beam and showed that metal foam is an efficient

heat sink for cooling such windows.

Mancin et al. [38] has experimentally investigated the heat transfer performance of aluminum

foam. They tested the aluminum foam of 5, 10, 15, 20PPI with 0.92-0.93% porosity to find out the

heat transfer coefficient and pressure drop across the foam. The heat transfer coefficient was found

to increase with the air mass flow rate and pressure drop increased with the pore density.

Additionally, they have also investigated the effect of varying foam core height on heat transfer

behavior.

All the aforementioned studies used brazing to bond metal foam to metal plates. The research

group at CACT is using a novel technique of thermal spray coating to fabricate metal foam heat

exchangers. Jazi et al. [39] performed experiments with metal foam (10, 20PPI) coated with skins

of Inconel 625, to determine the permeability of coated 𝑁𝑖 foam heat exchangers (500ºC). A heater

with variable heat flux was attached to the external skin of the metal foam heat exchanger and the

variation in Nusselt number with Reynolds number was measured.

Tsolas and Chandra [40] experimentally studied the forced convection in thermally sprayed metal

foam heat exchanger (270ºC). They studied the pressure drop and heat transfer characteristics for

10 and 40PPI copper and nickel foam heat exchanger fabricated using thermal spray coating

method under constant heat flux conditions.

Recently Muley et al. [41] has done a technology assessment of high temperature heat exchangers

for exhaust gas recovery system (EGR) application to control 𝑁𝑂𝑥 emissions. The test was

conducted using stainless steel and 𝑁𝑖 − 𝐶𝑟 alloy foam heat exchanger in a cross flow arrangement

where compressed air at 540ºC was used to heat the surface and mixture of ethylene glycol and

water as coolant. They emphasized a need for improved brazing/joining methods for attaching

foam to metal surfaces to improve heat exchanger performance.

Guarino et al. [42] carried out an experimental study on 5, 10 and 20 PPI aluminum foam where

they investigated the heat transfer coefficient and pressure drop and the flow of forced humid air.

They found a significant growth of pressure in 20PPI foam, while 10PPI performed best in terms

of heat transfer coefficient.

8

Fiedler et al. [43] conducted an experimental and numerical analysis of the thermal resistance of

metal foam. They studied the thermal contact and electrical resistance in metal foam-graphite

assemblies for air cooled fuel cell application. They tried to minimize the thermal contact

resistance by compressing rather than using brazing. It was found that electrical contact resistance

was found to govern the total resistance of a metal foam-graphite assembly. Fiedler et al. [44]

separated material and contact resistance and used finite element method to find out the material

resistance. Their results indicated a linear dependence of contact resistance on conductive contact

area.

Chumpia and Hooman [45] performed an experimental study on five tubular aluminum foam heat

exchangers installed horizontally in a cross flow arrangement inside an open circuit wind tunnel.

Thermal resistance and pressure drop for each sample was determined. The performance of foam

heat exchangers was compared with conventional fin heat exchangers. The tubular foam heat

exchangers with suitable foam thickness performed better than their counterpart.

T’joen et al. [46] experimentally investigated the heat exchangers made of aluminum tube covered

with thin layers of (4-8 𝑚𝑚) of metal foam. They compared the results with helically finned tubes,

and found that foam tubes with smaller foam height and smaller spacing showed best performance.

They pointed out the need for a good bonding method and concluded that epoxy bonding can have

a detrimental effect on heat transfer performance.

De Jaeger et al. [47] worked on investigation of four different bonding techniques for aluminum

foam samples. They concluded that among four bonding processes i.e. press fit bonding, epoxy

bonding, brazing and co-casting, brazing yields the lowest thermal contact resistance.

Forced convection through porous media is analyzed using one of two assumptions: local thermal

equilibrium (LTE) or local thermal non-equilibrium (LTNE). LTE, which is also called one-

equation model [48, 49], assumes local thermal equilibrium between the solid and fluid phases

which means there is very high heat transfer between the two phases so that the temperature

difference between them vanishes. LTNE, which is also called two equation model, is based on

the assumption of local thermal non-equilibrium (LTNE) between the two phases, so that a

significant temperature difference exists between them. For heat exchanger applications, where

the difference between thermal conductivities of solid and fluid is significant [50, 51] the LTNE

9

assumption is necessary to understand the heat transfer behavior through porous structures. Since

the LTNE assumption requires information about the thermal conductivities of the individual

phases and the interfacial heat transfer coefficient between them, which is usually not known

without experimentation, the one-equation model has been used in many studies [50-52]. However,

the use of a one-equation model is not appropriate for a number of problems [53-56], where a local

thermal non-equilibrium model is necessary.

Alazmi and Vafai [57] analyzed the effect of variant boundary conditions for the case of constant

wall heat flux based on the local thermal non-equilibrium model. They proposed a comprehensive

set of correlations that correlate foam parameters with the total Nusselt number. Under the

assumption of local thermal non-equilibrium, Ichimiya [58] used the two-equation model, for low

thermal conductivity ceramic foams and still fit the numerical results with experimental data. Lee

and Vafai [59] determined the analytical solution for the above mentioned two-equation model by

considering diffusion term only in the transverse direction (the direction of the applied heat flux)

without consideration of thermal dispersion. The dispersion conductivity accounts for the effects

of pore-level hydrodynamics on the macroscopic transport and essentially represents the enhanced

mixing due to the presence of the solid phase.

By using the two energy equations introduced by Hsu [60] and Hsu et al. [61], Nakayama et al.

[62] presented exact solutions for two fundamental steady heat transfer cases, namely, one-

dimensional steady heat conduction in a porous slab with internal heat generation, and also

thermally developing unidirectional flow through a semi-infinite porous medium.

In order to carry out analytical /numerical study on heat exchangers made of porous structures

most of the papers listed above have assumed either constant wall heat flux or constant wall

temperature boundary condition. Therefore, a similar approach is adopted for experimental

investigation of heat transfer behavior through porous media, and experimental setups are usually

designed to simulate one of these boundary conditions.

At the end of the literature review we have identified three areas requiring more investigations,

and this thesis has contributed to filling this gap. The first area that needs more experimentation is

high temperature testing of metal foam. As shown in the literature review, metal foam for heat

exchanger application has been tested at temperatures less than 300ºC. Only Muley et al. [41] did

10

a review assessment on metal foam at temperature up to 550 ºC. He tested metal foam at 540ºC

and showed a need for better contact between metal foam and the shell. The second area which

needs more investigations is a means to provide better contact (low contact resistance) between

metal foam and shell. Finally there is a need a correlation to characterise the flow through metal

foam. Therefore, this thesis focuses on the high temperature testing of metal foam (750ºC), we

tested the heat exchanger fabricated through a novel method of thermal spray coating that provided

a metallic bond between shell and strut. We have found a correlation that can be used to predict

heat transfer with similar geometries used in this thesis.

Research Objectives

The main objectives of this project were:

To fabricate and test metal foam heat exchanger that can withstand high temperatures

(~750°C)

To characterize the flow and heat transfer characteristics of these heat exchangers

To develop analytical model and correlation that can be used to predict the performance of

the heat exchangers

The following tasks were completed to achieve these objectives

(i) Heat exchangers were fabricated from 10 and 40PPI nickel foam by two different

techniques i.e. thermal spray coating and conventional brazing technique

(ii) A burner test rig was fabricated to carry out high temperature (~750°C) testing of

different metal foam heat exchangers under similar test conditions

(iii) Another experimental rig using an infrared camera was built to observe the surface

temperature distribution of foam heat exchangers at a lower temperature (~300°C)

11

(iv) The performance of these heat exchangers was compared on the basis of heat transfer

characteristics such as volumetric heat transfer coefficient, cooling effectiveness and

hydraulic characteristics

(v) An analytical model, based on the LTNE assumption, was developed for the analysis

of experimental results

(vi) Finally, the metal foam was tested for heat shield application by studying the effect of

transpiration cooling through porous skins sprayed on the metal foam

Organization of Thesis

The thesis is organized as follows:

Chapter 1 introduces the thesis by describing the area of applications, a literature

review and outlining the focus of the thesis

Chapter 2 describes a theoretical overview of convective heat transfer through metal

foam. The metal foam structure is analyzed and properties of 10 and 40PPI 𝑁𝑖 foam used

in this study are presented

Chapter 3 fabrication of heat exchangers based on two different techniques i.e. thermal

spray coating method and conventional brazing method is described in detail

Chapter 4 fabrication of burner test rig is explained in detail. The experimental setup

for high temperature testing and test procedure is discussed. The instrumentation for

pressure drop testing is also explained

Chapter 5 The results of high temperature tests carried out on burner test rig are

analyzed and discussed in detail. An analytical model based on LTNE assumption is also

12

derived. The experimental results are found to be in good agreement with the predicted

results

Chapter 6 provides details on IR test set-up and experimental procedure followed for

low temperature tests. The results and discussion for low temperature tests are also

summarized in this chapter

Chapter 7 the heat shield application of metal foam is discussed. Experimental results

obtained from high temperature set-up and IR test set-up are used to study transpiration

cooling through metal foam

Chapter 8 summarizes the results and contributions from the present thesis

.

13

2 Chapter 2

Metal Foam Structure and its Properties

Introduction

Recent developments in processing technology have led to a range of novel lightweight materials

being developed for many engineering applications. High porosity open-cell metal foams are a

category of such materials that have shown great potential for thermal management applications

where a large amount of heat needs to be transferred from a fluid in a small volume of solid.

Because of their interesting properties, metal foams are used in applications such as structural

elements for aerospace, automotive, and building systems, thermal management systems, filters

and catalyst carriers. Metal foams have a high specific surface area that creates a greatly increased

solid-fluid heat transfer interface, while the pores provide a tortuous fluid path that creates

turbulence in the flow. It is found from the literature that the heat transfer performance of thermal

systems can be significantly increased by incorporating metal foams; however there is still

considerable research required on the subject to investigate the behavior of fluid flowing through

the porous material and the heat transfer occurring in the medium.

Characterization of Metal Foam Geometric Properties

Metallic foams are characterized structurally by their cell topology, whether they have open cells

or closed cells, their relative density, cell size, cell shape and anisotropy. The microstructure of

high porosity open-cell materials often consists of small ligaments forming a network of inter-

connected dodecahedral-like cells. The shape and size of these open cells vary throughout the

14

medium which makes the structure random and anisotropic. The principal geometrical and

physical parameters that define metal foam are;

(i) The pore density which is defined as the number of pores that can be measured in a

linear inch and its unit is PPI (pores per linear inch).The open cell foams in this study

have pore density of 10 and 40PPI

(ii) The pore size, 𝑑𝑝 is defined by the equivalent diameter of one of the faces of

dodecahedron unit. The average pore diameter, 𝑑𝑝, can be calculated from the nominal

pore density (PPI) as;

𝑑𝑝 =25.4

𝑃𝑃𝐼 (2.1)

(iii) 𝑑𝑓 is the equivalent diameter of the fiber cross-section. In case of hollow fibers the

hollowness ratio is defined as 𝑟𝑓, where 𝑑𝑖 and 𝑑𝑓 are the inner and outer fiber diameter

𝑟𝑓 =𝑑𝑖

𝑑𝑓 (2.2)

(iv) Porosity 휀 (void volume fraction) is the ratio of the void volume to the total volume.

Metal foams have a porosity ranging from 0.80 to 0.99. The foams considered in this

work had a porosity range of 0.93 to 0.97

휀 =𝑉𝑣𝑜𝑖𝑑

𝑉𝑡𝑜𝑡𝑎𝑙 (2.3)

(v) Specific surface area 𝛼𝑠𝑓, of foam is the exposed surface area within a given volume

of foam. High specific surface area allows for increased contact with the fluid flowing

15

through the foam. The twisting arrangement of the fluid passageways in the foam

creates turbulence in the fluid, thus increasing convection. This leads to a more efficient

heat exchange system, in a smaller volume

𝛼𝑠𝑓 =𝑆

𝑉 (2.4)

where 𝑆 is the total surface area (𝑚2) inside the unit cell and V is the unit cell volume (𝑚3).

Figure 2-1: (a) Metal Foam Structure, (b) Unit cell representation

Unit Cell Representation

In order to study their geometric properties some representative unit-cell models have been

developed over the past few decades for open-cell metallic foams. As shown in Figure 2-1a foam

cell is usually a polyhedron with 12–14 faces in which each face has a pentagonal or hexagonal

shape (bounded by five or six filaments). Due to the geometric complexity and the random

orientation of the solid phase of the porous medium, the solution of the transport equations inside

the pores is difficult to obtain, and this is where empirical models have been introduced.

(a) (b)

16

Boomsma and Poulikakos [63] modeled open-cell metal foams based on a fundamental periodic

unit of eight cells. Fluid flow was then modeled computationally utilizing a three-dimensional

cellular unit along with periodic boundary conditions.

Du Plessis et al. [64] established models for pore diameter estimation as a function of tortuosity,

porosity, total volume and fluid–solid interface area of a cubic representative unit cell (CRUC), a

foam cell geometric approximation, and also represented as a function of the width of the cubic

representative unit cell (𝑑 = 𝑑𝑝 + 𝑑𝑓). Other models by Du Plessis et al. and Fourie and Du Plessis

[64, 65] for pore and fiber diameters are presented as functions of porosity, tortuosity and the width

of the cubic representative unit cell.

Calmidi [20] developed a model to estimate fiber diameter as a function of porosity, pore diameter

and shape function for a cubic unit cell and also presented a modified model utilizing a three-

dimensional dodecahedron unit cell structure. The authors showed that this model has a maximum

deviation of ±7% from measured values for pore and fiber diameters. Calmidi and Mahajan.[18,

19] used a dodecahedron approximation for the unit cells to derive thermo-physical properties of

metal foams. In their unit cell approximation, the foam structure is assumed to be generated by

packing these cells. The angle between two pentagonal faces in a dodecahedron shape is 109o

while to fill the space with three equal cells the faces that share one edge need to have angle of

360° 3⁄ = 120° . An empirically determined tuning parameter is included in the majority of

existing models which is determined by a comparison with experimental data.

For the present study nickel foam of 10 and 40PPI pore density is used. The foam parameters

calculated in this thesis are calculated using model by Calmidi and Mahajan based on

dodecahedron approximation [18, 19]. Table 2.1 lists the measured and nominal specifications of

the cell structure. The measurement of these parameters is taken from scanning electron

microscopy (SEM) (TM3000, Hitachi High-Technologies Canada Incorporated, Toronto, ON,

Canada) and image analysis software (IMAGEJ v.1.43, National Institutes of Health, Bethesda,

MD). The samples were cut using an electro discharge machine (EDM) that provides smooth

edges. For each sample 5 SEM images were taken and 5 cells were measured to calculate the

average cell size. Large differences in the thermal conductivities of the solid and fluid phases (2-3

orders of magnitude) as well as the high porosity of the medium make it necessary to define an

17

effective thermal conductivity. The effective thermal conductivity (𝑘𝑒 =4.98 𝑊 𝑚𝐾⁄ ) used in this

thesis is also calculated from the model introduced by Calmidi and Mahajan [18, 19].

Figure 2-2: A typical metal foam structures of 10 and 40PPI pore density

Table 2.1: Cell properties of 𝑵𝒊 Foam Sample

Parameters Ni Foam Ni Foam

Nominal pore size (PPI) a 10 40

Nominal porosity, 휀 a 94% 94%

Nominal pore diameter, 𝑑𝑝 = 25.4/𝑃𝑃𝐼 (𝑚𝑚) a 2.54 0.635

Measured pore diameter, 𝑑𝑝 (𝑚𝑚) b 2.771 0.742

Measured 𝑑𝑓/𝑑𝑝b 0.119 0.128

Modeled 𝑑𝑓/𝑑𝑝 c 0.159 0.157

Surface area density, 𝛼𝑠𝑓 a 0.600 2.30

Surface area density, 𝛼𝑠𝑓 c 0.407 1.626

a Provided by the manufacturer, b Measured at Center for Advanced Coating Technologies (CACT) [40]

c Model by Calmidi and Mahajan [18]

Figure. 1 A typical metal foam structure of 10 and 40PPI pore density

10PPI 40PPI

18

Summary

In this chapter the important parameters that are used to characterize the structure of metal foam

are briefly discussed. The metal foam structure is analyzed and the properties of 10 and 40PPI

nickel foam used in this thesis are listed.

19

3 Chapter 3

Fabrication of Metal Foam Heat Exchangers

Introduction

This chapter will focus on the fabrication process of the metal foam heat exchangers developed

for the present study. A new method of creating a heat exchanger shell by thermal spray coating

has been used for making heat exchangers. Four nickel foam heat exchangers were fabricated for

high temperature testing, using two different methods, i.e. using vacuum furnace and plasma

spraying technique and conventional brazing method. Two heat exchangers, one of 10PPI and one

of 40PPI foam were made using the conventional brazing method and two (10 and 40PPI foam)

heat exchangers from plasma spraying technique. A hollow channel with similar external

dimensions was also made for comparison purpose.

Bonding Techniques

To build a heat exchanger a shell has to be placed around the metal foam to contain the fluid

flowing through it. Heat is conducted through the shell to the foam struts and from their surface it

is convected away by the fluid. The connection between the shell and foam struts is extremely

important since imperfect contact creates a thermal contact resistance [66] that limits heat transfer.

Reducing the contact resistance between the shell and foam can significantly improve heat transfer

[44, 67]. Methods such as brazing, cladding, epoxy bonding, press-fitting and co-casting have been

used to create a shell around metal foam [47]. Brazing has been identified as the best method

among all these techniques, providing good bonding between sheet and foam and significantly

enhancing heat transfer [68]. However, vacuum brazing is an expensive process requiring a

vacuum furnace. The size of the heat exchanger that can be manufactured is limited by the space

available in the furnace. It is also difficult to bond the foam to a surface that is not flat. There is

20

still a need for an efficient and cost-effective technique to connect the foam struts to an exterior

shell [46] .

Jazi et al. [39] used thermal spray technology to spray a metal skin onto the exterior of nickel foam

to form a heat exchanger. A layer of epoxy was used to fill in the pores on the surface of the foam

and metal layer plasma sprayed on top of the epoxy. The epoxy was then burned away in a vacuum

furnace. This technique was shown to give high heat transfer rates to cooling air flowing through

the foam [40]. Thermal spraying assures that the skin is metallurgically bonded to each strut on

the exterior surface of the foam, minimizing contact resistance. However, applying and burning

off the epoxy is still a time consuming process that can potentially leave residue on the foam

surface.

In this chapter of the thesis heat exchangers are developed, using a new method for spraying a

metal skin on the exterior surface that did not require the application of an epoxy, to test that the

heat exchanger could operate at high temperature (750°C); to compare the performance of the

thermally sprayed heat exchanger with a conventional brazed foam heat exchanger. A thin nickel

foil was wrapped around the exterior surface of 10𝑚𝑚 thick layers of nickel foam which was

placed in a vacuum furnace to braze the foil to the foam struts. A plasma spray torch was used to

spray an Alloy 625 coating on the surface of the foil, forming a skin approximately 500𝜇𝑚 thick.

Nickel foams with two different pore sizes were used, 10 and 40PPI.

Plasma Sprayed Heat Exchangers

Figure 3-1 shows photographs of the different steps involved in fabrication of the thermally

sprayed heat exchangers tested in this study. Heat exchangers were fabricated using 10𝑚𝑚 thick

nickel foam of 10 and 40PPI pore densities. Pieces of metal foam were cut to a size of 200𝑚𝑚 ×

70𝑚𝑚 × 10𝑚𝑚 (𝐿 × 𝑊 × 𝐻) using an EDM machine so that they could be press fit into the frame

of the heat exchanger as shown in Figure 3-1a. The heat exchanger frames were fabricated from

1.2𝑚𝑚 thick Inconel sheet (Inconel HX, McMaster Carr, Princeton NJ) in which were inserted

0.813𝑚𝑚 compression fittings, three on each end, to provide air inlets and outlets (see Figure

3-1a). Before spraying a coating on the foam a temporary surface had to be provided to prevent

21

the penetration of molten droplets into the open cells of the foam. A 0.05𝑚𝑚 thick 𝑁𝑖 foil was

attached to the top surface of the foam using a brazing foil (MBF alloy 51, Metglas, Inc. Conway,

SC 29526) with a nominal composition of 15𝑤𝑡. % 𝐶𝑟, 7.25𝑤𝑡. % 𝑆𝑖, 0.06𝑤𝑡. % 𝐶, 1.5 𝑤𝑡. % 𝐵

and the remainder 𝑁𝑖. Brazing was done in a vacuum furnace at a temperature of 1190 °C for 5

minutes. Once the foil was attached to the foam it was grit blasted to prepare it for thermal spray

coating (see Figure 3-1b). A plasma spray coating was applied on top of the foil using a

commercially available Alloy 625 powder (AMDRY 625, Metco, Westbury, NY) with a nominal

composition of 21.5𝑤𝑡. % 𝐶𝑟, 8.5𝑤𝑡. % 𝑀𝑜, 3𝑤𝑡. % 𝑁𝑏, 3𝑤𝑡. % 𝐹𝑒, 0.5𝑤𝑡. % 𝐶𝑜, and the

remainder 𝑁𝑖. Figure 3-2 shows a SEM image of the Alloy 625 powder which had spherical

particles with diameters ranging from 45 to 90𝜇𝑚. Thermal spraying was done using an

atmospheric plasma spraying torch (SG-100 torch, Praxair Surface Technologies, Indianapolis,

IN) with the optimized process parameters listed in Table 3.1. During the plasma spraying process

the foam channel was air cooled to avoid overheating. Figure 3-1c shows the surface formed by

plasma spraying. An Inconel sheet, 1.2𝑚𝑚 thick, was brazed to the bottom of the heat exchanger

(see Figure 3-1d) using the same brazing foil. Since no heat transfer was desired through this

surface the Inconel sheet was not brazed to the foam but only to the frame of the heat exchanger.

Table 3.1: Plasma spraying parameters

Parameters Value

Plasma Current, (𝐴) 650

Plasma Power (𝑘𝑊) 27

Primary gas, 𝐴𝑟, (SLPM) 55

Carrier gas, 𝑁2 , (SLPM) 4.8

Feed rate, (GPM) 25

Spray distance (𝑚𝑚) 80

Number passes 20

22

Figure 3-1: Photographical view of the steps involved in fabrication of heat exchangers (10, 40PPI foam core)

Frame of Heat exchanger Bracket Foam Core

(a) Foam core press fit inside the frame of heat exchanger

(b) Ni foil brazed on top surface of the foam

(c) Thermally sprayed Alloy 625 skin on top of the Ni foil

shown in (b)

(d) Inconel sheet (t=1.2mm) brazed to the frame to form the

bottom side of the heat exchanger shown in (b)

23

Figure 3-3 shows an SEM image of a cross-section through the thermally sprayed Alloy 625 skin

on 𝑁𝑖 foam (10PPI). The average thickness of the thermally sprayed metallic coating was

approximately 300𝜇𝑚 while the brazed foil added another 50 to100𝜇𝑚 to the total thickness (the

𝑁𝑖 foil and brazing foil were each 50𝜇𝑚 thick). The thickness of the brazed foil varied with

location since the diffusion kinetics of the brazing material depend on factors such as the distance

from the struts, strut thickness, applied loads and temperature variations. The nickel foam struts

are well connected to the thermally sprayed metallic skin. The foil bent to conform to the surface

of the foam struts (see Figure 3-3), providing much better contact that can be achieved when

bonding foam to a rigid sheet.

Figure 3-2: Morphology of the Alloy 625 powder

Figure 3-3: Cross section image of thermally sprayed skin on Ni foam

Bending is advantage

24

Figure 3-4 shows an SEM image of a cross-section through the sprayed coating. Image analysis

showed that the average porosity was approximately 6% and energy dispersive x-ray spectroscopy

(EDS) conducted in the SEM showed that the oxide content was 8%. Figure 3-4a is divided in to

three regions. Region 1 is the Alloy-625 skin that is plasma sprayed over the surface of the 𝑁𝑖 foil.

Region 2 consists of the 𝑁𝑖 and brazing foils, while region 3 is largely a 𝑁𝑖 foam strut. The 𝑁𝑖 and

𝐶𝑟 concentrations derived from the EDS measurements are mapped on the region shown in Figure

3-4a and Figure 3-4b shows the presence of 𝑁𝑖 in all three regions. Figure 3-4c shows that 𝐶𝑟

metal from the brazing foil (coloured in blue) diffused a few micrometres into the 𝑁𝑖 struts and

created metallurgical bonds between the foil and 𝑁𝑖 struts. The SEM images and EDS results at

the interfaces between the foam strut and foil, and the foil and sprayed skin show that the foil

surface was well bonded with the surface of the 𝑁𝑖 strut and with the thermally sprayed metallic

skin.

Figure 3-4: EDS elemental mapping of skin-foam interface

(b)

(a)

(c)

25

The bond strength of the thermally sprayed skin on the foam was measured using a pull-off

adhesion tester (PosiTest, Defelsko Corporation, USA). Figure 3-5 shows images of the nickel foil

prior to spraying (Figure 3-5a), the surface of the thermally sprayed coating (Figure 3-5b) and the

location where the coating was removed by the pull-off tester (Figure 3-5c).Its clearly seen from

Figure 3-5d that the failure occurred in the foam not at the interface between foam and skin. This

test was done at three different positions on each sample and the results were averaged. The

average adhesion strength of the thermally sprayed skin on the 𝑁𝑖 foam was 260.66 𝑝si

(1792𝑘𝑃𝑎).

Figure 3-5: (a) Ni foil brazed to foam (b) Thermally sprayed foil (c ) result after pull-off test (d) The foam

chunk attached to the aluminum dolly after pull-off test

Conventional Brazed Heat Exchangers

Two heat exchangers were fabricated by brazing Inconel sheets to the foam (40 and 10PPI) instead

of applying a thermal spray coating; Figure 3-6 shows a photograph of one of these. The size of

the heat exchangers was the same as the thermally sprayed heat exchangers (200𝑚𝑚

×70𝑚𝑚 ×10𝑚𝑚). The frame was again made from 1.2𝑚𝑚 thick nickel alloy sheets (Inconel HX,

McMaster Carr, Princeton NJ), and similar fittings were installed at the inlet and outlet ends of the

frame. A 50𝜇𝑚 thick nickel-alloy brazing foil (MBF 51, Metglas Inc. SC, USA) was used to attach

the Inconel sheet to the upper surface of the nickel foam. The bottom face sheet was not brazed to

the foam but only to the edges of the external frame, using the same brazing foil.

(b) (a) (c) (d)

26

Brazing was carried out at 1190°C in a vacuum furnace for 5 minutes. Figure 3-6c shows an SEM

image of a cross-section through the casing of a 40PPI foam heat exchanger. It can be seen that

not all the struts were bonded to the casing since it was rigid and did not conform fully to the

surface of the foam, which may increase the thermal contact resistance between the sheet and

foam.

Figure 3-6: (a) 40PPI foam heat exchanger (b) The core of 40PPI heat exchanger (d) Microstructure of 40PPI

foam

Another sample with 40PPI foam was fabricated to test the augmentation of heat transfer by adding

fins on the top surface. These fins were fabricated from low carbon steel perforated sheet

(McMaster Carr) with 3.175𝑚𝑚 holes spaced 4.76𝑚𝑚 apart. The perforated sheet was cut into 7

pieces of 12 𝑚𝑚 ×40 𝑚𝑚 ×1𝑚𝑚 (𝐿 × 𝑊 × 𝑡) by EDM. The fins were initially spot welded at

one point to hold the position. Then a 2𝑚𝑚 thick Inconel coating was sprayed using a wire arc

spray technique to provide good thermal contact between the base surface and the fins. The fin

spacing was selected as 25𝑚𝑚.

(a)

(b)

(c)

27

Figure 3-7: (a) Side view of conventional brazed 40PPI fin heat exchanger with the foam core (b) Front view

of the conventional brazed 40PPI fin heat exchanger

Summary

In this chapter of the thesis fabrication process of 10 and 40PPI heat exchanger is explained. The

heat exchangers are fabricated by two techniques i.e. novel technique of using thermal spray

process and conventional brazing technique. The plasma sprayed heat exchangers provided better

contact that can be achieved when bonding foam to a rigid sheets such as in case of conventional

brazed heat exchangers.

(a) (b)

28

4 Chapter 4

Fabrication of High Temperature Test Rig

and Experimental Methods

Introduction

In this chapter of the thesis the experimental apparatus and test procedure for high temperature

testing of the heat exchangers is described. First the fabrication of the burner test rig, which was

built to operate at high temperature (>1000ºC), is described followed by the details of experimental

procedure. The test rig is developed to study the performance of different metal foam heat

exchangers (discussed in chapter 3) exposed to hot gases. The experiments are performed at two

inlet gas temperatures (550ºC and 750ºC). The heat exchangers are cooled by passing air, which

is used as working fluid in all the experiments, through them. The flow rate of the coolant through

the heat exchanger was varied between 5 to 200SLPM. The surface temperature, air temperature

inside the heat exchanger and air inlet and outlet temperatures were recorded during the tests. The

experimental procedure is repeated for different samples and results are compared.

Fabrication of High Temperature Test Rig

A diagram of the test rig is shown in Figure 4-1. It consisted of four main components: a

combustion chamber; ignition system; test section; and a convergent exhaust duct

4.2.1 The Combustion Chamber

The first section is a combustion chamber. The combustion chamber was used to burn methane

and generate hot gases for the experiment and was fabricated from a copper cylinder with an inside

29

diameter of 20𝑚𝑚 with 4𝑚𝑚 thick walls. The combustion chamber was surrounded by a water

cooling jacket and methane and air were premixed inside it.

4.2.2 The Igniter

The second section is an igniter. It was made up of stainless steel. The walls were 4𝑚𝑚 thick and

255𝑚𝑚 long. It was used to connect the combustion chamber to the test section. A spark plug to

ignite the fuel-air mixture was inserted in divergent section of the test rig which was connected to

the exit of the combustion chamber. A quartz window was installed in the divergent section to

allow ignition to be observed. A K-type thermocouple (KMQXL-125-G-6, Omega Engineering,

Stamford, CT) was inserted through the side wall, 10𝑚𝑚 before the main test section, to measure

the temperature of the hot gas entering the test section.

4.2.3 The Test Section

The main test section was a metal duct with a square inner cross section of 80𝑚𝑚 × 80𝑚𝑚 and

200𝑚𝑚 long made of 4𝑚𝑚 thick stainless steel plate. The heat exchanger formed the bottom plate

of the test section. Five holes were drilled through the top wall of the duct to insert thermocouples

(K-type, CHAL-005- Unsheathed fine gage, OMEGA ENGINEERING, Stamford, CT) via

0.813𝑚𝑚 compression fittings. The holes were drilled along the length of the duct spaced 50𝑚𝑚

apart. The thermocouples were attached to the surface of the heat exchanger by using high-

temperature, thermally conductive paste (Pyro-Duct 597-A AREMCO Products Inc, Valley

cottage, NY) with 𝑘 = 9.1 𝑊 𝑚𝐾⁄ to measure the local wall temperature along the channel. High

temperature insulation (Cerachem Blanket 𝑘 = 0.1 𝑊 𝑚𝐾⁄ , MORGAN Thermal Ceramics) was

wrapped around the entire test rig to minimize heat losses through the walls. The stainless steel

convergent section was 250 𝑚𝑚 long and mated with the exit of the test section. A K-type

thermocouple was located at the end to measure the temperature of the gas exiting the test system.

30

4.2.4 The Convergent Section

The exhaust was made up of stainless steel with 250𝑚𝑚 long × 4𝑚𝑚 thick walls. It was mated

with the exit of the test section and served as a gas discharge from the system. A K-type

thermocouple (KMQXL-125-G-6, OMEGA ENGINEERING Stamford, CT) was fitted at the end

to measure the uniform temperature of the gas exiting the test system.

Figure 4-2: SOLIDWORKS model of the test rig

31

Figure 4-3: Photograph of the test rig

Measurement System for High Temperature Tests

shows the schematic of the experimental apparatus and measurement system. The measurement

system can be subdivided into two i.e. heating system and a cooling system.

4.3.1 The Heat Source and Heating System

The heating system consisted of a gas supply unit, a water cooling unit and an ignition unit. 𝐶𝐻4

and 𝑂2 were stored in cylinders supplied by Linde Industrial Gases Canada. The gases were

controlled by needle valves and mass flow controllers (FMA 5500 Omega Engineering Inc.

Stamford. CT, USA) mounted on a gas flow control panel. The desired flow rate of gases was

released by adjusting the flow controllers connected to the control panel. The control panel was

provided with ball valves connected to each gas supply line, to shut off the gas supply when the

operation was finished. At the back of the control panel, two flashback arrestors (Scott 55-85B,

Scott Specialty Gases, Plumsteadville, PA, USA) were mounted on 𝐶𝐻4 and 𝑂2 line respectively.

The safety devices were installed downstream of the flow controllers to prevent the flame from

burning back and causing damage. As a safety measure, two check valves (Parker C series,

32

Figure 4-4: (a) Schematic of the measurement system (b) Schematic of the wall and air measurement

locations

(a)

mpl

Test Section

Wall temperature

measurement:

Thermocouples attached to

surface of heat exchanger

Air temperature

measurement:

Thermocouples penetrated

inside the heat exchanger

to measure the air

temperature

Air in Air out

(b)

Heat Exchanger wall

33

Parker Hannifin Corp. Cleveland, OH, USA) were also installed to prevent backflow from the

combustion chamber to the gas hoses.

Untreated city water was circulated through a water coolant jacket around the combustion chamber

to protect the combustion chamber subjected to high temperature during the experimental run. A

NGK CR7HSA spark plug (NGK Spark Plugs Canada Limited, Scarborough, On, Canada) was

attached to the ignition unit. Hot gases generated inside the combustion chamber, were passed

through the test section and finally discharged into the fume hood. A K-type thermocouple

(KMQXL-125-G-6 OMEGA ENGINEERING Stamford, CT) was introduced upstream of the test

section in order to measure the gas inlet temperature. Five K-type thermocouples (CHAL-005-

Unsheathed fine gage, OMEGA ENGINEERING Stamford, CT) were inserted through five holes

in the test section to measure the surface temperature at five axial locations. The ceramic shielding

was used to protect the thermocouple from heating. Air temperature inside the heat exchanger was

also recorded at five different points. Three K-type thermocouple (KMQXL-125-G-6 OMEGA

ENGINEERING Stamford, CT) were mounted horizontally across the height of the exit of the test

section to measure the bulk temperature of the exit gas. Finally, one K-type thermocouple

(KMQXL-125-G-6 OMEGA ENGINEERING Stamford, CT) was attached at the end of the

diffusing section to measure the bulk temperature of the discharge gas.

4.3.2 The Cooling System

The main components of the cooling system are: a pressure regulator, a rotormeter, pressure

differential gauge and two mass flow-meters. Dry compressed air was drawn from the compressor

with a line pressure of 110𝑝𝑠𝑖 (758.4 𝑘𝑃𝑎) inside the test laboratory. The air was then driven

through the pressure regulator (Model R37221-600, Ingersoll-Rand plc, Dublin, Ireland) via 1/4"

tubing connected to the globe valve. Coolant air with a set pressure of 5𝑝𝑠𝑖 (34.4𝑘𝑃𝑎) was passed

through the rotameter that was adjusted to release the desired flow rate of the air between 5-

200SLPM. The measurement of the air entering the heat exchanger was done by mass flow-meter

(FMA 1843, OMEGA ENGINEERING Stamford, CT) mounted upstream before the heat

exchanger. Finally, air was introduced into the sample via dedicated mated with compression

fittings. Another mass flow-meter (FMA 1843, OMEGA ENGINEERING Stamford, CT) was

mounted downstream of the test sample, to measure the amount of the air leaving the system. The

34

pressure drop through the test sample was monitored by using a digital pressure gage (Model

DPG409050, Omega Engineering, Sunbury, OH).

Experimental Procedure for High Temperature Tests

The experimental procedure consisted of two main steps i.e. the leakage test, and the forced

convection test. Leakage test was performed prior to forced convection test for every sample.

4.4.1 The Leakage Test

A leakage test was performed on the heat exchanger and the mated fittings and tubes to ensure that

the system did not experience air loss during operation. To prevent leakage through the fittings,

teflon tape was wrapped around their threads before tightening. The leakage test apparatus

consisted of two flow-meters connected upstream and downstream of the heat exchanger. It was

important to have the system under pressure to detect any leaks. Air flowed through the system

while a mixture of soapy water was sprayed on each joint and corners of the heat exchanger and

dedicated fittings. Any leak location was identified by bubble formation at that specific point. The

amount of air going into the system and leaving the system was also measured by flow-meters.

The difference between the two readings gave an estimate of air loss, if any. At low flow rate

there was no leakage observed in the system. As the flow rate increased the estimated that the

leakage through the fittings were less than 2% of the air supplied to the heat exchanger.

35

Figure 4-5: Schematic of the leakage test setup

4.4.2 The Force Convection Test

The experiment was started by initiating the ignition of fuel (𝐶𝐻4) and oxidizer (𝑂2). Prior to

ignition, the convergent section of the test rig was removed to avoid any explosion hazard. The

gas pressures (𝐶𝐻4 ,𝑂2) were set to 50𝑝𝑠𝑖 (344𝑘𝑃𝑎) by adjusting the pressure regulator mounted

on each gas cylinder. Water was circulated through the cooling system around the combustion

chamber by opening the water inlet and outlet valves. Once ignition was achieved the flow rates

of 𝐶𝐻4 and 𝑂2 were gradually increased and kept constant throughout the test. Initially, the flame

appeared outside the combustion chamber, and then propagated back into the combustion chamber

as the gas flow was adjusted. The divergent section was carefully joined to the test section and

insulated at the connection after successful ignition. The hot gases were continuously passed

through the test section, heating the sample that formed the bottom surface of the test chamber,

before exiting into the fume hood. The temperature of the gas entering the test section and the

surface temperatures of the sample were closely monitored using a DAQ (OMB-DAQ-56,

OMEGA ENGINEERING) during heat-up to observe the thermal steady state of the system.

Air in

Air out

Heat Exchanger

Mass flow- meter in Mass flow- meter out

36

Figure 4-6: Flow direction of the gases in hot section and air in cold section

The forced convection experiment was started by introducing controlled airflow into the sample.

A range of air flow rates between 5 to 200SLPM was used for tests, as measured by the in-line

mass flow-meter. The lowest flow rate of 5SLPM corresponded to a flow velocity of 0.12𝑚 𝑠⁄ for

the sample cross-section of 70𝑚𝑚 × 10𝑚𝑚 while the highest flow rate of 200SLMP corresponded

to a flow velocity of ~5𝑚 𝑠⁄ . The surface temperature of the heated surface was monitored

carefully and the air temperature inside the heat exchanger also recorded at five different points.

The bulk temperature of the coolant entering and exiting the system was recorded. The system was

left running state until steady state was achieved, which took approximately 60 to 120 minutes of

operation. Once steady state was achieved, the output of the thermocouples were recorded using a

data acquisition system. Each measurement was recorded, at 15 minutes intervals, for the range of

flowrate between 5 to 200SLPM. The experiment was repeated 3 times to report the final set of

data. The pressure difference across the sample was also recorded using a digital pressure gage

(Model DPG409050, Omega Engineering, Sunbury, OH).

Pressure Drop Apparatus

Figure 4-7 shows the appratus for pressure drop measurements. It consisted of an air supply , a

pressure controller , a flow-meter upstream of the sample and a flow-meter downstream of the

sample. A digital pressure gauge was mounted between the inlet and outlet of the sample.

Compressed air from laborarory was driven through the dedicated tubing by adjusting the globe

Combustion

gas out

Cooling water

in out

Air exiting the heat

exchanger

Air entering the heat

exchanger O2,

CH4

37

valve to control the ammount of air released into the system. A pressure controller was connected

upstream of the flow-meter and the air flow rate through the system was varied from 5-200SLPM.

The air then entered the sample and escaped to the surroundings. Before each experimental run

the set-up was checked for air leaks.

Figure 4-7: Apparatus for pressure drop measurement

Summary

The fabrication of the test rig used to perform high temperature tests on heat exchangers described

in chapter 3 is explained in detail. The test procedure with details of apparatus is discussed. The

pressure drop measurement apparatus and procedure is also briefly mentioned in this chapter.

Air supply

Glo

be v

alv

e

Pressure

Controller

Mass Flow- Meter Mass Flow- Meter

Digital Pressure Gauge

Sample

Air out

38

5 Chapter 5

High Temperature Heat Exchanger Tests

Introduction

This chapter reports the results of an experimental investigation of the heat transfer performance

of thermally sprayed metal foam heat exchangers at high temperatures (~750ºC). Forced

convection experiments were carried out on thermally sprayed and conventional braze heat

exchangers, fabricated from 10 and 40PPI 𝑁𝑖 foam. Nickel foil was brazed to the exterior surface

of 10𝑚𝑚 thick layers of 10 and 40PPI 𝑁𝑖 foam. A plasma torch was used to spray an Inconel

coating on the surface of the foil. A burner test rig was built to produce hot combustion gases that

flowed over exposed face of the heat exchanger. Cooling air flowed through the foam heat

exchanger at rates of up to 200SLPM. Surface temperature and air inlet /exit temperatures were

measured.

The performance of thermally sprayed heat exchangers is compared with conventional brazed heat

exchangers by calculating the heat transferred to the coolant (��), thermal contact resistance

(𝑅"𝑐𝑜𝑛𝑡), and the volumetric heat transfer coefficient (ℎ𝑣). At low flow rates the convective

resistance is large (~4x10-2 𝑚2𝑘 𝑤⁄ ) and the effect of thermal contact resistance is negligible. At

higher flow rates the convective resistance decreases (~2x10-3𝑚2𝐾 𝑤⁄ ) and the lower contact

resistance of the thermally sprayed heat exchanger provides better performance than that of the

brazed heat exchangers. The average heat transfer to air flowing through the foam was 36% higher

for the thermally sprayed heat exchangers than conventional brazed heat exchangers. The

volumetric heat transfer coefficient ℎ𝑣 was determined for both 10 and 40PPI heat exchangers.

Experimental heat transfer coefficients were obtained by varying air velocity between 0.1~5m 𝑠⁄ .

The value of ℎ𝑣 for 40PPI foam heat exchangers was found to be higher than that of 10PPI heat

exchangers. An analytical model was developed assuming local thermal non-equilibrium (LTNE)

39

and predictions from model were found to be in good agreement with experimental results. The

hydraulic characteristics of metal foam are also discussed briefly.

Hydraulic Characteristics

Darcy’s Law [6] predicts that at low flow velocities the pressure drop across porous media is a

linear function of flow velocity. At higher velocities a quadratic term is added to account for the

effect of drag forces on the pressure gradient [25] . The extended Darcy flow model widely used

to model pressure drop through porous media is:

∆𝑃

𝐿=

𝜇

𝐾𝑢𝑎 +

𝜌𝐶𝐹

√𝐾𝑢𝑎

2 (5.2.1)

Where ∆𝑃 is the pressure drop across the sample (𝑁/𝑚2), 𝐿 is the length of the sample (𝑚), 𝜇 is

the dynamic viscosity (𝑘𝑔/𝑚𝑠 ) of the fluid, 𝑢𝑎 and 𝜌 are the velocity (m/s) and density of the

fluid ( 𝑘𝑔/𝑚3) respectively. 𝐾 is the permeability of the foam ( 𝑚2) and 𝐶𝐹 the inertia coefficient.

The last two parameters define the hydraulic characteristics of metal foam. A least squares fit of

Eq. (5.2.1) to experimental pressure drop data gives values of 𝐾 and 𝐶𝐹. Table 1 reports the values

for inertia coefficient and permeability obtained for 10 and 40 PPI nickel foam samples. The

permeability of 40 PPI foam sample is lower than that of the 10 PPI sample, which is due to its

smaller pore size that increases the resistance to flow and caused the inertia coefficient 𝐶𝐹 to be

larger which gives resistance to flow due to drag. Previous results in the literature [40, 69, 70] have

shown similar trends. Some of the results from literature are shown in the table. The results of

pressure drop tests for two heat exchangers are plotted in Figure 5-1. The foam with smaller pore

size and larger pore density generated a larger pressure drop. The results show good agreement

with the reported literature. The details for uncertainty in measurement of permeability and inertia

coefficient can be found in Appendix A.

40

Table 5.1: Hydraulic properties of Ni Foam Sample and comparison with literature

Parameters Foam PPI K (x 10–8) (𝑚2) 𝐶𝐹

Present work Ni 10 7.99 0.0112

Present work Ni 40 1.54 0.0431

Tsolas and Chandra [40] Ni 10 8.83 0.0326

Tsolas and Chandra [40] Ni 40 2.34 0.0640

Bhattacharya et al [23] Al 10 11.00 0.0700

Bhattacharya et al [23] Al 40 5.20 0.0940

Calmidi [20] Al 10 14.90 0.0990

Calmidi [20] Al 40 5.50 0.1010

Figure 5-1: Length normalized pressure drop curves based on 200mm length of 10 and 40PPI nickel foam

heat exchanger versus velocity

41

Pressure drop results for different flow velocities can be non-dimensionalized in terms of the

friction factor . where (𝑑ℎ), the hydraulic diameter of the channel, is defined in terms of the height

(H) and width (W) of the channel:

𝑓 = (∆𝑃

𝐿)

𝑑ℎ

𝜌u𝑎2 (5.2.2)

𝑑ℎ =2 𝐻𝑊

𝐻 + 𝑊 (5.2.3)

Fluid flow velocity is non-dimensionalized as a Reynolds number with the square root of

permeability √𝐾 selected as a characteristic length [71].

𝑅𝑒𝑘 =𝜌𝑢𝑎√𝐾

𝜇 (5.2.4)

Friction factor can be correlated using Darcy number (𝐷𝑎 = 𝐾/𝑑ℎ2) by substituting Eq. (5.2.1) in

(5.2.2);

𝑓 = 1

𝑅𝑒𝑘 𝐷𝑎1/2+

𝐶𝐹

𝐷𝑎1/2 (5.2.5)

Eq. (5.2.5) was fitted to experimental data to give following correlations for 10 and 40PPI foams:

𝑓10 𝐷𝑎1/2 = 1

𝑅𝑒𝑘+ 0.011 (5.2.6)

𝑓40 𝐷𝑎1/2 = 1

𝑅𝑒𝑘+ 0.0431 (5.2.7)

42

Figure 5-2: Friction factor versus Reynolds number for Ni foam from Beavers and Sparrow [69] and Al foam

from Kim et al. [21] from literature is also presented

Figure 5-2 shows that at low Reynolds number 𝑅𝑒𝑘 < 10 the predicted 𝑓𝐷𝑎1/2 values are in good

agreement with the experimental data for 10 and 40PPI foams but at higher flow rates, for 𝑅𝑒𝑘 ≥

10, the experimental values of 10PPI foam show some deviation from predicted values.

Heat Transfer Characteristics

5.3.1 Surface Temperature Behavior and Peclet Number

Heat transfer through the foam depends upon two competing mechanisms: conduction through the

struts and convection through the coolant. The Peclet number (𝑃𝑒) is a non-dimensional number

that compares the magnitude of convection to that of conduction during heat transfer:

𝑃𝑒 =𝑄𝑐𝑜𝑛𝑣

𝑄𝑐𝑜𝑛𝑑 (5.3.1)

43

The heat conduction through a channel with a foam core is given by

𝑄𝑐𝑜𝑛𝑑 = 𝑘𝑠𝐴𝑠∆𝑇

𝐻⁄ |𝐹𝑜𝑎𝑚

= 𝑘𝑠(1 − 휀)𝐻 𝑊 ∆𝑇𝐻⁄ (5.3.2)

where ∆𝑇 is a characteristic temperature difference, 𝑘𝑠 is the thermal conductivity of solid

(𝑊 𝑚 𝐾⁄ ), 𝐴𝑡 = 𝐻 × 𝑊 the cross-sectional area through which conduction is taking place (𝑚2),

𝐴𝑠 = 𝐴𝑡(1 − 휀) is the area of the solid fraction of foam excluding the voids (𝑚2), and 휀 is the

porosity. The channel height (𝐻) is taken as a characteristic length scale (m). The heat transfer rate

due to convection over the same temperature difference ∆𝑇 is given by:

𝑄𝑐𝑜𝑛𝑣 = ��𝑐𝑝,𝑎∆𝑇 (5.3.3)

For a given characteristic temperature ∆𝑇, Eq. (5.3.1) can be written as:

𝑃𝑒 =��𝑐𝑝,𝑎

𝑘𝑠(1 − 휀)𝑊 (5.3.4)

Figure 5-3 shows surface temperature variation of thermally sprayed and conventional brazed 40

PPI heat exchangers at low flow rates of 5 and 10SLPM respectively. The surfaces of both heat

exchangers are heated by hot combustion gases at 750ºC that enter at 𝑋 = 0 and leave at 𝑋 =

200𝑚𝑚 (Figure 5-3). In foam heat exchangers the heat is conducted from the wall through the

struts that act as fins conducting heat from the upper surface to the air flowing through it. When

the air is blown at low flow rates (5-10) SLPM the Peclet number is small (Pe < 1 ) and the heat

that is conducted through the foam is convected away slowly by the fluid, leading to an increase

in temperature. The maximum surface temperature was achieved at approximately 𝑋 =

150𝑚𝑚 and decreased thereafter (Figure 5-3). At low airflow rates a significant portion of the

total heat transfer through the heat exchanger was due to conduction through the metal foam and

Inconel frame to the stainless steel tubing and convergent sections, where it dissipated to the

surrounding air.

As the flow rate was increased to 20SLPM, when Pe~1 , the maximum temperature on the skin

was again achieved at 𝑋 = 150𝑚𝑚 but it becomes constant afterwards and the negative

temperature gradient at the end of the heat exchanger was no longer visible (Figure 5-4). It shows

44

the heat conducted in through the struts is convected away by the coolant and conduction effect at

the exit become small.

At a higher flow rate of 60SLPM ( Figure 5-4) the wall temperature decreases further indicating

higher rates of heat transfer for higher velocities as anticipated in forced convection and the

maximum temperature shifted towards the exit (𝑋 = 200𝑚𝑚). At the highest flow rates

(200SLPM) when 1 < Pe < 10 and convection becomes stronger, entrance and exit effects are

negligible and the temperature variation is nearly linear. The maximum temperature is achieved at

the exit of the heat exchanger (𝑋 = 200𝑚𝑚) ( Figure 5-4) showing that convection is the main

heat transfer mechanism along the length of the heat exchanger and heat conduction is negligible

by comparison.

The graphs for 10 PPI foam heat exchangers at low and high flow rates are given in Appendix B.

Figure 5-5 shows the air temperature behaviour of 40PPI heat exchangers at low flow rates of 5

and 10SLPM. The maximum surface temperature was obtained at approximately 𝑋 = 150𝑚𝑚 and

decreased at the end. For higher flow rates the maximum surface temperature was found at the exit

of the channel (𝑋 = 200𝑚𝑚) (Figure 5-6). The air temperatures followed the similar trend as

observed in surface temperature graphs. Since the heated test section is preceded by the stainless

steel bracket and tubing, the axial conduction in the wall carries significant amount of heat

upstream in the unheated region that causes preheating of the coolant and the initial temperature

of the air measured at the inlet of the test section (𝑋 = 0) increases substantially as indicated in all

air temperature graphs. The air temperature distribution of 10PPI foam heat exchangers exhibited

the similar pattern at low and high flow rates as observed in case of 40PPI heat exchangers. The

graphs for air temperature of 10PPI heat exchangers are given in Appendix B.

45

Figure 5-3: Local wall temperature of 40PPI plasma sprayed and conventional brazed heat exchangers at 5

and 10SLPM (Pe<1)

Figure 5-4: Local wall temperature of 40PPI plasma sprayed and conventional brazed heat exchangers at

20(Pe~1), 60 and 200SLPM (Pe>1)

46

Figure 5-5: Local air temperature of 40PPI plasma sprayed and conventional brazed heat exchangers at 5

and 10SLPM (Pe<1)

Figure 5-6: Local air temperature of 40PPI plasma sprayed and conventional brazed heat exchangers at

20(Pe~1), 60 and 200SLPM (Pe>1)

47

Figure 5-7 shows the cooling air temperature rise (𝑇𝑎𝑜 − 𝑇𝑎𝑖) for both thermally sprayed and

conventional brazed foam heat exchangers as a function of Peclet number. At low Peclet number

(Pe < 1 ) the temperature difference tends to increase, which is due to the effect of axial

conduction that cannot be ignored at low flow rates for higher temperature applications. The air

temperature difference eventually decreases as a linear function of Peclet number after reaching a

threshold. The effect of axial conduction may be neglected once a sufficiently large Peclet number

is achieved.

Figure 5-7: Air temperature difference of 10 and 40PPI plasma sprayed and conventional brazed heat

exchangers at different Pe number

5.3.2 Heat transferred to the Air and Performance Comparison

The heat generated by the combustor was 490𝑊, which is indicated by the horizontal line in Figure

5-8. An energy balance gives the heat transfer rate to the air flowing through the heat exchanger:

�� = ��𝑎 𝐶𝑝,𝑎(𝑇 𝑎,𝑜 − 𝑇 𝑎,𝑖) (5.3.5)

48

where, ��𝑎 is the air mass flow rate (𝑘𝑔 𝑠⁄ ), 𝐶𝑝,𝑎 is the specific heat capacity of air (𝐽 𝑘𝑔𝐾⁄ ), and

𝑇 𝑎,𝑜 and 𝑇 𝑎,𝑖 the temperatures of the air leaving and entering the heat exchanger. Figure 5-8 shows

the energy transferred from the hot gases to the cooling air passing through the heat exchanger as

a function of air flow rate. Results are shown for both thermally sprayed and conventional brazed

heat exchangers made of 10 and 40PPI foam. Data for heat transfer to an empty channel with the

same dimensions is also shown for comparison. All heat exchangers show higher heat transfer

compared to an empty channel.

The best performance was obtained from the 40PPI thermally sprayed heat exchanger, which

transferred a maximum of approximately 370𝑊 of heat to the cold air out of the 490𝑊 supplied

to it. It was estimated that approximately 10% of the input heat was lost to the surroundings through

the insulation surrounding the test duct. The plasma sprayed heat exchangers show significantly

higher heat transfer than those made from the conventional brazed heat exchangers. On average,

the 40PPI thermally sprayed heat exchanger outperforms the 40PPI conventional brazed heat

exchanger by a 36% and 10PPI plasma sprayed heat exchanger outperforms the 10PPI

conventional brazed heat exchanger by 32% (Figure 5-9). In general, the 40PPI foam heat

exchangers show higher heat transfer than those made from 10PPI foam. Compared to the 10PPI

plasma sprayed heat exchanger, the 40PPI plasma sprayed heat exchanger shows an average

enhancement of 82% in heat transfer (Figure 5-10). The latter shows an increase of 93% at

maximum flow rate of 180SLPM then the former.

It is seen from Figure 5-8 that the heat transfer increased rapidly as the mass flow rate increased

to 60SLPM, and then began to level out. As the airflow velocity through the foam is increased the

convective heat transfer coefficient increases, enhancing heat transfer. However, as the thermal

resistance on the cold side of the heat exchanger is reduced that on the hot side becomes more

dominant. The effect of increasing the heat transfer rate through the foam therefore has a

diminishing effect on the overall heat transfer which is limited by the hot side thermal resistance.

The heat exchange can be further improved by adding the fins on the top surface of the heat

exchanger, and in order to show that a simple experiment was performed on a sample with 40PPI

conventional brazed heat exchanger with fins installed on the top surface facing hot gases (chapter

3 Figure 3-7). Figure 5-11 shows the comparison of 40PPI brazed foam heat exchangers with and

without fins. It can be found that heat transfer is increased by 17% by adding the fins on the top

49

surface of the heat exchangers. Fin geometry, fin height, fin spacing etc. are some factors that play

important role in heat transfer. Since the primary focus of the thesis was to study the heat transfer

through metal foam, fin heat exchangers were not studied further.

Figure 5-8: Heat transferred to air through 10 and 40PPI plasma sprayed and conventional brazed heat

exchangers at different flow rate

50

Figure 5-9: Comparison between 10 and 40PPI thermally sprayed and conventional brazed heat exchangers

Figure 5-10: Comparison between 40 and 10PPI thermally sprayed heat exchangers and empty channel

51

Figure 5-11: Comparison between 40PPI conventional braze heat exchangers with fin and without fin

The performance comparison of the 10 and 40PPI thermally sprayed heat exchangers is given in

Figure 5-12. As the pressure drop increases the heat transfer rate grows continuously for the 40

PPI heat exchangers. At a flow rate of 140SLPM the 10PPI foam has a maximum pressure drop

of 275𝑃𝑎 corresponding to a heat transfer rate of 187𝑊, while the 40PPI heat exchangers reach a

maximum pressure drop of 1700𝑃𝑎 at 350W. The increase in heat transfer rate results in a pressure

drop penalty, so there is always a trade-off between pressure drop and heat transfer.

52

Figure 5-12: Performance comparison between 10 and 40PPI plasma sprayed heat exchangers

Figure 5-13: (a) Plasma sprayed (b) conventional brazed (c) conventional brazed with fin heat exchangers

(b)

(c)

(a)

53

5.3.3 Contact Resistance and Air Side Resistance

In a foam heat exchanger heat is conducted through the shell to the foam struts and from their

surface it is convected away by the fluid .The connection between the shell and foam struts is

extremely important since imperfect contact creates a thermal contact resistance [66] that limits

heat transfer. Reducing the contact resistance between the shell and foam can significantly improve

heat transfer [44, 72].

The overall heat transfer coefficient (𝑈𝑜,𝑊 𝑚 2𝐾⁄ ) between the heated wall of the heat exchanger

and the cold air stream can be defined as:

𝑈𝑜 =��𝑐

𝐴𝑏∆𝑇𝑙𝑚 (5.3.6)

where 𝐴𝑏 = 𝐿 × 𝑊 is the area of the heat exchanger wall (𝑚2) and ∆𝑇𝑙𝑚, the logarithmic mean

temperature difference (LMTD), calculated between the wall and air is defined as

∆𝑇𝑙𝑚 =(𝑇𝑠,𝑖 − 𝑇𝑎,𝑖) − (𝑇𝑠,𝑜 − 𝑇𝑎,𝑜)

ln(𝑇𝑠,𝑖 − 𝑇𝑎,𝑖)

(𝑇𝑠,𝑜 − 𝑇𝑎,𝑜)

(5.3.7)

where 𝑇 𝑠,𝑖 and 𝑇 𝑠,𝑜 are the wall temperatures at the inlet and outlet of the heat exchanger base

plate. Figure 5-14 shows the variation of 𝑈𝑜 for the 40PPI foam heat exchangers and Figure 5-15

shows it for 10PPI foam heat exchangers. In both the cases the plasma sprayed heat exchangers

had higher heat transfer coefficients than the conventional brazed heat exchangers.

54

Figure 5-14: Overall heat transfer coefficient for 40PPI heat exchangers

Figure 5-15: Overall heat transfer coefficient for 10PPI heat exchangers

55

The heat transfer path from the hot surface to the cold air can be represented by a simple resistance

network of three resistances in series (Figure 5-16); the conduction resistance of the surface brazed

to or sprayed on the foam (𝑅"𝑐𝑜𝑛𝑑); the contact resistance between the surface and the

foam (𝑅"𝑐𝑜𝑛𝑡); and the convective resistance through the foam (𝑅"𝑐𝑜𝑛𝑣). Summing these three

resistances gives the total resistance 𝑅"𝑡𝑜𝑡 per unit area of the network, which is the reciprocal of

the overall heat transfer coefficient.

𝑅"𝑡𝑜𝑡 =1

𝑈𝑜 = 𝑅"𝑐𝑜𝑛𝑣 + 𝑅"𝑐𝑜𝑛𝑡 + 𝑅"𝑐𝑜𝑛𝑑 (5.3.8)

The thermal resistance per unit area of a flat plate is 𝑅"𝑐𝑜𝑛𝑑 = 𝑡/𝑘, where 𝑡 and 𝑘 are the thickness

(m) and thermal conductivity (𝑊 𝑚 𝐾⁄ ), of the material. Previous measurements of heat transfer

in foams [38] have shown that the convective heat transfer coefficient for air flow through foam

is of order of magnitude ℎ𝑐~102 𝑊 𝑚 2𝐾⁄ , which means that 𝑅"𝑐𝑜𝑛𝑣 = 1/ℎ𝑐 is typically ~10-2

𝑚2𝐾 𝑊⁄ . 𝑅"𝑐𝑜𝑛𝑑 which is 5.26 x 10-5 𝑚2𝐾 𝑊⁄ for conventional brazed heat exchangers and

4.44x10-6 𝑚2𝐾 𝑊⁄ for plasma sprayed heat exchangers, is therefore much smaller than 𝑅"𝑐𝑜𝑛𝑣 and

can be neglected in Eq. (5.3.8). If we further assume that 𝑅"𝑐𝑜𝑛𝑡 <<𝑅"𝑐𝑜𝑛𝑣 for the case of the

plasma spray coated foam, we can simplify Eq. (5.3.8) to:

𝑅"𝑐𝑜𝑛𝑣 =1

𝑈𝑜 (5.3.9)

Figure 5-16: Resistance network from coating to foam

56

Figure 5-17 and Figure 5-18 show the variation of 𝑅"𝑐𝑜𝑛𝑣 with air velocity for the both plasma

sprayed and conventional brazed heat exchangers with air velocity through the foam. At low

velocity (<1𝑚 𝑠⁄ ) the convective resistance was as high as 4x10-2 𝑚2𝐾 𝑊⁄ , but as the velocity

increased it decreased to a value of approximately 2x10-3 𝑚2𝐾 𝑊⁄ and did not change significantly

with velocity.

Figure 5-17: Air side resistance of brazed foam heat exchanger

57

Figure 5-18: Air side resistance of plasma sprayed foam heat exchanger

Assuming that 𝑅"𝑐𝑜𝑛𝑣 is a function of the foam geometry, and is therefore the same for both plasma

sprayed and conventional brazed heat exchangers, 𝑅"𝑐𝑜𝑛𝑡 can be calculated for the brazed heat

exchangers from Eq. (5.3.8). As shown in Figure 5-19 the apparent contact resistance is higher at

low velocity which is due to the high conduction at low flow rates. As the velocity increases contact

resistance becomes constant. The trend is similar for 40 and 10PPI foam heat exchangers.

58

Figure 5-19: Variation of contact resistance with air velocity for 10 and 40PPI heat exchangers

The contact resistance of 10PPI foam heat exchanger was approximately 50% higher than that for

40PPI heat exchanger, perhaps due to difficulty in evenly brazing the all of the struts of the 10PPI

foam to the Inconel sheet. At low air velocity (<1𝑚 𝑠⁄ ) 𝑅"𝑐𝑜𝑛𝑣 is large (~4x10-2 𝑚2𝐾 𝑊⁄ ) and

therefore differences in the values of 𝑅"𝑐𝑜𝑛𝑡, which is two orders of magnitude smaller, between

the conventional brazed and plasma sprayed heat exchangers do not significantly influence heat

transfer (Figure 5-17 and Figure 5-18). However, as air velocity increases and 𝑅"𝑐𝑜𝑛𝑣 decreases to

2x10-3 𝑚2𝐾 𝑊⁄ , the lower contact resistance of the plasma sprayed heat exchanger produces a

significant improvement in heat transfer. This resulted in a higher surface temperature of the

plasma sprayed heat exchanger compared to the conventional brazed heat exchanger and also a

higher heat transfer to the air flowing through the heat exchangers.

59

5.3.4 Volumetric Heat Transfer Coefficient

Heat transfer coefficients for heat exchanger applications are typically calculated for convective

heat transfer between the heat exchanger wall and the fluid. When considering metal foam heat

exchangers it is also necessary to know heat transfer coefficients between the fluid stream and the

solid matrix of the porous foam. Two type of heat transfer coefficients are typically defined: the

interstitial heat transfer coefficient (ℎ𝑠𝑓) based on the internal surface area of the foam; and the

volumetric heat transfer coefficient (ℎ𝑣), based on the volume of the foam.

The volumetric heat exchanger coefficient ℎ𝑣( 𝑊/𝑚3𝑘) is defined as

ℎ𝑣 =��𝑐

∆𝑇𝑙𝑚∀ (5.3.10)

where ∀ is the volume of the foam (𝑚3) . The interstitial heat transfer coefficient

ℎ𝑠𝑓 =��𝑐

∆𝑇𝑙𝑚𝐴𝑠𝑓 (5.3.11)

Where Asf is the total internal area of contact between the solid and fluid in the foam (𝑚2). Taking

the ratio of the two coefficients,

ℎ𝑣

ℎ𝑠𝑓=

𝐴𝑠𝑓

∀= 𝛼𝑠𝑓 (5.3.12)

where 𝛼𝑠𝑓( 𝑚2/𝑚3) is the surface area density of the foam. Details of the derivation are given in

Appendix C.

Figure 5-20 shows the variation of ℎ𝑠𝑓 with increasing air velocity for both 10 and 40PPI foams.

The heat transfer coefficient is higher at lower pore density with 10PPI foam having a heat transfer

coefficient up to 3.5 times higher than 40PPI foam. This increase in ℎ𝑠𝑓 can be attributed to the

larger pore size (𝑑𝑝10 𝑑𝑝40⁄ = 3.99) and fiber diameter (𝑑𝑓10 𝑑𝑓40⁄ = 3.49) of 10PPI foam.

Figure 5-21 shows a comparison with published values in the literature for the ratio of ℎ𝑠𝑓 for

10PPI foams to those for 40PPI foams of both nickel and aluminum.

60

Figure 5-20: Variation of interstitial ( hsf) heat transfer coefficient with air velocity for 10 and 40PPI heat

exchangers

Figure 5-21: Ratio of interstitial ( hsf) heat transfer coefficient of 10PPI and 40PPI. Comparison with

literature (Tsolas and Chandra [40] and Mancin et al.[38]) is also shown

61

Figure 5-22: Variation of volumetric heat transfer coefficient with air velocity for 10 and 40PPI foams

Figure 5-22 shows volumetric heat transfer coefficient of thermally sprayed and brazed foam heat

exchangers. It is observed that at low velocity, two curves (10 and 40PPI) collapsed onto a single

curve, but, as the velocity increased; the curve for 10PPI foam gradually deviated from 40 PPI

foam. None of the curves appears to level-off indicating that the heat transfer coefficient may

increase further by increasing the velocity. The deviation in curves for two different pore densities

(10 and 40PPI) can be addressed by analysing the foam parameters. As discussed earlier the 10PPI

has approximately 4 times higher 𝑑𝑝 , yet only has a surface area density of 400 𝑚2/𝑚3 owing to

the larger pore diameter, which decrease the pores per linear inch and thereby reduces the surface

area per unit volume. That is why the volumetric heat transfer coefficient of 40 PPI foam is higher

than 10 PPI foam since it has 4 times higher surface area density, 1629 𝑚2/𝑚3 , comparatively

10PPI foam. This shows that pore size is an important parameter as it affects the surface area

density of the foam which in turns affects the surface area available for heat transfer. The

dependence of volumetric heat transfer coefficient on pore diameter has been reported in the

literature [16, 24, 31].

62

The previous studies related to metal foam are performed mostly on aluminum, copper, FeCrAIY

and ceramic foams while no information on 𝑁𝑖 foam is available. Figure 5-23 and Figure 5-24

show a comparison of volumetric heat transfer coefficient with previous study [40] on 𝑁𝑖 foam

for two different pore densities. The comparison of present study with the previous study is in

satisfactory agreement even though the trend seems to be inconsistent between the two studies. In

both cases i.e. 10PPI foam (Figure 5-23) and 40PPI foam (Figure 5-24) the heat transfer coefficient

for [40] reached a maximum value at low velocity and steadily levels-off thereafter unlike the

present study. It is further seen that the results of the present study have same order of magnitude

as shown by [24, 31].

Figure 5-23: Comparison of volumetric heat transfer coefficient for 10PPI heat exchangers with literature

[40]

63

Figure 5-24: Comparison of volumetric heat transfer coefficient for 40PPI heat exchangers with literature

[40]

5.3.5 Nusselt Number

Selection of hydraulic diameter as a characteristic length is not a good estimate to find Nusselt

number since the foam structure consists of numerous interconnected tortuous passages. Therefore,

pore diameter 𝑑𝑝 is a reasonable choice for the characteristic length to determine the Nusselt

number and Reynolds number in porous structure.

𝑁𝑢𝑑𝑝 =ℎ𝑣𝑑𝑝

2

𝑘𝑎 (5.3.13)

𝑅𝑒𝑑𝑝 =𝑢𝑎𝑑𝑝

𝜈 (5.3.14)

Nusselt number calculated based on pore diameter is used to perform a comprehensive comparison

of present study with the available literature. Our results are in good agreement with the available

literature. The discrepancies can be explained based on reasonable arguments.

64

As shown in Figure 5-25 the results of Younis and Viskanta [16] and Hwang et al. [24] are on the

higher end. The main reason is the experimental technique used to calculate volumetric heat

transfer coefficient. Since these two authors used a transient analysis method their results are

higher than all other studies as the latter are based on using a steady-state method. The steady-state

method, generally, under predicts the results yet is more practical to use [31]. In comparison with

the study of [16] although the pore diameters are approximately same as used by us, our samples

have 7.4% higher porosity which can be a reason for lower heat transfer coefficient besides the

steady-state measurement technique. Hwang et al. [24] used approximately the same foam

parameters but observed higher 𝑁𝑢 because of the transient measurement technique. Our results

for ( 𝑑𝑝=2.77𝑚𝑚 and porosity~0.94) are in good agreement with Calmidi and Mahajan [19] and

Fuller et al.[31] . Calmidi and Mahajan[19] used the 𝑑𝑝 ranging from 2.58-2.9 𝑚𝑚 and porosity

ranging from 0.90 to o.95 for 𝐴𝑙 foams. Our results for approximately the same foam parameters

(𝑑𝑝=2.77 𝑚𝑚 and porosity~0.94), are slightly higher than his measurements. This difference can

be attributed to the size effects as our samples have about three times less height than theirs and

experimental losses will be larger.

Figure 5-25: Comparison with literature. Nusselt number based on pore diameter vs Reynold number based

on pore diameter

65

Analytical Model

Heat transfer in porous media can be studied analytically using one of two models: the one-

equation model that assumes that there is high convective heat transfer between the porous solid

and gas and that the temperature difference between them is negligible; or the two-equation model

that calculates the temperature distribution in each phase separately. The one equation mode

assumes local thermal equilibrium (LTE) so that:

⟨𝑇𝑠⟩ = ⟨𝑇𝑓⟩ = ⟨𝑇⟩ (5.4.1)

Alternately, the two-equation model assumes that significant temperature difference exists

between the two phases so that there is local thermal non-equilibrium (LTNE). For heat exchanger

applications, where the difference between the thermal conductivities of solid and fluid is

significant, assuming LTNE is more appropriate. However, since this requires information about

the effective thermal conductivities of the individual phases and the interfacial heat transfer

coefficient between them, which requires experimentation, the one-equation model has been used

in many studies e.g. [51-56] even though it was not really appropriate [54-56] .

A schematic diagram of the side view of the foam core heat exchanger is shown in Figure 5-26.

The heat exchanger, with height 𝐻, is initially at room temperature and then exposed to the stream

of hot combustion gases. The top surface of the metal foam sample is in contact with gases that

enter the test section at 750ºC. The bottom surface is insulated. Air at room temperature enters the

metal foam with varying flow rates and carries heat from the heated surface. The velocity of the

flow is assumed to be uniform and thermo-physical properties are assumed to be constant. The

coordinate system used is shown in the figure with the direction of flow parallel to the x-axis.

The surface temperature along the axial direction is variable and the uniform heat flux is assumed

to be applied to the wall. The surface temperature of the heat exchanger is experimentally

determined at five axial locations. It is assumed that the surface is divided into a large number of

sections to which we apply the superposition theorem. Heat flux is calculated from the measured

temperature profile, which is then averaged and considered constant on the wall.

66

Figure 5-26: Schematic of the analytical model for foam heat exchanger

The analysis is based on the assumption that the air is not in the thermal equilibrium with the solid

struts of the metal foam (LTNE). Therefore two separate energy equations are required to describe

the fluid and solid medium.

Energy equation for the fluid flowing through the metal foam:

𝜌𝑓 𝐶𝑃𝑓 𝑢𝐷

𝜕⟨𝑇⟩𝑓

𝜕𝑥=

𝜕

𝜕𝑦[𝑘𝑓𝑒

𝜕⟨𝑇⟩𝑓

𝜕𝑦] − ℎ𝑣(⟨𝑇⟩𝑓 − ⟨𝑇⟩𝑠) (5.4.2)

Energy equation for the solid part of the metal foam:

0 =𝜕

𝜕𝑦[𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦] − ℎ𝑣(⟨𝑇⟩𝑠 − ⟨𝑇⟩𝑓) (5.4.3)

Where, ′⟨ ⟩′ symbol refers to the volume average of the quantity. The physical aspects of

averaging are discussed in details in [48, 71]. 𝑢𝐷 is the Darcian velocity such that 𝑢𝐷 = 휀 𝑢𝑝 where

𝑢𝑝 is the velocity at pore level. ⟨𝑇⟩𝑓 is the fluid temperature and ⟨𝑇⟩𝑠 is solid temperature. 𝑘𝑓𝑒

and 𝑘𝑠𝑒 are the thermal conductivities of fluid and solid respectively.

Boundary Conditions

(i) The total heat applied to the system is constant. q′′ is the heat flux applied to the wall

q′′ = [𝑘𝑓𝑒 𝜕⟨𝑇⟩𝑓

𝜕𝑦 |

𝑦=𝐻

+ 𝑘𝑠𝑒 𝜕⟨𝑇⟩𝑠

𝜕𝑦 |

𝑦=𝐻

] = 𝐶𝑜𝑛𝑠𝑡 (5.4.4)

(ii) The bottom surface (𝑦 = 0) is insulated so that:

��′′ = 𝒄𝒐𝒏𝒔𝒕.

⬚

��′′ = 𝟎 (𝐚𝐝𝐢𝐚𝐛𝐚𝐭𝐢𝐜)

Ni Foam Air out Air in

x

y H −𝒌

𝝏𝑻

𝝏𝒚 𝒚=𝑯

x

y

67

𝜕𝑇𝑓

𝜕𝑦 |

𝑦=0=

𝜕𝑇𝑠

𝜕𝑦

𝑦=0= 0 (5.4.5)

Adding Eq. (5.4.2) and Eq. (5.4.3)

𝜌𝑓 𝐶𝑃𝑓 𝑢𝐷

𝜕⟨𝑇⟩𝑓

𝜕𝑥=

𝜕


𝜕⟨𝑇⟩𝑓

𝜕𝑦+ 𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦] (5.4.6)

Integrating Eq. (5.4.6) over y (from 0 to H):

𝜕

𝜕𝑥∫ 𝜌𝑓 𝐶𝑃𝑓 𝑢𝐷 ⟨𝑇⟩𝑓𝑑𝑦

𝐻

0

= 𝑘𝑓𝑒

𝜕⟨𝑇⟩𝑓

𝜕𝑦 |

𝑦=𝐻+ 𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦 |

𝑦=𝐻− 𝑘𝑓𝑒

𝜕⟨𝑇⟩𝑓

𝜕𝑦 |

𝑦=0

− 𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦 |

𝑦=0

(5.4.7)

Where LHS of Eq. (5.4.7)

∫ 𝜌𝑓 𝐶𝑃𝑓 𝑢𝐷 ⟨𝑇⟩𝑓𝑑𝑦𝐻

0

= 𝜌𝑓 𝐶𝑃𝑓𝑉 ⟨𝑇⟩𝐵𝐻 (5.4.8)

Where, ⟨𝑇⟩𝐵 is the bulk mean temperature of the fluid across the channel cross section at each

point along the length. Eq. (5.4.8) shows the definition of bulk temperature .Finally applying the

boundary conditions Eq. (5.4.4) and Eq. (5.4.5) in Eq. (5.4.7)

𝜌𝑓 𝐶𝑃𝑓𝑉 𝐻𝜕⟨𝑇⟩𝐵

𝜕𝑥= q′′ (5.4.9)

And the bulk temperature variation along the axial direction is:

68

𝜕⟨𝑇⟩𝐵

𝜕𝑥=

𝜕⟨𝑇⟩𝑠

𝜕𝑥=

𝜕⟨𝑇⟩𝑓

𝜕𝑥=

q′′

𝜌𝑓 𝐶𝑃𝑓𝑉𝐻=

4q′′

𝜌𝑓 𝐶𝑃𝑓𝑉𝐷ℎ (5.4.10)

where 𝐷ℎ = 4𝐻(hydraulic diameter for parallel plate). The temperature gradients in Eq. (5.4.10)

are independent of position, implying that they are constant and the same for both fluid and solid

phases. The RHS of the equation shows that the axial temperature gradient is reduced to a constant

by applying boundary conditions Eq. (5.4.4) and Eq. (5.4.5).

Substituting Eq. (5.4.10) in Eq. (5.4.6)

𝑢𝐷

𝑉

q′′

𝐻=

𝜕


𝜕⟨𝑇⟩𝑓

𝜕𝑦+ 𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦] (5.4.11)

Considering 𝑢𝐷 𝑉 = 1⁄ for uniform velocity profile (inside the channel filled with foam) and

integrating Eq. (5.4.11) (from 0 to y):

q′′

𝐻(𝑦 − 0) = 𝑘𝑓𝑒

𝜕⟨𝑇⟩𝑓

𝜕𝑦|𝑦

+ 𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦|𝑦

− 𝑘𝑓𝑒

𝜕⟨𝑇⟩𝑓

𝜕𝑦 |

𝑦=0− 𝑘𝑠𝑒

𝜕⟨𝑇⟩𝑠

𝜕𝑦 |

𝑦=0 (5.4.12)

Applying boundary condition Eq. (5.4.5) and integrating again over y (from y to H):

q′′

2𝐻(𝐻2 − 𝑦2) = 𝑘𝑓𝑒 (⟨𝑇⟩𝑓|

𝑦=𝐻− ⟨𝑇⟩ 𝑓|

𝑦) + 𝑘𝑠𝑒 (⟨𝑇⟩𝑠|𝑦=𝐻 − ⟨𝑇⟩𝑠|𝑦)

= 𝑘𝑓𝑒 (𝑇𝑤 + ⟨𝑇⟩𝑓) + 𝑘𝑠𝑒 (𝑇

𝑤 − ⟨𝑇⟩𝑠)

(5.4.13)

(iii) Where 𝑇𝑤 is the wall temperature, temperature at the interface between porous medium

and solid wall

⟨𝑇⟩𝑠|𝑦=𝐻 = 𝑇𝑤 ; ⟨𝑇⟩𝑓|𝑦=𝐻

= 𝑇𝑤 (5.4.14)

69

Rearranging Eq. (5.4.13) based on ⟨𝑇⟩𝑓 :

⟨𝑇⟩𝑓 = (𝑇𝑤) −𝑘𝑠𝑒

𝑘𝑓𝑒

(⟨𝑇⟩𝑠 − 𝑇𝑤) − q

′′

2𝐻 𝑘𝑓𝑒

(𝐻2 − 𝑦2) (5.4.15)

Now substituting Eq. (5.4.15) in Eq. (5.4.3)

0 =𝜕


𝜕⟨𝑇⟩𝑠

𝜕𝑦] − ℎ𝑣⟨𝑇⟩𝑠 + ℎ𝑣𝑇𝑤 −

𝑘𝑠𝑒 ℎ𝑣

𝑘𝑓𝑒

(⟨𝑇⟩𝑠 − 𝑇𝑤)

−q

′′ℎ𝑣

2𝐻 𝑘𝑓𝑒

(𝐻2 − 𝑦2)

(5.4.16)

Changing variable from ⟨𝑇⟩𝑠 to ⟨𝑇⟩𝑠 − 𝑇𝑤

𝜕


𝜕(⟨𝑇⟩𝑠 − 𝑇𝑤)

𝜕𝑦] −

𝑘𝑠𝑒 ℎ𝑣

𝑘𝑓𝑒

(⟨𝑇⟩𝑠 − 𝑇𝑤) − ℎ𝑣(⟨𝑇⟩𝑠 − 𝑇𝑤)

= q

′′ℎ𝑣

𝑘𝑓𝑒

(𝐻2 − 𝑦2)

2𝐻

(5.4.17)

Further simplification gives:

𝜕


𝜕(⟨𝑇⟩𝑠 − 𝑇𝑤)

𝜕𝑦] −

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )

𝑘𝑓𝑒 ℎ𝑣(⟨𝑇⟩𝑠 − 𝑇𝑤) =

q′′ℎ𝑣

𝑘𝑓𝑒

(𝐻2 − 𝑦2)

2𝐻 (5.4.18)

It should be noted that ⟨𝑇⟩𝑠 − 𝑇𝑤 is a function of y since;

𝜕(⟨𝑇⟩𝑠 − 𝑇𝑤)

𝜕𝑥=

𝜕⟨𝑇⟩𝑠

𝜕𝑥−

𝜕𝑇𝑤

𝜕𝑥=

q′′

𝜌𝑓 𝐶𝑃𝑓 𝑢𝐷 𝐻−

q′′

𝜌𝑓 𝐶𝑃𝑓 𝑢𝐷 𝐻= 0 (5.4.19)

There is no x functionality in subtraction of the two slopes

70

𝑘𝑠𝑒

𝜕2(⟨𝑇⟩𝑠 − 𝑇𝑤)

𝜕𝑦2−


𝑘𝑓𝑒 ℎ𝑣(⟨𝑇⟩𝑠 − 𝑇𝑤) =

q′′ℎ𝑣

𝑘𝑓𝑒

(𝐻2 − 𝑦2)

2𝐻 (5.4.20)

Eq. (5.4.20) is a 2nd order ODE with constant coefficients. To simplify the notation, we set:

𝑘𝑠𝑒 = 𝛼 (𝑘𝑠𝑒 + 𝑘𝑓𝑒 )

𝑘𝑓𝑒 ℎ𝑣 = 𝛽

q′′ℎ𝑣

𝑘𝑓𝑒

(𝐻2 − 𝑦2)

2𝐻= 𝛾 (5.4.21)

The solution for the homogenous part is:

𝑍 = ⟨𝑇⟩𝑠 − 𝑇𝑤 𝛼𝑚2 − 𝛽 = 0 𝑚 = ±√ 𝛽

𝛼

(5.4.22)

𝛼 𝑍′′1 − 𝛽𝑍1 = 0

→ 𝑍1 = 𝐶1 𝑒

√ 𝛽

𝛼 𝑦

+ 𝐶2 𝑒−√

𝛽

𝛼 𝑦

Particular solution is in the form of 2nd order ODE

𝑍2 = 𝐴𝑦2 + 𝐵𝑦 + 𝐶

𝑍′2 = 2𝐴𝑦 + 𝐵

𝑍′′2 = 2𝐴

(5.4.23)


𝑘𝑠𝑒 (2𝐴) − (𝑘𝑠𝑒 + 𝑘𝑓𝑒 )

𝑘𝑓𝑒 ℎ𝑣(𝐴𝑦2 + 𝐵𝑦 + 𝐶) =

q′′ℎ𝑣

𝑘𝑓𝑒

(𝐻2 − 𝑦2)

2𝐻 (5.4.24)

The coefficients of Eq. (5.4.23)

71

B=0

(5.4.25)

− (𝑘𝑠𝑒 + 𝑘𝑓𝑒 )

𝑘𝑓𝑒 ℎ𝑣𝐴 =

− q′′ ℎ𝑣

2𝐻 𝑘𝑓𝑒 → 𝐴 =

q′′

2𝐻 (𝑘𝑠𝑒 + 𝑘𝑓𝑒 )

𝑘𝑠𝑒

2 q′′

2𝐻 (𝑘𝑠𝑒 + 𝑘𝑓𝑒 )−

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )ℎ𝑣 𝐶

𝑘𝑓𝑒 =

q′′ℎ𝑣

𝑘𝑓𝑒

𝐻

2 →

𝐶 =(𝑘𝑠𝑒 )(𝑘𝑓𝑒 )

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )2 (

q′′

ℎ𝑣𝐻 ) −

q′′

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 ) 𝐻

2

The final solution of Eq. (5.4.20) after simplification is

⟨𝑇⟩𝑠 − 𝑇𝑤 = 𝐶1 𝑒√ 𝛽

𝛼 𝑦

+ 𝐶2 𝑒−√ 𝛽

𝛼 𝑦

+q

′′

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 ) (

𝑦2 − 𝐻2

2𝐻)

+(𝑘𝑠𝑒 )(𝑘𝑓𝑒 )

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )2 (

q′′

ℎ𝑣𝐻 )

(5.4.26)


⟨𝑇⟩𝑓 − 𝑇𝑤 = −𝑘𝑠𝑒

𝑘𝑓𝑒 [𝐶1 𝑒

√ 𝛽 𝛼

𝑦+ 𝐶2 𝑒

−√ 𝛽 𝛼

𝑦] −

q′′


𝐻2 − 𝑦2

2𝐻)

− (𝑘𝑠𝑒

𝑘𝑠𝑒 + 𝑘𝑓𝑒 )

2

(q

′′

ℎ𝑣𝐻 )

(5.4.27)

Appling boundary condition, Eq. (5.4.15) and simplification (𝐶1 = 𝐶2 = 𝐶):

⟨𝑇⟩𝑠 − 𝑇𝑤 = 𝐶 (𝑒√ 𝛽

𝛼 𝑦

+ 𝑒−√ 𝛽

𝛼 𝑦

) −q

′′

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )(𝐻2 − 𝑦2

2𝐻)


(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )2

q′′

ℎ𝑣𝐻

(5.4.28)

72

⟨𝑇⟩𝑠 − 𝑇𝑤 = 2𝐶 𝑐𝑜𝑠 ℎ √ 𝛽

𝛼𝑦 −

q′′


2𝐻)



q′′

ℎ𝑣𝐻

(5.4.29)

Eq. (5.4.29) is rearranged form of Eq. (5.4.29)

⟨𝑇⟩𝑓 − 𝑇𝑤 = −𝑘𝑠𝑒

𝑘𝑓𝑒 2𝐶 𝑐𝑜𝑠 ℎ √

𝛽

𝛼𝑦 −

q′′


𝐻2 − 𝑦2

2𝐻)

− (𝑘𝑠𝑒


2

(q

′′

ℎ𝑣𝐻 )

(5.4.30)

Considering the condition ⟨𝑇⟩𝑠|𝑦=𝐻 = 𝑇𝑤 put y=H in equation Eq. (5.4.28) and Eq. (5.4.29)

0 = 2𝐶 𝑐𝑜𝑠 ℎ √ 𝛽

𝛼𝐻 +

(𝑘𝑠𝑒 )(𝑘𝑓𝑒 )


q′′

ℎ𝑣𝐻 (5.4.31)

𝐶 =1

2 𝑐𝑜𝑠 ℎ√ 𝛽 𝛼 𝐻

−(𝑘𝑠𝑒 )(𝑘𝑓𝑒 )


q′′

ℎ𝑣𝐻

(5.4.32)

Sub C from Eq. (5.4.31)into Eq. (5.4.29) for ⟨𝑇⟩𝑠 − 𝑇𝑤

⟨𝑇⟩𝑠 − 𝑇𝑤 =

(

1 −𝑐𝑜𝑠 ℎ √ 𝛽

𝛼 𝑦

𝑐𝑜𝑠 ℎ √ 𝛽 𝛼 𝐻)

{(𝑘𝑠𝑒 )(𝑘𝑓𝑒 )


q′′

ℎ𝑣𝐻 }

−q

′′


2𝐻)

(5.4.33)

73

Substituting C into Eq.(5.4.30) for ⟨𝑇⟩𝑓 − 𝑇𝑤

⟨𝑇⟩𝑓 − 𝑇𝑤 =

(

𝑐𝑜𝑠 ℎ √ 𝛽

𝛼 𝑦


{−𝑘𝑠𝑒

𝑘𝑓𝑒

q′′

ℎ𝑣𝐻 } − (

𝑘𝑠𝑒


2

(q

′′

ℎ𝑣𝐻 )

−q

′′


𝐻2 − 𝑦2

2𝐻)

(5.4.34)

⟨𝑇⟩𝑓 − 𝑇𝑤 =

(


𝛼 𝑦

𝑐𝑜𝑠 ℎ √ 𝛽 𝛼 𝐻

− 1

)

(𝑘𝑠𝑒


2

(q

′′

ℎ𝑣𝐻 )

−

{

𝑘𝑠𝑒

(𝑘𝑠𝑒 + 𝑘𝑓𝑒 )(


𝛼 𝑦


− 1

)

+ 1

}

−q

′′


𝐻2 − 𝑦2

2𝐻)

(5.4.35)

To summarize:

⟨𝑇⟩𝑓 − 𝑇𝑤 = 𝑘𝑠𝑒



𝛼 𝑦


− 1

)

(𝑘𝑠𝑒


q′′

ℎ𝑣𝐻 ))

−q

′′


𝐻2 − 𝑦2

2𝐻)

(5.4.36)

⟨𝑇⟩𝑠 − 𝑇𝑤 = 𝑘𝑓𝑒



𝛼 𝑦


(𝑘𝑠𝑒


q′′

ℎ𝑣𝐻 ))

−q

′′


𝐻2 − 𝑦2

2𝐻)

(5.4.37)

74

Non-dimensionalizing Eq. (5.4.36) and Eq. (5.4.37)

⟨𝑇⟩𝑓 − 𝑇𝑤

𝐻q′′


= (𝑘𝑠𝑒 )

2



𝛼 𝑦


− 1

)

(1

ℎ𝑣(𝐻)2) −

𝐻2 − 𝑦2

2(𝐻)2

(5.4.38)

⟨𝑇⟩𝑠 − 𝑇𝑤

𝐻q′′


= 𝑘𝑓𝑒 𝑘𝑠𝑒



𝛼 𝑦


(1

ℎ𝑣(𝐻)2) −

𝐻2 − 𝑦2

2(𝐻)2

(5.4.39)

The input parameters to this model are thermo-physical properties of the foam and the heat flux

applied to the system which are assumed to be constant and one of the temperatures i.e. either ⟨𝑇⟩𝑠

or ⟨𝑇⟩𝑓 depending upon the required output. Knowing the input parameters, this model is able to

predict the temperature difference (⟨𝑇⟩𝑓 − ⟨𝑇⟩𝑤) if ⟨𝑇⟩𝑠 is known or (⟨𝑇⟩𝑠 − ⟨𝑇⟩𝑤) if ⟨𝑇⟩𝑓 is a

known parameter. Since ℎ𝑣 is implicitly present in the equations (5.4.38) and (5.4.39), the solution

is easier if it is a known parameter and serves as an input to the model. Since ℎ𝑣 is typically

unknown, the model uses an iterative process to find the required temperature difference. An initial

guess for ℎ𝑣 is provided in Eq. (5.4.38), the model performs iterations for different values of ℎ𝑣

untill the analytically calculated temperature curve for ⟨𝑇⟩𝑓 fits with experimentally measured

temperature ⟨𝑇⟩𝑓with 7% error. The value of ℎ𝑣 is selected where experimentally fluid

temperature matches reasonably with computed values. This ℎ𝑣 value is then used in Eq. (5.4.39)

to find solid phase temperature inside the channel.

This model has limitation on the air flow rate. At low flow rate, where conduction is significant,

the results obtained from this model deviate from the measured temperatures since no

consideration is made for axial conduction.

For our analysis the desired output is,⟨𝑇⟩𝑠 the temperature of the solid (struts) inside the channel

at the mid of the channel height since we already have ⟨𝑇⟩𝑓 from experiments. We provided our

75

input parameters (thermo-physical properties of foam, Table, heat flux and ⟨𝑇⟩𝑓) to find the solid

temperature.

Figure 5-27 shows the temperature distribution of solid and fluid inside 10PPI foam channel at

90SLPM. The markers in each figure represent the experimental air temperature and the lines

passing through them indicates the fluid temperature calculated by the model. There is a reasonable

agreement between analytically predicted results and experimentally measured fluid temperature.

The predicted solid temperature at the mid of the channel height is also shown in the figure. The

value of ℎ𝑣 shown on each figure is the value where we get reasonable agreement between

predicted and measured temperatures. Figure 5-28 shows the temperature distribution of solid and

fluid inside 10PPI foam channel at 120SLPM. It is observed that the temperature difference

between solid and fluid phase is higher at 90SLPM because the heat transfer coefficient inside the

channel is low and the low conductive fluid restrict the fluid conduction to next to the wall. But as

the flow rate increases to 160SLPM the temperature difference between solid and fluid phase

reduces because of the increased internal heat exchange between solid and fluid phases.


Flow rate=90SLPM

ℎ𝑣=1.96 x104𝑊 𝑚3𝐾⁄

76


Conclusions

Thermally sprayed foam heat exchangers are tested at high temperature (550ºC and 750ºC) and

heat transfer enhancement is compared with conventional brazed foam heat exchangers. It is found

that novel heat exchangers fabricated using plasma spray deposition are seen to form a strong bond

with the struts of the metal foam, minimizing thermal contact resistance and providing better

performance. The main findings can be concluded as follows:

(i) The heat transfer to coolant air flowing through the foam was significantly higher for

the thermally sprayed heat exchangers than the brazed heat exchangers. The difference

was small at low airflow rate (<30SLPM) but increased at higher flow rate. On the

average thermally sprayed heat exchangers showed 36% higher heat transfer than

conventional brazed heat exchangers

Flow rate=160SLPM

ℎ𝑣=2.47 x104𝑊 𝑚3𝐾⁄

77

(ii) At low flow rates the convective resistance is large (~4x10-2𝑚2𝐾/𝑊) and the effect

of thermal contact resistance is negligible. At higher flow rates the convective

resistance decreases (~2x10-3𝑚2𝐾/𝑊) and the lower contact resistance of the

thermally sprayed heat exchanger provides better performance than the brazed heat

exchangers

(iii) The contact resistance for the 10PPI foam heat exchanger was approximately 50%

higher than that for the 40PPI heat exchanger due to the difficulty in evenly brazing all

the struts of the 10PPI foam to the Inconel sheet

(iv) The volumetric heat transfer coefficient of 40PPI foam is found to be higher than 10

PPI foam since it has 4 times higher surface area density, 1629𝑚2/𝑚3, comparatively

10PPI foam (400𝑚2/𝑚3). Approximately 4 times higher 𝑑𝑝 of 10PPI foam decrease

the number of pores per linear inch and thereby reduces the surface area per unit volume

that causes less hv than 40PPI foam

(v) Nusselt number calculated based on pore diameter is used to perform a comprehensive

comparison of present study with the available literature. Our results are in good

agreement with the available literature [19, 31]. The discrepancies with [16, 24] are

explained based on measurement technique

(vi) A model for thermal analysis of forced convection in channel completely filled with a

porous medium is established based on local thermal non equilibrium assumption.

There is a reasonable agreement between analytically predicted results and

experimentally measured fluid temperature with an error of less than 7%. It is found

that degree of local thermal non equilibrium is more pronounced at low flow rate. As

the flow rate increased the difference between solid and fluid decreases

78

Chapter 6

Testing of Cross-Flow Heat Exchangers at

Low Temperature

Introduction

A second test rig was developed that allowed observation of the heat exchanger surface, which

was used to record infrared images that gave the surface temperature distribution of foam heat

exchangers exposed to relatively low temperature (300ºC) air. A cross flow heat exchanger was

fabricated by brazing a thin shell of Inconel on to a 60𝑚𝑚 × 60𝑚𝑚 × 10𝑚𝑚 piece of 40PPI

nickel foam. A high-power electric heater (Skorpion TM, 4.5𝑘𝑊) was used to blow hot air at

300°C vertically in a cross flow arrangement over the heat exchanger while air at room temperature

was passed through it. The airflow rate on the cold side was continuously varied while the hot air

flow rate was either kept constant or varied during the experiments. A high temperature infrared

camera (IR) (FLIR SC5000, FLIR Systems Inc., Wilsonville,OR) was used to record the surface

temperature distribution under various conditions and heat exchanger effectiveness, volumetric

heat transfer coefficient and Nusselt number were calculated as a function of air flow rates. The

volumetric heat transfer coefficient obtained for 40PPI nickel foam was found to be in good

agreement with the literature.

79

Figure 6-1: Schematic of the cross flow heat exchanger showing the air and gas flow directions across the test

sample

Sample Description

Figure 6-2a shows a schematic of the 40PPI foam heat exchangers used in the low temperature

tests. The heat exchangers were fabricated from 𝑁𝑖 foam with 40PPI pore density and had a size

of 60𝑚𝑚 × 60 𝑚𝑚 ×10𝑚𝑚 (𝐿 × 𝑊 × 𝐻). An Inconel shell, made from 1.2𝑚𝑚 thick nickel alloy

sheets (Inconel HX, McMaster Carr, Princeton NJ) that can resist temperatures up to 1000°C, was

brazed to the foam core. Brazing was used to attach Inconel sheets to the upper surface of the

nickel foam in a vacuum furnace as discussed in chapter 4. A hollow sample with similar external

dimensions (Figure 6-2b) was also made for comparison purpose.

Hot air exit

Hot air inlet (hot air is passing over both the

sides of the sample fitted inside the test section)

Air out

Air in

Sample

80

Figure 6-2: Photographs of (a) 40PPI test sample (b) Hollow sample

Experimental Setup and Procedure

The experimental apparatus consists of four main sections: coolant supply, test section, heating

source and data acquisition system (Figure 1.3). A channel made of stainless steel with an inner

cross section of 60𝑚𝑚 × 10𝑚𝑚 was used to supply cooling air at room temperature to the heat

exchanger (Figure 1.4). The channel was 1𝑚 long to allow the air flow to become fully developed

before it entered the test section. A mass flow controller was located at the entrance of the channel

and three K-type thermocouples were fitted at the heat exchanger inlet to measure the inlet air

temperature while another three thermocouples measured the temperature of the gas leaving the

sample. Heat conduction from the inlet and outlet channels was minimized by inserting insulating

material between heat exchanger and connecting brackets. Four K-type thermocouples were

attached to the surface of the heat exchanger, one at each corner. Symmetric heating of the heat

exchanger was accomplished by blowing hot air over its exterior surfaces using a heater positioned

20𝑚𝑚 below the test section. To minimize heat loss from the heater the external surface of the

heater was covered with insulation. A high temperature infrared camera (FLIR SC5000, FLIR

Systems Inc, Wilsonville OR) was positioned 1m away from the sample to capture images of the

surface.

40PPI foam core

Hollow sample

(a) (b)

81

The test was started by introducing the air at room temperature into the heat exchanger at flow

rates varying from 20 to 100SLPM, corresponding to average flow velocities of 0.5 to 3.3𝑚 𝑠⁄

through the heat exchanger that had a cross-section of 60𝑚𝑚 × 10𝑚𝑚. The hot air was blown

over the sample under three different conditions: (i) constant flow rate of 90 SLPM, (ii) varying

flow rate to maintain coolant to hot air mass flow ratio of 0.5, and (iii) varying flow rate to maintain

coolant to hot air mass flow ratio of 1. The system was left running until steady state was achieved,

which took approximately 15 minutes of operation. Once steady state was attained, the output from

the thermocouples was recorded using a data acquisition system. Three measurements were

recorded and then averaged to give the final set of data. The measurements were recorded for the

brazed foam heat exchanger and the hollow channel.

Figure 6-3: Schematic of the experimental setup for low temperature test

82

Figure 6-4: Photograph of the experimental setup for low temperature test

Sample

Development section

Test section

83

6.3.1 Uniform Heating

In order to achieve uniform heating of the sample the outlet temperature of the heater was measured

across the cross section of the heater outlet duct prior to the experiment. A 10PPI foam piece,

20𝑚𝑚 thick and 60𝑚𝑚 in diameters, was inserted into the heater outlet duct to use as a flow

straightener to allow uniform heating of the sample. The 10PPI foam had a low pressure drop

across it. Figure 6-5 compares the temperature profile at the exit of the heater outlet duct both with

and without the foam insert measured using a rake of 6 thermocouples (Figure 1.6).

Figure 6-5: Outlet temperature of the heater when foam was inserted in outlet duct as a flow straightener,

and when there was no foam.

84

Figure 6-6: temperature measurement at the exit of the heater outlet duct outlet (a) with foam as a flow

straightener (b) without any flow straightener

6.3.2 Measured Parameters and IR Calibration

In experiments the wall temperature of the sample, the cross-flowing hot air inlet and outlet

temperatures, the coolant inlet and outlet temperatures were measured using K-type

thermocouples. The temperature distributions on the heat exchanger surface were obtained using

a FLIR infrared imaging system. Four K-type thermocouples were attached to the surface in order

to calibrate the temperatures recorded by the camera to actual temperature on the surface. The

system was calibrated by adjusting the emissivity to get the same temperatures as measured by the

thermocouples at the surface, with the temperature differences between the IR measurements and

the thermocouple measurements being less than ±1ºC. The calibration curve is shown in

Figure 6-7. The test was started by introducing the air at room temperature into the heat exchanger

at flow rates varying from 20 to 100SLPM, corresponding to average flow velocities of 0.5 to

3.3𝑚 𝑠⁄ through the heat exchanger cross-section.

Probes

(a) (b)

Exit of the heater outlet duct

Insulation

85

Figure 6-7: The calibration curve between thermocouple and IR temperature

6.3.3 Error and Uncertainty

The infrared camera used to record the temperature measurement, is a FLIR Therma CAM SC

5000 directly connected to a laptop computer with Altair thermal imaging software installed. The

temperature measuring range of this camera is -20 to 3000°C with an accuracy of ±1%. The overall

uncertainty associated with the temperature measurement with K-type thermocouple is the

combined elemental error of the data acquisition system and the thermocouple is, ±1.23°C. Details

can be found in Appendix B.

The measurement of the air entering the heat exchanger was done by mass flow-meter (FMA 1843,

OMEGA ENGINEERING Stamford, CT) for the flow range of 5 to 200SLPM accurate to within

±1.5% of full scale (FS).

86

Results and Discussion

6.4.1 Surface Temperature Distribution

The variation in surface temperature of 40 PPI brazed heat exchanger is illustrated in this section

for three different cases:

Case 1: The sample is heated by hot air blown over it at a constant flow rate of 90SLPM while the

flow rate of coolant is varied from 20 to 120SLPM in increments of 20SLPM. Figure 6-8 illustrates

the surface temperature distribution of the foam heat exchanger (left) and a hollow channel (right)

of the same size under the same experimental conditions. The directions of the hot air and the

coolant flow are also shown by the arrows at the right side. The hot gases enter the test section

from the bottom edge (𝑥1-𝑥2), and exit from the top edge (𝑦1-𝑦2), symmetrically heating the

sample, where the coordinates are labelled in each image of Figure 6-8. The coolant is introduced

into the sample from the left edge (𝑥1-𝑦1) and exits from the right edge (𝑥2-𝑦2).

An important purpose of studying surface temperature distribution is to identify the hot and cold

spot locations which may lead to failure in the structure. When the air is blown at low flow rate of

20SLPM (Figure 6-8a) the cold and hot regions, for foam sample, are clearly identifiable visually

in comparison with the hollow sample (Figure 6-8b) which shows high temperature all over the

surface. The cold spot is located in the vicinity of coordinate 𝑦1 since it is far from the heat source

therefore receives minimum heat and encounters coolant at low temperature as it is closest to the

coolant inlet. The hot spot is located in the vicinity of coordinate 𝑥2 as it is nearest to the heat

source, besides that, it is located far from the coolant inlet therefore coolant which passes through

this region is already preheated due to convection cooling taking place in the porous medium. The

arrangement of the hot and cold spot locations was as anticipated in any cross flow arrangement

of heat exchanger. As the flow rate of the coolant increased to 40SLPM the low temperature zone

expanded significantly and the high temperature region reduced further for the foam heat

exchanger (Figure 6-8c) however a low-intensity cooling region is visible on the surface of the

hollow sample (Figure 6-8d). As the flow rate increased further to 100SLPM the low temperature

region expanded greatly covering approximately 75% of the surface, by visual inspection, and the

high temperature zone remained confined to a shape of a quarter circle in the vicinity of

87

coordinate 𝑥2. This is because at increased airflow rate the effect of heat conduction to the fluid

through the foam becomes more significant contributing to higher heat transfer to the coolant and

lower surface temperature. The locations of hot and cold spots were still the same for the foam

heat exchanger. For the hollow sample the hot spots were mainly distributed around the edge 𝑥1 −

𝑥2.

We have performed the heat exchanger analysis using an established effectiveness and NTU (𝜖 −

𝑁𝑇𝑈) method, which is strongly dependent on thermal heat capacity ratio 𝐶𝑟 that defines the

quantity of heat a fluid can transport per unit change in temperature, where 𝐶𝑟 = 𝐶𝑚𝑖𝑛 𝐶𝑚𝑎𝑥⁄ ,

𝐶𝑚𝑖𝑛 = (�� 𝐶𝑝)𝑐 heat capacity rate of cold fluid and 𝐶𝑚𝑎𝑥 = (�� 𝐶𝑝)

ℎ heat capacity rate of hot

fluid. In order to compare our results with available (𝜖 − 𝑁𝑇𝑈) curves we varied the flow rates of

hot air and coolant in a manner to collect data for 𝐶𝑟 = 0.5 and 1. The thermographs obtained for

𝐶𝑟 = 0.5 and 𝐶𝑟 = 1 are discussed in case 2 and 3 respectively.

Case 2 The mass flow rate of the hot air and coolant were varied maintaining a constant ratio 𝐶𝑟 =

𝐶𝑚𝑖𝑛 𝐶𝑚𝑎𝑥⁄ = 0.5. Qualitatively, the surface temperature and distribution of hot and cold regions

(Figure 6-9) exhibited a similar profile as observed in case 1 for the foam heat exchanger. For the

hollow sample the cold and hot regions become identifiable at higher flow rate and hot spots are

found to be induced on the surface randomly more towards bottom edge 𝑥1- 𝑥2.

Case 3 The mass flow rate of the hot air and coolant were varied maintaining a constant ratio of

𝐶𝑟 = 𝐶𝑚𝑖𝑛 𝐶𝑚𝑎𝑥⁄ = 1. In case 3 (Figure 6-10) . Again, a similar pattern of cold and hot regions

was observed for the foam heat exchanger and the hollow channel as observed in case 1.

Figure 6-11 shows the average surface temperature for case 1.When the coolant is introduced at

20SLPM the foam heat exchanger showed average surface temperature of 55ºC, in comparison

with the hollow sample which showed an average temperature of 150ºC. The average surface

temperature is given by ThermoVision LabView (program 3.3.1) by averaging the temperature

over the entire area. The presence of the foam reduced the average surface temperature by ~63 %

for the coolant flow rate of 20SLPM since the struts of the foam act as fins conducting heat from

the upper surface to the air flowing through it. When the flow rate was increased to 120SLPM, the

average surface temperature of foam sample was reduced to ~70% in comparison with the hollow

88

sample. Figure 6-12 shows the average surface temperature of foam and hollow samples for case

2. At the highest coolant flow rate the foam heat exchanger showed average surface temperature

of 42ºC which is ~47% less than the average temperature shown by a hollow sample at the same

flow rate. For case 3 (Figure 6-13) at the highest coolant flow rate the foam heat exchanger showed

the average surface temperature of 38ºC, which is ~50% less than the average surface temperature

recorded for hollow sample for the same flow rate.

89

Figure 6-8: IR thermographs for foam heat exchanger and hollow channel for case 1 where hot air flow rate

was kept constant to 90SLPM and coolant flowrate was varied to (a),(b) 20SLPM (c),(d)40SLPM and

(e),(f)120SLPM. The average temperature measured from FLIR infrared camera is also mentioned on each

thermograph

Coolant flow

direction

Hot air flow direction

x1 x2

y1

y2 y2 y1

x1 x2

Foam Heat Exchanger

(a) 𝑇𝑎𝑣𝑔 = 54℃

Hollow Sample

(b) 𝑇𝑎𝑣𝑔 = 150℃

(c) 𝑇𝑎𝑣𝑔 = 51℃ (d) 𝑇𝑎𝑣𝑔 = 149℃

(f) 𝑇𝑎𝑣𝑔 = 145℃ (e) 𝑇𝑎𝑣𝑔 = 42℃

y2 y1

x1 x2

y2 y1

x1 x2

x2

y2 y1

x1

y2 y1

x1 x2

90

Figure 6-9: IR temperature distribution of 40PPI foam heat exchanger and hollow channel for case 2 i.e.

when the hot air and coolant flow rate were varied in a ratio such that 𝑪𝒓 = 𝑪𝒎𝒊𝒏 𝑪𝒎𝒂𝒙⁄ = 𝟎. 𝟓 .The hot air

and coolant flowrates are (a),(b) 20 ,10SLPM (c),(d) 60,30SLPM, and(e),(f) 140,70SLPM. The average

temperature measured from FLIR infrared camera is also mentioned on each thermograph

Coolant flow

direction


(a) 𝑄ℎ

= 20𝑆𝐿𝑃𝑀, 𝑄𝑐

= 10𝑆𝐿𝑃𝑀

Foam Heat Exchanger

(a) 𝑇𝑎𝑣𝑔 = 53℃

Hollow Sample

(b) 𝑇𝑎𝑣𝑔 = 97℃

(c) 𝑇𝑎𝑣𝑔 = 49℃ (d) 𝑇𝑎𝑣𝑔 = 94℃

(e) 𝑇𝑎𝑣𝑔 = 42℃ (f) 𝑇𝑎𝑣𝑔 = 81℃

91

Figure 6-10: IR temperature distribution of 40PPI foam heat exchanger and hollow channel for case 3 i.e.

when the hot air and coolant flow rate were varied in a ratio such that 𝑪𝒓 = 𝑪𝒎𝒊𝒏 𝑪𝒎𝒂𝒙⁄ = 𝟏 .The hot air and

coolant flowrates are (a),(b) 35,35SLPM and (c),(d) 75,75SLPM. The average temperature measured from

FLIR infrared camera is also mentioned on each thermograph

Coolant flow

direction


(a) 𝑇𝑎𝑣𝑔 = 47.10℃

(c) 𝑇𝑎𝑣𝑔 = 38.02℃

(b) 𝑇𝑎𝑣𝑔 = 85.62℃

(d) 𝑇𝑎𝑣𝑔 = 75.13℃

Foam Heat Exchanger Hollow Sample

92

Figure 6-11: Average temperature taken from IR thermographs (FLIR ThermoVision LabView) for 40PPI

foam heat exchanger and hollow channel for case 1



93



6.4.2 Heat Removed and Performance Evaluation

An energy balance gives the heat transfer rate, ��, to the air flowing through the heat exchanger is:

where, ��𝑎 is the air mass flow rate of the coolant air (𝑘𝑔 𝑠⁄ ), 𝐶𝑝,𝑎 is the specific heat capacity of

air(𝐽 𝑘𝑔𝐾⁄ ), and 𝑇 𝑎,𝑜 and 𝑇 𝑎,𝑖 the temperatures of the air leaving and entering the heat exchanger.

Figure 6-14 shows that on the average the heat transferred to the air flowing through the foam heat

exchanger is more than three times (��𝑓𝑜𝑎𝑚 ��ℎ𝑜𝑙𝑙𝑜𝑤 = 3.41⁄ ) that of the heat transferred in the

hollow sample. It is evident that the presence of foam has enhanced the heat transfer significantly.

�� = ��𝑎 𝐶𝑝,𝑎(𝑇 𝑎,𝑜 − 𝑇 𝑎,𝑖)

(6.4.1)

94

Figure 6-14: Heat transferred to the air flowing through the foam heat exchanger for case 1

6.4.3 NTU - Effectiveness of Heat Exchanger

Heat transfer effectiveness (𝜖) of the heat exchanger is defined as the actual heat transfer rate

divided by the maximum possible heat transfer rate. The maximum possible heat transfer rate is

defined based on the temperature difference between the average inlet surface and air temperature.

The effectiveness is determined using the inlet and outlet temperatures of the fluids as well as the

heat capacity ratios.

𝜖 =(��𝑐𝑝)𝑎

(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

(��𝑐𝑝)𝑚𝑖𝑛(𝑇𝑠,𝑖 − 𝑇𝑎,𝑖)

6.4.2

𝑇𝑠,𝑖 is the average surface temperature at the hot air inlet section (Figure 6-1). The number of

transferred units (𝑁𝑇𝑈) can be calculated using the following equation

𝑁𝑇𝑈 =𝑈𝐴

(��𝑐𝑝)𝑚𝑖𝑛

(6.4.3)

95

Whare, (��𝑐𝑝)𝑚𝑖𝑛

heat capacity rate of the fluid with minimum heat capacity, 𝑈 is the overall heat transfer

coefficient between heated wall and cold air stream and 𝐴 is the area of heat exchanger wall (𝑚2).

𝑈𝐴 is define as;

𝑈𝐴 =��

∆𝑇𝑙𝑚

(6.4.4)

The logarithmic mean temperature difference (𝐿𝑀𝑇𝐷) calculated between the wall and air for the

cross flow heat exchanger is defined as;

∆𝑇𝑙𝑚 =(𝑇𝑠,𝑖 − 𝑇𝑎,𝑜) − (𝑇𝑠,𝑜 − 𝑇𝑎,𝑖)

ln(𝑇𝑠,𝑖 − 𝑇𝑎,𝑜)

(𝑇𝑠,𝑜 − 𝑇𝑎,𝑖)

𝐹 (6.4.5)

where 𝐹 is the correction factor which depends on the flowrate ratio, the temperature profile, and

the heat exchanger configurations. For crossflow arrangement with mixed/unmixed configuration

is taken from [72].

Figure 6-15 illustrates the non-dimensional representation of the heat transfer performance of the

crossflow metal foam heat exchanger. The graph shows two solid lines representing the 𝜖 − 𝑁𝑇𝑈

curves for mixed/un-mixed fluids given in [72] for 𝐶𝑟 = 𝐶𝑚𝑖𝑛 𝐶𝑚𝑎𝑥⁄ = 0.5 and 1. It can be

observed from the graph, the average effectiveness for the foam heat exchanger for 𝐶𝑟 = 0.5 is

around 75% (𝑁𝑇𝑈=3.2) and the average effectiveness for hollow sample is only 10.6%

(𝑁𝑇𝑈=0.47). For the case of 𝐶𝑟 = 1, the average effectiveness of foam heat exchanger is 60%

(𝑁𝑇𝑈=2.54) and hollow sample is 25 % (𝑁𝑇𝑈=0.29). For both the cases hollow sample has lowest

value of effectiveness. It can be concluded that for a specific foam heat exchanger the maximum

effectiveness can be obtained for𝑁𝑇𝑈 < 3.

96

Figure 6-15: The effectiveness NTU graph. Theoretical values are taken from[75]

6.4.4 Nusselt number

The heat transfer coefficient can be non-dimensionalized to give the Nusselt number while the fluid

flow velocity is non-dimensionalized to give the Reynolds number. The hydraulic diameter of the

channel (𝑑ℎ) is used as the length scale for evaluating these dimensionless numbers.

𝑁𝑢𝑑ℎ =h𝑑ℎ

𝑘𝑎 (6.4.6)

𝑅𝑒 =𝜌𝑎𝑢𝑎 𝑑ℎ

µ𝑎 (6.4.7)

where, ℎ the heat transfer coefficient ( 𝑊 𝑚 2𝐾⁄ ) and hydraulic diameter (𝑚) of the rectangular

channel are defined as:

ℎ =��𝑐

𝐴𝑏 ∆𝑇𝑙𝑚 (6.4.8)

97

𝑑ℎ =2 A𝐶

𝐻 + 𝑊 (6.4.9)

where, 𝐴𝑏 = 𝐿 × 𝑊 is the base area (𝑚2), 𝐿,𝐻 and 𝑊 are the length, height and width of the channel

(m), 𝑘𝑎, is the thermal conductivity of the air (𝑊/𝑚𝐾), 𝜌𝑎, µ𝑎 , and 𝑢𝑎 are density ( 𝑘𝑔/𝑚3),

dynamic viscosity (𝑚2 𝑠⁄ ) and velocity (𝑚 𝑠⁄ ) of the air evaluated at bulk mean temperature (i.e. 𝑇 =

(𝑇 𝑎,𝑜 + 𝑇 𝑎,𝑖)/2).

Figure 6-16: Nusselt versus Reynold for 40PPI heat exchanger tested in cross flow arrangement in IR test set-

up

Figure 6-16 illustrates Nusselt number based on Reynolds number for hollow and foam samples.

As shown in the figure, average Nusselt number for the foam sample is about 5 times higher than

the hollow sample. The increase in heat transfer for the foam heat exchanger is predominantly

caused by the flow mixing due to the presence of the foam. The results show that 𝑁𝑢 increases

with 𝑅𝑒 because, as the flow velocity increases greater heat transfer is observed.

98

6.4.5 Agreement of Model Predictions with Experimental Measurement

In this section a comparison is made between analytically predicted and experimentally measured

temperatures at 20SLPM (Figure 6-17) and at 60SLPM (Figure 6-18). The analytical model has

already been discussed in chapter 5. The input parameters to this model are thermo-physical

properties of the foam and the heat flux applied to the system which are assumed to be constant

and one of the temperatures i.e. either ⟨𝑇⟩𝑠 (temperature of struts inside the channel) or

⟨𝑇⟩𝑓(temperature of the air inside the channel) depending upon the required output. Knowing the

input parameters, this model is able to predict the temperature difference (⟨𝑇⟩𝑓 − ⟨𝑇⟩𝑤) if ⟨𝑇⟩𝑠 is

known or (⟨𝑇⟩𝑠 − ⟨𝑇⟩𝑤) if ⟨𝑇⟩𝑓 is a known parameter. For our analysis the desired output is,⟨𝑇⟩𝑠

the temperature of the solid (struts) inside the channel at the mid of the channel height and ⟨𝑇⟩𝑓.

We provided our input parameters (thermo-physical properties of foam, heat flux and ℎ𝑣) to find

the solid temperature. The markers in each figure represents the experimental air temperature

measured at the inlet and exit of the heat exchanger and the lines passing through them indicate

the calculated fluid temperature by the model. There is a reasonable agreement between

analytically predicted results and experimental values of fluid temperature. The temperature

difference between solid and fluid phase is higher at 20SLPM (Figure 6-17) because the heat

transfer coefficient inside the channel is low and the low conductive fluid restrict the fluid

conduction to next to the wall. But as the flow rate increases to 60SLPM (Figure 6-18) the

temperature difference between solid and fluid phase reduces because of the increased internal

heat exchange between solid and fluid phases. The value of ℎ𝑣 shown on each figure is the value

where we get reasonable agreement between predicted and measured temperatures. This value was

taken from experiments and entered as input.

99

Figure 6-17: Experimentally measured and analytically predicted non-dimensionalized temperatures for

40PPI heat exchanger tested in cross flow arrangement in IR test set-up

Flow rate=20SLPM

ℎ𝑣=2x104𝑊 𝑚3𝐾⁄

Flow rate=60SLPM

ℎ𝑣=4x104𝑊 𝑚3𝐾⁄

100

Figure 6-18: Experimentally measured and analytically predicted non-dimensionalized temperatures for

40PPI heat exchanger tested in cross flow arrangement in IR test set-up

Summary

The main contributions of this chapter were to measure surface temperature distributions for nickel

foam heat exchangers under different flow conditions and to determine the enhancement in heat

transfer due to the foam. Another purpose of this chapter was to exemplify the accuracy of the

analytical model for different flow configurations of the heat exchanger. A cross flow nickel foam

heat exchanger was designed and analysed for this purpose.

(i) The thermographs captured from IR camera are used to identify the hot and cold spot

locations and to analyze the cooling pattern of the surface

(ii) For heat transfer analysis, the ϵ − NTUanalysis is performed and compared with the

literature [72]. ϵ − NTU curves for a range of heat capacity between 1.0 and 0.5 have

been obtained. The results show an increase in the effectiveness of 35% (60%-25%) at

𝐶𝑟 = 1 by using foam heat exchanger. The effectiveness is increased to 64% (75%-

10.6%) at 𝐶𝑟 = 0.5 by using foam heat exchanger. It can be concluded that for a

specific foam heat exchanger the maximum effectiveness can be obtained for NTU <

3

(iii) Finally the analytical model was used to determine the temperature of the solid inside

the heat exchanger. The analytical model predicted the solid temperature inside the

foam channel for different flow rates. The bulk fluid temperature was estimated that

showed a reasonable agreement between analytically predicted and experimental

measured results

101

Chapter 7

Fabrication of Heat Shield from Metal Foam

Introduction

The heat transfer characteristics of transpiration cooling through thermally sprayed 40PPI metal

foam with an average particle diameter of 85𝜇𝑚 was experimentally investigated. Heat shields

made with Inconel skins plasma sprayed on 40PPI nickel foam were tested at high temperature

(~750ºC). The skins were made porous, allowing some air to escape though them and create a thin

film of cooling air on the surface exposed to high temperatures. The coolant flows through the

solid matrix of the foam and removes heat by convection, with the foam providing a large surface

area to cool the back of the skin. A burner test rig (discussed in chapter 4) was built to generate

the hot gases (~750ºC) that flowed over the exposed surface of the heat shield. The cooling air was

introduced at different velocities 0.1~5𝑚 𝑠⁄ and surface temperatures were measured using

thermocouples. The effect of the air injection rate on the external surface temperature distribution

was investigated. It was noted that a small amount of coolant injection significantly reduces heat

transfer from the hot gases. In comparison with a non-porous thermally sprayed surface the surface

temperature of the heat shield was reduced by 24% at the lowest injection rate and 41% at the

highest injection rate. The blowing ratio, defined as the mass flow rate of coolant divided by the

mass flow rate of hot gas, was varied from 0.016 to 2. The cooling efficiency was found to vary

from 90-95%.

A second set of experiments was performed on a different test setup where a high power electric

heater (Skorpion TM, 4.5𝑘𝑊) was used to produce hot air at 300°C. Air at room temperature was

passed through the thermally sprayed test sample while hot air from the heater was blown over it.

A high temperature infrared camera (IR) (FLIR SC5000, FLIR Systems Inc., Wilsonville, OR)

102

was used to record the surface temperature distribution under various flow conditions. Hot spots

on the surface of the heat shield were also identified using an IR camera with the experimental

setup described in chapter 6.

Background and Motivation

In an effort to increase thermal efficiency the operating temperature of advanced gas turbine

engines has increased to a range of 1370ºC-1425ºC. This increase in turbine temperatures has led

to high heat transfer to components such as turbine blades and combustor liners, and as a result

these components may be exposed to temperatures higher than the melting point of the material

they are made of [73]. Components lying in the hot gas path in gas turbines are made from nickel

based super alloys that offer a combination of micro-structural stability, strength, ductility,

toughness, and oxidation resistance at elevated temperatures. However, fabricating components

from super alloys using conventional technologies such as casting, forging, welding, and

machining is expensive.

It is essential to develop effective techniques to cool the interior walls of gas turbines, and the most

commonly used cooling method is known as ‘film cooling’, in which air introduced through holes

in the combustor wall forms an insulating layer between the hot gases and the wall, preventing it

from overheating. Film cooling air is introduced through rows of evenly spaced holes that are

generally made using either electro discharge machining (EDM) method or laser drilling [74]. A

significant portion of the cost of manufacturing a gas turbine can be attributed to the expense of

designing and laser drilling complicated passages through which cooling gases flow. Film cooling

also draws a significant amount of air from the compressor, which reduces the overall efficiency

of the engine [73, 74].

Transpiration cooling is a promising cooling concept where the coolant effuses through a porous

surface creating a thin shield of air without disturbing the flow field significantly. The idea was

proposed in the 1950s by Hartnett and Eckert [75] and Eckert and Livingood [76]. Recently

transpiration cooling has been experimentally [77-84] and numerically [85-88] studied by a

number of researchers using porous materials. Meinert et al. [77] profiled the influence of gas

transpiration on skin friction and heat transfer by measuring the velocities and temperatures in the

103

boundary layer and developed empirical correlations describing the skin friction and heat transfer

reduction as a function of the injection rate. Wang et al.[78] used an infrared camera to investigate

the transpiration cooling of a cylindrical, porous tube made from sintered chromium-nickel steel

with a porosity of 21%. Ding et al.[82] used a sintered porous plate to experimentally investigate

transpiration cooling performance. They used an infrared thermal image system to measure surface

temperature variations. It was shown that the cooling effectiveness increases as the mainstream

Reynolds number increased and the wall temperature decreased along the flow direction. Ostu et

al. [89] experimentally studied transpiration cooling of porous ceramics made of sintered alumina

particles. Recently, Xu et al.[90] carried out an experimental study of transpiration cooling of

sintered woven wire mesh structures with different porosities (휀 =55%, 47%, 37%) at varying

blowing ratios. They concluded that the surface temperature decreased along the main flow

direction as the blowing ratio was increased and that the transpiration cooling efficiency was

higher than the film cooling efficiency for the sample with the highest (휀 =55%) porosity. They

concluded that there was a need for experimental investigation of other porous structures.

The Centre for Advanced Coatings Technology (CACT) at the University of Toronto has

developed a novel method of fabricating foam sandwich structures suitable for high temperature

applications. The nickel foam, which is ductile, can be easily formed to the desired shape and then

coated with super alloys such as Inconel to make them resistant to high temperatures. Surface skins

made of super alloys are deposited on the preformed foam core by thermal spray deposition in

which metal or ceramic wires or powders are fed into a high temperature gas jet where they melt

while being sprayed onto a surface. The molten droplets coalesce and freeze upon impact, forming

a dense, solid layer. The spraying process eliminates most machining and forming and significantly

reduces manufacturing costs. Sprayed skins can be made from high-temperature alloys or

ceramics, which are otherwise very difficult to shape. Cooling gas circulates through the open cell

foam, eliminating the need to drill complex cooling channels. The objective of this work was to

find a method of spraying porous skins on metal foams so that gas effusion can be used to enhance

surface cooling.

Most of the previous investigations on transpiration cooling have analysed relatively simple

structures such as porous plates made by sintering or wire meshes. Little work has been done on

testing at high temperatures (~700ºC) and high blowing ratios. The objective of this study is to test

104

the transpiration cooling of thermally sprayed sandwich structures made of 40PPI Ni foam core,

at high temperature (750ºC) and blowing ratio (0.016 to 2).

Deposition of Porous Skins on Metal Foam

A 40PPI 𝑁𝑖 foam sheet, 10𝑚𝑚 thick, was cut using EDM into pieces that were either

200 𝑚𝑚 ×70 𝑚𝑚 (Figure 7-1a) or 70𝑚𝑚 ×70𝑚𝑚 in size. Before skins were sprayed onto the

foam pieces four of their surfaces were sealed with a semi-solid epoxy resin-nickel powder paste,

leaving open two faces to serve as the air inlet and outlet. The coated areas were cured to create a

temporary surface to prevent penetration of molten droplets into the form pores during thermal

spraying. The surface of the epoxy skin was grit blasted to remove extra paste and expose the tips

of foam struts, which helped to increase the adhesion of the sprayed layer to the metal foam. This

is shown in Figure 7-1b for the rectangular sample.

Porous skins were deposited by plasma spraying a mixture of Inconel and polyester powders, and

then subsequently burning away the polyester. Polyester powder was injected externally through

a specially designed feeding port located 50𝑚𝑚 in front of the plasma torch nozzle.

Samples ready testing are shown in Figure 7-1c. For depositing porous skins a commercially

available Alloy 625 powder (AMDRY 625, Metco) with the nominal composition of

21.5𝑤𝑡. % 𝐶𝑟, 8.5𝑤𝑡. % 𝑀𝑜, 3𝑤𝑡. % 𝑁𝑏, 3𝑤𝑡. % 𝐹𝑒, 0.5𝑤𝑡. % 𝐶𝑜, and the remainder 𝑁𝑖 was used

as a feedstock material. A micrograph of the polyester powder is shown in Figure 7-2. Plasma

spraying was done with an atmospheric plasma torch (SG-100 torch, Praxair Surface

Technologies) using the spray settings given in Table 7.1. During plasma spraying the foam

channel was constantly cooled by blowing air through it to avoid overheating. The polyester was

removed from the coating by post-deposition heat treatment at 450C for 3 hrs. For comparison a

second sample was prepared with exactly the same coating thickness but with zero porosity.

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Table 7.1: Selected spraying parameters for co-deposition spraying

Parameters Value

Plasma current , (𝐴)

600

Primary gas , 𝐴𝑟, (SLPM) 60

Carrier gas, 𝑁2, (SLPM) (Alloy-625) 4

Feeder disk rotation speed, (rpm) (Alloy-625) 4

Carrier gas, 𝑁2, (SLPM) (Polyester) 3

Feeder disk rotation speed, (rpm) (Polyester) 5

External polyester feeding position, (𝑚𝑚) 50

Spray distance,(𝑚𝑚) 120

Post heat treatment temperature (C) 450

The microstructure of the plasma sprayed skins foam was examined by using a Hitachi TM3000

scanning electron microscope (SEM) equipped with energy dispersive x-ray spectroscopy (EDS).

Figure 7-3 shows a micrograph through a porous coating with a uniformly distributed porosity (휀)

of 30%. It proved possible to get porosity as high as 30% (by volume) while still maintaining the

microstructural integrity of the coating. Feeding position and feeding rate of the polyester powder

play a significant role in determining coating homogeneity and porosity. For instance, locating the

feeding port 25 mm from the torch nozzle produced an inhomogeneous microstructure with 45%

porosity, resulting in poor mechanical integrity of the coating. Adhesion strength of the thermally

sprayed skin was examined by standard pull-off test. The details of the standard pull-off test have

already been discussed in chapter 4. Figure 7-4 shows the results of a pull-off test for the porous

surface. It is seen that failure occurred at the interface between the foam and skin, unlike the

106

previous case discussed in chapter 4. The average adhesion strength of the thermally sprayed skin

on the 𝑁𝑖 foam was 150-180𝑝si (1034 − 1241𝑘𝑃𝑎).

Uniformity of the porosity was tested by blowing air through the foam sample using the test set-

up shown in Figure 7-5 that consisted of a mass flow-meter (FMA 1843, OMEGA

ENGINEERING Stamford, CT), a pressure gage (Model DPG409050, Omega Engineering,

Sunbury, OH) and an air tank. The foam sample, a round disc 50𝑚𝑚 in diameter, was mounted at

the top of the air tank. The air at constant inlet pressure was blown through the air tank at different

flow rates. A mixture of soapy water was sprayed on the test sample to observe the bubbles formed

by blowing the air through the porous foam disc. From visual inspection (see Figure 7-5) it is seen

that bubbles are formed all over the surface, confirming that porosity is uniformly distributed.

Figure 7-1: (a) Sample A: 40PPI Ni foam, (b) Foam with temporary skin (c) Foam with metallic skin

(a) (b) (c)

107

Figure 7-2: SEM microstructure of pore former (polyester)

Figure 7-3: SEM microstructure of Co-deposition sprayed porous Alloy-625 coating

108

Figure 7-4: (a) surface after pull-off test (b) Alloy-625 coating attached to the aluminum dolly after the test

Figure 7-5: Test apparatus to visually inspect the uniform porosity of the sample

(a) (b)

Bubbles formation on the surface is uniform

Air tank

Flow- meter

Pressure gage

109

Results and Discussion

High temperature testing was done on the larger sample (휀 = 30%) shown in Figure 7-1 where

hot combustion gases at 750°C were passed over the exterior surface of the heat shield while

cooling air was passed through it. The burner test rig already described in chapter 4 was used for

tests.

The mass flow rate of the air that escapes through the porous surface was measured using two

mass flow-meters (FMA 1843, OMEGA ENGINEERING Stamford, CT) mounted upstream and

downstream of the test sample. The difference between the two readings gave an estimate of the

air that effuses from the porous surface as shown in Figure 7-6. There was a linear relationship

between the mass flow rate of coolant injected into the channel and the mass flow rate of coolant

effused from the porous surface. It was estimated that approximately 70% of the coolant injected

into the channel escaped from the porous surface.

Figure 7-6: The amount of air effused from the porous surface for the amount of air supplied in to the

sample

110

Knowing the mass flux of the main stream and the air leaking from the pores, the blowing ratio

(M) is defined as:

𝑀 =𝜌𝑐 𝑈𝑐

𝜌∞ 𝑈∞=

𝑚𝑐𝐴∞

𝑚∞𝐴𝑐 (7.4.1)

Where 𝜌𝑐, 𝜌∞ and 𝑈𝑐, 𝑈∞ are the density (𝑘𝑔 𝑚3⁄ ) and velocity (𝑚 𝑠⁄ ) of the average coolant

leaking through the porous surface per unit area of wall surface [88] and main stream gas

respectively. 𝐴𝑐 is the area of porous wall surface (containing open and solid parts) [88] and 𝐴∞

is area of cross section (𝑚2) of hot air channel respectively. Figure 7-7 shows the axial surface

temperature variation along the length of the porous sample when hot gas at 750ºC was flowing

over it. As shown in Figure 7-7b the main stream flow (hot gas) and coolant flow are in the same

direction i.e. entering at 𝑥 = 0 and exiting at 𝑥 = 200𝑚𝑚 (left to right) and the thermocouple

locations are indicated in the schematic (Figure 7-7b).

Figure 7-7 compares the surface temperature profile for both porous and non-porous surfaces under

the same flow conditions At low blowing ratio (𝑀= 0.016) the difference between average wall

temperature of porous and non-porous surface is approximately 21% which increases to 40% at

higher blowing (𝑀=2). At 𝑀 = 0.016 the maximum surface temperature was achieved at

approximately 𝑥 = 150𝑚𝑚 (Figure 7-7) and decreased thereafter due to conduction losses

through the stainless steel bracket and tubing. The effect of axial conduction is no longer visible

at high blowing ratio where convection heat transfer dominates conduction losses and the surface

temperature increases in the direction of flow.

At low blowing ratios the air that effuses out of the heat shield surface is heated up strongly before

mixing with the hot gases, due to its longer residence time. This results in only 21% reduction

insurface temperature by comparison with the non-porous surface. At high blowing ratio the

temperature reduction is increased to 40%, because, as the coolant mass flux is increased, the rate

at which heat is convected from the porous surface into the air effusing through the leading edge

becomes equal or less than the rate at which heat is removed by transpiration.

111

Figure 7-7: (a) Surface temperature measured by thermocouples in burner test rig at 750ºC gas inlet

temperature (b) Schematic of the sample A under experimental condition for understanding of the

temperature measurements

The cooling enhancement due to transpiration cooling can be found by calculating the convection

heat loss for both porous and non-porous surface under the same conditions. An energy balance

gives the convection heat transfer to the air flowing through the porous channel.

�� = ��𝑎 𝐶𝑝,𝑎(𝑇 𝑎,𝑜 − 𝑇 𝑎,𝑖) (7.4.2)

where ��𝑎 is the mass flow rate (𝑘𝑔 𝑠⁄ ) of the air supplied to the sample, 𝐶𝑝,𝑎 is the specific heat

capacity of air (𝐽 𝑘𝑔𝐾⁄ ), and 𝑇 𝑎,𝑜 and 𝑇 𝑎,𝑖 the temperatures of the coolant leaving and entering

the porous channel. Assuming that conduction losses are same for porous and non-porous surface,

the difference in convective heat transfer gives the net heat reduction due to transpiration cooling.

The results for heat lost by transpiration cooling are plotted in Figure 7-8. The figure shows that

112

transpiration cooling effects are significant for blowing ratios 𝑀 > 0.15 and maximum net heat

reduction occurs at 𝑀 =2.

Figure 7-8 Convection heat transfer and convection loss due to transpiration cooling at different blowing

ratios

The performance of film cooling is quantified by a parameter known as film-cooling efficiency

defined by:

𝜂 =𝑇∞ − 𝑇𝑤

𝑇∞ − 𝑇𝑐 (7.4.3)

where 𝜂 is the film cooling efficiency; 𝑇𝑤 is the wall temperature; 𝑇∞ is the temperature of the hot

gas; and 𝑇𝑐 is the temperature of the injected coolant. The value of cooling efficiency varies from

0 where there is no cooling to 1 when the efficiency is maximum.

Figure 7-9 shows surface temperature distribution and cooling efficiency at 𝑀=0.016. It is

observed that cooling efficiency is maximum at the leading edge where 𝑇= 230 C and tends to

decrease initially and then becomes constant afterwards (Figure 7-9). The higher value of 𝜂 at the

beginning may be due to significant conduction loss from the brackets holding the sample. At

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𝑀=2, 𝜂 stays nearly constant with an increase of only 1% from the leading edge to the trailing

edge while the temperature increases along the length of the heat exchanger (Figure 7-10).

The distribution of cooling efficiency along the surface at different blowing ratios is plotted in

Figure 7-11. Except for the lowest blowing rate (𝑀=0.016), cooling efficiency for all other cases

follows a similar trend. The cooling efficiency increases by increasing the injection rate. The rate

of increase becomes less significant for blowing ratio > 0.15. Figure 7-12 shows average efficiency

over the surface as a function of blowing ratios. The cooling efficiency reaches its maximum value

of 96% at the highest blowing ratio, 𝑀=2 which is the point where maximum net heat reduction

was observed. The net increment in average cooling efficiency from lowest to highest blowing

ratio was found to be only 7%.

Figure 7-13 shows average cooling efficiency of transpiration cooling taking place on three

different surfaces. Liu et al.[85] used a porous flat plate made of sintered stainless steel particle of

𝑑𝑝 = 45𝜇𝑚 and porosity 42.8% to measure the efficiency at different blowing ratios. The

maximum efficiency obtained in case of a porous flat plate was approximately 70% at 𝑀 ~3. Xu

et al. [90] used sintered wire mesh of different pore diameters to (𝑑𝑝 = 66.9~93.7𝜇𝑚) and

porosity (37~55%) to find the transpiration cooling effect over the surface. At 𝑀 ~1.8, they were

able to get approximately 55% of the cooling efficiency. In these tests we are able to get

approximately 95% cooling efficiency using the metal foam structure.

114

Figure 7-9: Surface temperature and cooling efficiency as a function of distance at M=0.016

Figure 7-10: Surface temperature and cooling efficiency as a function of distance at M=2

115

Figure 7-11: Cooling efficiency as a function of distance at different blowing ratios

Figure 7-12: Average cooling efficiency as a function of blowing ratios

116

Figure 7-13: Average cooling efficiency as a function of blowing ratios comparison with literature

The heat transfer data can be presented in the form of the Stanton number (St), which is a

normalized heat flux defined as

𝑆𝑡 =��″

𝜌∞ 𝐶𝑝∞ 𝑢∞(𝑇∞ − 𝑇𝑤) (7.4.4)

Where ��″ is heat flux (𝑊 𝑚2⁄ ), 𝜌∞ is the density (𝑘𝑔 𝑚3⁄ ), 𝐶𝑝∞ specific heat capacity (𝐽 𝑘𝑔𝐾⁄ ),

and 𝑢∞ velocity of the hot gas (𝑚 𝑠⁄ ). The decrease in the ratio shows the reduction in heat flux

due to effect of cooling. In Figure 7-14 the Stanton number decreases as a function of Reynolds

numbers which shows the cooling is more effective at higher blowing ratios. The initial peak at

low Reynolds in both the cases, porous and non-porous surface, can be attributed to significant

conduction occurring at low flow rates. Low Reynolds show the Stanton number reduction of 52%

between porous and non-porous surface which is twice as large as any reduction observed on

medium Reynolds (~25% reduction). The effect of cooling is again evident from the significant

reduction (46%) of Stanton number at maximum Reynolds.

117

Figure 7-14: Stanton number ratio of porous to non-porous surface as a function of Reynolds number

Figure 7-15 shows the thermographs obtained from the IR camera for the smaller, square samples

prepared with porous skins. In all four cases the blowing ratio stays below 1.5. The flow enters

from right side and exits from the left. The front and back surfaces of sample are subjected to

uniform heating. It is observed that as the blowing ratio increases the surface temperature tends to

decrease due to the formation of a thin layer of cold air that escapes from the pores and covers the

surface .As shown in case (a) temperature contours show a narrow low temperature region

appearing on the top right section of the porous surface. Relatively high temperature contours are

formed in the downstream region where the coolant exits. The highest temperature is observed at

the bottom left side of the porous surface. At low blowing ratio 𝑀 =0.14~0.16 coolant is not

uniformly cooling the surface due to low mass flux. As the blowing ratio increased to 𝑀 =0.5, in

case of (c), the low temperature zone widens which reduces the high temperature region. This is

due to accumulation of the cooling air over the surface that creates a film that protects the surface

from hot air. The low temperature zone grows further in case(d) when blowing ratio was increased

to 𝑀=1.42. It is clearly visible at higher blowing ratio that the sample has homogeneous porosity

which helps to decrease local temperature variations in temperature and produces a uniformly

temperature distribution on the surface of the sample.

118

Figure 7-15: IR image of surface temperature of 40 PPI thermally sprayed foam at different blowing ratios

(a) M=0.14 (b) M=0.16

(C) M=0.5 (d) M=1.42

119

Experimental Errors and Uncertainty Analysis

All thermocouples used in this study are K-type. Thermocouples were calibrated using ice and a

hot plate at constant temperature before installation. Model OMB-DAQ-56 – 22-bit data

acquisition model is designed by OMEGA for high accuracy and resolution, featuring 20-channel

analog input slots and a USB 2.0 connector allowed connecting to a PC for power, and it has an

accuracy of 0.015% of reading plus 0.002% of range. Personal DaqViewTM a graphical software,

which is programmed by OMEGA, is used for data acquisition. It has built-in Type-K

thermocouple reading, with range from -100 to 700 C .The overall uncertainty associated with the

temperature measurement is the combined elemental error of the data acquisition system and the

thermocouple is, ±1.24 C. Details can be found in appendix B.

The infrared camera used to record the temperature measurement, is a FLIR Therma CAM SC

5000 directly connected to a laptop computer with Altair thermal imaging software installed. The

temperature measuring range of this camera is -20 to 3000 C with an accuracy of ±1%. Calibration

curve is shown in Figure 7-16.

Figure 7-16: Calibration curve between thermocouple measurements and IR measurements

120

The measurement of the air entering the heat exchanger was done by mass flow-meter (FMA 1843,

OMEGA ENGINEERING Stamford, CT) for the flow range of 5 to 200SLPM accurate to within

±1.5% of full scale (FS).

The uncertainty in blowing ratio is found to be 2.12% and the uncertainty of cooling efficiency

varies from 4.9%~2.5% for 𝑀=0.016 and 2. Details are given in appendix B.

Summary

A sandwich structure fabricated by spraying porous skins on 40PPI metal foam is used to

experimentally investigate the efficiency of transpiration cooling. It is found that cooling

efficiency increases with the blowing ratio and decreases along the surface from leading to trailing

edge. The sandwich structure is capable of producing a uniform thin layer of coolant to effectively

cool the surface. Cooling efficiency of 95% can be obtained by using sandwich structures made

from 40PPI foam. Heat transfer can be reduced by 40% compared to an impervious surface.

The metal foam has an advantage over a simple porous plate as it provides cooling by two different

phenomena, conduction cooling and transpiration cooling at the same time and reduces the heat

transfer significantly. It is found from comparison with the literature [85, 90] that metal foam has

better cooling efficiency than both sintered porous plates and wire meshes.

121

Chapter 8

Summary and Conclusions

This thesis reports an experimental investigation of heat transfer in heat exchangers and heat

shields made by spraying Inconel skins on nickel foam. A high temperature burner test rig was

fabricated and the heat exchangers were tested at high temperature (550ºC and 750ºC). The heat

transfer performance of thermally sprayed heat exchangers was compared with that of

conventional brazed foam heat exchangers. It was found that heat exchangers fabricated using

plasma spray deposition form a strong bond between the sprayed skins and the struts of the metal

foam, minimizing thermal contact resistance and providing improved heat transfer.

A second test rig was developed that allowed observation of the heat exchanger surface, which

was used to record infrared images that gave the surface temperature distribution of foam heat

exchangers exposed to relatively low temperature (300ºC) air. A high temperature infrared camera

was used to record the surface temperature distribution under various flow conditions and heat

exchanger effectiveness, volumetric heat transfer coefficient and Nusselt number were calculated

as a function of air flow rates.

The transpiration cooling efficiency of heat shields made by thermally spraying porous Inconel

skins onto 40 PPI metal foam was experimentally investigated at high temperatures (~750ºC). The

skins had an average skin porosity of 30%, allowing the air to escape though them and create a

thin film of cooling air on the surface exposed to high temperatures. Most of the previous

investigations on transpiration cooling have analysed relatively simple structures such as porous

plates made by sintering or wire meshes.

The main findings of the thesis can be summarized as follows:

122

(i) The heat transfer to coolant air flowing through the foam was significantly higher for

the thermally sprayed heat exchangers than conventional brazed heat exchangers. The

difference was small at low airflow rate (<30SLPM) but increased at higher flow rate.

On average thermally sprayed heat exchangers gave 36% higher heat transfer than

conventional brazed heat exchangers

(ii) At low flow rates the convective resistance of the foam heat exchanger is large (~4x10-

2 𝑚2𝐾/𝑊) and the effect of thermal contact resistance is negligible. At higher flow

rates the convective resistance decreases (~2x10-3𝑚2𝐾/𝑊) and the lower contact

resistance of the thermally sprayed heat exchanger provides better performance than

the brazed heat exchangers

(iii) The contact resistance for the 10PPI foam heat exchanger was approximately 50%

higher than that for the 40PPI heat exchanger due to the difficulty in evenly brazing all

the struts of the 10PPI foam to the Inconel sheet

(iv) The volumetric heat transfer coefficient of 40 PPI foam is found to be higher than 10

PPI foam since it has four times higher surface area density (1629 𝑚2/𝑚3) compared

to 10PPI foam (400𝑚2/𝑚3). Approximately 4 times higher 𝑑𝑝 of 10PPI foam decrease

the pores per linear inch and thereby reduces the surface area per unit volume that

causes less ℎ𝑣 than 40PPI foam

(v) The Nusselt number for forced convection through nickel foams, calculated based on

pore diameter, is found to be in good agreement with the available literature [16, 19]

(vi) A model for thermal analysis of forced convection in channels completely filled with a

porous medium is established based on local thermal non equilibrium assumption.

There is a reasonable agreement between analytically predicted results and

experimentally measured fluid temperature with an error of less than 7%. It is found

that local thermal non equilibrium effects are more pronounced at low flow rate. As the

flow rate increased the temperature difference between solid and fluid decreases

123

(iv) The thermographs captured from IR camera are used to identify the hot and cold spot

locations and to analyze the cooling pattern of the surface. For heat transfer analysis,

𝜖 − 𝑁𝑇𝑈 analysis is performed and compared with the literature [72]. The 𝜖 − 𝑁𝑇𝑈

curves for a range of heat capacity between 1.0 and 0.5 have been obtained. The results

show an increase in the effectiveness of 35% (60%-25%) at 𝐶𝑟 = 1 by using foam heat

exchanger. The effectiveness is increased to 64% (75%-10.6%) at 𝐶𝑟 = 0.5 by using

foam heat exchanger. It can be concluded that for a specific foam heat exchanger the

maximum effectiveness can be obtained for NTU < 3

(vii) It is found that the transpiration cooling efficiency of thermally sprayed metal foam

increases with the blowing ratio and decreases along the surface from leading to trailing

edge. Cooling efficiency of 95% can be obtained by using sandwich structures made

from 40PPI foam. Heat transfer can be reduced by 40% compared to an impervious

surface. The metal foam has an advantage over simple porous plate as it provides

cooling by two different phenomena, convection and transpiration cooling and reduces

the heat transfer significantly. It is found from comparison with the literature [85, 90]

that metal foam has better cooling efficiency than both sintered porous plates and wire

meshes

124

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131

APPENDIX A

Uncertainty and Error Analysis

Temperature Uncertainty

We have K-type thermocouples for our study. The thermocouple voltages were recorded by a data

acquisition system (DAQ) and transmitted directly to a personal computer. The DAQ system

consists of the following components:

(i) Model OMB-DAQ-56 – 22-bit data acquisition model is designed by OMEGA for high

accuracy and resolution, featuring 20-channel analog input slots and a USB 2.0 connector

allowed connecting to a PC for power, and it has an accuracy of 0.015% of reading plus

0.002% of range

(ii) Personal DaqViewTM – a graphical software, which is programmed by OMEGA, is used

for data acquisition. The range for K-type is -200-1200C

The measured uncertainty associated with digital data acquisition systems is calculated using

method of root-sum-squares (RSS) presented by [91]. The design-stage uncertainty associated with

the data acquisition system is given as;

𝑢𝐷𝐴𝑄 = √𝑢0 + 𝑢𝑐 (1)

Where 𝑢0 the zero-order uncertainty that is caused by random error and 𝑢𝑐 is the instrument

uncertainty that is caused by systematic error. In this case, the zero-order uncertainty equals one-

half of the instrument resolution. Based on the manufacturer’s specification, the random error is

negligible because of a small resolution, the numerical valve of which is 1 2𝑀⁄ where 𝑀 is the

bits, in this case𝑀 = 22.

For example, for the temperature of 100C that is detected by a Type-K thermocouple. The

uncertainty associated with the data acquisition system is,

𝑢𝐷𝐴𝑄 = √𝑢02 + 𝑢𝑐

2 (2)

132

𝑢𝐷𝐴𝑄 = √(100°𝐶 𝑋 0.00015 + 1400°𝐶 𝑋 0.00002)2 + 0 (3)

𝑢𝐷𝐴𝑄 = ±0.043 (4)

For the Type-K thermocouples used in our study, the accuracy is ±1.2 C based on the

manufacturing specification. The resolution of Personal DaqView-TM for Type-K thermocouples

is ±0.001 C, thus the zero-order uncertainty is equal to 0.0005 C. Hence the uncertainty associated

to the thermocouples is,

𝑢𝑇ℎ𝑒𝑟𝑚𝑜𝑐𝑜𝑢𝑝𝑙𝑒 = √(1.2℃)2 + (0.0005℃)2 = ±1.2℃ (5)

The overall uncertainty associated with the temperature measurement is the combined elemental

error of the data acquisition system and the thermocouple is,

𝑢𝑇 = √(𝑢𝐷𝐴𝑄)2

+ (𝑢𝑇ℎ𝑒𝑟𝑚𝑜𝑐𝑜𝑢𝑝𝑙𝑒)2

= ±1.24℃ (6)

Uncertainty in Hydraulic Characteristics

The uncertainties generated by the least-squares curve fit are given by the general formula for error

propagation as described by [92]. If 𝐴 and 𝐵 can be treated as functions of 𝑥𝑖 and 𝑦i, the

uncertainties in coefficients of Equation (5.2.1) are determined as

𝛿𝐴 = √∑ (𝜕𝐴𝜕𝑥𝑖

⁄ 𝛿𝑥𝑖)2

𝑛

+ ∑ (𝜕𝐴𝜕𝑦𝑖

⁄ 𝛿𝑦𝑖)2

𝑛

(7)

𝛿𝐵 = √∑ (𝜕𝐵𝜕𝑥𝑖

⁄ 𝛿𝑥𝑖)2

𝑛

+ ∑ (𝜕𝐵𝜕𝑦𝑖

⁄ 𝛿𝑦𝑖)2

𝑛

(8)

133

Each 𝑖 term represents a single experimental data pair, Darcy ow velocity and length-normalized

pressure drop. 𝛿𝑥𝑖 and 𝛿𝑦𝑖 are the uncertainties in the velocity and the pressure drop which are

determined from the accuracy of the experimental instrumentation used to measure the respective

quantities. The corresponding partial derivatives were calculated and inserted in in order to yield

𝛿𝐴 and 𝛿𝐵. The uncertainty in the value of 𝐾 is equal to the uncertainty in the value of 𝐴 assuming

that there is zero uncertainty in the value of dynamic viscosity, thus the following relationship is

given

𝜎𝐾 = 𝛿𝐴 𝐴⁄ (9)

The uncertainty in the inertial-coefficient is derived in a similar fashion, assuming that there is

zero uncertainty in the density term, the uncertainty in the inertia-coefficient is given as

𝜎𝐶𝐹 = 𝛿𝐵 𝐵⁄ (10)

The uncertainty in measurement of permeability and inertia coefficient for 10 and 40PPI is 13.7%,

11.3% and 3.1% , 5.7% respectively.

The uncertainty of blowing ratio is from error associated with 𝑚 and can be calculated as from

following equation

∆𝑀

𝑀= √(

∆𝑚𝑐

𝑚𝑐)

2

+ (∆𝑚∞

𝑚∞)

2

(11)

Similarly, uncertainty for cooling efficiency is associated with the temperature𝑇𝑤, 𝑇∞and 𝑇𝑐 and

can be calculated from following equation

∆𝜂

𝜂= √(

𝑇𝑊 − 𝑇𝐶

(𝑇∞ − 𝑇𝐶 )(𝑇∞ − 𝑇𝑊 )∆𝑇∞)

2

+ (∆𝑇𝑊

𝑇𝑊 − 𝑇∞)

2

+ (∆𝑇𝐶

𝑇𝐶 − 𝑇∞)

2

(12)

134

APPENDIX B

Surface and air temperature graphs for 10PPI foam heat exchangers

Figure 8-1: Local wall temperature of 10PPI plasma sprayed and conventional brazed heat exchangers at 5

and 10SLPM (Pe<1)

135

Figure 8-2: Local wall temperature of 10PPI plasma sprayed and conventional brazed heat exchangers at

20(Pe~1), 60 and 200SLPM (Pe>1)

Figure 8-3: Local air temperature of 10PPI plasma sprayed and conventional brazed heat exchangers at 5

and 10SLPM (Pe<1)

Figure 8-4: Local air temperature of 10PPI plasma sprayed and conventional brazed heat exchangers at

20(Pe~1), 60 and 200SLPM (Pe>1)

136

APPENDIX C

Derivation for Eq. (5.3.5) for calculating volumetric heat transfer coefficient

The log mean temperature difference between fluid flowing inside foam and the substrate wall

∆𝑇𝑙𝑚 =(𝑇𝑠,𝑖 − 𝑇𝑎,𝑖) − (𝑇𝑠,𝑜 − 𝑇𝑎,𝑜)

𝑙𝑛(𝑇𝑠,𝑖 − 𝑇𝑎,𝑖)

(𝑇𝑠,𝑜 − 𝑇𝑎,𝑜)

(1)

∆𝑇𝑙𝑚 =∆𝑇𝑖 − ∆𝑇𝑜

𝑙𝑛 (∆𝑇𝑖

∆𝑇𝑜)

(2)

ℎ𝑐 =��𝑐

𝐴𝑏 ∆𝑇𝑙𝑚=

��𝑎𝐶𝑝,𝑎(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

𝐴𝑏 ∆𝑇𝑙𝑚 (3)

where,

ε = Af

At , ma = 𝜌𝑢𝑝Af = 𝜌𝑢𝑝εAt (4)

Sub Eq.(4) in Eq.(3)

ℎ𝑐 =��𝑐

𝐴𝑏 ∆𝑇𝑙𝑚=

𝜌𝑢𝑝휀𝐴𝑐𝑡𝐶𝑝,𝑎(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

𝐴𝑏 ∆𝑇𝑙𝑚 (5)

Rearranging Eq.(5)

𝜌𝑢𝑝휀𝐶𝑝,𝑎(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

∆𝑇𝑙𝑚=

ℎ𝑐𝐴𝑏

𝐴𝑐𝑡 (6)

𝑤ℎ𝑒𝑟𝑒, 𝐴𝑐𝑡 = 𝑊𝐻 𝑎𝑛𝑑 Ab = L 𝑊, 𝑣𝑜𝑙𝑢𝑚𝑒 = ∀= 𝐿 𝑊 𝐻, 𝑢𝑝 =𝑢𝐷

𝐴𝑐𝑡 (7)

𝜌𝑢𝑝휀 𝐶𝑝,𝑎(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

∆𝑇𝑙𝑚=

ℎ𝑐𝑊 ∆𝑥

𝑊𝐻 (8)

137

ℎ𝑐 ∆𝑥

𝐻 =


∆𝑇𝑙𝑚 (9)

ℎ𝑐(𝑥) =𝜌𝑢𝑝휀𝐶𝑝,𝑎(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

∆𝑇𝑙𝑚 𝐻

∆𝑥 (10)

where, ℎ𝑐 is heat transfer coefficient (𝑊 𝑚2𝐾⁄ ) for ℎ𝑠𝑓 from Eq.(6) replace ℎ𝑐𝐴𝑏 by ℎ𝑠𝑓𝐴𝑠𝑓 and

multiply both side by volume∀

𝜌𝑢𝑝휀Cp,a(Ta,o − Ta,i)

∆Tlm=

h𝑠𝑓Asf

Ac,t

∀

∀ (11)


∆𝑇𝑙𝑚=

ℎ𝑠𝑓 𝐻𝑊∆𝑥

𝑊𝐻

𝐴𝑠𝑓

∀ (12)


∆𝑇𝑙𝑚= ℎ𝑠𝑓 ∆𝑥 𝛼𝑠𝑓 (13)

ℎ𝑠𝑓(𝑥) =𝜌𝑢𝑝휀(𝑇𝑎,𝑜 − 𝑇𝑎,𝑖)

∆𝑇𝑙𝑚

1

∆𝑥 𝛼𝑠𝑓 (14)

ℎ𝑣 = ℎ𝑠𝑓 𝛼𝑠𝑓 (15)

ℎ𝑣 = ℎ𝑠𝑓 𝛼𝑠𝑓 (16)

where 𝛼𝑠𝑓 is surface area density (𝑚2 𝑚3⁄ ) , ℎ𝑠𝑓 interstitial heat transfer coefficient(𝑊 𝑚2𝐾⁄ )

and ℎ𝑣 is volumetric heat transfer coefficient (𝑊 𝑚3𝐾⁄ )

For Eq. (5.3.10): rearrange Eq. (6) for ℎ𝑐


∆𝑇𝑙𝑚=

ℎ𝑐𝐴𝑏

𝐴𝑐,𝑡 =

ℎ𝑐𝐿 𝑊

𝑊𝐻 =

ℎ𝑐∆𝑥 𝑊

𝑊𝐻 (17)

138


∆𝑇𝑙𝑚

𝐻

∆𝑥= ℎ𝑐 (18)

Further simplification and comparing Eq. (18) and (13)


∆𝑇𝑙𝑚

1

∆𝑥= ℎ𝑠𝑓 𝛼𝑠𝑓 =

ℎ𝑐

𝐻 (19)

ℎ𝑠𝑓 𝛼𝑠𝑓 = ℎ𝑉 =ℎ𝑐

𝐻 (20)

139

APPENDIX D

Surface and Air Temperature Data

Thermal spray 40PPI 550 ºC

Flowrate Ts1 Ts2 Ts3 Ts4 Ts5 Ta1 Ta2 Ta3 Ta4 Ta5

SLPM ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC

5 207.86 271.68 289.88 288.52 268.04 141.99 249.97 262.17 269.28 245.58

10 172.59 241.08 274.10 284.29 277.05 113.76 219.47 246.16 266.49 261.03

15 152.07 218.41 254.99 271.47 275.45 97.18 192.10 224.42 252.13 261.04

20 135.98 198.16 235.61 255.74 267.24 85.95 171.16 205.53 236.56 253.19

25 123.71 182.15 218.24 240.06 256.43 77.29 154.15 188.50 220.31 241.57

30 113.39 167.43 201.05 223.26 243.21 70.50 139.06 172.32 203.48 227.50

40 100.57 149.98 179.66 201.44 225.12 61.93 120.09 151.86 181.26 207.35

50 95.76 134.11 160.02 181.07 206.44 55.98 105.59 134.94 161.24 187.54

60 83.77 116.56 136.58 155.45 180.94 48.70 88.15 113.59 135.69 160.00

70 78.27 105.53 121.70 138.26 163.00 44.28 77.59 99.73 118.49 141.05

80 76.42 99.17 113.56 128.67 152.33 41.70 71.39 91.47 108.21 129.92

90 75.14 96.55 108.55 122.47 145.51 40.17 67.87 86.72 101.93 122.44

100 74.08 94.72 105.49 118.41 140.33 38.73 65.25 82.89 96.81 117.11

120 71.44 91.12 99.11 109.97 130.74 36.52 59.71 75.24 87.31 106.23

140 70.18 88.67 94.55 104.34 123.19 35.69 56.64 70.50 81.34 98.87

160 66.81 85.13 89.07 97.44 114.83 34.12 53.52 65.70 74.86 90.98

180 64.14 84.32 85.58 92.76 108.80 32.98 50.86 62.06 70.53 85.55

200 62.14 80.90 85.22 93.29 104.05 32.11 48.55 59.04 67.28 81.21




5 408.88 504.52 518.97 510.08 482.60 283.64 467.85 482.89 494.02 458.74 10 321.34 470.65 508.68 512.58 490.50 225.59 428.54 477.61 495.03 475.44 15 278.63 398.30 445.61 454.42 442.81 167.66 362.07 406.78 438.80 428.75 20 249.93 370.59 423.07 439.65 439.53 145.73 326.83 379.23 421.43 427.87 25 219.45 336.25 390.43 412.75 423.55 121.69 282.10 337.92 385.89 408.64 30 201.71 315.12 370.17 394.95 410.54 110.18 257.20 315.89 366.22 393.38 40 179.77 283.68 334.64 363.24 386.90 93.37 220.26 278.93 330.50 366.41 50 158.63 251.99 296.81 323.94 351.35 80.17 185.28 237.60 286.72 324.39 60 139.89 225.72 264.32 291.17 326.13 62.57 156.65 204.10 251.64 292.10 70 129.92 208.52 241.45 267.51 308.12 63.40 138.97 181.35 225.86 266.68 80 119.50 191.22 219.79 243.27 284.74 57.45 122.43 158.62 199.99 239.16 90 107.15 173.79 198.43 220.46 264.14 50.83 106.33 137.95 176.87 215.16

100 104.31 171.82 195.83 216.34 254.86 49.67 102.75 131.77 169.64 203.57 120 98.62 161.34 179.63 197.79 239.12 46.18 89.65 112.85 148.68 182.43 140 91.69 150.21 167.27 182.95 221.66 43.19 80.08 99.06 133.09 162.36 160 87.33 142.56 157.12 172.32 211.39 41.08 72.89 89.19 121.89 150.11 180 79.91 137.83 151.83 167.43 204.81 40.33 67.82 83.97 117.16 138.34 200 78.46 116.77 142.61 160.98 183.57 39.16 62.85 80.27 105.15 126.88

140

Braze 40PPI 550 ºC



5 209.83 264.63 282.48 281.98 259.82 150.88 234.78 259.13 256.06 235.91

10 171.55 224.64 256.08 270.34 266.28 113.74 189.51 228.86 248.54 251.34

15 150.89 197.09 230.82 249.75 255.40 94.91 157.76 198.09 226.74 243.47

20 135.14 173.42 206.45 227.58 239.70 81.47 133.73 172.15 203.75 229.16

25 124.32 157.53 185.57 207.18 221.54 72.43 116.12 150.38 181.24 211.38

30 116.36 145.41 169.93 190.30 205.63 65.51 103.16 133.32 162.76 195.67

40 105.35 130.19 151.75 170.04 186.76 57.62 87.94 113.65 139.91 174.50

50 96.66 117.10 136.08 153.23 169.80 51.81 77.46 99.45 122.81 156.76

60 88.63 106.21 121.02 135.97 151.86 46.71 67.05 84.91 104.70 136.82

70 82.55 100.44 113.71 126.74 137.28 44.01 61.97 77.63 95.37 120.96

80 79.56 94.67 106.39 117.51 129.18 41.30 56.89 70.35 86.04 112.27

90 76.57 89.03 99.19 108.45 121.09 38.66 51.92 63.23 76.91 103.57

100 74.61 86.76 95.43 103.76 115.15 37.23 49.23 59.07 71.98 97.41

120 70.43 81.53 88.09 94.35 103.78 34.39 44.40 52.60 63.25 85.64

140 66.10 78.06 82.10 86.92 95.08 32.18 40.80 47.65 57.16 77.31

160 61.42 75.73 78.73 82.07 89.09 31.00 38.47 44.68 53.51 71.87

180 58.00 72.73 75.21 77.18 83.24 29.89 36.26 41.72 49.77 66.44

200 55.00 71.68 72.82 72.94 77.97 29.15 34.72 39.56 46.93 61.88

Braze 40PPI 750 ºC



5 379.37 477.18 497.14 495.34 462.32 262.78 436.54 481.08 490.73 442.09 10 316.68 425.56 470.72 486.49 472.16 195.10 374.78 452.05 483.48 459.18 15 283.11 382.64 433.52 459.54 461.62 164.03 320.68 400.97 450.40 452.94 20 244.76 327.54 374.41 404.51 417.63 130.14 244.75 319.20 377.45 407.28 25 227.76 303.55 347.99 378.95 396.55 116.53 216.83 287.27 346.74 385.47 30 206.55 272.87 311.93 340.52 360.02 100.81 182.74 243.21 300.18 346.24 40 185.45 242.59 277.30 304.50 326.66 86.87 153.52 204.89 258.62 310.22 50 167.06 216.15 246.56 270.81 292.16 75.32 128.51 170.81 218.95 272.52 60 148.63 190.39 215.85 236.81 256.69 63.97 105.69 138.33 179.60 233.11 70 134.18 170.94 192.59 210.82 229.23 56.48 90.21 115.68 150.80 203.20 80 126.12 159.05 177.64 193.45 209.29 52.35 80.38 100.67 131.44 181.73 90 119.75 150.43 167.18 181.79 195.84 48.94 73.76 91.09 118.99 167.63

100 113.42 141.50 156.96 170.14 182.98 46.26 67.97 82.53 107.97 154.16 120 103.33 127.82 140.11 151.08 162.22 41.36 58.58 68.88 89.38 131.78 140 96.84 118.77 129.06 138.27 147.84 38.60 52.78 60.75 78.43 117.26 160 91.26 111.04 120.24 128.14 136.93 36.40 48.76 55.13 70.64 106.73 180 87.26 104.96 112.70 119.74 125.62 37.40 45.00 50.02 63.50 98.28 200 84.65 98.74 113.62 130.11 129.75 41.01 44.29 54.30 73.34 97.30

141




5 207.08 281.72 304.97 316.83 318.84 172.12 249.31 281.63 288.00 275.61 10 154.37 217.12 244.34 265.24 269.96 122.93 184.82 225.56 241.32 246.37 15 137.73 193.21 224.71 250.61 251.36 109.38 158.25 207.77 229.44 229.80 20 118.88 170.14 194.56 215.31 234.07 94.90 136.74 179.12 201.65 212.46 25 102.42 149.18 171.67 191.54 210.65 78.95 115.21 154.66 177.38 190.97 30 97.46 141.58 162.22 180.73 198.05 74.42 106.57 142.56 164.76 179.67 40 89.02 126.45 144.27 160.55 177.72 63.82 90.38 122.22 142.56 158.47 50 81.78 115.51 130.49 144.26 161.18 56.04 78.74 106.89 125.59 141.22 60 77.89 107.06 118.04 129.01 144.29 52.81 70.83 94.46 110.22 124.45 70 69.81 90.90 104.21 113.41 127.21 46.07 62.06 81.71 95.37 107.78 80 65.35 89.23 99.25 107.04 120.68 44.66 57.83 74.97 86.88 99.20 90 57.53 75.68 86.31 97.97 111.67 38.07 50.76 65.85 77.51 88.51

100 55.77 73.20 84.18 93.99 105.14 36.87 49.41 63.24 72.99 82.28 120 53.05 68.67 80.47 87.99 100.12 35.99 47.32 58.75 67.26 75.35 140 48.95 61.31 73.26 79.05 91.96 31.64 42.14 52.45 59.98 67.42 160 45.31 56.41 67.04 74.82 86.19 30.22 37.93 47.18 55.27 61.65 180 44.93 54.36 64.86 71.50 79.27 29.15 36.42 44.61 51.19 56.83 200 42.60 52.39 57.57 66.78 72.81 26.60 35.19 40.97 47.31 51.42




5 296.97 403.53 414.34 407.46 390.99 269.98 385.29 411.58 400.95 364.81

10 263.32 381.18 402.17 407.04 399.68 232.70 354.62 399.65 401.64 376.84

15 218.00 330.29 357.54 372.57 375.68 187.86 298.05 352.45 366.23 356.91

20 198.88 303.30 331.98 351.28 360.17 163.19 264.34 320.03 338.87 337.73

25 175.20 268.07 296.10 318.07 332.65 138.81 225.81 279.45 301.55 309.45

30 159.41 243.03 269.70 292.47 310.15 121.82 199.47 250.09 273.66 285.91

40 144.82 216.26 239.92 261.85 282.30 102.42 166.76 212.82 236.45 253.56

50 136.34 198.40 218.72 238.24 259.96 92.50 146.94 188.08 210.93 230.07

60 123.19 175.46 190.78 206.81 228.52 77.85 121.24 156.56 177.48 199.02

70 114.97 159.44 171.95 185.15 206.48 71.73 108.24 138.83 157.47 178.22

80 108.08 148.75 159.10 170.23 190.93 66.57 99.03 126.35 142.38 161.27

90 97.36 135.03 142.74 152.19 172.18 55.69 84.98 110.03 124.79 142.85

100 93.88 130.56 136.19 144.45 164.10 51.09 78.55 102.23 116.02 133.89

120 89.87 121.41 124.84 130.30 148.57 45.77 68.97 89.50 101.77 118.31

140 85.08 111.81 114.19 118.06 134.28 40.42 60.17 77.88 88.76 104.38

160 80.91 103.59 105.23 107.88 122.64 38.38 55.10 71.04 80.64 94.66

180 75.77 97.55 97.59 98.47 112.04 34.29 49.49 63.76 72.49 84.88

200 65.63 93.71 94.72 96.86 111.03 29.79 44.99 59.20 66.69 77.40

142

Braze 10PPI 550 ºC



5 202.70 252.03 280.89 289.82 286.85 164.38 213.90 255.59 269.18 265.96

10 158.90 194.76 231.10 253.15 269.84 122.82 159.51 205.69 232.60 247.07

15 131.41 163.22 197.94 222.89 249.11 103.88 132.32 174.86 204.08 224.17

20 115.14 134.29 171.34 195.57 221.09 89.64 111.69 149.68 177.81 199.22

25 98.93 119.88 148.33 169.44 190.56 77.98 94.21 125.32 148.92 169.92

30 93.26 113.35 136.82 156.71 177.94 73.15 86.87 114.68 136.38 156.73

40 85.15 101.67 122.13 140.97 163.31 66.95 78.16 102.58 122.56 141.10

50 77.61 88.63 109.34 126.10 147.76 60.67 70.07 90.85 107.99 124.64

60 71.43 83.63 99.14 113.98 135.03 55.76 63.94 81.82 96.81 111.42

70 66.04 80.47 90.76 102.36 121.01 50.65 57.31 72.82 85.13 97.99

80 62.24 75.93 85.67 95.64 113.61 48.10 53.15 68.11 79.65 90.26

90 54.57 70.99 82.27 90.20 107.33 40.62 49.51 63.57 74.19 83.59

100 53.60 67.96 79.86 85.28 100.49 38.20 46.23 59.03 68.86 77.17

120 51.92 64.42 77.50 81.94 96.42 36.70 44.09 55.49 65.15 72.60

140 47.16 53.05 70.33 75.84 86.98 33.10 39.27 47.75 56.74 63.26

160 44.90 50.36 65.28 72.99 81.74 31.04 36.86 43.80 51.81 58.00

180 44.74 49.39 60.54 69.67 76.14 29.82 35.78 41.65 48.61 54.17

200 42.48 47.39 54.80 65.18 71.75 27.99 34.58 39.16 44.78 49.89

Braze 10PPI 750 ºC



5 293.12 374.32 392.68 386.02 348.83 248.01 312.76 357.33 356.14 335.41

10 243.07 327.95 365.53 376.73 359.32 205.49 266.61 328.25 351.19 347.84

15 209.68 286.25 330.77 350.46 347.57 174.03 225.45 289.89 324.20 333.63

20 188.42 257.04 298.59 320.90 326.33 151.59 193.39 253.99 291.20 308.57

25 169.79 229.61 269.01 292.53 304.23 134.19 168.24 223.85 261.73 283.45

30 157.13 209.41 245.80 268.78 283.49 122.18 150.55 200.93 237.32 258.73

40 138.54 181.70 213.63 235.23 253.76 105.72 127.00 170.25 203.34 223.64

50 126.16 162.92 190.51 209.99 229.45 94.17 110.37 147.71 177.45 196.99

60 114.11 144.45 168.20 185.62 205.39 83.46 95.54 126.97 153.61 170.85

70 104.50 130.28 150.48 165.95 185.57 74.97 83.92 110.96 134.30 150.87

80 97.56 119.59 137.43 151.40 171.18 69.19 76.28 99.67 120.59 137.18

90 91.97 111.36 126.58 139.36 157.96 58.30 69.93 90.37 108.67 124.91

100 87.80 104.63 119.75 131.24 148.98 54.89 65.58 84.08 101.40 114.98

120 80.50 94.50 105.73 115.10 131.73 49.36 58.27 73.25 87.65 98.45

140 75.10 86.16 95.37 102.98 119.61 44.81 52.91 65.24 77.32 87.09

160 71.54 81.18 87.70 94.29 109.48 41.58 49.19 59.53 69.49 78.70

180 68.75 76.52 81.51 87.56 101.57 38.19 46.46 55.39 64.16 71.55

200 65.12 71.66 75.88 81.28 93.50 33.96 43.77 51.01 58.35 64.44

143

APPENDIX E

Pressure Drop Data

Flowrate ∆p/L (pa/m)

SLPM 10PPI 40PPI

5 28 154

10 60 338

20 132 495

30 204 743

40 303 945

50 372 1148

60 450 1553

70 546 1958

80 660 2588

90 723 4028

100 870 5445

120 1126 7020

140 1374 8708

Heat Transfer in Metal Foam Heat Exchangers at High ... · Pakeeza Hafeez Doctor of Philosophy...

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Transcript of Heat Transfer in Metal Foam Heat Exchangers at High ... · Pakeeza Hafeez Doctor of Philosophy...